Bulletin of Iranian Mathematical Society
Volume:43 Issue: 6, 2017

ýIn this essay we introduce and study the notion of dimension for observers via Caratheodory structures and relative probability measuresý. ýWe show that the dimension as a three variables function is an increasing function on observersý, ýand decreasing function on the cuts of an observerý. ýWe find observers with arbitrary non-negative dimensionsý. ýWe show that Caratheodory dimension for observers is an invariant object under conjugate relationsý. ýCaratheodory dimension as a mappingý, ýfor multi-dimensional observers is consideredý. ýNews spread is modeled via multi-dimensional observersý.

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 paraSasaki-Einstein manifold. Several consequences of this result are discussed. Finally, an illustrative example is constructed.

ýIn this paper we focus on the Cauchy problem for the generalizedý ýIBq equation with damped term in n -dimensional spaceý. ýWe establish the global existence and decay estimates of solution with L q (1≤q≤2) initial valueý, ýprovided that the initial value is suitably smallý. ýMoreoverý, ýwe also show that the solution is asymptotic to the solution u L to the corresponding linear equation as time tends to infinityý. ýFinallyý, ýasymptotic profile of the solution u L to the linearized problem is also discussedý.

L be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space H with dimH≥3ý, ýAlgLý ýthe CSL algebra associated with L and M be an algebra containing AlgLý. ýThis article is aimed at describing the form ofý ýadditive mapppings F1ý,ýF2ý,ýG1ý,ýG2:AlgL⟶M satisfying functional identityý ýF1(X)Y(Y)X屭(Y)恭(X)=0 for all Xý,ýY∈AlgLý. ýAs an application generalized inner biderivations and commutingý ýadditive mappings are determinedý.

ýIt is shown thatý ýif M is an Artinian module over a ringý ýRý, ýthen M has Noetherian dimension αý, ýwhere α is a countable ordinal numberý, ýif and only if ωα≤l(M)≤ωαý, ýwhere l(M) isý ýthe length of Mý, ýi.e., the least ordinal number such that the interval [0ý,ý l(M)) cannot be embedded in the lattice of all submodules of M.

ýTriangular matrix rings are examples of trivial extensionsý. ýIn this article we determine the structure of derivations and biderivations of the trivial extensionsý, ýand thereby we describe the derivations and biderivations of the upper triangular matrix ringsý. ýSome related results are also obtainedý.

In a non-complete graph Γ, a vertex triple (u,v,w) with v adjacent to both u and w is called a 2-geodesic if uneqw and u,w are not adjacent. The graph Γ is said to be 2-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of 2-geodesic transitive graphs of prime power order. Next, we classify such graphs which are also vertex quasiprimitive.

This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.

ýLet C be a semidualizing moduleý. ýWe first investigate the properties ofý ýfinitely generated GC-projective modulesý. ýThený, ýrelative to Cý, ýwe introduce and study the rings over whichý ýevery submodule of a projective (flat) module is GC-projective (flat)ý, ýwhich we call C-Gorenstein (semi)hereditary ringsý. ýIt is proved that every C-Gorenstein hereditary ring is both coherent and C-Gorenstein semihereditary.

ýIn the paperý, ýwe study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interiorý. ýThený, ýtheir applications to optimality conditions for quasi-relative efficient solutions are obtainedý. ýOur 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.

ýA recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring R/I(G) is at most matching number of Gý, ýdenoted by match(G)ý. ýIn this paperý, ýwe provide a generalization of this result for powers of edge idealsý. ýMore preciselyý, ýwe show that for every graph G and every s≥1ý, ý reg(Rý/ýI(G)s)≤(2s−1)|E(G)|s−1match(G).

Let (A) be a complex (n×n) 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, star-congruent 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.

ýIn this paperý, ýalgebraic investigations on sup-Σ -algebras are presentedý. ýA representation theorem forý ýsup-Σ-algebras in terms of nuclei and quotients is obtainedý. ýConsequentlyý, ýthe relationship betweený ýthe congruence lattice of a sup-Σ -algebra and the lattice of its nuclei is fully developed.

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-implicit methods. Numerical simulations are performed to show the effectiveness of the present method that are in preference to the prior methods.

In this paper we considered some new classes of multivalent functions by using Aouf-Silverman-Srivastava operator and derived some important results using convolution and subordination technique. This new class is an extension of a class which introduced before.

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 set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.

In this paper, we show that an L1-2-type surface in the three-dimensional hyperbolic space H3⊂R41 either is an open piece of a standard Riemannian product H1(−1−−−−−√)×S1(r) , or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are de ned. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of a strongly zero-product, strongly Jordan zero-product and strongly Lie zero-product preserving map on a certain class of normed algebras are investigated.

In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.

ýLet G be a non-abelian group and let Γ(G) be the non-commuting graph of Gý. ýIn 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)ý, ýwhere N(x)={u∈G | x and u are adjacent in Γ(G)} is the open neighborhood of x in Γ(G)ý. ýWe introduce a new graph determined by equivalence classes of non-central elements of Gý, ýdenoted ΓE(G)ý, ýas the graph whose vertices are {[x] | x∈G∖Z(G)} and join two distinct vertices [x] and [y]ý, ýwhenever [x,y]≠1ý. ýWe prove that group G is AC-group if and only if ΓE(G) is complete graphý. ýAmong other resultsý, ýwe show that the graphs of equivalence classes of non-commuting graph associated with two isoclinic groups are isomorphic.

In this paperý, ýwe have shown that the coset diagrams for theý ýaction of a linear-fractional group Γgenerated by the linear-fractionalý ýtransformations r:z→z−1z and s:z→−12(z) oný ýthe rational projective line is connected and transitiveý. ýBy using coset diagramsý, ýwe have shown that r3=s4=1 are defining relations for Γý. ýFurthermoreý, ýwe have studied some important results for the action of group Γ on realý ýquadratic field Q(n−−√)ý. ýAlsoý, ýwe have classified all the ambiguous numbers in the orbit.

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued 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 set-valued view.

The sharp bounds for the third and fourth coefficients of Ma-Minda 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 close-to-convex functions

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.

ýSuppose that Xt is a one-dimensional and real-valued Levyý ýprocess started from X0=0ý, ýwhich ({\bf 1}) its nonnegativeý ýjumps measure ν satisfying ∫ýýRmin{1,x2}ν(dx)

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian 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.

ýLet M(Xý,ýAý,ýμ) be the ring of real-valued measurable functionsý ýon a measure space (Xý,ýAý,ýμ)ý. ýIn this paperý, ýwe characterize the maximal ideals in the rings of real measurable functionsý ýand as a consequenceý, ýwe determine when M(Xý,ýAý,ýμ) is a hereditary ring.

ýIn this paperý, ýwe characterize and find the number of subdirectlyý ýirreducible acts over some classes of semigroupsý, ýsuch as zeroý ýsemigroupsý, ýright zero semigroupsý ýand strong chain of left zero semigroups.

ýIn this paperý, ýwe investigate the number of 1-factors of aý ýgeneralized Petersen graph P(N,k)and get a lower bound for theý ýnumber of 1-factors of P(N,k) as k is oddý, ýwhich shows that theý ýnumber of 1-factors of P(N,k) is exponential in this case andý ýconfirms a conjecture due to Lovász and Plummer (Anný. ýNew York Acadý. ýSciý. ý576(2006)ý, ýnoý. ý1ý, ý389-398).

ýThe proximal point algorithmý, ýwhich is a well-known tool for findingý ýminima of convex functionsý, ýis generalized from the classicalý ýHilbert space framework into a nonlinear settingý, ýnamelyý, ýgeodesicý ýmetric spaces of nonpositive curvatureý. ýIn this paper we propose aný ýiterative algorithm for finding the common element of theý ýminimizers of a finite family of convex functions and the common ýfixed points of a finite family of quasi-nonexpansive multivaluedý ýmappings in Hadamardý ýspaces.

ýIn this paperý, ýwe introduce a new sumý ýanalogous to Gauss sumý, ýthen we use the properties of theý ýclassical Gauss sums and analytic method to study the hybrid meaný ývalue problem involving this new sums and Dedekind sumsý, ýandý ýgive an interesting identity for it.

In this paper our focus is to study certain covering properties in topological spaces by using semi-open covers. A part of this article deals with Rothberger-type covering properties. The notions of s-Rothberger, almost s-Rothberger, star s-Rothberger, almost star s-Rothberger, strongly star s-Rothberger spaces are defined and corresponding properties are investigated.

ýIt is shown that the knowledge of a surjective morphism X→Y of complexý ýcurves can be effectively usedý ýto make explicit calculationsý. ýThe method is demonstratedý ýby the calculation of j(nτ) (for some small n) in terms of j(τ) for the elliptic curve ýwith period lattice (1,τ)ý, ýthe period matrix for the Jacobian of a family of genus-2 curvesý ýcomplementing the classic calculations of Bolzaý ýand explicit general formulae for branched covers of an elliptic curve with exactly one ramification point.

ýIn this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary ringsý. ýIn particularý, ýwe also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.

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.

ýHereý, ýwe investigate a conjecture posed by Amiri and Ariannejad claimingý ýthat if every maximal subfield of a division ring D has trivial normalizerý, ýthen D is commutativeý. ýUsing Amitsur classification ofý ýfinite subgroups of division ringsý, ýit is essentially shown that ifý ýD is finite dimensional over its center then it contains a maximalý ýsubfield with non-trivial normalizer if and only if D∗ contains aý ýnon-abelian soluble subgroupý. ýThis result generalizes a theorem ofý ýMahdavi-Hezavehi and Tignol about cyclicity of division algebras of prime index.

ýLet Ai,Bi,Xi,i=1,…,m,be n-by-n matrices such that ý∑mi=1|Ai|2 and ý∑mi=1|Bi|2 are nonzero matrices and each Xi isý ýpositive semidefiniteý. ýIt is shown that if f is a nonnegative increasing ýconvex function on [0,∞) satisfying f(0)ýý=0ý, ýthen
ý2sj⎛⎝⎜f⎛⎝⎜∣∣∑mi=1A∗ýýiXiBi∣∣∥∥∑mi=1|ýýAi|2∥∥∥∥∑mi=1|ýýBi|2∥∥−−−−−−−−−−−−−−−−−−−−−−−−−√⎞⎠⎟⎞⎠⎟≤sj(⊕ýými=1f(2Xi))ý
ýfor j=1,…,n
ý. ýApplications of our results are given.

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.

ýIn this paperý, ýsome properties of pre-monotone operators are provedý. ýIt is shown that in a reflexive Banach spaceý, ýa full domain multivalued σ-monotone operator with sequentially norm×weak∗ closed graph is norm×weak∗ upper semicontinuousý. ýThe notion of σ-convexity is introduced and theý ýrelations between the σ-monotonicity and σ-convexity is investigatedý. ýMoreoverý, ýsome results on the sum and difference of two σ-monotone operators is considered.

ýIn this paperý, ýfirst we study the weak and strong convergence of solutions to theý ýfollowing first order nonhomogeneous gradient systemý ý{−x′(t)=∇ϕ(x(t))(t), a.e.\ \ on (0,∞)ýýx(0)=x0∈H to a critical point of ϕý, ýwhereý ýϕ is a C1 quasi-convex function on a real Hilbert spaceý ýH with Argminϕ≠∅ and f∈L1(0,∞;H)ý. ýThese results extend theý ýresults in the literature to non-homogeneous caseý. ýThen theý ýdiscrete version of the above system by backward Eulerý ýdiscretization has been studiedý. ýBeside of the proof of theý ýexistence of the sequence given by the discrete systemý, ýsomeýýresults oný ýthe weak and strong convergence to the critical point of ϕ are also provedý. ýThese results when ϕ is pseudo-convex (therefore the critical pointsý ýare the same minimum points) may be applied in optimization for approximation of aý ýminimum point of ϕý.