Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171201Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight21112124975ENL.LiSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, P.R. China and School of Mathematics and Statistics, Chongqing TechnologyBusiness University, Chongqing 400067, P.R. China.C.-L.TangSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, P.R. China.Journal Article20150708This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight. We apply the variational methods to prove the existence of ground state solution.http://bims.iranjournals.ir/article_975_ecb7585b5b420bce9f6305db16fb169e.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171201The ranks of the classes of $A_{10}$212521351266ENA.B.M.BasheerSchool of Mathematical and Computer Sciences, University of Limpopo (Turfloop), P. Bag X1106, Sovenga 0727, South Africa.Journal Article20160512Let $G $ be a finite group and $X$ be a conjugacy class of $G.$ The rank of $X$ in $G,$ denoted by $rank(G{:}X),$ is defined to be the minimal number of elements of $X$ generating $G.$ In this paper we establish the ranks of all the conjugacy classes of elements for simple alternating group $A_{10}$ using the structure constants method and other results established in [A.B.M. Basheer and J. Moori, On the ranks of the alternating group $A_{n}$, Bull. Malays. Math. Sci. Soc..http://bims.iranjournals.ir/article_1266_a66ae7592033b2fce476a115f015c8c9.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230$n$-Array Jacobson graphs213721521072ENH.Ghayourerdowsi University of Mashhad, International Campus, Mashhad, Iran.A.ErfanianDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.A.AzimiDepartment of Mathematics, University of Neyshabur, P. O. Box 91136-899, Neyshabur, Iran.M.Farrokhi D. G.Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20150417We generalize the notion of Jacobson graphs into $n$-array columns called $n$-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an $n$-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.http://bims.iranjournals.ir/article_1072_3d36aa6ead210c64097db60ede73c5ad.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Inequalities for the polar derivative of a polynomial with $S$-fold zeros at the origin215321671087ENE.KhojastehnezhadDepartment of Mathematics, University of Semnan, Semnan, Iran.M.BidkhamDepartment of Mathematics, University of Semnan, Semnan, Iran.Journal Article20160818Let $p(z)$ be a polynomial of degree $n$ and for a complex number $\alpha$, let $D_{\alpha}p(z)=np(z)+(\alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $\alpha$. Dewan et al proved that if $p(z)$ has all its zeros in $|z| \leq k,\ (k\leq 1),$ with $s$-fold zeros at the origin then for every $\alpha\in\mathbb{C}$ with $|\alpha|\geq k$,<br /> \begin{align*}<br /> \max_{|z|=1}|D_{\alpha}p(z)|\geq<br /> \frac{(n+sk)(|\alpha|-k)}{1+k}\max_{|z|=1}|p(z)|.<br /> \end{align*} In this paper, we obtain a refinement of above inequality. Also as an application of our result, we extend some inequalities for polar derivative of a polynomial of degree $n$ which does not vanish in $|z|< k$, where $k\geq 1$, except $s$-fold zeros at the origin. http://bims.iranjournals.ir/article_1087_e2275691daabd2435b3f62bfe31eedef.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230On $\Phi$-$\tau$-quasinormal subgroups of finite groups216921821088ENY.MaoInstitute of Quantum Information Science, Shanxi Datong University
Datong 037009, P.R. China.X.MaSchool of Mathematics and Computer, University of Datong of Shanxi, Datong 037009, P.R. China.X.TangSchool of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P.R. China.J.HuangSchool of mathematics and statistics, Jiangsu Normal University
Xuzhou, 221116, P.R. China.Journal Article20160115Let $\tau$ be a subgroup functor and $H$ a $p$-subgroup of a finite group $G$. Let $\bar{G}=G/H_{G}$ and $\bar{H}=H/H_{G}$. We say that $H$ is $\Phi$-$\tau$-quasinormal in $G$ if for some $S$-quasinormal subgroup $\bar{T}$ of $\bar{G}$ and some $\tau$-subgroup $\bar{S}$ of $\bar{G}$ contained in $\bar{H}$, $\bar{H}\bar{T}$ is $S$-quasinormal in $\bar{G}$ and $\bar{H}\cap\bar{T}\leq \bar{S}\Phi(\bar{H})$. In this paper, we study the structure of a group $G$ under the condition that some primary subgroups of $G$ are $\Phi$-$\tau$-quasinormal in $G$. Some new characterizations about $p$-nilpotency and solubility of finite groups are obtained.http://bims.iranjournals.ir/article_1088_42c83e5c0a23d661fa95aaa1ad32dcfa.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Linear codes with complementary duals related to the complement of the Higman-Sims graph218322041253ENB.G.RodriguesSchool of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban 4000, South Africa.Journal Article20160531In this paper we study codes $C_p(\overline{{\rm HiS}})$ where $p =3,7, 11$ defined by the 3- 7- and 11-modular representations of the simple sporadic group ${\rm HS}$ of Higman and Sims of degree 100. With exception of $p=11$ the codes are those defined by the row span of the adjacency matrix of the complement of the Higman-Sims graph over $GF(3)$ and $GF(7).