On the admissibility of function spaces of typeB p,q s andF p,q s,and boundary value problems for non-linear partial differential equations

u=f(x)+S(u), S — , u-G(u), G — . B _p,q ^s () -F _p,q ^s (). R _n — . — . _p,q ^s F _p,q ^s .     

Quasiclassical asymptotic behavior of the scattering cross section for asymptotically homogeneous potentials

One considers the total scattering cross section on the potential gV(x), x^m, m3, for large values of the coupling constant g and of the wave number k. One assumes that V(x)(x/|1x|)|x|^–, 2>m+1, as ¦x¦. It is shown that for gk^–1 , g^3–ak^2(a–2) the scattering cross section is equal asymptotically to _a(gk^–1), x=(m–1)(–1)^–1. Here the coefficient _a is determined only by the function and the number . Under the additional conditions >0, V>0, the indicated asymptotic behavior holds in the large domain gk^–1 , gk^a–z c(gk^–1), >0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 105–136, 1986.     

Waterman classes and triangular sums of double Fourier series

Let ^a ={nln^a (n+1)}, where a R. The following results are established: For every &fnof ^a BV ((- ]²), the triangular partial sums of its Fourier series are uniformly bounded if a = -1, and converge everywhere if a < -1.For every a>0, there exists &fnof ^a BV ((- ]²) such that the triangular partial sums of its Fourier series are unbounded at the point (0;0).     

On the parameter estimation of diffusional type processes with constant coefficients (Elementary Gaussian Processes)

, (1). 3, , ()=, (8) (16). [1], . (28) (31) ( 5), - (. [3]).

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The author thanks Professor M.Arató for having pointed out this problem, and for his valuable suggestions.     

Some Properties of Finite Morphisms on Double Points

For a finite morphism f : X Y of smooth varieties such that f maps X birationally onto X=f(X), the local equations of f are obtained at the double points which are not triple. If C is the conductor of X over X, and are the subschemes defined by C, then D and are shown to be complete intersections at these points, provided that C has the expected codimension. This leads one to determine the depth of local rings of X at these double points. On the other hand, when C is reduced in X, it is proved that X is weakly normal at these points, and some global results are given. For the case of affine spaces, the local equations of X at these points are computed.     

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 .     

Morera type theorems on the unit disc

, . . : , , , , .     

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 the Global Solvability of the Cauchy Problem for Singular Functional Differential Equations

Sufficient conditions are found for the global solvability of the weighted Cauchy problem where f : C([a, b]; R ⁿ) L _loc([a, b]; R ⁿ) is a singular Volterra operator, c ₀ R ⁿ, h : [a, b] [0, +] is a function continuous and positive on [a, b], and · is the norm in R ⁿ.     

A generalized integral with applications to trigonometric series

, . . .

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The authors wish to thank the referee whose comments improved the presentation of the paper. In fact, the present form of Lemma 2, which was originally very long, is due to the referee.     

The self-similar solutions to a fast diffusion equation

A quasilinear equation u -x·u/2+f(u)=0 is studied, wheref(u)=–u+u , > 0, 0<. <1, >1 andx R ⁿ. The equation arises from the study of blow-up self-similar solutions of the heat equation _t =+. We prove the existence and non-existence of ground state for various combination of , and . In particular, we prove that when / < forn=1,2 or / < (n + 2) /(n – 2) forn 3 there exists no non-constant positive radial self-similar solution of the parabolic equation, but for many cases where / > (n + 2)/(n – 2) there exists an infinite number of non-constant positive radial self-similar solutions.     

Estimating Equations with Nuisance Parameters: Theory and Applications

In a variety of statistical problems the estimate _n of a parameter is defined as the root of a generalized estimating equation G_n(_nn)=0 where _n is an estimate of a nuisance parameter . We give sufficient conditions for the asymptotic normality of #x0398;_n defined in this way and derive their asymptotic distribution. A circumstance under which the asymptotic distribution of #x0398;_n will not be influenced by that of _n) is noted. As an example, we consider a covariance structure analysis in which both the population mean and the population fourth-order moment are nuisance parameters. Applications to pseudo maximum likelihood, generalized least squares with estimated weights, and M-estimation with an estimated scale parameter are discussed briefly.     

On convergence and summability of Fourier series

. , , –1<<0. .

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The present work was written on the basis of two earlier works received byAnalysis Mathematica on January 16, 1979, and July 20, 1979.     

On the exactness of a theorem of G.A. Fomin

, . . [1] - . .     

On an inequality of Longnecker and Serfling

— [2], [5], [7], [8], , , . , . , .     

Асимптоический Анализ Распределения Статистики Диксона

. u 60-u u     

Direct and converse imbedding theorems for seminormed spaces

. n=2 . ., 103 498      

m-Systems and Partial m-Systemsof Polar Spaces

LetP be a finite classical polar space of rankr, withr 2. A partialm-systemM ofP, with 0 m r - 1, is any set (₁), ₂,..., _k ofk ( 0) totally singularm-spaces ofP such that no maximal totally singular space containing _i has a point in common with (_{1 2} ... _k) — _i,i = 1, 2,...,k. In a previous paper an upper bound for ¦M¦ was obtained (Theorem 1). If ¦M¦ = , thenM is called anm-system ofP. Form = 0 them-systems are the ovoids ofP; form =r - 1 them-systems are the spreads ofP. In this paper we improve in many cases the upper bound for the number of elements of a partialm-system, thus proving the nonexistence of several classes ofm-systems.Dedicated to Hanfried Lenz on the occasion of his 80th birthday