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N. V. Arakelyan, Yu. A. Kutoyants,

On the identification of the source of emission on the plane | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(75-81)
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We consider the problem of identification of the position and the moment of the beginning of a radioactive source emission on the plane. The acts of emission constitute inhomogeneous Poisson processes and are registered by K
detectors on the plane. We suppose that the moments of arriving of the signals at the detectors are measured with some small errors. Then, using these estimate, we construct the estimators of the position of source and the moment of the
beginning of emission. We study the asymptotic properties of these estimators for large signals and prove their consistency.

 

 

MSC2010: 62M02, 62G10, 62G20.

 


Keywords: inhomogeneous Poisson process, parameter estimation, localization on the plane.

 

Narek V. Arakelyan    araqelyannarek@gmail.com                                                    

 

Yuri A. Kutoyants      kutoyants@univ-lemans.fr 

 

T. A. Grigoryan,

Some results on regular expressions for multitape finite automata | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(82-90)
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We consider sets of word tuples accepted by multitape finite automata. We use the known notation for regular expressions that describes languages accepted by one-tape automata. Nevertheless, the interpretation of the “concatenation" operation is different in this case. The algebra of events for multitape finite automata is defined in the same way as for one-tape automata. It is shown that the introduced algebra is a Kleene algebra. It is also, shown that some known results for the algebra of events accepted by one-tape finite automata are valid in this case too.

 


MSC2010: 68Q45


Keywords: regular expressions, algebra of events, multitape finite automata.

 

 

Tigran A. Grigoryan               tigran.grigoryan1995@gmail.com 

H. A. Hakopian , H. M. Kloyan ,

On the dimension of spaces of algebraic curves passing through n-independent nodes | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(91-100)
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Let the set of nodes X in the plain be n-independent, i.e., each node has a fundamental polynomial of degree n: Suppose also that |X|=(n+1)+n+···+(n-k+4)+2 and 3≤k≤ n-1: We prove that there can be at most 4 linearly independent curves of degree less than or equal to k passing through all the nodes of |X|. We provide a characterization of the case when there are exactly 4 such curves. Namely, we prove that then the set X has a very special construction: all its nodes but two belong to a (maximal) curve of degree k-2: At the end, an important application to the Gasca-Maeztu conjecture is provided.

 

MSC2010: 14H50, 41A05, 41A63.


Keywords: algebraic curves, n-independent nodes, maximal curves, Gasca-Maeztu conjecture.

 

 

Hakop A. Hakopian               hakop@ysu.am 

 

Harutyun M. Kloyan            arutkloyan@gmail.com 

G. L. Adamyan , V. K. Ohanyan ,

Covariogram of a right parallelepiped | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(101-108)
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In this paper we obtain explicit expressions for the covariogram and the orientation-dependent chord length distribution of a right parallelepiped with square base.

 


MSC2010: 60D05, 52A22, 53C65.


Keywords: orientation dependent chord length distribution, convex body.

 

 

Viktor K. Ohanyan                          victoohanyan@ysu.am 

 

Garik L. Adamyan                          garikadamyan97@gmail.com 

 

 

This work of the first author was supported by SCS of MES RA, in the frame of the research project no. 18T-1A252.

A. V. Kerobyan,

Transfer of loads from a finite number of elastic overlays with finite lengths to an elastic strip through adhesive shear layers | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(109-118)
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This article deals with the problem of an elastic infinite strip, which is strengthened along its free boundary by a finite number of finite overlays with different elastic characteristics and small constant thicknesses. The interaction between the strip and the overlays is mediated by adhesive shear layers. The overlays are deformed under the action of horizontal forces. The problem of determination of unknown stresses acting between the strip and overlays are reduced to a system of Fredholm integral equations of the second kind for a finite number of unknown functions defined on different finite intervals. It is shown that in the certain domain of variation of the characteristic parameter of the problem this system of integral equations in Banach space may be solved by the method of successive approximations. Particular cases are discussed and the character and behaviour of unknown shear stresses are investigated.

 


MSC2010: 74M15.


Keywords: contact, overlays (stringers), elastic infinite strip, adhesive shear layer, system of integral equations, operator equation.

 

Aghasi V. Kerobyan                         agas50@ysu.am 

V. P. Gabriyelyan,

On a linearized coverings of a cubic homogeneous equation over a finite field. Lower bounds | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(119-126)
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We obtain lower bounds for the complexity of linearized coverings for some sets of special solutions of the equation          x1x2x3+x2x3x4+⋅⋅⋅+x3nx1x2+x1x3x5+x4x6x8+⋅⋅⋅+x3n-2x3nx2=b over an arbitrary finite field.

 


MSC2010: Primary 97H60; Secondary 14N20, 51E21.


Keywords: linear algebra, finite field, coset of linear subspace, linearized covering.

 

 

Varouzhan P. Gabriyelyan                    var.gabrielyan@ysu.am

Ed. V. Yeghiazaryan,

Asymptotic estimates of the number of solutions of systems of equations with determinable partial Boolean functions | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(127-131)
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In this paper we investigate a class of equation systems with determinable partial (not everywhere defined) Boolean functions. We found the asymptotic estimate of the number of solutions of equation systems in the “typical” case (for the whole range of changes in the number of equations).

 


MSC2010: Primary 06E30; Secondary 94C10.


Keywords: Boolean equations, solution of equation, partial Boolean functions.

 

 

Eduard V. Yeghiazaryan                   e.yeghiazaryan@ysu.am 

A. Zh. Babajanyan , L. A. Odabashyan , D. S. Hambaryan, B. A. Hovhannisyan,

Real-time sensing the glucose concentration by quadratic-shaped microwave sensor | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(132-137)
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In this study we present a microwave sensor based on the quadratic-shape and designed for detecting glucose concentration in aqueous solutions by using a microwave near-field electromagnetic interaction technique. We found a linear relationship between the microwave S11 reflection coefficient of the suggested system and the concentration of glucose in solution. Due to this linear relationship we were able to determine the glucose concentration in the range of 0–250 mg/dL at an operating frequency near 3.6 GHz. The measured minimum detectable signal was 0,0044 dB/(mg/dL) and the measured minimum detectable concentration was 6.8 mg/dL. These results suggest that the
system we offer has a high enough accuracy for non-contact glucose monitoring and provides a promising basis for developing a non-invasive glucometer.

 

MSC2010: Primary 00A79; Secondary 74M05.


Keywords: quadratic resonator, microwave sensor, glucose concentration.

 

Babken A. Hovhannisyan                 babken.hovhannisyan.96@gmail.com 

 

David S. Hambaryan                       davidhambaryanysu@gmail.com 

 

Levon A. Odabashyan                     levonodabashyan@mail.ru  

 

Arsen Zh. Babajanyan                     barsen@ysu.am 

 

This work was supported by SCS of MES RA, in the frame of the research project no. 18T -1C114.

M. A. Davtyan, R. G. Petrosyan,

Invariant solution of the Dirac equation in crossed electric and magnetic fields (H > E) | Proceedings of the YSU: Physical and Mathematical Sciences 2019 #53(138-141)
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In the article exact analytical and invariant solutions for both spinless and half-spin relativistic charged particles in crossed constant electric and magnetic fields, when H > E have been found. It is shown that in both cases the problem reduces to that of quantum harmonic oscillator.

 


MSC2010: 81V10.


Keywords: invariant solution, crossed electric and magnetic fields, Klein–Gordon equation, Dirac equation.

 

 

Rubik G. Petrosyan

 

Mher A. Davtyan                                   mher.davtyan@ysumail.am