Bulletin of Iranian Mathematical Society
Volume:41 Issue: 5, 2015

‎This paper deals with the singular Sturm-Liouville expressions‎ ‎‎ℓy=‎−‎y″+q(x)y=λy‎‎‎ ‎on a finite interval‎, ‎where the potential function q is real and‎ ‎has a singularity inside the interval‎. ‎Using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of Sturm-Liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the eigenvalues are obtained‎, ‎and proves the stability of the‎ ‎solution of the inverse spectral problem.

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L), which is ring of real-valued continuous functions for frame L, does not have more than one element. Also, z-filters are introduced in terms of pointfree topology. Then the relationship between z-filters and ideals, particularly maximal ideals, is examined. Finally, it is shown that the family of all zero sets is a base for the collection of closed sets.

Let C 0 (alpha) denote the class of concave univalent functions defined in the open unit disk mathbbD. Each function finC 0 (alpha) maps the unit disk mathbbD onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L)  2(dim(L2))2. We also give give some examples sup- porting our results.

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subordinations. Both the coefficient bounds and the techniques presented are new and we hope that this paper will inspire future researchers in applying our approach to other related problems.

In this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. We obtain one results, which can give a negative answer to an uniqueness question relate to the Bruck conjecture dealt by Liu and Yang. Meanwhile, we also establish a difference analogue of the Bruck conjecture for entire functions of order less than 2, which improves some results obtained by Liu and Yang.

This paper is concerned with the following elliptic system:left{begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. for xinR N, where V, b and W are 1-periodic in x, and f(x,t), g(x,t) are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and establish the existence of ground state solutions with mild assumptions on f and g.

In this paper, we prove the Hyers-Ulam stability of the symmetric functional equation f(ph 1 (x,y))=ph 2 (f(x),f(y)) in random normed spaces. As a consequence, we obtain some random stability results in the sense of Hyers-Ulam-Rassias.

In this paper, we prove some approximate fixed point results for proximinal valued beta -contractive multifunctions on metric spaces. We show that our results generalize some old fixed point results in the literature.

In the literature of life-testing, general progressive censoring has been studied extensively. But, all the results have been developed under the key assumption that the units under test are independently distributed. In this paper, we study general progressively Type-II censored order statistics arising from identical units under test which are jointly distributed according to an Archimedean copula with completely monotone generator (GPCOSARCM-II). Density, distribution and joint density functions of GPCOSARCM-II are all derived. Finally, some examples of GPCOSARCM-II are provided.

The purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

In this paper, we consider singular and degenerate parabolic equations u t =(x a lphau x) x +u m (x 0, t)v n (x 0, t),quadv t =(x b etav x) x +u q (x 0, t)v p (x 0, t), in (0,a)times(0,T), subject to null Dirichlet boundary conditions, where m,n,p,qge0, alpha,betain[0,2) and x 0 in(0,a). The optimal classification of non-simultaneous and simultaneous blow-up solutions is determined. Additionally, we obtain blow-up rates and sets for the solutions. The singular rates for the derivation of the solutions are given.

In this paper, we show that every surjective n -homomorphism (n -anti-homomorphism) from a Banach algebra A into a semisimple Banach algebra B is continuous.

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed differential equation is solved analytically using the RKM. An error estimate and two numerical examples are provided to illustrate the effectiveness of the present method. The results of numerical examples show that the present method is accurate and efficient.

We first characterize tau -complemented modules with relative (pre)-covers. We also introduce an extending module relative to tau -pure submodules on a hereditary torsion theory tau and give its relationship with tau -complemented modules.

In this paper, we propose a parametric uniform approximation method to solve NP-hard absolute value equations. For this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. By solving the parametric smooth nonlinear equation using Newton method, for a decreasing sequence of parameters, we can get the solution of absolute value equation. It is proved that the method is globally convergent under some weaker conditions with respect to existing methods. Moreover, preliminary numerical results indicate effectiveness and robustness of our method to solve absolute value equations.

Let mathbbF be an algebraically closed field of prime characteristic p>2 and (g,[p]) a finite-dimensional restricted Lie superalgebra over mathbbF. It is showed that anyfinite-dimensional indecomposable g -module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of g. These quotient superalgebras are called the generalized reduced enveloping superalgebras, which generalize the notion of reduced enveloping superalgebras. Properties and representations of these generalized reduced enveloping superalgebras are studied. Moreover, each such superalgebra can be identified as a reduced enveloping superalgebra of the associated restricted Lie superalgebra.

Let (M 2n, g) be a real hypersurface with recurrent shape operator and tangent to the structure vector field xi of the Sasakian space form widetildeM(c). We show that if the shape operator A of M is recurrent then it is parallel. Moreover, we show that M is locally a product of two constant phi− sectional curvature spaces.

A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.