In this interesting paper, the authors investigate questions of continuity in probabilistic normed spaces. It is proved that vector addition is continuous with respect to the norm-induced topology where as multiplication by a fixed scalar can be discontinuous.Reviewer: Ismat Beg (Kuwait)...
Then is equivalent to the fuzzy norm where B is the closed unit ball of X. The lower semi-continuity of is an essential condition which guarantees the continuity of , where 0 < e < 1. As the last result, we prove that : if is a fuzzy norm on a finite dimensional vector space, ...
Vector spaces considered in this paper are assumed to be real. Let S be a normed vector space. The distance from [Math Processing Error] to the set [Math Processing Error] we denote by [Math Processing Error]. We denote an open ball of radius r around [Math Processing Error] by [Math...
It is known that the intensity of the induced ( d -2)-flat process divided ... J Mecke - 《Mathematische Nachrichten》 被引量: 23发表: 1986年 Intersection properties of polyhedral norms We investigate the family of intersections of balls in a finite-dimensional vector space with a polyhedral...
A0 and A1 are Banach spaces which are continuously embedded in a Hausdorff topological vector space. Th... C Wei,Y Sagher - 《Arkiv För Matematik》 被引量: 50发表: 1990年 Independence and conditional possibility for strictly monotone triangular norms In the literature there are different ...
1. Stoichiometric attributes that depend only on the fractions of elements present and not what those elements actually are. These include the number of elements present in the compound and several Lp norms of the fractions. General-purpose method to create materials property models 2. Elemental ...
In this paper we introduce some local versions of Bishop–Phelps–Bollobás type property for operators. That is, the function η which appears in their definitions depends not only on a given ε>0, but also on either a fixed norm-one operator T or a fixed norm-one vector x. We investig...
2. The Setting: Linear Vector Spaces and Their Properties HF Weinberger 被引量: 158发表: 1974年 Arithmetic groups and their generalizations : what, why, and how Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric...
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates, semi-norms, polar forms, and inner products. The notation is ...
A number of key properties and applications of real and complex Chebyshev polynomials of the first and second kinds are here reviewed. First, in the overall context of Lp norms (1≤p≤∞), there is a review of the orthogonality and minimality...