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http://bims.iranjournals.ir/article_1268_89.html
Thu, 30 Nov 2017 20:30:00 +0100Existence of ground state solutions for a class of nonlinear elliptic equations with fast ...
http://bims.iranjournals.ir/article_975_89.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.Thu, 30 Nov 2017 20:30:00 +0100The ranks of the classes of $A_{10}$
http://bims.iranjournals.ir/article_1266_89.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..Thu, 30 Nov 2017 20:30:00 +0100$n$-Array Jacobson graphs
http://bims.iranjournals.ir/article_1072_89.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.Fri, 29 Dec 2017 20:30:00 +0100Inequalities for the polar derivative of a polynomial with $S$-fold zeros at the origin
http://bims.iranjournals.ir/article_1087_89.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 $|z| leq k, (kleq‎ ‎1),$ with $s$-fold zeros at the origin then for every‎ ‎$alphainmathbb{C}$ 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 $kgeq 1$‎, ‎except $s$-fold zeros at the origin‎. Fri, 29 Dec 2017 20:30:00 +0100On $\Phi$-$\tau$-quasinormal subgroups of finite groups
http://bims.iranjournals.ir/article_1088_89.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 $bar{H}capbar{T}leq bar{S}Phi(bar{H})$‎. ‎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.Fri, 29 Dec 2017 20:30:00 +0100Linear codes with complementary duals related to the complement of the Higman-Sims graph
http://bims.iranjournals.ir/article_1253_89.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.Fri, 29 Dec 2017 20:30:00 +0100Zero elements and $z$-ideals in modified pointfree topology
http://bims.iranjournals.ir/article_1090_89.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. Fri, 29 Dec 2017 20:30:00 +0100Modules whose direct summands are FI-extending
http://bims.iranjournals.ir/article_1091_89.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?Fri, 29 Dec 2017 20:30:00 +0100Duality for the class of a multiobjective problem with support functions under ...
http://bims.iranjournals.ir/article_1096_89.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 literatureFri, 29 Dec 2017 20:30:00 +0100The $w$-FF property in trivial extensions
http://bims.iranjournals.ir/article_1095_89.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.Fri, 29 Dec 2017 20:30:00 +0100Localization at prime ideals in bounded rings
http://bims.iranjournals.ir/article_1098_89.html
In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.Fri, 29 Dec 2017 20:30:00 +0100$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles
http://bims.iranjournals.ir/article_1102_89.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.Fri, 29 Dec 2017 20:30:00 +0100On the fixed number of graphs
http://bims.iranjournals.ir/article_1103_89.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.Fri, 29 Dec 2017 20:30:00 +0100Filter theory in MTL-algebras based on Uni-soft property
http://bims.iranjournals.ir/article_1104_89.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.Fri, 29 Dec 2017 20:30:00 +0100Determination of a jump by Fourier and Fourier-Chebyshev series
http://bims.iranjournals.ir/article_1107_89.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.Fri, 29 Dec 2017 20:30:00 +0100Improved logarithmic-geometric mean inequality and its application
http://bims.iranjournals.ir/article_1110_89.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.Fri, 29 Dec 2017 20:30:00 +0100On rational groups with Sylow 2-subgroups of nilpotency class at most 2
http://bims.iranjournals.ir/article_1113_89.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 $G$.Fri, 29 Dec 2017 20:30:00 +0100Historic set carries full hausdorff dimension
http://bims.iranjournals.ir/article_1115_89.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.Fri, 29 Dec 2017 20:30:00 +0100On subgroups of topologized fundamental groups and generalized coverings
http://bims.iranjournals.ir/article_1116_89.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.Fri, 29 Dec 2017 20:30:00 +0100Hölder continuity of a parametric variational inequality
http://bims.iranjournals.ir/article_1120_89.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.Fri, 29 Dec 2017 20:30:00 +0100Self-similar solutions of the Riemann problem for two-dimensional systems of ...
http://bims.iranjournals.ir/article_1121_89.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 problemFri, 29 Dec 2017 20:30:00 +0100Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion ...
http://bims.iranjournals.ir/article_1123_89.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.Fri, 29 Dec 2017 20:30:00 +0100Bounds for the dimension of the $c$-nilpotent multiplier of a pair of Lie algebras
http://bims.iranjournals.ir/article_1126_89.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.Fri, 29 Dec 2017 20:30:00 +0100Solving two-dimensional fractional integro-differential equations by Legendre wavelets
http://bims.iranjournals.ir/article_1127_89.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.Fri, 29 Dec 2017 20:30:00 +0100Extensions of the Hestenes-Stiefel and Polak-Ribiere-Polyak conjugate gradient methods with ...
