ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632054

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The polynomialsPnandQm, having degreesnandmrespectively, withPnmonic, that solve the approximation problemwill be investigated for their asymptotic behaviour, in particular in connection with the distribution of their zeros. The symbolOmeans that the left-hand side should vanish at the origin at least to the ordern+m+1. This problem is discussed in great detail in a series of papers by Saff and Varga. In the present paper we show how their results can be obtained by using uniform expansions of integrals in which Airy functions are the main apprcudmants. We shall focus on the important diagonal case whenn=mand the polynomialsPnandQm, as well as the remainderEn,n,(z) =Pn(z)e−z+Qn(z) can be expressed in terms of Hankel and Bessel functions. The approximate location of the zeros ofPn,QmandEn,nare given in terms of the known zeros of certain Airy functions. An application is given in which the asymptotic information on the zeros is used to obtain an estimate in an approximation of the unit block function by means of the polynomialsPn,Qn.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632055

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In recent years, the pioneering q-series methods initiated by Rogers and extended by Bailey have found extensive applications in number theory and physics. In this paper we show how some of the work of D.B. Sears can be understood and extended once it has been related to the Bailey Transform.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632056

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Aq-analogue of a formula of G.N. Watson that gives the product of two non-terminating Gaussian hypergeometric functions as a sum of twoF4Appell series is obtained. of the many possibleq-extensions of the2F1function, the one that reduces to the well-known Askey-Wilson polynomial when specialized to a terminating series, is chosen. The product formula is shown to reduce to Watson's formula in the limitq→ 1.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632057

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper, we study the local bifurcations of critical periods in the neighbourhood of a non-degenerate centre of a cubic system in Kapteyn's normal form. We find that this system has no isochronous centres. We show that at most three local critical periods bifurcate from a centre at the origin. Moreover there exist perturbations which lead to the maximum number of critical periods.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632058

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We investigate the structure of semilatticesK0(X) of all ordered compactifications of ordered topological spaces X with a one-point Nachbin-compactification. These semilattices and their isomorphic copies are calledocl-semilattices. We give an abstract characterization of allocl-lattices by means of certain generalized stably continuous frames. A finite ordered set is shown to be a dualocl-semilattice iff it is a distributive tensor, that is, a 2-consistently complete meet-semilatticeTwhose principal ideals are distributive and which contains two disjoint elementsto,t1such thats= (to&s) V (t1∧s) for alls∈T. More generally, we characterize those dualocl-semilattices which are finite unions of principal ideals.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632059

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper we establish some new criteria when a mild solution of an inhomogeneous Cauchy problem for an abstract parabolic equation is either classical or strong solution. The results for linear equations are then applied to give new criteria of classical solvability of semilinear problems.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632060

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A cylindrically symmetric metric with two degrees of freedom is considered in connection with Einstein's field equations corresponding to a perfect fluid distribution with heat flow. A class of cylindrically symmetric cosmological models with heat flux is derived. The models have non-zero expansion, shear and acceleration. The heat flux and non-geodetic nature of the stream lines are intimately related with the inhomogeneity. An explicit expression for the temperature distribution in the models is also obtained. A homogeneous stiff-fluid model is derived as a particular case. All the models of our class have a big bang singularity at t = 0 at which all physical and kinematical parameters diverge.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632061

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

LetSbe an excellent extension of a ringR1,ManS-module andNanR-module. It is proved thatMsis anSI-module iffMRis anSI-module and thatNRis anSI-module iff (N⊗RS) is anSI-module. The notions ofGV-modules (V-modules, orS3I-modules), hereditary modules and cohereditary modules are also discussed.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632062

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We consider the following two selection principles for topological spaces:

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632063

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor