Reconstructing Coefficients of Series from Certain Orthogonal Systems of Functions

We consider a series with respect to a multiplicative Price system or a generalized Haar system and assume that the martingale subsequence of its partial sums converges almost everywhere. In this paper we prove that, under certain conditions imposed on the majorant of this sequence, the series is a Fourier series in the sense of the A-integral (or its generalizations) of the limit function if the series is considered as a series with respect to a system with supp _n < . In similar terms, we also present sufficient conditions for a series to be a Fourier series in the sense of the usual Lebesgue integral. We give an example showing that the corresponding assertions do not hold if supp _n = .     

Resampling student'st-type statistics

The present paper establishes conditional and unconditional central limit theorems for various resampling procedures for thet-statistic. The results work under fairly general conditions and the underlying random variables need not to be independent. Specific examples are then them(n) (double) bootstrap out ofk(n) observations, the Bayesian bootstrap and two-samplet-type permutation statistics. In case whenm(n)/k(n) is bounded away from zero and infinity necessary and sufficient conditions for the conditional central limit law of the bootstrapt-statistics are established. For high resampling intensity whenm(n)/k(n) tends to infinity the following general result is obtained. Without further other assumptions the bootstrap makes the resampledt-statistic automatically normal. The results are based on a general conditional limit theorem for weighted resampling statistics which is of own interest.     

On a certain property of the BurkillSCP-integral

We establish a necessary condition for theSCP-integrability of a function and use it to construct an example of a function possessing a continuousSCP-majorant andSCP-minorant on a closed interval, but nonintegrable over this interval in the sense of theSCP-integral. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 599–606, April, 1999.     

OnA-stable implicit Runge-Kutta methods

An elementary proof is given of theA-stability of implicit Runge-Kutta methods for which the corresponding rational function is on the diagonal or one of the first two subdiagonals of the Padé table for the exponential function. The result is extended to give necessary and sufficient conditions for theA-stability ofn-stage methods of order greater than or equal to 2n–2.     

Functional law of iterated logarithm for additive functionals of reversible Markov processes

1.IntroductionandMainResultsAssumethat(Xt),.T(T~NorAl)isaPolishspaceE-valuedMarkovprocess,definedon(fi,F,(R),(ot),(P-c)..E),withitssemigroupoftransitionkernels(Pt).Here(ot)isthesemigroupofshiftsonfisuchthatX.(otw)~X. t(w),Vs,tET;(R)isthenaturalfiltration.Throughoutthispaperweassumethat(Pt)issymmetricandergodicwithrespectto(w.r.t.forshort)aprobabilitymeasurepon(E,e)(eistheBorela--fieldofE),i.e.,.Symmetry:(Ptf,g)~(f,Pig):~isfptgdp,acET,if,gCL'(P);.ErgodicitytFOranyfEL'(P),ifPtf~f…     

Sufficient conditions for a control to be a strong minimum

The control literature either presents sufficient conditions for global optimality (for example, the Hamilton-Jacobi-Bellman theorem) or, if concerned with local optimality, restricts attention to comparison controls which are local in theL -sense. In this paper, use is made of an exact expression for the change in cost due to a change in control, a natural extension of a result due to Weierstrass, to obtain sufficient conditions for a control to be a strong minimum (in the sense that comparison controls are merely required to be close in theL ₁-sense).     

On concrete characterization of universal hypergraphic automata

In this paper, we consider structured automata without output signals whose state sets are endowed with an algebraic structure of hypergraphs. The main result of the paper is a theorem where we obtain necessary and sufficient conditions for the possibility of defining on the state set of some automaton A a structure of a hypergraph H such that the automaton A will be the universal hypergraphic automaton.     

Hilbert subsets ands-integral points

A classical tool for studying Hilbert's irreducibility theorem is Siegel's finiteness theorem forS-integral points on algebraic curves. We present a different approach based ons-integral points rather thanS-integral points. Given an integers>0, an elementt of a fieldK is said to bes-integral if the set of placesv ∈M _K for which |t|_v > l is of cardinality ≤s (instead of contained inS for “S-integral”). We prove a general diophantine result fors-integral points (Th.1.4). This result, unlike Siegel's theorem, is effective and is valid more generally for fields with the product formula. The main application to Hilbert's irreducibility theorem is a general criterion for a given Hilbert subset to contain values of given rational functions (Th.2.1). This criterion gives rise to very concrete applications: several examples are given (§2.5). Taking advantage of the effectiveness of our method, we can also produce elements of a given Hilbert subset of a number field with explicitely bounded height (Cor.3.7). Other applications, including the case thatK is of characteristicp>0, will be given in forthcoming papers ([8], [9]).     

A denjoy-type integral for Banach-valued functions

In this paper, we shall show that theHL ϕ-integral and the Denjoy ϕ-integral, defined in [2] are equivalent.     

Continuously controlledA-theory

To anycontrolled space over the metric spaceB we can associate itsboundedly controlled algebraic K-theory, a functor designed to give information about the space of stable bounded concordances of manifolds homotopy equivalent toX. Generalizing a construction of D. R. Anderson, F. X. Connolly, S. Ferry, and E. K. Pedersen, we define another functor, calledcontinuously controlled A-theory, which depends only on thetopology of the control space, not itsmetric properties. In the special case whereB=R ₊, this functor is (more or less by definition) the same asproper A-theory. We prove that under certain conditions on the controlled space the natural transformation from boundedly controlledA-theory to continuously controlledA-theory is a weak homotopy equivalence, and hence defines a generalized homology theory. Continuously controlledK-theory is used in the approaches of G. Carlsson, E. K. Pedersen, and S. Ferry, S. Weinbergervto theK-theory Novikov conjecture.     

Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems

The purpose of this paper is to derive, in a unified way, second order necessary and sufficient optimality criteria, for four types of nonsmooth minimization problems: thediscrete minimax problem, thediscrete l ₁-approximation, the minimization of theexact penalty function and the minimization of theclassical exterior penalty function. Our results correct and supplement conditions obtained by various authors in recent papers.     

Homomorphisms,separable extensions,and Morita maps for weak module algebras

By using a trace one element, we give a sufficient and necessary condition for a weak module algebra A to be a projective left A#H-module, where A#H denotes the weak smash product. We also give some differentiated conditions for the weak smash product to be a separable extension on the weak module algebra A and get the weak structure theorem in the category of weak (H,A)-Hopf modules.     

Henstock and McShane integrals for Banach-valued functions

We solve the problem of the equivalence of theH L-integral and the Henstock integral in Banach spaces. Namely, we prove that the Saks-Henstock lemma is valid in a Banach space if and only if it is finite-dimensional. Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 860–870, June, 1999.     

Eigenvalue location using certain matrix functions and geometric curves

The main inertia theorem gives necessary and sufficient conditions that an n×n complex matrix A have no eigenvalues on the imaginary axis of the complex plane. In this paper corresponding necessary and sufficient conditions are given that A have no eigenvalues on any arbitrary circle, line, and certain other curves in the complex plane. Generalizations of the second part of the main inertia theorem give inclusion regions for the eigenvalues of A.     

Some mathematical problems in seriation

Some mathematical aspects of seriation are studied in this paper. Certain conditions on an abundance or an incidence matrix have been given in the past which imply that there exists a permutation of its rows so that the resulting matrix is a Q matrix (in which case the original matrix is said to be a pre-Q). These types of results have applications to chronologically ordering archaeological provenances under certain circumstances. Unfortunately these conditions are deficient both theoretically and practically, in that for much archaeological data the conditions are not necessarily true yet the corresponding provenances do have chronological orderings. Here we are able to generalize these results in two ways. First we are able to establish necessary and sufficient conditions on the rows of a matrix for it to be pre-Q. These conditions are local in that they concern only certain triples and quadruples of the rows. Secondly, we are able to interpret seriation in terms of a ternary relation R on a set A and prove the results in this general context. In this form the theorem says that if only certain of the triples and quadruples are R-strings, then the whole set A is an R-string, and so has a linear order consistent with the ternary relation R. This would appear to generalize a theorem of P. C. Fishburn. Both aspects of the generalization mean that the results stated herein have a wider applicability than those given heretofore. Possibly more importantly than this is that they lead to numerical invariants, called the fixing number and the related linear rigidity, of such an R-string on A. The archaeological interpretation of these is given in the paper and data supplied which illustrates this point. Finally various other conditions on products and representations of relations are stated which imply that A is an R-string. One of these generalizes and completes a theorem of D. G. Kendall.     

非自治p(t)-拉普拉斯系统周期解的存在性

本文研究一类非自治p(t)-Laplace系统.利用鞍点定理和极小作用原理,获得了周期解存在的充分条件,推广和改进了文献[8]中的结果.     

Stable modification of explicitLU factors for simplex updates

This paper presents a method for modifying anLU factorization of a matrixA when a Simplex update is performed onA. At each stage of the algorithm, two options are allowed, and in one of these a row permutation ofL is made so that theLU structure is always maintained. The expanding file of operators used in other methods is not required. The result, of an error analysis is presented in which the error is bounded by the growth in the partial sums ofLU. Various pivotal strategies which minimize a growth bound are discussed and an example is given in which the worst case for growth occurs repeatedly. Numerical results from experiments on ill-conditioned problems show no tendency for error growth.     

On radicals of triangular operator algebras

SupposeB is a type IC ^*-algebra admitting a diagonalD in the sense of Kumjian, and letE be the conditional expectation fromB ontoD. A subalgebraA ofB is called triangular with diagnoalD ifA∩A*=D. Theorem: Under the above assumptions the Jacobson radical ofA equals the intersection ofA with the kernel of the conditional expectationE. Although the statement of the theorem is coordinate free, the proof requires the use of coordinates in essential ways. A theorem by Kumjian allows us to represent everyC ^*-algebra admitting a diagonal as theC ^*-algebra of a certain groupoid. This enables us to apply the techniques of topological groupoids as developed by Renault and Muhly. A very convenient way of expressing a triangular subalgebra of theC ^*-algebra of a T-groupoid is given by the Spectral Theorem for Bimodules, due to Qui, which is a descendent of the Spectral Theorem for Bimodules due to Muhly and Solel, and to Muhly, Saito and Solel in the context of von Neumann algebras.     

New results of periodic solutions for a kind of Duffing type p-Laplacian equation

By using Mawhin–Manásevich continuation theorem, some new sufficient conditions for the existence and uniqueness of periodic solutions of Duffing type p-Laplacian differential equation are established, which are complement of previously known results.     

On automorphisms of finite Abelian <Emphasis Type="Italic">p</Emphasis>-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A _p . For a finite abelian p-group A of type (k ₁, ..., k _n ), simple necessary and sufficient conditions for an n × n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k ₁, k ₂) is analyzed. This work has begin during the visit of the second author to the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University during the period July 31–August 13, 2005. This visit was supported by the Nicolaus Copernicus University and a grant from Cnpq.