https://armjmath.sci.am/index.php/ajm/gateway/plugin/WebFeedGatewayPlugin/atomArmenian Journal of Mathematics2023-12-06T10:01:33+00:00Anry Nersessiannerses@instmath.sci.amOpen Journal Systems<p><strong>Editor in Chief - <a href="http://math.sci.am/user/anry-nersesyan">Anry Nersessian</a></strong> (Institute of Mathematics NAS, Armenia)</p> <p><strong> Deputy Editor - <a href="http://math.sci.am/user/rafayel-barkhudaryan">Rafayel Barkhudaryan</a></strong> (Institute of Mathematics NAS, Armenia)<strong><br /></strong></p> <p><strong>Managing Editor - <a href="http://math.sci.am/user/linda-khachatryan">Linda Khachatryan</a></strong> (Institute of Mathematics NAS, Armenia)<br />e-mail: <a href="mailto:ajm@instmath.sci.am">ajm@instmath.sci.am </a></p>https://armjmath.sci.am/index.php/ajm/article/view/1014Unit Group of the Group Algebra $\mathbb{F}_qGL(2,7)$2024-03-13T12:20:29+00:00Namatchivayam Umapathy SivaranjaniElumalai NandakumarGaurav MittalRajendra Kumar Sharma
<p>In this paper, we consider the general linear group $GL(2, 7)$ of $2 \times 2$ invertible matrices over the finite field of order $7$ and compute the unit group of the semisimple group algebra $\mathbb{F}_qGL(2,7)$, where $\mathbb{F}_q$ is a finite field. For the computation of the unit group, we need the Wedderburn decomposition of $\mathbb{F}_qGL(2,7)$, which is determined by first computing the Wedderburn decomposition of the group algebra $\mathbb{F}_q(PSL(3, 2)\rtimes C_2)$. Here $PSL(3,2)$ is the projective special linear group of degree 3 over a finite field of 2 elements.</p>
2024-03-13T00:00:00+00:00Copyright (c) 2024 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/1061Characterization of the Three-Variate Inverted Dirichlet Distributions2023-12-14T12:14:03+00:00Mohamed Ben Farah
<p>In this paper, we prove a characterization of three-variate inverted Dirichlet distributions by an independence property. The main technical challenge was a problem involving the solution of a related functional equation.</p>
2023-12-14T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/948A Combinatorial Interpretation of the Padovan Generalized Polynomial Sequence2023-11-28T12:18:03+00:00Renata Passos Machado VieiraFrancisco Regis Vieira AlvesPaula Maria Machado Cruz Catarino
<p>We investigate a combinatorial interpretation of the Padovan polynomial sequence, also addressing its polynomial extensions. We thus include the Tridovan polynomial sequence, Tetradovan polynomial sequences, leading up to the Z-dovan polynomial generalization.</p>
2023-11-28T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/908The Geometry of the Projective Action of $\text{SL}(3,\mathbb{R})$ from the Erlangen Perspective2024-01-11T13:23:27+00:00Debapriya BiswasIpsita Rajwar
<p>In this paper, we have investigated the projective action of the Lie group $\text{SL}(3,\mathbb{R})$ on the homogeneous space $\mathbb{RP}^2$. In particular, we have studied the action of the subgroups of $\text{SL}(3,\mathbb{R})$ on the non-degenerate conics in the space $\mathbb{RP}^2$. Using the Iwasawa decomposition of $\text{SL}(2,\mathbb{R})$, we demonstrate that the isotropy subgroup of the projective unit circle is isomorphic to $\text{PSL}(2,\mathbb{R})$ under certain conditions.</p>
2024-01-11T00:00:00+00:00Copyright (c) 2024 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/931On the Links between Miura Transformations of Bogoyavlensky Lattices and Inverse Spectral Problems for Band Operators2024-02-13T13:12:40+00:00Andrey Osipov
<p>We consider semi-infinite and finite Bogoyavlensky lattices<br />$$<br />\overset\cdot a_i =a_i\left(\prod_{j=1}^{p}a_{i+j}-\prod_{j=1}^{p}a_{i-j}\right),<br />$$<br />$$<br />\overset\cdot b_i = b_i\left(\sum_{j=1}^{p}<br />b_{i+j}-\sum_{j=1}^{p}b_{i-j}\right),<br />$$<br />for some $p\ge 1$, and Miura-like transformations between these systems, defined for $p\ge 2$. Both lattices are integrable (via Lax pair formalism) by the inverse spectral problem method for band operators, i.e., operators generated by band matrices. The key role in this method is played by the moments of the Weyl matrix of the corresponding band operator and their evolution in time. We find a description of the above-mentioned transformations in terms of these moments and apply this result to study finite Bogoyavlensky lattices and, in particular, their first integrals.</p>
2024-02-13T00:00:00+00:00Copyright (c) 2024 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/946On the Distance Spectrum and Distance-Based Topological Indices of Central Vertex-Edge Join of Three Graphs2023-10-10T13:21:27+00:00T. HarithaA.V. Chithra
<p>In this paper, we introduce a new graph operation based on a central graph called central vertex-edge join (denoted by $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$) and then determine the distance spectrum of $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$ in terms of the adjacency spectra of regular graphs $G_1$, $G_2$ and $G_3$ when $G_1$ is triangle-free. As a consequence of this result, we construct new families of non-D-cospectral D-equienergetic graphs. Moreover, we determine bounds for the distance spectral radius and distance energy of the central vertex-edge join of three regular graphs. In addition, we provide its results related to graph invariants like eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, Wiener index. Using these results, we calculate the topological indices of the organic compounds Methylcyclobutane $(C_5H_{10})$ and Spirohexane $(C_6H_{10})$.</p>
2023-10-10T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/826A Mesh-Free Algorithm to Solve an Inverse Source Problem for Degenerate Two-Dimensional Parabolic Equation from Final Observations2023-05-20T12:11:57+00:00Khalid Atifi
<p>The main purpose of this work is to propose a new network architecture model for deep learning applied to solve an inverse source problem for a two-dimensional degenerate parabolic equation from final observations with degeneracy occurring anywhere in the spatial domain.</p>
2023-05-20T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/793Nonlocal Solvability of the Cauchy Problem for a System with Negative Functions of the Variable $t$2023-03-22T13:14:27+00:00Marina Dontsova
<p>We obtain sufficient conditions for the existence and uniqueness of a local solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$ and show that the solution has the same $x$-smoothness as the initial function. We also obtain sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$.</p>
2023-03-22T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/900Optimality of the Least Sum of Logarithms in the Problem of Matching Map Recovery in the Presence of Noise and Outliers2023-03-30T06:01:35+00:00Tigran GalstyanArshak Minasyan
<p>We consider the problem of estimating the matching map between two sets of feature-vectors observed in a noisy environment and contaminated by outliers. It was already known in the literature that in the outlier-free setting, the least sum of squares (LSS) and the least sum of logarithms (LSL) are both minimax-rate-optimal. It has been recently proved that the optimality properties of the LSS continue to hold in the case the data sets contain outliers. In this work, we show that the same is true for the LSL as well. Therefore, LSL has the same desirable properties as the LSS, and, in addition, it is minimax-rate-optimal in the outlier-free setting with heteroscedastic noise.</p>
2023-03-30T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/854A Note on Location of the Zeros of Quaternionic Polynomials2023-04-27T13:30:45+00:00Irfan Ahmad WaniAdil Hussain
<p>The purpose of this paper is to investigate the extensions of the classical Eneström-Kakeya theorem and its various generalizations concerning the distribution of zeros of polynomials from the complex to the quaternionic setting. Using a maximum modulus theorem and the zero set structure in the recently published theory of regular functions and polynomials of a quaternionic variable, we construct new bounds of the Eneström-Kakeya type for the zeros of these polynomials. The obtained results for this subclass of polynomials and slice regular functions give generalizations of a number of results previously reported in the relevant literature.</p>
2023-04-27T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/763A New Family of Number Sequences: Leonardo-Alwyn Numbers2023-04-13T13:48:47+00:00Hasan Gökbaş
<p>In this study, we define a new type of number sequence called Leonardo-Alwyn sequence. We obtain the Binet formula, generating function and some relations for these numbers. Moreover, we give the matrix representation of the Leonardo-Alwyn numbers.</p>
2023-04-13T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/762On Non-Comaximal Graphs of Ideals of Commutative Rings2023-02-08T13:30:54+00:00Bikash BarmanKukil Kalpa Rajkhowa
<p>In this paper, we relate some properties of non-comaximal graph of ideals of a commutative ring with identity with the properties of the ring.</p>
2023-02-08T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/851Generalized Rational Evaluation Subgroups of the Inclusion between Complex Projective Spaces2023-09-05T13:11:42+00:00Jean-Baptiste Gatsinzi
<p>We use a model of mapping spaces to compute the generalized rational Gottlieb groups of the inclusion $i_{n,k}: \mathbb{C}P^n \hookrightarrow \mathbb{C}P^{n+k}$ between complex projective spaces.</p>
2023-09-05T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/803Acceleration of Convergence of Fourier Series Using the Phenomenon of Over-Convergence2022-12-12T07:26:07+00:00Anry Nersessian
<p>In recent publications of the author, the phenomenon of over-convergence was discovered, and a spectral method has been presented for accelerating the convergence of truncated Fourier series for smooth functions. On this basis, a certain parametric system that is biorthogonal to the corresponding segment of the Fourier system turned out to be unusually effective. This article reconsiders some approaches and makes some adjustments to previous publications. As a result, two improved schemes for the recovery of a function based on a finite set of its Fourier coefficients are proposed. Numerical experiments confirm a significant increase in the efficiency of corresponding algorithms in typical classes of smooth functions. In conclusion, some prospects for the development and generalization of the above approaches are discussed.</p>
2022-12-12T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/839Existence of Solutions for a Fractional Boundary Value Problem at Resonance2022-12-21T13:19:22+00:00Anabela S. Silva
<p>In this paper, we focus on the existence of solutions to a fractional boundary value problem at resonance. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin.</p>
2022-12-21T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/694Weak Type Estimate of Singular Integral Operators on Variable Weak Herz-Type Hardy Spaces2023-03-10T13:19:51+00:00Hamza Brahim BoularesDouadi DrihemWafa Hebbache
<p>This paper is concerned with the boundedness properties of singular integral operators on variable weak Herz spaces and variable weak Herz-type Hardy spaces. Allowing our parameters to vary from point to point will raise extra difficulties, which, in general, are overcome by imposing regularity assumptions on these exponents, either at the origin or at infinity. Our results cover the classical results on weak Herz-type Hardy spaces with fixed exponents.</p>
2023-03-10T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/817On the Minimal Annulus of Triangles and Parallelograms2023-01-26T13:43:39+00:00Salvatore Vassallo
<p>Sharp upper and lower bounds for the isoperimetric deficit of triangles or parallelograms with the minimal annulus of radii $R$ and $r$ are given.</p>
2023-01-26T00:00:00+00:00Copyright (c) 2023 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/632Bifurcation Analysis of a Piecewise Smooth Map with Two Asymptotes2022-10-02T10:58:34+00:00Roya Makrooni
<p>In this paper, we consider a discontinuous piecewise smooth system involving four parameters and two asymptotes, recently introduced as a model in engineering sciences. We classify and investigate its bifurcation behaviour. A local bifurcation analysis of the system in the range of parameters which has not been studied so far is undertaken and then supported by numerical computations. This reveals the existence of a flip bifurcation depends on the power singularity. Moreover, we state that a set of positive measure of points with divergent dynamic behaviour exists.</p>
2022-10-02T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/626Hypergeometric connections between balancing polynomials and Chebyshev polynomials of first and second kinds2022-09-23T13:52:07+00:00Adikanda BeheraPrasanta Kumar Ray
<p>In the present study, we find several connections between balancing polynomials and the Chebyshev polynomials of the first and second kinds. The Chebyshev polynomials of the first and second kinds are expressed as the sum of two terms of balancing polynomials with hypergeometric coefficients. As an inversion, the balancing polynomials are also expressed as the sum of two terms of the Chebyshev polynomials of the first kind and the Chebyshev polynomials of the second kind with hypergeometric coefficients.</p>
2022-09-23T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/659Geometry associated with the $\text{SL}(3,\mathbb{R})$ action on homogeneous space using the Erlangen program2022-08-16T19:36:01+00:00Debapriya BiswasIpsita Rajwar
<p>We investigate the action of the Lie group $\text{SL}(3,\mathbb{R})$ on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of $\text{SL}(3,\mathbb{R})$ are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points.</p>
2022-08-16T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/651Generalization of an Eneström-Kakeya type theorem to the quaternions2022-06-29T13:26:56+00:00Robert B. GardnerMariah Taylor
<p>The well-known Eneström-Kakeya theorem states that polynomial $p(z)=\sum_{\nu =0}^n a_\nu z^\nu$, where $0\leq a_0\leq a_1\leq \cdots\leq a_n$, has all of its (complex) zeros in $|z|\leq 1$. Many generalizations of this result exist in the literature. In this paper, we extend one such result to the quaternionic setting and state one of the possible corollaries.</p>
2022-06-29T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/718Groups whose derived subgroup is not supplemented by any proper subgroup2022-07-08T11:26:55+00:00Shiv NarainSunil KumarGaurav MittalSandeep Kumar
