Results of comparison of parameters of crossing of distribution of multidimensional correlation components of polarizing Raman ranges with control on polarizing characteristics at recognition of nanoparticles of silver are given in polyair fibers on vector-matrix modeling and generation of multidimensional correlation
data. The assessment of reliability of recognition of nanoparticles was carried out on joint probability of normal distributions of intensivnost of the Raman spectrograms of fibers of polyair

Butov, K.V.

Danilova, S.A.

Dobrovolskaya, T.A.

Emelyanov, V.M.

Emelyanov, V.V.

English

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 8 No 3, 03048(3pp) (2016) Том 8 № 3, 03048(3cc) (2016) 
 
 
2077-6772/2016/8(3)03048(3) 03048-1  2016 Sumy State University 
Short Communication 
 
Assessment of Reliability of Recognition of Nanoparticles of Silver on Polyester Fibers on 
Two-dimensional Models and Experimental Data of the Raman Ranges  
 
T.A. Dobrovolskaya*, V.M. Emelyanov, S.A. Danilova, V.V. Emelyanov, K.V. Butov  
 
Southwest State University, 94, 50 let Octyabrya st., 305040 Kursk, Russia  
 
(Received 04 May 2016; published online 03 October 2016) 
 
Results of comparison of parameters of crossing of distribution of multidimensional correlation compo-
nents of polarizing Raman ranges with control on polarizing characteristics at recognition of nanoparticles 
of silver are given in polyair fibers on vector-matrix modeling and generation of multidimensional correla-
tion data. The assessment of reliability of recognition of nanoparticles was carried out on joint probability 
of normal distributions of intensivnost of the Raman spectrograms of fibers of polyair.  
 
Keywords: Vector-matrix modeling, Polyester fiber, Silver nanoparticles, The Raman ranges, Polarizing 
characteristics of the Raman spectroscopy, Mathematical modeling of ranges, Multidimensional correlation 
components of the Raman ranges, Reliability of recognition, Probability of crossing of dispersions of normal 
multidimensional distributions, Generation of multidimensional correlation data. 
 
DOI: 10.21272/jnep.8(3).03048 PACS numbers: 02.60.Cb, 02.70.Rr 
 
 
                                                          
* emelianov@nm.ru. 
1. INTRODUCTION 
 
The Raman ranges of polyester fibers contain more 
than 9 information peaks. However sensitivity of usual 
recognition on amplitude of peaks on polyester fibers 
doesn't allow to estimate existence of nanoparticles of 
silver with rather acceptable reliability.  
It is considerable to increase reliability of recogni-
tion of the nanoparticles which are on fibers of fabrics, 
detection of correlation polarizing characteristics of the 
Raman spectroscopy allows. 
In works [1-6] identification of nanoparticles is giv-
en in polyair fibers. But it is complicated to define the 
modes of drawing nanoparticles on fibers and especially 
change of quantity of particles at operation because of 
their small quantity.  
In this work the method of vector-matrix drawing 
up analytical expressions and an assessment of equiva-
lent radius of curvature on the basis of correlation data 
on object of system of a nanoparticle - polyester fiber is 
considered. 
In view of a gromozdskost of an analytical type of 
system of analytical expressions of the second order 
with a large number of unknown to 9, in work it is of-
fered to use a vector-matrix form of record of system of 
nonlinear quadratic expressions and further the deci-
sion of this system of the nonlinear quadratic equations 
in the Mathcad programming environment. 
The offered researches allow to increase the accura-
cy of recognition of the fibers covered with nanoparti-
cles of silver or uncovered nanoparticles according to 
polarizing characteristics of the Raman ranges with use 
of methods of a vector-matrix analytical assessment of 
the parameters of crossing of distribution 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 peaks of ranges of the 
Raman combinational radiation have been previously 
made, at the same time correlation matrixes are re-
vealed rXY1, rXYAg9_0_8 and parameters of distribu-
tions population mean (MEN), average quadratic devia-
tion () taking into account polarization of radiation 
on X-across and on Y - along fibers at the same time for 
one measurement [7]. 
Modeling of statistical data for identification of 
crossings of ellipses of distributions of values of inten-
sivnost of peaks of spectrograms has been carried out. 
Generation of the set amount of casual values was car-
ried out according to the special program developed in 
the environment of MathCad Edition 14 [7-10]. 
 
2.2 The Processing of the Experimental Data 
 
For identification of R – the radius of curvature of 
ellipses of crossing of the generated data it is necessary 
to write down it in vector-matrix analytical expressions 
on coordinates of points of intersection. In this work the 
system only of two vector-matrix analytical expressions 
is considered 
 
 R2  XT∑ – 1 X for R0 and R1.  
 
The analytical assessment of R0 and R1 – curvature 
radiuses on points of intersection of ellipses of distribu-
tions is made on vector-matrix analytical expressions 
(1-2): 
 


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
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



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






  
3
3
3
3
1
3
3
3
3
9YAg
9MENAg9.2005
9XAg
9MENAg42.401
0
9YAg
9MENAg9.2005
9XAg
9MENAg42.401
:0R (1)
 
 
 T.A. DOBROVOLSKAYA, V.M. EMELYANOV, S.A. DANILOVA, ET AL. J. NANO- ELECTRON. PHYS. 8, 03048 (2016) 
 
 
03048-2 

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3
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3
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Y
MENY9.2005
X
MENX42.401
1
Y
MENY9.2005
X
MEX42.401
:1R (2) 
 
 0 12.455609107R    
 
 0 3.5292505022R    
 
 1 13.3038634609R    
 
 0 3.647446156R    
 
Probability density for a point of intersection of el-
lipses of distribution of intensivnost of reradiation of 
the Raman ranges is specified in expressions (3-4): 
 
 
  
2
0R
5.02
3,3
e
8_0_9rXYAg1)2(
1
:0p





 

 
(3) 
 
  
2
1R
5.0
2
3,3
e
1rXY1)2(
1
:1p








 
(4)
 
 
р0  3.52510 – 4        р1  9.89210 – 4 
 
3. DESCRIPTION AND ANALYSIS OF RESULTS 
 
At vector-matrix modeling of analytical crossing of el-
lipses of distribution coordinates on 9 peaks are received. 
When comparing with experimental data when 
modeling with use of generation of multidimensional 
correlation dependences of coordinate of crossing of 
ellipses of distribution following: 
for cross polarization of X 
XEnT  (508.31   187.17   269.05   401.42   477.04 
551.12   670.90   334.39   712.03) 
     for longitudinal polarization of Y 
YEnT  (590.97   558.13   827.27   2005.9   2945.7   
1138.8   1318.1   133.93   166.18) 
Equivalent radius of ellipses when crossing for fiber 
without nanoparticles 
R0EnT  (2.281    2.829    2.417    3.529    2.399 
 2.714    2.453    2.578    3.436)   
and the equivalent radius of ellipses when crossing for  
fiber with nanoparticles 
R1EnT  (4.679    4.232    2.795    3.647    3.060    4.015    
2.704   5.646   2.774)    
At the choice of points of intersection of the ellipses 
of distribution constructed on population means, aver-
age quadratic deviations and correlation coefficients 
with selection of equivalent radius of ellipses of distri-
bution 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) 
for longitudinal polarization of Y 
YРnT  (486.00   373.44   770.96   2095.7   2731.2   
1059.1   1214.3   105.60   154.13)   
and the equivalent radius of curvature of ellipses 
when crossing  
RPnT  (2.636   1.463   2.538   3.584   2.40    3.335   
2.241   3.255   3.122).    
For a point of intersection of ellipses of distribution 
at the radius of R0En and R1En probability density on 
(3-4) are estimated 
p1T  (1.337∙10 – 5  3.17∙10 – 5 0.0105  9.89∙10 – 4 
7.99∙10 – 3 1.404∙10 – 4 0.0327  4.094∙10 – 8 7.36∙10 – 3) 
p0T  (0.0142  2.91∙10 – 3 8.95∙10 – 3 3.52∙10 – 4 
9.014∙10 – 3 4.73∙10 – 3 7.85∙10 – 3 5.758∙10 – 3 4.35∙10 – 4) 
Average values of density of probability on p1 and 
p0 will be 
pT  (7.107∙10 – 3  1.471∙10 – 3  9.725∙10 – 3 6.71∙10 – 4 
8.5∙10 – 3  2.43∙10 – 3  0.02  2.88∙10 – 3  3.897∙10 – 3). 
Probabilities of crossing of ellipses of distribution on 
peaks of ranges for nanofibre with nanoparticles 
Q1T  (0.99998  0.99997  0.98949  0.99901  0.99280  
0.99986  0.96727  0.99999  0.99263) 
and for fiber without nanoparticles 
Q0T  (0.98582  0.99708  0.99105  0.99965  0.99099  
0.99527  0.99215  0.99424  0.99956) 
Average values of probability of crossing of ellipses 
of distribution following: 
QT  (0.99290  0.99853  0.990275  0.99933  0.99154  
0.99756  0.97971  0.99712  0.99609) 
 
4. CONCLUSIONS  
 
In figure 1 the comparative analysis of increase of 
informational content of an assessment of reliability is 
submitted.  
At the same time in figure 1a, the continuous line 
has presented measurements at cross polarization of X 
with generation multidimensional correlation data; and 
dotted – in figure 1a – measurements in cross X and 
longitudinal Y directions taking into account coeffi-
cients of correlation and equivalent radius of an ellipse 
in a point of intersection of ellipses, in figure 1b –  
 
 
                                                  a 
 
                                                 b 
 
Fig. 1 – Increase of informational content of an assessment of 
reliability at application of two-dimensional measurement 
 ASSESSMENT OF RELIABILITY OF RECOGNITION OF NANOPARTICLES… J. NANO- ELECTRON. PHYS. 8, 03048 (2016) 
 
 
03048-3 
measurements in cross X and longitudinal Y directions 
taking into account coefficients of correlation and den-
sity of probability in a point of intersection. 
The analysis of results of research has shown that 
the offered method gives an essential prize in an as-
sessment of reliability of definition of the modes of 
drawing nanoparticles of silver on fibers. So, increase 
in reliability on equivalent radius произошдо by 1521 
times, and on probability density – by 1491 times. 
 
 
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Assessment of Reliability of Recognition of Nanoparticles of Silver on Polyester Fibers on Two-dimensional Models and Experimental Data of the Raman Ranges

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Assessment of Reliability of Recognition of Nanoparticles of Silver on Polyester Fibers on Two-dimensional Models and Experimental Data of the Raman Ranges

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SocioEconomic Challenges Journal (Sumy State University)