In this paper, we introduce the concepts of Armendariz ideals and abelian ideals and record some results involving them.

In this paper, a distribution free approach to the parameter estimation of a simple bilinear model with periodic coefficients is presented. The proposed method relies on minimum distance estimator based on the autocovariances of the squared process. Consistency and asymptotic normality of the estimator, as well as hypotheses testing, are derived. Numerical experiments on simulated data sets are presented to highlight the theoretical results.

Let D be an integrally closed domain with quotient field K, * be a star operation on D, X, Y be indeterminates over D, and . Let b be the b-operation on R, and let be the star operation on D defined by . Finally, let Kr(R, b) (resp., Kr(D, )) be the Kronecker function ring of R (resp., D) with respect to Y (resp., X, Y). In this paper, we show that Kr(R, b) Kr(D, ) and Kr(R, b) is a kfr with respect to K(Y) and X in the notion of [2]. We also prove that Kr(R, b) = Kr(D, ) if and only if D is a . As a corollary, we have that if D is not a , then Kr(R, b) is an example of a kfr with respect to K(Y) and X but not a Kronecker function ring with respect to K(Y) and X.

The goal of this paper is to study extension problems of several continuities in computer topology. To be specific, for a set take a subspace (X, ) induced from the Khalimsky nD space (, ). Considering (X, ) with one of the k-adjacency relations of , we call it a computer topological space (or a space if not confused) denoted by . In addition, we introduce several kinds of k-retracts of , investigate their properties related to several continuities and homeomorphisms in computer topology and study extension problems of these continuities in relation with these k-retracts.

We study a relationship between sets of uniqueness, weakly sufficient sets and sampling sets in the space of holomorphic functions with polynomial growth on the unit ball of ().

We provide the set of left-invariant minimal unit vector fields on the semi-direct product , where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form which are unimodular and of type (R).

As an application of 'reverse engineering' technique introduced by R. Fintushel, D. Park and R. Stern [9], we present a simple way to construct an infinite family of exotic (2n+2l-1)(2n+4l-1)'s for all , .

We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand, it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme, we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.

In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation: for any fixed nonzero integers s, t, r with .

We prove that the reduced free product of matrix algebras over abelian -algebras is not the minimal tensor product of reduced free products of matrix algebras over abelian -algebras. It is shown that the reduced group -algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian -algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian -algebras is not isomorphic to the tensor product of a nuclear -algebra and a reduced free product of abelian -algebra. We discuss the freeness of free product -factors and solidity of free product -factors weaker than that of Ozawa. We show that the freeness in a free product is related to the existence of Cartan subalgebras in free product -factors. Finally, we give a free product factor which is not solid in the weak sense.

In this paper we define the -mixed curvature function of a convex body. We develop a formula connection the support function of -mixed projection body with Fourier transform of the -mixed curvature function. Using this formula we solve an analog of the Shephard projection problem for -mixed projection bodies.

A new class of generalized open sets in a topological space, called e-open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of -semi-preopen (or -open) sets and weaker than both -semiopen sets and -preopen sets. In order to investigate some different properties we introduce two strong form of e-open sets called e-regular sets and e--open sets. By means of e--open sets we also introduce a new class of functions called strongly -e-continuous functions which is a generalization of -precontinuous functions. Some characterizations concerning strongly -e-continuous functions are obtained.

For convex subsets X of a topological vector space E, we show that a KKM principle implies a Fan-Browder type fixed point theorem and that this theorem implies generalized forms of the Sion minimax theorem.

In this paper, strongly cotorsion (torsion-free) modules are studied and strongly cotorsion (torsion-free) dimension is introduced. It is shown that every module has a special -preenvelope and an ST -cover for any based on some results of cotorsion pairs from [9]. Some characterizations of strongly cotorsion (torsion-free) dimension of a module are given.

In this paper, several properties of endomorphism rings of modules are investigated. A multiplication module M over a commutative ring R induces a commutative ring of endomorphisms of M and hence the relation between the prime (maximal) submodules of M and the prime (maximal) ideals of can be found. In particular, two classes of ideals of are discussed in this paper: one is of the form and the other is of the form for a submodule N of M.

In this paper we investigate complete spacelike (r - 1)-maximal (i.e., ) hypersurfaces with two distinct principal curvatures in the anti-de Sitter space (-1). We give a characterization of the hyperbolic cylinder.

Anderson-Smith [1] studied weakly prime ideals for a commutative ring with identity. Blair-Tsutsui [2] studied the structure of a ring in which every ideal is prime. In this paper we investigate the structure of rings, not necessarily commutative, in which all ideals are weakly prime.

In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.