摘要:

Two techniques for the analysis of differential equations, the Lie method of extended groups and the Painlevé analysis, are reviewed. The implications for integrability in the case of the existence of symmetries in the former or the possession of the Painlevé property in the latter are explored. By way of an example an equation which arises in shear-free flow of a spherically symmetric perfect fluid with conformal symmetry in general relativity is given an extensive treatment with both techniques.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631831

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We characterize the condition

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631832

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The paper is a complement to the survey: M.I.Ostrovskii “Topologies on the set of all subspaces of a Banach space and related questions of Banach space geometry”, Quaestiones Math. 17 (1994). It contains proofs of some results on stability of properties of Banach spaces with respect to the geometric opening stated in the survey without proofs.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631833

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We analyse static spherically symmetric spacetimes in general relativity. For a particular choice of one of the gravitational potentials we show that the solution of the Einstein field equations is reduced to generating a solution of the hypergeometric differential equation. Some exact solutions are presented in terms of special functions and we demonstrate, with the assistance of MATHEMATICA, that these solutions may be reexpressed in terms of elementary functions. We regain a well known static model from our results.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631834

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Bulk viscosity is expected to play an important role in cosmology, especially with regard to various dissipative processes which are believed to occur at certain stages of the evolution of the universe. By now bulk viscosity has been well studied in general relativity, both in the Robertson-Walker cosmological models as well as in the other Bianchi models. However, its role in alternative theories of gravity has not been studied much. Brans-Dicke theory is the most seriously considered alternative to general relativity. In this paper, some Robertson-Walker cosmological models are derived in Brans-Dicke theory which could be relevant to the inflationary scenario.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631835

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We say that a normed spaceXhas the Daugavet property (DP) if for every finite rank operatorKinXthe equality ∥I+T∥ = 1 + ∥T∥ holds. It is known thatC[0,1] andL1[0,1] haveDP. We prove that ifXhasDPthenXhas no unconditional basis. We also discuss anti-Daugavet property, hereditaryDP-spaces and construct a strictly convex normed space havingDP.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631836

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

N. Dunford and J.T. Schwartz gave a complete characterization of those matrices of (bounded) Fourier multiplier operators acting inL2(RN)nwhich are spectral operators, [4; ch. XV]. In the present note this characterization is extended to the setting ofLP(G)n, whereGis a locally compact abelian group and 1 < p < ∞; see Theorem 2.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631837

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This paper brings together the theory of observational cosmology and the null-cone characteristic initial value problem (CIVP) of numerical relativity. A computer code is constructed which calculates the past behaviour of the Universe from input data that is, in principle, measurable. For practical reasons the code is limited to the case of axisymmetry without rotation. The construction of the code brings to light an interesting general point about observational cosmology. In a big-bang universe it is impossible, even in principle, to determine the state of the universe at early times. For the Einstein-de Sitter model this limit ist0/27, wheret0means now.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631838

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Numerical solution of the wave equation in the form of close lower and upper bounds provides a secure a posteriori error estimate that can be used for efficient accuracy control. The method considered in this paper uses some monotone properties of the differential operator in the wave equation to construct bounds for the solution in the form of trigonometric polynomials ofx. Aspects of the numerical implementation, the accuracy of the computed bounds and some numerical examples are discussed.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631839

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A 0-dominating function 0DF of a graphG= (V,E) is a functionf:V→ [0,1] such that ΣxεN(v)f(x) ≥ 1 for each ν εVwithf(v) = 0. The aggregate of a 0DFfis defined byag(f) = ΣvεVf(v) and the infimum and supremum of the set of aggregates over all minimal 0DFs of a graph are denoted by γ0and Γ0respectively. We prove some properties of minimal 0DFs and determine γ0and Γ0for some classes of graphs.

ISSN:1607-3606    

DOI:10.1080/16073606.1996.9631840

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor