摘要:

We determine infinite products in the field of Laurent series with the property that the truncations of the product yield every second continued fraction convergent of the product. We mention some related examples and specialize to obtain numerical results.

ISSN:0025-5793    

DOI:10.1112/S0025579300006380

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300006392

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

摘要:

AbstractUsing several transformation formulae from Ramanujan's second Notebook we achieve distribution results on random variables related to dynamic data structures (so‐called “tries”). This continues research of Knuth, Flajolet and others via an approach that is completely new in this subject.

ISSN:0025-5793    

DOI:10.1112/S0025579300006409

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

摘要:

This article considers the effect of more than one quotient and improves a theorem of Tong which is a generalization of a theorem of Segre on asymmetric approximation.

ISSN:0025-5793    

DOI:10.1112/S0025579300006410

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300006422

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S0025579300006434

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

摘要:

Almost seventy years ago Jeffery [1] showed that a finite velocity can result at infinity when the biharmonic equation is solved for the titled problem. Here, we extend his calculations to show that finite vorticity is the more general conclusion, and then indicate a resolution of the apparent paradox.

ISSN:0025-5793    

DOI:10.1112/S0025579300006446

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

摘要:

AbstractIn this paper two expansions are obtained by contour integration methods for the velocity potential describing two‐dimensional time‐harmonic surface waves due to a free‐surface wave source on water of infinite depth in the presence of surface tension. First the series expansion atr= 0 is found and then the asymptotic expansion asKr®¥, whereKis the wave number for progressive waves andrthe radial distance from the source. The corresponding expansions for the more important submerged wave source in terms of the radial distance from the image source in the free surface may then easily be deduced. The latter are required in a number of surface wave problems, particularly those of a short‐wave asymptotic nature, and are also relevant in obtaining expansions for finite constant depth.

ISSN:0025-5793    

DOI:10.1112/S0025579300006458

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

ISSN:0025-5793    

DOI:10.1112/S002557930000646X

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY

摘要:

AbstractLetXbe a reflexive Banach space. This article presents a number of new characterizations of the topology of Mosco convergence TM for convex sets and functions in terms of natural geometric operators and functional. In addition, necessary and sufficient conditions are given for TM to agree with the weak topology generated by {d(x,C):xєX}, where each distance functional is viewed as a function of the set argument.

ISSN:0025-5793    

DOI:10.1112/S0025579300006471

出版商:London Mathematical Society    

年代:1991

数据来源: WILEY