Generalized kolmogorov inequalities for martingales

The classical ebyev inequality leads to an inequality for martingales which is often called the Kolmogorov inequality. It is shown here that many generalized ebyev inequalities for random variables lead in a similar way to martingale inequalities, and that the corresponding martingale inequality is sharp when the ebyev inequality is.On leave from Tel-Aviv University. Presently at the University of California, Berkeley.Research supported by National Science Foundation Grant MPS75-06173     

Necessity of the Cramer, Linnik, and Statulevičius Conditions for Large-Deviation Probabilities

In this paper, we study the necessity of the Cramer, Linnik, and Statuleviius conditions in theorems on large-deviation probabilities. We also show that the Statuleviius condition is a generalization of the Cramer and Linnik conditions. Bibliography: 7 titles.     

On Generalizations of Ostrowski Inequality and Some Related Results

Some generalizations of the Ostrowski inequality, the Milovanovi-Peari-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.     

Chemical trees enumeration algorithms

In the chemical community the need for representing chemical structures within a given family and of efficiently enumerating these structures suggested the use of computers and the implementation of fast enumeration algorithms. This paper considers the isomeric acyclic structures focusing on the enumeration of the alkane molecular family. For this family, Trinajsti et al. (1991) devised an enumeration algorithm which is the most widely known and utilized nowadays. Kvasnika and Pospichal (1991) have proposed an algorithmic scheme which, from the computational complexity point of view, can prove to be more efficient than the Trinajsti one, nevertheless, this algorithm, to the best of our knowledge, has never been implemented. Indeed an efficient implementation requires the introduction of non trivial data structures and other computational tricks. The main contribution of this paper consists of the definition of the implementation details of Kvasnika-Pospichals algorithm, in a comparison of Trinajstis, Kvasnika-Pospichals and two new algorithms, proposed here, in terms of both computational complexity analysis and running times.AMS classification: 05A15, 05C05, 05C30, 05C90Part of this work has been developed during a visit of the first two authors at the EPFL of Lausanne     

Determination of Convex Bodies by Projection Functions

This paper is concerned with an investigation to what extent a convex body is determined by projection functions. We introduce the notion of convex bodies that are almost determined by their brightness function and give a geometric characterization of these bodies. We further prove that, for i 2,...,d–2, a polytope is determined by its ith projection function, if all of its (i+1)-faces are parallelepipeds. Both results extend work by Gardner and Voli [4].     

Inequality for second characteristic values of positive operators of certain classes

A homogeneous additive operator A, positive on a cone K of a Banach space E partially ordered by K, is investigated. It is assumed that K is a reproducing cone in E and that A has a characteristic vector u₀: Au₀ = ₀u₀ in K. It is proved that if for some 1, then any other characteristic value of A satisfies the inequality ||<(-1)/(+1) ₀. This is the best possible upper bound in the class of operators considered.Translated from Matematicheskie Zametki, Vol. 19,No. 1, pp. 27–33, January, 1971.The author takes this opportunity to thank M. A. Krasnosel'skii for his interest in this work.     

On the growth order of partial sums of non-orthogonal series

a _k f _k , f _k L ₂, w-, (2), w(n) — . a _k f _k N {a _k }l ₂, {a _k }l ₂ ( 1, 2, 1a, 2a). ( 2) [8]. , {a _k } w-.     

Remarks on multiple Fourier series

: (1) ( , , ), (2) ( —, , ). , .     

Eine Methode zur Berechnung quasistationärer Temperaturzustände bei gesteuerten Wärmeleitvorgängen in festen Körpern

Summary In a recent paperVodika solves a special problem of heat conduction with local and time-dependent boundary conditions. As the method does not seem very suitable for solving problems of this kind, the solution for the most general case is given. As an example the problem treated byVodika is solved, and the equality of both results is shown.     

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.     

On Mordell's Equation

In an earlier paper we developed an algorithm for computing all integral points on elliptic curves over the rationals Q. Here we illustrate our method by applying it to Mordell's Equation y²=x³⁺k for 0 k Z and draw some conclusions from our numerical findings. In fact we solve Mordell's Equation in Z for all integers k within the range 0 < | k | 10 000 and partially extend the computations to 0 < | k | 100 000. For these values of k, the constant in Hall's conjecture turns out to be C=5. Some other interesting observations are made concerning large integer points, large generators of the Mordell–Weil group and large Tate–Shafarevi groups. Three graphs illustrate the distribution of integer points in dependence on the parameter k. One interesting feature is the occurrence of lines in the graphs.     

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.     

Congruences and Ideals of Effect Algebras

This paper is devoted to a general investigation of congruences and ideals in effect algebras. One of our main results is the existence of an order isomorphism between Riesz congruences and Riesz ideals. We also answer an open question of Dvureenskij and Pulmannová by showing that an ideal is a Riesz ideal if and only if it is closed under generalized Sasaki projections.     

Some inequalities for fourier coefficients in inner product spaces

Some inequalities for Fourier coefficients in inner product spaces and related results are given. These inequalities complement, in a sense, some of the results in a recent book due to Mitrinovi, Peari and Fink.This research was supported by a grant from La Trobe University     

On summability of subsequences of partial sums of trigonometric Fourier series

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

Generalization of Gδ*-Diagonals and ωΔ-Spaces

In this paper we introduce the concepts of a quasi-G*-diagonal and quasi--space as generalizations of the concepts of G*-diagonal and -space respectively. It is shown that a quasi-Moore space may be characterized in terms of these concepts. As a consequence we obtain the following metrization theorems: every paracompact -space with quasi-G-diagonal is metrizable and every collectionwise normal quasi--space is metrizable.     

Mean-value type functional equations

Summary In this work the following two conjectures concerning mean-value type functional equations are proved: then-dimensional octahedron and cube equations are equivalent (conjectured by D. Z. Djokovi and H. Haruki), and the continuous solutions of these equations on ⁿ are linear combinations of a given harmonic polynomial (conjectured by H. Haruki).     

Messbare Mengen von Massen und Inhalten

Let X be a completely regular space. The customary -field is the coarsest -field on the space of Bairemeasures on X which makes (A) measurable for any Baire set A. We compare the customary -field with the Baire and Borel -field induced by the weak* topology which lies on the dual space C(X). In (2.3) it is shown that the customary -field is just the Baire -field. In part 3 necessary and sufficient conditions are given under which the set of -smooth measures is measurable with respect to the Borel -field which lies on the positive cone of the space of finitely additive, regular measures C(X). Finally, a decomposition theorem for generalized kernels is proved. The -smooth part of a generalized kernel is a kernel again if certain conditions are fulfilled.     

On strong summability of polynomial expansions

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Dedicated to Professor L. Leindler on his 50^th birthday     

Applications of matrix functions

A, ()=0, c(z)- T - TY=AY. A y(t)=y(, t) Ty=y Y(t). - c(T)y=0.