Sheaves on Involutive Quantaloids

We extend the well-known notions of a singleton, complete -set, presheaf and sheaf over a complete Heyting algebra or a right-sided idempotent quantale to arbitrary involutive quantaloids. We show that sheaves on and complete -sets come to the same thing. This paper can be considered as a symmetric version of an earlier work of the author.     

Opérateurs différentiels associés à certaines représentations unitaires d'un groupe de Lie résoluble exponentiel

Soient G = exp g un groupe de Lie résoluble exponentiel et H = exp h un sous-groupe connexe de G. Soient un caractère unitaire de H et = Ind_H ^G. Soit D(G/H) l'algèbre des opérateurs différentiels G-invariants sur G/H. Une question posée par Duflo et Corwin-Greenleaf consiste à voir si la finitude des multiplicités de est équivalente à la commutativité de D (G/H). Nous répondons positivement à cette question quand H est normal dans G. Lorsque H n'est pas normal, nous préparons le terrain pour d'espaces homogènes nilpotents et nous répondons à la question dans différents cas. Nous étudions finalement l'algèbre D (G) ^H , des opérateurs différentiels qui laissent l'espace des vecteurs C de invariant et qui commuttent avec l'action de H sur cet espace.     

On an application of infinitely divisible distributions to quadrature problems

— - , .     

О Тригонометрическом (0, 2)-Интерполировании

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Orders of one-sided approximations of functions inL p -metric

. L _p , 0<p<, . , f, {E _n (f) _p } ₁ p>0 .

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The author expresses his thanks to S. B. Stekin for the attention he has paid to this work.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Eine Charakterisierung der (Rk,Sk+1)-Ringe

Ohne ZusammenfassungDie Ergebnisse dieser Note sind enthalten in der vom Verfasser als Habilitationsschrift eingereichten Arbeit Basische Elemente in Moduln über noetherschen Ringen.     

Inversion and structure formulae for a generalized Laplace transform

, D_v(.) , .     

About generalized ideals in a distributive lattice

Let L be a distributive lattice characterized by a ternary operation (, ,), where (a,b,c)=(ab)(bc)(ac)=(ab)(ac)(bc), a,b,cL. The note considers convex sublattices of L, called generalized ideals of L generated by the operation (, ,). Some remarks have been stated about the graph of a distributive lattice.     

Quasianapole Interaction of Charged Fermions

We obtain the analytic expression for the total cross section of the reaction e ^– e ⁺l ^– l ⁺ (l=,) taking possible quasianapole interaction effects into account. We find numerical restrictions on the interaction parameter value from data for the reaction e ^– e ^+–+ in the energy domain below the Z ⁰ peak.     

On measures that agree on balls

The fundamental result: if and v are two finite Borel measures, defined in the spaceL ^p[0, 1] (1p<) or in C(K) (K is a metric compactum without isolated points), then from the equalities (B)=v(B) for all balls B of radius 1 there follows that =v. In addition, in the spaces C(K) and _p (1p<) from the inequalities (B) v(B) there follows that v.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 122–128, 1989.     

Relaxation of a Quadratic Functional Defined by a Nonnegative Unbounded Matrix

We study the lower semicontinuous envelope in L^p(), F, of a functional F of the form F(u)=A uudx where A=A(x) is not strictly elliptic and not bounded. We prove that F; may also be written as F;(u)= Buudx with B=AP A for a matrix P which is the matrix of an orthogonal projection. In the one-dimensional case, we characterize the domain of F and we explicit the matrix P.     

On the Mechanism for Nonlinear Representations of the Lorentz Group Arising in Quantum Field Theory

A mechanism is identified that leads to the correct law for the relativistic Wigner function transformation with respect to the Lorentz group as long as the corresponding relativistic wave functions have special transformation properties.     

Subsets with Restricted Movement

Let G be a finite permutation group on a set with no fixed points in and let m and k be integers with 0 < m < k. For a finite subset of the movement of is defined as move() = max_gG| ^g \ |. Suppose further that G is not a 2-group and that p is the least odd prime dividing |G| and move() m for all k-element subsets of . Then either || k + m or k (7m – 5) / 2, || (9m – 3)/2. Moreover when || > k + m, then move() m for every subset of .     

0-1-sequences of Toeplitz type

Summary 0-1-sequences are constructed by successive insertion of a periodic sequence of symbols 0, 1 and hole into the holes of the sequence already constructed. Assuming that finally all holes are filled with symbols 0, 1, an almost periodic point in shift space results. Under certain conditions, it is even strictly ergodic. It is proved that the attached invariant measure has pure point spectrum, and a rather explicit expression for eigenvectors is obtained.     

A new derivation of Frisch's algorithm for calculating vertex-pair connectivity

In this paper we give a new and conceptually simple version of Frisch's algorithm for calculating the vertex connectivity of a graph. We show how this algorithm is obtained immediately from the Ford and Fulkerson labelling algorithm by using a 2-ply scanning step. Data structures are introduced which lead to efficiencies in execution, and the final algorithm is presented in a go-to-less notation.This work was supported in part by U.S. Army Research Office, Durham under contract DA HC04 69 C 0012, and NSF Grant GJ-965.     

Configuration of subgroups in the special linear group over a skew field with infinite center

Let T be a skew field with infinite center, let be the special linear group over T of degree 3, and let be the subgroup of diagonal matrices with unit Dieudonee determinant. It is proved that for each intermediate subgroup H, H , there exists a net of order n such that ( H N().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 5–12, 1989.In conclusion, the author would like to thank his instructor Z. I. Borevich, as well as N. A. Vavilov, for their assistance.     

Commutation Relations in an Indefinite-Metric Space

We describe the irreducible regular representations of the algebra of operators a and b defined by [a,b]=1 and ba=a ⁺ b ⁺ in an arbitrary nondegenerate closed indefinite-metric space. We find the relation of this algebra to the generalized Heisenberg algebra.     

Charakterisierung semisimplizialer Mengen durch Unterteilung und Graphen

We define a subdivision functor G for semisimplicial sets such that GXGY implies XY for all pairs of semisimplicial sets X, Y and (GX)¹(GY)¹ implies XY, too, but only, as far as we know, for pairs of weakly degenerate semisimplicial sets X, Y. These results are analogous to theorems on simplicial complexes which have been proved by Finney [1] and Segal [6].

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In der Literatur werden semisimpliziale Mengen auch oft als complete semisimplicial complexes, abgekürzt css complexes bezeichnet. Wir halten uns hier im wesentlichen an die Terminologie von K. Lamotke [5].     

Distribution of the supremum of sums of independent variables with negative drift

Let {_n} be a sequence of identically distributed independent random variables,M₁=<0,M ₁ ² <;S ₀=0,S _n =₁+₂,+...+ _{n, n}1;¯ S=sup {S _n n=0.} The asymptotic behavior ofP(¯ St) as t is studied. If _t ^P (₁x dx=0((t)), thenP(¯ St)– 1/¦¦ _t P (₁x dx=0((t)) (t) is a positive function, having regular behavior at infinity.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 763–770, November, 1977.The author thanks B. A. Rogozin for the formulation of the problem and valuable remarks.