hаука – 2012 - Электронная библиотека | Электронная

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6. – . 23 – 26.
The appliance of IT technologies during biology lessons makes them more interesting, visual, dynamic, helps pupils to understand and remember the material better. IT technologies allow be more effective organizing lessons feedback, give more opportunities to form information using skills and to develop creative abilities of pupils.
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, 1992. – C. 11 – 17.
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, 1977. – 244 .
4.
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http://www.nemanenvironment.org. –
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2004. – 56 .
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., 1990. – 279 .
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: http://www.vgr.by/home/tema-nomera/5284-
The hydrochemical characteristics of water of the river Neman is represented, its dynamics and peculiarities of its
change under the influence of wastewaters is studied. Concentrations of some chemicals in the sediments near the spot of effluent discharges in the river Neman are determined by X-ray fluorescent method. The main pollutants of the river waters are
identified.
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599.73
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2012
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2008
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2010
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: 21.03.2011
In territory of hunting economy Volkovysk «B R» 3 species of hoofed animals of mammals of group Artiodactyla Sus
scrofa, Capreolus capreolus, Alces alces. Carrying out of researches on monitoring during the period with 2007 for 2012 has shown
increase in number Alces alces, Capreolus capreolus and reduction of number Sus scrofa. The hunting grounds of detour 3 hunting
economy Volkovysk «B R» are rather perspective for housekeeping on Sus scrofa, Capreolus capreolus.
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The effective organisation of educational process at modern school is impossible without use of the individually-differentiated
approach to pupils.
– .
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581.13
.
.
VACCINIUM VITIS-IDAEA
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–
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.
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,
Vaccinium vitis-idaea L. (
[2],
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Vaccinium vitis-idaea L.,
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2010-2011 .
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:
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.
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(40 – 50) Vaccinium vitis-idaea L.
Vaccinium vitis-idaea L.
.
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,
,
–
.
,
-26,
.
) [5].
Statistica 6.0.
–
,
Pinetum (sylvestris) Pleurosiosum
(schreberi), Pinetum (sylvestris) Hylocomiosum (splendentis), Betuleto (pubescentis)
Pinetum (sylvestris)
Sphagnosum (angustifolii), Betuleto (pubescentis) Pinetum (sylvestris) Hylocomiosum (splendentis),
Betuletum (pendulae) Pleurosiosum (schreberi).
,
-2012:
16
. . 2. –
–
, 2012
–
-
16 – 93 %.
2010 . (
17 %
45 %
20 %
:
9 %.
–
1)
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2011 . (
(
–
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1)
7 %)
35 %,
-
.
,
,
–
2010 .:
,
47 %.
1–
,
2010 – 2011
–
2011
,
19,7
24,0
22,2
17,4
17,9
18
10,0
1,6
23,3
25
25
27
22,2
17,6
34,4
25
22,3
16,4
17,6
20,8
19,0
18,3
17,8
17,6
16,9
15,7
17,4
17,9
18
17,6
16,9
15,7
19,5
30,1
64,6
13,1
39,2
11,7
23,8
3,8
25
24
25
25
27
25
25
24
Vaccinium vitis-idaea L.
.
.
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2010
–
2010 .
-
,
2011 ,
(
2).
2–
,
2010 – 2011
Vaccinium vitis-idaea L.
,
.
,%
46,19±0,16
44,78±0,07
12,36±0,04
13,73±0,04
2010
2011
:
–
41 – 46 %
46 – 67 % (
–
2,57±2,19
2,05±1,41
1,39±0,38
1,21±0,48
,
2010 – 2011
:
,
1).
0,038±0,004
0,070±0,004
0,057±0,005
0,049±0,004
–
,
9,90±0,86
22,42±0,55
5,36±0,27
7,47±0,52
–
,
–
.
69 – 73 %
33 %,
,
2010 .,
,
2010 .
Vaccinium vitis-idaea L.,
,
,
,
,
,
[6].
,
,
.
,
-
Vaccinium vitis-idaea L. [7].
,
,
(2010 .)
.
(2010-2011)
:
,
,
-
17
.
,
[7].
,
,
,
-
,
[6] (
,
1).
-
.
,
,
Vaccinium vitis-idaea L.
.
,
-
[6, 7].
.
1–
,
Vaccinium vitis-idaea L.
,
,
,
,
,
-
,
:
.
.
1.
,
.
.
/
.
.
,
.
.
,
.
.
. – 2006. –
//
1. – . 1 – 11.
2.
:
3.
4.
.:
5.
/
6.
7.
», 2008. – . 2:
, . .
:
, . .
, 1983. – 196 .
, . .
. .
,
. .
, . .
, . .
:
3 ./
.
.
/ . .
.
,
.
. .
.
.–
.–
:
:
.
.–
/ . .
.:
.–
/ . .
.:
:
, 1998. – 60 .
, 1989. – 464 .
.–
:
, 1981. – 80 .
.
. – 472 .
., 2008. – 255 .
/ . .
.–
.
-
-2012:
18
. . 2. –
, 2012
The leaves of Vaccinium vitis-idaea synthesized low number of biologically active substances in weather conditions that are
close to normal. For large differences in weather conditions during the summer in the leaves of Vaccinium vitis-idaea content
of biologically active compounds is increased by 30 – 70%.
. .
,
,
,
.
574.583
. .
)
.
-
.
,
,
,
.
.
-
0,6 0,73.
54
.
–
4
.
,
,
.
[1].
,
–
.
.
-
,
.
.
.
14
,
2011
–
.
12 – 15 .
(
2
.
98
9 ³/ .
.
-
30
-
.
1140
.
),
².
.
5
.
5
.
,
: 8.00
15.00
2
15.00
,
,
4
,
1.
2
1 – 1,5
19.00
[2, 3],
4
,
.
[4 – 7].
54
.
,
.
,
.
.
Bacillariophyta – 26
Chlorophyta – 21
),
Euglenophyta – 1
(48 %
(38 %),
-
Cyanophyta – 6
»
.
[8].
,
.
-
1.
1–
1
Bacillariophyta
Centrophyceae
Pennatophyceae
Protococcophyceae
Conjugatophyceae
Ulothrichophyceae
Volvocophyceae
Chroococcophyceae
Hormogoniophyceae
Euglenophyceae
Chlorophyta
Cyanophyta
Euglenophyta
:
-
.
2
2
2
2
1
1
1
2
1
14
2
5
5
3
1
1
1
3
1
22
2
9
7
3
1
1
2
3
1
29
2
18
13
5
1
1
2
3
1
46
19
Pennatophyceae –
18
,
:
.
–
.
Protococcophyceae 13
, Conjugatophyceae
,
5
.
,
2–
2.
2
Bacillariophyta
Centrophyceae
Pennatophyceae
Protococcophyceae
Conjugatophyceae
Volvocophyceae
Chroococcophyceae
Hormogoniophyceae
Euglenophyceae
:
Chlorophyta
Cyanophyta
Euglenophyta
Pennatophyceae 23
Conjugatophyceae 4
.
,
2
2
1
2
1
1
2
1
12
,
2
5
4
3
1
2
2
1
20
–
2
9
5
3
1
3
2
1
26
Protococcophyceae
2
23
12
4
1
3
2
1
48
,
12
,
.
,
,
0,6-0,73;
-
0,3.
,
Bacillariophyta
Chlorophyta.
,
.
,
agardhii Gom.
.
Melosirales Raphales.
Araphales.
,
Scenedesmus Meyen, Tetrastrum Link. Closterium Nitzsch.
Microcystis Kutz. Elenk. Anabaena Bory.
– 16
,
– 24
.
Merismopedia tenuissima Lemm.
Oscillatoria
Chlorophyta,
Nitzchia Hass,
(Anabaena, Microcystis).
,
(Scenedesmus, Closterium, Tetraëdron Corda).
Pinnularia Hust., Fragilaria Kütz.
Euglenophyta.
Euglenophyta
.
4
Bacillariophyta
–
,
-
Chlorophyta.
.
Cyanophyta
.
,
,
2.
Anabaena flos-aquae,
,
Merismopedia Lemm.
.
Chlorophyta
Bacillariophyta (13
),
,
Euglenophyta
Oscillatoria.
1
,
.
Bacillariophyta.
1
Bacillariophyta (18
).
.
Microcystis, Anabaena
.
Chlorophyta,
2 –
.
-
.
(
2
)
-
1.
(45
).
,
,
.
,
.
-
,
,
.
.
-2012:
20
. . 2. –
, 2012
1–
.
:
1.
54
15
23
31
4
9
.
2.
Bacillariophyta Chlorophyta
20
2
– Chlorophyta (17
, 36 %).
1
(43 %
).
Bacillariophyta – 25
(52 %),
-
.
3.
.
1.
,
16
//
19
2.
.
.
2004 . –
, . .
.:
3.
4.
5.
6.
7.
8.
:
:
,
, 2004. – C. 21 – 22.
,
/
:
.
.
-
II
:
.-
/ . .
.–
, 2003. – 57 .
, . .
. – 1989. – . 25. – 4. – . 3 – 21.
, . .
.
. 2.
Centrales Mediales //
.
. . .
, . .
.
. 3.
Pennales //
.
. . .
, . .
–
:
, 1984. – 336 .
, . .
, 1990. – 208 .
, . .
.
(
) / .
.
//
.
.–
.:
.
.
, 1949.
.
.–
.:
.
.
/ . .
/ .
,
.
.
.
/
.
.–
, 1950.
//
.
. . .
-
:
.
.–
:
, 1999. – 396 .
The specific structure of a phytoplankton at two stations of the river Molchad around Gezgalsky hydroelectric power station is
investigated. The maximum specific variety of a phytoplankton is observed on the river from May to August. For a seasonal suktsessiya of types of a phytoplankton of this river the classical scheme isn't characteristic that, probably, is a consequence of rhythmical
work of hydroelectric power station. The specific structure of both stations on the studied site is rather poor and quite similar. The
calculated factors of similarity of Syorensen for the majority of tests are in limits 0,6-0,73. During research in a plankton of the river
Molchad 54 types of algas from 4 departments were revealed.
– . .
,
.
004.9
. .
«
Tetrapoda,
Amphibia»,
«
3
5
»
.
-
,
,
.
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,
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-
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).
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(
).
(
[2, . 173].
,
).
«
-
»,
-
,
.
.
100
«
»
: 48 –
230
, 52 –
.
,
,
.
,
-
.
«
, 1-330101 –
1-310101 –
197/
»
25.05.2009 (
,
.
»
:
.),
,
«
-0.
.
-1.
(
Acrania Urochordata).
-2.
Vertebrata,
Agnatha.
-3.
Gnathostomata,
Pisces (Anamnia).
-4.
Tetrapoda,
Amphibia.
-5. Amniota,
Reptilia,
–
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(
).
.
,
.
-0
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Amphibia»
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-5
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Tetrapoda,
«
-
«
Tetrapoda,
-3
( )–
).
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Amphibia»
Tetrapoda,
Amphibia»:
-2012:
22
-0.
-1.
1.1.
1.2.
1.3.
1.4.
1.5.
-2.
2.1.
2.2.
2.3.
2.4.
2.5.
-3.
3.1.
3.2.
3.3.
3.4.
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4.2.
4.3.
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, 2012
.
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(
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-
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«
.
-R) – «
»,
65
–
-5
»
(
.
(
)–«
-
»
,
.
Power Point – 2007,
Windows.
PowerPoint
,
,
,
,
.
-
,
MS PowerPoint,
.
(
),
,
.
«
– 2009».
,
7.0
−
−
.
– 2009»
Delphi
«
Object Pascal
,
,
:
,
;
:
,
;
−
−
−
−
-
[3, . 27].
;
;
,
;
:
(
;
,
−
−
–
),
-
;
(
-
);
−
.
;
−
,
[4, . 21].
-
23
,
«
«
Tetrapoda,
Amphibia»,
»
5
3
-
.
,
,
.
–
-
.
1.
,
. .
.
.
.–
, . .
2.
[
]:
.…
.
: http://www/lib.ua-ru.net/diss//con/159745.html
., 2005. – 172 . –
»(
«
//
15 – 16
2003 . /
,
3.
, . Power Point 2003
4.
, . .
. .
, . .
.
«
, . .
») / . .
:
«
»/ .
,
,
.–
. – .:
.
:
«
.
.
.-
,
, 2003. – . 173 – 184.
», 2004. – 304 .
//
:
: 13.00.02 /
.
.,
,
2005 . –
,
/
, 2005. –
. 19 – 25.
This paper the developed educational-methodical complex of discipline «Vertebrate Zoology» and «Supraclassis Tetrapoda,
classis Amphibia» modular program, including five theoretical and three additional modules describes. The modular training system
substantially increases quality of specialist preparation, promotes a new type of education personnel as it is directed on realisation of
continuous and rhythmic studying of a teaching material during for a semester or all academic year. It is aimed at control strengthening over depth and quality of trainees learning styles and developing their skills of regular self-study.
–
,
. .
,
,
.
611.822.1
. .
.
,
,
,
,
.
.
,
-
,
.
,
,
-
,
[1].
,
,
.
,
–
,
,
-
[2].
,
[3].
–
.
.
200±25 .
(
80
,
).
-2012:
24
–
. . 2. –
, 2012
,
(
2
5
10
20
45
90
7
7
7
7
7
7
42
:
)
7
6
7
7
7
4
38
3-5
-
.
:
,
,
.
.
.
-
.
,
.
,
,
-
.
,
.
,
(Leica CM 1840,
(-196 0 ),
20
.
) (-15
0
,
)
,
,
,
.
.
.
(
,
,
,
)
–
( irculaty) –
( spect) –
-
4,
.
«Statistica 6.0 for Windows».
<0,05 (U-
–
,
(Me±IQR).
:
,
,
,
,
,
-
.
.
(2, 5, 10, 20, 45, 90
-
)
-
.
.
6,3 % (Z=2,71; =0,01),
0,6 % (Z=-2,14;
=0,03).
1,6 % (Z=2,00; =0,05).
-
3,7 % (Z=2,00; =0,05).
4,1 % (Z=2,14; =0,03).
5
13,4 % (Z=-3,00;
19,1 % (Z=-3,00;
8,0 % (Z=-2,29;
5,5 %
,
2,9 % (Z=-2,43; =0,02),
=0,003),
=0,003).
14,2 % (Z=-3,00; =0,003),
7,2 % (Z=-3,00; =0,003)
5
8,9 % (Z=-3,00; =0,003),
=0,003)
=0,003),
=0,02).
(Z=-2,29; =0,02),
5,1 % (Z=-3,00;
6,9 % (Z=3,00;
9,9 %
25
(Z=-2,86; =0,004),
=0,022),
4,7 % (Z=-2,43; =0,02),
4,7 % (Z=-2,29; =0,02),
6,06 % (Z=-2,29;
7,2 % (Z=-3,00; =0,003).
4,6 % (Z =-2,286; =0,022),
17,3 % (Z=-3,00; =0,003),
3,5 % (Z=-2,86; =0,004),
12,3 % (Z=-2,86; =0,004),
16,4 % (Z=-3,00; = 0,003).
,
.
22,0 % (Z=-2,43; =0,02),
13,3 % (Z=-2,71; =0,01),
27,7 % (Z=-2,86; =0,004)
31,7 % (Z=-3,00; =0,003)
,
16,0 %
(Z=-3,00; =0,003)
46,5 % (Z=-2,14; =0,032).
5,8 % (Z=3,00; =0,003)
:
23,6 % (Z=-2,57; =0,01),
16,8 % (Z=-3,00; =0,003),
20,3 % (Z=-2,71; =0,01),
11,2 % (Z=-2,43; =0,02),
13,7 % (Z=-2,57;
=0,01)
26,6 % (Z=-2,71; =0,01).
13,6 % (Z=-2,43; =0,02),
17,9 % (Z=-2,14; =0,03),
28,3 % (Z=-2,57; =0,010),
9,7 % (Z=-2,43; =0,015)
21,1 % (Z=-2,57; =0,01).
12,9 %
(Z=3,00; =0,003)
:
25,5 % (Z=-3,00; =0,003),
39,1 % (Z=-3,00; =0,003),
17,8 % (Z=-3,00; =0,003),
21,6 %
(Z=-2,86; =0,004)
41,5 % (Z=-3,00; =0,003).
14,5 % (Z=-2,75; =0,01)
-
.
5,0 % (Z=2,49; =0,01),
47,2 % (Z=2,36; =0,02).
3,1 % (Z=1,98; =0,05).
12,6 % (Z=2,49; =0,01),
12,0 % (Z=-2,49; =0,01)
2,3 % (Z=1,98; =0,05).
5,6 % (Z=2,08; =0,04)
5,6 % (Z=-2,72; =0,01)
10,1 %(Z=-2,40; =0,02),
,
11,5 % (Z=-2,56; =0,01),
15,2 % (Z=-2,24; =0,03).
5,0 % (Z=-2,56; =0,01)
13,0 % (Z=2,72; =0,01).
5,1 % (Z=2,08; =0,04).
90
,
-
:
1,6 % (Z=2,08; =0,04),
(Z=2,65; =0,01).
2,3 % (Z=2,65; =0,01)
2,9 % (Z=2,65; =0,01),
1,3 %
-
4,4 % (Z=-2,65; =0,01).
2,8 % (Z=-2,65; =0,01).
4,2 % (Z=2,65; =0,01),
2,3 % (Z=2,65; =0,01).
3,0 % (Z=2,65; =0,01),
-
.
2-
,
10-20
45
;
;
.
90
,
,
.
.
.
-
.
1.
, . .
:
2.
3.
, . .
, . .
.
.
/ . .
.
/ . .
: 14.00.23 / . .
.–
., 2003. – 44 .
. – ., 2002. – 96 .
, . .
. – .,
, 1995. – 272 .
-2012:
26
. . 2. –
, 2012
Experimental subhepatic cholestasis at rats invokes significant morphometrical indicators in neurons of lateral and medial kernels of forward horns of a spinal cord. The similar picture is characteristic for swelling of cages at destruction of their cytoskeleton.
These greatest changes are defined in a lateral kernel of forward horns of a spinal cord.
–
.
,
,
.
,
-
.
598.2
. .
(FAL O TINNUNCULUS)
2010 – 2011
.
.
)
,
.
(
78 %
97,5 %
:
).
.
.
85,2 %
,
9%
.
.
,
,
[1].
III
1700
-
,
.
1200-
[2].
,
:
,
.
[3].
,
-
[1, 4, 5].
,
:
,
,
,
-
9-
.
10 – 15
“
.
,
”
-
,
[5].
(
:
)
2010 – 2011 .
1)
2010 – 2011
.
; 2)
.
2010 – 2011
.
( I
IV
2010 – 2011
.
)
1
.
,
.
(
.
2)
.
)
(
,
-
.
,
100 .
,
2010 2011
.
.
,
(Circus pygargus) [6, 7, 8]. K
,
,
.
.
,
,
-
,
,
.
27
(
•
•
•
•
•
tus
.
•
•
•
1):
(
,
Rodentia,
,
Sorecidae);
Microtus spp.;
M. arvalis (
,
M. rossiae-meridionalis);
(M. oeconomus);
Apodemus spp. (
,
Mus musculus);
Lacerta / Zootoca spp. (Lacerta agilis / Zootoca vivipara);
;
Coleoptera.
.
(
1).
2011 .,
,
– 83,4% [1].
1–
.
Micromys minu-
2010 – 2011
5
66,7%
93,2%
2010 – 2011
.
(%)
.
-
Micro-tus
spp.
M.
arvalis
M.
oecon
omus
Apode
-mus
spp.
Lacerta
/Zootoca
Coleoptera
1. (2010)
148
54,1
12,2
22,3
3,4
1,4
1,4
4,1
1,4
1. (2011)
2. (20102011)
40
47,5
15
32,5
0
2,5
0
2,5
0
227
40,1
11,5
24,2
2,2
0
7,9
8,4
5,7
415
45,8
12,0
24,3
2,4
0,7
4,8
6,3
3,6
(
)
97,5 % 85,2 %
(
.
1).
Microtus – 37,9 %
47,5 %
38,7 %
Microtus arvalis
22,3 %
32,5 % 24,3 %
Microtus oeconomus
0 3,4 %
2,4 %
Apodemus.
.
( 0
7,9 %
)
Lacerta / Zootoca
2,5 %
8,4 %
6,3 %
(
Coleoptera) – 3,6 %
.
78 %
.
,
.
0
.
(
2010 2011
.
1)
(
5
2
=1,222; p <0,7476),
,
1
, df = 3,
–
(
NS) (
2).
2–
1
,
2
-
2010 – 2011
Lacerta /
Zootoca
Coleoptera
p<0,2985
p<0,45
p<0,64
p<0,45
p<0,00001
p<0,001
p<0,05
p<0,01
(df = 3,
(
2
.
,
-
1 (2010)
1 (2011)
1
2,5 % 0,7 %
4,8 %
-
2).
2
=15,518; p <0,001),
,
-
-2012:
28
. . 2. –
(
, 2012
2)
[6].
1.
,
(
,
)
.
2.
3.
.
(
)
,
,
.
(
1)
,
,
.
4.
,
,
(
– «nestlings period») –
3-
1,
,
–
2.
.
.
2010 – 2011
.
97,5 %
(
):
85,2 %
–
,
9 %.
78 %
: -
.
,
,
.
-
.
1.
,
. .
)/ . .
(1761 – 1847):
. 132 – 135.
2.
3.
,
. .
.
4.
.
7.
8.
.–
.
/ .
.,
:
.
(Fal o tinnunculus)
. 2502012 . –
:
2012,
, 2 – 4
, 2006. – 320 .
//
.
.
(Fal o tinnunculus L., 1758)
, .
: .
.
.
, 2012. –
. – . 11.
., 1982. – . 158 – 220.
, .
.
6.
.
.
,
.–
5.
//
//
III
.
.
.
.,
, 16 – 18
(Fal o tinnunculus)
. 2252011 . –
:
,
.
./ .
,
-
. 2002007 . –
.
.
, 2007. – . 72 – 77.
,
. .
.
/
. .
,
. .
//
,
(1786 – 1853):
VII
.
..
.,
, 26 – 28
, 2011. – . 67 – 68.
, . .
(Circus pygargus L.)
/ . .
//
:
.
.
.
»,
, 24 – 25
2008 . –
, 2008. – . 58 – 64.
Vintchevski, Dz. Zmiany sk adu pokarmu b otniaka kowego Circus pygargus w trakcie trwania sezonu l gowego na obszarze
zachodniej Bia orusi / Dz. Vintchevski // Wi cek, J., Polak, M., Kucharczyk, M., Grzywaczewski, G., Jerzak, L. Ptaki – rodowisko – Zagro enia – Ochrona. Wybrane aspekty ekologii ptaków. – Lublin: LTO, 2009. – . 295 – 307.
Vintchevski, Dz. Comparison of a diet of the Montagu`s Harrier (Circus pygargus L.) during breeding season in two distinct
plots in the Western Belarus / Dz. Vintchevski, A. Yasievitch // Stud. i Mat. CEPL. – 2009. – 3 (22) – P. 110 – 117.
We analyzed a diet of 2 pairs of Common Kestrel nesting in 2010 – 2011 at different parts of the city Hrodna (W Belarus).
Main category of prey for falcons were small rodents (mainly M. arvalis & M. oeconomus) – 85,2% of all pr y items (n=415). But at
different nests we found different importance of that and other categories of prey. Possible causes of differences are discussed.
. .
,
.
591.524.1(28):594.3
. .
.
.
,
2011 .
.
,
,
-
,
.
9
.
Limnaea stagnalis
.
5
.
,
.
,
Planorbarius corneus,
.
–
,
.
-
29
,
),
,
(
-
.
,
.
,
,
;
,
,
-
.
,
,
.
-
,
.
.
5
:
«
2011
(
»(
1,
3),
«
(
)
,
1x1 .
.
(
5).
»(
