

2018 . 

Bulletin of Iranian Mathematical Society
ISSN 1017060X
دوماهنامه  ( )
7 2017




 The wFF property in trivial extensions G.W. Chang , H. Kim * Pages 22592267 Abstract Full Text [PDF 129KB]   Let D be an integral domain with quotient field K، E be a Kvector space، R=D∝E be the trivial extension of D by E، and w be the socalled woperation. In this paper، we show that R is a wFF ring if and only if D is a wFF domain; and in this case، each wflat wideal of R is winvertible.
Keywords: w, flat module; w, FF ring; trivial extension
  
 Modules whose direct summands are FIextending O. Tasdemir *, F. Karabacak Pages 22272231 Abstract Full Text [PDF 95KB]   A module M is called FIextending 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 FIextending module is also FIextending. In this study، it is given some answers to the question that under what conditions a direct summand of an FIextending module is an FIextending module?
Keywords: Extending module; direct summand; left exact preradical
  
 Perturbation bounds for ginverses with respect to the unitarily invariant norm L. Meng * Pages 26552662 Abstract Full Text [PDF 106KB]   Let complex matrices A and B have the same sizes. Using the singular value decomposition، we characterize the ginverse B(1) of B such that the distance between a given ginverse of A and the set of all ginverses 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 ginverse. These results generalize and improve the existing results published recently to some extent.
Keywords: g, inverse; additive perturbation bound; multiplicative perturbation bound; unitarily invariant norm
  
 Localization at prime ideals in bounded rings E. Akalan , B. Sarac Pages 22692274 Abstract Full Text [PDF 101KB]   In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.
Keywords: Localization; projective ideal; eventually idempotent ideal; bounded rings
  
 Lp boundedness of the Bergman projection on some generalized Hartogs triangles T. Beberok * Pages 22752280 Abstract Full Text [PDF 99KB]   In this paper we investigate a two classes of domains in Cn generalizing the Hartogs triangle. We prove optimal estimates for the mapping properties of the Bergman projection on these domains.
Keywords: Hartogs triangle; Bergman projection; Bergman kernel
  
 On the fixed number of graphs I. Javaid * , M. Murtaza, M. Asif, F. Iftikhar Pages 22812292 Abstract Full Text [PDF 132KB]   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 kset of vertices of G is a fixing set of G. A graph G is called a kfixed 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 distancetransitive kfixed graph.
Keywords: Fixing set; stabilizer; fixing number; fixed number
  
 Improved logarithmicgeometric mean inequality and its application L. Zou * Pages 23232326 Abstract Full Text [PDF 72KB]   In this short note، we present a refinement of the logarithmicgeometric mean inequality. As an application of our result، we obtain an operator inequality associated with geometric and logarithmic means.
Keywords: Taylor's Theorem; logarithmic mean; geometric mean; operator inequality
  
 On rational groups with Sylow 2subgroups of nilpotency class at most 2 S. Jafari, H. Sharifi * Pages 23272337 Abstract Full Text [PDF 114KB]   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 2subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on G and also via nilpotency and nonnilpotency assumption of G.
Keywords: Rational group; nilpotency class; Markel group
  
 Historic set carries full hausdorff dimension G.Z. Ma * Pages 23392347 Abstract Full Text [PDF 110KB]   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 nonuniformly hyperbolic dynamical systems.
Keywords: Historic set; Moran set; non, uniformly hyperbolic
  
 Hölder continuity of a parametric variational inequality X.F. Hu , X.B. Li * Pages 23712381 Abstract Full Text [PDF 117KB]   In this paper، we study the Hölder continuity of solution mapping to a parametric variational inequality. At first، recalling a realvalued 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 singlevalued solution mapping for the problem. Finally، we apply these results to a traffic network equilibrium problem.
Keywords: Holder continuity; gap function; parametric variational inequality; traffic network equilibrium problem
  
 Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations P. Chen * Pages 23932410 Abstract Full Text [PDF 143KB]   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.
Keywords: Existence; uniqueness; weak solution; variation problem; N, function
  
 Bounds for the dimension of the cnilpotent multiplier of a pair of Lie algebras H. Arabyani * Pages 24112418 Abstract Full Text [PDF 88KB]   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.
Keywords: Pair of Lie algebras; Schur multiplier; c, nilpotent multiplier
  
 Solving twodimensional fractional integrodifferential equations by Legendre wavelets M. Mojahedfar, A. Tari Marzabad * Pages 24192435 Abstract Full Text [PDF 575KB]   In this paper، we introduce the twodimensional Legendre wavelets (2DLWs)، and develop them for solving a class of twodimensional integrodifferential equations (2DIDEs) 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.
Keywords: Two, dimensional integro, differential equations; fractional operators; Legendre wavelets; operational matrix
  
 Extensions of the HestenesStiefel and PolakRibierePolyak conjugate gradient methods with sufficient descent property S. BabaieKafaki *, R. Ghanbari Pages 24372448 Abstract Full Text [PDF 127KB]   Using search directions of a recent class of threeterm conjugate gradient methods، modified versions of the HestenesStiefel and PolakRibierePolyak 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 DolanMore performance profile.
Keywords: Unconstrained optimization; conjugate gradient method; sufficient descent property; line search; global convergence
  
 On a Picone's identity for the Ap(x)Laplacian and its applications S.H. Rasouli * Pages 24492455 Abstract Full Text [PDF 100KB]   We present a Picone's identity for the Ap(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.
Keywords: Picone's identity; mathcalAp(x), Laplacian; Nonlinear elliptic problems
  
 On the Noetherian dimension of Artinian modules with homogeneous uniserial dimension A.R. Alehafttan, N. Shirali * Pages 24572470 Abstract Full Text [PDF 128KB]   In this article، we first show that nonNoetherian Artinian uniserial modules over commutative rings، duo rings، finite Ralgebras and right Noetherian rings are 1atomic exactly like Zp∞. 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 Rmodule with homogeneous uniserial dimension، where R is a locally Noetherian (or، a Noetherian duo) ring، then ndim A≤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 quuniserial modules and by using this concept، we observe that if A is an Artinian Rmodule، such that any of its submodules is quuniserial، where R is a right duo (or، a right Noetherian) ring، then ndim A≤1.
Keywords: Noetherian dimension; homogeneous uniserial dimension; atomic modules
  
 Distinguishing number and distinguishing index of natural and fractional powers of graphs S. Alikhani *, S. Soltani Pages 24712482 Abstract Full Text [PDF 146KB]   The distinguishing number (resp. index) D(G) (D′(G)) of a graph G is the least integer dsuch that G has an vertex labeling (resp. edge labeling) with d labels that is preserved only by a trivial automorphism. For any n∈N، the nsubdivision of G is a simple graph G1n which is constructed by replacing each edge of G with a path of length n. The mth 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 mth power of the nsubdivision of G، i.e.، (G1n)m or nsubdivision of mth power of G، i.e.، (Gm)1n. 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⩾3 with maximum degree Δ(G)، and for k⩾2، D(G1k)⩽⌈Δ(G)−−−−−√k⌉. Finally we prove that for m⩾2، the fractional power of G، i.e.، (G1k)m and (Gm)1k are distinguished by at most three edge labels.
Keywords: Distinguishing index; distinguishing number; fractional power
  
 Determination of a jump by Fourier and FourierChebyshev series M. Avdispahic, Z. Sabanac * Pages 23072321 Abstract Full Text [PDF 142KB]   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 FourierChebyshev series are also derived.
Keywords: Fourier series; generalized bounded variation; jump discontinuities
  
 Characterization of 22 full diversity spacetime codes and inequivalent full rank spaces H. Momenaee Kermani *, M. Ashenab Pages 24832493 Abstract Full Text [PDF 139KB]   In wireless communication systems، spacetime 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 spacetime codes. In this paper، using the equivalent definition of full diversity spacetime codes، we first characterize all real and complex 22 rate one linear dispersion spacetime 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 M2(C) and M2(R) whose nonzero elements are invertible. Finally، for any natural number n>1، we construct infinitely many inequivalent subspaces of Mn(C) whose nonzero elements are invertible.
Keywords: Space, time coding; linear dispersion; full diversity; full rank
  
 A characterization of orthogonality preserving operators E. Ansaripiri , R.G. Sanati *, M. Kardel Pages 24952505 Abstract Full Text [PDF 112KB]   In this paper، we characterize the class of orthogonality preserving operators on an infinitedimensional 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.
Keywords: Orthogonality preserving operators; adjoint of operators; isometry; unitary operators
  
 On subgroups of topologized fundamental groups and generalized coverings M. Abdullahi Rashid, B. Mashayekhy * , H. Torabi, S. Z. Pashaei Pages 23492370 Abstract Full Text [PDF 175KB]   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 compactopen topology and the whisker topology. Moreover، we present some conditions under which generalized coverings، semicoverings and coverings are equal.
Keywords: Generalized covering; quasitopological fundamental group; whisker topology; semilocally small generated; homotopically Hausdorff
  