$ We show that these codes have a similar decoding performance to that of their binary counterparts obtained from the Higman-Sims graph. In particular, we show that these are linear codes with complementary duals, and thus meet the asymptotic Gilbert-Varshamov bound. Furthermore, using the codewords of weight 30 in $C_p(\overline{{\rm HiS}})$ we determine a subcode of codimension 1, and thus show that the permutation module of dimension 100 over the fields of 3, 7 and 11-elements, respectively is the direct sum of three absolutely irreducible modules of dimensions 1, 22 and 77. The latter being also the subdegrees of the orbit decomposition of the rank-3 representation.http://bims.iranjournals.ir/article_1253_82f0207ea7f159c1fbcdbf2bda09cf56.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Zero elements and $z$-ideals in modified pointfree topology220522261090ENA.A.EstajiFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University,
P.O. Box 397, Sabzevar, Iran.A.Karimi FeizabadDepartment of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.M.ZarghaniFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University,
P.O. Box 397, Sabzevar, Iran.0000-0002-4580-0023Journal Article20160911In this paper, we define and study the notion of zero elements in topoframes; a topoframe is a pair $(L, \tau)$, abbreviated $L_{ \tau}$, consisting of a frame $L$ and a subframe $ \tau $ all of whose elements are complemented elements in $L$. We show that the $f$-ring $ \mathcal{R}(L_\tau)$, the set of $\tau$-real continuous functions on $L$, is uniformly complete. Also, the set of all zero elements in a topoframe is closed under the formation of countable meets and finite joins. Also, we introduce the notion of $z$-filters and $z$-ideals in modified pointfree topology and make ready some results about them. http://bims.iranjournals.ir/article_1090_17ec79f62279ac897d5fe7ebab2a0ff0.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Modules whose direct summands are FI-extending222722311091ENO.TasdemirDepartment of Mathematics, Balkan Campus, Trakya University, 22030 Edirne, Turkey.F.KarabacakDepartment of Mathematics, Yunus Emre Campus, Education Faculty, Anadolu University, 26470 Eskisehir, Turkey.Journal Article20160720A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$. It is not known whether a direct summand of an FI-extending module is also FI-extending. In this study, it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?http://bims.iranjournals.ir/article_1091_7994dad656774b761f268faf15e8955e.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Duality for the class of a multiobjective problem with support functions under $K$-$G_f$-invexity assumptions223322581096ENI.P.DebnathDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, India.S.K.GuptaDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, India.Journal Article20160705In this article, we formulate two dual models Wolfe and Mond-Weir related to symmetric nondifferentiable multiobjective programming problems. Furthermore, weak, strong and converse duality results are established under $K$-$G_f$-invexity assumptions. Nontrivial examples have also been depicted to illustrate the theorems obtained in the paper. Results established in this paper unify and extend some previously known results appeared in the literaturehttp://bims.iranjournals.ir/article_1096_85013b0bfd27489b5e154ca9baeafd3d.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230The $w$-FF property in trivial extensions225922671095ENG.W.ChangDepartment of Mathematics Education,
Incheon National University, Incheon 22012,
Republic of Korea.H.KimSchool of Computer and Information Engineering, Hoseo University, Asan 31499,
Republic of Korea.Journal Article20160808Let $D$ be an integral domain with quotient field $K$, $E$ be a $K$-vector space, $R = D \propto E$ be the trivial extension of $D$ by $E$, and $w$ be the so-called $w$-operation. In this paper, we show that $R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and in this case, each $w$-flat $w$-ideal of $R$ is $w$-invertible.http://bims.iranjournals.ir/article_1095_d06f8dc061cfad739bf3eb28268245a3.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Localization at prime ideals in bounded rings226922741098ENE.AkalanHacettepe University, Department of Mathematics, 06800 Beytepe, Ankara, Turkey.B.SaraçHacettepe University, Department of Mathematics, 06800 Beytepe, Ankara, Turkey.Journal Article20160722In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.http://bims.iranjournals.ir/article_1098_c5be1040f7c106f382e2d16e3c9dd327.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles227522801102ENT.BeberokSabanci University, Orta Mahalle, Universite Caddesi No: 27, Lojmanlari G7-102, Tuzla, 34956 Istanbul, Turkey.Journal Article20161029In this paper we investigate a two classes of domains in $\mathbb{C}^n$ generalizing the Hartogs triangle. We prove optimal estimates for the mapping properties of the Bergman projection on these domains.http://bims.iranjournals.ir/article_1102_c8f9b4afbe18af80c73696409cfed7fa.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230On the fixed number of graphs228122921103ENI.JavaidCentre for advanced studies in Pure and Applied Mathematics,
Bahauddin Zakariya University Multan, Pakistan.M.MurtazaCentre for advanced studies in Pure and Applied Mathematics,
Bahauddin Zakariya University Multan, Pakistan.M.AsifCentre for advanced studies in Pure and Applied Mathematics,
Bahauddin Zakariya University Multan, Pakistan.F.IftikharCentre for advanced studies in Pure and Applied Mathematics,
Bahauddin Zakariya University Multan, Pakistan.Journal Article20160809A set of vertices $S$ of a graph $G$ is called a fixing set of $G$, if only the trivial automorphism of $G$ fixes every vertex in $S$. The fixing number of a graph is the smallest cardinality of a fixing set. The fixed number of a graph $G$ is the minimum $k$, such that every $k$-set of vertices of $G$ is a fixing set of $G$. A graph $G$ is called a $k$-fixed graph, if its fixing number and fixed number are both $k$. In this paper, we study the fixed number of a graph and give a construction of a graph of higher fixed number from a graph of lower fixed number. We find the bound on $k$ in terms of the diameter $d$ of a distance-transitive $k$-fixed graph.http://bims.iranjournals.ir/article_1103_6cf076c09b16e5ab488956cbcfb99dc5.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Filter theory in MTL-algebras based on Uni-soft property229323061104ENG.MuhiuddinDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia.A.M.Al-roqiDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203 Jeddah 21589, Saudi Arabia.S.AldhafeeriDepartment of Mathematics, College of basic education, Public authority for applied education and training, Kuwait.Journal Article20161023The notion of (Boolean) uni-soft filters in MTL-algebras is introduced, and several properties of them are investigated. Characterizations of (Boolean) uni-soft filters are discussed, and some (necessary and sufficient) conditions for a uni-soft filter to be Boolean are provided.<br /> The condensational property for a Boolean uni-soft filter is established.http://bims.iranjournals.ir/article_1104_0122114dd4208fd2c85fb7f526d0e470.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Determination of a jump by Fourier and Fourier-Chebyshev series230723211107ENM.AvdispahicUniversity of Sarajevo, Deaprtment of Mathematics, Zmaja od Bosne 33-35, 71 000 Sarajevo, Bosnia and Herzegovina.Z.SabanacUniversity of Sarajevo, Deaprtment of Mathematics, Zmaja od Bosne 33-35, 71 000 Sarajevo, Bosnia and Herzegovina.0000-0001-8122-496XJournal Article20160930By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of harmonic bounded variation. This is achieved without the finiteness assumption on the number of discontinuities. Two results on determination of jump discontinuities by means of the tails of integrated Fourier-Chebyshev series are also derived.http://bims.iranjournals.ir/article_1107_f7490af1557c52224e87a714057dc4e6.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Improved logarithmic-geometric mean inequality and its application232323261110ENL.ZouSchool of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P.R. China.Journal Article20161022In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.http://bims.iranjournals.ir/article_1110_a2473c8ce3620a45bb9b80377280bcee.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230On rational groups with Sylow 2-subgroups of nilpotency class at most 2232723371113ENS.JafariDepartment of Mathematics, Faculty of Science, Shahed University, Tehran, Iran.H.SharifiDepartment of Mathematics, Faculty of Science, Shahed University, Tehran, Iran.Journal Article20160413A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.http://bims.iranjournals.ir/article_1113_58118f7c20f56a8f682e23695d8efc9e.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Historic set carries full hausdorff dimension233923471115ENG.-Z.MaSchool of Mathematics and Statistics, Anyang Normal University, Henan, 455000, China.Journal Article20160307We prove that the historic set for ratio of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional non-uniformly hyperbolic dynamical systems.http://bims.iranjournals.ir/article_1115_1c9ffd5a7475a95dd5b010f5426739bf.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230On subgroups of topologized fundamental groups and generalized coverings234923701116ENM.Abdullahi RashidDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad, Iran.B.MashayekhyDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad, Iran.H.TorabiDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad, Iran.S. Z.PashaeiDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad, Iran.Journal Article20161107In this paper, we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps.
More precisely, we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology. Moreover, we present some conditions under which generalized coverings, semicoverings and coverings are equal.http://bims.iranjournals.ir/article_1116_8152556e767eda520078c714dca68e25.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Hölder continuity of a parametric variational inequality237123811120ENX.F.HuDepartment of Electronic Engineering,
Chongqing City Management College,
Chongqing, 401331, China.X.B.LiCollege of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China.Journal Article20160707In this paper, we study the Hölder continuity of solution mapping to a parametric variational inequality. At first, recalling a real-valued gap function of the problem, we discuss the Lipschitz continuity of the gap function. Then under the strong monotonicity, we establish the Hölder continuity of the single-valued solution mapping for the problem. Finally, we apply these results to a traffic network equilibrium problem.http://bims.iranjournals.ir/article_1120_3a0fbd1dd9a32d7853f443d5e6ca9ee8.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Self-similar solutions of the Riemann problem for two-dimensional systems of conservation laws238323921121ENS.AyadDepartment of Mathematics, University of Oran1 Ahmed Ben Bella.
Laboratory of Fundamental and Applicable Analysis of Oran. BP 1524
El Menaouar, Oran, Algeria.Journal Article20160929In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problemhttp://bims.iranjournals.ir/article_1121_26684545248f1df176c79bb1a94bf1c4.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations239324101123ENP.ChenDepartment of Mathematics, Shanghai University, Shanghai 200444, China.Journal Article20161207In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.http://bims.iranjournals.ir/article_1123_7319df9a4111d5ef1d112580fe279f75.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Bounds for the dimension of the $c$-nilpotent multiplier of a pair of Lie algebras241124181126ENH.ArabyaniDepartment of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.Journal Article20161119In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.http://bims.iranjournals.ir/article_1126_77d79494191993b54fb703b7b2bb6ffd.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Solving two-dimensional fractional integro-differential equations by Legendre wavelets241924351127ENM.MojahedfarDepartment of Mathematics, Shahed University, Tehran, Iran.A.Tari MarzabadDepartment of Mathematics, Shahed University, Tehran, Iran.Journal Article20151209In this paper, we introduce the two-dimensional Legendre wavelets (2D-LWs), and develop them for solving a class of two-dimensional integro-differential equations (2D-IDEs) of fractional order. We also investigate convergence of the method. Finally, we give some illustrative examples to demonstrate the validity and efficiency of the method.http://bims.iranjournals.ir/article_1127_13f6e0db0fd1a7124eeba0587cc7fb54.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171201Extensions of the Hestenes-Stiefel and Polak-Ribiere-Polyak conjugate gradient methods with sufficient descent property243724481128ENS.Babaie-KafakiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box 35195--363, Semnan, Iran.R.GhanbariFaculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box: 9177948953, Mashhad, Iran.Journal Article20160823Using search directions of a recent class of three--term conjugate gradient methods, modified versions of the Hestenes-Stiefel and Polak-Ribiere-Polyak methods are proposed which satisfy the sufficient descent condition. The methods are shown to be globally convergent when the line search fulfills the (strong) Wolfe conditions. Numerical experiments are done on a set of CUTEr unconstrained optimization test problems. They demonstrate efficiency of the proposed methods in the sense of the Dolan-More performance profile.http://bims.iranjournals.ir/article_1128_0b073c64c95e8808e5bc16015697853c.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230On a Picone's identity for the $\mathcal{A}_{p(x)}$-Laplacian and its applications244924551137ENS.H.RasouliDepartment of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran.Journal Article20150921We present a Picone's identity for the $\mathcal{A}_{p(x)}$-Laplacian, which is an extension of the classic identity for the ordinary Laplace. Also, some applications of our results in Sobolev spaces with variable exponent are suggested.http://bims.iranjournals.ir/article_1137_05c4064c2f06bc59855a9bd882a9da8d.