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ISSN : 1226-0657
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Vol.10 No.4
Abstract
Let N be a right near-ring. N is said to be strongly reduced if, for <TEX>$a\inN$</TEX>, <TEX>$a^2 \in N_{c}$</TEX> implies <TEX>$a\;\in\;N_{c}$</TEX>, or equivalently, for <TEX>$a\inN$</TEX> and any positive integer n, <TEX>$a^{n} \in N_{c}$</TEX> implies <TEX>$a\;\in\;N_{c}$</TEX>, where <TEX>$N_{c}$</TEX> denotes the constant part of N. We will show that strong reducedness is equivalent to condition (ⅱ) of Reddy and Murty's property <TEX>$(^{\ast})$</TEX> (cf. [Reddy & Murty: On strongly regular near-rings. Proc. Edinburgh Math. Soc. (2) 27 (1984), no. 1, 61-64]), and that condition (ⅰ) of Reddy and Murty's property <TEX>$(^{\ast})$</TEX> follows from strong reducedness. Also, we will investigate some characterizations of strongly reduced near-rings and their properties. Using strong reducedness, we characterize left strongly regular near-rings and (<TEX>$P_{0}$</TEX>)-near-rings.
Abstract
Let R be a prime ring with characteristic different from two and let <TEX>$\theta,\varphi,\sigma,\tau$</TEX> be the automorphisms of R. Let d : <TEX>$R{\rightarrow}R$</TEX> be a nonzero (<TEX>$\theta,\varphi$</TEX>)-derivation. We prove the following results: (i) if <TEX>$a{\in}R$</TEX> and [d(R), a]<TEX>$_{{\theta}o{\sigma},{\varphi}o{\tau}}$</TEX>=0, then <TEX>$\sigma(a)\;+\;\tau(a)\;\in\;Z$</TEX>, the center of R, (ii) if <TEX>$d([R,a]_{\sigma,\;\tau)\;=\;0,\;then\;\sigma(a)\;+\;\tau(a)\;\in\;Z$</TEX>, (iii) if <TEX>$[ad(x),\;x]_{\sigma,\;\tau}\;=\;0;for\;all\;x\;\in\;RE$</TEX>, then a = 0 or R is commutative.
Abstract
Let <TEX>$\cal{K}$</TEX> be the extension Hilbert space of a Hilbert space <TEX>$\cal{H}$</TEX> and let <TEX>$\Phi$</TEX> be the faithful <TEX>$\ast$</TEX>-representation of <TEX>$\cal{B}(\cal{H})$</TEX> on <TEX>$\cal{k}$</TEX>. In this paper, we show that if T is an irreducible <TEX>${\omega}-hyponormal$</TEX> operators such that <TEX>$ker(T)\;{\subset}\;ker(T^{*})$</TEX> and <TEX>$T^{*}T\;-\;TT^{\ast}$</TEX> is compact, then <TEX>$\sigma_{e}(T)\;=\;\sigma_{e}(\Phi(T))$</TEX>.
Abstract
In this paper, we consider the existence of the solutions to the generalized vector variational-type inequalities for set-valued mappings on Hausdorff topological vector spaces using Fan's geometrical lemma.
Abstract
In this paper, we introduce the concepts of t-intuitionistic fuzzy products and t-intuitionistic fuzzy subgroupoids. And we study some properties of t-products and t-subgroupoids.
Abstract
In this paper we prove common fixed point theorems for four mappings, under the condition of weakly compatible mappings in Menger spaces, without taking any function continuous. We improve results of [A common fixed point theorem for three mappings on Menger spaces. Math. Japan. 34 (1989), no. 6, 919-923], [On common fixed point theorems of compatible mappings in Menger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].
Abstract
We compare the computing times on the bicubic B-spline dueing to the algorithms.
Abstract
Let <TEX>$CS_\alpha(\beta)$</TEX> denote the class of normalized strongly <TEX>$\alpha$</TEX>-close-to-convex functions of order <TEX>$\beta$</TEX>, defined in the open unit disk <TEX>$\cal{U}$</TEX> of <TEX>$\mathbb{C}$</TEX. by , <TEX>${\mid}arg{(1-{\alpha})\frac{f(z)}{g(z)}+{\alpha}\frac{zf'(z)}{g(z)}}{\mid}\;\leq\frac{\pi}{2}{\beta}(\alpha,\beta\geq0)$</TEX> such that <TEX>$g\; \in\;S^{\ask}$</TEX>, the class of normalized starlike unctions. In this paper, we obtain the sharp Fekete-Szego inequalities for functions belonging to <TEX>$CS_\alpha(\beta)$</TEX>.
Abstract
The Fuglede-Putnam Theorem is that if A and B are normal operators and X is an operator such that AX = XB, then <TEX>$A^{\ast}= X<T^{\ast}B^{\ast}$</TEX>. In this paper, we show that if A is <TEX>$\omega$</TEX>-hyponormal and <TEX>$B^{\ast}$</TEX> is invertible <TEX>$\omega$</TEX>-hyponormal such that AX = XB for a Hilbert-Schmidt operator X, then <TEX>$A^{\ast}X = XB^{\ast}$</TEX>.
Abstract
In the present paper, we treat a Finsler space with a special (<TEX>${\alpha},\;{\beta}$</TEX>)-metric <TEX>$L({\alpha},\;{\beta})\;\;C_1{\alpha}＋C_2{\beta}+{\alpha}^2/{\beta}$</TEX> satisfying some conditions. We find a condition that a Finsler space with a special (<TEX>${\alpha},\;{\beta}$</TEX>)-metric be a Berwald space. Then it is shown that if a two-dimensional Finsler space with a special (<TEX>${\alpha},\;{\beta}$</TEX>)-metric is a Landsberg space, then it is a Berwald space.