Bulletin of Iranian Mathematical Society
Volume:42 Issue: 6, 2016

We present an application of the dual Gabor frames to imageý ýprocessingý. ýOur algorithm is based on finding some dual Gaborý ýframe generators which reconstructs accurately the elements of theý ýunderlying Hilbert spaceý. ýThe advantages of these dualsý ýconstructed by a polynomial of Gabor frame generators are comparedý ýwith their canonical dualý.

We obtain the asymptotic expansion of the sequence with general term AnGný, ýwhere An and Gn are the arithmetic and geometric means of the numbers \d(1),\d(2),…,\d(n)ý, ýwith \d(n) denoting the number of positive divisors of ný. ýAlsoý, ýwe obtain some explicit bounds concerning Gn and AnGn.

Let R be a noncommutative prime ring ofý ýcharacteristic different from 2ý, ýU the Utumi quotient ring of Rý, ýC (=Z(U)) the extended centroidý ýof Rý. ýLet 0≠a∈R and f(x1,…,xn) a multilinearý ýpolynomial over C which is noncentral valued on Rý. ýSupposeý ýthat G and H are two nonzero generalized derivations of Rý ýsuch that a(H(f(x))f(x)−f(x)G(f(x)))∈C for allý ýx (x1,…,xn)∈Rný. ý one of the following holdsý: ýf(x1,…,xn)2 is central valued on R and there exist b,p,q∈U suchý ýthat H(x)=px for all x∈Rý, ýG(x)=bx for all x∈R with a(p−q)∈C;ý ýthere exist p,q∈U such that H(x)=px for all x∈Rý, ýG(x)=qx for all x∈R with ap=0;ý f(x1,…,xn)2 is central valued on R and there exist q∈Uý, ýλ∈C and an outer derivation g of Uý ýsuch that H(x)=xqλx−g(x) for all x∈Rý, ýG(x)=qx(x) for all x∈Rý, ýwith a∈C;ý
R satisfies s4 and there exist b,p∈U suchý ýthat H(x)=px for all x∈Rý, ýG(x)=bx for all x∈Rý.

Let M be a non-zero finitely generated module over a commutative Noetherian local ring (R,m) with dimR(M)=tý. ýLet I be an ideal of R with grade(I,M)=cý. ýIn this article we will investigate several natural homomorphisms of local cohomology modulesý. ýThe main purpose of this article is to investigate when the natural homomorphisms γý:ýTorRc(k,HcI(M))→k⊗RM and ηý:ýExtdR(k,HcI(M))→ExttR(ký,ýM) are non-zero where d:=t−cý. ýIn fact for a Cohen-Macaulay module M we will show that the homomorphism η is injective (respý. ýsurjective) if and only if the homomorphism Hdm(HcI(M))→Htm(M) is injective (respý. ýsurjective) under the additional assumption of vanishing of Ext modulesý. ýThe similar results are obtained for the homomorphism γý. ýMoreover we will construct the natural homomorphism TorRc(ký,ýHcI(M))→TorRc(ký,ýHcJ(M)) for the ideals J⊆I with c=grade(I,M)=grade(J,M)ý. ýThere are several sufficient conditions on I and Jto provide this homomorphism is an isomorphism.

In this paperý, ýwe propose a feasible interior-point method forý ýconvex quadratic programming over symmetric conesý. ýThe proposed algorithm relaxes theý ýaccuracy requirements in the solution of the Newton equation systemý, ýby using an inexact Newton directioný. ýFurthermoreý, ýwe obtain aný ýacceptable level of error in the inexact algorithm on convexý ýquadratic symmetric cone programming (CQSCP)ý. ýWe also prove that the iterationý ýbound for the feasible short-step method isý ýO(n−−√log1ε)ý, ýandý ýO(nlo 1ε) for the large-step method which coincide with the currently bestý ýknown iteration bounds for CQSCPs.

We study the existence of soliton solutions for a class ofý ýquasilinear elliptic equation in R2with critical exponential growthý. ýThis model has been proposed in the self-channeling of aý ýhigh-power ultra short laser in matterý.