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230On the Noetherian dimension of Artinian modules with homogeneous uniserial dimension245724701146ENA.R.AlehafttanDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.N.ShiraliDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Journal Article20170115 In this article, we first show that non-Noetherian Artinian uniserial modules over commutative rings, duo rings, finite $R$-algebras and right Noetherian rings are $1$-atomic exactly like $\Bbb Z_{p^{\infty}}$. Consequently, we show that if $R$ is a right duo (or, a right Noetherian) ring, then the Noetherian dimension of an Artinian module with homogeneous uniserial dimension is less than or equal to $1$. In particular, if $A$ is a quotient finite dimensional $R$-module with homogeneous uniserial dimension, where $R$ is a locally Noetherian (or, a Noetherian duo) ring, then $n$-dim $A\leq 1$. We also show that the Krull dimension of Noetherian modules is bounded by the uniserial dimension of these modules. Moreover, we introduce the concept of qu-uniserial modules and by using this concept, we observe that if $A$ is an Artinian $R$-module, such that any of its submodules is qu-uniserial, where $R$ is a right duo (or, a right Noetherian) ring, then $n$-dim $A\leq 1$.http://bims.iranjournals.ir/article_1146_2706ad754c4976e7ef148b92f0a82975.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171201Distinguishing number and distinguishing index of natural and fractional powers of graphs247124821148ENS.AlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran.S.SoltaniDepartment of Mathematics, Yazd University, Yazd, Iran.Journal Article20161004The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$
such that $G$ has an vertex labeling (resp. edge labeling) with $d$ labels that is preserved only by a trivial
automorphism. For any $n \in \mathbb{N}$, the $n$-subdivision of $G$ is a simple graph $G^{\frac{1}{n}}$ which is constructed by replacing each edge of $G$ with a path of length $n$.
The $m^{th}$ power of $G$, is a graph with same set of vertices of $G$ and an edge between two vertices if and only if there is a path of length at most $m$ between them in $G$.
The fractional power of $G$, is the $m^{th}$ power of the $n$-subdivision of $G$, i.e., $(G^{\frac{1}{n}})^m$ or $n$-subdivision of $m$-th power of $G$, i.e., $(G^m)^{\frac{1}{n}}$. In this paper we study the distinguishing number and the distinguishing index of the natural and the fractional powers of $G$. We show that the natural powers more than one of a graph are distinguished by at most three edge labels. We also show that for a connected graph $G$ of order $n \geqslant 3$ with maximum degree $\Delta (G)$, and for $k\geqslant 2$, $D(G^{\frac{1}{k}})\leqslant \lceil \sqrt[k]{\Delta (G)} \rceil$. Finally we prove that for $m\geqslant 2$, the fractional power of $G$, i.e., $(G^{\frac{1}{k}})^m$ and $(G^m)^{\frac{1}{k}}$ are distinguished by at most three edge labels.http://bims.iranjournals.ir/article_1148_6e91ca9abade6c5324063dfe5d00fcce.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces248324931174ENH.Momenaee KermaniDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.M.AshenabDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranYoung Researchers Society, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20170128In wireless communication systems, space-time codes are applied to encode data when multiple antennas are used in the receiver and transmitter. The concept of diversity is very crucial in designing space-time codes. In this paper, using the equivalent definition of full diversity space-time codes, we first characterize all real and complex $2\times 2$ rate one linear dispersion space-time block codes that are full diversity. This characterization is used to construct full diversity codes which are not derived from Alamouti scheme. Then, we apply our results to characterize all real subspaces of $M_{2}(\mathbb{C})$ and $M_{2}(\mathbb{R})$ whose nonzero elements are invertible. Finally, for any natural number $n>1$, we construct infinitely many inequivalent subspaces of $M_{n}(\mathbb{C})$ whose nonzero elements are invertible.http://bims.iranjournals.ir/article_1174_53974d9400ee9e1f4349ffd74f245181.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230A characterization of orthogonality preserving operators249525051181ENE.Ansari-piriDepartment of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran.R.G.SanatiInstitute of Higher Education of ACECR(Academic Center of Education and Culture Research), Rasht branch, Iran.M.KardelDepartment of Mathematics, University Campus 2, University
