Sur les Mesures Simultanement Invariantes Pour les Transformations x » {λx} ET x » {βx}

We show that for reasonable couples of Pisot number and , there is no measure simultaneously invariant by the two transformations of [0, 1], x {x} and x {x}, and Bernoulli (or weak Bernoulli) for one of the transformations.     

Nielsensche Realisierungssätze für Seifertfaserungen

Let M be a closed aspherical manifold and A a finite subgroup of the outer automorphism group Out ₁M of ₁M. A necessary (and in many cases also sufficient) condition for realising A by the induced action of an isomorphic group of homeomorphisms of M is the existence of an extension 1₁MEA1 to the abstract kernel (A,₁M, AOut ₁M). If the center of ₁M is nontrivial, this condition need not be fulfilled ([14]). We showed in [25] however that one can always find a surjection BA of a finite group B with abelian kernel such that there exists an extension to the abstract kernel (B,₁M,BAOut₁M), and one can try to realize B instead of A. The main result of the present paper is a characterisation of all such groups B (for a given A) which can be realized by a group of homeomorphisms. The class of manifolds considered here consists of certain Seifert fiber spaces in arbitrary dimensions but the main result is purely algebraic and can be applied to other classes of manifolds, for example to flat Riemannian manifolds.     

The Navier―Stokes Problem in a Two-Dimensional Domain with Angular Outlets to Infinity

The NavierStokes problem in a plane domain with two angular outlets to infinity is provided, as usual, either with the flux condition or with the pressure drop one. For small data it is proved that there exists a solution with the decay O(|x|^-1) of the velocity field as |x| (if one of the angles is equal to or greater than , then additional symmetry assumptions are needed). Since the nonlinear and linear terms are asymptotically of the same power, the results are based on a complete investigation of the linearized Stokes problem in weighted spaces with a detached asymptotics (the angular parts in the representations are not fixed). Bibliography: 16 titles.     

A conditional dilatation equation

Summary The following theorem holds true. Theorem. Let X be a normed real vector space of dimension 3 and let k > 0 be a fixed real number. Suppose that f: X X and g: X × X are functions satisfying x – y = k f(x) – f(y) = g(x, y)(x – y) for all x, y X. Then there exist elements and t X such that f(x) = x + t for all x X and such that g(x, y) = for all x, y X with x – y = k.     

On the positive definiteness of n ↦ epnα for α close to 2

For >2, let Q ⁺() be the infimum of those q>0 for which the function n e^pn is positive definite on N ₀ for every pq. We shall prove that Q ⁺()0 as 2.     

Topological transitivity of cylindrical cascades

The existence is proved of a topologically transitive (t.t.) homeomorphism U of the space W = × Z of the formU (, z)=(T,, z+f ()) ( , z Z), where is a complete separable metric space, T is a t.t. homeomorphism of onto itself, Z is a separable banach space, andf is a continuous map: z. For the special case W = S¹×R, T=+ ( is incommensurable with 2) the existence is proved of t.t. homeomorphisms (1) of two types: 1) with zero measure of the set of transitive points, 2) with zero measure of the set of intransitive points. An example is presented of a continuous functionf: S¹R for which the corresponding homeomorphism (1) is t.t. for all incommensurable with 2.Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 441–452, September, 1973.The author thanks D. V. Anosov for advice and interest in the work.     

Local decay in time of solutions to Schrödinger's equation with a dilation-analytic interaction

For a Schrödinger operator H=–+V in L²(³ with a dilation-analytic potential V decaying as r^–2– at infinity we prove that a scattering solution exp(-itH)f generically decays as t^–3/2 for t     

A Selection Theorem for Strongly Regular Multivalued Mappings

We prove the following generalization of a theorem of Ferry concerning selections of strongly regular multivalued maps onto the class of paracompact spaces: Let : X (Z, ) be a map of a paracompact space X into a metric space (Z, ) whose values (x) are complete subspaces of Z and absolute extensors (AE), for every x X. Suppose that can be represented as = , where : X Y is a continuous singlevalued map of X onto some finite-dimensional paracompact space Y and : Y (Z, ) is a strongly regular map. Then for every closed subset A X and every selection r : A Z of the map |A : A Z, there exists an extension : X Z of r such that is a selection of the map . We also prove a local version of this theorem.     

Lower functions for asymmetric Lévy processes

Summary Let {X _t } be a ¹ process with stationary independent increments and its Lévy measurev be given byv{yy>x}=x ^–L ₁ (x), v{yy<–x}=x ^–L ₂ (x) whereL ₁,L ₂ are slowly varying at 0 and and 0<1. We construct two types of a nondecreasing functionh(t) depending on 0<<1 or =1 such that lim inf a.s. ast 0 andt for some positive finite constantC.This research is partialy supported by a grant from Korea University     

More projective geometry associated with unramified double covers of curves of genus four

Sunto Sia : YY un rivestimento doppio non diramato di una curva di genere quattro definita su C e a moduli generali. Sia il punto di 2-divisione associate a . In questa nota si studia il sistema 2 delle quardriche di contatto al modello canonico di Y, associato al dato rivestimento.e si esplicita una biezione tra l'insieme delle theta-caratteristiche dispari di Y che diffeiscono per e l'insieme dell theta caratteristiche dispari dell curve di genere tre la cui Jacobiana e isomorfa (come v.a.p.p.) alla varieta di Prym P(f Y Y)     

Periodic solutions of differential equations in Banach spaces

Let X be a Banach space, DX, f: [0,)xDX continuous and -periodic. In this paper we consider various conditions on D and f sufficient for existence of an -periodic solution of the differential equation u=f(t,u). In the main, we shall assume that D is closed bounded and convex and f satisfies a boundary condition at D such that D is flow invariant for u=f(t,u). The map f is assumed to be either compact or dissipative or a certain perturbation of such maps.     

Complete Subobjects of Fuzzy Sets Over MV-Algebras

A subobjects structure of the category -FSet of -fuzzy sets over a complete MV-algebra is investigated, where an -fuzzy set is a pair A = (A, ) such that A is a set and : A × A is a special map. Special subobjects (called complete) of an -fuzzy set A which can be identified with some characteristic morphisms A ^* = (L × L, ) are then investigated. It is proved that some truth-valued morphisms are characteristic morphisms of complete subobjects.     

Complex whitham deformations in problems with “integrable instability”

The focusing nonlinear Schrödinger equation with finite-density boundary conditions as |x| is considered. The asymptotic behavior of the solution ast is investigated by means of the complex theory of deformations of Whitham.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 393–419, September, 1995.     

The degree of maps between certain 6-manifolds

For manifolds M,M of the form S² e⁴ e⁶ we compute the homomorphisms H_*M H_*M between homology groups which are realizable by a map F: M M.     

Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity

It is proved that a quasiconvex sequence _v of convergence factors transforms Fourier series of functions whose moduli of continuity do not exceed a given modulus of continuity(gd) into uniformly convergent series if and only if _n (1/n) log n 0 for n . The sufficiency of this condition is already known.Translated from Matematicheskie Zametki, Vol. 8, No. 5,pp. 619–623, November, 1970.     

Existence of Moduli for Bi-Lipschitz Equivalence of Analytic Functions

We show that the bi-Lipschitz equivalence of analytic function germs (², 0)(, 0) admits continuous moduli. More precisely, we propose an invariant of the bi-Lipschitz equivalence of such germs that varies continuously in many analytic families f _t : (², 0)(, 0). For a single germ f the invariant of f is given in terms of the leading coefficients of the asymptotic expansions of f along the branches of generic polar curve of f.     

The convergence to a Gaussian process of the number of empty cells in the classical problem of distributing particles among cells

We consider a case in which n particles are distributed independently of one another in N cells. We examine the behavior of the number of empty cells, ₀ (n), as a random function of the parameter n when n, N. We prove that for suitable variation of the time parameter, ₀ (n) will converge to a Gaussian process in the following cases: a) n/N, n/N^– l _nN; b) n/N0, n²/N.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp, 97–104, July, 1968.     

High-Energy Relations Between Elastic Scattering Amplitudes of Particles and Antiparticles

We find conditions under which the ratio of particle and antiparticle total scattering cross sections as s. If the forward elastic scattering amplitudes become purely real asymptotically, then their ratio tends to –1. We prove that /_–(s)1 for ₊(s)/m ², where m is the -meson mass. We show that the asymptotic relations obtained have finite-energy analogues for some processes.     

Kennzeichnungen hyperbolischer Bewegungen durch Lineationen

LetI ⁿ be the set of points ofn-dimensional hyperbolic geometry,n2. THEOREM 1. LetfI ⁿ I ⁿ be a surjection such that images of hyperbolic lines are contained in hyperbolic lines. Thenf is a hyperbolic motion. THEOREM 2. IffIⁿ Iⁿ maps hyperbolic lines onto hyperbolic lines, then the image off is a hyperbolic line, orf is a hyperbolic motion. We note that Theorem 1 is a consequence of [3, Theorem 2.4].

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Herrn Professor Helmut Karzel zum 70. Geburtstag gewidmet     

On the equivalence of renormalizations in standard and dimensional regularizations of 2D four-fermion interactions

We discuss the problem of equivalence between the standard (integer-dimensional d=2) and the d=2+ dimensional renormalization schemes for the complete U_N-symmetrical four-fermion interaction model. To ensure the multiplicative renormalizability of the theory, we need three charges in the first case; in the second, we need an infinite series of independent charges g {g_n, n=0, 1, ...}. After the usual MS-renormalization. there exists a UV-finite renormalization of fields. Charges gg'(g) exist such that the renormalized Green's functions in the limit 0 depend only on the three lower charges g'_n(g) with n=0, 1, 2. rather than on the whole set. This ensures the possibility of establishing the equivalence of the two renormalization schemes. The results of calculations in the MS scheme up to two loops for the -functions, and up to three loops for the anomalous field dimension are presented. These are presented together with the derivation of the projection technique relations, which allows one to express the higher renormalized composite operators of the 4F-interaction via the lower ones in the limit 0.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 1, pp. 27–46, April, 1996.Translated by L. O. Chekhov.