Vasilev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed., Sobolev Inst. Math., Novosibirsk (2006).] as follows: Does there exist a positive integer k such that there are no k pairwise nonisomorphic nonabelian finite simple groups with the same graphs of primes? Conjecture: k=5.
In [Zvezdina, On nonabelian simple groups having the same prime graph as an alternating group, Siberian Math. J., 2013] the above conjecture is positively answered when one of these pairwise nonisomorphic groups is an alternating group.
In this paper, we continue this work and determine all nonabelian simple groups, which have the same prime graph as the nonabelian simple group Dn(q).

In this paperý, ýby using four functionals fixed point theoremý, ýwe obtain sufficient conditions for the existence ofý ýat least one positive solution of an nth-order m-point boundary value problemý. ýAs an applicationý, ýwe give an example to demonstrate our main result.

We call a ring R right generalized semiperfect if every simple right R-module is an epimorphic image of a flat right R-module with small kernelý, ýthat isý, ýevery simple right R-module has a flat B-coverý. ýWe give some properties of such rings along with examplesý. ýWe introduce flat strong covers as flat covers which are also flat B-covers and give characterizations of A-perfectý, ýB-perfect and perfect rings in terms of flat strong covers.

In this paperý, ýwe formulate the sixth-order boundary value problem as Fredholm integral equation by finding Green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problemý. ýAlso nonexistence results are obtainedý. ýAn example is given to illustrate the results of paperý.

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

In this paperý, ýwe give some necessary conditions for a complexý ýdifference equation of Malmquist typeý ý∑j=1nf(z)=P(f(z))Q(f(z))ý, ýwhere n(∈N)≥2ý, ýand P(f(z)) and Q(f(z)) areý ýrelatively prime polynomials in f(z) with small functions asý ýcoefficientsý, ýadmitting a meromorphic function of finite orderý. ýMoreoverý, ýthe properties of finite order transcendental meromorphicý ýsolutions for complex difference equationý ý∏nj=1f(z)=P(f(z))/Q(f(z)) are also investigated.

This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the
critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.

We prove that a remainder Y of a non-locally compactý ýrectifiable space X is locally a p-space if and only ifý ýeither X is a Lindel\"{o}f p-space or X is σ-compactý, ýwhich improves two results by Arhangelskiiý. ýWe also show that if a non-locally compactý ýrectifiable space X that is locally paracompact has a remainder Y which has locally a Gδ-diagonalý, ýthen both X and Y are separable and metrizableý, ýwhich improves anotherý ýArhangelskii's resultý. ýIt is proved that if a non-locally compact paratopological group G has a locally developable remainder Yý, ýthen either G and Y are separable and metrizableý, ýor G is a σ-compact space with a countable networký, ýwhich improves a result by Wang-He.

The object of the present paper is to study spacetimes admittingý ýquasi-conformal curvature tensorý. ýAt first we prove that a quasi-conformally flat spacetime is Einsteiný ýand hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfyingý ýEinstein's field equation with cosmological constant is covariant constantý. ýNextý, ýwe prove that if the perfect fluid pacetime withý ývanishing quasi-conformal curvature tensor obeys Einstein's field equation without cosmological constantý, ýthen the spacetime has constant energy density and isotropic pressure and the perfect fluid always behaveý ýas a cosmological constant and also such a spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field Uý. ýMoreoverý, ýit is shown that in a purely electromagnetic distribution the spacetime with vanishing quasi-conformal curvature tensor is filled withý ýradiation and extremely hot gasesý. ýWe also study dust-like fluid spacetime with vanishing quasi-conformal curvature tensor.

In this paperý, ýwe study the Lp (1

In this paperý, ýwe prove a multiplicity result for some biharmonic elliptic equation of Kirchhoff type and involving nonlinearities with critical exponential growth at infinityý. ýUsing some variational arguments and exploiting the symmetries of the problemý, ýwe establish a multiplicity result giving two nontrivial solutionsý.

Recentlyý, ýHussain et al.ý, ýdiscussed the concept of wt-distance on aý ýmetric type spaceý. ýIn this paperý, ýwe prove some fixedý ýpoint theorems for classes of contractive type multi valued operatorsý, ýby using wt -distances in the setting of a complete metric type spaceý. ýThese results generalize a result of Feng and Liu on multi-valued operators.

We prove the existence of PPF dependent coincidence points for a pair of single-valued and multi-valued mappings satisfying generalized contractive conditions in Banach spacesý. ýFurthermore, the PPF dependent fixed point and PPF dependent common fixed point theorems for multi-valued mappings are proved.