eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 1 9 article M. Rossafi rossafimohamed@gmail.com 1 S. Kabbaj samkabbaj@yahoo.fr 2 LaSMA Laboratory Department of Mathematics Faculty of Sciences, Dhar El Mahraz University Sidi Mohamed Ben Abdellah, B. P. 1796 Fes Atlas, Morocco Laboratory of Partial Differential Equations, Spectral Algebra and Geometry Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco Frames play significant role in various areas of science and engineering. Motivated by the work of Chander Shekhar, S. K. Kaushik and Abas Askarizadeh, Mohammad Ali Dehghan, we introduce the concepts of $K$-frames for $B(mathcal{H, K})$ and  we establish some result. Also, we consider the relationships between $K$-Frames and $K$-Operator Frames for $B(mathcal{H})$. http://ijmsi.ir/article-1-1315-en.pdf Frame K-operator frame C^*-algebra Hilbert C^*-modules. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 11 26 article I. Akkus iakkus.tr@gmail.com 1 E. Kilic ekilic@etu.edu.tr 2 N. Omur neseomur@kocaeli.edu.tr 3 Department of Mathematics, Faculty of Arts and Science, Kırıkkale University, TR-71450 Kırıkkale, Turkey Department of Mathematics, TOBB University of Economics and Technology, TR-06560 Ankara, Turkey Department of Mathematics, Faculty of Arts and Science, Kocaeli University, TR-41380 Kocaeli, Turkey In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh. http://ijmsi.ir/article-1-1319-en.pdf Linear recurrences Generalized Fibonacci and Lucas sequences Diophantine equations Continued fractions. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 27 46 article A. Abkar norouzian.m67@gmail.com 1 M. Norouzian abkar@sci.ikiu.ac.ir 2 Department of Pure Mathemathics, Faculty of Science, Imam Khomeini International University, Qazvin 34149, Iran Department of Pure Mathemathics, Faculty of Science, Imam Khomeini International University, Qazvin 34149, Iran We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings as a subclass. The existence and convergence of coincidence-best and coincidence quasi-best proximity points in the setting of convex metric spaces are investigated. http://ijmsi.ir/article-1-1333-en.pdf Coincidence-best proximity point Cyclic-noncyclic contraction Quasi-cyclic-noncyclic contraction Uniformly convex metric space. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 47 55 article T. Mondal tapumondal@gmail.com 1 Department of Mathematics Dr. Bhupendra Nath Duta Smriti Mahavidyalaya, Hatgobindapur, Burdwan - 713407, West Bengal, India In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left $k$-radicals $Lambda(a)={x in S | a stackrel{l}{longrightarrow^{infty}} x}$ induced by the transitive closure $stackrel{l}{longrightarrow^{infty}}$ of the relation $stackrel{l}{longrightarrow}$ which induce the equivalence relation $lambda$. Again non-transitivity of $stackrel{l}{longrightarrow}$ yields an expanding family {$stackrel{l}{longrightarrow^n}}$ of binary relations which associate subsets $Lambda_n(a)$ for all $a in S$, which again induces an equivalence relation $lambda_n$. We also define $lambda(lambda_n)$-simple semirings, and characterize the semirings which are distributive lattices of $lambda(lambda_n)$-simple semirings. http://ijmsi.ir/article-1-1320-en.pdf Principal left k-radical Distributive lattice congruence Completely semiprime k-ideal λ-simple semiring Distributive lattice decomposition eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 57 70 article S. Erden erdensmt@gmail.com 1 Department of Mathematics, Faculty of Science, Bartın University, Bartın-Turkey We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are of bounded variation are obtained. http://ijmsi.ir/article-1-1332-en.pdf Function of bounded variation Perturbed Ostrowski type inequalities. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 71 83 article E. Golpar-Raboky g.raboky@qom.ac.ir 1 E. Babolian babolian@khu.ac.ir 2 Department of Mathematics, University of Qom, Qom, Iran Department of Computer Science, Kharazmi University, Tehran, Iran The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factorizations by using the null space generators of some special nested submatrices of a matrix textit{A}. http://ijmsi.ir/article-1-1358-en.pdf Linear systems Quadrant interlocking factorization WZ factorization ZW factorization Null space generator. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 85 97 article S. O. Shah omarshah89@yahoo.com 1 A. Zada zadababo@yahoo.com 2 Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem  is used for obtaining  existence and uniqueness of solutions. By means of   abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish  Hyers-Ulam stability and Hyers-Ulam-Rassias stability results. There are some primary lemmas, inequalities and relevant assumptions that helps in our stability results. http://ijmsi.ir/article-1-1335-en.pdf Hyers-Ulam stability Time scale Impulses Delay dynamic system Gr"{o}nwall's inequality Abstract Gr"{o}nwall lemma Banach fixed point theorem. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 99 109 article A. Osipov oab@list.ru 1 Krasovskii Institute of Mathematics and Mechanics, Ural Federal University, Ural State University of Economics, Yekaterinburg, Russia For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence.  We study a functional characterization of the covering property of Hurewicz. http://ijmsi.ir/article-1-1337-en.pdf $U_{fin}(mathcal{O} Omega)$ Hurewicz property Selection principles $C_p$ theory $U_{fin}(mathcal{O} Gamma)$. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 111 123 article M. Bidkham mdbidkham@gmail.com 1 E. KhojastehnezadZHAD khojastehnejadelahe@gmail.com 2 Department of Mathematics, University of Semnan, Semnan, Iran Department of Mathematics, University of Semnan, Semnan, Iran In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities. http://ijmsi.ir/article-1-1389-en.pdf Inequality Polynomial Derivative Maximum modulus Restricted zeros. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 125 133 article R. Daskalov daskalovrn@gmail.com 1 Department of Mathematics and Informatics, Technical University of Gabrovo, Bulgaria An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in  $PG(2, q)$ is denoted by $m_r(2,q)$.  In this paper we present  a new $(184,12)$-arc in PG$(2,17),$  a new $(244,14)$-arc and a new $(267,15$)-arc in $PG(2,19).$ http://ijmsi.ir/article-1-1360-en.pdf Finite projective plane $(n r)$-arc in a projective plane $(l t)$-blocking set in a projective plane Maximum size of an $(n r)$-arc Linear codes. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 135 144 article A. Hamoud drahmed985@yahoo.com 1 K. Ghadle drkpghadle1974@gmail.com 2 Department of Mathematics, Taiz University, Taiz, Yemen Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India This paper establishes a study on some important latest innovations in the uniqueness of solution for Caputo fractional Volterra-Fredholm integro-differential equations. To apply this, the study uses Banach contraction  principle and Bihari's inequality.  A wider applicability of these techniques are based on their reliability and reduction in the size of the mathematical work. http://ijmsi.ir/article-1-1366-en.pdf Caputo fractional derivative Volterra-Fredholm integro-differential equation Banach contraction principle Bihari’s inequality. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 145 151 article S. A. Moosavi s.a.mousavi@qom.ac.ir 1 Faculty of Basic Science, University of Qom, Qom, Iran Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of  $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is connected to a vertex $a in cd^*(G)$ if and only if $p|a$. In this paper, we investigate the structure of a group $G$  whose graph $B(G)$ has five vertices. Especially we show that all these groups are solvable. http://ijmsi.ir/article-1-1390-en.pdf Bipartite divisor graph Character degree Solvable group. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 153 163 article N. Soltankhah soltan@alzahra.ac.ir 1 N. Kh. Khademian ir.khademian@gmail.com 2 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran A  $ mu $-way  $ G $-trade ($ mu geq 2) $  consists of $ mu $ disjoint decompositions of some simple (underlying) graph $ H $ into copies of a graph $ G. $  The   number of copies of the  graph $ G $ in  each of the decompositions is the volume of the $ G $-trade and   denoted by $ s. $ In this paper, we determine all values  $ s $ for which there exists a $  mu $-way   $ K_{1,m} $-trade of  volume $ s $  for underlying graph  $ H=K_{2m,2m} $ and $ H=K_{2m} $. http://ijmsi.ir/article-1-1740-en.pdf Trade $ G $-trade $ mu $-way $ G $-trade Trade spectrum. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 165 176 article B. Senoussi se2014bendhiba@gmail.com 1 M. Bekkar bekkar_99@yahoo.fr 2 Department of Mathematics, Ecole Normale Sup´erieure, Mostaganem, Algeria Department of Mathematics, Faculty of Sciences, University of Oran, Algeria In this paper we study translation surfaces with the non-degenerate third fundamental form in Lorentz- Minkowski space $mathbb{L}^{3}$. As a result, we classify translation surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form $III$ on the surface. http://ijmsi.ir/article-1-1400-en.pdf Surfaces of coordinate finite type Translation surfaces Laplace operator. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 177 190 article M. Ahmadi maryam_ahmadi2662@yahoo.com 1 J. Moghaderi j.moghaderi@hormozgan.ac.ir 2 Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran Let $R$ be a commutative ring with identity. A proper submodule $N$ of an $R$-module $M$ is an n-submodule if $rmin N~(rin R, min M)$ with $rnotinsqrt{Ann_R(M)}$, then $min N$. A number of results concerning n-submodules are given. For example, we give other characterizations of n-submodules. Also various properties of n-submodules are considered. http://ijmsi.ir/article-1-1393-en.pdf n-ideal n-submodule. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 191 206 article I. Baglan isakinc@kocaeli.edu.tr 1 F. Kanca fatma.kanca@fbu.edu.tr 2 V. Mishra vishnunarayanmishra@gmail.com 3 Department of Mathematics, Kocaeli University, Kocaeli 41380, Turkey Department of Computer Engineering, Fenerbahce University, Istanbul, Turkey Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India In this work, we tried to find the inverse coefficient in the Euler problem with over determination conditions. It showed the existence, stability of the solution by iteration method and linearization method was used for this problem in numerical part. Also two examples are presented with figures. http://ijmsi.ir/article-1-1401-en.pdf Inverse Coefficient Problem Periodic boundary condition Euler Bernoulli equation Fourier method. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 207 217 article Ş. Altinkaya sahsenealtinkaya@gmail.com 1 Department of Mathematics, Beykent University, 34500, Istanbul, Turkey The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries. http://ijmsi.ir/article-1-1408-en.pdf Bi-concave functions Al-Oboudi differential operator Coefficient estimates. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 219 225 article Y. Sawano yoshihiro-sawano@celery.ocn.ne.jp 1 S. M. Tabatabaie sm.tabatabaie@qom.ac.ir 2 Department of Mathematics, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan Department of Mathematics, University of Qom, Qom, Iran In this paper, as a main result for Morrey spaces, we prove that the set $mathcal M_q^p(mathbb R^n)backslashbigcup_{q<rleq p}mathcal M_r^p(mathbb R^n)$ is spaceable in $mathcal M_q^p(mathbb R^n)$, where $0<q<p<infty$.} http://ijmsi.ir/article-1-1399-en.pdf Spaceability‎ ‎Morrey spaces‎ ‎Banach spaces. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 227 237 article M. Crasmareanu mcrasm@uaic.ro 1 Faculty of Mathematics, University "Al. I. Cuza", Iasi, 700506, Romania This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given products are proposed. http://ijmsi.ir/article-1-1418-en.pdf Circle Quaternion Product Octonion Projective Geometry. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2022-04 17 1 239 259 article I. Singh inderdeeps.ma.12@gmail.com 1 Sh. Kumar sheoks53@gmail.com 2 Department of Physical Sciences, Sant Baba Bhag Singh University, Jalandhar-144030, Punjab, India Department of Mathematics, Dr. B.R.Ambedkar National Institute of Technology, Jalandhar-144011, Punjab, India As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numerical method based on Taylor series expansion and Haar wavelets is presented for solving coupled system of nonlinear partial differential equations. Efficiency and accuracy of the proposed method is depicted by comparing with classical methods. http://ijmsi.ir/article-1-1413-en.pdf Haar wavelet Taylor series Collocation points Nonlinear coupled evolution equations Operational matrices.