4),
,
,
.
.
162; 2, . 126],
141],
-
2),
[3, . 163],
[5, . 96].
10
[1, .
[4, .
-
[6].
625
,
9
,6
,6
: Viviparus contectus Mull., Bithynia tentaculata L., Planorbarius corneus L.,
Planorbis nitidus L., Limnaea stagnalis L., Limnaea ovata Drap., Limnaea auricularia L., Valvata piscinalis Mull.,
Sphaerium corneum L.
9
,
1
Bivalvia –
Sphaerium corneum.
.
,
88,89 %
(
1) 99,04 %
(
2).
.
1%
11 %
89 %
Gastropoda
99 %
Bivalvia
1–
2–
.
.
S. corneum
-
1).
1–
.
1
1. Planorbarius corneus
2. Limnaea stagnalis
3. Planorbis nitidus
4. Limnaea auricularia
5. Limnaea ovata.
6. Valvata piscinalis.
7. Bithynia tentaculata
8. Viviparus contectus
9. Sphaerium corneum
7
9
16
2
3
22
76
2
100
«
27
10
6
6
112
13
247
5
426
»
4
1
14
1
4
8
54
1
83
.
-2012:
30
. . 2. –
.
.
: V. ontectus,
48,16 %; 17,92 %; 17,44 %
(3,36 % 1,12 %). L.
-
,
V. piscinalis, L. stagnalis P. orneus,
9,12 %
. B. tentaculata
ovata
(
= 1,6).
0,96 % 0,32 %
,
L. auricularia
: S. orneum
, 2012
P. nitidus,
(
2).
2–
(
1. Planorbarius corneus
2. Limnaea stagnalis
3. Planorbis nitidus
4. Limnaea auricularia
5. Limnaea ovata
6. Valvata piscinalis
7. Bithynia tentaculata
8. Viviparus contectus
9. Sphaerium corneum
)%
9,12
17,44
0,32
1,12
1,6
17,92
3,36
48,16
0,96
57
109
2
7
10
112
21
301
6
625
.
,
2
(56,25 % 76,0 %
» – V. contectus, (65,06 %
(
),
57,98 %
(
1
L. stagnalis
«
-
2)
3).
3–
1
1. Planorbarius corneus
2. Limnaea stagnalis
3. Planorbis nitidus
4. Limnaea auricularia
5. Limnaea ovata.
6. Valvata piscinalis
7. Bithynia tentaculata
8. Viviparus contectus
9. Sphaerium corneum
43,75
56,25
-
2
3
22,0
76,0
2,0
-
6,34
2,35
1,41
1,41
26,29
3,05
57,98
1,17
4
1,20
16,87
1,20
4,82
9,64
65,06
1,20
.
,
5
(
40 %)
5–
S. orneum
(
80 %
( 20 %).
,
.
,
:1–
(
), 3 –
4-
), 2 –
( 60 %), 4 –
(
L. stagnalis P. orneus ,
. L. auricularia, L. ovata, B. tentaculata, V. ontectus,
P. nitidus. V. iscinalis
,
,
-
4).
4–
%
1. Planorbarius corneus
2. Limnaea stagnalis
3 Planorbis nitidus
4. Limnaea auricularia
5. Limnaea ovata.
6. Valvata piscinalis
7. Bithynia tentaculata
8. Viviparus contectus
9. Sphaerium corneum
4
4
1
2
2
1
2
2
2
80
80
20
40
40
20
40
40
40
.
31
5–
1
1
2
3
4
2
3
0,66
0,66
0,29
0,25
4
0,29
0,25
0,25
0,22
0,25
0,22
0,88
0,88
,
(
«
»(
3
(
2),
.
9
,
,
99,04 %
.
,
.
5.
6.
,
Limnaea stagnalis.
,
Planorbarius corneus
,
3.
4.
6
.
88,89 %
1.
2.
-
5).
.
,6
1
4).
,
-
.
, . .
, . .
/ . .
. – .:
, 1971. – . 162 – 163.
(Coleoptera: Carabidae)
/ . .
//
. – 2002. – 3. – . 126 – 137.
, . .
/ . .
. – .:
, 1990. – . 163 – 183.
Gzechowski, W. Carabid beetles of moist meadows in the Masovian Lowland Memor / W. Gzechowski. – Zool. – 1989. –
W. 43. – C. 141 – 167.
, . .
/ . .
.–
:
, 1999. – C. 96 – 97.
/
. . .
, . .
. – .:
, 1977. – . 152 – 174.
Studying of specific structure of molluscs litoral zones of reservoirs of Grodno. Definition of their number, studying of distribution on reservoirs. Definition and the analysis of the general domination, a degree of domination of a species in gathering, degrees
of a constancy of a species, specific riches.
– . .
,
-
.
37.01
. .
, . .
.
,
-
.
.
,
,
,
.
-
.
,
-
,
XXI
».
«
«
»
,
,
1983
»
.
«
«
».
,
,
.
,
,
-2012:
32
2020
«
»(
. . 2. –
, 2012
–
– 2020).
,
-
–
,
,
–
,
» [1, . 11].
.
.
,
,
,
—
[2].
,
.
.
(
)
-
.
.
«
»
1
-
.
,
,
,
-
.
(
-
1).
,
.
,
,
-
.
.
,
,
-
,
.
«
».
21
»
60 %
«
.
:
,
:« ,
-
,
».
,
» [2, . 27 – 28].
,
,
,
.
,
50 %
(
,
,
,
2).
1–
2–
,
,
»
»
,
-
33
,
-
;
(
);
,
,
,
2009
.
2012
»
«
.
-
«
».
,
,
.
.
,
-
.
.
.
,
,
.
,
,
–
-
.
,
–
,
?
.
–
,
,
.
,
,
,
,
,
,
-
,
,
,
-
[3].
«
–
»(
,
,
,
,
.1
,
,
1
,
).
-
.
,
,
,
.
.
.
,
,
,
,
.
,
-
.
1,3
.
2001
,
2,2
.
1961.
21 %.
1,6
-
«
-
,
.
.
» (3,2
(3,6
)
),
(1,6
)(
3).
,
(1,8
-
).
3–
1–
4–
;2–
;5–
;3–
;6–
-
;
-2012:
34
. . 2. –
, 2012
,
,
.
,
,
-
.
,
,
,
.
,
.
,
.
–
.
.
.
,
,
,
,
,
,
.
,
,
,
.
.
,
XXI
,
.
,
,
,
,
,
.
-
,
.
.
1.
/
;
. – 200 .
, . .
, . .
2.
3.
:
//
/ . .
, . .
.
.
. –
.–
.–
2020
:
44.
:
.
.
., 2006. – 96 .
Environmental education of youth and the formation of their motivation to act for the benefit of sustainable development of the
state. The role and importance of educational institutions in the formation of environmental knowledge for action for the benefit of
sustainable development.
– . .
,
,
-
.
619.616
. .
1
23
(
,
,
,
)
(85 – 87%)
1.
,
-
.
1
Aspergillus flavus
-
B1.
.
,
,
.
,
,
,
.
,
1-
,
.
,
.
.
-
,
,
.
1,
Aspergillus flavus
,
,
Aspergillus
80 %
rasiticus.
,
,
.
1
,
.
,
[1; 2].
-
35
–
2010
2011
.
,
(
1
,
,
,
)
.
B1
)
2010-2011
23
.(
(
,
,
-
1).
.
.
:
1
(
(
).
.
)
1
30711- 2001 [1].
(98:2)
,
,
-
.
.
1.
:
1
.
,
.
,
1.
23-
1:
)
«
»(
(23
[3].
«
)
(
»
»
«
).
-
1
WATERS Allians.
,
1
.
:
-
23-
,
2.(
–
;
«
»
»–
«
1
;
«
«
»–
)(
»
«
1).
»
,
1
.
»
«
).
»(
«
1
.
–
(
«
0,005
1
-
,
»
)
.
«
»
«
»
-
.
.
-31.
60 – 75%.
1.
Aspergillus flavus
84 %,
1.
1–
B1
1
(%)
2010 .:
2010 .:
«
–
»
–
-
.
–
«
61,2
-
65,0
»
79,1
– .
70,4
–
«
»
–
«
»
2011 .:
«
–
-
64,6
84,2
»
-
–
.
0,0096
85,1
76,2
–
77,6
«
»–
«
»–
»
-
84 %.
« .
»
-
70,3
75,4
-2012:
36
. . 2. –
, 2012
1
«
» –
«
«
»
»–
–
»
«
–
«
–
.
0,002
87,1
0,004
87,1
»
68,9
»
«
71,3
»
71,3
2011 .
– .
64,0
– .
69,5
– .
64,9
–
«
»
–
-
«
»
–
–
68,0
-
«
68,0
»
«
65,1
»
60,7
,
.
,
,
84,2 %
.
1,
2011 ,
.
«
,
»
-
«
»
.
-
,
Aspergillus flavus
23
1.
:
.
3
4) (
1 (
10 ,
2).
.
1
2)
–
100
.
30
(10-2, 10-3).
(
-
(
5–7
25 – 26
°).
.
,
1
,
(
1
.
.
-
2)
,
3
1
4)
2).
2–
1
,%
1,
1
1.
»
2.
»
3.
0,002
(4,6±0,6)*103
0,004
(4,3±0,6)*103
»
(2,9±0,6)*102
»
(1,1±0,08)*102
4.
Aspergillus flavus – 81;
Penicillium sp. – 17;
Aspergillus sp. – 2.
Aspergillus flavus – 63,
Aspergillus sp. – 37.
Aspergillus sp.– 32;
Penicillium sp.– 25;
Mucor – 43.
Aspergillus flavus – 13;
Aspergillus sp. – 40;
Penicillium sp.– 1;
Mucor – 46.
37
(
1)
2(
,
-
1)
3(
1).
1–
(23(
)
2(
1)
1)
,
»
.
»
2).
sp., Mucor sp.
.
-6
1
2 – 63 %) (
2).
3
1
43 %,
Aspergillus
Aspergillus flavus,
25 %
.
,
( Aspergillus flavus, Aspergillus sp., Penicillinum
.
,
Aspergillus.
Aspergillus flavus (
1 – 81 %,
Mucor,
4 – 46 %.
3 – 32 %,
4 – 40 %).
Aspergillus flavus (13 %).
Penicillum.
2 – Aspergillus flavus (
4
3
1)
-2012:
38
.
,
. . 2. –
(
,
,
.
1
,
, 2012
,
)
-
,
,
.
,
1
.
.
1
,
1
,
.
1
( 1
)
Aspergillus flavus
.
1.
,
. .
:
//
2.
/
. – 2000. –
/ . .
, . .
, 2007. – . 1. – . 283 – 304.
,
10
. 1980 .
, . .
3.
2773-80
. .
1. – . 2 – 12.
, . .
,
.
.
,
//
.–
. .
-
.:
-
,
Three samples of grain (from 23) with detection flatoxin 1 were stored at the increased humidity (85-87 %) within several
months. In the infected barley it is revealed ten times more than microscopic fungus in comparison with barley without mycotoxin.
–
. .
,
,
-
.
579.68
. .
.
.
«
»
.
.
,
,
-
.
.
,
Saccharomyces cerevisiae.
Pseudomonas putid
.
,
.
,
,
.
,
,
,
,
[1 – 3].
,
:
1.
.
-
.
,
,
.
,
,
-
.
.
3
0,25 – 2,5
3
10
,
– 10 – 20
,
,
3
.
,
,
.
.
,
2.
,
.
.
,
.
,
,
,
,
-
,
.
3.
.
,
.
.
.
,
.
,
-
,
.
,
:
,
,
.
-
,
.
,
39
,
,
,
.
-
,
.
4.
.
,
,
,
,
,
,
.
.
,
,
-
,
,
,
:
,
.
»
«
(
.
.
.
-
.
)
.
.
.
–
.
»
.
«
-
.
.
2011 .
4-
.
:
1:
2:
3:
4:
.
.
.
.
, 500
, 500
, 500
, 500
«
.
(
)
(
-
)
[4].
Saccharomyces cerevisiae
.
2,0 – 3,7
.
/ 3,
–
,
[5].
.
.
-
.
,
,
».
.
(
Pseudomonas putid
»
«
,
,
) [6].
,
.
,
.
(
«
»
1,3 – 2,1
.
,
1–
1).
.
,
(3,7±0,8) ⋅103
(4,7±0,4) ⋅103
(5,3±0,4) ⋅103
(16,3±12,2) ⋅103
1
2
3
4
-
,
(2,3±1,1) ⋅103
(4,7±1,1) ⋅103
(2,0±0,3) ⋅103
(63,3±11,9) ⋅103
/
3
(2,0±0,1) ⋅103
(4,1±1,0) ⋅103
(4,5±2,5) ⋅103
(27.1±18) ⋅103
4.
3,1 – 6
5,3 – 31
.
.
2
3
:
,
-
,
-
.
.
«
.
«
1,6 – 2
(
2).
-
,
,
2
.
2–
«
.
1
2
3
4
(1.0±0,1) ⋅10
(0,5±0,3) ⋅10
(1,0±0,4) ⋅10
(12,5±3,5) ⋅10
».
,
(1,3±0,7) ⋅10
(0,8±0,7) ⋅10
(0,5±0,1) ⋅10
(2,3±0,4) ⋅10
/
3
(2,0±0,1) 10
(1,0±0,1) 10
(0,5±0,7) 10
(25,5±3,5) 10
-2012:
40
. . 2. –
, 2012
.
,
-
.
4,6 – 51
.
,
2.1.2.12-33-2005
[7].
,
,
.
,
,
[8].
«
»
P.putid
29
36 %
,
,
(
2-
3).
,
-
2,8
.
3-
P.putid
,
,
3–
P. putid , %
,
1
2
3
4
.
.
134,4
105,9
37,6
37,6
48 100 %
177,8
218,5
259,2
266,6
4–
S. cerevisiae, %
28,8
49,5
97,9
61,8
–
,
1
2
3
4
,
S. cerevisiae
4).
( 62 %),
(
-
.
.
336,1
356,2
244,0
256,1
(
,
256,1
208,1
324,2
224,1
,
(
100 %).
90,4
28,6
42,9
142,9
P. putid )
(
S. cerevisiae)
.
,
«
»
.
,
.
.
,
«
,
.
»
,
.
.
,
,
.
,
,
,
,
,
.
.
,
,
,
.
1.
, . .
/ . .
, . .
.–
:
-
, 1973. – 258 .
2.
3.
4.
5.
, . .
. – .:
, . .
. .
. – .:
, . .
, . .
/ . .
;
. . .
;
-
, 2003. – 348 .
/
, 2003. – 512 .
/
. .
/ . .
. – .:
, . .
, 1990. – 89 .
.–
.:
, 1989. – 288 .
41
6.
7.
, . .
/ . .
.–
, 2004. – 124 .
2.1.2.12-33-2005 «
»,
2005 . 198.
, . .
, . .
:
8.
. .
28
/
,
. .
.
//
.
.,
,1–2
2006 . –
, 2006. – . 284 – 286.
It is studied the microbiological structure of water of the river Neman near to release of sewage of Open Society Grodno Azot
and city treatment facilities of Grodno. It is established biological pollution of water of the river Neman after receipt sewage in it.
– . .
,
,
,
.
615.099.08 + 612.3.354
. .
,
,
.
,
,
,
.
.
,
,
(
).
.
,
-
.
,
,
,
[1, c. 85 – 87].
,
.
.
-
.
[2, c. 20 – 21].
(
),
,
.
,
(
–
.),
,
).
.
-
(
,
,
,
,
(
,
),
,
[3, c. 5].
,
-
,
,
.
,
.
,
,
[4, c. 419].
–
.
,
,
,
-
.
.
-
,
–
,
.
,
,
,
),
.
–
,
,
,
.
-
-2012:
42
.
,
c
14.
,
14 (
,
– PBS,
)
37 ° .
).
2-
(5 %
2)
(
M
. . 2. –
.
,
DMEM,
25
1
,
,
:5
, 10
, 20
)
(GSH)
-
[5, c. 97],
[6, c. 74].
[7, c. 56].
-2- ]-2,5-
3-[4,5-
(
)
.
(H2DCFDA).
.
2,72,7-
H2DCFDA
H2DCF
2,7 –
(H2DCF).
(DCF),
.
1
(tBHP)
(p<0,05)
3,7
,
.
(
(p<0,05)
.
.
1
, 2012
,
.
M
4,3
-
.
,
-
.
,
4,2
.
,
(10
)
(p<0,05)
24,7
(p<0,05)
,
-
.
,
14
,
tBHP-
1.
10000.
1–
14
100
Mel
.
%,
-
N
100
tBHP-
(545
-
)
47
0.5081 ± 0.008879
10000
100
24
0.4499 ± 0.01196 *
8855
88,55
24
0.4861 ± 0.008922 #
9567
95,67
50
Mel+100
tBHP
22
0.4830 ± 0.01005 #
9506
95,06
100
Mel+100
tBHP
22
0.4436 ± 0.01215 *
8731
87,31
500
Mel+100
tBHP
24
0.4038 ± 0.007806 *#
7947
79,47
24
0.4441 ± 0.01250 *
8740
87,4
100
Trp
50
Trp+100
tBHP
24
0.5855 ± 0.007504 *#
11523
115,23
100
Trp+100
tBHP
23
0.5714 ± 0.006999 * #
11246
112,46
500
Trp+100
tBHP
22
0.5570 ± 0.009576 *#
10962
109,62
24
0.4596 ± 0.01621 *
9046
90,46
100
Suc
50
Suc+100
tBHP
21
0.5720 ± 0.01300 *#
11258
112,58
100
Suc+100
tBHP
21
0.5617 ±0.007451 *#
11055
110,55
500
Suc+100
tBHP
22
0.5324 ± 0.01178 #
10478
104,78
100
±
tBHP.
:
, # -p<0,05
-
; * -p<0,05
,
,
50
,
.
50
100
(
),
tBHP
500
).
(10 M tBHP)
,
(
-
43
.
(
2).
,
)
(100
(50
,
, 500
)
-
.
,
,
,
.
2–
,
0
100
100
Mel
50
Mel+100
tBHP
100
Mel+100
tBHP
500
Mel+100
tBHP
100
Trp
50
Trp+100
tBHP
100
Trp+100
tBHP
500
Trp+100
tBHP
100
tBHP (I *10-3,
100
Suc
50
Suc+100
tBHP
100
Suc+100
tBHP
500
Suc+100
tBHP
30
0.02483 ±
0.0005917
0.06614 ±
0.002452 *
0.02947 ±
0.0005510
0.01413 ±
0.0002431 *#
0.09424 ±
0.001845 *#
0.1356 ±
0.003711 *#
0.02716 ±
0.0003995 *#
0.05581 ±
0.001548 *#
0.05486 ±
0.001969 *#
0.05675 ±
0.001889 *#
0.02834 ±
0.0004189 *#
0.04391 ±
0.0009653 *#
0.04511 ±
0.001234 *#
0.04463 ±
0.001257 *#
: * -p<0,05
)
60
0.04919 ±
0.0005974
0.2870 ±
0.004599 *
0.04810 ±
0.0008417
0.02312 ±
0.0004289 *#
0.3737 ±
0.005177 *#
0.4957 ±
0.008569 *#
0.04508 ±
0.0008211 *#
0.2397 ±
0.006354 *#
0.2922 ±
0.009302 *
0.2446 ±
0.007095 *#
0.04808 ±
0.0005808 #
0.2199 ±
0.002704 *#
0.2661 ±
0.008910 *
0.2635 ±
0.009168 *#
120
0.07916 ±
0.001696
0.5212 ±
0.006984 *
0.07324 ±
0.001671 #
0.01872 ±
0.0002863 *#
0.7685 ±
0.008768 *#
0.9418 ±
0.01766 *#
0.06874 ±
0.001279 *#
0.4941 ±
0.01568 *
0.6327 ±
0.02010 *#
0.5105 ±
0.01083 *
0.07299 ±
0.001109 #
0.4159 ±
0.004847 *#
0.5339 ±
0.01717 *
0.5045 ±
0.02372 *
0.1106 ±
0.002101
0.8369 ±
0.008223 N *
0.1206 ±
0.002502 #
0.02942 ±
0.0006910 *#
1.232 ±
0.02227 *#
1.407 ±
0.03020*#
0.1154 ±
0.001881 #
0.9188 ±
0.02117 *#
0.9172 ±
0.02621 *#
0.9147 ±
0.01368 *#
0.1260 ±
0.002052 *#
0.7048 ±
0.008692 *#
0.7870 ±
0.05572 *
0.7180 ±
0.03065 *#
, # -p<0,05
,
100
tBHP
,
-
,
,
tBHP-
in vitro
,
,
14
.
50
-
,
,
.
.
,
,
,
,
,
,
-
.
1.
2.
, . .
.
/ . .
. – .:
, 1996. – 134 c.
, . .
/ . .
//
. – 2000. – 3. – . 20 – 27.
3.
, . .
:
/ . .
//
.–
1996. – 4. – . 2 – 10.
4. Bendich, A., Machlin, I. J., Scandurra, O., Rurton, G. W., Wayner, D. D. M. The atioxidant role of vitamin C // Adv. in
Free Radical Biology & Medicine. – 1986. – . 419.
-2012:
44
. . 2. –
, 2012
5. Stocks, J. The auto-oxidation of human red cells lipid induced by hydrogen peroxide / J. Stocks, T. L. Dormandy // Br. J. of
Haematology. – 1971. – Vol. 20 – P. 95 – 111.
6. Ellmann, G. L. Tissue sulfhydryl groups / G. L. Tllman // Arch. Biochem. Biophys. – 1959. – Vol. 82. – P. 70 – 77.
7. Mossman, T. Rapid colorimetric assay for cellular growth and survival: application to proliferation and cytotoxicity /
T. Mossman // Immunol. Methods. – 1983. – Vol. 65. – P. 55 – 63.
Results of many studies suggest a role of oxidative stress (high levels of free radicals and a simultaneous decline of antioxidant
defense mechanisms) in the development of many pathological processes. The oxidative stress is associated with disturbance of antioxidant-prooxidant balance in the cells and tissues and accompanied by impairment of cellular metabolism and cell death. We have
studied the antioxidant effect of natural polyphenols and melatonin during organic hydroperoxide-induced oxidative stress in various
cell cultures. The results obtained demonstrated pronounced cytoprotective effect of therapeutic doses of melatonin and natural polyphenols that resulted in the decrease of cell oxidative damage, reducing reactive oxygen species (ROS) generation and increasing cell
survival.
. .
,
.
,
,
.
556
. .
,
.
.
.
.
.
.
,
,
.
,
.
,
-
,
,
,
,
-
[1, . 116].
.
4250
2
,
01.01.2009 .
. 12,4 %
– 16,8 %).
– 18 (
– 38,8
350
2
,
,
– 78,09
(
– 25391 ,
226
. 3) [2 – 5].
– 106779
5 ,
.
-
,
-
.
.
[6, . 123].
.
.
.
.
-
.
,
-
.
– .
:
, .
: .
, .
– .
, .
.,
;
– 1946 – 1966 .,
– 1967 – 1990 .,
;
– 1991 – 2008 .,
.
.
1922 – 2008 .
(
– .
– 1922 – 1945
;
,
.
– .
.
1922 – 2008
,
.,
4
,
1).
45
1–
–
.
– .
,
1922 – 1945
1946 – 1966
228
80
1967 – 1990
125
61
1991 – 2008
.
.
.
– .
– .
– .
,
3
,
227
79
71
55
159
68
1922 – 1945
695
75
1946 – 1966
681
83
1967 – 1990
462
63
1991 – 2008
290
59
528
70
1922 – 1945
990
77
1946 – 1966
975
69
1967 – 1990
667
57
1991 – 2008
484
55
971
65
1922 – 1945
-
-
1946 – 1966
98
58
1967 – 1990
86
58
1991 – 2008
1922 – 1945 .
( 25 – 43 7 – 18 %
. 1946 – 1966 .
5 – 19 %
.
1967 – 1990 .
13 – 21 9 – 12%
,
13 6 %
1991 – 2008 . (39 – 56 9 – 18%)
53
50
79
55
23 – 43
)
,
.
– .
,
.
.
(
1–
1).
,
-2012:
46
. . 2. –
, 2012
:
,
,
.
(
2).
1922 – 2008
.,
,
-
,
.
,0
2–
,
–
.
.
.
.
1922 – 1945
-20
-18
-16
-18
– .
– .
– .
– .
1946 – 1966
-17
-14
-12
-15
1967 – 1990
-15
-13
-11
-14
1991 – 2008
-10
-8
-7
-9
,
,
-
,
.
,
,
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.
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.
–
,
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.
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.
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.
,
-
.
1946–1966
.
.
,
-
,
.
,
,
-
,
.
1.
2.
. .
, . .
/ . .
.–
, 2008. – . 1:
.–
, 2008. – . 2:
, . .
3.
. .
4.
2008. – . 3:
5.
01.01.1982 – 2008 . /
6.
;
.
. . .
,
/
. . .
. . .
.–
:
:
:
. – 161 .
:
. – 161 .
:
3 .–
,
688
, 2008. – 245 .
.–
:
.–
, 2006. – 160 .
3 .;
.
. – 224 .
: 3 .;
.
:
.
.
./
, 1975. – 240 .
The atical describes analysis of the change climatic element: the maximum water storage in snow, as the main factor causing
fluctuations in space and time of maximum discharge and strata of the spring flood runoff in rivers of Neman basin. It defines the
nature of the influence of melioration drainage runoff during spring flood in this basin.
– . .
,
.
,
,
.
47
67.02
. .
.
,
-
.
-
,
-
,
.
.
,
,
-
.
(
)
[1].
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»
.
–
,
(
,
,
,
(
),
,
,
),
. .
.
,
45
.
:
1050-88.
(
),
,
.
-
.
(
,
)
,
.
.
–
,
,
,
,
.
,
( 1,4-4
.
-
)
.
(
,
)
,
(
).
,
,
3000
.
-
,
,
:
[2].
» .
«
-
(
-63).
,
.
,
-
.
.
-63
-
,
.
550-580°
500
.
.
«
-2299,
1)
2)
3)
–6
– 150
»
-
:
;
;
–
.
:
1)
–
;
-2012:
48
2)
3)
4)
5)
6)
(
0,01 – 0,012
600 HV;
1) 1,4
.–
(
, 2012
);
;
370 HV;
+
:
,
1–
;
(500:1)
:
1)
2)
2000
.
-
30 000
3)
4)
5)
6)
.
30 000
,
.
– 6% ,
,
–
.
.
.
,
c
,
−
−
−
−
−
-
:
;
,
,
;
;
;
,
.
1.
2.
3.
,
,
.
,
,
:c .
/ .
.
:
.
.
/
.
, . .
/
.
[
. . .
. – .:
.];
.–
.
. . .
:
, 2002. – 163 .
, 1976. – 256 .
.–
:
,
2008. – 519 .
Production of gas spring rod with ionized nitrogen nitriding in glow discharge plasma can: reduce energy consumption, reduce
the number of operations, reduce the cost of details, to solve the problem of environmental protection.
.
,
.
,
.
49
621.643
. .
,
,
.
-
,
.
,
.
.
.
.
,
.
,
(
)
-
,
,
.
.
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-
,
.
,
,
.
-
,
,
.
,
.
.
-
,
.
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,
-
,
.
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-
.
.
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-
,
(
).
;
,
-
.
;
,
.
,
.
-
–
.
5
.
.
–
,
–
,
.
,
,
-
.
,
,
.
,
,
,
-
.
,
,
.
,
,
:
(
.),
,
(
,
(
,
,
,
.),
,
.).
,
.
-
(
),
):
,
,
.
-2012:
50
.–
, 2012
1–
.
,
,
-
.
.
,
.
.
,
( · )
2–
,
-
,
.
.
.
:
,
,
,
.
.
,
-
,
.
,
,
-
,
,
.
51
,
,
,
,
.
1.
2.
, . .
, . .
, 2005. – 72 .
, . .
:
: 3, . .
//
3.
4.
/ .
/
./ . .
.–
.
.–
.
,
, 2002. – 52 .
, . .
, . .
.–
:
, 2006. – . 3. – 35 .
:
/
. – 2002. –
.:
.
-
3. – 31 .
In this paper we analyze the market and technology of materials used in the construction of modern pipelines. Determine the
most rational types of insulating materials suitable for use in the construction of pipelines. Identified components of the economic
effect, the application of pre-insulated pipes. The influence of material structure on the thermal insulation characteristics. The variants of composite materials based on the foam matrix.
. .
,
,
,
.
-
.
621.9
. .
CALS.
60
,
.
CALS,
,
-
,
,
,
CALS.
,
,
,
«
,
»,
.
-
,
,
.
3-250.35.01,
».
,
«
-
,
-
,
.
,
LS-Dyna,
,
.
,
«
«
–
»(
. 1) [1].
»
,
,
40 ,
25
(18
).
-
.
,
SolidWorks [2].
«
,
–
LsPrePost
.
»,
NXUnigraphics 5,
LS-Dyna,
.
-
-2012:
52
.–
, 2012
1–
3-250.35.01 [1]
:
,
−
(
−
-
. 2);
;
−
.
2–
3-250.35.01 [1]
,
(
,
. 3).
40
,
,
60
60
(
).
-
4.
4–
3–
–
3-250.35.01
3-250.35.01
53
,
,
,
.
,
.
,
,
.
–
60
.
40
,
,
,
-
60
.
50…52 HRC
58…60 HRC,
42…43 HRC,
.
,
60
,
-
,
(
.)
«
–
».
3-250.35.01
60
,
1
1654-86
5000
2
5000
3
2000
Ø 32
– 98
Ø 50
– 98
Ø 55
– 98
Ø 160
– 99
Ø 150
– 99
Ø 150
– 68
Ø 160
– 68
– 100
Ø 50
– 100
Ø 55
Ø 160
– 100
– 100
Ø 150
– 100
– 70
Ø 160
– 70
– 100
Ø 50
– 100
Ø 55
– 100
Ø 160
– 100
Ø 150
– 100
– 70
Ø 160
– 70
100
120
70
Ø 32
Ø 150
120
70
Ø 32
Ø 150
100
100
120
70
-
,
,
,
.
1.
, . .
//
,
2.
/ . .
.
:
. . ANSYS
-1, 2004. – 512 .
. 6.
.
. – 2011. –
/ . .
1 (116). – . 77 – 81.
, . .
, .
.
.–
, . .
-
.:
-
Possibilities of optimization of the turning cartridge details with CALS-technology are considered. The use of low-hardenability
steel 60PP for the manufacture of the gear wheel is proposed. This work improves the reliability of industrial equipment.
. .
,
,
,
.
-
-2012:
54
.–
, 2012
691.332.5
. .
.
.
«
1998 – 2015
.»
,
2015 .
.
-
,
-
.
,
.
:
,
,
.
.
,
.
1,7
–
.
,
.
,
.
–
,
,
,
,
[1-3].
,
.
.
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-
.
,
,
.
:
,
,
,
.
,
.
-
,
,
.
.
,
,
.
.
.
D 400-500
«
».
-3.
-3 –
,
-
.
300, 400
.
500
–
3
,
-
.
.
-3
,
0,5, 1
1,5%
.
.
[4-7].
55
(
.
(
. 1)
)
-
,
-3
1%.
1–
,
-3, %
0
378
359
322
3
300
400
500
3
3
0,5
436
416
376
1
476
449
399
1,5
483
456
405
,
300, 400
3
500
,
-
100×100×100
1%
-3.
. 2-4.
2–
0
0,52
0,78
2,02
3
300
400
500
,
-3, %
1
0,73
1,12
3,05
3
3
3–
3
,
3
300
400
500
-3, %
1
303
398
502
0
308
402
512
3
3
4–
,%
3
300
400
500
-3, %
1
16
17
17
0
21
22
24
3
3
.
,
,
,
.
-
,
, ,
,
-
,
10
.
,
(
)
-
.
.
,
,
,
,
-
.%
-
,
,
,
,
.
1
-3
1.
-2012:
56
.–
, 2012
1–
,
-3
1.
2.
3.
4.
5.
6.
7.
, . .
1990. – 183 .
, . .
. .
.–
,
.
.
. .
.–
12852.0-77.
01.09.1994. – 4 . –
10180-90.
01.09.2006. – 31 . –
12730.1-78.
5 .–
19.
12730.2-78.
4 .–
19.
1%
1,5
– 1,6
/
.
.
. .
/
. .
.–
.:
,
.
.
,
,
, 2004. – 381 .
.
, 2006. – 446 .
.
19.
/
. .
,
.
,
.–
12852-67;
. 01.07.1978
.–
10180-78;
. 01.01.91
19.
.
.–
.
.–
12730-67;
. 01.01.80
01.06.2007. –
12852.2-77;
. 01.01.80
01.06.2007. –
Investigated the influence of specific chemical additives on the physical-mechanical properties of composite building materials
based on silicates. Shown the efficiency of plasticizing agents to increase the strength of porous silica concrete.
. .
,
.
678.046.36
.
.
,
.
6.
,
.
,
.
.
.
-
:
57
−
,
;
−
,
.
,
-
,
.
,
,
-
.
6 (
6)
,
.
-6
-
,
,
.
.
.
,
.
-
,
[2].
,
.
,
,
-
,
,
,
.
:
,
:
,
.
,
,
1000
.
,
,
-
.
.
.
-6
0,1; 0,5
1
3
.%.
,
100
-
.
.
, .
,
.
,
,
(
.
).
m(
)
-
,
:
( , )
–
–
S–
m–
τ–
=
S⋅m
, / 10
τ
,
, ;
, ;
(
11645-73);
, ;
: = 230 º , = 21,17 ,
, .
1
,
2
.
,
,
1.
1–
7,46
7,1
7,98
5,44
8,21
7,74
-2012:
58
.–
, 2012
, . .
.
,
.
,
,
,
.
-
.
+
.
,
.
-
,
.
2.
2–
-6
.
-6, 0,1
.%
-6, 0,5
.%
-6, 1
.%
1,
0,8033
0,7307
0,6826
0,6080
2,
0,7593
0,7237
0,6986
0,6058
3,
0,7868
0,7402
0,7111
0,6251
0,7831
0,7315
0,6974
0,6130
3,92
3,636
3,487
3,065
,
503,21,
/10
1.
,
-
,
,
,
.
,
.%
1–
,
,
-
,
.
,
,
,
,
,
.
.
-
59
:
1.
,
.
.
[
. .
. .
2.
,
:
.];
. . .
, . .
.–
,
, 2000.
, .
3.
:
.
, . .
. .
,
, 2007. – 431 .
:
.…
.
,
.
/
,
/
.–
:
.
/
.–
.
.
.
,
, 1999. – 164 .
This paper discusses the need for multifunctional use of the available fillers of polymeric matrices. Unsubstantiated nature of
the activity of dispersed particles of blue clay and the influence of activated filler on the rheological properties of polyamide 6 melt.
. .
,
,
,
-
.
620.178.153.4:620.178.169
. .
.
,
.
.
,
«
»
[1, 2].
-
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(
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),
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[3-6].
.
6(
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Rilsan, Arkema,
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»
-
),
«
(
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«
»,
-
).
,
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,
-
.
,
(
)
.
(
,
11,
),
(
6),
(75
.
:
– 3-4 .
– 10-30
– 350-360° ,
.
40
– 10
,
250-350
,
-
-2012:
60
.–
, 2012
NT-206.
1-
-4 .
-1
pV: p = 2
, V = 0,5
(
)
«
»
-
.
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,
,
–
–
-
.
1
2.
)
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11+
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,
10×10
; –
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6+
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10×10
; –
1.
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,
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**,
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-
61
3–
,%
4
11 (Rilsan)
6
6+
8
0,04
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0,02
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0,20
0,40
0,26
3–
6
.
,
-
6
11 (Rilsan).
,
6
-
.
6
11
.
1.
, . .,
, . .
/
.
. .
.–
.:
, 2010. –
456 .
2.
. .
3.
, . .
[
, . .
.];
. .
. . .
.–
:
, 2006. – 403 .
(
,
, 2005. – 260 .
.–
:
4.
.–
5.
/
, . .
. .
/
)/
.
.
/
.
,
.
.
.
,
[
.] //
3. – 2008. – . 76 – 81.
//
», .
6.
:
:
«
2011 . – . 183 – 186.
/ . .
, 19 – 20
, . .
II
«
», .
, 17 – 18
2012 . –
:
:
, . .
//
-
:
, 2012. – . 48 – 51.
Were researched the structure and physical-mechanical properties of fluorine-containing composites based on aliphatic polyamides. This article shows results of the tribological wear testing of polyamide coatings, modified nanophase particles of fluorinecontaining polymer-oligomer components.
. .
,
.
-2012:
62
.–
, 2012
678.8
. .
.
,
,
.
,
,
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.
,
100
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[1].
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. 1).
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Al (
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Al,
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»,
.
; )
Fe+
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– Al;
)
,
,
,
Al
,
,
.
: Fe – Cu; Fe – Fe; (
. 2-3).
Fe.
-
-2012:
64
2–
Fe (
–
.–
45) – Fe (
–
, 2012
08 )
-
, I·10-11
Fe (
Fe (
–
08 );
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Fe+
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–
– Fe
– Fe +
)
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)
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-
, I·10-11
Fe ( )
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Fe ( ) – Cu (
)
Fe – Cu +
Fe+
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Fe+
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2
3
4
Fe (
)
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7,258
,
.
,
,
-
.
,
,
(
45,
08
),
.
,
,
-
.
1.
/ . .
[
.] //
..
, . .
2.
:
.,
, 19 – 20
»
.
.
-
»:
2011 .; .
. . .
:
, 2009. – 31 .
– . 297 – 307.
/ .
.
.–
.:
«
The aim is to develop new polymer composite materials with optimal office performance and study of the effect of the coating
rotaprint ultrafine polytetrafluoroethylene tribosystems in knots. According to data obtained tribotests found that sustained release
film with low resistance and high shear adhesion activity generated in the case of applying rotaprint coatings to both bodies involved
in the process of friction.
– .
,
.
,
,
.
294.36
. .
,
.
.
-
65
.
,
–
.
:
.
[1].
:
,
.
–
[2].
,
-
.
.
:
,
.
,
,
. [5].
(1D, 2D
3D),
.
,
,
.[4]
1D-
.
:
. 2D2D»
«
2.5D-
.
.
.
,
,
.
2D-
-
3D-
.
,
,
,
-
.
Moldflow Adviser 2012 (
MF).
. Moldflow Adviser 2012
,
,
Autodesk
,
-
,
.
.
1.
.
SolidWorks 2011.
2.
.
(Autodesk Moldflow Adviser 2012).
-
.
1).
3
.
,
-
,
.
,
142
,
95,4
.
1–
«Gate Locations»
.
-2012:
66
2–
.–
, 2012
3D-
3.
3D-
,
-
.
,
,
.
-
.
,
,
.
:
,
,
(
,
),
.
3
;
4
,
,
.
.
3–
.
-
67
1–
;2–
;3–
;4–
4–
;5–
.
(
;6–
).
(
)
– Autodesk
« -
.
MoldFlow Adviser 2012.
SolidWorks 2011
».
1.
2.
, .
//
http://cadobzor.ru/
/ .
.–
;
CAD
.
. . .
[
.:
, 2009. – 208 .
]. – 2011. –
:
: 10.11.2011.
3.
. .
, . .
//
[
http://www.barvinsky.ru/articles/art_041_global_market_of_cae_2010.htm. –
4.
5.
.–
/
]. – 2011. –
:
: 21.10.2011.
/ . .
, . .
//
: http://www.barvinsky.ru/articles/
[
]. – 2011. –
art_044_temperature_in_hot_runners_mold.htm. –
: 25.10.2011.
MoldFlow –
// Autodesk [
: http://www.autodesk.ru/adsk/servlet/pc/index?siteID=871736&id=14659045. –
]. – 2011. –
: 25.09.2011.
This work shows how to use the computer software for the design of the mold. Conducted the computer analysis of molding
polymer products with cold and hot runner gating systems.
. .
,
,
.
678.01:621.7:627.217
. .
,
. .
6
11
.
-
,
.
.
.
,
,
,
,
-
,
,
-
.
-
[1].
-2012:
68
(
.–
, 2012
)
,
.
-
,
.
.
100
,
,
,
[1 – 5].
10
(
)
,
).
(
.
,
0,01 – 0,05,
,
,
,
,
,
-
.
,
,
-
,
,
,
.
–
6 (210/310
80 – 200
.
.
)
11 (“Rilsan”)
.
(
)
–
(
NT-206.
(
(
«
», .
).
252.
),
).
,
,
) [2-4].
(
,
(
,
-
)
.
(
,
1)
,
-
,
.
,
.
,
,
.
1–
–
[1]
6
(
1,5
11
. %)
,
,
.
1.
.
69
1–
Ra,
76,8
68,9
45,6
55,6
40,3
25,5
6
6 + 0,5
.%
6+1
.%
11
11 + 0,5
.%
11 + 1
.%
.(
)
6
11
2
)
)
3.
)
)
)
)
2–
6( , )
0,5
.%( , )
1
.%( , )
.
,
1,5-2
6
1
.%
Ra = 96,9-76,8
45,6-52,6
,
(
11
6
(
,
2 , , ).
(
<50
0,5 %
20 % (
.
)
1,5-2
<50
.)
Ra=40,3
,
.
3).
1
.%
11
-
Ra=25,5
11
)
.
)
)
)
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)
3–
11 ( , )
0,5
.%( , )
1
.%( , )
.
,
6
,
.
-
-
.
,
,
6
1
6 1,5 – 2
,
11 – 2
.%
-
(
1).
,
,
-
.
-
,
.
-6
-11 (
«Rilsan»)
,
1.
:
, 2006. – 523 .
,
.
,
/ .
.
[
.];
.
.
.–
:
-2012:
70
2.
[
.]. –
(
,
,
, 2005. – 260 .
,
. – 2000. – . 6,
:
, 2006. – 403 .
:
)/
.–
.
.
,
.
.
, 2012
,
.
3.
[
.] //
,
4.
.
;
,
5.
. . .
.
.–
.
, . .
. .
/ . .
/
. . .
.–
:
-
.];
.
.
.
,
, 1999. – 164 .
6.
.
/ . .
[
/
:
-
1. – . 31–39.
,
.–
.
. .
[
.];
, 2009. – 532 .
This paper presents the results of modifying the volume of powder compositions based on polyamide 6 and polyamide 11 dispersed synthetic fluorine-containing components. The estimation of the parameters of the functional characteristics of the formed
coatings deposited from composite formulations developed by flyuodization. An analysis of the impact of the energy state of the
fillers on the technological aspects of the formation of compounds.
. .
,
-
.
66.03:66.011:66.017
. .
CALS,
.
,
CALS-
.
.
6(
,
6)
.
,
-
.
,
.
,
,
.
:
,
,
,
,
.
,
(
)
,
,
,
,
. .
,
-
,
,
.
,
,
.
,
,
[1].
,
,
-
,
,
.
-
,
.
«
,
» [1, 2].
,
«
»
«
».
,
.
[3].
,
.
-
71
,
-
[4, 5].
CALSDS-10
40
.
Dietze & Schell Maschinenfabrik Gmbh & co. kg.
6(
–
).
,
-
.
(
65-375 ,
. 1).
-
,
–
260-1500
.
.
«
:
– 24
– 1200
»
– 2500
,
«
»
,
-
.
-
CAD-
AutoCAD 2012, SolidWorks 2012
SolidWorks [6].
1–
,2–
COSMOSWorks,
,3–
,4–
1–
(
); 2)
45 (
1–
,2–
( -
. 2, 3): 1)
; 3)
40).
,3–
1–
,4–
,2–
,3–
,4–
3–
2–
DS-10
DS-10
,
,
,
45,
[4, 5].
-2012:
72
1,8
(
.–
, 2012
. 4).
4–
SolidWorks 2012
«
. 5): 1)
.
-
».
; 2)
; 3)
. 6
«
»
.
)
)
)
5–
)
; )
; )
)
)
6–
«
)
.
»
; )
(
.
-
)
,
CALS,
,
.
1.
,
.
.
/
2.
:
. . .
, . .
:
, . .
/ . .
.–
3.
4.
.
, . .
/ . .
,
,
:
,
, 2010. – 157 .
,
.:
«
: 10.05.2012.
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.–
,
, 2008. – 354 .
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»[
»
//
, .
, 19 – 20
.
,
]. –
:
2012 . –
80-
XX
:
:
-
: http://grodno., 2012. – . 106 – 111.
.
73
5.
,
.
.
/
:
6.
.:
.
.
, . .
:
II
, 2012. – . 99 – 102.
, . . SolidWorks.
, 2006. – 800 .
//
:
.-
.
., .
, 17 – 18
/
.
2012 . –
.
[
.]. –
In this article proposed design and materials science solutions of improvement in the rewinder work. These obtained solutions
were confirmed by the results of in-process and bench testing. Were conducted virtual testing with the help of CALS-technologies.
. .
,
.
629.3:004.94
. .
,
-
.
,
,
,
.
,
Aided Design) —
,
3D
CAD (Computer
-
,
.
CAE (Computeraided engineering) [1].
«
»
.
«
,
)
(
»,
,
.
,
-
[2].
,
(
)
,
.
,
,
.
,
-
.
.
35
27.2-05757883-202:2009.
-
.
,
,
-
45º
,
.
(
-
),
54 HRC.
35
.
,
.
,
,
.
35.
20,
.
.
-
-2012:
74
.–
20
, 2012
,
.
,
17000
-
.
.
,
.
1–
,
35
1050-88,
SolidWorks
,
-
,
.
2–
:
,
,
17000
:
,
20.
.
.
.
-
75
,
,
,
,
(
,
2
351,571
Ø105 ×6
2
(257,241
,
,
257241376
,
.
20,
2
3).
-
.
17000
),
,
.
3–
35
-
20,
.
.
:
1.
2.
, .
,
. .
.
;
.
(CAD/CAM/CAE) /
:
. . .
.–
.–
.:
,
:
, 2004. – 560 .
,
/
, 2006. – 409 .
.
.
, .
.
,
The structural features of the seam weld the shaft, an analysis of the stress-strain state of a virtual model of the propeller shaft
tube and pipe material selection is made in order to improve performance.
. .
,
,
,
.
-
.
621.892
. .
,
.
-
,
,
.
,
,
.
,
,
,
.
,
,
.
.
,
[1 – 6].
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76
.–
, 2012
,
,
,
,
,
.
,
,
.
,
,
,
-
.
,
A. Begelinger
,
,
,
De Gee A.W.
.
,
.
,
,
.
,
.
,
.
,
,
.
,
(
«
».
),
[7]
,
.
,
.
-24,
-150 .
-
(
)
).
-
5
(
.).
«
».
.
,
,
-
(80-90 %)
.
:
,
,
,
.
,
,
,
,
(
-24)
0.00
0.02
0.04
Absorbance Units
0.06
0.08
0.10
0.12
(
1800
1–
5
1600
1400
1200
Wavenumber cm-1
-24 (1)
.%
1000
800
-24,
(2)
. 1).
,
-
77
«
,
»
-1
1146-1229
-150
. 2).
2.0
1.5
0.0
0.5
1.0
Absorbance Units
2.5
3.0
(
1800
1600
1400
1200
Wavenumber cm-1
2–
5
-150
1000
(1),
.%
800
-150 ,
(2),
(3)
.
67.5
87
,
-150
-24
56.5
42.5
.
,
,
.
-
,
.
,
,
.
3
.
2
y = 7,1443x - 22,774x + 85,318
180
,
150
120
90
60
30
0
0
0,5
1
2
,
5
.%
3–
-24
,
-
.
,
[8]
,
,
,
,
.
,
.
[7].
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-2012:
78
1.
2.
, . .
, . .
1999. 374 .
3.
, . .
4.
, . .
,
:
/ . .
/
.
/ . .
.–
, . .
.
.
.–
,
, . .
.
.:
. .
.:
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:
.
, 1981.
, 2012
303 .
.
.,
354 .
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5.
, . .
/ . .
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, . .
/
.
[
.] //
,
:
, .
,
, 11 – 15
. 2008 . /
.
.
»;
.
.
.
, 2008.
. 26 – 33.
8.
.
/ . .
.] //
XXI
: .
XVII
..
.,
, 13 – 18
2010 .: 4 . /
,
.: . .
[
.]. –
:
, 2010.
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The structure and rheological properties of lubricating greases modified nanophase particles of fluorine-containing polymer of
oligomeric compounds are studied. It is shown that the introduction of the nanomodifiers into the polymer matrix increases the
strength characteristics of the matrices, so the effectiveness of the lubricant increases.
– .
,
.
,
,
.
538.911
. .
,
.
.
,
,
-
[1 – 3].
,
.
,
[4],
[7].
[5]
[6],
[5 – 7],
,
[2-6].
,
– 10
)
1,7-4
,
4
:
1,5 – 10
, 1,5 – 2,5
,
,
–
.
-
–
(0,5
-
,
-
,
,
.
,
(
[8].
),
[9].
,
,
Ti-Al-N.
,
,
Ti-Al
Ti1–xAlxN
(
40
)
,
,
Ti-Si-N
Ti Al [10, 11].
[12].
x
0,5 – 0,6.
-
[12].
,
Al-Ti-N
.
,
279.048.
1
,
-
79
(7,5 ÷ 32)·10–3
,
– 50 .
.
,
,
(
)
11
-
.
,
.
-
AlTiN,
.
AlTiN,
AutoScan,
. 1 – 2.
.
-
.
Al-Ti-N,
.
(
-
. 3).
1–
1,1·10-2
AlTiN: –
3,2·10-2
(· 300)
60 %
100
50
, –
%
80
40
60
30
40
20
10
20
0
0
2–
1,1·10-2
: –
AlTiN,
, –
)
)
3–
: –
Al-Ti-N,
,
3,2·10-2
1,1·10
-2
,
Al-Ti-N,
–
,
3,2·10-2
-
-2012:
80
.–
, 2012
.
-
,
(
. 1, 2).
,
(
. 4).
.
.
1,1·10-2
Al-Ti-N, c
Al-Ti-N
,
,
– 75,5 HRC,
,
3,2·10-3
,
,
.
,
,
.
3,2·10-3
Al-Ti-N,
)
– 84,5 HRC.
:
.
,
-
.
)
4–
Al-Ti-N,
-2
: –
1,1·10
,
, –
3,2·10-2
Al-Ti-N,
-
.
.
,
.
.
,
Al-Ti-N
.
–50
,
,
,
-
.
»
.
1.
, . .
/ . .
, . .
. – .:
, 1994. – 496 c.
2.
,
.
.
/
.
.
,
. .
. – .:
, 1978. – 295 .
3.
, . .
/ . .
, . .
. – .:
, 1977. – 216 .
4.
, . .
/ . .
, . .
, . .
.–
:
, 1976. – 416 .
5.
, . .
/ . .
, . .
. – .:
, 1983. – 336 .
6.
, . .
/ . .
. – .:
, 1981. – 352 .
7.
, .
/ .
. – .:
, 1988. – 376 .
8.
, . .
/ . .
.–
:
, 1980. – 260 .
9.
, . .
/ . .
. – .:
, 1986. – 206 .
10. Ding, X. Abrasive wear resistance of Ti 1–x Al x N hard coatings deposited by a vacuum arc system with lateral rotating cathodes / X. Ding, C. T. Bui, X. T. Zeng // Surf. And Coat. Technol. – 2008. – Vol. 203. – P. 680 – 684.
11. Mechanical properties and machining performance of Ti 1–x Alx N-coated cutting tools. plating / A. Horling [et al.] // Surf.
And Coat. Technol. – 2005. – Vol. 191. – P. 384 – 392.
12.
/ . .
[
.]. –
:
, 2005. – 96 .
The morphology and structure of the surface layers of aluminum and titanium nitrides coatings on a metal surface are studied. The
character of the mutual influence of layers on the distribution of the active centers and interfacial interactions energy is established.
– .
,
.
.
,
,
81
004.9
. .
SimPy (Simulation in Python)
Python.
.
.
.
–
-
,
,
-
.
–
.
–
,
,
,
-
.
,
.
,
.
,
,
,
.
,
,
-
:
1)
2)
3)
4)
5)
(
)
;
;
;
;
.
.
,
.
,
.
,
-
.
,
.
:
,
-
.
,
),
,
.
—
,
,
-
.
.
.
.
(Howard-Matalytski) –
,
HM
S1 ,S2 ,...,Sn .
n
.
,
[1].
,
-
.
.
), 2)
: 1)
(
-
).
,
,
(
,
,
,
,
.
-2012:
82
. . 2. –
,
,
, 2012
,
-
.
.
.
,
.
,
,
,
.
(
:
,
–
(
)
).
-
,
.
,
.
«
»
,
, «
,
,
.
,
.
«
«
.
»
»
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-
,
.
,
,
,
,
.
«
»,
.
,
.
-
,
.
,
,
.
–
(
,
).
-
–
,
–
,
–
-
,
.
SimPy (Simulation in Python) –
,
-
Python.
– Process
Resource –
.
.
.
Monitor,
(
,
-
1).
.
,
),
-
S4
.
.
,
,
.
-
-
)
-
)
)
S2
S1
S3
1-
,
:
P = pij
4×4
0
0
 0

0
0
 0
=
0
0
0

 0,5 0,25 0,25

µ1 (t ) = sin(5t + 1), µ 2 (t ) = 3t + 2, µ3 (t ) = 1 + sin 4t , µ 4 (t ) = 4t − 1,
1

1
1

0 
.
:
-
83
[0,3],
S2 –
2
3
3,
:
S3 –
1,
2
, K1 = 25 , 100
:
0
0
0
0


0 0 0



0
0 0  ( 2)  0 0 0
0
=
, r =
0
0
0 0
0 0 0



 30 400 380 0 
 20 50 70



S1 –
-
S4 –
25
r (1)
1.
, K 2 = 100 .
-
0

0
.
0

0 
.
(
-
2).
v1(t)
2800
2100
1400
700
2
4
6
8
t
S1
2–
.
,
SimPy
-
Python.
.
1.
, . .
, 2008. – 771 .
/
.
.
,
. .
,
.
.–
:
This article describes the basic principles of simulation NM-networks with priorityapplications using discrete-event simulation
using open software library SimPy (Simulation in Python) package of Python. We also consider the use of simulation forsolving the
problems of finding the expected revenue given the logistics of the transport system.
.
.
,
,
,
.
517.925 (075.8)
. .
,
.
,
.
.
,
,
-
-2012:
84
y=
∞
∑h
mt
− mν−s
. . 2. –
, 2012
,
(1)
m =0
s, ν ∈ N.
[1, . 35]
 p −k ν
t ( )

k =1 
j=1

,
p


p − k )ν
s
pν
(

αk t
t t −


=
k
1


∞
.
h 0 t pν +
y=
k
∑  h − ∑ α h
j k−j
k
(2)
∑
H = h k+ j
–

p
0
,
.
1.
2 2 1
1
w ′′ + ww ′w ′′ + 3w ′3 − w 2 w ′2 .
3
3
3
= −10
h 02 = −1 ,
w ′w ′′′ =
h 01
h 02 = −1
(3)
h 01 = −10
–5, 6,
1, 3.
,
ν = − r = 5 , h 01 = −10 .
(1),
:
26 2
17 3
1351
2651
h2 = −
h1 , h 3 =
h1 , h 4 = −
h14 , h 5 =
h15 ,
135
450
182250
1822500
,
hi,
p=2
(4)
ß1, ß2,
-
h2 = β1h1 + β 2 , h3 = β1h2 + β 2 h1 , h4 = β1h3 + β 2 h 2
(5),
1
1
β1 = − h1 , β2 = −
h12 .
5
1350
h1 = 5h
(4),
(3)
(
−5 ( t − t 0 ) 2 ( t − t 0 ) + h
4
w=
( t − t0 )
10
5
+ h ( t − t0 )
2.
h 01
h 02 = −1
(5)
5
)
1
+ h2
54
.
(6)
w ′′′ = ww ′′ + 5w ′2 − w 2 w ′ .
= −6
h 02 = −1 ,
(7)
–5, 6,
h 01 = −6
1, 5.
,
s = 1 , ν = − r = 5 , h 0 = −6 .
(1),
:
1
1 3
1
1
h 2 = − h12 , h 3 =
h1 , h 4 = −
h14 , h 5 =
h15 ,
5
25
125
625
(8)
,
2
w=−
z = t − t0 .
,
3
4
6 h1
h
h
h
+ 6 − 111 + 1 16 − 1 21 + ... ,
z z
5z
25 z
125 z
(9),
(9)
,
h
h
b1 = 16 , q = − 15 .
z
5z
,
,
(7)
6(t − t 0 ) + h
.
(t − t0 ) (t − t0 )5 + h
h1 = 5h
-
5
w=−
(
)
(10)
3.
(
w ′′′ = 6w 2 w ′ + d w ′ − w 2
)
2
, d=
18
9±7 3
.
(11)
85
3
,
h01 = −1
3
3
2, 5.
h03 = 1 ±
3
(1),
s = 1 , ν = −r = 5 , h 0 = 1 ± 2 3 .
h01 = −1 , h 02 = 1 ± 2 3
h02 = 1 ± 2 3
3, 4,
–5, 12,
,
h03 = 1 ±
-
:
h2 =
1 97 3 ± 243 2
1 67 3 ± 126 3
1 67163 3 ± 116373 4
⋅
h1 , h 3 =
⋅
h1 , h 4 =
⋅
h1 ,
165 7 3 ± 9
225 21 3 ± 38
1125 33733 3 ± 58419
h5 =
h6 =
1
2401891537 3 ± 4160198334
⋅
,
16875 656882709 3 ± 1137754238
(12)
1
5255155215396320724433 3 ± 9102195834726994619553 6
⋅
h1 ,
84375 2348364191466334374557 3 ± 4067486094295098031581
,
p=3
hi ,
(
β1 , β 2 , β3 ,
)
h3 = β1h2 + β 2 h1 + 1 ± 2 3 β 3 , h 4 = β1h3 + β 2 h2 + β 3 h1 ,
h 5 = β1h4 + β 2 h3 + β 3 h2 , h 6 = β1h5 + β 2 h4 + β 3 h3 .
(13)
1
1
2
β1 = ± h1 3 , β 2 = m
25 3 m 51 h1 , β 3 = 0 .
(13),
(12),
15
9075
(11)
h1 = 165h
(
(1 ± 2 3 ) ( t − t
w=
0
)10 + 11( 9 m
( t − t 0 ) ( ( t − t 0 )10 m 11
)
(
)
3 h ( t − t 0 ) ± 6 4 3 m 13 h 2
5
(
) )
3h ( t − t 0 ) ± 3 25 3 m 51 h 2
5
)
.
(14)
4.
w IV = 18ww′′ + 9 w′ 2 − 24 w 3 .
h01 = 1
h02 = 5 ,
h02 = 5
(15)
h01 = 1
3, 4, 8,
–5, 8, 12.
,
(1),
s = 2 , ν = −r = 5 , h0 = 5 .
11 2
2 3
7
13
4
5
h2 =
h1 , h3 =
h1 , h4 =
h1 , h5 =
h1 , …
180
675
54000
2430000
,
hi ,
p=2
:
(16)
β1 , β2 ,
h2 = β1h1 + 5β 2 , h3 = β1h2 + β 2 h1 , h4 = β1h3 + β 2 h2 .
(17),
(16),
(15)
5(t − t 0 ) + 20h(t − t 0 )
8
w=
(17)
1
1 2
β1 = h1 , β 2 = −
h1 .
15
900
h1 = 30h
3
((t − t ) − h)
2
5
.
(18)
0
5.
w IV = 3ww′′′ + 9w′w′′ − 3w 2 w′′ − 6ww′ 2 .
h01 = −1 h02 = −2 ,
h02 = −2
1, 3, 4,
–2, 3, 4.
,
(1),
s = 1 , ν = −r = 1 , h0 = −2 .
1 2
1 3
1 4
1 5
1 6
h2 = − h1 , h3 = h1 , h4 = − h1 , h5 = h1 , h6 = − h1 , …
2
4
8
16
32
,
w=−
z = t − t0 .
(19)
h01 = −1
2
3
4
2 h1 h1
h
h
+
−
+ 1 − 1 + ... ,
z z 3 2z5 4z 7 8z9
:
(20)
-2012:
86
. . 2. –
, 2012
,
2
h
b1 = − , q = − 12 .
z
2z
,
h1
=a
2
,
(19)
w=
.
− 2(t − t 0 )
(t − t0 )2 + a
-
(21)
(3), (7), (11), (15), (19)
(6), (10), (14),
(18), (21).
.
,
.
,
1.
, . .
. .
/
.
. – 2000. – 3. – . 33 – 39.
.
/
. 2.
,
,
.
.
,
.
.
,
,
-
,
This article provides a formula for finding rational solutions of differential equations for the negative resonance. Also, specific
examples should be shown how to find all the coefficients used in this formula.
.
.
,
-
,
,
,
.
004.91+347.78.031
. .
.
,
,
.
.
.
,
-
.
.
, ,
,
,
,
,
,
-
.
,
,
,
-
–
.
,
,
-
,
.
,
,
,
,
,
,
-
,
.
,
,
, ,
,
-
.
,
,
.
,
-
,
-
87
,
,
,
,
-
,
,
.
,
,
-
.
,
,
,
,
,
,
,
.
,
,
.
,
,
-
,
,
,
.
,
,
,
,
-
,
.
.
,
,
,
-
.
,
,
,
.
,
.
.
,
,
.
.
.
.
.
,
,
,
,
,
-
.
/ ... /
(
;
-
).
(
;
;
).
/
(
;
;
;
).
.
.
.
.
/
/
.
.
.
,
.
,
,
[1, 2].
(
)
-
,
.
-
,
.
,
(
)
.
OAuth,
Google, Facebook, Twitter
.
-
,
.
-2012:
88
. . 2. –
, 2012
:
−
−
−
−
;
;
;
.
(
,
),
(
,
.1
. 2).
1–
2–
.
,
,
,
,
,
-
.
,
.
-
89
,
,
.
1. What Cloud Computing really means [Electronic resource]. – Mode of access: http://www.infoworld.com/d/cloudcomputing/what-cloud-computing-really-means-031. – Date of access: 28.04.2012.
2. QuickStudy: Application Programming Interface (API) [Electronic resource]. – Mode of access:
http://www.computerworld.com/s/article/ 43487/Application_Programming_Interface. – Date of access: 28.04.2012.
This article describes the general approaches to create the staffing system of the higher education institution for the Grodno
region. Special attention is paid to the specific areas of implementation identification, subject area investigation, the main advantages
of the proposed system description and justification.
. .
,
,
,
.
517.925.3
. .
,
.
[1, . 174].
,
.
R–
:
(
.
)
 x& = θ ⋅ γ 0 − x − x ⋅ y n ,

&
n
 y = n ⋅ α ⋅ γ 0 − x − x ⋅ y + δ ⋅ (z − y ),
 z& = λ ⋅ x + γ ⋅ µ − z,
1
0

, λ1 ∈ R , λ1 < 0 , N –
n∈N , θ , γ 0 , α , δ ∈R
.
,
(1)
R3
.
.
(1)
:
(
)
(1)
,
.
γ 0 − x − x ⋅ y n = 0,

 z − y = 0,
λ ⋅ x + γ ⋅ µ − z = 0.
0
 1
2).
nα
a 0 = θγ 0 , a1 = θ , b =
, b1 = δ , b 2 = λ1 , b3 = γ 0 µ .
θ
1,
:
 x& = a 0 − a1 x − a 2 x ⋅ y n ,

&
n
 y = b ⋅ a 0 − a1 x − a 2 x ⋅ y + b1 ⋅ (z − y ),
 z& = b ⋅ x − z + b .
2
3

,
(2)
 x& = − a1 x − a 2 x ⋅ y n ,

&
n
 y = b ⋅ − a1 x − a 2 x ⋅ y + b1 ⋅ (z − y ),
 z& = b ⋅ x − z.
2

(3)
(
,
(
-
)
(2)
,
(
)
-2012:
90
(3)
:
(
, 2012
)
 x ⋅ a1 + a 2 ⋅ y n = 0,

 z − y = 0,
b ⋅ x − z = 0.
 2
,
. . 2. –
(3)
R3
,
-
:
,
:
n –
n –
1.
2.
a1
>0,
a2
a
) − 1 <0,
a2
) −
,
(3)
;
O(0,0,0 ) .
(3)
O(0,0,0 )
− ba1
b2
,
1.
2.
3.
4.
5.
a1 , b1 ∈ R
a1 , b1 ∈ R
a1 , b1 ∈ R
a1 , b1 ∈ C
a1 , b1 ∈ C
C –
b1 = 0
(3)
(1)
1.
.
(3)
− a1 − λ
,
z

x = b ,
2

 x = 0,

a

1)  y = 0, 2)  y n = − 1 ,
a
2

 z = 0,

 z = y.



 −1 − γ 0 −
A



 −1 − γ 0 +
B


(γ 0 µ + 1)
2
2λ1
0
:
0
− b1 − λ
b1 = (− a1 − λ )⋅ (− b1 − λ ) ⋅ (− 1 − λ ) = 0,
0
−1 − λ
λ1 = −1, λ2 = − a1 , λ3
:
O(0,0,0 ) –
a1 , b1 > 0 ,
O(0,0,0 ) –
a1 , b1 < 0 ,
O(0,0,0 ) –
,
a1 ⋅ b1 < 0
Re (a1 ) > 0 , Re (b1 ) > 0 ,
Re (a1 ) < 0 , Re (b1 ) < 0 ,
, Re (a ) –
(3)
,
n =1
(γ 0 µ + 1)
+ 4γ 0 λ1 − 1 + γ 0 −
,
(γ 0 µ + 1)2 + 4γ 0 λ1
2λ1
(3).
,
2
= −b1 .
.
O(0,0,0 ) –
O(0,0,0 ) –
.
.
.
bx − y = c .
,
Oz .
:
+ 4γ 0 λ1
2λ1
(γ 0 µ + 1)2 + 4γ 0 λ1
−1 + γ 0 +
.
.
2λ1
,
,
(γ 0 µ + 1)2 + 4γ 0 λ1 
−1 + γ 0 −
2λ1
(γ 0 µ + 1)2
−1 + γ 0 +
2λ1
(x 0 , y 0 , z 0 )
:
,



+ 4γ 0 λ1 
.


−θδ − θδλ − θλ − θλ − θ y0δ − θ y0δλ − θ y0 λ − θ y0 λ − λ nα x0 − λ nα x0 − λδ − λ δ − λ 2 − λ 3 − θ x0δλ1 = 0,
.
θ = 1, α = 0, δ = 1,
2.
(1),
γ 0 = 2, µ = 2, λ1 = −3, n = 1 ,
:
2
2
 x& = 2 − x − x ⋅ y,
&
 y = z − y,
 z& = −3 ⋅ x + 4 − z,

(4)
2

: A ,2,2  , B(1,1,1) .
3

2
2
(4)
91
A:
( −3 − β ) ⋅ ( −1 − β )2 − 2 = 0,
:
β1 = −
β 2, 3 =
3
3
35 + 3 129
4
5
−
− ,
3
3
3 35 + 3 129 3
 3 35 + 3 129

35 + 3 129
2
5 1
4
.
+
− ± i 3  −
+

3
3
6
3
2
3
35 + 3 129
3 35 + 3 129 

B:
( −2 − β ) ⋅ ( −1 − β )2 + 3 = 0,
:
β1 =
3
316 + 36 77
2
4
+
− ,
3
6
3 316 + 36 77 3
 3 316 + 36 77

316 + 36 77
1
4 1
2
.
−
− ± i 3 
−

3
3
12
3
2
6
3 316 + 36 77
3 316 + 36 77 

A
,
(4)
B–
.
β 2, 3 = −
1.
,
.
3
.
. .
/
. – 2-
.–
.:
.
,
-
.
,
, 1990. – 488 .
In this paper we consider an autonomous third-order polynomial right hand sides, which is a mathematical model of genetic
circuits. The system is investigated by methods of qualitative theory of differential equations. The states of equilibrium are found,
their classification is given and their stability is investigational on Lyapunov.
–
,
.
.
,
,
-
.
517.5
. .
–
[–1,1]
–
–1
1.
-
.
.
.
[1, 2].
,
: 1)
ak ∈ R ,
,
C,
R
.
.
{a k } k+∞=1 –
| a k |< 1 ; 2)
ak ∈ C ,
,
al = ak ; 3) a1 = 0 .
:
µn ( x ) =
n
x + ak
∑ arccos 1 + a x ,
k =1
-
al ,
k
-2012:
92
λ n ( x)
µ n′ ( x) = −
, λ n ( x) =
1− x2
xk , k = 1, K , n − 1 –
. . 2. –
1 − a k2
n
∑ 1+ a
k =1
k
x
, 2012
.
N n (x ) ,
N n ( x) =
sin µ n ( x )
1− x 2
x0 = −1 , xn = 1 .
, x ∈ [−1;1].
f ∈ C[−1;1]
x k , k = 1, K , n
L(1)
n (x, f ) =
f (1)N n (x)
+
λ n (1)
n −1
∑(−1)
k +1
(1 + x k )(1 − x)N n (x)
.
λ n (x k )(x − x k )
f (x k )
k=1
(1)
f ( x ) ≈ L(n1) ( x, f ) ,
1
∫
1
f ( x)
−1
n −1
f ( x k )(1 + x k )
(−1) n f (1)
1+ x
dx ≈
π+
π.
1− x
λ n (1)
λ n (x k )
k =1
1
∑
f ( x)
−1
.
∫
−1
f ∈ C[−1;1]
1.
∫
1+ x
1+ x
dx ≈ L(n1) ( x, f )
dx.
1− x
1− x
(1)
n −1
(−1) k +1 f ( x k )(1 + x k )
f (1)
1+ x
dx =
In +
Ik ,
λ n (1)
λn ( xk )
1− x
k =1
1
∫
∑
L(n1) ( x, f )
−1
1
In =
∫
−1
1
sin µ n ( x )
dx,
1− x
∫
Ik =
−1
sin µ n ( x)
dx.
x − xk
Ik
1
Ik =
(
)(
)
x = 1− y 2 / 1+ y 2 .
∫
−1
sin µ n ( x )
dx, k = 1,..., n − 1.
x − xk
,
1− y 2 
 = sin Φ n ( y ) −
sin µ n 
 1+ y 2 


