فهرست مطالب
Bulletin of Iranian Mathematical Society
Volume:43 Issue: 7, 2017
 تاریخ انتشار: 1396/11/20
 تعداد عناوین: 40


Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weightPages 21112124This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weightý. ýWe apply the variational methods to prove the existence of ground state solutioný.Keywords: Self, similar solution?, ?variational methods?, ?ground state solution?

The ranks of the classes of A10Pages 21252135ýLet G be a finite group and X be a conjugacy class of G. Theý ýrank of X in G, denoted by rank(G:X), is defined toý ýbe the minimal number of elements of X generating G. In thisý ýpaper we establish the ranks of all the conjugacy classes ofý ýelements for simple alternating group A10 using the structureý ýconstants method and other results established iný ý[A.B.Mý. ýBasheer and Jý. ýMooriý, ýOn the ranks of the alternating group Aný, ýBullý. ýMalaysý. ýMathý. ýSciý. ýSoc..Keywords: Conjugacy classes, rank, generation, structure constant, alternating group

Pages 21372152We 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?

Pages 21532167ýLet p(z) be a polynomial of degree n and for a complex number αý, ýlet Dαp(z)=np(z)(α−z)p′(z) denote the polar derivative of the polynomial p(z) with respect to αý. ýDewan et al provedý ýthat if p(z) has all its zeros in z≤k, (k≤ýý1), with sfold zeros at the origin then for everyý ýα∈C with α≥ký,
ýýmaxz=1Dαp(z)≥ýý(n)(α−k)1鉦z=1p(z)ý.ý
In this paperý, ýwe obtain a refinementý ýof above inequalityý. ýAlso as an application of our resultý, ýwe extend some inequalities forý ýpolar derivative of a polynomial of degree n whichý ýdoes not vanish in zKeywords: Polynomial?, ?inequality?, ?maximum? ?modulus?, ?polar derivative?, ?restricted zeros? 
Pages 21692182ýLet τ be a subgroup functor and H a psubgroup of a finite group Gý. ýLet G¯=G/HG and H¯=H/HGý. ýWe say that H is Φτquasinormal in G if for some Squasinormal subgroup T¯ of G¯ and some τsubgroup S¯ of G¯ contained in H¯ý, ýH¯T¯ is Squasinormal in G¯ and H¯∩T¯≤S¯Φ(H¯)ý. ýIn this paperý, ýwe study the structure of a group G under the condition that some primary subgroups of G are Φτquasinormal in Gý. ýSome new characterizations about pnilpotency and solubility of finite groups are obtained.Keywords: S, quasinormal subgroups, p, nilpotent subgroups?, ?subgroup functor, soluble group?

Linear codes with complementary duals related to the complement of the HigmanSims graphPages 21832204ýIn this paper we study codes Cp(HiS¯¯¯¯¯¯¯¯) where p=3,7ý,ý11 defined by the 3ý ý7ý ýand 11modular representations of the simple sporadic group HS of Higman and Sims of degree 100ý. ýWith 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 graphý. ýIn particularý, ýwe show that these are linear codes with complementary dualsý, ýand thus meet the asymptotic GilbertVarshamov boundý. ýFurthermoreý, ýusing the codewords of weight 30 in Cp(HiS¯¯¯¯¯¯¯¯) we determine a subcode of codimension 1ý, ýand thus show that the permutation module of dimension 100 over the fields of 3ý, ý7 and 11elementsý, ýrespectively is the direct sum of three absolutely irreducible modules of dimensions 1ý, ý22 and 77ý. ýThe latter being also the subdegrees of the orbit decomposition of the rank3 representationý.Keywords: Strongly regular graph?, ?Higman, Sims graph?, ?linear code?, ?automorphism group?

Pages 22052226ýIn this paperý, ýwe define and study the notion of zero elements in topoframes; a topoframe is a pairý ý(Lý,ýτ)ý, ýabbreviated Lτý, ýconsisting of a frame L and aý ýsubframe τ all of whose elements are complemented elements iný ýLý. ýWe show thatý ýthe fring R(Lτ)ý, ýthe set of τreal continuous functions on Lý, ýis uniformly completeý. ýAlsoý, ýthe set of all zero elements in a topoframeý ýis closed under the formation of countable meets and finite joinsý. ýAlsoý, ýwe introduce the notion of zfilters and zideals in modified pointfree topologyý ýand make ready some results about themý.Keywords: Topoframe?, ?zero element?, ?z, filter?, ?z, ideal?, ?prime ideal

Pages 22272231ýA module M is called FIextending if every fully invariant submodule of M is essential in a direct summand of Mý. ýIt is not known whether a direct summand of an FIextending module is also FIextendingý. ýIn this studyý, ýit 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?

Pages 22332258ýIn this articleý, ýwe formulate two dual models Wolfe and MondWeir related to symmetric nondifferentiable multiobjective programming problemsý. ýFurthermoreý, ýweaký, ýstrong and converse duality results are established under KGfinvexity assumptionsý. ýNontrivial examples have also been depicted to illustrate the theorems obtained in the paperý. ýResults established in this paper unify and extend some previously known results appeared in the literatureKeywords: Multiobjective programming?, ?K, Gf, invexity?, ?support function?, ?efficient solutions?, ?duality?

Pages 22592267ýLet D be an integral domain with quotient field Ký, ýE be a Kvector spaceý, ýR=D∝E be the trivial extension of D by Eý, ýand w be the socalled woperationý. ýIn this paperý, ýwe show thatý ýR is a wFF ring if and only if D is a wFF domain; andý ýin this caseý, ýeach wflat wideal of R is winvertible.Keywords: w, flat module?, ?w, FF ring?, ?trivial extension?

Pages 22692274In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.Keywords: Localizationý, ýprojective idealý, ýeventuallyý ýidempotent idealý, ýbounded rings

Pages 22752280ýIn this paper we investigate a two classes of domains in Cn generalizing the Hartogs triangleý. ýWe prove optimal estimates for the mapping properties of the Bergman projection on these domains.Keywords: Hartogs triangle?, ?Bergman projection?, ?Bergman kernel

Pages 22812292ýA set of vertices S of a graph G is called a fixing set of Gý, ýif only the trivial automorphism of G fixes every vertex in Sý. ýThe fixing number of a graph is the smallest cardinality of a fixingý ýsetý. ýThe fixed number of a graph G is the minimum ký, ýsuch that ýevery kset of vertices of G is a fixing set of Gý. ýA graph Gý ýis called a kfixed graphý, ýif its fixing number and fixed numberý ýare both ký. ýIn this paperý, ýwe study the fixed number of a graphý ýand give a construction of a graph of higher fixed number from aý ýgraph of lower fixed numberý. ýWe find the bound on k in terms ofý ýthe diameter d of a distancetransitive kfixed graphý.Keywords: Fixing set?, stabilizer?, fixing number?, fixed number?

Pages 22932306ýThe notion of (Boolean) unisoft filtersý ýin MTLalgebras is introducedý, ýand several properties of them areý ýinvestigatedý. ýCharacterizations of (Boolean) unisoft filters are discussedý, ýand some (necessary and sufficient) conditionsý ýfor a unisoft filter to be Boolean are providedý.
ýThe condensational property for a Boolean unisoft filter is established.Keywords: MTL, algebras?, ?(Boolean) filter?, ?(Boolean) uni, soft filter? 
Pages 23072321ýBy observing the equivalence of assertions on determining the jump of aý ýfunction by its differentiated or integrated Fourier seriesý, ýwe generalize aý ýprevious result of Kvernadzeý, ýHagstrom and Shapiro to the whole class ofý ýfunctions of harmonic bounded variationý. ýThis is achieved without the finiteness assumption oný ýthe number of discontinuitiesý. ýTwo results on determination of jumpý ýdiscontinuities by means of the tails of integrated FourierChebyshev series are also derived.Keywords: Fourier series?, ?generalized bounded variation?, ?jump discontinuities?

Pages 23232326In 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

Pages 23272337A 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

Pages 23392347ýWe prove that the historic set for ratioý ýof Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensionalý ýnonuniformly hyperbolic dynamical systems.Keywords: Historic set?, ?Moran set?, ?non, uniformly hyperbolic?

Pages 23492370ýIn this paperý, ýwe are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering mapsý.
ýMore preciselyý, ýwe find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compactopen topology and the whisker topologyý. ýMoreoverý, ýwe present some conditions under which generalized coveringsý, ýsemicoverings and coverings are equal.Keywords: Generalized covering?, ?quasitopological fundamental group?, ?whisker topology?, ?semilocally small generated?, ?homotopically Hausdorff? 
Pages 23712381ýIn this paperý, ýwe study the Hölder continuity of solution mapping to a parametric variational inequalityý. ýAt firstý, ýrecalling a realvalued gap function of the problemý, ýwe discuss the Lipschitz continuity of the gap functioný. ýThen under the strong monotonicityý, ýwe establish the Hölder continuity of the singlevalued solution mapping for the problemý. ýFinallyý, ýwe apply these results to a traffic network equilibrium problem.Keywords: Holder continuity, gap function, parametric variational inequality, traffic network equilibrium problem

Pages 23832392In this paper, a new approach is applied to study the selfsimilar 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 problemKeywords: Self, similar solutions, Riemann problem, Hyperbolic conservation laws, Smooth solutions

Pages 23932410ýIn this paperý, ýwe study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equationsý. ýBy a priori estimatesý, ýdifference and variation techniquesý, ýwe establish the existence and uniqueness of weak solutions of this problem.Keywords: Existence, uniqueness, weak solution, variation problem, N, function

Pages 24112418ýIn this paperý, ýwe study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equationsý. ýBy a priori estimatesý, ýdifference and variation techniquesý, ýwe establish the existence and uniqueness of weak solutions of this problem.Keywords: Pair of Lie algebras, Schur multiplier, c, nilpotent multiplier

Pages 24192435ýIn this paperý, ýwe introduce the twodimensional Legendre wavelets (2DLWs)ý, ýand develop them for solving a class of twodimensional integrodifferential equations (2DIDEs) of fractional orderý. ýWe also investigate convergence of the methodý. ýFinallyý, ýwe 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?

Pages 24372448Using 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?

Pages 24492455ýWe present a Picone's identity for theý ýAp(x)Laplacianý, ýwhich is an extension of the classicý ýidentity for the ordinary Laplaceý. ýAlsoý, ýsome applications of ourý ýresults in Sobolev spaces with variable exponent are suggested.Keywords: Picone's identity, mathcalAp(x), Laplacian, Nonlinear elliptic problems?

Pages 24572470ýIn this articleý, ýwe firstý ýshow that nonNoetherian Artinian uniserial modules overý ýcommutative ringsý, ýduo ringsý, ýfinite Ralgebras and rightý ýNoetherian rings are 1atomic exactly like Zp∞ý. ýConsequentlyý, ýwe show that if R is a right duo (orý, ýa rightý ýNoetherian) ringý, ýthen the Noetherian dimension of an Artinianý ýmodule with homogeneous uniserial dimension is less than or equalý ýto 1ý. ýIn particularý, ýif A is a quotient finite dimensionalý ýRmodule with homogeneous uniserial dimensioný, ýwhere R is aý ýlocally Noetherian (orý, ýa Noetherian duo) ringý, ýthen ndim ýA≤ýý1ý. ýWe also show that the Krull dimension of Noetherian modules isý ýbounded by the uniserial dimension of these modulesý. ýMoreoverý, ýwe introduce the concept of quuniserial modules and by using thisý ýconceptý, ýwe observe that if A is an Artinian Rmoduleý, ýsuch thatý ýany of its submodules is quuniserialý, ýwhere R is a right duo (orý, ýa right Noetherian) ringý, ýthen ndim ýA≤1.Keywords: Noetherian dimension, homogeneous uniserial dimension, atomic modules

Pages 24712482ýThe distinguishing number (resp. index) D(G) (D′(G)) of a graph G is the least integer dýýsuch that G has an vertex labeling (resp. edge labeling) with d labels that is preserved only by a trivialý ýautomorphismý. ýFor any n∈Ný, ýthe nsubdivision of G is a simple graph G1n which is constructed by replacing each edge of G with a path of length ný.
ýThe mth power of Gý, ýis 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.ý
ý The fractional power of Gý, ýis the mth power of the nsubdivision of Gý, ýi.e.ý, ý(G1n)m or nsubdivision of mth power of Gý, ýi.e.ý, ý(Gm)1ný. ýIn this paper we study the distinguishing number and the distinguishing index of the natural and the fractional powers of Gý. ýWe show that the natural powers more than one of a graph are distinguished by at most three edge labelsý. ýWe also show that for a connected graph G of order n⩾3 with maximum degree Δ(G)ý, ýand for k⩾2ý, ýD(G1k)⩽⌈Δ(G)−−−−−√k⌉ý. ýFinally we prove that for m⩾2ý, ýthe fractional power of Gý, ýi.e.ý, ý(G1k)m and (Gm)1k are distinguishedý ý by at most three edge labelsý.Keywords: Distinguishing index?, ?distinguishing number?, ?fractional power? 
Pages 24832493ýIn wireless communication systemsý, ýspacetime codes are applied to encode data when multiple antennas are used in the receiver and transmitterý. ýThe concept of diversity is very crucial in designing spacetime codesý. ýIn this paperý, ýusing the equivalent definition of full diversity spacetime codesý, ýwe first characterize all real and complex 2×2 rate one linear dispersion spacetime block codes that are full diversityý. ýThis characterization is used to construct full diversity codes which are not derived from Alamouti schemeý. ýThený, ýwe apply our results to characterize all real subspaces of M2(C) and M2(R) whose nonzero elements are invertibleý. ýFinallyý, ýfor any natural number n>1ý, ýwe construct infinitely many inequivalent subspaces of Mn(C) whose nonzero elements are invertible.Keywords: Space, time coding?, ?linear dispersion?, ?full diversity?, ?full rank?

Pages 24952505ýIn this paperý, ýwe 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 Hý. ýWe show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operatorý. ýAlsoý, ýwe prove that every compact normal operator is a strongly orthogonality preserving operatorý.Keywords: Orthogonality preserving operators?, ?adjoint of operators?, isometry?, unitary operators?

Pages 25072516ýLet R be a ringý ýwith the Jacobson radical J(R) and let π:R→R/J(R) beý the canonical mapý. ýThen π induces an order preserving group homomorphismý ýK0π:K0(R)→K0(R/J(R)) and aný ýaffine continuous map S(K0π) between the state space St(R/J(R)) and theý ýstate space St(R).ý ýIn this paperý, ýwe consider the natural affine map S(K0π). We give a condition under which S(K0π) isý ýan affine homeomorphismý. ýAt the same timeý, ýwe discuss the relationship between semilocal rings and semiperfect rings by using theý ýaffine map S(K0π).Keywords: State space?, ???(K0)?? group?, ?pre, ordered group?, ?affine map?

Pages 25172530In 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?

Pages 25312545ýIn this paper we provide sufficient condition for existence of aý ýunique Hilbert valued (Hvalued) periodicallyý ýcorrelated solution to the first order autoregressive modelý ýXn=ρnXn−1ý, ýfor \ n∈Zý, ýandý ýformulate the existing solution and its autocovariance operatorý. ýAlso we specially investigate equivalent condition for theý ýcoordinate process ⟨Xn,v⟩ý, ýforý ýarbitrary element v in Hý, ýto satisfy in someý ýautoregressive modelý. ýFinallyý, ýwe extend our result to theý ýautoregressive process with finite orderý.Keywords: Second order process?, autoregressive process?, periodically correlated process?, ?Hilbert valued process?, linear? ?operator?

Pages 25472565ýWe present some existence and convergence results for a general class of nonexpansive mappings in partially ordered hyperbolic metric spacesý. ýWe also give some examples to show the generality of the mappings considered herein.Keywords: Hyperbolic metric space?, ?nonexpansive mapping?, ?condition (C)

Pages 25672576ýLet G be a finite pgroup of order pn andý ýM(G)=p12n(n−1)−t(G)ý, ýwhere M(G)ý ýis the Schur multiplier of G and t(G) is a nonnegative integerý. ýThe classification of such groups G is already known for t(G)≤ýý6ý. ýThis paper extends the classification to t(G)=7.Keywords: Schur multiplier, Nonabelian tensor square, p, Group

Pages 25772583ýIn 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?

Pages 25852615Suppose 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),]
ýýxmPj(x)=∑n=02mam,n(j)Pj−n(x)ý,
ýwe find the coefficients b(p,q,ℓý,ýr)i,j in the expansioný
ýýxℓyr∇px∇qyf(x,y)=xℓýýyrf(p,q)(x,y)=∑m,n=0∞ýýa(p,q)m,nPm(x)Pn(y),a(0,0)m,n=am,ný,
ýWe give applications of these results in solving partial differenceý ýequations with varying polynomial coefficientsý, ýby reducing them toý ýrecurrence relations (difference equations) in the expansioný ýcoefficients of the solutioný.Keywords: ?Hahn?, ?Meixner?, ?Kravchuk, Charlier? ?polynomials, expansion coefficient, recurrence relations, linear? ?difference equations, connection coefficients 
Pages 26172634ýWe firstly prove the completeness of the category of crossed modules in a modified category of interestý. ýAfterwardsý, ýwe define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrowsý. ýThese constructions unify many corresponding results for the cases of groupsý, ýcommutative algebras and can also be adapted to various algebraic structuresý.Keywords: Modified category of interest?, ?crossed module?, ?cat object?, ?limit?

Pages 26352653ýThe concept of selfsimilarity on subsets of algebraic varietiesý ýis defined by considering algebraic endomorphisms of the varietyý ýas `similarity' mapsý. ýSelfsimilar fractals are subsets of algebraic varietiesý ýwhich can be written as a finite and disjoint union ofý ý`similar' copiesý. ýFractals provide a framework in whichý, ýone caný ýunite some results and conjectures in Diophantine geometryý. ýWeý ýdefine a wellbehaved notion of dimension for selfsimilar fractalsý. ýWe alsoý ýprove a fractal version of Roth's theorem for algebraic points oný ýa variety approximated by elements of a fractal subsetý. ýAs aý ýconsequenceý, ýwe get a fractal version of Siegel's theorem on finiteness of integral pointsý ýon hyperbolic curves and a fractal version of Falting's theorem ýon Diophantine approximation on abelian varietiesý.Keywords: Self, similarity, Diophantine approximation, arithmetic dynamics

Pages 26552662Let 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