 State spaces of K0 groups of some rings J. Ren * Pages 25072516 Abstract Full Text [PDF 114KB]   Let R be a ring with the Jacobson radical J(R) and let π:R→R/J(R) be the canonical map. Then π induces an order preserving group homomorphism K0π:K0(R)→K0(R/J(R)) and an affine continuous map S(K0π) between the state space St(R/J(R)) and the state space St(R). In this paper، we consider the natural affine map S(K0π). We give a condition under which S(K0π) is an affine homeomorphism. At the same time، we discuss the relationship between semilocal rings and semiperfect rings by using the affine map S(K0π).
Keywords: State space; (K0) group; pre, ordered group; affine map
  
 Nonlinear Picone identities to Pseudo pLaplace operator and applications T. Feng, M. Yu * Pages 25172530 Abstract Full Text [PDF 132KB]   In this paper، we derive a nonlinear Picone identity to the pseudo pLaplace 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 pLaplace system، a Sturmian comparison principle to the pseudo pLaplace equation، a new Hardy type inequality with weight and remainder term، a nonnegative estimate of the functional associated to pseudo pLaplace equation.
Keywords: Nonlinear Picone identity; pseudo p, Laplace equation; pseudo p, Laplace system
  
 Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight L. Li , C.L. Tang * Pages 21112124 Abstract   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.
Keywords: Self, similar solution; variational methods; ground state solution
  
 On the existence of Hilbert valued periodically correlated autoregressive processes N. Mohammadi Jouzdani , S. Mahmoodi *, A. Parvardeh Pages 25312545 Abstract Full Text [PDF 137KB]   In this paper we provide sufficient condition for existence of a unique Hilbert valued (Hvalued) periodically correlated solution to the first order autoregressive model Xn=ρnXn−1+Zn، for \ n∈Z، and formulate the existing solution and its autocovariance operator. Also we specially investigate equivalent condition for the coordinate process ⟨Xn،v⟩، for arbitrary element v in H، to satisfy in some autoregressive model. Finally، we extend our result to the autoregressive process with finite order.
Keywords: Second order process; autoregressive process; periodically correlated process; Hilbert valued process; linear operator
  
 The ranks of the classes of A10 A.B.M. Basheer * Pages 21252135 Abstract   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 A10 using the structure constants method and other results established in [A.B.M. Basheer and J. Moori، On the ranks of the alternating group An، Bull. Malays. Math. Sci. Soc..
Keywords: Conjugacy classes; rank; generation; structure constant; alternating group
  
 Existence and convergence results for monotone nonexpansive type mappings in partially ordered hyperbolic metric spaces R. Shukla *, R. Pant, Z. Kadelburg, H. Nashine Pages 25472565 Abstract Full Text [PDF 144KB]   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.
Keywords: Hyperbolic metric space; nonexpansive mapping; condition (C)
  
 nArray Jacobson graphs H. Ghayour , A. Erfanian *, A. Azimi , M. Farrokhi D. G Pages 21372152 Abstract Full Text [PDF 171KB]   We generalize the notion of Jacobson graphs into narray columns called narray Jacobson graphs and determine their connectivities and diameters. Also، we will study forbidden structures of these graphs and determine when an narray Jacobson graph is planar، outer planar، projective، perfect or domination perfect.
Keywords: Jacobson graph; connectivity; planar graph; outer planar graph; perfect graph
  
 Characterization of finite pgroups by the order of their Schur multipliers (t(G)=7) S.H. Jafari * Pages 25672576 Abstract Full Text [PDF 119KB]   Let G be a finite pgroup of order pn and M(G)=p12n(n−1)−t(G)، where 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)≤6. This paper extends the classification to t(G)=7.
Keywords: Schur multiplier; Nonabelian tensor square; p, Group
  
 Inequalities for the polar derivative of a polynomial with Sfold zeros at the origin E. Khojastehnezhad, M. Bidkham * Pages 21532167 Abstract Full Text [PDF 130KB]   Let p(z) be a polynomial of degree n and for a complex number α، let Dαp(z)=np(z)+(α−z)p′(z) denote the polar derivative of the polynomial p(z) with respect to α. Dewan et al proved that if p(z) has all its zeros in z≤k، (k≤1)، with sfold zeros at the origin then for every α∈C with α≥k، maxz=1Dαp(z)≥(n+sk)(α−k)1+kmaxz=1p(z). 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
Keywords: Polynomial; inequality; maximum modulus; polar derivative; restricted zeros
  
 An extension of the WedderburnArtin Theorem H. Khabazian * Pages 25772583 Abstract Full Text [PDF 95KB]   In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.
Keywords: Duo; artinian; distributive; uniserial; structural matrix
  
 On Φτquasinormal subgroups of finite groups Y. Mao *, X. Ma, X. Tang, J. Huang Pages 21692182 Abstract Full Text [PDF 157KB]   Let τ be a subgroup functor and H a psubgroup of a finite group G. Let G=G/HG and H=H/HG. We say that H is Φτquasinormal in G if for some Squasinormal subgroup T of G and some τsubgroup S of G contained in H، HT is Squasinormal in G and H∩T≤SΦ(H). In this paper، we study the structure of a group G under the condition that some primary subgroups of G are Φτquasinormal in G. Some new characterizations about pnilpotency and solubility of finite groups are obtained.
Keywords: S, quasinormal subgroups; p, nilpotent subgroups, subgroup functor; soluble group
  
 Recurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials H.M. Ahmed * Pages 25852615 Abstract Full Text [PDF 188KB]   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)،] xmPj(x)=∑n=02mam،n(j)Pj+m−n(x)، we find the coefficients b(p،q،ℓ،r)i،j in the expansion xℓyr∇px∇qyf(x،y)=xℓyrf(p،q)(x،y)=∑m،n=0∞a(p،q)m،nPm(x)Pn(y)،a(0،0)m،n=am،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.
Keywords: Hahn; Meixner; Kravchuk and Charlier polynomials; expansion coefficient; recurrence relations; linear difference equations; connection coefficients
  
 Linear codes with complementary duals related to the complement of the HigmanSims graph B.G. Rodrigues * Pages 21832204 Abstract   In this paper we study codes Cp(HiS) where p=3،7،11 defined by the 3 7 and 11modular representations of the simple sporadic group 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 HigmanSims 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 HigmanSims graph. In particular، we show that these are linear codes with complementary duals، and thus meet the asymptotic GilbertVarshamov bound. Furthermore، using the codewords of weight 30 in Cp(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 11elements، 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 rank3 representation.
Keywords: Strongly regular graph; Higman, Sims graph; linear code; automorphism group
  
 Limits in modified categories of interest K. Emir * , S. Cetin Pages 26172634 Abstract Full Text [PDF 146KB]   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.
Keywords: Modified category of interest; crossed module; cat object; limit
  
 Selfsimilar solutions of the Riemann problem for twodimensional systems of conservation laws S. Ayad * Pages 23832392 Abstract Full Text [PDF 112KB]   In this paper، a new approach is applied to study the selfsimilar solutions of 22 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
Keywords: Self, similar solutions; Riemann problem; Hyperbolic conservation laws; Smooth solutions
  
 Filter theory in MTLalgebras based on Unisoft property G. Muhiuddin *, A.M. Alroqi, S. Aldhafeeri Pages 22932306 Abstract Full Text [PDF 111KB]   The notion of (Boolean) unisoft filters in MTLalgebras is introduced، and several properties of them are investigated. Characterizations of (Boolean) unisoft filters are discussed، and some (necessary and sufficient) conditions for a unisoft filter to be Boolean are provided. The condensational property for a Boolean unisoft filter is established.
Keywords: MTL, algebras; (Boolean) filter; (Boolean) uni, soft filter
  
 Duality for the class of a multiobjective problem with support functions under KGfinvexity assumptions I.P. Debnath *, S.K. Gupta Pages 22332258 Abstract Full Text [PDF 185KB]   In this article، we formulate two dual models Wolfe and MondWeir related to symmetric nondifferentiable multiobjective programming problems. Furthermore، weak، strong and converse duality results are established under KGfinvexity 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
Keywords: Multiobjective programming; K, Gf, invexity; support function; efficient solutions; duality
  
 Zero elements and zideals in modified pointfree topology A.A. Estaji , A. Karimi Feizabad , M. Zarghani * Pages 22052226 Abstract Full Text [PDF 177KB]   In this paper، we define and study the notion of zero elements in topoframes; a topoframe is a pair (L،τ)، abbreviated Lτ، consisting of a frame L and a subframe τ all of whose elements are complemented elements in L. We show that the fring R(Lτ)، the set of τreal 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 zfilters and zideals in modified pointfree topology and make ready some results about them.
Keywords: Topoframe; zero element; z, filter; z, ideal; prime ideal
  
 Selfsimilar fractals and arithmetic dynamics A. Rastegar * Pages 26352653 Abstract Full Text [PDF 152KB]   The concept of selfsimilarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Selfsimilar 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 wellbehaved notion of dimension for selfsimilar 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.
Keywords: Self, similarity; Diophantine approximation; arithmetic dynamics
  
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