Bulletin of Iranian Mathematical Society
Volume:42 Issue: 5, 2016

In this paperý, ýwe investigate a damped Korteweg-deý ýVries equation with forcing on a periodic domainý ýT=R/(2πZ) ý. ýWe can obtain that if theý ýforcing is periodic with small amplitudeý, ýthen the solution becomesý ýeventually time-periodic.

In this paperý, ýwe consider an inverse boundary value problem for two-dimensional heat equation in an annular domainý. ýThis problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curveý. ýTo this endý, ýthe boundary integral equation method is usedý. ýSince the resulting system of linear algebraic equations is ill-posedý, ýthe Tikhonov first-order regularization procedure is employed to obtain a stable solutioný. ýDetermination of regularization parameter is based on L-curve techniqueý. ýSome numerical examples for the feasibility of the proposed method are presentedý.

There is a flatness property of acts over monoids called Condition (PWP) whichý, ýso farý, ýhas receivedý ýmuch attentioný. ýIn this paperý, ýwe introduce Condition GP-(P)ý, ýwhich is a generalization of Condition (PWP)ý. ýFirstlyý, ýsome characterizations of monoids by Condition GP-(P) of theirý ý(cyclicý, ýRees factor) acts are givený, ýand many known results are generalizedý. ýMoreoverý, ýsome possible conditions on monoids that describe when their diagonal acts satisfy Condition GP-(P) are foundý. ýFinallyý, ýusing some new types of epimorphismsý, ýan alternative description of Condition GP-(P) (resp.ý, ýCondition (PWP) is obtainedý, ýand directedý ýcolimits of these new epimorphisms are investigated.

We study dual integral equations which appear in formulation of theý ýpotential distribution of an electrified plate with mixed boundaryý ýconditionsý. ýThese equations will be converted to a system ofý ýsingular integral equations with Cauchy type kernelsý. ýUsingý ýChebyshev polynomialsý, ýwe propose a method to approximate theý ýsolution of Cauchy type singular integral equation which will beý ýused to approximate the solution of the main dual integralý ýequationsý. ýNumerical results demonstrate effectiveness of this method.

The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator methodý. ýSome results related to random sums of independent geometric distributed random variables are also investigated.

Let G be a finite groupý. ýAn element g∈G is called non-vanishingý, ýif forý ýevery irreducible complex character χ of Gý, ýχ(g)≠0ý. ýThe bi-Cayley graph \BCay(G,T) of G with respect to a subset T⊆Gý, ýis an undirected graph withý ývertex set G×{1,2} and edge set {{(x,1),(tx,2) ∣x∈Gý,ý t∈T}ý. ýLet \nv(G) be the setý ýof all non-vanishing elements of a finite group Gý. ýWe show that g∈\nv(G) if and only if the adjacency matrix of \BCay(G,T)ý, ýwhere T=\Cl(g) is theý ýconjugacy class of gý, ýis non-singularý. ýWe prove that ýif the commutator subgroup of G has prime order pý, ýthený ý(1) g∈\nv(G) if and only if |\Cl(g)|

It is commonly accepted that fractional differential equations playý ýan important role in the explanation of many physical phenomenaý. ýForý ýthis reason we need a reliable and efficient technique for theý ýsolution of fractional differential equationsý. ýThis paper deals withý ýthe numerical solution of a class of fractional differentialý ýequationý. ýThe fractional derivatives are described based on theý ýCaputo senseý. ýOur main aim is to generalize the Chebyshev cardinalý ýoperational matrix to the fractional calculusý. ýIn this worký, ýtheý ýChebyshev cardinal functions together with the Chebyshev cardinalý ýoperational matrix of fractional derivatives are used for numericalý ýsolution of a class of fractional differential equationsý. ýThe mainý ýadvantage of this approach is that it reduces fractional problems toý ýa system of algebraic equationsý. ýThe method is applied to solveý ýnonlinear fractional differential equationsý. ýIllustrative examplesý ýare included to demonstrate the validity and applicability of theý ýpresented techniqueý.

In this paperý, ýa numerical procedure for an inverse problem ofý ýsimultaneously determining an unknown coefficient in a semilinear ýparabolic equation subject to the specification of the solution atý ýan internal point along with the usual initial boundary conditions ýis consideredý. ýThe method consists of expanding the requiredý ýapproximate solution as the elements of the inverse quadraticý ýradial basis functions (IQ-RBFs)ý. ýThe operational matrix ofý ýderivative for IQ-RBFs is introduced and the new computationalý ýtechnique is used for this purposeý. ýThe operational matrix ofý ýderivative is utilized to reduce the problem to a set of algebraicý ýequationsý. ýSome examples are given to demonstrate the validity andý ýapplicability of the new method and a comparison is made with theý ýexisting results.

In this paperý, ýwe investigate some results on natural metrics on the μ-normal functions and meromorphic Qp-classesý. ýAlsoý, ýthese classes are shown to be complete metric spaces with respect to the corresponding metricsý. ýMoreoverý, ýcompact composition operators Cϕ and Lipschitz continuous operators acting from μ-normal functions to the meromorphic Qp-classes are characterized by conditions depending only on ϕ.

Let \pA be a commutative Banach algebra and \eX be a left Banach \pA-moduleý. ýWe study the setý ý\Dec\pA(\eX) of all elements in \pA which induce a decomposable multiplication operator on \eXý. ýIn the case \eX=\pAý, ý\Dec\pA(\pA) is the well-known Apostol algebra of \pAý. ýWe show that \Dec\pA(\eX) is intimately related with the largest spectrally separable subalgebra of \pA and in this contextý ýwe give some results which are related to an open question if Apostol algebra is regular for any commutative algebra \pA
ý.

Let A be a C∗ algebraý, ýTý:ýA→A be a linear map which satisfies the functional equation T(x T(y)=T2(xy),T(x∗)=T(x)∗ý. ýWe prove that under each of the following conditionsý, ýT must be the trivial map T(x)=λx for some λ∈R: ýý ýi) A is a simple C∗-algebraý. ýii) A is unital with trivial center and has a faithful trace such that eachý ýzero-trace element lies in the closure of the span of commutator elementsý. ýiii) A=B(H) where Hýý is a separable Hilbert spaceý. ýFor a given field Fý, ýwe consider a similar functional equation {T(x)T(y)=T2(xy),T(xtr)= (x)tr,} where T is a linear map on Mn(F) andý ý"tr"ý ýis the transpose operatorý. ýWe prove that this functional equation has trivial solution for all n∈N if and only if F is a formally real fieldý.

The full automorphism group of U6(2) is a group of the form U6(2):S3. The group U6(2):S3 has a maximal subgroup 29:(L3(4):S3) of order 61931520. In the present paper, we determine the Fischer-Clifford matrices (which are not known yet) and hence compute the character table of the split extension 29:(L3(4):S3).

Let R be a ∗-prime ring with centerý ýZ(R)ý, ýd a non-zero (σ,τ)-derivation of R with associatedý ýautomorphisms σ and τ of Rý, ýsuch that σý, ýτý ýand d commute with ′∗′ý. ýSuppose that U is an ideal of R such that U∗=Uý, ýand Cσ,τ={c∈ýýR | cσ(x)=τ(x)c for~all x∈R}. In the present paperý, ýit is shown that if characteristic of R is different from two andý ý[d(U),d(U)]σ,τ={0}, then R is commutativeý. ýCommutativity of R has also been established in case ifý ý[d(R),d(R)]σ,τ⊆Cσ,τ.

In this paperý, ýwe propose two iterative methods for finding a common solution of a finite family of equilibrium problems ýfor pseudomonotone bifunctionsý. ýThe first is a parallel hybrid extragradient-cutting algorithm which is extended from theý ýpreviously known one for variational inequalities to equilibrium problemsý. ýThe second is a new cyclic hybridý ýextragradient-cutting algorithmý. ýIn the cyclic algorithmý, ýusing the known techniquesý, ýwe can perform and develop practical numerical experiments.

Let X be a class of R-modulesý. ýIn this paperý, ýwe investigate \;X-injective (projective) and DG-X-injective (projective) complexes which are generalizations of injective (projective) and DG-injectiýýve (projective) complexesý. ýWe prove that some known results can be extended to the class of \;X-injective (projective) and DG-X -injective (projective) complexes for this general settings.

In this paperý, ýsome KKT type sufficient global optimality conditionsý ýfor general mixed integer nonlinear programming problems withý ýequality and inequality constraints (MINPP) are establishedý. ýWe achieveý ýthis by employing a Lagrange function for MINPPý. ýIn additioný, ýverifiable sufficient global optimality conditions for general mixedý ýinteger quadratic programming problems are derived easilyý. ýNumericalý ýexamples are also presented.

The excessive index of a bridgeless cubic graph G is the least integer ký, ýsuch that G can be covered by k perfect matchingsý. ýAn equivalent form of Fulkerson conjecture (due to Berge) is that every bridgelessý ýcubic graph has excessive index at most fiveý. ýClearlyý, ýPetersen graph is a cyclically 4-edge-connected snark with excessive index at least 5ý, ýso Fouquet and Vanherpe asked whether Petersen graph is the only one with that propertyý. ýH\"{a}gglund gave a negative answer to their question by constructing two graphs Blowup(K4ý,ýC) and Blowup(Prismý,ýC4)ý. ýBased on the first graphý, ýEsperet et alý. ýconstructed infinite families of cyclically 4-edge-connected snarks with excessive index at least fiveý. ýBased on these two graphsý, ýwe construct infinite families of cyclically 4-edge-connected snarks E0,1,2,…ý,ý(k−1) in which E0,1,2 is Esperet et al.'s constructioný. ýIn this noteý, ýwe prove that E0,1,2,3 has excessive index at least fiveý, ýwhich gives a strongly negative answer to Fouquet and Vanherpe's questioný. ýAs a subcase of Fulkerson conjectureý, ýH\"{a}ggkvist conjectured that every cubic hypohamiltonian graph has a Fulkerson-coverý. ýMotivated by a related result due to Hou et al.'sý, ýin this note we prove that Fulkerson conjecture holds on some families of bridgeless cubic graphs.

In this paper we try to extend geometric concepts in the context of operator valued tensorsý. ýTo this endý, ýwe aim to replace the field of scalars R by self-adjoint elements of a commutative C⋆-algebraý, ýand reach an appropriate generalization of geometrical concepts on manifoldsý. ýFirstý, ýwe put forward the concept of operator-valued tensors and extend semi-Riemannian metrics to operator valued metricsý. ýThený, ýin this new geometryý, ýsome essential concepts of Riemannian geometry such as curvature tensorý, ýLevi-Civita connectioný, ýHodge star operatorý, ýexterior derivativeý, ýdivergence,..ý. ýwill be considered.

Here we construct and count all ordinary irreducible characters of Sylow p-subgroups of the Steinberg triality groups 3D4(p3m).

The vertex arboricity ρ(G) of a graph G is the minimum number of subsets into which the vertex set V(G) can be partitioned so that each subset induces an acyclic graphý. ýA graph G is called list vertex k-arborable if for any set L(v) of cardinality at least k at each vertex v of Gý, ýone can choose a color for each v from its list L(v) so that the subgraph induced by every color class is a forestý. ýThe smallest k for a graph to be list vertex k-arborable is denoted by ρl(G)ý. ýBorodiný, ýKostochka and Toft (Discrete Mathý. ý214 (2000) 101-112) first introduced the list vertex arboricity of Gý. ýIn this paperý, ýwe prove that ρl(G)≤2 for any toroidal graph without 5-cyclesý. ýWe also show that ρl(G)≤2 if G
contains neither adjacent 3-cycles nor cycles of lengths 6 and 7.