http://bims.iranjournals.ir/article_1128_89.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.Thu, 30 Nov 2017 20:30:00 +0100On a Picone's identity for the $\mathcal{A}_{p(x)}$-Laplacian and its applications
http://bims.iranjournals.ir/article_1137_89.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.Fri, 29 Dec 2017 20:30:00 +0100On the Noetherian dimension of Artinian modules with homogeneous uniserial dimension
http://bims.iranjournals.ir/article_1146_89.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 ‎$Aleq‎ ‎1$‎. ‎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 $‎Aleq 1$.Fri, 29 Dec 2017 20:30:00 +0100Distinguishing number and distinguishing index of natural and fractional powers of graphs
http://bims.iranjournals.ir/article_1148_89.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 $kgeqslant 2$‎, ‎$D(G^{frac{1}{k}})leqslant lceil sqrt[k]{Delta (G)} rceil$‎. ‎Finally we prove that for $mgeqslant 2$‎, ‎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.Thu, 30 Nov 2017 20:30:00 +0100Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces
http://bims.iranjournals.ir/article_1174_89.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 $2times 2$ 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.Fri, 29 Dec 2017 20:30:00 +0100A characterization of orthogonality preserving operators
http://bims.iranjournals.ir/article_1181_89.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.Fri, 29 Dec 2017 20:30:00 +0100State spaces of $K_0$ groups of some rings
http://bims.iranjournals.ir/article_1191_89.html
‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition under which $S(K_0pi)$ is‎ ‎an affine homeomorphism‎. ‎At the same time‎, ‎we discuss the relationship between semilocal rings and semiperfect rings by using the‎ ‎affine map $S(K_0pi).$Fri, 29 Dec 2017 20:30:00 +0100Nonlinear Picone identities to Pseudo $p$-Laplace operator and applications
http://bims.iranjournals.ir/article_1192_89.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.Thu, 30 Nov 2017 20:30:00 +0100On the existence of Hilbert valued periodically correlated autoregressive processes
http://bims.iranjournals.ir/article_1195_89.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 $nin mathbb{Z}$‎, ‎and‎ ‎formulate the existing solution and its autocovariance operator‎. ‎Also we specially investigate equivalent condition for the‎ ‎coordinate process $leftlangle X_{n},vrightrangle $‎, ‎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.Fri, 29 Dec 2017 20:30:00 +0100Existence and convergence results for monotone nonexpansive type mappings in partially ...
http://bims.iranjournals.ir/article_1199_89.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.Fri, 29 Dec 2017 20:30:00 +0100Characterization of finite $p$-groups by the order of their Schur multipliers ($t(G)=7$)
http://bims.iranjournals.ir/article_1206_89.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 $t(G)=7$.Fri, 29 Dec 2017 20:30:00 +0100An extension of the Wedderburn-Artin Theorem
http://bims.iranjournals.ir/article_1212_89.html
‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.Fri, 29 Dec 2017 20:30:00 +0100Recurrences and explicit formulae for the expansion and connection coefficients in series of ...
http://bims.iranjournals.ir/article_1213_89.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),] $$‎ ‎x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x)‎,$$ ‎we find the coefficients $b_{i,j}^{(p,q,ell‎ ,‎,r)}$ in the expansion‎ $$‎ ‎x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell‎ ‎}y^{r}f^{(p,q)}(x,y) =sumlimits_{m,n=0}^{infty‎ ‎}a_{m,n}^{(p,q)},P_{m}(x)P_{n}(y),,,a_{m,n}^{(0,0)}=a_{m,n}‎,$$ ‎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.Fri, 29 Dec 2017 20:30:00 +0100Limits in modified categories of interest
http://bims.iranjournals.ir/article_1222_89.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.Fri, 29 Dec 2017 20:30:00 +0100Self-similar fractals and arithmetic dynamics
http://bims.iranjournals.ir/article_1246_89.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.Fri, 29 Dec 2017 20:30:00 +0100Perturbation bounds for $g$-inverses with respect to the unitarily invariant norm
http://bims.iranjournals.ir/article_1256_89.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.Fri, 29 Dec 2017 20:30:00 +0100