Bulletin of Iranian Mathematical Society
Volume:41 Issue: 2, 2015

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions dx(t)∈F(t,x(t))dt+G(t,x(t))dW t in which the multifunction F is semimonotone and hemicontinuous and the operator-valued multifunction G satisfies a Lipschitz condition. We define the It\^{o} stochastic integral of operator set-valued stochastic processes with respect to the cylindrical Brownian motion on separable Hilbert spaces. Then, we generalize the existence results for differential inclusions in [H. Abedi and R. Jahanipur, Nonlinear differential inclusions of semimonotone and condensing type in Hilbert spaces, \textit{Bull. Korean Math. Soc.}, {52} (2015), no. 2, 421--438.] to the corresponding stochastic differential inclusions using the methods discussed in [R. Jahanipur, Nonlinear functional differential equations of monotone-type in Hilbert spaces, {\it Nonlinear Analysis} {\bf 72} (2010), no. 3-4, 1393--1408, R. Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, {\it Stoch. Anal. Appl.}, {\bf 21} (2003), 161--181, and R. Jahanipur, Stochastic functional evolution equations with monotone nonlinearity: existence and stability of the mild solutions, {\it J. Differential Equations} {\bf 248} (2010), no. 5, 1230--1255.]

In this paper the periodic solutions of fourth order delay differential equation of the form x. ... (t)+ax. .. (t)+f(x ¨ (t−τ(t)))+g(x ˙ (t−τ(t)))+h(x(t−τ(t)))=p(t) is investigated. Some new positive periodic criteria are given.

Suppose f is a map from a non-empty finite set X to a finite group G. Define the map ζ f G: G⟶N∪{0} by g↦|f −1 (g)|. In this article, we show that for a suitable choice of f, the map ζ f G is a character. We use our results to show that the solution function for the word equation w(t 1, t 2, …,t n)=g (g∈G) is a character, where w(t 1, t 2, …,t n) denotes the product of t 1, t 2, …,t n, t −1 1, t −1 2, …,t −1 n in a randomly

In this paper, we defined two classes S ∗ p (n,λ,A,B) and\\ K p (n,λ,A,B) of meromorphic p− valent functions associated with a new linear operator. We obtained convolution properties for functions in these classes.

In this article, we develop the Sinc-Galerkin method based on double exponential transformation for solving a class of weakly singular nonlinear two-point boundary value problems with nonhomogeneous boundary conditions. Also several examples are solved to show the accuracy efficiency of the presented method. We compare the obtained numerical results with results of the other existing methods in the literature. The results of this paper confirm that our method is very fast, simple and considerably accurate.

In this paper, by modifying Cheng-Yau ′ s technique to complete hypersurfaces in S n+1 (1), we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {\em Math. Ann.} {305} (1996), 665--672].

In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder ′ s fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in the literatures.

In this paper we define a new type of rings”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

It is known that the directed cycle of order n uniquely achieves the minimum spectral radius among all strongly connected digraphs of order n≥3. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order n≥4.

In this paper we consider the second order nonlinear neutral delay partial difference equation Δ n Δ m (x m,n +a m,n x m−k,n−l)+f(m,n,x m−τ,n−σ)=b m,n, m≥m 0, n≥n 0. Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation. Three nontrivial examples are given to illustrate the advantages of our results.

The aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. Our results present random versions and extensions of some well-known results in the current literature.

Let R=⊕ n∈N 0 R n be a Noetherian homogeneous ring with local base ring (R 0, m 0), M and N two finitely generated graded R -modules. Let t be the least integer such that H t R + (M,N) is not minimax. We prove that H j m 0 R (H t R + (M,N)) is Artinian for j=0,1. Also, we show that if cd(R +, M,N)=2 and t∈N 0, then H t m 0 R (H 2 R + (M,N)) is Artinian if and only if H t+2 m 0 R (H 1 R + (M,N)) is Artinian.

