Converse results on equiconvergence of interpolating polynomials

, n- n- 1 , . , , ( « ») f .     

Inversion and structure formulae for a generalized Laplace transform

, D_v(.) , .     

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.     

On summability of subsequences of partial sums of trigonometric Fourier series

n- (n1) fL ^p ([–, ] ⁿ ),=1 = (L C) . , , f([–, ] ⁿ ).     

More on directed colimits of models

M. Richter has proved that whenever a classK of -structures has a finitary first-order axiomatization then the inclusionK Str preserves all existing directed colimits (see [7]). We will generalize this result to classes of -structures having an infinitary first-order axiomatization in a larger signature . We will also show that, as categories, these classes have a natural characterization.In honour of Dieter Pumplün on the occassion of his 60th birthday     

Threshold theorems for a stochastic model of an epidemic with natural immunization

A stochastic model of an epidemic is investigated, taking account of the removal of ill members of the population (by death, by recovery with immunization, by isolation) and natural immunization. Limiting distributions are found for the size of the epidemic, the number immunized ₁, and their sum, under the assumption that the original number of susceptible individuals n and the number of ill individuals m , while n 1,n ₀< , where and are the coefficients for the contraction of the disease and of immunization respectively.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 385–392, September, 1970.     

Lipschitz and darbo conditions for the superposition operator in ideal spaces

Summary In this paper we give necessary and sufficient conditions for the superposition operator Fx(s)=f(s, x(s)) to satisfy a Lipschitz condition Fx₁ - Fx₂kx₁ - x₂ or a Darbo condition (FN)k(N) in ideal spaces of measurable functions, where is the Hausdorff measure of noncompactness. Moreover, we characterize a large class of spaces in which the above mentioned two conditions are equivalent.

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Sunto In questo lavoro diamo delle condizioni necessarie e sufficienti perchè l'operatore di sovrapposizione Fx(s)=f (s, x(s)) soddisfi alla condizione di Lipschitz Fx₁–Fx₂ kx₁–x₂ o quella di Darbo (FN)k(N) in spazi ideali di funzioni misurabili, ove è la misura di non compattezza di Hausdorff. Inoltre, caratterizziamo un'ampia classe di spazi in cui le suddette due condizioni sono equivalenti.

     

On Fourier multipliers between Besov spaces with 0 <p o ≤ min{1,p 1}

, 0<0 min{1,p1}.     

Holomorphic Solutions of Some Functional Equations II

We study a certain type of functional equation, which is of significance from the view point of systems of difference equations. Let the characteristic values of the system be and The case that either || > 1 or 0 < || < 1 has been treated in a former paper. The case that = 1, || = 1 with 1 will be given in another paper. The present note deals with the case = = 1, the most difficult case.AMS Subject Classification (1991): 39A10 39B05     

On the minimum modulus of a multiple Dirichlet series with monotone coefficients

We establish conditions under which the relation M(x, F) (x, F) m(x, F) holds except for a small set, as ¦x¦ + for an entire function F(z) of several complex variables z (p2) represented by a Dirichlet series, where M(x, F) = sup{¦F(x+iy¦: y ^p}, m(x, F) = inf{¦F(x+iy)¦: y ^p} (x, F) being the maximal term of the Dirichlet series, and x ^p.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 21–25.     

On aU-set for multiple Walsh series

m- (m2) , - , .     

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].     

Four-dimensional compact projective planes with doubly transitive action on the fixed pencil

We consider a four-dimensional compact projective plane =( , ) whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil × R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag pW, acts transitively on _p \{W}, and fixes no point in the set W{p}. We study the actions of and N on and on the pencil _p \{W}, in the case that does not contain a three-dimensional elation group. In the special situation that acts doubly transitively on _p {W}, we will determine all possible planes . There are exactly two series of such planes.     

On equivalence of rearrangements of the Haar system in dyadic Hardy and BMO spaces

H={h ₁,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H ={h _(I),I} . , , . L ^p .

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Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday

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This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153.     

Convergence of random products of compact contractions in Hilbert space

Let {T₁, ..., T_N} be a finite set of linear contraction mappings of a Hilbert space H into itself, and let r be a mapping from the natural numbers N to {1, ..., N}. One can form S_n=T_r(n)...T_r(1) which could be described as a random product of the T_i's. Roughly, the S_n converge strongly in the mean, but additional side conditions are necessary to ensure uniform, strong or weak convergence. We examine contractions with three such conditions. (W): x_n1, Tx_n1 implies (I-T)x_n0 weakly, (S): x_n1, Tx_n1 implies (I-T)x_n0 strongly, and (K): there exists a constant K>0 such that for all x, (I-T)x²K(x²–Tx²).We have three main results in the event that the T_i's are compact contractions. First, if r assumes each value infinitely often, then S_n converges uniformly to the projection Q on the subspace _i= ₁ ^N [x|T_ix=x]. Secondly we prove that for such compact contractions, the three conditions (W), (S), and (K) are equivalent. Finally if S=S(T₁, ..., T_N) denotes the algebraic semigroup generated by the T_i's, then there exists a fixed positive constant K such that each element in S satisfies (K) with that K.     

On the almost everywhere convergence of double Fourier series of integrable functions

, . . Q _k [0,2],k=1,2, — . F(x, y)L(T), T=[0, 2]², G(x, y)L(T) , G(x,y)=F(x,y) Q=Q ₁ ×Q ₂ - .     

L 2(R n )-extremal problems on the basis of incomplete information

. ( ), R ⁿ L ₂(R ²).

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The author is supported by the National Natural Science Found of China.     

Edge Coloring of Embedded Graphs with Large Girth

Let G be a simple graph embedded in the surface of Euler characteristic ()0. Denote _e(G), and g the edge chromatic number, the maximum degree and the girth of the graph G, respectively. The paper shows that _e(G)= if 5 and g4, or 4 and g5, or 3 and g9. In addition, if ()>0, then _e(G)= if 3 and g8. Acknowledgments.The authors would like to thank Dr. C.Q. Zhang for carefully reading several versions of this paper during its preparation and for suggesting several stylistic changes that have improved the overall presentation.     

Stationary Solutions of the Fractional Kinetic Equation with a Symmetric Power-Law Potential

The properties of stationary solutions of the one-dimensional fractional Einstein--Smoluchowski equation with a potential of the form x ^2m+2, m=1,2,..., and of the Riesz spatial fractional derivative of order , 12, are studied analytically and numerically. We show that for 1<2, the stationary distribution functions have power-law asymptotic approximations decreasing as x ^–(+2m+1) for large values of the argument. We also show that these distributions are bimodal.     

On the Cesàro summability of orthogonal sequences

(C, ). , . 0<<1. 1) - ( _k ), _k =a _k , (C, ), . 2) , , (C, ) ; _k = =¦a _k ¦.