Analytical estimates of crossing of ellipses of distribution at recognition of nanoparticles of colloidal
silver are given in polyair fibers on multidimensional correlation components of the Raman ranges with
control according to polarizing characteristics. Reliability of recognition of nanoparticles was estimated on
joint probability of normal distributions of intensivnost of the Raman spectrograms of nanoparticles of silver
on polyair fibers depending on longitudinal and cross polarization of laser radiation on all range of a
range with the analysis of 9 main peaks

Butov, K.V.

Danilova, S.A.

Dobrovolskaya, T.A.

Emelyanov, V.M.

Emelyanovа, О.V.

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 7 No 4, 04032(3pp) (2015) Том 7 № 4, 04032(3cc) (2015)   2077-6772/2015/7(4)04032(3) 04032-1  2015 Sumy State University Development of a Technique of an Analytical Assessment of Crossing of Ellipses  of Distribution on Polarizing Raman Ranges at Identification of Nanoparticles  of Silver on Polyester Fibers  T.A. Dobrovolskaya*, V.M. Emelyanov, S.A. Danilova, О.V. Emelyanovа, K.V. Butov  Southwest state University, 94, 50 let Octyabrya, 305040 Kursk, Russia  (Received 28 September 2015; published online 10 December 2015)  Analytical estimates of crossing of ellipses of distribution at recognition of nanoparticles of colloidal silver are given in polyair fibers on multidimensional correlation components of the Raman ranges with control according to polarizing characteristics. Reliability of recognition of nanoparticles was estimated on joint probability of normal distributions of intensivnost of the Raman spectrograms of nanoparticles of sil-ver on polyair fibers depending on longitudinal and cross polarization of laser radiation on all range of a range with the analysis of 9 main peaks.  Keywords: Polyester fiber, Nanoparticles of colloidal silver, The Raman ranges, Polarizing characteristics of the Raman spectroscopy, Mathematical modeling of ranges, Multidimensional correlation components of the Raman ranges, Reliability of recognition.   PACS numbers: 02.60.Cb, 02.70.Rr                                                             * emelianov@nm.ru 1. INTRODUCTION  Correlation polarizing characteristics of the Raman spectroscopy allow to increase considerably reliability of recognition of the nanoparticles which are on fibers of fabrics. In works [1-7] identification of nanoparticles on pol-yair fibers is estimated. But to define the modes of drawing nanoparticles on fibers and especially their change at operation it is complicated because of their small quantity.  The offered researches allow to increase the accuracy of recognition of the fibers covered with nanoparticles of silver or uncovered nanoparticles according to polarizing characteristics of the Raman ranges with use of methods of an analytical assessment of crossing of ellipses of distri-bution of intensity of polarizing Raman ranges.  2. DESCRIPTION OF THE SUBJECT AND METHODS OF RESEARCH  2.1 Experimental Procedure  Experiments on measurement of casual values of distribution of intensivnost of ranges of the Raman combinational radiation were previously made, thus correlation matrixes (Fig. 1) and parameters of distri-butions (1) taking into account polarization of radiation on X-across and on Y- along fibers at the same time for one measurement are revealed:  rXY10.977730.798650.964340.97520.973420.937360.990960.87290.932040.965780.763320.951480.969190.982440.915040.988290.883490.935670.981750.826190.952140.964960.970440.927370.986010.840440.912860.979340.798720.967330.978170.975510.940710.99280.873750.936570.986890.805780.977680.988740.983030.9540.998680.86660.952760.975560.795390.961590.972850.972470.933650.989520.873970.929410.988010.830440.969420.977820.970350.949360.992090.850020.928610.60270.245580.645280.679260.740550.550320.710.884610.70750.77860.423470.826630.856550.893340.748370.870450.962110.88746                                                       a rXYAg9_0_80.5529950.0727070.249720.4231430.2182460.4988180.2982020.3408950.1446160.5513860.0598230.2439480.4270490.1961890.5061060.2761260.373650.1373140.5843330.1102940.2847340.4568380.1828040.5313240.2630920.3194590.1071370.5780840.0962630.2768690.4535280.1770640.5293850.2578160.3362610.1102320.8125680.4505150.5910590.7119630.112850.757710.0322430.0056250.2192360.5821310.1024630.2892410.460170.1691920.5322670.2518630.3077720.1037910.8104290.4487210.5852840.707980.1066140.7552370.0270180.0164190.2152680.705690.3286230.4593550.5834010.0558890.6359970.132890.0880090.067110.7014130.2980.4210980.5744150.0628920.6426510.135780.2095830.051273  b  Fig. 1 – Correlation matrixes of the Raman polarizing spec-trograms of polyester fibers after drying under natural condi-tions in the range of frequencies 54.3÷3110 sm – 1: a – polariza-tion across and along fibers with silver nanoparticles; b – po-larization across and along fibers without silver nanoparticles  In Fig. 1 it is visible that korellyatsionny matrixes have the big range of dispersion of values from 0.99868 till 0.24558 in the presence of nanoparticles of silver (fig. 1a), and for fibers without nanoparticles range from 0.812568 to – 0.340895. Parameters of distributions (1), and, population means considerably differ on intensity of peaks of rang-es with polarization across fibers X and along fibers Y. Along fibers intensity is much higher even several times both for fibers without nanoparticles, and for fibers with nanoparticles. Characteristic is that at polarization along fibers in-tensity of the central peaks 4, 5, 6 and 7 is much higher than extreme peaks 1, 2, 3, 8 and 9 almost by 20 times. It specifies that maximum efficiency of measurements of the Raman ranges at polarization along fibers is found. However there is a task about check of informa-tional content at measurement of peaks of polarizing ranges of the Raman radiation. MENXT  (698.207 266.156 384.805 659.824 661.551 852.41 849.92 412.99 796.091), XT  (84.487 50.527 47.174 73.693 77.891 89.624 87.343 16.679 31.712), MENYT  (745.167 457.096 1196.862 4023.730  V.M. EMELYANOV, Т.А. DOBROVOLSKAYA, ET AL. J. NANO- ELECTRON. PHYS. 7, 04032 (2015)   04032-2 4073.140 1775.226 1780.878 182.674 196.222), YT  (115.383 74.971 626.399 571.34 270.561 255.402 29.143 15.207), MENXAg9T  (395.233 140.846 213.373 332.365 344.734 478.977 510.665 270.979 539.491), YAg9T  (60.722 35.107 27.743 40.744 55.448 46.836 65.423 24.641 50.471), MENYAg9T  (599.064 365.357 968.096 3224.61 2929.766 1431.412 1342.996 136.366 150.694),  YAg9T  (120.429 74.806 195.827 612.321 706.978 273.100 321.016 32.870 29.676).                    (1)   2.2 The Processing of the Experimental Data  We will carry out modeling of statistical data for identification of crossings of ellipses of distributions of values of intensivnost of peaks of spectrograms. We will create the general correlation matrix for full generation of data on the basis of initial matrixes of Fig. 1 and we will receive a correlation matrix of RXY1 with a general size of 38  38. Generation of the set amount of casual values is carried out in normal way to the law and a matrix of RXY1 for what the built-in MathCad Edition 14 [4-6] function is used. Further we define a vector of own numbers from the general correlation matrix of RXY1. As the generated casual values possess some corre-lation which is negatively affecting modeling accuracy, it is necessary to lead them to an uncorrelated look for what the special program developed in the environment of MathCad Enterprise Edition 11 is used. The values of data of modeling received by such transformation possess the correlation aspiring to zero. Further we will transform uncorrelated values through a fundamental matrix of UR of a correlation matrix of RXY1 to the correlated. For automatic identification of crossing of ellipses of distribution it is necessary to solve system of the ana-lytical equations and it will give coordinates of a point of intersection. In this work the system only of two equations is considered. The analytical assessment of crossing of ellipses of distributions is made according to the decision of sys-tem of the equations with finding of coordinates of a point of intersection:  rXY13   0.97817;          rXYAg9_0_83   0.453528; f(x,y) ((x-MENXAg93)/XAg93)2 - 2 rXYAg9_0_83((x-MENXAg93)/XAg93)((y-MENYAg93)/(YAg93) + ((y-MENYAg93)/YAg93)2-43.201055[1- (rXYAg9_0_83)2];  g(x,y)((x-MENX3)/X3)2-2rXY13((x-MENX3)/X3) ((y-MENY3)/Y3)+((y-MENY3)/Y3)2-43.201055 [1- (rXY13)2]; x  400            y  2000       f(x,y)  0       g(x,y)  0 v  Find(x,y) v  (405.701697, 2036.720505) f(v0, v1) = 7.12710-5                       g(v0, v1)  9.99710-4.                                                (2)  The decision of system of the analytical equations (2) is made by criterion of crossing of ellipses not in two points, and in one for coordinates of limit values Х0(1)  485.948874 and Х0(2)  485.948889 for Ro2  41.7321043. For double crossing of ellipses of distribution the transition point from one crossing is revealed (only contact) Ro2  41.733 Х0  486.01424. For coordinate Y0(1)  481.103016 and Y0(2)  481.103048 for Ro2  41.7321043 limit value of crossing is revealed. At the beginning of double cross-ing the transition point from one point of intersection is revealed Ro2  41.733 Y0  481.16753.  Coordinates of limit values Х3(1)  485.948874 and Х3(2)  485.948889 for R32  41.7321043. For double crossing of ellipses of distribution the transition point from one crossing is revealed (only contact) R32  43.2027 Х3  405.766908. For coordinate Y3(1)  2036.720524 and Y3(2)  2036.720505 for R32  43.201055 limit value of crossing is revealed. At the beginning of double cross-ing the transition point from one point of intersection is revealed R32  43.2027 Y3  2037.098168.  3. DESCRIPTION AND ANALYSIS OF RESULTS  At an analytical assessment of crossing of ellipses of distribution with the decision of system of the equa-tions coordinates on 9 peaks are received:  for cross polarization of X XAnT  (485.949  192.204  267.401  405.702  474.262  566.027  653.626  349.531  695.899)                            (3) for longitudinal polarization of Y YAnT  (481.103  373.014  771.483  2036.72  2729.72  1061.13  1212.73  105.587  153.743)                             (4) and the equivalent radius of curvature of ellipses when crossing RAnT  (2.632      1.463      2.537      3.578      2.399      3.336      2.234      3.255      3.159)                                (5)    Fig. 2 – Increase of informational content of reliability when using two-dimensional measurement in cross X and longitudi-nal At the directions taking into account correlation coeffi-cients: __ measurements at cross polarization of X; …. meas-urements in cross X and longitudinal At the directions taking into account correlation coefficients  In comparison with experimental data when model-ing with use of generation of multidimensional correla-tion dependences of coordinate of crossing of ellipses of distribution following:  for cross polarization of X XЭnT  (508.31   187.17   269.05   401.42   477.04   551.12   670.90   334.39   712.03)                                  (6) for longitudinal polarization of Y  DEVELOPMENT OF A TECHNIQUE OF AN ANALYTICAL ASSESSMENT… J. NANO- ELECTRON. PHYS. 7, 04032 (2015)   04032-3 YЭnT  (590.97   558.13   827.27   2005.9   2945.7   1138.8   1318.1   133.93   166.18)                                  (7)  At a choice of points of intersection of the ellipses of distribution constructed on population means, average quadratic deviations and correlation coefficients with selection of equivalent radius of ellipses of distribution crossing coordinates are received:  for cross polarization of X XРnT  (488.20   192.22   267.37   409.82   474.45   565.68   654.19   349.52   697.07)                                 (8) for longitudinal polarization of Y  YРnT  (486.00   373.44   770.96   2095.7   2731.2   1059.1   1214.3   105.60   154.13)                                 (9) and the equivalent radius of curvature of ellipses when crossing RPnT  (2.636     1.463     2.538     3.584     2.403     3.335     2.241     3.255     3.122).                                (10)  4. CONCLUSIONS   The method giving substantial increase estimates reliability of definition of the modes of drawing nano-particles of silver on fibers that illustrates Fig. 2 was as a result offered.   REFERENCES   1. V.M. Emelyanov, T.A. Dobrovolskaya, V.V. Emelyanov, E.J. Orlov, Nanotechnics 2, 81 (2013). 2. V.M. Emeljanov, T. Dobrovol’skaja, S. Danilova, V. Emeljanov, E. Orlov, Open J. Metal 3 No 3, 29 (2013). 3. V.M. Emelyanov, T.A. Dobrovolskaya, S.A. Danilova, V.V. Emelyanov, K.V. Butov, E.J. Orlov, J. Nano- Electron. Phys. 5 No 4, 04001 (2013). 4. V.M. Emelyanov, T.A. Dobrovolskaya, V.V. Emelyanov, E.J. Orlov, Modern Problems of Science and Education 6 (2013). 5. V.M. Emelyanov, T.A. Dobrovolskaya, V.V. Emelyanov, E.J. Orlov, Fundamental Res. 10, 3310 (2013). 6. V.M. Emelyanov, T.A. Dobrovolskaya, S.A. Danilova, V.V. Emelyanov, Natural and Eng. Sci. 6, 415 (2013). 7. V.M. Emelyanov, T.A. Dobrovolskaya, S.A. Danilova, V.V. Emelyanov, K.V. Butov, E.J. Orlov, Science of Science 6 (2013).   

Development of a Technique of an Analytical Assessment of Crossing of Ellipses of Distribution on Polarizing Raman Ranges at Identification of Nanoparticles of Silver on Polyester Fibers

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 7 No 4, 04032(3pp) (2015) Том 7 № 4, 04032(3cc) (2015) 
 
 
2077-6772/2015/7(4)04032(3) 04032-1  2015 Sumy State University 
Development of a Technique of an Analytical Assessment of Crossing of Ellipses  
of Distribution on Polarizing Raman Ranges at Identification of Nanoparticles  
of Silver on Polyester Fibers 
 
T.A. Dobrovolskaya*, V.M. Emelyanov, S.A. Danilova, О.V. Emelyanovа, K.V. Butov 
 
Southwest state University, 94, 50 let Octyabrya, 305040 Kursk, Russia 
 
(Received 28 September 2015; published online 10 December 2015) 
 
Analytical estimates of crossing of ellipses of distribution at recognition of nanoparticles of colloidal 
silver are given in polyair fibers on multidimensional correlation components of the Raman ranges with 
control according to polarizing characteristics. Reliability of recognition of nanoparticles was estimated on 
joint probability of normal distributions of intensivnost of the Raman spectrograms of nanoparticles of sil-
ver on polyair fibers depending on longitudinal and cross polarization of laser radiation on all range of a 
range with the analysis of 9 main peaks. 
 
Keywords: Polyester fiber, Nanoparticles of colloidal silver, The Raman ranges, Polarizing characteristics 
of the Raman spectroscopy, Mathematical modeling of ranges, Multidimensional correlation components of 
the Raman ranges, Reliability of recognition. 
 
 PACS numbers: 02.60.Cb, 02.70.Rr 
 
 
                                                          
* emelianov@nm.ru 
1. INTRODUCTION 
 
Correlation polarizing characteristics of the Raman 
spectroscopy allow to increase considerably reliability of 
recognition of the nanoparticles which are on fibers of 
fabrics. 
In works [1-7] identification of nanoparticles on pol-
yair fibers is estimated. But to define the modes of 
drawing nanoparticles on fibers and especially their 
change at operation it is complicated because of their 
small quantity.  
The offered researches allow to increase the accuracy 
of recognition of the fibers covered with nanoparticles of 
silver or uncovered nanoparticles according to polarizing 
characteristics of the Raman ranges with use of methods 
of an analytical assessment of crossing of ellipses of distri-
bution of intensity of polarizing Raman ranges. 
 