In this paper, the main aim is to introduce the class mathcalU p (lambda,alpha,beta,k 0) of p -harmonic mappings together with its subclasses mathcalU p (lambda,alpha,beta,k 0)capmathcalT p and mathcalU p (lambda,alpha,beta,k 0)capmathcalT 0 p, and investigate the properties of the mappings in these classes. First, we give a sufficient condition for mappings to be in mathcalU p (lambda,alpha,beta,k 0) and also the characterization of mappings in mathcalU p (lambda,alpha,beta,k 0)capmathcalT p for max, fraclambda−frac12lambda+1leqalphaleqlambda. Second, we consider the starlikeness of mappings in mathcalU p (lambda,alpha,beta,k 0)capmathcalT 0 p for max, fraclambda−frac12lambda+1leqalphaleqlambda. Third, extreme points of mathcalU p (lambda,alpha,beta,k 0)capmathcalT p for max0,fraclambda−frac12lambda+1leqalphaleqlambda are found. The support points of mathcalU p (lambda,alpha,beta,k 0)capmathcalT p for max0,fraclambda−frac12lambda+1leqalphaleqlambda and convolution of mappings in mathcalU p (lambda,alpha,beta,k 0)capmathcalT p for max0,fraclambda−frac12lambda+1leqalphaleqlambda are also discussed.

Let R be a reversible ring which is α -compatible for an endomorphism α of R and f(X)=a 0 +a 1 X+⋯+a n X n be a nonzero skew polynomial in R[X;α]. It is proved that if there exists a nonzero skew polynomial g(X)=b 0 +b 1 X+⋯+b m X m in R[X;α] such that g(X)f(X)=c is a constant in R, then b 0 a 0 =c and there exist nonzero elements a and r in R such that rf(X)=ac. In particular, r=ab p for some p, 0≤p≤m, and a is either one or a product of at most m coefficients from f(X). Furthermore, if b 0 is a unit in R, then a 1, a 2, ⋯,a n are all nilpotent. As an application of the above result, it is proved that if R is a weakly 2-primal ring which is α -compatible for an endomorphism α of R, then a skew polynomial f(X) in R[X;α] is a unit if and only if its constant term is a unit in R and other coefficients are all nilpotent.

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of W n are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds related by a conformal mapping preserving the Einstein tensor with a gradient covector field. Then, we prove that a Weyl manifold W n and a flat Weyl manifold W ~ n, which are in a conformal correspondence preserving the Einstein tensor are Einstein-Weyl manifolds. Moreover, we show that an isotropic Weyl manifold is an Einstein-Weyl manifold with zero scalar curvature and we obtain that a Weyl manifold W n and an isotropic Weyl manifold related by the conformal mapping preserving the Einstein tensor are Einstein-Weyl manifolds.

In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.

Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude depend on some rational functions.

In this paper we give some general results on the non-split extension group overlineG n =2 2n cdot Sp(2n,2),ngeq2. We then focus on the group overlineG 4 =2 8 cdot Sp(8,2). We construct overlineG 4 as a permutation group acting on 512 points. The conjugacy classes are determined using the coset analysis technique. Then we determine the inertia factor groups and Fischer matrices, which are required for the computations of the character table of overlineG 4 by means of Clifford-Fischer Theory. There are two inertia factor groups namely H 1 =Sp(8,2) and H 2 =2 7: Sp(6,2), the Schur multiplier and hence the character table of the corresponding covering group of H 2 were calculated. Using the information on conjugacy classes, Fischer matrices and ordinary and projective tables of H 2, we concluded that we only need to use the ordinary character table of H 2 to construct the character table of overlineG 4. The Fischer matrices of overlineG 4 are all listed in this paper. The character table of overlineG 4 is a 195times195 complex valued matrix, it has been supplied in the PhD Thesis of the first author, which could be accessed online.

G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo''s fixed point theorem for solving infinite system of linear equations in some sequence spaces.

Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.

In this errata, we reconsider and modify two propositions and their corollaries which were written on epi-retractable and co-epi-retractable modules.