摘要:

Let (un)nbe a linear recurrence sequence of integers and letb> 1 be a natural number. In this paper, we show that under some mild technical assumptions the basebexpansion of |un| has at leastclogn/log lognnon-zero digits whennis large, wherec> 0 is a computable constant depending on the initial sequence (un)nandb. Our results complement the results of C.L. Stewart from [9]. Some diophantine applications are also presented.

ISSN:1607-3606    

DOI:10.2989/16073600009485986

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Since the introduction of closure operators in topology (Riesz [1909], Kuratowski [1922] and others) many authors have defined and studied closure operators in other branches of mathematics (e.g. Birkhoff [1937] in Algebra and Birkhoff [1940] in Lattice Theory) and in more general contexts. In particular, the introduction of the categorical notion of closure operators (e.g. see Dikranjan and Giuli [1987]) has unified various important notions and has led to interesting examples and applications in diverse areas of mathematics (see for example, Dikranjan and Tholen [1995]).

ISSN:1607-3606    

DOI:10.2989/16073600009485987

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

It has been known for many years that there exist non-constant entire functionsfwhich decay to 0 along every infinite line. Recently it has been shown that if 0 <α< 1/2, then there exist entire functionsfsuch that exp(|z|α)f(z) → 0 (z→ ∞,z∈S) for every stripS; moreover there is a vector spaceMwhich consists of such functions and which is dense in the space of all entire functions with the topology of local uniform convergence. In this note the result is shown to hold for everyα> 0. The proof depends upon a theorem about tangential harmonic approximation on unbounded sets. As a corollary, a new result is proved about the class of entire functions which have zero integral on every doubly infinite line.

ISSN:1607-3606    

DOI:10.2989/16073600009485988

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

This paper introduces the notion of a commutative C*-algebra in a Grothendieck topos E and subsequently that of the spectrum MFnAofA, presented as the locale determined by an appropriate propositional theory in the topos E which describes the basic properties of a multplicative linear functional onA. Further, the locale CEof complex numbers in the topos E is defined in a similar manner and some of its basic properties are established, such as its complete regularity and the compactness of the unit square in CE. Finally, it is shown that the locale MFnAis compact and completely regular, extending the classical result that the multiplicative linear functionals on a commutative C*-algebra form a compact Hausdorff space in the weak*topology.

ISSN:1607-3606    

DOI:10.2989/16073600009485989

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

It is shown, for a commutative C*-algebra in any Grothendieck topos E, that the locale MFnAof multiplicative linear functionals onAis isomorphic to the locale MaxAof maximal ideals ofA, extending the classical result that the space of C*-algebra homomorphisms fromAto the field of complex numbers is isomorphic to the maximal ideal space ofA, that is, the Gelfand-Mazur theorem, to the constructive context of any Grothendieck topos. The technique is to present MaxA, in analogy with our earlier definition of MFnA, by means of a propositional theory which expresses one's natural intuition of the notion involved, and then to establish various properties, leading up to the final result, by formal reasoning within these theories.

ISSN:1607-3606    

DOI:10.2989/16073600009485990

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In this paper we use an equivalent form of Titchmarsh's Convolution theorem to show that the Volterra operator is an example of a quasi-nilpotent operator on a Hilbert space that is not positive with respect to any basis ofL2(0,1). In proving this, it then becomes clear how to generalize this to any operatorTwith the property that ifMis an invariant subspace ofTandTx∈Mthenx∈M.

ISSN:1607-3606    

DOI:10.2989/16073600009485991

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In this note, we study a stronger version of the (PDE) condition for an inclusion of Krull domainsR↪Sand show how it relates to divisoriality and flatness properties ofSwith respect toR.

ISSN:1607-3606    

DOI:10.2989/16073600009485992

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Given two one-sided Markov chains, the authors illustrate a procedure for ascertaining whether they are essentially the same. Precisely, they show how one can determine whether they are block-isomorphic. An application to hydrology is investigated with an example.

ISSN:1607-3606    

DOI:10.2989/16073600009485993

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

IfXis a Banach space such that Π1(X,l1) = Π2(X,l1), we prove the following results: 1) A bounded sequence (xn) lies inside the range of someX-valued measure if and only if the operator (αn) ∈l1→ Σnαnxn∈Xis 1-summing, and 2) IfAis a bounded subset ofXlying in the range of someX**-valued measure, thenAis necessarily contained in the range of someX-valued measure.

ISSN:1607-3606    

DOI:10.2989/16073600009485994

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Using the examples given by S.J. Dilworth and M. Girardi, we prove that the set of all nowhere Pettis differentiable functions is aGδ-dense set in the space of allX-valued Pettis integrable functions on [0, 1]. Also an another example of a dense set in the space of all Pettis integrable functions is given.

ISSN:1607-3606    

DOI:10.2989/16073600009485995

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor