A generalized Laplace transform of generalized functions

- . . . , .     

Fixed-width confidence intervals for contrasts in the means

The sequential procedure developed by Bhargava and Srivastava (1973, J. Roy. Statist. Soc. Ser. B, 35, 147–152) to construct fixed-width confidence intervals for contrasts in the means is further analyzed. Second-order approximations for the first two moments of the stopping time and the coverage probability associated with the sequential procedure, are obtained. A lower bound for the number of additional observations after stopping is derived, which ensures the mxact probability of coverage. Moreover, two-stage, three-stage and modified sequential procedures are proposed for the same estimation problem. Relative advantages and disadvantages of these sampling schemes are discussed and their properties are studied.     

Target-Oriented Branch and Bound Method for Global Optimization

We introduce a very simple but efficient idea for branch and bound (&) algorithms in global optimization (GO). As input for our generic algorithm, we need an upper bound algorithm for the GO maximization problem and a branching rule. The latter reduces the problem into several smaller subproblems of the same type. The new & approach delivers one global optimizer or, if stopped before finished, improved upper and lower bounds for the problem. Its main difference to commonly used & techniques is its ability to approximate the problem from above and from below while traversing the problem tree. It needs no supplementary information about the system optimized and does not consume more time than classical & techniques. Experimental results with the maximum clique problem illustrate the benefit of this new method.     

Waterman classes and spherical partial sums of double Fourier series

f(x,y) ₀BV(T²), ={1/n} _n=1 .

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Dedicated to Professor Károly Tandori, the outstanding mathematician and academician on his seventieth birthday

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This work was done under the financial support of the Russian Foundation for Fundamental Scientific Research, Grant 93-01-00240.     

An in-core/out-of-core method for solving large scale assignment problems

We describe how the shortest augmenting path method can be used as basis for a so called in-core/out-of-core approach for solving large assignment problems in which the data cannot be kept in central memory of a computer. Here we start by solving the assignment problem on a sparse subgraph and then we introduce the remaining edges in an outpricing/reoptimization phase. We introduce several strategies which enable to keep the working subgraph sparse throughout the procedure and even lead to an all in-core code which is faster than the basic shortest augmenting path code.

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Zusammenfassung Wir beschreiben einen sogenannten In-Core/Out-of-Core Ansatz auf der Basis der kürzesten erweiternden Wege Methode für die Lösung gro\er Zuordnungsprobleme, für die die gesamte Kostenmatrix nicht im Zentralspeicher des Rechners gehalten werden kann. Bei diesem Ansatz wird in einer ersten Phase ein Zuordnungsproblem über einem dünnen Teilgraph optimal gelöst. In einer zweiten Phase werden dann die nicht berücksichtigen Kanten mittels der optimalen Duallösung bewertet (outpricing) und gegebenenfalls eine Reoptimierung durchgeführt. Durch Anwendung spezieller Strategien wird es möglich, während der gesamten Lösung den im Zentralspeicher abzuspeichernden Teilgraphen dünn zu halten. Weiterhin zeigt sich, da\ dieser Ansatz zu einem neuen Verfahren führt, das der zugrunde liegenden kürzesten erweiternden Wege Methode überlegen ist.

     

Decrease orders of theL p -moduli of continuity (0<p≦∞)

k — , 0<p, _k(p) — k- L _p ¹ ; >0, - , (0, ), (t)0 (t0), (t) ,t ^–(t) . _k(p), , 0<p1 _{k(p) (k– 1)p+1}, 1<p — _k , .     

Flowchart machines

Let denote a conventional flowchart. Any algorithm can be represented by a flowchart. If action nodes in call then is a recursive flowchart. We show how to decompose arbitrary non-self-modifying programs into structure and atomic parts. We specifically give the synthesis procedure for a controller . can serve as the only sequencer in an execution of . If is recursive then is a pushdown machine, otherwise is a finite state machine. The next-state functionf and the output functiong of represent respectively all of the structure-, i.e. the programmer-oriented-, and all of the atomic-, i.e. the data-oriented-, parts of .f defines the flow or pattern of computations andg the actual transformations or operations on data. Thus we construct and analyze programs by constructing and analyzing their sequencers .     

