Bulletin of Iranian Mathematical Society
Volume:43 Issue: 1, 2017

We study harmonic analysis on cocommutative KPC-hyper-groupsý, which is a generalization of DJS-hypergroupsý, ýintroduced by Kalyuzhnyiý, ýPodkolzin and Chapovskyý. ýWe prove that there is a relationship betweený ýthe associated measures μ and γμý, ýwhere μ isý ýa Radon measure on KPC-hypergroup Q and γ is a character on Q.

Highest weight modules of the double affine Lie algebra slˆˆ2 are studied under aý ýnew triangular decompositioný. ýSingular vectors of Verma modules areý ýdetermined using a similar condition with horizontal affine Lieý ýsubalgebrasý, ýand highest weight modules are described under theý ýcondition c1>0 and c2=0.

Generalizing the notion of character amenability for Banachý ýalgebrasý, ýwe study the concept of φ-Connes amenability ofý ýa dual Banach algebra A with predual A∗ý, ýwhere φ is a homomorphism from A onto Cý ýthat lies in A∗ý. ýSeveral characterizations ofý ýφ-Connes amenability are givený. ýWe also prove that theý ýfollowing are equivalent for a unital weakly cancellativeý ýsemigroup algebra l1(S)ý: (i) S is χ-amenableý. (ii) l1(S) is χ^-Connes amenableý. (iii) l1(S) has a χ^-normalý, ývirtual diagonalý.

n our paper [Aý. ýBý. ýMý. ýBasheer and Jý. ýMooriý, ýOn a group of the form 210:(U5(2):2)] we calculated the inertia factorsý, ýFischer matrices and the ordinary character table of the splitý ýextension 210:(U5(2):2) by means of Clifford-Fischerý ýTheoryý. ýThe second inertia factor group of 210:(U5(2):2)ý ýis a group of the form 21−:((31:8):2). Theý ýpurpose of this paper is the determination of the conjugacy classesý ýof G¯¯¯¯ using the coset analysis methodý, ýthe determinationý ýof the inertia factorsý, ýthe computations of the Fischer matrices andý ýthe ordinary character table of the split extension G¯¯¯¯=ýý21−:((31:8):2) by means of Clifford-Fischerý ýTheoryý. ýThrough various theoretical and computational aspects weý ýwere able to determine the structures of the inertia factor groupsý. ýThese are the groups H1=H2=(31:8):2, H3=ýýQD16 and H4=D12. The Fischer matricesý ýFi of G¯¯¯¯, which are complex valuedý ýmatricesý, ýare all listed in this paper and their sizes range betweený ý2 and 5ý. ýThe full character table of G¯¯¯¯, which is 41ýý×41complex valued matrixý, ýis available in the PhD thesis ofý ýthe first authorý, ýwhich could be accessed onlineý.

In this paperý, ýfirstý, ýwe investigate the construction of compact sets of Ck and Ck0ý ýby proving ``Cký,ýCk0−version ý" ýof Arzel\`{a}-Ascoli theoremý, ýand then introduce new measures of noncompactness on these spacesý. ýFinallyý, ýas an applicationý, ýwe study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixed point theorem associated with these new measures of noncompactnessý. ýFurtherý, ýsome examples are presented to show the efficiency of our results.

For a set of non-negative integers~Lý, ýthe L-intersection number of a graph is the smallest number~l for which there is an assignment of subsets Av⊆{1,…ý,ýl} to vertices vý, ýsuch that every two vertices u,v are adjacent if and only if |Au∩Av|∈Lý. ýThe bipartite L-intersection number is defined similarly when the conditions are considered only for the vertices in different partsý. ýIn this paperý, ýsome lower bounds for the (bipartite) L-intersection number of a graph for various types L in terms of the minimum rank of graph are obtainedý. ýTo achieve the main results we employ the inclusion matrices of set systems and show that how the linear algebra techniques give elegant proof and stronger results in some cases.

Let L be a Lie algebraý, ýDer(L) be the set of all derivations of L and Derc(L) denote the set of all derivations α∈Der(L) for which α(x)∈[x,L]:={[x,y]|y∈L} for all x∈Lý. ýWe obtain an upper bound for dimension of Derc(L) of the finite dimensional nilpotent Lie algebra L over algebraically closed fieldsý. ýAlsoý, ýwe classify all finite dimensional nilpotent Lie algebras L over algebraically closed fields for which dimDerc(L) attains its maximum value.

In this paper we consider contact CR-warped product submanifolds of the type M=NT×fN⊥, of a nearly Kenmotsu generalized Sasakian space form M¯(f1ý,ýf2ý,ýf3) and by use of Hopf's Lemma we show that M is simply contact CR-product under certain conditioný. ýFinallyý, ýwe establish a sharp inequality for squared norm of the second fundamental form and equality case is discussedý. ýThe results in this paper generalize existing results in the literature.

This article presents a systematic study for structure of finite wavelet framesý ýover prime fieldsý. ýLet p be a positive prime integer and Wpý ýbe the finite wavelet group over the prime field Zpý. ýWe study theoretical frame aspects of finite wavelet systems generated byý ýsubgroups of the finite wavelet group Wp.

A module is said to be PI-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of PI-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper surfaces in projective spaces over complex numbers and obtain results when the PI-extending property is inherited by direct summands. Moreover, we show that under some module theoretical conditions PI -extending modules with Abelian endomorphism rings have indecomposable decompositions. Finally, we apply our former results, getting that, under suitable hypotheses, the finite exchange property implies the full exchange property.

It is well known that every (real or complex) normed linear space L is isometrically embeddable into C(X) for some compact Hausdorff space Xý. ýHere X is the closed unit ball of L∗ (the set of all continuous scalar-valued linear mappings on L) endowed with the weak∗ topologyý, ýwhich is compact by the Banach--Alaoglu theoremý. ýWe prove that the compact Hausdorff space X can indeed be chosen to be the Stone--Cech compactification of L∗∖{0}ý, ýwhere L∗∖{0} is endowed with the supremum norm topology.

Let Ω be a class of unitalý ýC∗-algebrasý. ýWe introduce the notion of a local tracial Ω-algebraý. ýLet A be an α-simple unital local tracial Ω-algebraý. ýSuppose that α:G→Aut(A) is an action of a finite group G on Aý ýwhich has a certain non-simple tracial Rokhlin propertyý. ýThen the crossed product algebraý ýC∗(G,A,α) is a unital local tracial Ω -algebra.

In this paperý, ýwe consider the following Kirchhoff-type equationsý: ý−ý(a∫R3|∇u|2)Δu(x)u=λ f(x,u)ý,ýin R3, ýu(x)>0ý,ýin R3, ýu∈H1(R3)ý,ý ý ýýýwhere a,b>0 are constants and λ is a positive parameterý. ýThe aim of this paper is to study the existence of positive solutions for Kirchhoff-type equations with a nonlinearity in the critical growth under some suitable assumptions on V(x) and f(x,u) ý. ýRecent results from the literature are improved and extended.

Let p(z)=zsh(z) where h(z) is a polynomialý ýof degree at most n−s having all its zeros in |z|≥k or in |z|≤ký. ýIn this paper we obtain some new results about the dependence of |p(Rz)| on |p(rz)| for r2≤rR≤k2ý, ýk2≤rR≤R2 and for R≤r≤k ý. ýOur results refine and generalize certain well-known polynomial inequalitiesý.

A p-group G is called a CAC-p-group if CG(H)/H is ýcyclic for every non-cyclic abelian subgroup H in G with H≰ýýZ(G)ý. ýIn this paperý, ýwe give a complete classification ofý ýfinite CAC-p-groupsý.

Using variational argumentsý, ýwe prove the existence of infinitelyý ýmany solutions to a class of p-biharmonic equation iný ýRNý. ýThe existence ofý ýnontrivialý ýsolution is established under a newý ýset of hypotheses on the potential V(x) and the weight functionsý ýh1(x)ý,ýh2(x).

ýUsing variational argumentsý, ýwe prove the existence of infinitelyý ýmany solutions to a class of p-biharmonic equation iný RNý. ýThe existence ofý ýnontrivialý ýsolution is established under a newý ýset of hypotheses on the potential V(x) and the weight functionsý h1(x)ý,ýh2(x) ý.

In a recent paper Cý. ýMiguel proved that the diameter of the commuting graph of the matrix ring Mn(R) is equal to 4 if either n=3 or n≥5ý. ýBut the case n=4 remained opený, ýsince the diameter could be 4 or 5ý. ýIn this work we close the problem showing that also in this case the diameter is 4.

In this paper we study the existence of nontrivialý solutions for a variational inequality on the half-lineý. ýOurý ýapproach is based on the non-smooth critical point theoryý ýfor Szulkin-type functionals.

The purpose of this paper is to introduce a new mapping for a finiteý ýfamily of accretive operators and introduce an iterative algorithmý ýfor finding a common zero of a finite family of accretive operatorsý ýin a real reflexive strictly convex Banach space which has aý ýuniformly G\^ateaux differentiable norm and admits the dualityý ýmapping jφý, ýwhere φ is a gauge function invariantý ýon [0,∞)ý. ýFurthermoreý, ýwe prove the strong convergence underý ýsome certain conditionsý. ýThe results obtained in this paper improveý ýand extend the corresponding ones announced by many othersý.