摘要:

We characterize the Sheffer sequences by a single convolution identitywhereF(y)is a shift‐invariant operator. We then study a generalization of the notion of Sheffer sequences by removing the requirement thatF(y)be shift‐invariant. All these solutions can then be interpreted as cocommutative coalgebras. We also show the connection with generalized translation operators as introduced by Delsarte. Finally, we apply the same convolution to symmetric functions where we find that the “Sheffer” sequences differ from ordinary full divided power sequences by only a constant

ISSN:0022-2526    

DOI:10.1002/sapm19949211

年代:1994

数据来源: WILEY

摘要:

In many practical situations where Görder vortices are known to arise, the underlying basic velocity profile is three‐dimensional. Only in recent years have studies been made of the stability of vortices in three‐dimensional flows, and it has been shown that only a small crossflow velocity component is required in order to stabilize the Görder mechanism completely. For large Görder number (G ≫ 1) flows, the most unstable linear vortex within a two‐dimensional boundary layer has a wavenumber ofO(G⅕) and a corresponding growth rate ofO(G⅗). Imposition of a crossflow component of sizeO(Re−½G⅗) (whereReis the Reynolds number of the flow) is sufficient to cause these higher wavenumber Gertler modes to decay. Indeed, for certain crossflow/vortex wavenumber combinations, the vortices can be made neutrally stable. A weakly nonlinear analysis of near neutral modes reveals that this slight nonlinearity is stabilizing and so can lead to finite amplitude equilibrium states. In the present work, we give a nonlinear account of the fate of theO(G⅕) wavenumber vortices as they evolve downstream. A study of the large wavenumber modes within a two‐dimensional boundary layer [5], has shown that the effect of this strong nonlinearity is destabilizing and leads to a finite distance breakdown in the flow structure. Here we include the influence of the crossflow component and demonstrate how the stabilizing effects of crossflow and the destabilizing nature of nonlinearity compete. Our calculations can also describe unsteadiness in the vortex structure and they allow us to speculate upon the relative likelihoods of observing various members of the nonlinear G

ISSN:0022-2526    

DOI:10.1002/sapm199492117

年代:1994

数据来源: WILEY

摘要:

Some mathematical details of the parabolized stability equations (PSE) [4] are investigated. In particular, the sources of (unwanted) ellipticity in these equations are identified and suggestions are made for their suppression. Both the compressible and incompressible equations in primitive‐variable formulation are discussed. Remarks are also made on the velocity‐vorticity formulation. A slight modification to the PSEs usually method of treatment of streamwise derivatives higher than first is proposed. Also, an expression is derived for limiting the streamwise gradient of the pressure shape funct

ISSN:0022-2526    

DOI:10.1002/sapm199492141

年代:1994

数据来源: WILEY

摘要:

Singular perturbation techniques are used to study the solutions of nonlinear second order elliptic boundary value problems defined on arbitrary plane domains from which a finite number of small holes of radius ρi(ε) have been removed, in the limit ε → 0. Asymptotic outer and inner expansions are constructed to describe the behavior of solutions at simple bifurcation and limit points. Since bifurcation usually occurs a eigenvalues of a linearized problem, we study in detail the dependence of the eigenvalues and eigenfunctions on ε, for ε → 0. These results are applied to the vibration of a rectangular membrane with one or two circular holes. The asymptotic analysis predicts a remarkably large sensitivity of eigenvalues and limit points to the ε‐domain perturbation considered in

ISSN:0022-2526    

DOI:10.1002/sapm199492155

年代:1994

数据来源: WILEY