Global Optimization Techniques for Solving the General Quadratic Integer Programming Problem

We consider the problem of minimizing a general quadratic function over a polytope in the n-dimensional space with integrality restrictions on all of the variables. (This class of problems contains, e.g., the quadratic 0-1 program as a special case.) A finite branch and bound algorithm is established, in which the branching procedure is the so-called integral rectangular partition, and the bound estimation is performed by solving a concave programming problem with a special structure. Three methods for solving this special concave program are proposed.     

On rearrangements of the Haar system in the space BMO

, .     

On the equivalence of some rearrangements of the two-parameter Haar system

h ₁, L _p .

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

Integrability of multiple Walsh series and Parseval's formula

f(x,y) _jk . , {c _jk} , f(x, )(, ) [0,1)&#x0445;[0,1) , - (0,0). , , f, - f. , , , [1] . . - [5] [6].

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This research is supported by National Science Council, Taipei, R.O.C. under Grant #NSC 84-2121-M-007-026.     

On the divergence of spherical sums of double Fourier-Haar series

. : [0, +) [0, +) - , u+ (u) (u)=o(u lnu). [0, 1]² f , ¦f¦ L([0, 1]²), - [0, 1]².     

Spectral orders and convolution

. (R) _{– –} fg(y)h(x–y) dx dy _{– –} f ^{^} (x)g ^{^} (y)h ^{^} (x–y)dx dy (f,g0) —:f×gf ^{^} ×g ^{^}(f,g 0) f^{^} g^{^} f g -, X — . , - f ₁f ₂ , f ₁ ^{^} ×gf ₂×g 0g. .     

On the distribution of points of maximal deviation in complex Čebyšev approximation

f — , . p _n (f) f . , n+2 , f–p _n (f) . , n . , .

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On the distribution of points of maximal deviation in complex ebyev approximation

     

Extension of functions,which are traces of functions belonging to 249-01249-01249-01on an arbitrary subset of the line

( , k) , ER f(x) f(x)H _k (R) (k2— ,=(t) — k- ). f(x) E (t).     

On Interpolation of the Fourier Maximal Operator in Orlicz Spaces

Let and be positive increasing convex functions defined on [0, ). Suppose satisfies the 2-condition, that is, (t)2 (C1t) for sufficiently large t, and has some nice properties. If -1(u)log(u+1) C2-1(u) for sufficiently large uthen we have S*(f) L CfL for all f L ([-, ])where S*(f) is the majorant function of partial sums of trigonometric Fourier series and fL is the Orlicz norm of f. This result is sharp.     

Joint norm of operators and an investigation of nonlinear problems

Nonlinear operator equations of the form x=Fx in a real-valued Hilbert space H are studied. If the operator F is completely continuous and admits the bound Fx< Bx+b, where B is a continuous linear operator then for B<1 the Schauder principle is applicable to the equation x=Fx and this equation possesses at least one solution x H. If the bound Fx<,B₁x+B₂x+b is valid where B₁ and B₂ are bounded linear operators then the simplest conditions for solvability of the equation x=Fx is of the form B₁+B₂<1. This condition could be relaxed. The proposed method is applied to the investigation of a two-point boundary problem (cf., e.g., [1–3]). New conditions for the existence of solutions are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1605–1616, December, 1990.     

Remarks on multiple Fourier series

: (1) ( , , ), (2) ( —, , ). , .     

Limiting behavior of certain mixtures of distributions

U — [0, 1] Y — . X=[1–U ^1/v /Y], U Y.     

Асимптоический Анализ Распределения Статистики Диксона

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