摘要:

Finite amplitude capillary‐gravity waves of permanent form on deep water are studied numerically. Bifurcation and limit lines are calculated. Pure and combination waves are continued to maximum amplitude. It is found that the height is limited in all cases by the surface enclosing one or more bubble

ISSN:0022-2526    

DOI:10.1002/sapm198062295

年代:1980

数据来源: WILEY

摘要:

We use the material of Parts I and II to obtain further results in sequence enumeration. These include the enumeration of sequences with respect to both maximalπ1andπ2‐paths, and the enumeration of sequences with distinguished substrings. We use the material to derive an enumerative proof of a generalization of a result of Foata and Schützenberger. Finally, we reconsider the enumeration of permutations with periodic pattern and show that the required generating function may be exhibited as the solution of a set of first‐order nonlinear differential equations. Subsequent work has shown these to be matrix Riccati equations, although we refer to them here as Volterra equ

ISSN:0022-2526    

DOI:10.1002/sapm1980622113

年代:1980

数据来源: WILEY

摘要:

We develop a Lie‐algebraic method that associates with each of the 34 distinct second‐order hypergeometric functions in two variables a canonical system of partial differential equations. The special functions arise by partial separation of variables in these simple systems. Some consequences are a demonstration that all such functions appear as solutions of the 4‐variable wave equation and a classification of the possible imbeddings. In each case the functions are characterized by first‐ and second‐order operators in the enveloping algebra of the conformal symmetry algebra for the wave equation. In some cases the 3‐variable wave and heat equations and the 2‐variable Helmholtz equation also arise. This intimate relationship between Horn functions and some fundamental equations of mathematical physics shows that these functions are more interesting than was previously recognized and permits use of the powerful tools of Lie theory and separation of variables to obtain properties of

ISSN:0022-2526    

DOI:10.1002/sapm1980622143

年代:1980

数据来源: WILEY

摘要:

An unexpected connection between a certain class of exponential approximation operators and polynomial sequences of binomial type was discovered by Ismail. Building on this result, we present a multivariate analogue of these exponential operators.

ISSN:0022-2526    

DOI:10.1002/sapm1980622175

年代:1980

数据来源: WILEY

摘要:

In this paper, we give an internal description of a weak map between two matroids on the same set. This description is similar to the description of an elementary strong map in terms of a modular cut.

ISSN:0022-2526    

DOI:10.1002/sapm1980622183

年代:1980

数据来源: WILEY