Proceedings of the YSU A: Physical and Mathematical Sciences
Proceedings of the YSU A: Physical and Mathematical Sciences aims to publish original research papers and survey articles in all areas of physics, mathematics and informatics. Proc. YSU A: Phys. Math. Sci. accepts also review articles, short communications, conference proceedings, algorithms, Ph.D and doctoral thesis’s and other items with a detailed exposition of results, proofs, experiments and examples. One of purposes is to reflect the progress of the research in all areas of physics, mathematics and informatics in Armenia and, by providing an international forum, to stimulate its further developments.
LOADS TRANSFER FROM THE SYSTEMS OF FINITE NUMBER FINITE-LENGTH STRINGERS TO AN INFINITE SHEET THROUGH ADHESIVE LAYERS
The article considers the problem for an elastic infinite plate (sheet), which along of two parallel lines of its upper surface is strengthened by systems of finite number finite-lenght stringers having different elastic properties. The interaction between infinite sheet and stringers take place through thin, uniform, elastic adhesive layers having other physical-mechanical properties and geometric configuration. The stringers are deformed under the action of horizontal concentrated forces, which are applied at one end points of stringers. The problem of determining unknown contact forces acting between infinite sheet and stringers is reduced to the system of Fredholm integral equations of second kind with respect to arbitrary finite number of unknown functions, which are specified along of two parallel lines on different finite intervals. Further, are determined of the change regions of the problem characteristic parameters, for which this system of integral equations allows the exact solution and which can be solved by the method of successive approximations. Some particular cases are considered and the character and behavior of unknown shear contact forces near the end points of the stringers are investigated. For these cases numerical results depending on the multiparameters of the problem are investigated in the previous article (A.V. Kerobyan, K.P. Sahakyan, Proc. YSU. Phys. Math. Sci. 57 (3) (2023), 86--100).
Copyright (c) 2025 Proceedings of the YSU https://creativecommons.org/licenses/by-nc/4.0/
STUDY OF $\mathrm{PbWO}_4$ CRYSTAL FOR ePIC EmCal PROTOTYPE
The study presents the characterization of $\mathrm{PbWO}_4$ crystals intended for the prototype of the EmCal electromagnetic calorimeter of the ePIC detector, which is being constructed at the Electron-Ion Collider in the Brookhaven National Laboratory at the USA. Measurements were performed on 20 crystals produced by "Crytur" company, each of which was then thoroughly examined under a microscope. Transversal transparency measurements were made at the center of the crystals, as well as at several fixed points equidistant from the center to the right and left sides to study uniformity. The average transparency of the crystals is 21.3%, 65.6%, and 71.7% for wavelengths of 360 nm, 440 nm, and 600 nm, respectively. The transmittance measurements repeated 10 times in the center of each crystal show that accuracy of our measurement is better than 10%. The light yield of $\mathrm{PbWO}_4$ was estimated to be an average 16 pe/MeV. The optical characteristics of Crytur crystals meet the requirements of the EIC electromagnetic calorimeter. After performing all the necessary measurements, 16 crystals in good condition were selected for the calorimeter prototype. A 4$\times$4 prototype of EmCal was designed, constructed and tested with cosmic muons.
ON A RESULT CONCERNING ALGEBRAIC CURVES PASSING THROUGH n-INDEPENDENT NODES
Let a set of nodes $\mathcal X$ in the plane be $n$-independent, i.e. each node has a fundamental polynomial of degree $n.$ Assume that $\#\mathcal X=d(n,n-3)+3= (n+1)+n+\cdots+5+3.$ In this paper we prove that there are at most three linearly independent curves of degree less than or equal to $n-1$ that pass through all the nodes of $\mathcal X.$ We provide a characterization of the case when there are exactly three such curves. Namely, we prove that then the set $\mathcal X$ has a very special construction: either all its nodes belong to a curve of degree $n-2,$ or all its nodes but three belong to a (maximal) curve of degree $n-3.$ This result complements a result established recently by H. Kloyan, D. Voskanyan, and H. Hakopian. Note that the proofs of the two results are completely different.
Copyright (c) 2022 Proceedings of the YSU https://creativecommons.org/licenses/by-nc/4.0/
FINITE-DIFFRENCE STOCHASTIC SCHEMES FOR MINIMIZING A STRONGLY QUASICONVEX NON-DIFFERENTIABLE FUNCTION ON $\mathbb{R}^n$: THE NURMINSKII METHOD
In this work, stochastic approximation methods based on finite differences are investigated for the problem of minimizing quasiconvex functions. The main result of this work is the derivation of convergence rate estimates for stochastic finite-difference methods in the case of quasiconvex functions. The obtained results significantly extend the applicability of stochastic finite-difference methods to nonsmooth quasiconvex optimization problems and provide a rigorous justification for their use in black-box settings where the oracle returns only function values.
Copyright (c) 2026 Proceedings of the YSU https://creativecommons.org/licenses/by-nc/4.0/
ADHESIVE CONTACT PROBLEM FOR AN INFINITE SHEET STRENGTHENED BY THREE PARALLEL FINITE-LENGTH STRINGERS
The article considers the problem for an elastic infinite sheet, which along of three parallel lines of its upper surface is strengthened by three parallel finite-length stringers having different elastic properties. The interaction between infinite sheet and three parallel stringers takes place through thin elastic adhesive layers having other physical-mechanical properties and geometric configuration. The stringers are deformed under the action of horizontal concentrated forces, which are applied at one end points of the stringers. The problem of determining the law of distribution of unknown contact forces acting between infinite sheet and stringers is reduced to the system of Fredholm integral equations of second kind with respect to three unknown functions, which are specified on three parallel finite intervals. Further, are determined of the change regions of the problem characteristic parameters, for which this system of integral equations allows the exact solutions and which can be solved by the method of successive approximations. Some special cases are considered and the character and behavior of unknown shear forces near the end points of the stringers are investigated. For these cases numerical results depending on the multiparameters of the problem are investigated in the article by A.V. Kerobyan and K.P. Sahakyan (Proc. YSU. Phys. Math. Sci., 57 (3) (2023), 86-100).
HERMITE MULTIVARIATE INTERPOLATION FORMULA
We present a new formula for the Hermite multivariate interpolation problem in the framework of the Chung--Yao approach.
KNOWLEDGE-DISTILLED VARIATIONAL BAYESIAN FRAMEWORK FOR EFFICIENT LARGE-SCALE IMAGE DEHAZING
Real-time processing of large-scale image databases with state-of-the-art dehazing methods presents a significant computational challenge: methods that achieve superior generalization typically require substantial inference time, limiting their deployment in real-time applications. High-performing methods employ complex multi-scale processing and deep architectures, typically achievin less than 5 FPS on high-resolution images. Building on the preliminary multi-scale variational Bayesian framework [1, 2], which achieves strong synthetic-to-real generalization, this paper proposes knowledge distillation to transfer the generalization capabilities of high-performance models to a lightweight Vision Transformer-based student network. The student leverages patch-based processing and reduced architectural complexity to achieve over $150\times$ speedup, while maintaining competitive performance through a theoretically-grounded distillation framework integrated into the variational Bayesian objective. Additionally, the atmospheric scattering model is extended to estimate space-variant atmospheric light, improving performance on varying haze regions. Trained solely on synthetic Haze4K data, the proposed method stays competitive on synthetic-to-real generalization and downstream object detection (on the augmented KITTI dataset) tasks, while achieving superior inference speed for large-scale real-world applications.
OPERATIONAL ENVIRONMENT FOR DYNAMIC LOADING AND MANAGEMENT OF MODULAR APPLICATIONS IN EMBEDDED SYSTEMS
Ensuring modularity under strict resource constraints is a critical challenge in the design of embedded systems. This paper presents "Part Only RTOS", an operational environment developed for devices based on 8-bit ATmega2560 microcontrollers. The core feature of the proposed system is the ability to dynamically load and execute application modules (in .bin format) from an SD card without requiring full hardware reprogramming. The developed three-tier architecture, comprising the Launcher, Bootloader, and Kernel, ensures reliable software validation via unique pattern matching and efficient memory utilisation. Experimental results demonstrate that the system kernel occupies less than $2.5~KB$ of Flash memory, and the loading time for a 10 KB module is approximately 132 ms. This solution enables the creation of flexible and high-performance modular embedded systems on low-power microcontroller platforms.
ON SUM EDGE-COLORINGS OF SOME REGULAR GRAPHS
A sum edge-coloring of a graph is an assignment of positive integers to the edges of the graph, so that adjacent edges correspond to different numbers (colors) and the sum of the numbers on all the edges is minimum possible. This minimum possible sum is called the edge-chromatic sum of the graph, and the minimal number of colors needed for a sum edge-coloring is called the edge-strength of the graph. In this paper, we give the exact values of the edge-chromatic sums and edge-strengths for cycle powers and generalized cycles.
NEAR-INTERVAL EDGE-COLORINGS OF COMPLETE BIPARTITE GRAPHS
A proper edge-coloring of a graph $G$ is a mapping $\alpha:E(G)\longrightarrow \mathbb{N}$ such that $\alpha(e)\not=\alpha(e')$ for every pair of adjacent edges $e$ and $e'$ in $G$. If $\alpha $ is a proper edge-coloring of $G$ and $v\in V(G)$, then $S_{G}\left(v,\alpha \right)$ denotes the set of colors appearing on edges incident to $v$. A proper edge-coloring $\alpha$ of a graph $G$ with colors $1,\ldots,t$ is called a near-interval $t$-coloring if all colors are used, and for each vertex $v\in V(G)$, $S_G(v,\alpha)$ is an interval of integers with no more than one gap. If a graph $G$ has such a coloring, the minimum number of colors in a near-interval coloring of a graph $G$ is denoted by $w^{1}(G)$. It is known that all complete bipartite graphs admit near-interval colorings. In this paper, we determine or bound the parameter $w^{1}(K_{m,n})$ ($m,n\in\mathbb{N}$) for complete bipartite graphs.
ON DEFICIENCY OF COMPLETE 3-PARTITE AND 4-PARTITE GRAPHS
A proper t-edge-coloring of a graph G is a mapping $\alpha: E(G)\rightarrow \{1,\ldots,t\}$ such that all colors are used, and $\alpha(e)\neq \alpha(e^{\prime})$ for every pair of adjacent edges $e,e^{\prime}\in E(G)$. If $\alpha $ is a proper edge-coloring of a graph G and $v\in V(G)$, then the spectrum of a vertex v, denoted by $S\left(v,\alpha \right)$, is the set of all colors appearing on edges incident to v. The deficiency of $\alpha$ at vertex $v\in V(G)$, denoted by $\mathrm{def}(v,\alpha)$, is the minimum number of integers that must be added to $S\left(v,\alpha \right)$ to form an interval, and the deficiency $\mathrm{def}\left(G,\alpha\right)$ of a proper edge-coloring $\alpha$ of G is defined as the sum $\displaystyle\sum_{v\in V(G)}\mathrm{def}(v,\alpha)$. The deficiency of a graph G, denoted by $\mathrm{def}(G)$, is defined as follows: $\mathrm{def}(G)=\min_{\alpha}\mathrm{def}\left(G,\alpha\right)$, where the minimum is taken over all possible proper edge-colorings of G. In 2019, Davtyan, Minasyan, and Petrosyan provided an upper bound on the deficiency of complete multipartite graphs. In this paper, we improve this bound for complete tripartite and some complete 4-partite graphs. We also confirm the conjecture that states the deficiency of a graph is bounded by the number of vertices of the graph for all tripartite graphs containing up to 10 vertices.
