http://bims.iranjournals.ir/ Bulletin of the Iranian Mathematical Society en daily 1 Fri, 01 Dec 2017 00:00:00 +0330 Fri, 01 Dec 2017 00:00:00 +0330 http://bims.iranjournals.ir/article_1268.html http://bims.iranjournals.ir/article_975.html ‎This 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_1266.html ‎Let $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_1072.html We 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_1087.html ‎Let $p(z)$ 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 $|\alpha|\geq k$‎, ‎\begin{align*}‎ ‎\max_{|z|=1}|D_{\alpha}p(z)|\geq‎ ‎\frac{(n+sk)(|\alpha|-k)}{1+k}\max_{|z|=1}|p(z)|‎. ‎\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_1088.html ‎Let $\tau$ 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_1253.html ‎In 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_1090.html ‎In 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_1091.html ‎A 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_1096.html ‎In 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 literature http://bims.iranjournals.ir/article_1095.html ‎Let $D$ 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_1098.html In 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_1102.html ‎In 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_1103.html ‎A 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_1104.html ‎The 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. ‎The condensational property for a Boolean uni-soft filter is established. http://bims.iranjournals.ir/article_1107.html ‎By 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_1110.html In 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_1113.html A 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_1115.html ‎We 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_1116.html ‎In 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_1120.html ‎In 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_1121.html In 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 problem http://bims.iranjournals.ir/article_1123.html ‎In 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.html ‎In 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_1127.html ‎In 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_1128.html Using 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_1137.html ‎We 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_1146.html  ‎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_1148.html ‎The 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_1174.html ‎In 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_1181.html ‎In 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_1191.html ‎Let $R$ 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_1192.html In 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_1195.html ‎In 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_1199.html ‎We 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_1206.html ‎Let $G$ 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_1212.html ‎In 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_1213.html Suppose 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),] $$‎ ‎x^{m}P_{j}(x)=\sum\limits_{n=0}^{2m}a_{m,\,n}(j)P_{j+m-n}(x)‎,$$ ‎we find the coefficients $b_{i,j}^{(p,q,\ell‎ ,‎\,r)}$ in the expansion‎ $$‎ ‎x^{\ell }y^{r}\,\nabla _{x}^{p}\nabla _{y}^{q}\,f(x,y)=x^{\ell‎ ‎}y^{r}f^{(p,q)}(x,y) =\sum\limits_{m,n=0}^{\infty‎ ‎}a_{m,n}^{(p,q)}\,P_{m}(x)P_{n}(y),\,\,a_{m,n}^{(0,0)}=a_{m,n}‎,$$  ‎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_1222.html ‎We 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_1246.html ‎The 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_1256.html Let 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.