of Guilan, P.O. Box 1914, Rasht, Iran(As a faculty member of (and supported by) Islamic Azad University, Zabol branch, Zabol, Iran. )Journal Article20170521In this paper, we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$. We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator. Also, we prove that every compact normal operator is a strongly orthogonality preserving operator.http://bims.iranjournals.ir/article_1181_ac6e9a52abbf950860c93074399ab8f1.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230State spaces of $K_0$ groups of some rings250725161191ENJ.RenAudio-visual Center, The Nanjing Institute of Tourism and Hospitality, 211100, Nanjing, P.R. China.Journal Article20170418Let $R$ be a ring with the Jacobson radical $J(R)$ and let $\pi\colon R\to R/J(R)$ be the canonical map. Then $\pi$ induces an order preserving group homomorphism $K_0\pi\colon K_0(R)\to K_0(R/J(R))$ and an affine continuous map $S(K_0\pi)$ between the state space $St(R/J(R))$ and the state space $St(R).$ In this paper, we consider the natural affine map $S(K_0\pi).$ We give a condition under which $S(K_0\pi)$ is an affine homeomorphism. At the same time, we discuss the relationship between semilocal rings and semiperfect rings by using the affine map $S(K_0\pi).$http://bims.iranjournals.ir/article_1191_e3849a0b67ab727cb48a0154db42ba3d.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171201Nonlinear Picone identities to Pseudo $p$-Laplace operator and applications251725301192ENT.FengDepartment of Applied Mathematics,
Northwestern Polytechnical University,
Xi'an, Shaanxi, 710072,
P.R. China.M.YuDepartment of Applied Mathematics,
Northwestern Polytechnical University,
Xi'an, Shaanxi, 710072,
P.R. China.Journal Article20161007In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight and remainder term, a nonnegative estimate of the functional associated to pseudo p-Laplace equation.http://bims.iranjournals.ir/article_1192_c065606badffd5fe4cb977c89c0de5c3.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230On the existence of Hilbert valued periodically correlated autoregressive processes253125451195ENN.Mohammadi JouzdaniDepartment of Mathematical
Sciences, Isfahan University of Technology, Isfahan, Iran.S.MahmoodiDepartment of Mathematical Sciences, Isfahan
University of Technology, Isfahan, Iran.A.ParvardehDepartment of Statistics, Faculty of Sciences, University of
Isfahan, Isfahan, Iran.Journal Article20170206In this paper we provide sufficient condition for existence of a unique Hilbert valued ($\mathbb{H}$-valued) periodically correlated solution to the first order autoregressive model $X_{n}=\rho _{n}X_{n-1}+Z_{n}$, for \ $n\in \mathbb{Z}$, and formulate the existing solution and its autocovariance operator. Also we specially investigate equivalent condition for the coordinate process $\left\langle X_{n},v\right\rangle $, for arbitrary element $v$ in $\mathbb{H}$, to satisfy in some autoregressive model. Finally, we extend our result to the autoregressive process with finite order.http://bims.iranjournals.ir/article_1195_5daaf15f086281252ac083bc654b1cfc.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Existence and convergence results for monotone nonexpansive type mappings in partially ordered hyperbolic metric spaces254725651199ENR.ShuklaDepartment of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India.R.PantDepartment of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India.Z.KadelburgFaculty of Mathematics, University of Belgrade, Studentski trg 16/IV, 11000 Beograd, Serbia.H.NashineDepartment of Mathematics, Texas A & M University, Kingsville, 78363-8202, Texas, USA.Journal Article20161210We present some existence and convergence results for a general class of nonexpansive mappings in partially ordered hyperbolic metric spaces. We also give some examples to show the generality of the mappings considered herein.http://bims.iranjournals.ir/article_1199_90b19cca8a330576f9bb4f3ff79cf8b8.