Anneaux polynomiaux a deux variables

Some types of extensions of skew fields are now known: Galois quadratic extensions ([7]), cyclic extensions ([1]), general quadratic extensions ([4]), binomial extensions ([5]). All these extensions belong to the class of pseudolinear extensions ([8]). A new class of extensions, the so-called «hexaphic extensions», which extends the class of pseudo-linear extensions, will be studied in the other papers in future. For this study, we introduce in this paper skew polynomials rings in two variables over a ring, which extend the well-known skew polynomial rings in one variable (pseudolinear) first studied by O. Ore ([10]).     

Intrinsic metrics and Lipschitz functions

We study the notions of measurable metric and Lipschitz function which were introduced by N. Weaver ([12]), in the framework of Dirichlet spaces. To this respect, we bring some precisions and complements to [15], notably concerning links with the notion of intrinsic metric ([2]). In the particular case of an abstract Wiener space, we establish the relationship between these notions and that of H-metric ([5]) and μ-a.e. H-Lipschitz continuous function ([4]).     

On the barrier problem for sine series with independent Gaussian coefficients

The barrier problem consisting in estimating the probability (1) is solved when the process u(z) belongs to a class of sine series with independent coefficients. The solution is obtained by identifying the process u with the positions of a vibrating string forced by white noise, for which the same barrier problem has been solved in a previous paper ([2]).     

Higher-order Nonlinear System of Equations of Changing Type

In practical problems there appears higher-order equations of changing type([1]). But, there are only a few of papers concerning this type of equations ([2]-[6]). In this paper, the global existence of regular solutions to the Initial-boundary value problem for a class of higher-order system of equations of changing type with a strong nonlinear term is studied.     

Local computation in linear logic

This work deals with the exponential fragment of Girard's linear logic ([3]) without the contraction rule, a logical system which has a natural relation with the direct logic ([10], [7]). A new sequent calculus for this logic is presented in order to remove the weakening rule and recover its behavior via a special treatment of the propositional constants, so that the process of cut-elimination can be performed using only “local” reductions. Hence a typed calculus, which admits only local rewriting rules, can be introduced in a natural manner. Its main properties — normalizability and confluence — has been investigated; moreover this calculus has been proved to satisfy a Curry-Howard isomorphism ([6]) with respect to the logical system in question. MSC: 03B40, 03F05.     

INSTABILITY OF SOLUTIONS OF A CERTAIN NON-AUTONOMOUS VECTOR DIFFERENTIAL EQUATION OF EIGHTH-ORDE R

In this paper, an instability criteria for nonlinear ordinary vector differential equation (1.1) is given. The result extends and includes the results of previous authors in ([1], [27]).     

I(L)-拓扑空间中的可数性、分离性与仿紧性

Kubiak^[9]与王戈平^[2]分别独立地引进了诱导I(L)-拓扑空间概念。本文用在[1]定义的L-拓扑空间的可数性、分离性与仿紧性等来刻画由它诱导的I(L)-拓扑空间的相应的这些性质。     

Strassen's invariance principle for random subsequences

Summary Necessary and sufficient conditions are given for Strassen's invariance principle ([6]) in case a random subsequence is considered. A few iterated logarithm laws for random subsequences are derived as corollaries. These results generalize, in particular, those obtained by Chow et al. ([1]).     

On a property of Cauchy-like matrices

We introduce in this Note a property connecting the generators of a Cauchy-like matrix to the generators of its Schur complements. This property (formulas (6)) yields to a recursive process that can be used to devise a fast and direct inversion algorithm for Cauchy-like matrices (Section 4). The approach considered here is substantially simpler than those developed in some recent works on the subject ([2], [4], [6], [7], [8]).     

Order and topology in projective Hjelmslev planes

The concept of an ordered projective Hjelmslev plane was intuitively introduced by Hjelmslev in Einleitung in die allgemeine Kongruenglehre ([9], [10]).This paper is concerned with formalizing and examing preorderings and orderings for projective Hjelmslev planes. In addition we show that orderings generated topologies of the point and line sets which render the plane a topological Hjelmslev plane ([19], [13]). These planes — unlike the ordinary ordered planes ([18]) — are, due to the existence of infinitesimals, non-archimedian, non-compact and disconnected with the neighbour classes as certain quasi-components.The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.     

