摘要:

To investigate the effects of finite amplitudes on the behavior of waves in a self‐gravitating medium, exact solutions of nonlinear waves are obtained in a simple situation. The waves are traveling in the direction of the axis of rotation of a homogeneous and uniformly rotating self‐gravitating medium. The nonlinear wave profile and the dispersion relation are obtained and compared with Jeans's linear theory. It is found that the wavelength‐amplitude plane can be divided into three regions: (1) a region where the shock wave is expected to form, (2) a region where the neutral wave exists, and (3) a region where there is gravitational instability. In the third case, it is expected that the unstable wave will eventually evolve to a neutral wave with finite amplitude. Based on this result, speculations are made on the evolution of the unstable density wave in a galaxy. It is established that the propagation of the nonlinear wave in a self‐gravitating medium is always “subsonic,” just as in the linear theory. The difference is that the maximum ratio of the phase speed to the sound speed of the basic state is 1 −A2for the isothermal case and (1 −A2)(γ + 1)/2for the polytropic case instead of 1 for the linear case, whereA2is the dimensionless depth of the valley of the density profile, and γ is the polytropic index. It is also shown that no solitary wave can be found in a homogeneous self‐gravitating medium. Comparison is made with nonlinear waves in a

ISSN:0022-2526    

DOI:10.1002/sapm19816511

年代:1981

数据来源: WILEY

摘要:

Leth(x) =e−αxk(x), where and λ0=0. The closure theorem,Vh=L1(ℝ), is proved for variousαandk(Vhis theL1‐closed variety generated byh). The Tauberian condition, |ĥ|>0, is not used, since generally this condition is difficult to compute directly. The functionsharise naturally in time series and analytic number theory. The technique of proof is constructive and depends on the semigroup {γj} generated by {λj}. The semigroup theory which consolidates and completes the results herein will be developed separately as “A closure problem for signals in semigroup invar

ISSN:0022-2526    

DOI:10.1002/sapm198165137

年代:1981

数据来源: WILEY

摘要:

A proof using the FKG inequalities of the following result is obtained. LetPbe a partially ordered set ona1⩽a2⩽ ⋯ ⩽amandb1⩽b2⩽ ⋯ ⩽bn. LetP(x) be the proportion of linear extentions ofPfor whichxholds. Ifxandyare disjunctions of conjunctions of additional inequalities of the formai⩾bj, thenP(xandy) ⩾P(x)P(y). An example is provided that shows the result can be false if we don't assume the {ai} and {bj} are l

ISSN:0022-2526    

DOI:10.1002/sapm198165181

年代:1981

数据来源: WILEY

摘要:

Symmetries of the nonlinear boundary value problems governing Bénard convection and Taylor vortices are described. Their effect on the corresponding bifurcation equation is deduced from the general analysis of Shearer (1978)

ISSN:0022-2526    

DOI:10.1002/sapm198165185

年代:1981

数据来源: WILEY