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Characterization of finite $p$-groups by the order of their Schur multipliers ($t(G)=7$)256725761206ENS.H.JafariDepartment of Mathematics, Mashhad branch, Islamic Azad University, Mashhad, IranJournal Article20170412Let $G$ be a finite $p$-group of order $p^n$ and $|{\mathcal M}(G)|=p^{\frac{1}{2}n(n-1)-t(G)}$, where ${\mathcal M}(G)$ is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer. The classification of such groups $G$ is already known for $t(G)\leq 6$. This paper extends the classification to $t(G)=7$.http://bims.iranjournals.ir/article_1206_4a5ae568dd14e6cf4e4e5dfe4687c965.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230An extension of the Wedderburn-Artin Theorem257725831212ENH.KhabazianDepartment of Mathematical Science, Isfahan University of Technology, Isfahan, Iran.0000-0003-2091-6940Journal Article20170206In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.http://bims.iranjournals.ir/article_1212_69f07f5026eb8ed76cc9168a2248eb14.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Recurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials258526151213ENH.M.AhmedDepartment of Mathematics, Faculty of Industrial Education, Helwan
University, Cairo-EgyptDepartment of Mathematics, Faculty of Sciences, Saqraa University,
Shaqraa-KSA.Journal Article20170411Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),]<br /> $$ x^{m}P_{j}(x)=\sum\limits_{n=0}^{2m}a_{m,\,n}(j)P_{j+m-n}(x),$$<br /> we find the coefficients $b_{i,j}^{(p,q,\ell ,\,r)}$ in the expansion<br /> $$ x^{\ell }y^{r}\,\nabla _{x}^{p}\nabla _{y}^{q}\,f(x,y)=x^{\ell }y^{r}f^{(p,q)}(x,y)<br /> =\sum\limits_{m,n=0}^{\infty }a_{m,n}^{(p,q)}\,P_{m}(x)P_{n}(y),\,\,a_{m,n}^{(0,0)}=a_{m,n},$$<br /> We give applications of these results in solving partial difference equations with varying polynomial coefficients, by reducing them to recurrence relations (difference equations) in the expansion coefficients of the solution.http://bims.iranjournals.ir/article_1213_131b7669ec7a41ec353661475728792f.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Limits in modified categories of interest261726341222ENK.EmirDepartment of Mathematics and Computer Science, Eskişehir Osmangazi University, Turkey.S.ÇetinDepartment of Mathematics, Mehmet Akif Ersoy University, Burdur, Turkey.Journal Article20170107We firstly prove the completeness of the category of crossed modules in a modified category of interest. Afterwards, we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows. These constructions unify many corresponding results for the cases of groups, commutative algebras and can also be adapted to various algebraic structures.http://bims.iranjournals.ir/article_1222_e14591523a7f710c9325a6fd421f7fec.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Self-similar fractals and arithmetic dynamics263526531246ENA.RastegarSharif University of Technology,Tehran, IranInstitute for Advanced Study, Princeton, USA.Journal Article20161202The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a finite and disjoint union of `similar' copies. Fractals provide a framework in which, one can unite some results and conjectures in Diophantine geometry. We define a well-behaved notion of dimension for self-similar fractals. We also prove a fractal version of Roth's theorem for algebraic points on a variety approximated by elements of a fractal subset. As a consequence, we get a fractal version of Siegel's theorem on finiteness of integral points on hyperbolic curves and a fractal version of Faltings' theorem on Diophantine approximation on abelian varieties.http://bims.iranjournals.ir/article_1246_b52e1ad99d6abc9c4958a326107bd224.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Perturbation bounds for $g$-inverses with respect to the unitarily invariant norm265526621256ENL.MengCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P.R. China.Journal Article20170630Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest perturbed $g$-inverse. These results generalize and improve the existing results published recently to some extent.http://bims.iranjournals.ir/article_1256_48f9f6287f956af831c7368cb1ae09b4.pdf