

2018 . 

Bulletin of Iranian Mathematical Society
ISSN 1017060X
دوماهنامه  ( )
6 2017




 Caratheodory dimension for observers M.R. Molaei, Y. Sayyari * Pages 15591570 Abstract Full Text [PDF 136KB]   In this essay we introduce and study the notion of dimension for observers via Caratheodory structures and relative probability measures. We show that the dimension as a three variables function is an increasing function on observers، and decreasing function on the cuts of an observer. We find observers with arbitrary nonnegative dimensions. We show that Caratheodory dimension for observers is an invariant object under conjugate relations. Caratheodory dimension as a mapping، for multidimensional observers is considered. News spread is modeled via multidimensional observers.
Keywords: Caratheodory structure; observer; news spread; Hausdorff dimension
  
 On threedimensional N(k) paracontact metric manifolds and Ricci solitons U.C. De *, S. Deshmukh, K. Mandal Pages 15711583 Abstract Full Text [PDF 119KB]   The aim of this paper is to characterize 3 dimensional N(k) paracontact metric manifolds satisfying certain curvature conditions. We prove that a 3 dimensional N(k) paracontact metric manifold M admits a Ricci soliton whose potential vector field is the Reeb vector field xi if and only if the manifold is a paraSasakiEinstein manifold. Several consequences of this result are discussed. Finally، an illustrative example is constructed.
Keywords: Ricci semisymmetric; cyclic parallel Ricci tensor; η, parallel Ricci tensor; Ricci soliton; Einstein manifold
  
 Decay estimates of solutions to the IBq equation Y. Zhang * , P. Li Pages 15851600 Abstract Full Text [PDF 163KB]   In this paper we focus on the Cauchy problem for the generalized IBq equation with damped term in n dimensional space. We establish the global existence and decay estimates of solution with L q (1≤q≤2) initial value، provided that the initial value is suitably small. Moreover، we also show that the solution is asymptotic to the solution u L to the corresponding linear equation as time tends to infinity. Finally، asymptotic profile of the solution u L to the linearized problem is also discussed.
Keywords: IBq equation; global existence; decay estimates; asymptotic profile
  
 Functional identities of degree 2 in CSL algebras D. Han * Pages 16011619 Abstract Full Text [PDF 142KB]   L be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space H with dimH≥3، AlgL the CSL algebra associated with L and M be an algebra containing AlgL. This article is aimed at describing the form of additive mapppings F1،F2،G1،G2:AlgL⟶M satisfying functional identity F1(X)Y+F2(Y)X+XG2(Y)+YG1(X)=0 for all X،Y∈AlgL. As an application generalized inner biderivations and commuting additive mappings are determined.
Keywords: Functional identity; CSL algebra; generalized inner biderivation; commuting mapping
  
 The length of Artinian modules with countable Noetherian dimension M. Davoudian *, O. Ghayour Pages 16211628 Abstract Full Text [PDF 103KB]   It is shown that if M is an Artinian module over a ring R، then M has Noetherian dimension α، where α is a countable ordinal number، if and only if ωα+2≤l(M)≤ωα+1، where l(M) is the length of M، i.e.، the least ordinal number such that the interval [0، l(M)) cannot be embedded in the lattice of all submodules of M.
Keywords: Artinian module; Noetherian dimension; atomic module; the length of an R, module
  
 On derivations and biderivations of trivial extensions and triangular matrix rings N.M. Ghosseiri * Pages 16291644 Abstract Full Text [PDF 122KB]   Triangular matrix rings are examples of trivial extensions. In this article we determine the structure of derivations and biderivations of the trivial extensions، and thereby we describe the derivations and biderivations of the upper triangular matrix rings. Some related results are also obtained.
Keywords: Trivial extension; triangular matrix ring; derivation; biderivation
  
 Twogeodesic transitive graphs of prime power order W. Jin * Pages 16451655 Abstract Full Text [PDF 117KB]   In a noncomplete graph Γ، a vertex triple (u،v،w) with v adjacent to both u and w is called a 2geodesic if uneqw and u،w are not adjacent. The graph Γ is said to be 2geodesic transitive if its automorphism group is transitive on arcs، and also on 2geodesics. We first produce a reduction theorem for the family of 2geodesic transitive graphs of prime power order. Next، we classify such graphs which are also vertex quasiprimitive.
Keywords: 2, geodesic transitive graph; 2, arc transitive graph; automorphism group
  
 Stability of Fbiharmonic maps S.M. Kazemi Torbaghan, M.M. Rezaii * Pages 16571669 Abstract Full Text [PDF 124KB]   This paper studies some properties of Fbiharmonic maps between Riemannian manifolds. By considering the first variation formula of the Fbienergy functional، Fbiharmonicity of conformal maps are investigated. Moreover، the second variation formula for Fbiharmonic maps is obtained. As an application، instability and nonexistence theorems for Fbiharmonic maps are given.
Keywords: Biharmonic maps; F, biharmonic maps; conformal maps; stability
  
 Gorenstein hereditary rings with respect to a semidualizing module G. Zhao , B. Zhang * Pages 16711677 Abstract Full Text [PDF 102KB]   Let C be a semidualizing module. We first investigate the properties of finitely generated GCprojective modules. Then، relative to C، we introduce and study the rings over which every submodule of a projective (flat) module is GCprojective (flat)، which we call CGorenstein (semi)hereditary rings. It is proved that every CGorenstein hereditary ring is both coherent and CGorenstein semihereditary.
Keywords: Semidualizing module; GC, projective module; GC, flat module; GC, (semi)hereditary ring; coherent ring
  
 Duality for vector equilibrium problems with constraints N.L.H. Anh * Pages 16791694 Abstract Full Text [PDF 146KB]   In the paper، we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasirelative interior. Then، their applications to optimality conditions for quasirelative efficient solutions are obtained. Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constraint space have possibly empty interior.
Keywords: Equilibrium problem; duality; optimality conditions; quasi, relative efficient solution; generalized subconvexlikeness
  
 An upper bound for the regularity of powers of edge ideals M. Moghimian * Pages 16951698 Abstract Full Text [PDF 79KB]   A recent result due to Ha and Van Tuyl proved that the CastelnuovoMumford regularity of the quotient ring R/I(G) is at most matching number of G، denoted by match(G). In this paper، we provide a generalization of this result for powers of edge ideals. More precisely، we show that for every graph G and every s≥1، reg(R/I(G)s)≤(2s−1)E(G)s−1match(G).
Keywords: Edge ideal; Castelnuovo, Mumford regularity; matching number
  
 Properties of matrices with numerical ranges in a sector D. Zhang *, L. Hou, L. Ma Pages 16991707 Abstract Full Text [PDF 120KB]   Let (A) be a complex (nn) matrix and assume that the numerical range of (A) lies in the set of a sector of half angle (α) denoted by (Sα). We prove the numerical ranges of the conjugate، inverse and Schur complement of any order of (A) are in the same (Sα) . The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product، starcongruent matrix and unitary matrix of polar decompostion are also included in the same sector. Furthermore، we extend some inequalities about eigenvalues and singular values and the linear fractional maps to this class of matrices.
Keywords: Numerical ranges; sector; positive definite; Toeplitz decomposition
  
 On nuclei of supΣalgebras X. Zhang *, Y. Zhou Pages 17091721 Abstract Full Text [PDF 119KB]   In this paper، algebraic investigations on supΣ algebras are presented. A representation theorem for supΣalgebras in terms of nuclei and quotients is obtained. Consequently، the relationship between the congruence lattice of a supΣ algebra and the lattice of its nuclei is fully developed.
Keywords: Sup, Σ, algebra; nucleus; congruence; quotient
  
 Highaccuracy alternating segment explicitimplicit method for the fourthorder heat equation G. Guo *, S. L Pages 17231737 Abstract Full Text [PDF 238KB]   Based on a group of new Saulyev type asymmetric difference schemes constructed by author، a highorder، unconditionally stable and parallel alternating segment explicitimplicit method for the numerical solution of the fourthorder heat equation is derived in this paper. The truncation error is fourthorder in space، which is much more accurate than the known alternating segment explicitimplicit methods. Numerical simulations are performed to show the effectiveness of the present method that are in preference to the prior methods.
Keywords: Fourth, order heat equation; alternating segment explicit, implicit method; high accuracy; parallel computation; unconditional stability
  
 Applications of convolution and subordination to certain pvalent functions S. Hussain *, J. Sokó,ł, , U. Farooq, M. Darus, T. Mahmood Pages 17391749 Abstract Full Text [PDF 129KB]   In this paper we considered some new classes of multivalent functions by using AoufSilvermanSrivastava operator and derived some important results using convolution and subordination technique. This new class is an extension of a class which introduced before.
Keywords: Multivalent function; convolution; Subordination; linear operator
  
 Hölder continuity of solution maps to a parametric weak vector equilibrium problem P. Preechasilp *, R. wangkeeree Pages 17511767 Abstract Full Text [PDF 145KB]   In this paper، by using a new concept of strong convexity، we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general setvalued one. Without strong monotonicity assumptions، the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.
Keywords: Vector equilibrium problem; solution mapping; Hölder continuity; linear scalarization
  
 Hyperbolic surfaces of L12type P. Lucas *, H.F. Ramí,rezOspina Pages 17691779 Abstract Full Text [PDF 118KB]   In this paper، we show that an L12type surface in the threedimensional hyperbolic space H3⊂R41 either is an open piece of a standard Riemannian product H1(−1+r2−−−−−√)S1(r) ، or it has non constant mean curvature، non constant Gaussian curvature، and non constant principal curvatures.
Keywords: Hyperbolic surface; Cheng, Yau operator; L1, finite, type surface; L1, biharmonic surface; Newton transformation
  
 The second dual of strongly zeroproduct preserving maps A.R. Khoddami * Pages 17811790 Abstract Full Text [PDF 99KB]   The notion of strongly Lie zeroproduct preserving maps on normed algebras as a generalization of Lie zeroproduct preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zeroproduct preserving. Also some hereditary properties of strongly Lie zeroproduct preserving maps are presented. Finally the second dual of a strongly zeroproduct، strongly Jordan zeroproduct and strongly Lie zeroproduct preserving map on a certain class of normed algebras are investigated.
Keywords: Strongly zero, product preserving map; strongly Jordan zero, product preserving map; strongly Lie zero, product preserving map; Arens regular
  
 Classification of solvable groups with a given property M. Rezaei *, Z. Foruzanfar Pages 17911800 Abstract Full Text [PDF 114KB]   In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are setwise relatively prime for any 5 distinct noncentral conjugacy classes.
Keywords: Frobenius group; conjugacy classes; graph; order
  
 The graph of equivalence classes and Isoclinism of groups R. Rezaei *, M. Varmazyar Pages 18011810 Abstract Full Text [PDF 126KB]   Let G be a nonabelian group and let Γ(G) be the noncommuting graph of G. In this paper we define an equivalence relation ∼ on the set of V(Γ(G))=G∖Z(G) by taking x∼y if and only if N(x)=N(y)، where N(x)={u∈G  x and u are adjacent in Γ(G)} is the open neighborhood of x in Γ(G). We introduce a new graph determined by equivalence classes of noncentral elements of G، denoted ΓE(G)، as the graph whose vertices are {[x]  x∈G∖Z(G)} and join two distinct vertices [x] and [y]، whenever [x،y]≠1. We prove that group G is ACgroup if and only if ΓE(G) is complete graph. Among other results، we show that the graphs of equivalence classes of noncommuting graph associated with two isoclinic groups are isomorphic.
Keywords: Non, commuting graph; graph of equivalence classes; Isoclinism
  
 Defining relations of a group Γ=G3,4(2,Z) and its action on real quadratic field M. Ashiq *, T. Imran, M. A. Zaighum Pages 18111820 Abstract Full Text [PDF 228KB]   In this paper، we have shown that the coset diagrams for the action of a linearfractional group Γgenerated by the linearfractional transformations r:z→z−1z and s:z→−12(z+1) on the rational projective line is connected and transitive. By using coset diagrams، we have shown that r3=s4=1 are defining relations for Γ. Furthermore، we have studied some important results for the action of group Γ on real quadratic field Q(n−−√). Also، we have classified all the ambiguous numbers in the orbit.
Keywords: Coset diagrams; modular group; linear, fractional transformations; real quadratic field; ambiguous numbers
  
 Entropy of a semigroup of maps from a setvalued view B. Hou* , X. Wang Pages 18211835 Abstract Full Text [PDF 131KB]   In this paper، we introduce a new entropylike invariant، named Hausdorff metric entropy، for finitely generated semigroups acting on compact metric spaces from a setvalued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreover، some notions of chaos are also well generalized for finitely generated semigroups from a setvalued view.
Keywords: Topological entropy; semigroups; entropy, like invariants; Hausdorff metric
  
 Initial coefficients of starlike functions with real coefficients S. Kumar , V. Ravichandran orcid *, S. Verma Pages 18371854 Abstract Full Text [PDF 144KB]   The sharp bounds for the third and fourth coefficients of MaMinda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of closetoconvex functions
Keywords: Coefficient estimates; starlike functions; close to convex functions; functions with positive real part; real coefficient
  
 Classifying pentavalnet symmetric graphs of order 24p B. Ling * Pages 18551866 Abstract Full Text [PDF 124KB]   A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2، 3، 5، 11 or 17، and up to isomorphism، there are only eleven such graphs.
Keywords: Symmetric graph; normal quotient; automorphism group
  
 Existence of positive solutions for a secondorder pLaplacian impulsive boundary value problem on time scales F. Tokmak Fen *, I.Y. Karaca Pages 18891903 Abstract Full Text [PDF 143KB]   In this paper، we investigate the existence of positive solutions for a secondorder multipoint pLaplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone، sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.
Keywords: Impulsive boundary value problems; p, Laplacian; positive solutions; fixed point theorem; Time scales
  
 When is the ring of real measurable functions a hereditary ring? H. Hejazipour, A. R. Naghipour * Pages 19051912 Abstract Full Text [PDF 104KB]   Let M(X،A،μ) be the ring of realvalued measurable functions on a measure space (X،A،μ). In this paper، we characterize the maximal ideals in the rings of real measurable functions and as a consequence، we determine when M(X،A،μ) is a hereditary ring.
Keywords: Measurable functions; hereditary rings; projective prime ideals
  
 Subdirectly irreducible acts over some semigroups Gh. Moghaddasi *, M. Mahmoudi Pages 19131924 Abstract Full Text [PDF 122KB]   In this paper، we characterize and find the number of subdirectly irreducible acts over some classes of semigroups، such as zero semigroups، right zero semigroups and strong chain of left zero semigroups.
Keywords: Subdirectly irreducible; chain of semigroups
  
 The lower bound for the number of 1factors in generalized Petersen graphs H. Ren , C. Yang *, J. Wang Pages 19251937 Abstract Full Text [PDF 343KB]   In this paper، we investigate the number of 1factors of a generalized Petersen graph P(N،k)and get a lower bound for the number of 1factors of P(N،k) as k is odd، which shows that the number of 1factors of P(N،k) is exponential in this case and confirms a conjecture due to Lovász and Plummer (Ann. New York Acad. Sci. 576(2006)، no. 1، 389398).
Keywords: Generalized Petersen graphs; matching; 1, factors; Fibonacci number
  
 Composition of resolvents and quasinonexpansive multivalued mappings in Hadamared spaces G. Zamani Eskandani *, S. Azarmi, M. Eslamian Pages 19391955 Abstract Full Text [PDF 135KB]   The proximal point algorithm، which is a wellknown tool for finding minima of convex functions، is generalized from the classical Hilbert space framework into a nonlinear setting، namely، geodesic metric spaces of nonpositive curvature. In this paper we propose an iterative algorithm for finding the common element of the minimizers of a finite family of convex functions and the common fixed points of a finite family of quasinonexpansive multivalued mappings in Hadamard spaces.
Keywords: Proximal point algorithm; CAT(0) spaces; Nonexpansive multivalued mappings
  
 A hybrid mean value involving a new Gauss sums and Dedekind sums X.X. Li *, W.P. Zhang Pages 19571968 Abstract Full Text [PDF 103KB]   In this paper، we introduce a new sum analogous to Gauss sum، then we use the properties of the classical Gauss sums and analytic method to study the hybrid mean value problem involving this new sums and Dedekind sums، and give an interesting identity for it.
Keywords: A new Gauss sums; Dedekind sums; hybrid mean value; identity; analytic method
  
 SemiRothberger and related spaces A. Sabah, M. Khan * Pages 19691987 Abstract Full Text [PDF 157KB]   In this paper our focus is to study certain covering properties in topological spaces by using semiopen covers. A part of this article deals with Rothbergertype covering properties. The notions of sRothberger، almost sRothberger، star sRothberger، almost star sRothberger، strongly star sRothberger spaces are defined and corresponding properties are investigated.
Keywords: Semi, open set, (star) semi, compact space; semi, Lindelöf space; s, Rothberger space; star s, Rothberger space
  
 A descent method for explicit computations on curves K. Filom * Pages 19892016 Abstract Full Text [PDF 270KB]   It is shown that the knowledge of a surjective morphism X→Y of complex curves can be effectively used to make explicit calculations. The method is demonstrated by the calculation of j(nτ) (for some small n) in terms of j(τ) for the elliptic curve with period lattice (1،τ)، the period matrix for the Jacobian of a family of genus2 curves complementing the classic calculations of Bolza and explicit general formulae for branched covers of an elliptic curve with exactly one ramification point.
Keywords: Algebraic curves; branched covers; elliptic curves
  
 Upper bounds for noetherian dimension of all injective modules with Krull dimension S.J. Hashemi Zadeh Dezfuli , M. Zholanezhad * Page 2017 Abstract Full Text [PDF 106KB]   In this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary rings. In particular، we also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.
Keywords: Noetherian dimension; Artinian modules; injective modules; comonoform right ideals; duo rings
  
 Locally finite basic classical simple Lie superalgebras M. Yousofzadeh * Pages 20272050 Abstract Full Text [PDF 215KB]   In this work، we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.
Keywords: Locally finite Lie superalgebra; finite dimensional basic classical simple Lie superalgebra; Cartan subalgebra; conjugacy classes
  
 On normalizers of maximal subfields of division algebras M. Motiee * Pages 20512056 Abstract Full Text [PDF 90KB]   Here، we investigate a conjecture posed by Amiri and Ariannejad claiming that if every maximal subfield of a division ring D has trivial normalizer، then D is commutative. Using Amitsur classification of finite subgroups of division rings، it is essentially shown that if D is finite dimensional over its center then it contains a maximal subfield with nontrivial normalizer if and only if D∗ contains a nonabelian soluble subgroup. This result generalizes a theorem of MahdaviHezavehi and Tignol about cyclicity of division algebras of prime index.
Keywords: Division algebras; cyclic algebras; soluble groups
  
 Singular values of convex functions of matrices Z. Ulukö,k * Pages 20572066 Abstract Full Text [PDF 118KB]   Let Ai،Bi،Xi،i=1،،m،be nbyn matrices such that ∑mi=1Ai2 and ∑mi=1Bi2 are nonzero matrices and each Xi is positive semidefinite. It is shown that if f is a nonnegative increasing convex function on [0،∞) satisfying f(0)=0، then 2sj⎛⎝⎜f⎛⎝⎜∣∣∑mi=1A∗iXiBi∣∣∥∥∑mi=1Ai2∥∥∥∥∑mi=1Bi2∥∥−−−−−−−−−−−−−−−−−−−−−−−−−√⎞⎠⎟⎞⎠⎟≤sj(⊕mi=1f(2Xi))
for j=1،،n . Applications of our results are given.
Keywords: Singular value; arithmetic, geometric mean; direct sum; positive semidefinite matrix; convex function
  
 A new hybrid conjugate gradient algorithm for unconstrained optimization X. Han, J. Zhang, J. Chen * Pages 20672084 Abstract Full Text [PDF 162KB]   In this paper، a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems. This new method can generate sufficient descent directions unrelated to any line search. Moreover، the global convergence of the proposed method is proved under the Wolfe line search. Numerical experiments are also presented to show the efficiency of the proposed algorithm، especially for solving highly dimensional problems.
Keywords: Unconstrained optimization problem; hybrid conjugate gradient algorithm; sufficient descent directions; global convergence
  
 Some results on premonotone operators M.H. Alizadeh *, M. Roohi Pages 20852097 Abstract Full Text [PDF 136KB]   In this paper، some properties of premonotone operators are proved. It is shown that in a reflexive Banach space، a full domain multivalued σmonotone operator with sequentially normweak∗ closed graph is normweak∗ upper semicontinuous. The notion of σconvexity is introduced and the relations between the σmonotonicity and σconvexity is investigated. Moreover، some results on the sum and difference of two σmonotone operators is considered.
Keywords: Generalized monotone operators; upper semicontinuous; convex function
  
 Nonhomogeneous continuous and discrete gradient systems: the quasiconvex case H. Khatibzadeh* , V. Mohebbi Pages 20992110 Abstract Full Text [PDF 121KB]   In this paper، first we study the weak and strong convergence of solutions to the following first order nonhomogeneous gradient system {−x′(t)=∇ϕ(x(t))+f(t)، a.e.\ \ on (0،∞)x(0)=x0∈H to a critical point of ϕ، where ϕ is a C1 quasiconvex function on a real Hilbert space H with Argminϕ≠∅ and f∈L1(0،+∞;H). These results extend the results in the literature to nonhomogeneous case. Then the discrete version of the above system by backward Euler discretization has been studied. Beside of the proof of the existence of the sequence given by the discrete system، someresults on the weak and strong convergence to the critical point of ϕ are also proved. These results when ϕ is pseudoconvex (therefore the critical points are the same minimum points) may be applied in optimization for approximation of a minimum point of ϕ.
Keywords: Gradient system; quasi, convex; backward Euler discretization; weak convergence; strong convergence
  
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