ON SUM EDGE-COLORINGS OF COMPLETE TRIPARTITE GRAPHS
A proper edge-coloring of a graph is called a sum edge-coloring if it minimizes the total sum of colors on all the edges of the graph. The aforementioned minimal sum is called the edge-chromatic sum of the graph, and the minimal number of colors needed for a sum edge-coloring is called the edge-strength of the graph. In this paper, upper bounds on the values of the edge-chromatic sums of some complete tripartite graphs are given, while for some other complete tripartite graphs, the exact values of both parameters are obtained.
ON THE CALCULATION OF THE COEFFICIENTS OF CUBIC SPLINES ON A SET OF EQUIDISTANT KNOTS
As is known, the coefficients of the interpolation cubic spline are found by solving a tridiagonal system of linear algebraic equations of a special type. To solve the system, a well-known numerical algorithm is usually used. In this paper, an alternative method for finding the coefficients of a natural cubic spline on a uniform set of knots is proposed. The method is based on the analytical inversion of the tridiagonal matrix, which made it possible to obtain closed-form expressions for the coefficients. This approach allows us both identify the analytical dependence of the spline coefficients on its values at the knots and obtain simple formulas for calculating these coefficients, by passing the solution of the system.
THE ANALYSIS OF VIBRATIONS OF CURVILINEAR TETRAGON WITH RECTILINEAR ANISOTROPY
The behaviour of frequencies of vibrations of curvilinear tetragon with a rectilinear anisotropy is investigated.
Copyright (c) 2001 Proceedings of the YSU https://creativecommons.org/licenses/by-nc/4.0/
ON THE REPRESENTATION OF FUNCTIONS BY SERIES OFLEGANDRE POLYNOMIALS IN WEIGHTED $ L_\mu ^q[-1, 1]$ SPACES
In this paper we construct the weighted $L_\mu ^q[-1, 1], q \in[1, 4/3]\cup [4, +\infty],$ and Legander series $\sum \limits_{k=1} ^\infty c_pP_k(x)$, which is universal in $L_\mu ^q [-1, 1]$.
EINSTEIN REPRESENTATION OF TENSOR-SCALAR THEORIES OF GRAVITATION
In this paper considerations on conformal transformations of tensor-scalar theory are represented. It is shown that under certain conditions conformal transformed theory of Jordan–Brans–Dicke is equivalent to Einstein theory with a minimally bounded scalar field source.
ON VIBRATIONS OF ELECTROCONDUCTIVE PLATE IN LONGITUDINAL MAGNETIC FIELD
The problem of vibrations of transversal-isotropic electroconductive plate in view of transversal shear strains and induced electromagnetic field at presence of constant longitudinal magnetic field is investigated.
NEW REPRESENTATION OF SLOWLY VARYING FUNCTIONS
For a slowly varying function $L(t)$ a new integral representation is obtained: $$L(t) = \mu(t)\int\limits_t_0 ^t b(x)d\ln x, t\geq t_0> 0, $$ where $\mu(t)$ is measurable on $[t_0, +\infty), b(t)$ is continuous on $[t_0, +\infty)$ and $\lim \limits_{t\ringrow + \infty}(b(t) / L(t))= 0.$ This representation allows to generalize D.D. Adamovich’s classical result on equivalent slowly varying functions and to extend the statement of A. A. Goldberg theorem.
TUNING OF LOCAL MULTICOMPUTERS TO SPECIFIC TASKS
The problem of tuning of computer systems to specific tasks is considered. A review of existing tools that provide tuning on different levels for a specific class of computer systems named local area multicomputers is presented. A comparative analysis of considered tools is given according to their functional characteristics.
TENDENCIES OF THE Mr|Gr|1|∞ MODEL’S STUDY
The article is a short review of a queuing model Mr|Gr|1|∞. First of all, methods for analysis of the Mr|Gr|1|∞ model’s characteristics with classic disciplines such as pre-emptive, head-of-the-line and alternating priorities are presented. A transition to analysis of parametric disciplines and further to class of conservative disciplines is justified and implemented. Special attention is paid to conditions for existence of stationary distributions and preservation laws. Particularly, two new preservation laws for stationary distributions of queue lengths are established. The range of optimization problems for the class of conservative disciplines and some of its subclasses are presented. Directions of asymptotic analysis under different traffic intensities are described. A new result for stationary waiting time distributions in terms of Laplace-Stilties transform is formulated in case of Kleinrock’s parametric discipline.
EQUIVARIANT GENERALIZATION OF FREUDENTHAL’S THEOREM. EQUIVARIANT n-MOBILITY
In the given paper the equivariant analogue of Freudenthal’s theorem in finite G-group is proved, which allows to generalize some results attained by Bogaty on n-mobility of topological distance.
INTEKSUBBAND ABSORPTION OF X-POLARIZED LIGHT IN QUANTUM WELL WITH DOUBLE δ-LIKE BARRIERS
The phenomenon of intersubband absorption of x-polarized light in quantum well with double δ-like barriers, caused by the electron effective mass coordinate dependence is considered. Analytical expressions for the oscillator strength for intersubband transitions and quantum efficiency of the optical absorption of photons under the enfluence of x-polarized light are obtained. It is shown that the absorption decreases with the increase of the opacity of surrounding δ-like barriers.
ON FACTORIZATION IN THE PROBLEM OF DIFFRACTION OF HARMONIC WAVE ON ELASTIC HALF INFINITE INCLUSION
The paper is devoted to the factorization of stress strain state of elastic space including half infinitive inclusion. Supposing that elastic inclusion is too thin the problem is reduced to the solution of boundary problem of harmonic wave diffraction on the half infinitive interval. Using the method of Wiener-Hopf and circulant method the boundary problem is reduced to the Wiener-Hopf matrix equation, which is completely solved. This solution allows to get analytical solution of the boundary problem.
STABILITY OF SYSTEMS WITH RETARDATION IN THE CASE OF SMALL INTEGRAL PERTURBATIONS
The paper considers the problem of stability of nonlinear differential equations systems with retardation when small integral perturbations effect the system in finite interval of time. Sufficient conditions are obtained, under which such systems are stable according to the acting force.
ON SOME SYSTEM OF PROPOSITIONAL LOGICS CALCULUS
In this paper generalizations of "modus ponens" rules are defined on the basis of which a certain system of propositional logics calculus is constructed to which both the Frege systems and the Frege systems with substitutions are polynomially brought.
FLOKE-LIAPUNOV'S THEOREM FOR DIRAC'S TWO-PARAMETER SYSTEM WITH PERIODICAL COEFFICIENTS
In this work matriciant, matrix of monodromy are defined, their properties are considered and Floke–Liapunov's theorem is proved for Dirac's two-parameter system with periodical coefficients.
This paper investigates the convolution polynomials and identities of vector spaces on the field. These results are based on tensor convolutions.
Let $0<t_0<t_1<...,\lim\limits_{n\rightarrow +\infty}t_n=+\infty, \sup\limits_{n}(t_{n+1}-t-n)<+\infty.$ For an upward convex slowly varying function $L(t)>0$ an equivalent slowly varying function $L_1(t)$ has been constructed that is convex, infinitely differentiable, and that coincides with $L(t)>0$ on a beforehand given numerical sequence ${t_n}$.
ON BOUNDARY CONDITION BY DIFFRACTION OF HARMONIC WAVE ON THE INFINITE INCLUSION
In the given article the jump type boundary condition is proved, which was considered in a boundary problem discussed in [1], connected with a harmonic wave diffraction on the half-infinite inclusion.
POLARIZATION FUNCTIONS OF NATURAL GYROTROPIC MEDIA EXISTING IN EXTERNAL MAGNETIC FIELD
The propagation of electromagnetic waves through a layer of naturally gyrotropic media in an external magnetic field is considered. The problem is solved by a method $4\times 4$ matrix of Beremann. The Jones matrixes are constructed; the reflection and transmission coefficients, the polarization azimuth and ellipticity of a passing wave are calculated. The specific features of polarization functions of own modes, eigen polarizations and polarization functions of an incident wave at which one of the own modes is not exited are investigated. It is shown, that in these media under certain conditions three own modes are excited.´