On the factor-web $$ {\boldsymbol{\bar{ W}}} $$ ( ρ, r,r) of the three-web W( r,r, r)

The notion of the factor-web [`(W)] \bar{W} (ρ, r, r) (1 ≤ ρ < r) is defined for the three-web W(r, r, r) formed on a 2r-dimensional differentiable manifold by three r-dimensional smooth foliations. Embedding of the factor-web in the initial web W(r, r, r) is constructed. This construction is a well-known geometric analog of the canonical extension of a Lie group of transformations to its parameter group.     

Diffusions réfléchies réversibles dégénérées

On a domain D in ^d, for a smooth enough probability density and a diffusion matrix which can degenerate, we construct the law Q ^s of a (x)d -symmetric reflecting process in D with matrix . Therefore, we use the associated Dirichlet form and a sequence of approximating processes already used by Pardoux and R. Williams in [23]. Under mild conditions on the boundary ofD (finite Minkowski content), we prove that Q ^s is the law of a semi-martingale and provide its decomposition. Comparing with the decomposition in additive functionals, we conclude that the process is reflected in the conormal direction ^* n where n denotes Chen's normal (cf [10]), that is, the reflection direction of the Brownian motion in Kuramochi compactification.     

多目标规划的r—有效解和r—最优

本文引入有限维向量空间的r-序类概念,讨论了它们的基本性质。在此基础上,定义了多目标规划的r-有效解和r-最优解,研究了它们与其它有关解之间的关系。     

Lokale Konvergenzbedingugen für trigonometrische Reihen und für Potenzreihen

Ohne ZusammenfassungHerrnFriedrich Lösch zum 60. Geburstag am 10. Dezember 1963 gewidmetDie Arbeit wurde unterstützt durch den National Research Council of Canada, als der Verfasser an der University of Western Ontario war.     

Integralgleichungen für einige Randwertprobleme für Gebiete mit Ecken

Summary Concerning conformal mapping and problems of the theory of elasticity, the classical integral equations are modified in order to treat the cases of not smooth boundary curves. As the kernels are still bounded, no difficulties of numerical computation arise.     

Varför Tunneldioder?

In the last two years the electronic industry has shown a great interest in tunnel diodes. This article gives a short explanation of the basic effect and summarizes the more important features of the device. The general fabrication technique is outlined, and some associated problems are discussed.     

Le régulateur p-adique

For all $n\in {\mathbf{N}}^1$, we define a p-adic regulator $R_p:K_{2n+1}({\mathbf{Q}}_p)\to {\mathbf{Q}}_p$ given by an explicit formula and we show that $R_p$ is non-trivial for $n=1$. The main ideas come from a Note published in 2000 for the transcendental case. To cite this article: N. Hamida, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Existenzfragen für Strahlensysteme

Ohne ZusammenfassungHerrn Professor Dr.Wolfgang Haack zum 60. Geburtstag gewidmet     

Marginalprobleme für Funktionen

Ohne Zusammenfassung     

Subordination des résolvantes

Résumé Soit (V ₎₀ une résolvante définie sur un espace mesurable telle que le noyau initial est borné; on trouve une condition nécéssaire et suffisante pour qu'un noyau borné U possède une résolvante (U ₎₀ telle que U V pour tout 0. On donne plusieurs applications de ce résultat.     

Wedderburnzerlegung für Jordan-Paare

In the first section we summarize some properties of Jordan pairs. Then we state some results about some groups defined by Jordan pairs.In the next section we construct a Lie algebra to a Jordan pair. This construction is a generalization of the wellknown Koecher-Tits-construction. We calculate the radical of this Lie algebra in terms of the given Jordan pair.In the last section we prove a Wedderburn decomposition theorem for Jordan pairs in the characteristic zero case. Some special cases in arbitrary characteristic have been shown by R. Carlson (see [5]). Also we show that any two such decompositions are conjugate under a certain group of automorphism. Analogous theorems will be shown for Jordan Triples.     

Non-Commutative Fejér Theorems

In this paper we prove that there are operators in the uniform Roe algebra ${C_u^*(G)}$ which cannot be approximated by the truncations of themselves, where G is a finitely generated group. We also give a sufficient condition for the operators which can be approximated by the truncations of themselves. For a countable discrete metric space X, we obtain the similar conclusions.     

Dn,r is not potentially nilpotent for n ⩾ 4r − 2

An n × n sign pattern A is said to be potentially nilpotent if there exists a nilpotent real matrix B with the same sign pattern as A. Let D_n,r be an n × n sign pattern with 2 ≤ r ≤ n such that the superdiagonal and the (n, n) entries are positive, the (i, 1) (i = 1,..., r) and (i, i ? r + 1) (i = r + 1,..., n) entries are negative, and zeros elsewhere. We prove that for r ≥ 3 and n ≥ 4r ? 2, the sign pattern D_n,r is not potentially nilpotent, and so not spectrally arbitrary.     

Zum Einbettungsproblem für Markoff-Prozesse

Every elementary Markov process with a polish state space and with a discrete set of time parameter dense in ₊, whose finite dimensional distributions are derived from a semigroup (K _t) of Markov kernels continuous in 0 ₊ and whose initial distribution satisfies K _t, can be imbedded in an elementary Markov process with the same state space and with parameter set ₊ so that the corresponding finite dimensional distributions are equal.     

Ein Existenzsatz für Elementarinhalte

An elementary content I is a real valued, non-negative, invariant and monotonous homomorphism on a decomposition structure of elementary figures. The semigroup (H,+,) of abstract classes is introduced (§3) by using the relation of equidecomposability and it's natural generalizations. Each elementary content divides into I= where and are canonical homomorphisms with respect to the relations studied before and : H + is a monotonous homomorphism called content (cf. Satz 3, §3). In §4 (Satz 4) the Existence-Theorem on contents is stated and it is proved in §5. The last section §6 gives the application on Archimedean decomposition structures including the case of volume measurement on polyhedrons.     

r重非正交小波包

该文讨论了由有限个尺度函数｛φ1，φ2，…，φr｝所生成的L2（R）上的多分辨分析．并考虑了L2（R）上直接小波分解和直接小波包分解，对（对偶）非正交小波包以及产生它们的基的稳定性作了较为深人的研究，获得了一些结果．     

Über räumliche Drehungen

Ohne Zusammenfassung