摘要:

The optimum generation of thrust by means of a rigid profile which performs periodic motions in an inviscid incompressible fluid is discussed. For the description of the flow a linear theory is used. Apart from the demand that a certain mean value of thrust has to be generated, the motions considered have to satisfy an inequality constraint on the contribution of the mean suction force at the leading edge to the total thrust and are furthermore subject to a constraint on their amplitude. This leads to an infinite‐dimensional nonconvex optimization problem. It is proved that for most values of the parameters involved there exists at least one optimum motio

ISSN:0022-2526    

DOI:10.1002/sapm198981293

年代:1989

数据来源: WILEY

摘要:

A simple model for combustion consisting of two parabolic equations is considered. It is shown that plane wave solutions exist. Certain invariant integrals are obtained, from which a nonexistence criterion is derived. The effect of the wave speed on the shape of the wave is deduced.

ISSN:0022-2526    

DOI:10.1002/sapm1989812117

年代:1989

数据来源: WILEY

摘要:

In is known that the equations [ut−g(u)ux]x= ±g′(u) describe pseudo‐spherical surfaces, i.e. that these equations are the integrability conditions for the structural equations of such surfaces, providedgsatisfiesg′+µg=θ. In this paper we obtain self‐Bäcklund transformations for these equations by a geometric method, and show how the inverse scattering method generates glo

ISSN:0022-2526    

DOI:10.1002/sapm1989812125

年代:1989

数据来源: WILEY

摘要:

We consider a certain cellular automaton recently introduced by Park, Steiglitz, and Thurston. By introducing appropriate mathematical notation, the interaction of simple particles evolving according to this automaton rule is completely characterized analytically. It is found that: (1) If two particles have different speed and they interact, then they interact solitonically and, although they may interact a number of times, they finally separate with the faster particle moving in front of the slower one. (2) If two particles have the same speed and are close enough so that they interact, there exist two cases: either they will interact only once and then they will separate, travelling independently of each other, or they will form a new periodic configuration by interacting forever.

ISSN:0022-2526    

DOI:10.1002/sapm1989812153

年代:1989

数据来源: WILEY

摘要:

This paper addresses questions about when modules of relative invariants of a finite groupGacting on a polynomial ringRare free over the ring of invariant polynomialsRG. A converse (first obtained by Shchvartsman) is proven of a result asserting that these modules are always free when the group is generated by pseudoreflections. We also re‐prove the characterization given by Shchvartsman of which charactersχof degree one have the above property, and deduce from this a characterization of whichGhave the above property for all their degree one characte

ISSN:0022-2526    

DOI:10.1002/sapm1989812181

年代:1989

数据来源: WILEY