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Vol.19 No.3
Abstract
We study lightlike submanifolds M of a semi-Riemannian manifold <TEX>$\bar{M}$</TEX> with a semi-symmetric non-metric connection subject to the conditions; (a) the characteristic vector field of <TEX>$\bar{M}$</TEX> is tangent to M, (b) the screen distribution on M is totally umbilical in M and (c) the co-screen distribution on M is conformal Killing.
Abstract
In this article, we study generalized slant cylindrical surfaces (GSCS's) with pointwise 1-type Gauss map of the first and second kinds. Our main results state that the right circular cones are the only rational kind GSCS's with pointwise 1-type Gauss map of the second kind.
Abstract
For each submanifold X in the sphere <TEX>$S^n$</TEX>; we show that the corresponding conormal bundle <TEX>$N^*X$</TEX> is Lagrangian for the Stenzel form on <TEX>$T^*S^n$</TEX>. Furthermore, we correspond an austere submanifold X to a special Lagrangian submanifold <TEX>$N^*X$</TEX> in <TEX>$T^*S^n$</TEX>. We also discuss austere submanifolds in <TEX>$S^n$</TEX> from isoparametric geometry.
Abstract
Based on the theory of a falling shadow which was first formulated by Wang([14]), a theoretical approach of the ideal structure in BH-algebras is established. The notions of a falling subalgebra, a falling ideal, a falling strong ideal, a falling <TEX>$n$</TEX>-fold strong ideal and a falling translation ideal of a BH-algebra are introduced. Some fundamental properties are investigated. Relations among a falling subalgebra, a falling ideal and a falling strong ideal, a falling <TEX>$n$</TEX>-fold strong ideal are stated. A relation between a fuzzy subalgebra/ideal and a falling subalgebra/ideal is provided.
Abstract
We introduce the concept of fuzzy <TEX>$r$</TEX>-minimal <TEX>${\beta}$</TEX>-open set on a fuzzy minimal space and basic some properties. We also introduce the concept of fuzzy <TEX>$r-M$</TEX> <TEX>${\beta}$</TEX>-continuous mapping which is a generalization of fuzzy <TEX>$r-M$</TEX> continuous mapping and fuzzy <TEX>$r-M$</TEX> semicontinuous mapping, and investigate characterization for the continuity.
Abstract
In this paper, we construct an extension (<TEX>$kX$</TEX>, <TEX>$k_X$</TEX>) of a space X such that <TEX>$kX$</TEX> is a weakly Lindel<TEX>$\ddot{o}$</TEX>ff space and for any continuous map <TEX>$f:X{\rightarrow}Y$</TEX>, there is a continuous map <TEX>$g:kX{\rightarrow}kY$</TEX> such that <TEX>$g|x=f$</TEX>. Moreover, we show that <TEX>${\upsilon}X$</TEX> is Lindel<TEX>$\ddot{o}$</TEX>ff if and only if <TEX>$kX={\upsilon}X$</TEX> and that for any P'-space X which is weakly Lindel<TEX>$\ddot{o}$</TEX>ff, <TEX>$kX={\upsilon}X$</TEX>.
Abstract
In this paper, the author defines a new generalized <TEX>${\eta}$</TEX>, <TEX>${\delta}$</TEX>, <TEX>${\alpha}$</TEX>)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (<TEX>${\eta}$</TEX>, <TEX>${\delta}$</TEX>, <TEX>${\alpha}$</TEX>)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.
Abstract
We research the properties of solutions of general higher order non-homogeneous linear differential equations and apply the hyper order to obtain more precise estimation for the growth of solutions of infinite order.
Abstract
There are several types of orders in a Quaternion algebra. Generally, zeta functions defined on orders of a Quaternion algebra give some informations on the ideal theory of orders. In this study, we investigate functional equalities between the zeta functions defined on orders of a Quaternion algebra.
Abstract
In this note we study Nesbitt's Inequality and modify it to make several inequalities. We prove some inequalities by using power series and Cauchy-Schwarz Inequality.