Speaker
Description
Method for processing and analysis of homogeneity of large sets of small-volume samples of low-intensity radiation streams.
Rabotkin V. A., Bliznyakov N.M., Vakhtel V.M., Kostomakha D.E.
Voronezh State University, Voronezh, Russia
E-mail: vakhtel@phys.vsu.ru
A method for processing and analyzing sequences of samples of variation series of values of identifiers I(ν(.)) of random vectors (RV) - ν for their corresponding samples of small volume n≤20 of counts k_i=0;1;2… of registered particles was proposed. The identifier I(ν(.)) is a functional in the form of a scalar product RV ν(.)=〖(ν〗0,ν_1,…,ν_l) of frequencies ν_i (k=i) of values of counts k_i in the sample
∑_0^l▒〖ν_i=n<20: I(ν)=I(ν|a)=(νa)=ν_0 a_0+⋯+〗 ν_l a_l
where a=〖(a〗_0,…,a_l) – is not a randomly given vector. For a given number M of vectors ν(.) the frequency distribution of I(ν) values represents sequences of ordered groups of peaks formed by:
similar in components ν_i RV
of homogeneous peaks formed by homogeneous RVs.
To evaluate the homogeneity of RV and peaks, it was proposed a test statistic G and a criterion of agreement based on the metric
G=1/q [∑(l=1)^l▒〖[(x_im-x_ir )/(x_im+x_ir )^2]〗]^(1/2),0≤G≤1.
It was shown that the homogeneity estimation of peaks considered also as random vectors m and rM_(1,m),M_(2,m),…,M_(l,m);M_(1,r),M_(2,r),…,M_(l,r) can be performed by the degree of their collinearity |M_m | |M_l |^(-1)∙M_m∙M_l=cosθ, where θ-is the angle between vectors and equality of |M_m |=|M_r | modules.
The proposed method allows identifying combinatorial types of RV, predicting frequencies of their realization 1<M_j and peaks formed by them - also random vectors M_jm,…,M_qmwith
∑l^q▒〖M(j,m)<10.〗
The method is effective at n<20; average k ̅<5.
References
BliznyakovN.M., VakhtelV.M., KostomakhaD.E., RabotkinV.A. VoronezhWinterMathematicalSchool. Voronezh: -VSU PublishingHouse 2022. p. 27-33.
| The speaker is a student or young scientist | No |
|---|---|
| Section | 6. Applications of nuclear methods in science and technology |