<p>In this paper, we introduce two new classes of groups that are described as weakly nilpotent and weakly solvable groups. A group $G$ is weakly nilpotent if its derived subgroup does not have a supplement except $G$ and a group $G$ is weakly solvable if its derived subgroup does not have a normal supplement except $G$. We present some examples and counter-examples for these groups and characterize a finitely generated weakly nilpotent group. Moreover, we characterize the nilpotent and solvable groups in terms of weakly nilpotent and weakly solvable groups. Finally, we prove that if $F$ is a free group of rank $n$ such that every normal subgroup of $F$ has rank $n$, then $F$ is weakly solvable.</p>
2022-07-08T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/715On the invertibility of one integral operator2022-04-30T07:45:17+00:00Grigor Kirakosyan
<p>The present paper considers an integral operator defined on the entire real axis, which differs from the Hilbert transform with terms where kernels are constructed using integral exponential functions. The considered operator has similar properties with respect to the Hilbert transform. The form of the inverse operator is obtained.</p>
2022-04-30T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/666Description of random fields by systems of conditional distributions2022-06-03T12:48:00+00:00Linda Khachatryan
<p>In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions. In the majority of cases, we provide necessary and sufficient conditions for the system to be a conditional distribution of a (unique) random field. The exception is Dobrushin-type systems for which only sufficient conditions are known. Also, we discuss possible applications of the considered systems.</p>
2022-06-03T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/628A generalization of connectedness via ideals2022-05-13T13:57:01+00:00Raúl Pachón
<p>In this paper, we define and study the $\diamond$-connected spaces as a generalization of the connectedness, and thus of the Ekici-Noiri and Modak-Noiri notions, through ideals.</p>
2022-05-13T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/576Evaluation subgroups of a map and the rationalized $G$-sequence2023-09-16T08:18:51+00:00Oteng Maphane
<p>In this paper, we determine, in terms of the Sullivan models, rational evaluation subgroups of the inclusion $ \mathbb{C} P(n)\hookrightarrow \mathbb{C} P(n+k) $ between complex projective spaces and, more generally, the $ G $-sequence of the homotopy monomorphism $ \iota: X\hookrightarrow Y $ between simply connected formal homogeneous spaces for which $ \pi_{\ast}(Y)\otimes \mathbb{Q}$ is finite-dimensional.</p> <p> </p> <p><strong>Editorial Board's note.</strong><em> We inform our readers that J.-B. Gatsinzi mentions in his work, published in Armen. J. Math. <a href="https://doi.org/10.52737/18291163-2023.15.9-1-6">vol. 15, no. 9, 2023</a>, that O. Maphane's paper contains a mistake. According to Gatsinzi, his Corollary 1 corrects Theorem 2.2 of the current paper. We contacted Maphane on this issue, and he agreed with Gatzinzi's statement.</em></p>
2023-09-16T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/525Exponential decay for a strain gradient porous thermoelasticity with second sound2022-03-03T07:29:18+00:00Afaf AhmimaAbdelfeteh Fareh
<p>In this paper, we consider a strain gradient porous elastic bar subjected to a thermal disturbance modelled by Cattaneo's law for heat conduction. We use the semigroup approach to prove the existence of a unique weak solution. Although the thermal dissipation induced by the second sound thermoelasticity is weaker than that caused by the classical heat conduction, we prove that the solution decays exponentially.</p>
2022-03-03T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/611Annular region containing all the zeros of lacunary-type polynomials2022-03-04T13:39:24+00:00Ashish KumarZahid ManzoorBashir Ahmad Zargar
<p>In this paper, we find the annular region containing all the zeros of lacunary-type polynomials, whose coefficients are subjected to certain restrictions.</p>
2022-03-04T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/592Controlled generalized fusion frame in the tensor product of Hilbert spaces2021-12-28T11:28:50+00:00Prasenjit GhoshTapas Kumar Samanta
<p>We present controlled by operators generalized fusion frame in the tensor product of Hilbert spaces and discuss some of its properties. We also describe the frame operator for a pair of controlled $g$-fusion Bessel sequences in the tensor product of Hilbert spaces.</p>
2021-12-28T00:00:00+00:00Copyright (c) 2021 Armenian Journal of Mathematicshttps://armjmath.sci.am/index.php/ajm/article/view/596Integral representation of one class of entire functions2022-02-10T09:44:13+00:00Ruslan Khats'
<p>In this paper, we study an integral representation of one class of entire functions. Conditions for the existence of this representation in terms of certain solutions of some differential equations are found. We obtain asymptotic estimates of entire functions from the considered class of functions. We also give examples of entire functions from this class.</p>
2022-02-10T00:00:00+00:00Copyright (c) 2022 Armenian Journal of Mathematics