1 1735-4463 ACECR at Tarbiat Modares University 1315 General Generalized Frames for B(H, K) Rossafi M. b Kabbaj S. c b LaSMA Laboratory Department of Mathematics Faculty of Sciences, Dhar El Mahraz University Sidi Mohamed Ben Abdellah, B. P. 1796 Fes Atlas, Morocco c Laboratory of Partial Differential Equations, Spectral Algebra and Geometry Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kenitra, Morocco 1 4 2022 17 1 1 9 27 04 2018 15 08 2019 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 $B(mathcal{H})$.
1319 General Diophantine Equations Related with Linear Binary Recurrences Akkus I. d Kilic E. e Omur N. f d Department of Mathematics, Faculty of Arts and Science, Kırıkkale University, TR-71450 Kırıkkale, Turkey e Department of Mathematics, TOBB University of Economics and Technology, TR-06560 Ankara, Turkey f Department of Mathematics, Faculty of Arts and Science, Kocaeli University, TR-41380 Kocaeli, Turkey 1 4 2022 17 1 11 26 07 05 2018 10 10 2019 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. 1333 General Coincidence Quasi-Best Proximity Points for Quasi-Cyclic-Noncyclic Mappings in Convex Metric Spaces Abkar A. g Norouzian M. h g Department of Pure Mathemathics, Faculty of Science, Imam Khomeini International University, Qazvin 34149, Iran h Department of Pure Mathemathics, Faculty of Science, Imam Khomeini International University, Qazvin 34149, Iran 1 4 2022 17 1 27 46 22 05 2018 26 01 2019 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. 1320 General Distributive Lattices of λ-simple Semirings Mondal T. i i Department of Mathematics Dr. Bhupendra Nath Duta Smriti Mahavidyalaya, Hatgobindapur, Burdwan - 713407, West Bengal, India 1 4 2022 17 1 47 55 07 05 2018 01 07 2019 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. 1332 General Some Perturbed Inequalities of Ostrowski Type for Functions whose n-th Derivatives Are Bounded Erden S. j j Department of Mathematics, Faculty of Science, Bartın University, Bartın-Turkey 1 4 2022 17 1 57 70 22 05 2018 06 05 2019 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. 1358 Special On the WZ Factorization of the Real and Integer Matrices Golpar-Raboky E. k Babolian E. l k Department of Mathematics, University of Qom, Qom, Iran l Department of Computer Science, Kharazmi University, Tehran, Iran 1 4 2022 17 1 71 83 07 07 2018 09 06 2019 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}. 1335 General Hyers-Ulam Stability of Non-Linear Volterra Integro-Delay Dynamic System with Fractional Integrable Impulses on Time Scales Shah S. O. m Zada A. n m Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan n Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan 1 4 2022 17 1 85 97 31 05 2018 19 01 2019 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. 1337 Special A Functional Characterization of the Hurewicz Property Osipov A. o o Krasovskii Institute of Mathematics and Mechanics, Ural Federal University, Ural State University of Economics, Yekaterinburg, Russia 1 4 2022 17 1 99 109 08 06 2018 12 07 2019 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. 1389 Special On Bernstein Type Inequalities for Complex Polynomial Bidkham M. p KhojastehnezadZHAD E. p Department of Mathematics, University of Semnan, Semnan, Iran Department of Mathematics, University of Semnan, Semnan, Iran 1 4 2022 17 1 111 123 11 08 2018 19 08 2020 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. 1360 General New Large (n, r)-arcs in PG(2, q) Daskalov R. Department of Mathematics and Informatics, Technical University of Gabrovo, Bulgaria 1 4 2022 17 1 125 133 11 07 2018 02 07 2019 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 $PG(2,19).$ 1366 Special Some New Uniqueness Results of Solutions for Fractional Volterra-Fredholm Integro-Differential Equations Hamoud A. Ghadle K. Department of Mathematics, Taiz University, Taiz, Yemen Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India 1 4 2022 17 1 135 144 12 07 2018 10 03 2019 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. 1390 General Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices Moosavi S. A. Faculty of Basic Science, University of Qom, Qom, Iran 1 4 2022 17 1 145 151 12 08 2018 12 07 2019 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. 1740 Special On the Volume of µ-way G-trade Soltankhah N. Khademian N. Kh. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran 1 4 2022 17 1 153 163 02 10 2019 28 12 2020 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} $. 1400 General Translation Surfaces of the Third Fundamental Form in Lorentz-Minkowski Space Senoussi B. Bekkar M. Department of Mathematics, Ecole Normale Sup´erieure, Mostaganem, Algeria Department of Mathematics, Faculty of Sciences, University of Oran, Algeria 1 4 2022 17 1 165 176 29 08 2018 22 06 2020 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. 1393 Special n-submodules Ahmadi M. Moghaderi J. Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran 1 4 2022 17 1 177 190 15 08 2018 07 11 2019 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. 1401 General Solution of Inverse Euler-Bernoulli Problem with Integral Overdetermination and Periodic Boundary Conditions Baglan I. Kanca F. Mishra V. 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 1 4 2022 17 1 191 206 30 08 2018 21 07 2019 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. 1408 General Bi-concave Functions Defined by Al-Oboudi Differential Operator Altinkaya Ş. Department of Mathematics, Beykent University, 34500, Istanbul, Turkey 1 4 2022 17 1 207 217 15 09 2018 12 07 2019 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. 1399 Special Spaceability on Morrey Spaces Sawano Y. Tabatabaie S. M. Department of Mathematics, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan Department of Mathematics, University of Qom, Qom, Iran 1 4 2022 17 1 219 225 29 08 2018 12 07 2019 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 $0<q<p<infty$.} 1418 General Quaternionic Product of Circles and Cycles and Octonionic Product for Pairs of Circles Crasmareanu M. Faculty of Mathematics, University "Al. I. Cuza", Iasi, 700506, Romania 1 4 2022 17 1 227 237 25 09 2018 27 03 2019 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. 1413 General Modified Wavelet Method for Solving Two-dimensional Coupled System of Evolution Equations Singh I. Kumar Sh. 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 1 4 2022 17 1 239 259 19 09 2018 06 01 2021 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.