We consider bilateral operator weighted shift T on (K) with weight sequence of positive invertible diagonal operators on K. We give a characterization for T to be hypercyclic, and show that the conditions are far simplified in case T is invertible.

Let R be an associative ring with identity and J(R) be the Jacobson radical of R. In this paper we investigate the generalization of the Jacobson radical of R, J＊ (R) say. Also we study the rings that J＊(R) = J(R).

Pseudo-parallel real hypersurfaces in complex space forms can be defined as an extrinsic analogues of pseudo-symmetric real hypersurfaces, that generalize the notion of semi-symmetric real hypersurface. In this paper a classification of the pseudo-parallel real hypersurfaces in a non-flat complex space forms is obtained.

Some new oscillation criteria for parabolic neutral delay difference equations corresponding to two sets of boundary conditions are obtained. Our results improve the well known results in the literature.

In this paper using integral representations for n-time differentiable mappings, we establish new generalizations of certain Ostrowski and Trapezoid type inequalities by using fairly elementary analysis.

A convex combination of two products with same degree of finitely many finite geometric series with each having even degree does not always have all its zeros on the unit circle. However, in this paper, we show that a polynomial obtained by just adding a finite geometric series multiplied by a large constant to such a convex combination has all its zeros on the unit circle.

In this paper, by using operations, some characterizations and some properties of fuzzy lower and upper continuous multifunctions and its weaker and stronger forms including fuzzy lower and upper weakly continuous, fuzzy lower and upper , fuzzy lower and upper strongly , fuzzy lower and upper almost strongly , fuzzy lower and upper weakly , fuzzy lower and upper almost continuous, fuzzy lower and upper super continuous, fuzzy lower and upper , are presented.

We investigate skew power series of -rigid p.p.-rings, where is an endomorphism of a ring R which is not assumed to be surjective. For an -rigid ring R, R[[]] is right p.p., if and only if R[[]] is right p.p., if and only if R is right p.p. and any countable family of idempotents in R has a join in I(R).

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.

In this paper, we prove that the Birget-Rhodes expansion of a group G is not a semi direct product of a semilattice by a group but it can be nicely embedded into such a semi direct product.

In this paper we find index form of the multiply warped product manifolds to investigate the physical properties from space-time.

Niebergall and Ryan posed many open problems on real hypersurfaces in complex space forms. One of them is "Are there any Ricci-parallel real hypersurfaces in complex projective space or complex hyperbolic space \ulcorner" The purpose of present paper is to prove the nonexistence of such hypersurfaces.

A punctured torus (1, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of elements of the Teichmuller space of a punctured torus using the matrix presentations of a pair of pants (0, 3) and the gluing method.

The definition of a D-admissible fuzzy subset for an operator domain D on a group G is modified to obtain new kinds of ()-fuzzy subgroups such as an ()-fuzzy normal subgroup, an (<)-fuzzy characteristic subgroup, an (<)-fuzzy fully invariant subgroup which are invariant under D. As results, some of the fundamental properties of such ()-fuzzy subgroups are obtained.ﾖ⨀ᔌ넀؀㔷〮㔻Ԁ䭃䑎䷗ᜓ੹5㘰㬅K䍄乍숗ጊ㤀Ѐ㔷㔻Ԁ䭃䑎䴀

We investigate change of the tensor induced by the conformal change in 7-dimensional g-unified field theory. These topics will be studied for the second class with the first category in 7-dimensional case.

An analogue of the Gram's inequality for n-inner product spaces is given. Further, a number of inequalities involving Gram's determinant are stated and proved in terms of n-inner products.

A group G is said to satisfy the minimal condition on normal subgroups of infinite index if there does not exist an infinite properly descending chain > > ... of normal subgroups of infinite index in G. We characterize the structure of locally nilpotent groups satisfying this chain condition.

We research properties of analytic functions which are exponentially decreasing or increasing. Also we show that the space of test functions is dense in the space of extended Fourier hyper-functions, and that the Fourier transform of the space of extended Fourier hyperfunctions into itself is an isomorphism and Parseval's inequality holds.