Isoparametric triple systems of FKM-type II

In this paper we shall present an effective method to compute the class number and the fundamental units of a certain non-galois number field, by using elliptic units. Our method is based on Schertz's formula on elliptic units ([6]), and very similar to that used in Gras' paper ([1]). Although our arguments are restricted to one special case, similar arguments can be applied to many other cases with suitable modifications, but these become very complicated.     

Nichtdifferenzierbare Morphismen differenzierbarer Räume

It is known ([4]) that under certain general conditions formal morphisms of differentiable spaces are differentiable. In this paper we show that these conditions are essentially necessary. Especially we establish the existence of formal, not differentiable morphisms of differentiable algebras. This solves a problem due to B. Malgrange ([1]).     

Konvexe Körper und Konvexität auf Grassmann-Kegeln IX: Stark konvexe Funktionen

Ohne ZusammenfassungTeile I–V gemeinsam mitH. Busemann undG. C. Shephard ([3], [4]). Teil VII siehe [5]. Teile VI und VIII vonG. C. Shephard ([6], [7]). — Die vorliegende Arbeit baut nur auf die Teile I und III auf.     

一个稳态PDE系统的状态约束极小能最优控制问题

本文研究一个由偏微分方程描述的调和型稳态系统带不等式或光顺约束条件的极小能最优控制问题。基于由笔者新近发展的样条函数最优解技术,我们对所论问题可以给出完整的显式解析型最优解。问题的最优解可以通过一种优雅的再生核结构来表达。这种新技巧还可以用来对其他不同领域如图象和信号的最优再现等问题作统一的处理,体现出样条函数新理论的优越性。 这种样条函数技巧的前身只能解决由常微分方程描述的集中参数系统问题。有关这方面的历史发展和评述可参阅笔者下面的综合报告。本文的结果是这一研究方向的新发展。     

可加广义代数格上的 Tietze 扩张定理

可加的广义代数格范畴与 T₀ 拓扑空间范畴相等价, 从这个观点出发, 作者把可加广义代数格作为一个闭集格, 在其上建立 Urysohn 引理和 Tietze 扩张定理. 这是拓扑理论在格上的一种新推广, 有助于格上拓扑理论的研究和广义连续格理论的应用.     

Serre’s conjecture and its consequences

After some generalities about the absolute Galois group of \mathbb Q\mathbb Q, we present the historical context in which Serre made his modularity conjecture. This was recently proved by Wintenberger and the author ([22], [23]), with an input of Kisin ([24]). The focus of these notes is on the applications of the conjecture. Some of the applications are based on the methods used in the proof.     

Der fàltungsalgorithmus für dreidimensionale radon–probleme †

Filtered backprojection is an efficient numerical method for inversion of the Radon and x-ray transform. It can be adapted to the three dimensional case ([10], [11]). In this paper we present a method to calculate convolution kernels for filtered backprojection in three dimensions.     

Some compact hypersurfaces of constant scalar curvature in a sphere

We construct some compact hypersurfaces of constant scalar curvature in a sphere with cohomogeneity 1([2]).The author is grateful to Professor K. Ogiue for his useful criticism.     

PRME AND k-PRIME IDEALS IN Ω-GROUPS

Abstract

In this paper we define two concepts of prime ideals for Ω-groups. The first generalizes the definitions of prime ideal in rings, nearrings, Γ-rings, associative algebras and Lie algebras. The second generalizes a concept defined for groups by ??ukin ([21]). We show that both lead to radicals in the sense of Hoehnke ([10]). Furthermore in the case of rings, Γ-rings, abelian zero-symmetric nearrings and cubic rings these two definitions coincide, thus obtaining a new characterization for the prime ideal. Zero-symmetric Ω-groups are defined analogously to the nearring case and a new characterization in term of ideals is given.     

A RADON-NIKODYM THEOREM FOR RIESZ SPACE VALUED MEASURES

ABSTRACT

In this note, as a consequence of the Radon-Nikodym theorem for positive operators given by Luxemburg and Schep ([6]), we obtain a Radon-Nikodym theorem for Riesz space valued measures similar to Wright's theorem ([11]).