± y k , y k = (1 − x k )/(1 + x k ) , k = 1, K , n − 1.
∞
I k = −(1 +
y k2 )
sin Φ n ( x )
∫
y −
2
−∞
y
1+ y 2
y k2
dy.
,
J k (z )
∞
J k ( z) =
∫
−∞
[3, . 92].
sin Φ n ( x)
y
y −z
1+ y 2
2
2
dy,
Ik
Ik = −(1 + yk2 )
[3, . 48]
lim
z → yk , Im z >0
J k (z).
,
sin Φ n ( y ) =
1 
2i 

n
y−zj
n
y − z j 
,

j

∏ y−z ∏ y−z
j =1
j
−
j =1
-
93
y2 +
zk
1

2i 
−∞

∞
=0.
1 − ak
y − zj
n
n
y − zj  1
y

dy.
2
2
2

j  y − z 1+ y
∏y−z ∏ y−z
∫
J k (z) =
1 + ak
−
j
j=1
j=1
(2)
J k (z )
1
( J k′ ( z ) − J k′′ ( z )),
2i
J k (z) =
∞
J k′ ( z ) =
y−zj
n
∫∏ y−z
− ∞ j =1
J k′ (z )
J k′ ( z ) = 2πi res
y=z
= 2πi lim
y=z
y − z 1+ y
2
j
n
∞
y
1
2
y−zj
∏ y−z
j =1
n y−
∏ y−z
j =1
=
2
2
y =i
z−zj
n
πi
∏ z−z
1 + z j =1
J k′′ (z )
2
πi
−
1+ z
j
∏ y−z
j =1
n
∏ z+z
1 + z j =1
J k′′ (z ) (2) ,
J k′ (z )
n
2
z−zj
z+zj
n
∏ z−z ∏ z+z
j
j =1
J k ( z) =
1  πi
2i  1 + z 2

z−zj
n
∏ z−z
j =1
=
+
j
j =1
n
πi
1+ z
2
∏
j =1
Ik ,
I k = −(1 + y k2 )
n
π
1+ z
2
j =1
k
y − z 1+ y 2
j
2
1
y −z
j
y
1
2
dy.
=
y
=
y+i
.
j
.
j
,
j
z + z j 
π
=

z + z j  1+ z 2
yk − z j
∏y
2
2
2
i−zj
∏i−z
j =1
y − z 1+ y 2
y= z, y=i.
j
y−zj
n
z+zj
n
πi
J k′′ ( z ) = −
2
j =1
y
1
2
y−zj
∏ y−z
+ 2πi res
y
1
+ 2πi lim
y =i
y + z 1+ y 2
j
y−zj
∫∏ y−z
n
y
y − z 1+ y
j
n
− ∞ j =1
1
2
zj
2
dy, J k′′ ( z ) =
−zj
n
z−zj
∏ z−z
j =1
.
j
= (−1) k +1 π .
In
I n = (−1) n π .
1
∫
f ( x)
−1
2.
1
∫
−1
.
[–1,1]
f ( x)
n −1
f ( x k )(1 + x k )
(−1) n f (1)
1+ x
dx ≈
π+
π.
1− x
λ n (1)
λ n (x k )
k =1
∑
x k , k = 0, K , n − 1 .
f ∈ C[−1;1]
n −1
f ( x k )(1 − x k )
(−1) n +1 f (−1)
1− x
+
dx ≈ π
π.
1+ x
λ n (−1)
λn ( xk )
k =1
∑
–
–1
1.
.
,
.
1.
. .
,
.
//
.
–
. – 2008. – . 52,
5. – . 11 – 15.
/
.
-2012:
94
2.
, . .
. – 1996. – . 40, 3. – . 42 – 46.
3.
, . .
. . 2. –
/ .
/ . .
.
, 2012
//
.–
-
:
, 1979. – 176 .
The rational interpolating process with nodes in the zeros of Chebyshev – Markov sine-fractures is considered. The
interpolating Lagrange function is obtained in this case. Using the Lagrange function new quadrature formulas are obtained.
– . .
,
,
,
,
.
004.91+347.78.031
. .
, . .
,
,
,
.
,
.
.
.
.
,
.
,
,
,
,
.
,
–
,
,
,
-
,
,
,
,
,
.
,
-
:
−
−
−
−
−
−
(
,
.);
;
;
;
;
,
.
,
,
.
,
,
.
,
,
(
:
-
).
,
,
,
,
-
[1].
,
(
),
,
,
,
.
,
,
,
,
,
.
–
,
.
.
.
.
,
,
:
-
,
. [2].
.
.
,
.
:
,
,
.
-
,
-
.
.
.
95
,
.
,
.
.
.
.
.
.
-
,
.
,
,
.
,
.
,
,
,
,
.
-
.
.
.
,
,
,
,
.
,
,
,
,
,
-
.
.
.
,
.
,
-
,
.
«
»
,
.
.
,
,
.
.
,
.
.
,
.
,
,
,
-
:
,
–
.
–
,
-
.
.
-
.
.
.
[3].
.
,
,
,
.
.
:
,
,
.
.
,
,
.
.
.
,
-
.
,
,
.
.
.
,
,
,
,
.
-
,
.
,
,
,
.
-2012:
96
. . 2. –
1
, 2012
.
1–
.
,
,
-
.
,
,
.
,
.
,
,
,
1.
, .
2.
news.asp?id=1265. –
3.
e_mail/e_mail.htm. –
,
,
.
/
]. –
[
: 15.04.2012.
[
: 01.04.2012.
].
–
.
.–
:
.:
, 2007. – 544 .
: http://www.arendazala.by/
http://cdo.bseu.by/library/ibs1/applic_l/
Sets out the general approach for creating an Internet portal, which supports research, communication and organizational
interaction. We consider its modular structure, as well as the advantages and disadvantages of such a structure. We describe the
possible functionality of the developed Internet portal.
. .
,
,
,
.
003.26
. .
,
.
,
,
-
.
.
,
.
.
.
,
«
»–
,
.
.
-
97
,
,
–
,
.
-
,
.
–
«
–«
», «
-
»
».
,
,
»
,
.
«
«
»
,
,
.
,
«
»
.
,
,
-
.
(RSA)
(
).
,
.
,
,
-
.
,
-
,
.
.
—
,
,
.
-
,
.
E
F
,
Y 2 + a1 XY + a3Y = X 3 + a2 X 2 + a4 X + a6
[1, . 84],
:
(1)
(1)
Y 2 = X 3 + aX 2 + b
E(F ) ,
,
(2)
(1)
–
,
,
,
.
,
Ο.
( x, y ) ∈ E ( F )
,
.
-
,
( x, y ) + Ο = Ο + ( x, y ) = ( x, y ), Ο + Ο = Ο .
(1)
( x1, y1 )
( x, y ) ,
( x2 , y2 )
[2, . 12]:
y2 − y1
2
, γ =λ ,
x2 − x1
 x = γ − x1 − x2 ,

 y = − y1 + λ ( x1 − x).
( x, y ) = ( x1, y1 ) + ( x1, y1 ) .
λ=
,
  3 x 2 + a 2
x =  1
 − 2 x1 ,
  2 y1 

3 x12 + a

 y = − y1 + 2 y ( x1 − x).
1

.
,
.
–
, DSA
.
34.10-2001 –
ISO/IEC 14888-3:2006/Amd 1:2010.
2010
.
1.
2.
3.
4.
5.
6.
:
.
.
.
.
.
,
.
.
1.
ANSI X9.62
NIST
.
-
-2012:
98
2.
[3, . 2].
. . 2. –
, 2012
,
.
.
,
.
,
.
,
[4, . 117].
3.
-
.
.
.
,
[5, . 3].
4.
.
-
.
.
,
P
4
15.
13
15P [4, . 111].
16P,
m
.
5.
.
.
,
-
,
.
1.
/ A. A.
2.
, . .
:
, . .
, . .
, . .
. – .:
, 2006. – 328 .
, . .
:
/ A. A.
, . .
, . .
. – .:
, 2006. – 268 .
3.
, .
.
2/ .
[
http://www.uic.unn.ru/~zny/compalg/Lectures/ca_02_quadraticresidue.pdf. –
: 16.04.2012.
4.
, .
:
/ .
–
, 2005. – 229 .
5.
, .
.
4[
http://www.uic.unn.ru/~zny/compalg/Lectures/ca_04_Shanks.pdf. –
: 16.04.2012.
]. –
:
, .
–
]. –
.:
:
The article concerns the main issues of the cryptography elliptic curve. The article studies the reasons of the interest to elliptic
curves and cryptography elliptic curve, main concepts of elliptic curves, coding algorithms and electronic digital signature on the
basis of elliptic curves and algorithms of problems of their implementation resolving.
. .
,
,
,
.
378.4
. .
,
.
,
,
-
.
.
–
,
,
,
-
[1].
,
–
[2].
.
.
(
.
,
.
,
.
)
,
,
[2– 4].
,
,
.
,
,
,
,
,
(
,
,
).
(
,
),
.
99
(
(
)
-
).
(
)
(
)
.
;
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-
;
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:
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;
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2.
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–
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(
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).
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-
(
).
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.
3.
.
.
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:
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.
4.
.
–
.
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-
.
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:
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,
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(
)
-
.
,
,
.
1).
1–
.
,
,
,
-
1.
-
-
;
.
;
–
-
,
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,
;
-
.
,
,
,
.
–
-
.
.
-
-
;
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-
.
.
-2012:
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. . 2. –
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1
2.
-
-
-
-
;
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–
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-
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.
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-
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-
3.
-
-
;
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,
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1.
2.
3.
4.
, . .
, . .
/ . .
, . .
, . .
.–
.:
/ . .
:
, 1986. – 240 .
/ . .
/ . .
.–
.:
, 1996. – 342 c.
.–
, 1986. – 371 c.
, . .
. – .:
, 1967. – 439 .
.
101
This article opens essence of concept «theoretical thinking», it tells about its main forms, types and components. Also it speaks
about requirement of formation of theoretical thinking at pupils on mathematics lessons.
–
.
. .
,
,
-
372.851
. .
.
–
,
.
,
-
,
.
,
,
,
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,
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-
,
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-
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–
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–
,
.
–
.
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-
,
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,
,
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-
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,
,
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,
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:
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,
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-
,
,
,
,
,
,
,
,
.
.
.
-
-2012:
102
. . 2. –
, 2012
.
:
,
-
,
.
,
,
,
cos x = 1 ,
,
,
.
cos 2 x cos x + sin 2 x sin x = 1 ,
,
.
π
4π
tg + tg
15
15 ,
tgx <
4π
π
1 − tg ⋅ tg
15
15
,
.
,
-
.
tgx < 3 ,
, tgx < tg
π
,
3
.
,
.
,
-
.
,
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-
«
»
«
».
.
-
.
.
:
−
,
,
,
-
;
−
,
,
,
,
;
−
,
,
:
-
.
,
.
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:
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,
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.
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-
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.
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,
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(
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.
1 + 2x 1 − x2
+ 2x2 = 1 .
2
,
-
103
 π π
= sin α , α ∈ − ;  .
 2 2
sin α + cos α
1 + 2 sin α cos α
π

= 1 − 2 sin 2 α ⇔
= cos 2α ⇔ sin α +  = cos 2α .
2
4
2

1 − x2 ≥ 0 ,
≤ 1.
sin u ≥ 0,

cos u = 1 ;

2
 π 3π 
u ∈ − ;  ,
sin u = sin 2u ⇔ 
,
<
sin
0
,
u
 4 4 


1
cos u = − .
2

π
π
6− 2
2


 π
,
: x1 = sin  −  =
, x 2 = sin  −  = −
.
4
2
3 4
 4
 π 3π 
u ∈ − ;  ,
 4 4 
1 + 2x 1 − x 2
1 
2
+ 2x2 = 1 ⇔
x + 1− x
2
2 
2

2
 = 1 − 2x ⇔

1 − 2x2 ≥ 0 .
,
π

u1 = 3 ,

u 2 = 0.
-
= 1 − 2x 2 .
2
, 1 − x2 ≥ x2 ,
1− x2 ≥ x ≥ .
,
:
= 1 − 2x 2 ⇔
2
π
=u,
4
x + 1 − x2
x + 1− x2 ≥ 0 ,
x + 1− x2
α+
x + 1 − x2
2
(
)
= 1 − x2 − x2 ⇔
x + 1− x2
2



=  1 − x 2 + x  1 − x 2 − x  ⇔





2
2
 1− x + x = 0
 1 − x = −x
 
 1 

2
2
⇔
−  1 − x − x = 0 ⇔  1
⇔
⇔  1 − x + x 
1
2

 2 

= 1− x2 − x
+x

 1− x =
2
 2


2
2 x 2 = 1, x ≤ 0
1 − x 2 = x 2 , x ≤ 0
x = −


2

⇔
.
1
2 ⇔ 2
2 ⇔ 
2
2
6− 2
x
x
x
x
x
x
x
1
2
,
4
2
2
1
0
,
+
−
=
≥
−
−
=
+
+
≥
−


x =
2
2
2


4

.
-
.
,
,
;
.
,
.
-
.
1.
1968. – 431 .
2.
2004. – 320 .
3.
, . .
,
.
,
.
/
.
.
/
, . .
. – .:
:
.
.
. –
.
.:
. –
/ . .
,
.:
,
,
. .
-
, 1991. – 144 .
The theoretical framework and a set of rational methodological approaches to the formation and development of the creative
mathematical activity of students in the study trigonometry on the lessons of mathematics in the school of physics and mathematics
schools.
–
,
. .
,
,
,
.
-2012:
104
. . 2. –
, 2012
517.925.42
. .
-
.
–
.
.
dx
dy
= P(x, y),
= Q(x, y),
dt
dt
(1)
P, Q ∈ C1 (Ω), Ω ⊆ R 2 ,
2π .
x
(1)
( x, y )
Ω c = {( x, y ) : x ∈ [ x0 , x0 + 2π ], y ∈ R} ,
,
dx
dy
= f (x, y),
= g(x, y)
dt
dt
(2)
[1].
,
,
[2].
–
(1)
,
(1)
[3]
[4]
(2).
,
,
.
.
Ω x = {( x, y ) : x ∈ [ x0 , x0 + 2π ], γ 1 = γ 1 ( x) ≤ y ≤ γ 2 = γ 2 ( x )} ⊂ Ω c –
X = ( P , Q) –
,
(1)
Ωx ,
Ωx .
(1)
div( BX ) = 0
,
(
γ1
B ∈ C 1 (Ω x ) ,
,
.
),
,
γ2 ,
div(BX )
-
,
B
Ωx
[1].
(1)
(10)
,
.
.
x
Ψ (x, y) ∈ C1 (Ω x )
k ≠0
∂Ψ
∂Ψ
P+
Q > 0(< 0).
Φ = kΨdivX +
∂x
∂y
,
1
1. 2π
Ωx ,
(1)
1.
Ψ
W = {( x, y ) ∈ Ω x : Ψ ( x, y ) = 0} ,
1°. Β =| Ψ |1 / k
Ωx ,
Ψ
2°.
3°.
4°.
5°.
1.
,
–
,
Ωx
(3)
[6].
Ωx
(1)
;
(1)
W
;
;
W
W
,
1
Ωx ,
(1),
,
Ψ>0
Ωx ,
W
Wnc
,
Ψ < 0.
,
;
W.
Wcs .
W
2.
,
W.
Ωx ,
(1)
[5].
-
105
Ψ
1.
s
(1)
Ωx
Ωx ,
(1)
Ωx
,
s +1
W
k
.
,
, s −1
,
Ωx
,
k
Ωx
(1)
.
s +1
, Ψ > 0 ( Ψ < 0 ),
)
k sign(ΨΦ) < 0 ( k sign(ΨΦ) > 0 ).
1
s=0
.
(
3.
,
-
.
(1).
Ω x = {( x, y ) | x ∈ [0,2π ], y ∈ R}
x& = d 0 (x) + d1 (x)y + d 2 (x)y 2 , y& = h 0 (x) + h1 (x)y + h 2 (x)y2 + h 3 (x)y3 ,
hi ( x ) ∈ C ( R) , i = 0,3 , d j ( x) ∈ C ( R ) , j = 0,2
Ψ
(6)
Ψ ( x, y ) = Ψ0 ( x ) + Ψ1 ( x ) y + Ψ2 ( x) y 2 ,
Φ ( x, y )
0
-
.
2π –
1
(1)
(6)
.
Ψi ( x ) ∈ C 1 ( R ) .
(7)
y
Φ( x, y ) = Φ 4 ( x) y 4 + Φ 3 ( x ) y 3 + Φ 2 ( x ) y 2 + Φ1 ( x) y + Φ 0 ( x ),
Φ i (x) , i = 0, 4
h 0 , h1 , h 2 , h 3 ,
,
Φ(x, y) = Φ 0 (x) .
(8)
d 0 , d1 , d 2 , Ψ 0 , Ψ1 , Ψ 2
Φ(x, y)
k.
-
Φ i (x) , i = 1, 4
(8)
.
Φ 4 (x) = Ψ 2 (x)(kd '2 (x) + (3k + 2)h 3 (x)) + Ψ '2 (x)d 2 (x) ≡ 0 ,
Ψ 2 (x) = Ψ 2 ,
,
2
Φ 3 (x) = −Ψ1 (x)h 3 (x) − Ψ 2 (d1' (x) − h 2 (x)) + Ψ1' (x)d 2
3
−2Ψ 2 (d1' (x) − h 2 (x)) + 3Ψ1' (x)d 2
.
h 3 (x) =
3Ψ1 (x)
Φ 2 (x) =
+
2
3
d 2 (x) = d 2 .
k=−
Ψ 2 (x) , d 2 (x)
Φ3 (x) ≡ 0
Φ 2 ( x ) , Φ1 ( x )
Φ 0 ( x) ,
4Ψ 2 Ψ 0 (x)(d1' (x) − h 2 (x)) − Ψ12 (x)(2d1' (x) + h 2 (x)) − 2Ψ 2 Ψ1 (x)(d 0' (x) − 2h1 (x))
+
3Ψ1 (x)
3Ψ1 (x)(d 2 Ψ '0 (x) + Ψ1' (x)d1 (x)) − 6d 2 Ψ 0 (x)Ψ1' (x)
.
3Ψ1 (x)
Φ 2 ( x) ≡ 0
,
h1 ( x )
h1 (x) =
4Ψ 2 Ψ 0 (x)(d1' (x) − h 2 (x)) − Ψ12 (x)(2d1' (x) + h 2 (x)) − 2Ψ 2 Ψ1 (x)d 0' (x)
+
−4Ψ 2 Ψ1 (x)
3Ψ1 (x)(d 2 Ψ 0' (x) + Ψ1' (x)d1 (x)) − 6d 2 Ψ 0 (x) Ψ1' (x)
,
−4Ψ 2 Ψ1 (x)
Φ1 ( x) ≡ 0 ,
+
Φ1 (x) =
+
12Ψ 2 Ψ 0 (x)(d1' (x) + h 2 (x)) − Ψ12 (x)(2d1' (x) + h 2 (x)) + 3Ψ1 (x)(d 2 Ψ 0' (x) + Ψ1' (x)d1 (x))
+
−12Ψ 2
−12Ψ 2 (d1 (x)Ψ 0' (x) + d 0 (x)Ψ1' (x)) + 6(Ψ 2 Ψ1 (x)d '0 (x) − d 2 Ψ1' (x)Ψ 0 (x)) − 24Ψ 22 h 0 (x)
,
−12Ψ 2
h0 ( x)
h 0 (x) =
+
12Ψ 2 Ψ 0 (x)(d1' (x) + h 2 (x)) − Ψ12 (x)(2d1' (x) + h 2 (x)) + 3Ψ1 (x)(d 2 Ψ '0 (x) + Ψ1' (x)d1 (x))
+
24Ψ 22
−12Ψ 2 (d1 (x)Ψ 0' (x) + d 0 (x)Ψ1' (x)) + 6(Ψ 2 Ψ1 (x)d '0 (x) − d 2 Ψ1' (x)Ψ 0 (x))
.
24Ψ 22
-
-2012:
106
. . 2. –
, 2012
Φ 0 ( x)
Φ 0 (x) =
1
(24Ψ 22 Ψ1 (x)(Ψ 0' (x)d 0 (x) − Ψ 0 (x)d 0' (x)) + 16Ψ 22 Ψ 02 (x)(d1' (x) − h 2 (x)) +
24Ψ Ψ1 (x)
2
2
+4Ψ 2 Ψ 0 (x) Ψ12 (x)(d1 (x) + 2h 2 (x)) − 6d 2 Ψ1' (x)Ψ 0 (x)(Ψ12 (x) + 4Ψ 2 Ψ 20 (x)) + 6 Ψ 2 Ψ13 (x)d '0 (x) +
+3Ψ13 (x)(d 2 Ψ 0' (x) + Ψ 0' (x)d1 (x)) − Ψ14 (x)(2d1' (x) + h 2 (x)) + 12Ψ 2 Ψ1 (x)(Ψ 0 (x)(d 2 Ψ 0' (x) +
+Ψ1' (x)d1 (x)) − Ψ1 (x)(d1 (x)Ψ 0' (x) + Ψ1' (x)d 0 (x)))).
Φ 0 ( x)
(6)
x ∈ [0,2π ] ,
(7)
–
-
.
-
Ωx .
(6),
Ψ
Ψ = (y − a sin(x) − b)(y − c sin(x) − d),
(9)
,
W
(6)
1
Ωx
.
,
(6)
–
1
1
2
a = −c , d = −b , h2 ( x) = 0 , h3 ( x) = − , d 2 = , d1 = 1 , h0 ( x ) = c cos( x ) sin( x) − sb cos( x) ,
2
2
a, b, c, d ∈ R ,
.
(9).
3 2
(c (1 − cos 2 ( x )) − 2cb sin( x) + b 2 + (c 2 sin( x ) − cb) cos( x )) ,
Φ ( x, y ) = Φ 0 ( x)
4
c 2 3b2
3c 3 b c 4 sin x c 4 + b4
Φ 0 (x) = c 2 cos x sin x( +
+ 2(cb cos x − d 0 )) + cos3 x(
−
)+
+
4
2
2
2
2
b2 3c 2
c 4 cos 4 x
− cos 2 x(c 4 + 3c 2 b 2 ) + cb cos x(2d 0 − −
)+
+ 3c2 b2 − 2cbsin x(b2 + c 2 ).
2
2
2
c , b , d0
,
Φ0 > 0 .
,
c = 1 , b = 10 ,
d 0 = −100 ,
h1 ( x ) =
1
((701cos 2 (x) + 40 cos(x) − 4040) sin(x) cos(x) + 10601 − 5030cos(x) −
2
−602 cos 2 (x) + 30 cos 3 (x) + cos 4 (x)).
Φ 0 ( x) > 0
x ∈ [0;2π ] ,
(9)
–
Φ 0 (x) =
-
(6)
P(x, y) = −99.5 + 0.5(1 + y) 2 ,
Q(x, y) = cos x(sin x − 10) + (
(10)
.
,
Ψ1
(
lim
y →±∞
,
Ψ2 ,
Ω0 )
1,
(10)
303 3
15
3
15
y3
− cos 2 x − sin x + cos x( sin x − ))y − .
2
4
2
4
2
2
,
P ( x, y ) = 0
Q ( x, y ) = 0
(10)
.
y + sin x − 10 = 0
y − sin x + 10 = 0 ,
( .
1).
(10)
t
Ω0 .
-
dy
= m∞ ,
dt
Ω1
Ω2
(10)
-
.
1–
3
LC
(10)
107
.
2.
(10)
.
.
.
,
–
Ψ
(6)
,
Ψ
-
(7)
(6).
.
1.
, . .
/ . .
,
. – .:
, 1976. – 496 .
2.
, . .
/ . .
, . .
. – .:
, 1969. – 300 .
3.
, . .
/ . .
//
. – 1997. – . 33, 5. – . 689 – 699.
4.
, . .
/ . .
, . .
//
. – 2001. – . 37, 3. – . 384 – 390.
5.
, . .
/ . .
, . .
//
. .
.
. 2. – 2007. – 2 (52). – . 3 – 8.
6. Cherkas, L., Grin, A., Schneider, K. R. A new approach to study limit cycles on a cylinder / L. Cherkas, A. Grin, K. R. Shneider //
Dynamics of continuous, discrete and impulsive systems. Series A: Mathematical Analysis. – 2011. – 18. – . 839 – 951.
. .
The paper contains a one approach to obtain the exact evaluation of the number and localization of limit cycles surrounding the
cylinder for autonomous systems with the cylindrical phase space. It is based on the construction of the Dulac-Cherkas function.
Presented theoretical results are applied to a class of mentioned autonomous systems.
– . .
,
,
.
,
,
-
.
517.977.1
.
.
L32 [t1 − h, t1 ] × R 3
L32 [t1 − h, t1 ] × R 3
{x,y}.
{x,y}-
L32 [t1 − h, t1 ] × R 3
{x,y}.
,
.
L32 [t1 − h, t1 ] × R 3 .
.
(
):
x& (t ) = A1 x(t ) + A2 y (t ) + C1 x (t − h) + C2 y (t − h) + B1u (t ), x ∈ R , y ∈ R , u ∈ R ,
n1
n2
r
(1)
µ y& (t ) = A3 x(t ) + A4 y (t ) + C3 x(t − h) + C4 y (t − h) + B2 u (t ), t ∈ T = [ 0, t1 ] ,
{ x0 (⋅, µ ), y0 (⋅, µ )} = {ϕ (θ ),ψ (θ ),θ ∈ [−h, 0) } ,{ x(0), y(0)} = {x0 , y0 } .
(2)
Ai , Ci ,i = 1, 4, B j , j = 1, 2 –
T
, u (t ), t ∈ T – r
, ϕ (θ ), φ (θ ) –
r
n = n1 + n2 .
,
, u (⋅) ∈ U –
n1 -
-
n2
, µ ∈ (0, µ ], µ << 1 , x0 ∈ R , y0 ∈ R .
, µ–
,
, 0<h –
0
0
n1
n2
: 1) n 1 = 1, n2 = 2, r = 1 , 2) n 1= 1, n2 = 2, r = 2 .
n=3
µ
L32 [t1 − h, t1 ] × R 3 .
.
1. rankP% (eλ h , 0) = 3
2. rankN% (λ , eλ h , 0) = 3 ∀λ ∈ Λ 00 ;
3. rank[C , B] = 3 ,
[1]
,
λ;
µ:
-2012:
108
. . 2. –
µ >0.
L32 [t 1 − h, t 1 ] × R 3
(1), (2) {x, y} –
, 2012
~
P (e λh , µ ) = M −1P(e λh , µ ) K , P(eλh , µ ) = [ B( µ ), A(eλh , µ ) ⋅ B( µ ), A2 (eλh , µ ) ⋅ B( µ )],
~
N (eλh , µ ) = M −1 N (eλh , µ ), N (eλh , µ ) = [λE + A(eλh , µ ), B( µ )], A(e λh , µ ) = A( µ ) + C ( µ )e λh , A( µ ) = M ( µ ) A ,
0 
1 0
 A1 A2 


B1 
C1 C2 


C ( µ ) = M ( µ )C , B ( µ ) = M ( µ ) B , A = 
 , C = 
 , B =  , M = 0 1/ µ 0  .
 C3 C4 
 B2 
 A3 A4 
0 0 1/ µ 


1 0

K = 0 µ
0 0

1.
1

0
0
— K =
0
0

0

0

0 ,
µ 2 
0 0
1 0
0 µ
0 0
0 0
0 0
0 0 0 

0 0 0 
0 0 0 
.
µ 0 0 
0 µ2 0 

0 0 µ 2 
n 1= 1, n2 = 2, r = 1
(1), (2)
0
 0 0 1
 0 1 0


 


,
,
A =  0 1 0  C =  0 0 0  B =  − 1 .
 − 1 0 0
 −1 0 0
1




 
(
2 [1])
(3)
:
 0 − µ + eλh

~ λh
P (e , µ ) =  − 1
−µ
 1
0


−µ

,
−µ

µ + e λh µ − e λh − e 2 λh 

~
P ( z, µ ) ,
( z, µ ) = −( µ 2 + µ 2 z − zµ − 2 µz 2 + z 2 + z 3 ) —
z = eλh .

 0 eλ h
0

λ
1
e λh 0 




~ λh
~ λh
,
0
,
λ + 1 0 − 1 P (e ,0) =  − 1 0
0
N (e , µ ) = 
1


2 λh 
λh
λh 2
2
0 −e −e 
µλ 1 
0
− µ − e µ

λh
λ
0 
e
1
0
0 z
1
z 0
λ
 ~

 ~



~ λh
0 , N ( z,0) =  0 λ + 1 0 − 1 .
N (e ,0) =  0 λ + 1 0 − 1 , P ( z ,0) =  − 1 0
0
 1 0 − z − z2 
0
0
0
1 
0
0 1 




~
P ( z,0)
z (0) ∈ C ,
Z 00 = {−1,0,0} ,
Z 0 = Z 0 µ 0 ∪ Z 0 µc , Z 0 µ 0 = 2, Z 0 µc = 1.
~
P ( z ,0)
λ jk , j = 2,3, k = 0,±1,...,
.
arg z1 (0) = arg(1) = 0, ln z1 (0) = ln | −1 |= 0,
Λ 00 = {λ1k (0) = ln | z1 (0) | +i (arg z1 (0) + 2π k ), k = 0, ±1,...} = {2iπ k , k = 0, ±1,...},
Λ 0 µ 0 = {λ jk ( µ ) = ln | z j ( µ ) | +i(arg z1 (µ ) + 2π k ), j = 2, 3, k = 0, ±1,...},
Λ 0 µc = {λ1k ( µ ) = ln | z1 ( µ ) | +i (arg z1 ( µ ) + 2π k ), k = 0, ±1,...}.
.
( z, 0) = det P% ( z ,0) = − z 2 − z 3.
1.
,
1
2.
~
N (eλh ,0)
.
Λ00 = {2iπk , k = 0,±1,...} .
N% (e λ h ,0)
M 234
= −e ( λ + 1) ,
λh
.
.
109
 2iπ k

N% (−1, 0) =  0
 0

{2iπ k , k = 0, ±1,...} .
e2iπ kh ( 2iπ k + 1) ≠ 0 , k ≠ −
M 234 = e 2 iπkh ( 2 iπ k + 1) .
rankN% (λ , eλ h , 0) = 3 .
1
,
2iπ
1
−1 0 

i
π
k
2
+ 1 0 −1 .
0
0 1 
e 2iπ kh ( 2iπ k + 1) 0, ∀k = 0,±1,... .
0

0 1 0 

0 0 − 1 .
 −1 0 0 1 


[C,B]=  0
3.
.
[C,B]
,
,
.
µ ∈ 0, µ 0
,
L [t − h, t1 ] × R .
3
2 1
2.
-
— 1,
([C,B]) = 3.
,
,
, rank
)
{x, y} -
3
n 1 = 1, n2 = 2, r = 2
(1), (2)
 0 1 0
 0 0 1
 0 1
,

,

−1 0
B
=
A =  0 1 0  C =  0 0 0


 −1 0 0
 − 1 0 0
0 
1




2 [1])
:
(
 0 1 −µ + e λh
% λ h , µ ) =  −1 0
P(e
−1

1 0
0

(4)
0
0
−µ
−µ
−1 − e λ h
µ + e λh µ − e λh − e 2λh
e λh − e 2λh 

0
,

0

0
0
− e λh − e 2λh
 0 1 e λh
0
e λh − e 2 λh 
0 1


 ~ λh
0
0
,
− 1 0 , P (e ,0) =  − 1 0 − 1

 1 0 0 − 1 − e λh
0
0
λµ 1 0 


 λ
1
e λh 0 1 


~
N (e λh ,0) =  0
λ + 1 0 − 1 0 ,
 − 1 − eλh
0
0
1 0 

1
z 0 1
 0 1 z
 λ
0
0
z − z2 
 ~



~
(
,
0
)
0
1
0
N
z
=
λ
+
− 1 0 .
0
0
0 ,
P ( z ,0 ) =  − 1 0 − 1



2
−1− z
0
0 1 0 
0 

 1 0 0 −1 − z − z − z
 λ

~ λh
N (e , µ ) =  0
 − 1 − e λh

e λh
1
λ +1 0
~
P
,
.
,
,
0
.
z (0 ) ∈ C ,
~
P ( z,0)
λ jk , j = 2,3, k = 0, ±1,...,
,
,
z − z2
0
M 156 = − 1
0
0 ,
1 − z − z2
0
M 156 ( z ,0) = det M 156 = − z 2 − 2 z 3 − z 4 .
Z00 = {−1, −1, 0, 0} , Z 0 = Z 0 µ 0 ∪ Z 0 µ c , Z 0 µ 0 = 2, Z 0 µ c = 2.
P% ( z, 0)
.
arg z1 (0) = arg(1) = 0, ln z1 (0) = ln | −1 |= 0,
Λ 00 = {λ1k (0) = ln | z1 (0) | + i(arg z1 (0) + 2π k ), k = 0, ±1,...} = {2iπ k , k = 0, ±1,...},
Λ 0 µ 0 = {λ jk ( µ ) = ln | z j ( µ ) | +i (arg z1 ( µ ) + 2π k ), j = 3, 4, k = 0, ±1,...},
Λ 0 µc = {λlk ( µ ) = ln | zl ( µ ) | +i (arg zl ( µ ) + 2π k ), l = 1, 2, k = 0, ±1,...}.
.
-2012:
110
1
~
N (eλh ,0)
~
N (eλh ,0)
2.
M 234
.
= −e ( λ + 1) ,
e 2iπ kh ( 2iπ k + 1)
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 2iπ k
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1
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 0 0 1 0 1
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 −1 0 0 1 0
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,
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-
.
{2iπ k , k = 0, ±1,...} .
3.
-
Λ 00 = {2iπ k , k = 0, ±1,...} .
λh
M 234 = e 2 iπ kh (2iπ k + 1) .
, 2012
M 156 ( z ,0) = det M 156 = − z 2 − 2 z 3 − z 4
.
1.
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0 1
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{x, y} -
L [t1 − h, t1 ] × R .
3
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L32 [t 1 − h, t 1 ] × R 3
1.
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. .
/ . .
.–
-
//
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:
, 2012. – . 2.
.
.
. – . 135 – 139.
.:
The task {x, y} – controllability in L32[t1 − h, t1 ] × R3 for linear stationary singulyarno of indignant systems with delay the third
order with delay in a condition is considered. Sufficient conditions {x, y} – controllability in L32[t1 − h, t1 ] × R3 are considered at all
rather small values of parameter of a singulyarnost. Conditions don't depend on parameter, are expressed through matrix parameters
of system and have a rangovy appearance. Examples of application of the received conditions for the analysis {x, y} – controllability
in L32[t1 − h, t1 ] × R3 are given.
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2011
.–
1. – . 231 – 234.
The description of complex technology of collecting registration production data for offset printing house is provided. A
number of formal definitions is entered. In a basis of realization of technology the three-level model of automation of processes of
planning and the accounting of manufacturing enterprise with a order form of the organization of works lies. The technology is
described in a cut of three blocks: the material account, the accounting of receipt of orders in production and shipments of finished
goods, calculation of prime cost of the order.
–
,
. .
,
,
.
-2012:
114
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004.91+347.78.031
. .
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2
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2–
,
.
,
,
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.
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1.
M.
.NET 3.5
/ .
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.
, .
» 2009. – 1392 .
2.
PowerDesigner
/ . .
//
:
XV
.
..
.–
: 2006. – . 211 – 212.
3. Microsoft Patterns & Practices Team. «Microsoft® Application Architecture Guide». Microsoft Press-2009. – 560 .
,
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.
. C# 2008
. – .: OOO «
, . .
,
.
-
Article presents main approaches to the implementation of a universal and flexible architectural solution client-side web-based
systems. The advantages of a composite approach to the organization of architecture and functionality of the client. In particular,
describe the possible integration of client with the infrastructure system that supports the laser express expertize.
– . .
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,
,
.
-2012:
116
. . 2. –
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37.016:51:005.935.33
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10
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Testing allows the diagnostics of the results of learning, setting the level of academic achievements, the degree of competence.
Due to its advantages it may be productively used in combination with other approaches of control for providing effective feedback
according to the goals of diagnostics.
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3.
. . .
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6.
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5.
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4.
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:
1335-2002. –
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[
. 01.01.03. –
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.
:
There are some difficulties in designing compositions of self-compacting concrete on the basis of straining cement. On the
one hand it is necessary to execute demanded flow characteristics of concrete mixes, with another - to provide strength and deformation characteristics of concrete. Compositions of self-compacting concrete differ from traditional with presence additivesfiller, and also introduction of the agent inoculating viscosity of a liquid phase and a superplasticizer compatible to it. Introduction of these components, as a rule renders negative agency on deformations of expansion of self-compacting concrete, and also
promotes increase in a final shrinkage approximately on 30 … 50 % more, than at traditional concrete. In the given work researches of agency of the additive of a lime on deformation of expansion of self-compacting solutions on the basis of straining
cement are shown.
– . .
,
,
,
-
.
539.3.691.693
. .
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124
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[4].
,
,
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,
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,
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,
,
,
,
1.
2.
30494-96
:
.
//
: 02.04.2012.
//
: http:/www.vash-dom.by. –
: 02.04.2012.
//
-
.
[
:
[
]. –
. 1999-01-01. –
, 1999.
]. –
:
http:/www.mo-potolok.ru/. –
3.
4.
[
[
http:/www.art-con.ru. –
: 02.04.2012.
]. –
]. –
,
:
125
The article deals with building materials, currently used for finishing the ceiling space. A systematic requirements necessary to
implement the choice of decorative materials.
.
.
,
.
,
-
.
624.07
. .
,
.
XX
.
-
.
-
,
,
.
,
,
,
.
60-
20
.
-
,
,
−
(
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(
−
−
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(
70.
Marshall-Vega Inc.
:
.
,
);
80-90
-
));
;
,
.
(
,
.
(1998
.).
).
[3].
,
,
1986
.
,
-
,
.
EUROCRETE.
.
90-
20
100
,
.
:
–
.
,
.
,
60-70-
-
,
,
.
.
,
,
,
.
.),
,
,
,
,
,
-
.
,
,
,
.
,
,
1975
40
.
-
1989
,
.
,
,
,
-
.
.
:
,
.
.
-2012:
126
. . 2. –
.
, 2012
«
»,
«
,
»
.
,
2000
»
-
.
,
«
»
,
«
.
[4].
,
60-80-
XX
.
,
20
.
,
.
.
1975 .
-10
.
,
,
:
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-
.
.
.
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-
6
.
.
6
.
[5].
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[1, 2],
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1103-98.
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», 2011. – 46 .
«
[
]. –
. 1998-10-01. –
:
, 1998. – 36 .
;
. 2011-05-
.
//
[
: http://yazk.ru/istoriya-kompozitnoy-armatury.html. –
: 20.04.2012.
.
//
[
: http://ts-project.ru/poleznaya-informatsiya/istoriya-sozdaniya-plastikovoj-armatury. –
: 20.04.2012.
.
//
]. –
: http://alientechnologies.ru/articles/0000.php. –
: 20.04.2012.
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This article describes the history of non-metallic reinforcement in structures, prospects and problems of application of the reinforcement in Belarus
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-2012:
130
7.
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http//www.dekotrade.ru. –
. . 2. –
[
] /
, 2012
. –
:
: 01.04.2012.
8.
[
: http//propol. rb1.ru. –
: 01.04.2012.
,
,
: 02.04.2012.
[
: 03.04.2012.
9.
http // www.prom.ua. –
10.
,
httb//www.napol.ru. –
]/
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.–
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The article deals with building materials, currently used for finishing the ceiling space. A systematic requirements necessary to
implement the choice of decorative materials.
.
.
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.
624.014
. .
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M x max = Wx σ y .
M x max / A ,
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bf
c/bf
t
1
3
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40
100
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: h = 100, 200 300
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σ y = 250
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Wx
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-2012:
132
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. . 2. –
, 2012
,
-
Wxeff.
Eurocode 3 [4].
,
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,
(TheodorvonKarman),
,
.
.
-
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.
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,
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CFSteel,
Eurocode 3.
t=1
50
M x max / A
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200
(40,
).
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,
c/bf = 0,4
bf = 50
h=
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c/bf = 0,2
300
.
t = 1,5
h = 100
bf = 60...70
bf= 60
t = 2.3
t=2
h = 100
bf> 100 .
.
3
bf = 80
,
,
4–
;
,
h = 200
h = 200
300
y=
,
M x max / A
bf= 80...90
(h = 100
.
h=100
300
t=
.
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y
= 250
:
350
5.1
.
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bf= 60…90
(
-
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.
1.
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.
, . .
/
, . .
, . .
//
. – 2010. – 4. – . 37 – 39.
, . .
/ . .
– . – .:
.
, 1946. – 532 .
Adany, S. Buckling mode classification of memberswith open thin-walled cross-section by using FiniteStrip Method. Research
Report / S. Adany // JohnsHopkinsUniversity. – 2004. – 99 p.
EN 1993-1-3:2004 Eurocode 3. Design of steel structures. Part 1-3: General rules. Supplementary rules for cold-formed members and sheeting / Euro-pean Committee for Standardisation CEN. – Brussels, 2004. – 125 p
NAS (2004): North American Specification for thedesign of Cold-Formed Steel Structural Members /American Iron and Steel
Institute. – Washington, D.C.,AISI/COS/NASPEC, 2004.
II-23-81*
/
.- .:
, 1990. — 96 .
. .
2.
3.
4.
5.
6.
In this paper we examine the work of a thin-wall profile in accordance with current design standards. Displayed and analyzed patterns of
influence of the width of the belt width and limb C-shaped profile on the performance in a transverse bending with different thicknesses of steel.
–
.
.
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624.012.45
. .
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[4].
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134
. . 2. –
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[1].
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[1].
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(8
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(
~2
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(
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~1,5
-
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,
[1].
-
,
.
).
,
14
(4,4 %)
–
CaSO4.
[1].
,
.
-
,
.
5 – 10 %
,
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1
7
-
(
–
-
2,8 % [1].
,
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[1].
-
1335 «
.
».
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-
,
750 .
1,
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135
1.
, . .
.– :
, . .
, . .
, . .
. .
2.
. .
3.
/ . .
, . .
/
.–
:
, 1974. – 312 .
/ . .
, . .
//
:
:
2008 . /
, . .
4.
.
,
, 1980. – 256 .
,
XV
;
-
-
,
. . .
/ . .
[
,
.
.]. –
. – .:
, 27 – 28
, 2008. – 283 .
, 1983. – 248 .
The scope of tightening concrete theoretical approaches control the growth kinetics samonapryazheniya tightening of cement type M.
.
, . .
.
,
-
,
.
62.059
. .
,
–
.
.
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«
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500
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1–
).
-2012:
136
. . 2. –
, 2012
.
,
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2.7 3.0
2
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6.0 .
400
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137
3–
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-2012:
138
(
1)
. . 2. –
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. 4)
:
,
,
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,
;
2)
,
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-
10
.
,
,
.
–
.
,
–
,
,
– House
,
,
Home,
-
,
,
,
,
1.
2.
3.
.
.
, . .
1985. – 208 .
, . .
. .
.–
.–
., 1855. – 60 .
/ . .
, .
.
. –
:
,
/
:
, 2004. – 194 .
This article describes an environmentally friendly house with attached garage and conservatory. We describe the design decisions
taken in implementing the current problems and future requirements. Also there is conducted study of space-planning decisions.
. .
,
,
,
.
519.711.3
. .
.
-
.
.
:
,
.
. 143].
[1,
-
,
.
,
[2,
-
29, 3].
.
.
-
[4, . 70],
.
,
.
l.
m1 , m2 ,..., mn (
-
. 1 ).
)
)
1–
A = (δ ij )
n×n
,
δ ij
-
:
l
δ ij = ∫
0
M i ⋅M j
dx
EJ
(i, j = 1,..., n )
(1)
139
Mi
M
xj ,
(
xi
j
. 2)
2–
(1),
Mi
-
M j:
 l − xi
 l x, 0 ≤ x ≤ xi
Mi = 
,
l − x x , x < x ≤ l
i
 l i
xi ≤ x j .
,
l − x j
x, 0 ≤ x ≤ x j

 l
Mj =
.
l − x x , x < x ≤ l
j
j
 l
(1)
xj
(2)
Mi ⋅M j
Mi ⋅M j
Mi ⋅M j
dx + ∫
dx + ∫
dx .
δ ij = ∫
EJ
EJ
EJ
xi
xj
0
(2)
(3),
xj
xi
l


1
2
δ ij = 2 ( l − xi ) ( l − x j ) ∫ x 2 dx + xi ( l − x j ) ∫ ( l − x ) xdx + xi x j ∫ ( l − x ) dx 
l EJ 

0
xi
xj

xi
,
δ ij =
l
2
2
2
2
2
1 xi 2l x j + x j ( xi + x j ) − l ( xi + 3x j ) 
.
EJ
6l
(4)
xi > x j
(4)
,
(4)
xi ≤ x j .
,
.
j
i
(3)
n
A
,
 xi  2l 2 x j + x j ( xi2 + x 2j ) − l ( xi2 + 3x 2j )  , xi ≤ x j

1  
⋅
A = (δ ij ) =
.
n×n
2
2
2
2
2
6lEJ  x  2l x + x ( x + x ) − l ( x + 3x )  , x > x
j 
i
i
j
i
j
i 
i
j

: 1)
(5),
,
xi ≤ x j
xi > x j ;
2)
,
δ ij
,
xi ≤ x j ,
(5)
-
,
,
,
(5)
,
.
.
xi = x j ,
-
(5)
δ ii =
xi2 (1 − xi2 )
[0, xi ]
(1)
A = (δ ij )
n×n
3lEJ
, ( i = 1,..., n ) .
xi
 2
 xi  x j −
3
1  
=
⋅
xj
2EJ  2 
x x −
 j i 3
 
δ ii =
(
( xi ≤ x j ) .

 , xi ≤ x j

.

 , xi > x j

xi3
, ( i = 1,..., n ) .
3EJ
. 1 ),
,
-
(6)
-2012:
140
. . 2. –
,
(5)
, 2012
(6).
A
A − λE = 0 ,
E –
(7)
.
,
(5)
(6)
l,
EJ ,
.3
λi
(7),
( i = 1,.., n )
(5) (6).
4
(
n
5
100
).
(5), (6)
:
.
,
.3
max λi ( n ) = 10 −3 ( 0.0128 + 10.2659n ) ,
(8)
max λi ( n ) = −0.0442 + 0.0807n
,
,
(5)
n = 10 ,
(6)
,
-
max λi = 0
.
(8)
(5), (6)
n
,
4–
λi
,
A
0 < λi ≤ 10−3 ( 0.0128 + 10.2659n ) –
0 < λi ≤ −0.0442 + 0.0807 n –
( i = 1,.., n )
,
.
.
.5 6
(
).
,
.
5–
-
.
3–
,
4
90 %
0,
10 %
.5 6
A
0.
6–
-
141
(
)
-
.
:
,
.
,
-
,
,
.
Method of lumped masses for research on dynamics of statically determinate beam was studied. Universal formulas for automatic definition of elements for flexibility matrix were received. The research of spectral characteristics of received matrix was carried out.
1.
, . .
/ . .
, . .
. – 4.– :
, 1972. – 735 .
, . .
/ . .
,
. .
, . .
.–
:
, 2010. – 216 .
Darmawijoyo, Horssen W. T. van. On boundary damped for a weakly nonlinear wave equation / Darmawijoyo,
Horssen W. T. van. // Nonlinear Dynamics. – 2002. – Vol. 30. – P. 179 – 191.
/ . .
[
.];
.
. . .
. – .:
, 1984. – 415 .
2.
3.
4.
– . .
,
.
624.012.45
. .
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, . .
,
.
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-
,
.
,
.
.
-
–
15 – 30%.
,
-
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.
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,
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(
),
(
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)
,
-
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–
«
–
–
».
–
,
-
[1, . 13].
,
,
(
-
.
).
,
-
,
.
10-30
.
.
,
,
[2, . 189].
,
,
,
.
.
.
-
-2012:
142
. . 2. –
, 2012
(
) [3, . 112].
–
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,
,
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,
;
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[4, . 263].
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U-
.
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1–
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,
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-
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S–
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U=
SL
,
Vt
,
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/ ⋅ .
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KπηU
, .
ε
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–
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–
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= 0.00894 /(
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–
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;
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). 90000 –
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Zeta PALS (
(
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-
.
.
(
,
.
-
),
,
.
( 1-
–
;
2)
.
4πηkQR
ς =−
, B,
εIE
;k–
[5, . 69].
;Q–
–
;R–
SurPASS.
SurPASS
(
,
-
)
.
.
,
(
,
)
,
,
,
.
,
,
,
,
.
.
-
-
.
,
,
(
).
,
(
-
).
(
).
,
.
.
.
-
,
.
,
,
,
.
,
,
,
.
.
,
-
.
(
,
).
.
(
10-4 ),
,
,
.
.
,
,
,
.
.
,
( ).
.
µ
ε −1 M N A
µ2
⋅
=
⋅ (α +
P=
)
ε − 2 d 3ε 0
3kT
[6, . 173; 7, . 343].
-
-2012:
144
. . 2. –
, 2012
,
.
2–
1–
15×20
;2–
0,5
1° ; 5 –
30
3
;6–
;3–
); 4 –
(
(
;8–
;7–
)
.
:
2-3º ,
.
-
.
,
,
(
.)
-
.
= f(C), [8, . 4 – 5].
.
–
–
»,
.
,
,
.
1.
2.
3.
4.
5.
6.
7.
8.
,
.] //
.
.
, . .
, 1988. – 575 .
. .
, . .
.:
, 1989. – 463 .
, . .
, . .
.:
, 1968. – 246 .
, . .
, 1971. – 414 .
, . .
. .
, . .
–
10. – . 13 – 16.
. – 1978. –
:
-3 /
// .
.
/ .
.
,
. – .,
.–
/ . .
/ . .
, . .
,
.
.
.
[
.]. –
, 1984. – 368 .
/ . .
.
/ . .
.
.:
, 1973 .
, . .
, . .
, . .
,
.:
.–
. .
.–
.–
.:
//
-
//
.–
:
, 2009. – . 2. – 302 .
In article the action mechanism plastification additives for concrete is is short described such parametres of an estimation of efficiency of softeners as electrokinetic potential and the dipol moment, the reasons of their influence on plastification effect Are considered.
The basic methods of definition of these characteristics, and also measuring devices and a principle of their action are described.
. .
,
.
691.53
. .
.
,
.
145
.
,
,
-
,
.
,
,
,
,
.
,
:
,
.
310.3 [1]
,
310.1 [2].
,
:
-1
[4].
,
.
(
)
,
1
.
1.
1–
%
,%
–
0,2
0,35
0,5
0,2
0,35
0,5
1,0
1,5
2,0
0,2
0,35
0,5
1,0
1,5
2,0
(NaNO2)
,%
28,75
28,50
28,25
28,00
28,50
28,25
28,00
27,50
27,25
27,00
29,00
29,25
29,50
29,75
30,00
30,25
–
–
-0,87
-1,75
-2,65
-0,87
-1,75
-2,65
-4,46
-5,45
-6,42
0,93
1,72
2,56
3,39
4,20
5,00
500- 20
«
».
1–
,
,
1 – 7 %,
-
.
1 – 5 %.
[1]
[2].
:
,
-1
-
,
.
.
.
2
2
3.
-2012:
146
. . 2. –
, 2012
2–
%
(NaNO2)
–
–
0,2
0,35
0,5
1,0
1,5
2,0
0,2
0,35
0,5
1,0
1,5
2,0
,
3 – 40
4 – 10
4 – 00
3 – 55
3 – 45
3 – 40
3 – 50
3 – 30
3 – 10
1 – 10
0 – 45
0 – 30
0 – 20
500- 20
«
.
,
5 – 10
5 – 20
4 – 50
5 – 00
4 – 50
4 – 50
4 – 40
4 – 50
4 – 25
2 – 30
1 – 50
1 – 10
1 – 00
.
».
2–
2.1
1.00
0.33
1.9
1.7
0.50
1.5
1.17
.
0.35%
1.1
0.5%
0.75
%
0.2 %
1.3
1.83
0.9
1%
0.7
1.5%
1.17
0.5
2.50
2%
3.17
0.3
.
.
.
.
.
4.42
3.50
0.1
4.83
3.67
5.17
-0.1
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
,
3–
-500- 0
,
26,5 %.
-
.
,
7 – 81 %.
:
–
5 – 91 %;
–
147
310.4 [3].
,
,
,
,
,
[4].
.
-
0,46,
,
106 – 115
.
.
3
4.
3–
%
,
,%
(NaNO2)
(Na2 O3)
–
0,2
0,35
0,5
1,0
2,0
3,0
4,0
0,2
0,35
0,5
1,0
2,0
3,0
4,0
1,0
3,0
109,5
110,0
110,5
111,0
112,5
114,5
115,3
115,8
107,0
105,5
104,5
103,8
102,5
101,3
100,0
106,6
100,9
–
0,46
0,91
1,37
2,74
4,57
5,30
5,75
-2,28
-3,65
-4,57
-5,21
-6,39
-7,49
-8,68
-2,65
-7,85
5,0
100,0
4,57
–
500- 20
= 0,46.
4–
,
106 – 115
,
,
0,46
.
-
-2012:
148
1–3%
2 – 9 %,
. . 2. –
, 2012
3 – 5 %,
.
:
1.
28,75.
-500- 0
0,2
26,5 %,
-500- 20 –
29
30,25 %
.
-
2%
1–5%
2.
:
– 5 – 91 %;
– 7 – 81 %.
3.
– 0,46.
1–3%
2 – 9 %,
1.
3 – 5 %,
.
.
310.3-76. –
, 1976. – 9 .
.
2.
,
. 1978-01-01. –
310-60;
.
[
]:
.:
3.
.
310.4-76;
. 1983-01-07. –
4.
9147-73,
6675-73,
:
[
]:
-
.:
310.1-76. –
, 1976. – 3 .
[
310-60;
]:
[
]:
.:
.
6529-74;
. 1982-01-01. –
, 1980. – 18 .
. 1978-01-01. –
310.4-81. –
, 1981. – 17 .
9147-80. –
.:
-
The article deals with the study of the influence of some anti-freezing additions and additions quickening solidification on the
qualities of cement systems, in particular on an average density and the terms of freezing of cement solution as well as the changes in
the consistency of cement and sandy solution.
– .
.
,
.
,
-
.
539.3.691.693
. .
,
»
«
.
[1 – 2].
.
.
24104 [3].
6,29 .
200
,
3
.
[4].
3
20
29227 [5]
2
H2SO4
./
3
60
nO4
12738 [6]
3
3
250
0,1
,
.
40 – 45
.
:
V1 = 8,85
3
; V2 = 8, 75
3
; V = 8,80
3
.
,
:
5NaNO2 + 2KMnO4 + 3H 2 SO4 = 2MnSO4 + K 2 SO4 + 5NaNO3 + 3H 2 O.
./
100
3
3
-
149
NaNO2
C ( 1 NaNO2 ) ⋅ V ( 1 NaNO2 ) = C ( 1 KMnO4 ) ⋅ V ( 1 KMnO4 ),
2
2
5
5
C ( 1 NaNO2 ) –
2
(1)
; V ( 1 2 NaNO2 ) –
; C ( 1 KMnO4 ) –
5
;
V ( 1 KMnO4 ) –
5
.
(1)
:
C ( 1 NaNO2 ) =
2
C ( 1 NaNO2 ) =
2
0,1
C ( 1 KMnO4 ) ⋅ V ( 1 KMnO4 )
5
5
,
V ( 1 NaNO2 )
2
3
./
8,80
⋅ 20
3
3
= 0,227
(2)
./
3
.
NaNO2
W ( NaNO2 ) =
C ( 1 NaNO2 ) ⋅ Va ⋅ M ( 1 NaNO2 )
2
2
⋅ 100 %,
m0
M ( 1 NaNO2 ) –
2
(3)
,
M ( 1 NaNO2 ) =
2
M ( NaNO2 ) –
M ( NaNO2 )
,
Z
(4)
,
;Z –
,
.
69
M ( 1 NaNO2 ) =
2
W ( NaNO2 ) =
0,227
./
=34,5
2
⋅ 0,20
6,29
3
3
,
⋅ 34,5
⋅ 100 %=24,9 %.
,
24,9 %.
.
,
[7].
3
50
Cl2
3
0,05
.
Ba2+
25336 [8],
105±2
-
.
Na2SO4
.
-
BaCl2 + Na2CO3 = BaCO3 ↓ +2NaCl.
BaCO3
0,7536 .
Na2 O3
W ( Na2CO3 ) =
W(Na2 CO3 )=
Na2 O3
m( BaCO3 ) ⋅ M ( Na2CO3 ) V0
⋅ ⋅ 100 %,
M ( BaCO3 ) ⋅ m0
Va
0,7536 ⋅ 106
⋅ 6,29
197
⋅
200
50
Na2 O3 ⋅ 10H2O
3
3
⋅ 100 %=25,8 %.
(5)
-2012:
150
, 2012
W ( Na2 O3 ) ⋅ M ( Na2CO3 ⋅ 10H 2O )
,
M ( Na2 CO3 )
W ( Na2 O3 ⋅ 10H 2O ) =
M ( Na2CO3 ⋅ 10H 2 O ) –
; M ( Na2CO3 ) –
. . 2. –
(6)
,
-
,
W ( Na2 O3 ⋅ 10H 2 O ) =
,
.
25,8 % ⋅ 286
106
= 69,6 %.
69,6 %.
25,8 %,
1.
1–
.
%
%
%
%
%
(NaNO2)
(Na2 O3 · 10H2O)
-
(Na2 O3)
,
.
.
24,9
69,6
25,8
1
4,5
,
2),
(
-
.
,°
2–
,
,
.
.
.
,
,
.
The article deals with the study of the chemical structure of SSN derived as a secondary product at the public corporation
“Grodno Chemical Fibre” at the production of polyamide threads.
1.
, . .
/ . .
, . .
2.
3.
, . .
,
.
:
, . .
//
/ . .
:
, . .
24104-2001. –
,
.–
. – 2009. – 12. – .14 – 15.
.:
, 1974. – 263 .
24104-88;
. 2002-07-01. –
, 2001. – 8 .
151
4.
5.
.
/
.
.
.
20292-74;
. 1994-01-01. –
. . .
1.
.–
.:
.
. 1979-01-01. –
1978. – 4 .
, . .
7.
8.
1984-01-01. –
, 1992. – 400 .
29227-91. –
, 1992. – 15 .
12738-77. –
12738-67;
:
,
:
6.
:
.:
/ . .
, . .
.
.–
.:
:
.:
, 1968. – 508 .
:
25336-82. –
, 1982. – 102 .
,
.:
:
– .
.
,
.
.
,
-
.
624.07
. .
,
,
.
.
XX
.
-
,
.
.
,
,
,
.
,
,
,
.
-
(
,
)
.
80.
.
(
1986 .
.
-
)
1988 .
,
.
-
.
.
60(
.
70-
.
XX
-
,
.),
,
,
,
,
,
,
.
1972
,
-
.
1
1975
61,01
.
–
.
.
22 % ,
.
–
20 %.
1,7
.
9 ,
4
20×60
-
[3].
.
−
−
1103-98.
.
–
,1998 .
01-2011
)–
−
−
-
:
(
-
, 2011 .
[1]:
–
–
;
.
,
.
,
-2012:
152
. . 2. –
, 2012
,
,
,
-
.
,
.
,
,
.
,
,
.
-
,
.
.
:
,
-
.
,
,
-
,
.
.
,
-
,
-
.
.
,
.
,
,
.
,
.
,
[2].
,
.
,
,
,
,
,
.
,
,
,
,
.
,
,
,
.
.
.
,
100 °
–
,
.
.
-
,
.
,
,
,
,
.
,
,
,
,
,
.
-
.
.
.
,
,
,
.
,
,
,
.
5
.
20
.
+450 ° ,
-40
,
.
-40 °
.
35..50 %.
.
.
350 °
[2].
.
:
1,8-2
1500
3
,
80 %,
50 000
,
,
−
−
−
−
−
2,5 – 3 %,
65 %
-6
5,5-6,5·10 .
[2]:
;
,
;
;
,
;
;
,
-
153
−
−
−
−
−
−
;
:
;
;
9
;
30-40%;
.
:
−
−
−
−
4
,
,
;
,
;
;
.
,
-
[1]:
−
(
−
,
);
,
,
−
−
−
−
,
-
,
;
;
;
.
(
,
−
−
;
,
,
;
;
,
.
,
,
.
,
0,00001 ° 50 °
0,5
0,000012 ° ,
,
0,00001 ° .
.
,
.
-
,
-
70d.
,
.
–
.
-
.
.
-
.
,
.
.
.
,
,
.
,
,
,
.
,
,
,
.
,
,
-
,
,
[2].
,
.
.
-
.
1.
1103-98.
01. –
:
.
[
]. –
;
. 1998-10-
:
, 1998. – 36 .
2.
-01-2011.
. 2011-05-01. –
:
«
3.
.–
(
»:
«
[
: http://armatura.fo.ru/blog. –
)
[
]. –
», 2011. – 46 .
]/
: 15.04.2012.
;
-
In this article the basic properties of nonmetallic armature, its advantage and shortcomings are described, areas for effective
use of fiberglass armatures are defined. Possibilities of replacement of metal armature on the nonmetallic are described.
.
,
.
,
-2012:
154
. . 2. –
, 2012
539.3.691.693
. .
, . .
-
.
.
,
[1].
(NaNO2),
1.
(Na2CO3).
.
,
6084-100-0
-500-0
,
5802 [2]
28840 [3].
7,07
.
500- 20.
1
1.
1–
,
%
1
20 ° )
20 ° )
–
–
1
–
–
5
–
–
8
–
–
1
3
20 ° )
5
0,2
0,5
1
3,79
3,77
3,79
5,83
5,38
5,82
62,60
63,80
63,10
1,95
1,92
1,72
2,13
2,13
2,01
2,00
2,08
1,95
,
2
–
–
4,30
4,41
4,54
6,11
6,37
6,27
5,14
5,10
5,11
3
–
4,42
6,25
5,12
3,79
–
–
5,68
8,5
8,63
8,47
8,54
6,29
–
–
1,86
–
–
2,09
–
–
2,01
–
–
20 ° )
3
–
–
5
–
–
10
1,35
1,48
2,02
1,62
6,22
5,1
5,52
6,7
6,59
6,71
–
5,62
6,67
–
-
8,66
8,40
10,00
6,38
6,37
6,60
8,27
8,37
8,28
6,73
6,65
6,68
10,35
10,34
9,97
10,73
10,68
10,74
11,8
11,75
11,81
8,50
7,84
7,63
7,85
7,11
8,92
8,51
8,23
7,96
10,09
10,17
10,14
11,29
11,96
11,51
8,72
7
8,96
6,45
8,31
6,69
10,12
10,72
11,79
7,99
7,96
8,23
10,13
11,59
8,46
11,14
14,26
14,20
11,24
12,05
11,37
11,97
11,06
11,45
10,43
10,19
10,19
13,52
13,28
13,33
13,53
13,57
13,73
13,87
13,67
13,85
12,19
12,52
12,55
12,23
12,37
12,23
16,40
16,63
16,06
17,52
17,75
17,40
18,11
18,37
18,16
8,50
11,11
10,83
13,2
11,55
11,50
10,27
13,38
13,61
13,80
12,42
12,28
16,36
17,56
18,26
10,15
155
)
)
)
20
18
16
14
12
,
10
8
6
4
2
0
0
1
0,5%
3%
10%
2
.
.
3
4
5
0,2%
,
1%
5%
7
.
.
.
.
1–
–
:
; –
;
6
–
-2012:
156
. . 2. –
,
, 2012
1–8%
,
.
,
,
.
,
-
15 %,
1–3
.
.
1 – 5 %,
1–3
.
.
,
0,2
0,5 %
-
7-
.
[4]
,
1158 [5].
,
5° ,
2–
2
2.
,
,
%
1
-5 ° )
2
3
3
–
–
3,16
3,05
3,07
3
1,10
1,08
0,95
1,04
–
–
3
–
–
5,32
5,53
5,50
5,45
-5 ° )
,
3,09
4,05
4,45
4,46
3,22
3,12
3,24
6,77
6,91
6,78
4,32
3,19
6,82
-
.
2–
,
(
3%
5 ° )
.
.
(
,
5° )
3%
3%
3%
.
,
.
,
,
,
1, 3
24 – 38 %
-
.
5%
.
,
5°
,
.
–
.
157
1.
, . .
./
.
. .
2.
–
.: . .
/ . .
.
.) [
.]. –
[
]:
5802-78. –
, 1981. – 22 .
,
.
. 1993-01-01. – .:
;
.
3.
28840-90. –
4.
8905-87;
, .
. .
.]. –
:
.
, . .
//
:
, 2011. – 497 .
, . .
//
-2011: .
:
, 2011. – 497 .
5802-78;
. 1986-07-01. – .:
(
[
]:
, 1991. – 8 .
–
-2011: .
.
./
. .
;
5.
.: . .
(
.
1158-2008. –
. 2009-01-01. –
–
,
/
.)
:
]:
-
.[
:
, 2000. – 11 .
.
.
.
,
-
.
72.03(075.8)
.
XIV – XVII
.
,
-
.
,
,
,
,
-
.
XIV – XVII
.
.
:
(
)
(
,
),
.
,
-
.
.
,
,
.
XV .
–
-
,
.
,
,
(
.
,
1).
.
.
,
.
–
.
–
,
,
1–
.
. XIV – XVII
.
-2012:
158
1506 – 1510 .
,
,
. . 2. –
1568 .
, 2012
.
,
.
.
.
,
.
,
8 .
.,
,
70
.
.
–
–
,
,
.
.
-
.
.
-
.
,
,
-
,
.
-
.
[1, c.137].
,
.
.
:
.
(
)
12×12
,
.
,
-
.
,
,
,
«
.
–
,
,
».
,
,
,
,
.
1,25
XVII .
,
.
,
.
,
-
.
.
XVI .
.
.
,
-
,
.
20 – 30
. XVI .,
.
,
.
,
.
:
,
,
(
XVI –
,
. XVI . –
XVII .
,
,
[2, c.169].
. XVII .)
«
» [1, c.140].
(
2),
.
,
,
,
,
-
,
-
.
2–
.
XVII
.
. .
159
XVI .
,
.
,
.
-
,
-
.
,
.
.
1891 .
,
201941 – 1942 .
–
1983 .
. XX .
-
.
[2, c.171].
1968 .,
-
1987 .
.
.
,
(
,
,
[2, . 59] –
,
.
-
)
,
.
,
,
,
,
.
,
.
-
,
,
(
,
«
»
,
).
–
.
,
.
(
,
3
–
13 ., 9.
,
.)
,
525],
[3, .
:
.
,
,
,
,
.
» [4, c. 351].
,
.
-
,
.
–
,
.
:
,
,
–
-
,
-
.
,
.
1.
2.
,
. .
, . .
/
.
.–
:
, 2007. – 200 .
/ . .
.–
:
, 1986. –
240 .
3.
, . .
, 1978.
, .
, 1998. – 538 .
4.
.:
XIII – XVIII
.
/
.
./
;
.
.
.
.–
.
.
:
.
.–
In the work examined achitecture peculiarities of the Mirski Castle. Special attention is given to the research of the elements of
Gothic and Renaissance in castle erection. The study of reflection of the national colour traits in castle construction became the important part of the analysis.
– . .
.
,
,
-
-2012:
160
. . 2. –
, 2012
530.1
. .
.
,
,
.
.
,
.
,
.
-
,
.
.
-
.
(
)
-
.
,
,
:
–
(
.
.
.
gif).
jpeg
,
,
,
(
).
,
,
–
-
,
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,
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.
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,
,
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-
,
.
.
–
.
,
,
;
–
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.
-
;
–
1.
2.
–
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.
.
–
,
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,
» –
-
,
,
,
.
,
,
,
.
,
,
.
,
.
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,
,
.
,
,
.
–
,
,
,
–
.
,
,
,
ln3/ln2=1.584962501.
,
.
,
.
,
-
,
.
,
.
,
,
.
.
.
,
.
,
.
.
.
,
-
,
.
,
.
ln9/ln3=2.0.
,
161
1–
.
.
,
,
.
-
,
.
-
,
.
.
,
,
,
,
,
-
,
.
ln4/ln3=1,261859507.
2–
,
.
.
–
,
,
–
,
:
.
,
.
.3
:
.
,
,
,
.
-
,
.
,
.
(
)
( δ = 1 / 3 ).
60o
-
−60 o
.
.
.
,
(X1Y1) − (X2Y2 )
,
.
.
r
-2012:
162
. . 2. –
, 2012
3–
(
).
.
3
)
.
.
.
.
.
,
.
.
,
(Limited Diffusion Agregation –
.
, .
, .- .
, .
, .
, . .
, .
.–
,
/ .- .
:
, 1991.
.
/ .
,
/
-
.
).
.
/ .
,
-
,
–
1.
2.
3.
4.
5.
6.
.
,
,
LDA-
-
(
/
. – .:
. – .:
.
. .
.–
.
.–
.:
, 2000. – 352 .
, 2002.
, 1993.
.:
/ .
, 1993.
.–
:
, 2001.
Fractals find the increasing and the increasing application in a science. The principal cause of it consists that they describe the
real world sometimes even better, than the traditional physics or mathematics.
– . .
,
.
,
,
.
530.1
. .
.
,
1825
,
-
.
,
,
–
.
1907
.
-
.
.
,
,
,
.
,
-
.
,
(
. 1).
,
λ,
,
(
φ
.
,
,
X
[0, 2π] .
-
∆t
)
RND (
ξ ):
,
,
-
163
φ = 2πξ .
1–
λ =1,
,
:
∆x = λ cos φ,
∆y = λ sin φ.
,
∆t .
,
.
-
,
( x k , yk )
:
φk = 2πξk ;
x k = x k −1 + cos φk ;
y k = yk −1 + sin φk ;
t = 0 : x 0 = 0;
y0 = 0,
t=k.
)
,
. 2.
,
.
.
N max = 2000
–
(
,
.3
t = 10,100,1000 .
,
,
-
,
N max
.
.
,
,
–
,
,
.
«
.
,
,
.
.
,
.
2–
3–
4–
»
-
-2012:
164
. . 2. –
,
, 2012
.
,
.
.
.
( x ki , yki )
t=k
i
-
:
1)
rki2 = x 2ki + y2ki ;
2)
:
δ=
rki2
− Rm k ;
δ
Rm k := Rm k + ;
i
(i − 1) 
δ2 
Sm k :=
 Sm k +  ;
i 
i 
Rm k –
k
.
5–
3)
N max
(
-
,
):
N max
Sm k :=
Rm k
Sm k
N max
tk .
-
,
.
. 5.
,
,
-
165
r 2 = at + b .
.5
.
N max → ∞ .
:
,
,
-
,
,
.
,
,
.
,
,
.
,
,
.
,
r
r
,
r
r=
-
t
t
∑ ∆r
r
k
,
k =1
r
∆ rk –
k
.
 t r 
r2 = 
∆ rk 


 k =1

∑
t
=
∑
2
t
∑ ( ∆ r )2
=
+
k =1
t
∑∑ ( ∆ r ) ⋅ ( ∆r )
+
k =1
t
r
( ∆ r )2
r
∑∑ ( ∆r ) ⋅ ( ∆r )
r
r
i
i
r
r
k
i
=
k =1 i ≠ k
=t
,
k =1 i ≠ k
r
( ∆ r )2 = 1 ,
,
r
r
( ∆ri ) ⋅ ( ∆ri ) = 0 ,
,
.
,
,
-
–
.
.
( a = 1, b = 0 )
.
,
,
.
(
,
,
)
,
.
,
(
).
,
.
r + ∆r
r
,
2πr∆r .
,
–
-
–
.
1.
, 1976.
2.
3.
,
. .
/
, . .
, . .
.–
, 1978.
, . .
. .
4.
5.
, .
6.
,
. 29. – 424 .
/
.–
/
/ . .
.–
, 1977. – . 50.
. – .: 1968.
/ . .
/ .
.
.
.
. .
.
, 1976.
.
//
.–
.:
.–
,
-
.
.
., 1976. –
Brownian motion – in science, random motion of microscopic visiblesuspended in the liquid (or gas) particles (Brownian
particle) solids (dust grains, grains of particulate matter, particles of pollen, etc.) caused by the thermal motion of the fluid (or gas).
We should not confuse the term «Brownian motion» and «thermal motion»: the Brownian motion is a consequence and evidence of
the existence of thermal motion.
–
,
.
.
.
,
.
,
-2012:
166
. . 2. –
, 2012
678.01:620.3
. .
.
,
,
,
,
.
,
.
,
(
),
,
(1) [1]:
(xyz)
,
(x’y’z’).
C
cos x ' x
cos y ' x cos z ' x
C = cos x ' y cos y ' y cos z ' y ,
x, y, z –
,
(1)
cos x ' z cos y ' z cos z ' z
x’,y’,z’ –
-
.
,
abc αβγ (
,
. 1).
1–
(a, b, c)
,
(
)
,
( , , )
,
, b,
, ,z
 x
 
 
z
 
, M, M
–
1
a


1
−
M = 0


0

-
.
-
−1
,
,
:
x
=
y
,y
z
z
,
ctgγ
a
1
b sin γ
−
0
=
x
−1 y
z
,
[2]:
(2)




c cos β

 a b cos γ
c

(cos α − cos β cos γ ) ,
( M ) = 0 b sin γ

sin γ


c⋅r

 0
0
sin γ


cos γ cos α − cos β 
  a*r*
ar sin γ
  sin α *
cos β cos γ − cos α  
= 0
br sin γ
  0
 
sin γ
 
cr

a * ( cos β * − cos γ *cos α *)
sin α *
b *sin α *
0
(3)

a *cos β * 

b *cos α * 

c* 


(4)
167
(
r = 1 − cos 2 α − cos 2 β − cos 2 γ + 2cos α cos β cos γ
(
)
1
2
,
r∗ = 1 − cos 2 α∗ − cos 2 β∗ − cos 2 γ∗ + 2cos α∗ cos β∗ cos γ∗
a*, b*, c*, *, *, * –
1
2
,
[3].
:«
».
)
.
19
–
,
-
,
.
.
,
10−6 ÷ 10−8
(6 – 8
-
)
.
.
9
,
.
,
,
,
,
-
.
:
1–
+
:
,
–
,
–
+
+
+
+
–
+
,
+
+
+
+
–
,
–
-
.
,
,
(
,
,
,
(
(
(
),
).
-
),
,
) (
),
.
(h k l).
,
hkl
,
-
/h, b/k, /l,
, , z.
,
.
.
hkl
,
.
(hkl) ( hi )l
-
,
( hi )l = g ( hi )l .(
(5)
[1]:
( hi )l = M −1 gM ( hi )l .
(5, 6) ( hi )l –
(6)
,
.
( hi )l
. 2.
.
,
:
,
,
,
.
.
,
,
.
.
,
m3, 432, m3m
,
,
.
 S 
 (kkk) ,




.
 S 
 (h00) ,




k
h
,
,
-
-2012:
168
. . 2. –
2–
(
, 2012
(h00))
1
1, m
1
(h00)
2
2, 1 ,2/m,mm2,222,mmm
2
± ( ± h00)
3
3
−
33
 
( h 00 )
−
34
−
4
4,4/m,4mm,422,4/mmm, 4 , 4 2m
−
( ± h00)
−
6, 3 ,6m,3m,6mm,32,622, 3 m,
5
−
6
−
 
6/mmm, 6 , 6 m2
( h0h 1)
,
,
-
.
,
.
.
,
,
-
,
.
,
,
-
.
,
.
,
.
-
.
–
,
.
,
,
.
(
)
,
.
,
-
.
,
,
(
)
,
,
,
,
–
,
(
.
-
.
)
.
.
–
-
.
(
)
,
,
-
,
.
,
-
.
,
,
1.
, . .
[
.] //
2.
, . .
3.
, . .
/ . .
[
.];
.
,
. – 2009. –
4. – . 35 – 47.
:
.
/ . .
.–
:
.
. . .
, . .
.–
:
:
, 1998. – 78 .
,
,
, 2010. – 336 .
/ . .
-
:
-
The general form of regular polyhedral crystal habit built of nanocrystals of different shapes. It is shown that, depending on the
atomic interactions on the concentration of molecules, nanoparticles may have a habit of the shape of a sphere, ellipsoid of revolution, a triaxial ellipsoid, scales or whisker.
–
,
.
.
,
,
-
169
620.3
. .
S (r ) ,
.
.
.
.
,
–
–
,
,
:
,
.
.
,
.
,
.
-
.
–
,
.
.
,
–
.
,
,
.
,
L0,
.
( L0 = 100
-
),
.
. 1.
(S )
1–
SV –
,
,
, L0 –
1,
:
S (r) =
α, n –
.
SV
 L n 
exp α  0  − 1
 r 

3
(1)
,
2
,
.
,
-
L0
-
.
,
,
,
.
L0 =
h, k , m –
.
–
.
1
−1
1,5
⋅ h ( θ D ) 2 = 230 ( θ D ) 2
km
,
[ ],
(2)
; θD –
,
-2012:
170
,
.
.
. . 2. –
, 2012
[4],
.
,
.
[5],
,
,
-
,
,
,
,
5
.
.2
,
E0
( E)
2–
( E0 )
3
-1
-
.
[5]. L0 −
+
25
,
270
-1
(
SiO 2 ,
.
. 3.
.
,
-1
300
,
.
3–
SiO 2
800
[4]
.
( L0 > 100
«
«
),
o
1000 C [7]
Fe − Cr
a
,
-
Fe
»
».
7
,
. 4,
,
L0 ,
-
.
,
,
,
.
.
,
,
(
.
,
,
-
.).
.
,
,
.
,
-
171
.
15÷30
L0 = 8
,
,
[1]
4–
∆R
. L0 −
Fe − Cr
[6]
,
r ≈ 100
,
,
1.
r ≈ 30
.
.
-
, . .
:
/ . .
.];
.
. . .
, . .
.–
:
, 2009. – 439 .
, . .
:
,
,
:
/
. .
[
.];
.
. . .
, . .
.–
:
, 2010. – 336 .
, . .
/ . .
//
–2.
:
2003. –
. 3. – . 4 – 11.
, .
/ .
. – .:
.
..
. 1967. – 696 .
Ajayan, P.M., Schadler, L.S., Braun, A.V. Nanocomposite science and technology / P. M. Ajayan, L. S. Schadler,
A. V. Braun // Willey – VCY. Gmbh I Co KgaA, 2004. − 230 p.
, . .
/ . .
, . .
. − .:
, 1967. − 143 .
Poole, Ch. P., Owens, F. J. Introduction to nanotechnology / Ch. P. Poole, F. J. Owens // Wiley – interscience, 2003. – 320 p.
, .,
, .
. .:
, 2005. – 334 .).
[
2.
3.
4.
5.
6.
7.
We propose a unified function describing the dependence of the parameters of the physical properties of substances on the size
of the particles in the nanoscale. The method of bringing this function to a linear form. According to experimental data, the required
parameters.
–
,
.
.
,
,
-
.
584.1
. .
3-
6-
,
0, 1+ τ
0,±1
2
τ–
,
(532),
1984 .
3.
6-
.
3,
5.
.
-
Al
Mn.
.
.
[1],
,
,
,
.
1.
,
-
-2012:
172
1–
. . 2. –
, 2012
,
–
)
,
5.
.
,
,
,
,
-
.
.
.
(h, k, l),
,
.
(h, k, l)
-
,
.
,
.
5,
. 2)
(
. 3).
.
G,
3
m3m
:
-
 0 0 1 −1 0 0 1 0 0 


G =  1 0 0 , 0 − 1 0 , 0 1 0 .
 0 1 0 0 0 1 0 0 −1 


2–
3–
3
,
.
2
-
z.
xy.
,
0,
±1.
.
.
173
,
532 [3].
,
(
)
5.
3
z,
.
532
, p-
:
, t-
3-
5
yz
− λ(λ + 1)
λ + 0,5 0
t z = − λ(λ + 0,5) − λ(λ + 1) 0
0
0
1
p yz
3
yz,
τ
2
(2λ + 1)(τ + 2)
=
6
(2λ + 1)
−
3
−
(2λ + 1)(τ + 2)
6
τ 2 + 0,5
1
3
5
z
−
1
2
4 − τ2
10
4 − τ2
−
10
t yz = −
τ
2
3+ τ
2
0
pz =
4 − τ2
10
τ2 + 1
5
4τ 2 − 1
10
τ2 − 4
5
τ2 − 4
5
2τ 2 + 1
5
−
τ
τ =
5 −1
; λ –
2
,
2λ + 1
3
1
3
2λ + 1
3
3+ τ
2
τ
2
0
0
0
1
1 =x
x
1− x
λ=
,
3 −1
.
2
,
,
.
-
.
t
p=
p
:
1 0 0 0 0 0
0 0 1 0
0
0
0 0 1 0 0 0
0 0 0 1 0 0
1 0 0 0
0 1 0 0
0
0
0
0
t=
0 0 0 0 1 0
0 0 0 0 0 1
0 1 0 0 0 0
0 0 0 0 −1 0
0 0 0 0 0 −1
0 0 0 1
0
.
0
532 3-
[2].
532
,
,
(
,
),
,
.
.
,
.
,
-2012:
174
. . 2. –
, 2012
,
.
-
,
,
,
,
.
D. Shechtman 2011
-
.
,
,
,
, 6×6
.
.
6±1
-
3-
,
3-
3-
.
1. Shechtman, D., Blech, I., Gratias, D., Cohn, J.W. // Phys. Rev. Lett. – 1984. – V. 53. – P. 1951.
2.
, . .
3. .
//
. 1991. – . 36,
. 4. – . 809 – 812.
3.
, . .
/ . .
. .
,
. 2. – 2011. – 3. – . 129 – 135.
6-
/
,
. .
//
We construct the matrix generators of the point group symmetry of the dodecahedron (532), a 3 and 6 dimensional spaces.
Boreholes matrix generators are 0, 1 + τ and 0, ± 1, respectively. Where is the golden ratio.
–
,
.
.
,
,
-
.
537.226
. .
,
Al
Fe
,
.
.
.
,
,
.
,
,
.
.
.
(
)
[1].
(
,
. 1).
1–
.
-
175
,
.
-
,
-
.
«
»,
-
.
..
,
,
,
,
.
,
,
.
-
.
,
(hkl).
. 2
,
[1].
-
,
,
5
,
,
.
,
(1).
U ( x ) = U exp ( −λ ⋅ x ) ,
–
(1)
.
,
,
,
.
,
,
.
.
,
(
1),
-
.
2–
U(x).
; ,
; , –
–
–
,
;
-
–
.
–
x=0
:
,
,
,
-
,
.
(
)
,
.
.
.
(
-
)
∫
Ws = E ( x )e dx.
,
,W
,
:
W = Ws − E F .
(2)
,
(3)
-2012:
176
«
»
. . 2. –
, 2012
,
-
.
,
.
,
,
,
-
–
–
,
.
.
,
,
(
,
,
)
-
.
.
.
.
,
.
,
,
.
.
,
,
.
,
-
,
,
,
,
«
»
«
»
,
.
2( )
-
u, Ag, u.
3( , )
)
)
)
Cu, Ag, Au ( ),
3–
,
u, Ag,
[3].
( )
( )
u
,
.
.
,
(
,
.
)
,
-
,
.
.
,
,
,
,
.
,
,
.
.
,
-
.
,
,
,
[4].
,
,
,
,
,
.
1.
, . .
. .
, . .
, . .
//
.
. 8 (47). – . 60 – 66.
2.
, . .
1976. – 112 .
3.
, .
(
, .
. – .:
, 1978. – 352 .
4.
. – 2009. – 4. – .10.
.
.
/ .
.
.
. –
, .
, 2005 –
.
,
.
,
.
.
Tlln (S,Se) /
.- .
,
.–
.:
,
)/ .
/ .
.
[
.]. –
-
177
It has been established that the existence of electrostatic mosaic is possible for the surfaces of polycrystals Al and Fe in case of
their electrically neutral surfaces. The amount of surface charge is influenced by symmetry of Fermi surface.
–
.
,
.
,
,
-
.
37.01653
. .
,
SKY CHARTS
Sky Charts,
.
,
.
,
Sky Charts».
«
».
.
-
,
.
,
-
.
,
,
.
,
.
Sky
Charts.
:
12-
20
,
,
.
.
,
.
,
.
,
,
-
,
.
Sky Charts
,
,
,
,
,
,
,
.
.
:
,
:
(
),
,
-
,
,
.
.
:
(
,
)
(
Sky Charts
).
.
,
.
Preference
Catalog and Objects Parameters.
,
.
,
.
,
,
.
File – Online Recourses.
Date / Time
:
system time)
(use
.
Observatory
Chart Appearance
Projection
.
,
,
.
(
)
).
Eyepiece
, . .
.
CCD
.
= 9 (180°).
-
.
,
-
, . .
°
20
( -
.
«Eyepiece»
−
−
−
. .
= 0 (0°),
40
2000
:
2000 / 20 = 100;
40° / 100 = 4°;
4° × 601 = 241,
24
.
Identification
)
long –
Lines
(
(short –
.
)
,
,
,
,
-
,
:
,
,
,
.
Calendar
.
.
,
,
-2012:
178
,
),
,
,
. . 2. –
,
,
(
,
.
,
, 2012
-
,
.
,
,
(
,
).
,
.
.
,
.
–
:
1.
«Field min» = 0
catalog.
2.
3.
4.
5.
Stars 1.
«Field max» = 30).
.
TYCHO catalog (
SKY2000,
(nebulae),
«Show Eyepiece».
+100
,
,
51.
(Nebulae).
.
( . 1).
Find.
(
–
1–
6.
,
,
(
51,
,
.
(
),
(
,
. .).
,
. .),
.
.
B – V,
,
(
(
),
,
.
.
«ESO SkyCat DSS»
7.
(Online resource),
«Images»,
,
Connect.
,
2–
,
51,
,
,
,
.
,
,
.
,
.
(
).
51.
,
Object list.
,
+1040 ).
)(
,
«3' Ref. Cat. Bright Galaxies»
).
+0030 .
«Heasarc SkyView».
$temp.fit
M51.fit.
( .2).
.
-
179
8.
,
,
,
,
. .),
,
,
).
,
,
. 3.
.
«Intensity» «neg») (
(
51,
9.
(
,
,
.3).
).
«Suppress Image».
Background Image.
.
,
,
10.
( -
(
:
,
-
. .
:
: NGC
6543, M 32, M 1, M 95, M 96, M 105, NGC 3344, NGC3386, NGC 3115, M 97, M 82, M 63, M 94, M 106, M 64, M
85, M 100, M 57, NGC 6826, M 27, M 77, NGC 246, NGC 613, NGC 7793, NGC 1097, NGC 1232, M 78, Barnard 33,
NGC 3621, NGC 3109, M 104, NGC 5128, M 90.
.
,
,
,
(
,
Horizon Chart).
.
:
,
,
.
.
,
Sky Charts (
)
,
.
«
,
».
Astronomical computer program Sky Charts help to explore galaxies and nebulaes and allow monitoring of the galaxies to determine location and conditions of visibility. As a result of exploring astronomical computer program Sky Charts was developed lab
«Galaxy observation». Also to use the program can increase the interest in the study of astronomy.
– .
,
.
,
,
-
.
530.1
.
.
, . .
,
. .
, . .
(
)
.
.
.
,
,
,
[1].
.
,
,
,
,
,
.
,
-2012:
180
. . 2. –
[2].
, 2012
[3].
-
,
.
–
.
,
e
.
,
: m0 = m −
,
,
,l0 = σ,E0 = ε,
,
,
.
: τ0 = (m 0 ⋅σ2 / 2ε)0,5 , v0 = σ / τ0 ,a 0 = σ / τ20 ,F0 = σm0 / τ02 ,
σ,ε −
.
:
m'i = mi / m0
R ij = rij / σ,
Uij = u ij / ε,
τ' = τ / τ0
:
&&i = Fxi
mx
&&i = Fyi
my
(1)
&&i = Fzi
mz
Fxi , Fyi , Fzi –
,
i
,
.
(N − 1)
i
Fxi =
∂U (x j − xi )
,
∂R ij
rij
Fyi =
∂U (y j − yi )
,
∂R ij
rij
Fzi =
∂U (z j − zi )
,
∂R ij
rij
(
),
:
(2)
r r r
rij = rj − ri ,
rij2 = (x j − x i )2 + (y j − yi ) 2 + (z j − zi ) 2 ,
i = 1..N, j = 1..N,i ≠ j
U=
∑u
i, j
i, j
∂Uij
24
=
∂R ij R ij
.
6
12



 
 1  − 2  1   .
 R ij  
 R ij 


 

(1)
.
(
1.
2.
3. x 0i , y0i , z 0i , v x0i , v y0i , vz0i , i = 1..N
4.
5.
6.
:
)
τ'
m'i
∆τ .
):
σ
:
k=0
:
k = k +1
(
τ0 :
181
τ = k∆τ
7.
24
=
R ij
6
12



  (x − x i )
 1  − 2  1   j
,
 R ij   m i ⋅ R ij
 R ij 

 

24
8. a yi =
R ij
6
12



  (y − yi )
 1  − 2  1   j
,
 R ij   m i ⋅ R ij
 R ij 






a xi
a zi =
24
R ij
τ
τ + ∆τ :
6
12



  (z − z )
 1  − 2  1   j i

 
 R ij 

 R ij   m i ⋅ R ij

9.
t:
v xi,k = vxi,k −1 + a xi ∆τ,
10. v yi,k = v yi,k −1 + a yi ∆τ,
v zi,k = v zi,k −1 + a zi ∆τ
t:
11.
12. yi,k
zi,k
13.
14.
vxi,k −1 + vxi,k
a xi ∆τ2
,
2
2
v yi,k −1 + v yi,k
a yi ∆τ2
= yi,k −1 +
∆τ +
,
2
2
vzi,k −1 + vzi,k
a ∆τ2
= zi,k −1 +
∆τ + zi
,
2
2
τ < τmax
4,
.
x i,k = x i,k −1 +
∆τ +
10.
,
[4].
1–
.
,
.
,
.
.
(
-
1).
.
.
.
-
,
.
.
,
-
.
1.
2.
, . .
, . .[
/ . .
]. – 2008.
, . .
.–
.:
, 2001. – 356 .
-2012:
182
3.
4.
.
, . .,
, .
.
. . 2 .;
.
.[
.:
.
( .
]. – 2005.
/ .
.) [
.] /
.
,
. . 2. –
.
.
. .
,
.–
.
.
, 2012
, . .
, 2012. – . 237 – 239.
:
//
Molecular dynamics is modeled by the motion of particles (atoms) in the Van der Waals nanoclusters. We study and analyze
the geometric and dynamic characteristics of the atoms in the cluster. Compared to the dynamics of internal and surface atoms.
. .
,
.
,
,
.
539.21-022.532
. .
(
(
)
)
(
)
.
,
,
«
»
,
,
,
.
,
.
.
,
:«
»
. .
» [1].
«
,
-
,
,
:
N
P=
Wj –
, N –
j
∑w
j=1
V
j
(1)
,
,V –
,
,
.
N
,
[2, . 49].
(
(
)
-
)
= 0,74.
.
.
,
1,
).
(
1, ).
2.
1–
: )
(
2–
),
; )
( )
: )
.
; )
183
,
,
,
.
.
,
,
,
-
.
j-
nj,
– rj,
ρ j = n j / 4πrj2
(2)
j.
-
1000.
50
.
3
.
3–
a n(n-1)
3
.
.
,
,
[3, . 23 – 31].
.
,
.
«
–
-
».
,
,
.
,
,
(
,
(
,
4,
4, ).
4–
),
: )
-
; )
,
,
0,74,
-
0,76.
– 0,79,
–
,
0,81.
,
.
(
5).
,
«
«
»
-
»,
.
.
,
,
»
,
,
(
6).
,
«
-
-2012:
184
. . 2. –
, 2012
5–
6–
«
,
«
»
»
.
,
«
»
-
,
,
,
,
0,74.
7–
«
–
»
,
.
,
.
.
,
-
,
,
.
«
–
»
«
»
,
.
,
(
,
.
7).
,
,
,
,
-
.
1.
, . .
2002. – . XLVI, 5.
2.
, . .
3.
, . .
, . .
//
:
/ . .
.–
/ .
.:
//
.
.
.–
, 1972. – 396 .
/ .
. – 2010. – . 23 – 31.
.
.
,
. .
, . .
-
185
If the properties of closed packing spheres structures were analysed, there are two types of these packings. The coordination
numbers of different spheres are described.
–
,
.
,
-
.
539.21
. .
,
.
.
,
,
1000.
,
,
1
-
.
:
A 2 (s) =
A2 (s ) –
sin(2 πsrj )
1 n
,
∑ n j (f j )2
N j =1
2πsr
j
(1)
,s–
–
nj
, fj
rj –
j
.
2
(2)
-
F
.
,
A2 (s )
,
-
,
.
N
F(h, k, l) = ∑ f j cos 2π(hx j + ky j + lz j ),
1
, (hkl) –
fj –
(2)
, ( xyz ) j –
-
.
,
1000.
,
1
,
-
,
[1, . 67].
,
,
:
.
-
Fm3m ,
(
,
1).
,
–
:
2d sin θ = nλ,
d–
, –
L,
,
:
∆(2θ) =
–
λ
,
L cos(θ)
–
, n = 1, 2, 3,K .
.
-
(4)
.
(
)
,
,
(
(3)
)
.
,
-
-2012:
186
1–
, 2012
.
R2
R2
R2
R2
1
12
12
26
24
790
51
48
2170
76
72
3996
2
6
18
27
96
886
52
72
2242
77
96
4092
3
24
42
28
48
934
53
72
2314
78
0
4092
4
12
54
29
24
958
54
32
2346
79
96
4188
5
24
78
30
0
958
55
144
2490
80
24
4212
6
8
86
31
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1054
56
0
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108
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48
134
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6
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57
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6
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96
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36
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36
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5480
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626
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1960
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30
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240
5720
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674
48
24
1984
73
192
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682
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108
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3804
99
120
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766
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120
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100
84
5978
: R2 –
,
–
1–
fCu ( s ) ,
. . 2. –
,
(
,
f–
–
,
)
, f (s ) –
,s–
[2, . 331].
,
,
.
,
1-
,
[2, . 333].
,
«
-
187
»
,
-
.
.
,
,
,
,
,
,
-
.
.
.
.
F(hkl) .
.
(hkl),
F(hkl)
-
(hkl)
10!.
.
-
.
,
,
.
-
n f (s) ,
n–
n-
.
,
n
R (r) ,
,
,
:
A (s) =
∑f
r
∫
R ( r ) = A (s)
1.
, . .
, . .
, . .
, . .
., 1961. – 863 .
2.
j
s n 2πsr
,
2πsr
exp 2πsr
ds.
2πsr
/ . .
.–
:
, . .
-
, 2009. – 438 .
/ .
.
.–
.:
.
.
.-
.
Nanocrystals can be prepared either by dispersing the large crystal, or cultivation around the central atom. In the second case,
the growth of the particle can be considered as the formation of new coordination spheres around the central atom. We investigated
the coordination sphere, until 1000. Table 1 shows the number the squares of the radii of coordination spheres, their coordination
numbers, the number of atoms in a volume bounded by the coordination sphere.
–
,
.
.
,
,
-
.
378.018
. .
.
–
.
.
,
.
:
.
,
,
,
,
-
.
.
170
7 – 11
.
,
,
.
–
,
.
,
,
.
-
-2012:
188
,
. . 2. –
, 2012
,
-
.
.
,
(
),
),
(
.
,
.
«
».
-
,
.
,
,
.
.
-
.
,
—
.
.
, . .
,
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2)
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.
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,
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,
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-
,
.
.
(
),
,
,
,
.
,
,
.
,
,
> 100 %;
,
:
< 0 oC.
(
).
,
(
)
,
,
«
,
,
»
,
.
,
(
-
,
:
).
,
(
),
.
-
,
),
(
,
,
.
,
,
-
-2012:
190
. . 2. –
, 2012
.
,
-
(
).
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,
.
,
,
,
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,
.
:
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.
.),
,
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,
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The decision of problems concerns to practical methods of training and leans on active cogitative activity. Training of pupils to
the decision of problems in physics – difficult process. Stages which allocate during the decision of problems are shown. Each stage
is in detail considered.
–
,
.
.
,
,
-
.
548.4+548.7
. .
S(r),
-
.
S(r),
.
S(r).
-
.
.
,
–
.
-
[1].
,
.
,
.
,
.
1–
;
;
.
1
,
,
:
.
,
,
.
.
,
S(r) ,
-
191
.
-
2 [2, 3].
2–
. Sv –
, L0 –
-
S = S(r ) ,
2,
:
Sv
S(r) =
 L

exp α ( 0 ) n − 1
r


,
α, n –
.
L0
3
(1)
2
[4]:
L0 =
h, k, m
.
:
−1
−1
1,5
⋅ h (θD ) 2 = 230(θ D ) 2
km
,
,
(2)
; θ –
:
Y = αX (4).
3


 L  2  2 

0

X (r ) =  r  − 1
 r p L 
 

0 


S

Y (r ) = ln v


S(r )
(
α = tg (ϕ) .
(4)
3–
3).
(3)
(4)
S(r)
Y(X),
(
4).
-2012:
192
4–
R–
Y
X
,C–
Y=0
R
. . 2. –
S(r).
(
.(4) – (5))
(- ),
X
(4)
Y = α(X + A)
S(r) .
, 2012
:
(5)
:
ln
S0 (r ) –
Sv
(0)
S (r )
= αX
(6)
.
S (r ) .
(6): α = 0,0088 ,
0,89. α = 0,0018 ,
n =1.
= 1,09
= 5,52
n =2.
0,88.
0,40496
,
: α = 0,0045 ,
505 K , L 0 = 30,8
,
L0
.
L - 12,7
: α = 0,198 ,
0,84. α = 0,0021 ,
n =1.
n =2.
1337 K , L = 17,7
= -2,59
.
= -5,48
,
,
.
, α
,
n =2.
-
.
.
1.
= -0,59
0,88.
.
0,97. α = 0,0048 ,
n =1.
= -0,35
0,95.
-
L –
-
.
.
/
.
.
, . .
, . .
//
.–
:
. – 2008. – . 223 – 272.
, . .
,
/ . .
. – .:
, 2005. – 416 .
Ajayan, P. M. Nanocomposite science and technology / P.M. Ajayan, L. S. Schadler, A. V. Braun. – Weinheim: Willey, CY.
Gmbh ICo KgaA, 2004. – 230 p.
, . .
:
/ . .
//
.
2. – 2007. – 2. – . 65 – 71.
:
2.
3.
4.
We analyze the generalized function S (r), describing the dependence of the properties of substances on the size of the particles
in the nanoscale. The technique of adjusting the function S (r), obtained experimentally.
–
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193
378.018
. .
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[1].
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-2012:
194
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, 2012
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[4].
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:
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[3].
:
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.[5]
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-
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,
«
».
,
–
», «
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195
,
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—
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1.
2.
3.
4.
5.
:
/
.
/
.–
. .
. – 2010.
, . .
, . .
. .
, . .
.: . .
.:
, . .
, 1983.
/
.. . .
/ . .
//
.–
:
,
, 2006. – 172 .
.
,
:
.
,–
. – 1997 .
/
, . .
//
:
. – 2002. –
4.
Value of out-of-class work is considered. Creation of system of additional education and education allows keeping and
strengthening physical and mental health of children, steady interest to informative activity, and development of creative abilities of
children. Additional education at school – means of continuous formation and formation of the person.
–
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