On the Approximation of Functions on Locally Compact Abelian Groups

Questions of approximative nature are considered for a space of functions L ^p(G, ), 1 p , defined on a locally compact abelian Hausdorff group G with Haar measure . The approximating subspaces which are analogs of the space of exponential type entire functions are introduced.     

Reconstruction of a wiener field from its realizations on a curve

Let w(x, y), x 0 and y 0 be a Wiener field on the plane; be a curve given parametrically x=x() and y=y(), [0, 1], where x() is a positive, continuous, nondecreasing function; y() is a positive, continuous, nonincreasing function. A best estimate in the mean-square sense is constructed for w(u, v)(u, v) , based on the values w(x, y), (x, y) and its error is found.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 87–93, 1988.     

On K‐Theory of Simplicial Rings and Degreewise Constructions

We give a measure of the difference between Waldhausen's definition of the Ktheory of a simplicial ring and the definition we obtain by extending Quillen's definition degreewise. This has computational advantages as the degreewise Ktheory sometimes is simpler to work with.     

Sharpening of Stečkin's theorem to strong approximation with exponentp

— , B _n , B p1., , p=1 , - . , , , p.     

Transferring estimates for zonal convolution operators

_p - , . Ad- .     

Investigation of Haar and Franklin series in Hardy spaces

(L ¹,H) (, ) , ; H — . , , L ¹ . [13] , . , , , .     

Жизнь и деятельность яноша Бояи

: . BOLYAI.     

Einschließungsaussagen für gewöhnliche Differentialoperatoren

Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea ₂ and for given functions = we require =C ₀[0, 1] C ₂([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and .     

Discrete Newton methods and iterated defect corrections

Summary In this paper we present a general theory for discrete Newton methods, iterated defect corrections via neighbouring problems and deferred corrections based on asymptotic expansions of the discretization error.Dedicated to Professor Dr. J. Weisinger on the occasion of his sixty-fifth birthday     

Discretization with interpolating approximation

.     

A Niche Width Model of Optimal Specialization

Niche width theory, a part of organizational ecology, predicts whether specialist or generalist forms of organizations have higher fitness, in a continually changing environment. To this end, niche width theory uses a mathematical model borrowed from biology. In this paper, we first loosen the specialist-generalist dichotomy, so that we can predict the optimal degree of specialization. Second, we generalize the model to a larger class of environmental conditions, on the basis of the model's underlying assumptions. Third, we criticize the way the biological model is treated in sociological theory. Two of the model's dimensions seem to be confused, i.e., that of trait and environment; the predicted optimal specialization is a property of individual organizations, not of populations; and, the distinction between fine and coarse grained environments is superfluous.     

Application of a computer to the proof of a conjecture of Minkowski in the geometry of numbers

A computer-assisted proof is given of Minkowski's conjecture on the critical determinant of the region x^p+y^p<1 in the cases 1.03p 1.9745, p2.40, p2.577.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 163–180, 1977.     

On the angular derivative and univalence

f . , , — , A f f(). , , f() 0 . , , ,A , f . , f() - f() . , , . (1976) ( ¦f(z)¦<1) . . (1969) ( ).     

Один Способ Замены Переменных В теории Параболических Уравнений и Его Применение

. .-     

Compact elements in the lattice of radicals

Summary A radical R, in the sense of Kurosh--Amitsur, is said to be compact if, given any collection of radicals X such that R &le;;VX, we have R &le;;VX&apos; for some finite subcollection X&apos; of X. A ring A is said to be radical compact if the lower radical on the singleton {A} is compact. This paper explores the relationship between radical compact rings and rings satisfying certain finiteness conditions. Closure properties of the class of all radical compact rings are also investigated.     

On Sets of Planes in Projective Spaces Intersecting Mutually in One Point

Let be a projective space. In this paper we consider sets of planes of such that any two planes of intersect in exactly one point. Our investigation will lead to a classification of these sets in most cases. There are the following two main results:- If is a set of planes of a projective space intersecting mutually in one point, then the set of intersection points spans a subspace of dimension 6. There are up to isomorphism only three sets where this dimension is 6. These sets are related to the Fano plane.- If is a set of planes of PG(d,q) intersecting mutually in one point, and if q3, 3(q²+q+1), then is either contained in a Klein quadric in PG(5,q), or is a dual partial spread in PG(4,q), or all elements of pass through a common point.     

Symmetrization of functions in Sobolev spaces and the isoperimetric inequality

A positive measurable function f on R^d can be symmetrized to a function f^* depending only on the distance r, and with the same distribution function as f. If the distribution derivatives of f are Radon measures then we have the inequality f^*f, where f is the total mass of the gradient. This inequality is a generalisation of the classical isoperimetric inequality for sets. Furthermore, and this is important for applications, if f belongs to the Sobolev space H¹,P then f^* belongs to H¹,P and f^*_pf_p.     

Mixed-norm estimates for a class of integral operators

(, ) — R ^m ×R ⁿ . f R ^m ×R ⁿ f_p,q, f L _p (R ^m) x y, L^q(Rⁿ). ׃ _q,r cƒ _p,r , ׃ R ^m ×R ⁿ , , , q r . , ( ¦¦) K ₀ (y); p, g r , K ₀.     

On term by term dyadic differentiability of Walsh series

. . . . : {ja _j },j=1,2,... — , f(x) , , f ^[1](x) — f .     

Kelley-Morse+Types of well order is not a conservative extension of Kelley Morse

Summary Assuming the consistency ofZF + There is an inaccessible number of inaccessibles, we prove that Kelley Morse theory plus types is not a conservative extension of Kelley-Morse theory.This paper was partially supported by: Dirección de Investigación de la Pontificia Universidad Católica de Chile (DIUC); Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT)