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101.
Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set of nonassociative algebras of a fixed dimensionr< over a local fieldF. We obtain a space, which is notT 1. If the trivial algebra is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF *; forr3 the space is notT 1. The set of division algebras is open in.  相似文献   
102.
We continue our investigations started in a paper with the same title. The -length of a curve defined in this paper can be written as an integral along the curve. Furthermore, we determine necessary and sufficient conditions for the existence of a measure of orientated lines which generates a given non-symmetric pseudo-metric.

Herrn Prof. Dr. H.-J. Kanold zum 65. Geburtstag gewidmet  相似文献   
103.
Arithmetic formulae and an asymptotic expression for the order of magnitude of the arithmetic function ged (s, n) and of a generalisation of it are derived.  相似文献   
104.
This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where denotes the Laplacian, a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain LP-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems.  相似文献   
105.
It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers.  相似文献   
106.
Let ={e(u)|uI} be a one-parameter family of straight lines forming a ruledC r-2-surface E n (n2,r1) without singular generatorse(u) (uI). As a synopsis, a generalization and an improvement of various results already known about the strictional properties of ruled surfaces E n (especially in the casen=3) the author demonstrates a uniform geometrical way of defining and uniquely obtaining thestriction point S(u) and theparameter of distribution d(u) of a generatore(u) under the minimal assumptions thate(u)E n (n2) be noncylindrical andr1. Other methods of obtainingS(u) andd(u) are discussed in comparison, and special strictional properties ofskew ruled surfaces E n are proved.

Herrn Prof. Dr. H. R. Müller zum 65. Geburtstag  相似文献   
107.
The classical Gauss-Bonnet formula has the form I(gij)=2, where I(gij) represents a sum of three terms each of which depends on the metric tensor gij. It is shown that the first variation I of I(gij) with respect to the metric gij vanishes and that for the Euclidean metric ij we have I(ij)=2. From this the formula I(gij)=2 follows. In the process, explicit expressions are obtained for the first variation of each of the three terms which comprise I(gij). Furthermore, a general expression for the first variation of a multiple integral whose integrand is a scalar density depending on the metric tensor gij and its derivatives up to the second order is obtained with the aid of results of Rund [1].  相似文献   
108.
LetQ(u) be a positive definite quadratic form inr2 variables with a real symmetric coefficient matrix of determinantD. Given a real vectorb with 0b j <1, forx>0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)x, letV(x) be the volume of this ellipsoid andP(x)=A(x)–V(x). Let . By introduction of a parameter we shall show how the treatment of estimates onP(x) and onM(x) can be unified.  相似文献   
109.
Summary Letf i :A R ben real-valued objective functions on a convex setA -K m ,K:=R orC, n, mN. Letg: A R n be defined by , where for eachxA, (i 1 (x), ..., i n (x)) is a permutation of (1, ...,n) such that . In this paper we treat the problem of findingx *A such that , wherel-max denotes the lexicographic maximum. If the fi's are strongly quasiconcave we can reduce the problem stepwise until finally it is in the form of a scalar programming problem. Further, we consider conditions for the existence and uniqueness of a solution and discuss the relationship of the problem to the vector maximum (i.e. Pareto) and maxmin (i.e. Chebychev) problems.
Zusammenfassung f i :AR seienn reellwertige Zielfunktionen über einer konvexen MengeA-K m ,K:=R oderC, n, mN. g:AR n sei definiert durch , wobei für jedesxA (i 1 (x), ... i n (x)) eine Permutation von (1, ...,n) derart ist, daß Wir betrachten das Problem, einx *A so zu finden, daß , wobeil-max das lexikographische Maximum bedeute. Falls dief i stark quasikonkav sind, läßt sich das Problem stufenweise reduzieren, bis es schließlich die Gestalt eines skalaren Optimierungsproblems annimmt. Wir geben Existenz- und Eindeutigkeitsbedingungen an und besprechen Zusammenhänge mit dem Vektormaximumproblem (d.h. Pareto-Optimierung) und dem Maxmin-Problem (d.h. Tschebyscheff-Optimierung).
  相似文献   
110.
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