2. DESCRIPTION OF THE SUBJECT AND 
METHODS OF RESEARCH 
 
2.1 Experimental Procedure 
 
Experiments on measurement of casual values of 
distribution of intensivnost of ranges of the Raman 
combinational radiation were previously made, thus 
correlation matrixes (Fig. 1) and parameters of distri-
butions (1) taking into account polarization of radiation 
on X-across and on Y- along fibers at the same time for 
one measurement are revealed: 
 
rXY1
0.97773
0.79865
0.96434
0.9752
0.97342
0.93736
0.99096
0.8729
0.93204
0.96578
0.76332
0.95148
0.96919
0.98244
0.91504
0.98829
0.88349
0.93567
0.98175
0.82619
0.95214
0.96496
0.97044
0.92737
0.98601
0.84044
0.91286
0.97934
0.79872
0.96733
0.97817
0.97551
0.94071
0.9928
0.87375
0.93657
0.98689
0.80578
0.97768
0.98874
0.98303
0.954
0.99868
0.8666
0.95276
0.97556
0.79539
0.96159
0.97285
0.97247
0.93365
0.98952
0.87397
0.92941
0.98801
0.83044
0.96942
0.97782
0.97035
0.94936
0.99209
0.85002
0.92861
0.6027
0.24558
0.64528
0.67926
0.74055
0.55032
0.71
0.88461
0.7075
0.7786
0.42347
0.82663
0.85655
0.89334
0.74837
0.87045
0.96211
0.88746

























                                                       a 
rXYAg9_0_8
0.552995
0.072707
0.24972
0.423143
0.218246
0.498818
0.298202
0.340895
0.144616
0.551386
0.059823
0.243948
0.427049
0.196189
0.506106
0.276126
0.37365
0.137314
0.584333
0.110294
0.284734
0.456838
0.182804
0.531324
0.263092
0.319459
0.107137
0.578084
0.096263
0.276869
0.453528
0.177064
0.529385
0.257816
0.336261
0.110232
0.812568
0.450515
0.591059
0.711963
0.11285
0.75771
0.032243
0.005625
0.219236
0.582131
0.102463
0.289241
0.46017
0.169192
0.532267
0.251863
0.307772
0.103791
0.810429
0.448721
0.585284
0.70798
0.106614
0.755237
0.027018
0.016419
0.215268
0.70569
0.328623
0.459355
0.583401
0.055889
0.635997
0.13289
0.088009
0.06711
0.701413
0.298
0.421098
0.574415
0.062892
0.642651
0.13578
0.209583
0.051273

























 
 b 
 
Fig. 1 – Correlation matrixes of the Raman polarizing spec-
trograms of polyester fibers after drying under natural condi-
tions in the range of frequencies 54.3÷3110 sm – 1: a – polariza-
tion across and along fibers with silver nanoparticles; b – po-
larization across and along fibers without silver nanoparticles 
 
In Fig. 1 it is visible that korellyatsionny matrixes 
have the big range of dispersion of values from 0.99868 
till 0.24558 in the presence of nanoparticles of silver 
(fig. 1a), and for fibers without nanoparticles range 
from 0.812568 to – 0.340895. 
Parameters of distributions (1), and, population 
means considerably differ on intensity of peaks of rang-
es with polarization across fibers X and along fibers Y. 
Along fibers intensity is much higher even several 
times both for fibers without nanoparticles, and for 
fibers with nanoparticles. 
Characteristic is that at polarization along fibers in-
tensity of the central peaks 4, 5, 6 and 7 is much higher 
than extreme peaks 1, 2, 3, 8 and 9 almost by 20 times. 
It specifies that maximum efficiency of measurements 
of the Raman ranges at polarization along fibers is 
found. However there is a task about check of informa-
tional content at measurement of peaks of polarizing 
ranges of the Raman radiation. 
MENXT  (698.207 266.156 384.805 659.824 
661.551 852.41 849.92 412.99 796.091), 
XT  (84.487 50.527 47.174 73.693 77.891 89.624 
87.343 16.679 31.712), 
MENYT  (745.167 457.096 1196.862 4023.730 
 V.M. EMELYANOV, Т.А. DOBROVOLSKAYA, ET AL. J. NANO- ELECTRON. PHYS. 7, 04032 (2015) 
 
 
04032-2 
4073.140 1775.226 1780.878 182.674 196.222), 
YT  (115.383 74.971 626.399 571.34 270.561 
255.402 29.143 15.207), 
MENXAg9T  (395.233 140.846 213.373 332.365 
344.734 478.977 510.665 270.979 539.491), 
YAg9T  (60.722 35.107 27.743 40.744 55.448 
46.836 65.423 24.641 50.471), 
MENYAg9T  (599.064 365.357 968.096 3224.61 
2929.766 1431.412 1342.996 136.366 150.694), 
 YAg9T  (120.429 74.806 195.827 612.321 
706.978 273.100 321.016 32.870 29.676).                    (1) 
 
 
2.2 The Processing of the Experimental Data 
 
We will carry out modeling of statistical data for 
identification of crossings of ellipses of distributions of 
values of intensivnost of peaks of spectrograms. We will 
create the general correlation matrix for full generation 
of data on the basis of initial matrixes of Fig. 1 and we 
will receive a correlation matrix of RXY1 with a general 
size of 38  38. 
Generation of the set amount of casual values is 
carried out in normal way to the law and a matrix of 
RXY1 for what the built-in MathCad Edition 14 [4-6] 
function is used. Further we define a vector of own 
numbers from the general correlation matrix of RXY1. 
As the generated casual values possess some corre-
lation which is negatively affecting modeling accuracy, 
it is necessary to lead them to an uncorrelated look for 
what the special program developed in the environment 
of MathCad Enterprise Edition 11 is used. The values 
of data of modeling received by such transformation 
possess the correlation aspiring to zero. 
Further we will transform uncorrelated values 
through a fundamental matrix of UR of a correlation 
matrix of RXY1 to the correlated. 
For automatic identification of crossing of ellipses of 
distribution it is necessary to solve system of the ana-
lytical equations and it will give coordinates of a point 
of intersection. In this work the system only of two 
equations is considered. 
The analytical assessment of crossing of ellipses of 
distributions is made according to the decision of sys-
tem of the equations with finding of coordinates of a 
point of intersection: 
 
rXY13   0.97817;          rXYAg9_0_83   0.453528; 
f(x,y) ((x-MENXAg93)/XAg93)2 - 2 rXYAg9_0_83((x-
MENXAg93)/XAg93)((y-MENYAg93)/(YAg93) + ((y-
MENYAg93)/YAg93)2-43.201055[1- (rXYAg9_0_83)2]; 
 g(x,y)((x-MENX3)/X3)2-2rXY13((x-MENX3)/X3) 
((y-MENY3)/Y3)+((y-MENY3)/Y3)2-43.201055 
[1- (rXY13)2]; 
x  400            y  2000       f(x,y)  0       g(x,y)  0 
v  Find(x,y) 
v  (405.701697, 2036.720505) 
f(v0, v1) = 7.12710-5                      
 g(v0, v1)  9.99710-4.                                                (2) 
 
The decision of system of the analytical equations 
(2) is made by criterion of crossing of ellipses not in two 
points, and in one for coordinates of limit values 
Х0(1)  485.948874 and Х0(2)  485.948889 for 
Ro2  41.7321043. For double crossing of ellipses of 
distribution the transition point from one crossing is 
revealed (only contact) Ro2  41.733 Х0  486.01424. 
For coordinate Y0(1)  481.103016 and 
Y0(2)  481.103048 for Ro2  41.7321043 limit value of 
crossing is revealed. At the beginning of double cross-
ing the transition point from one point of intersection is 
revealed Ro2  41.733 Y0  481.16753.  
Coordinates of limit values Х3(1)  485.948874 and 
Х3(2)  485.948889 for R32  41.7321043. For double 
crossing of ellipses of distribution the transition point 
from one crossing is revealed (only contact) 
R32  43.2027 Х3  405.766908. 
For coordinate Y3(1)  2036.720524 and 
Y3(2)  2036.720505 for R32  43.201055 limit value of 
crossing is revealed. At the beginning of double cross-
ing the transition point from one point of intersection is 
revealed R32  43.2027 Y3  2037.098168. 
 
3. DESCRIPTION AND ANALYSIS OF RESULTS 
 
At an analytical assessment of crossing of ellipses of 
distribution with the decision of system of the equa-
tions coordinates on 9 peaks are received: 
 
for cross polarization of X 
XAnT  (485.949  192.204  267.401  405.702  474.262  
566.027  653.626  349.531  695.899)                            (3) 
for longitudinal polarization of Y 
YAnT  (481.103  373.014  771.483  2036.72  2729.72  
1061.13  1212.73  105.587  153.743)                             (4) 
and the equivalent radius of curvature of ellipses 
when crossing 
RAnT  (2.632      1.463      2.537      3.578      2.399      
3.336      2.234      3.255      3.159)                                (5) 
 
 
 
Fig. 2 – Increase of informational content of reliability when 
using two-dimensional measurement in cross X and longitudi-
nal At the directions taking into account correlation coeffi-
cients: __ measurements at cross polarization of X; …. meas-
urements in cross X and longitudinal At the directions taking 
into account correlation coefficients 
 
In comparison with experimental data when model-
ing with use of generation of multidimensional correla-
tion dependences of coordinate of crossing of ellipses of 
distribution following: 
 
for cross polarization of X 
XЭnT  (508.31   187.17   269.05   401.42   477.04   
551.12   670.90   334.39   712.03)                                  (6) 
for longitudinal polarization of Y 
 DEVELOPMENT OF A TECHNIQUE OF AN ANALYTICAL ASSESSMENT… J. NANO- ELECTRON. PHYS. 7, 04032 (2015) 
 
 
04032-3 
YЭnT  (590.97   558.13   827.27   2005.9   2945.7   
1138.8   1318.1   133.93   166.18)                                  (7) 
 
At a choice of points of intersection of the ellipses of 
distribution constructed on population means, average 
quadratic deviations and correlation coefficients with 
selection of equivalent radius of ellipses of distribution 
crossing coordinates are received: 
 
for cross polarization of X 
XРnT  (488.20   192.22   267.37   409.82   474.45   
565.68   654.19   349.52   697.07)                                 (8) 
for longitudinal polarization of Y  
YРnT  (486.00   373.44   770.96   2095.7   2731.2   
1059.1   1214.3   105.60   154.13)                                 (9) 
and the equivalent radius of curvature of ellipses 
when crossing 
RPnT  (2.636     1.463     2.538     3.584     2.403     
3.335     2.241     3.255     3.122).                                (10) 
 
4. CONCLUSIONS  
 
The method giving substantial increase estimates 
reliability of definition of the modes of drawing nano-
particles of silver on fibers that illustrates Fig. 2 was as 
a result offered. 
 
 
REFERENCES  
 
1. V.M. Emelyanov, T.A. Dobrovolskaya, V.V. Emelyanov, 
E.J. Orlov, Nanotechnics 2, 81 (2013). 
2. V.M. Emeljanov, T. Dobrovol’skaja, S. Danilova, 
V. Emeljanov, E. Orlov, Open J. Metal 3 No 3, 29 (2013). 
3. V.M. Emelyanov, T.A. Dobrovolskaya, S.A. Danilova, 
V.V. Emelyanov, K.V. Butov, E.J. Orlov, J. Nano- Electron. 
Phys. 5 No 4, 04001 (2013). 
4. V.M. Emelyanov, T.A. Dobrovolskaya, V.V. Emelyanov, 
E.J. Orlov, Modern Problems of Science and Education 6 
(2013). 
5. V.M. Emelyanov, T.A. Dobrovolskaya, V.V. Emelyanov, 
E.J. Orlov, Fundamental Res. 10, 3310 (2013). 
6. V.M. Emelyanov, T.A. Dobrovolskaya, S.A. Danilova, 
V.V. Emelyanov, Natural and Eng. Sci. 6, 415 (2013). 
7. V.M. Emelyanov, T.A. Dobrovolskaya, S.A. Danilova, 
V.V. Emelyanov, K.V. Butov, E.J. Orlov, Science of Science 6 
(2013). 
 
 


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Development of a Technique of an Analytical Assessment of Crossing of Ellipses of Distribution on Polarizing Raman Ranges at Identification of Nanoparticles of Silver on Polyester Fibers

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