In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map op...In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.展开更多
LetSp(n, R) be the sympletic group, and letK n * be its maximal compact subgroup. ThenG=Sp(n,R)/K n * can be realized as the Siegel domain of type one. The square-integrable representation ofG gives the admissible wav...LetSp(n, R) be the sympletic group, and letK n * be its maximal compact subgroup. ThenG=Sp(n,R)/K n * can be realized as the Siegel domain of type one. The square-integrable representation ofG gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent state. With the Laguerre polynomials, Hermite polynomials and Jacobi polynomials, two kinds of orthogonal bases for AW are given, and they then give orthogonal decompositions ofL 2-space on the Siegel domain of type one ?(? n , |y| *dxdy).展开更多
Abstract In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another conside...Abstract In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.展开更多
基金Project supported by National Natural Science Foundation of Chi-na (Grant No .10471087) ,and Shanghai Municipal Commission ofEducation (Grant No .03AK33)
文摘In this paper, we discuss a class of piecewise linear hyperbolic maps on the 2-torus. These maps arise in the second-order digital fdter with two＇ s complement arithmetic. By introducing codings underlying the map operations, we give some admissibility conditions for symbolic sequences and find some periodic properties of these symbolic sequences. Then we use these conditions to check the admissibility of periodic symbol sequences.
文摘LetSp(n, R) be the sympletic group, and letK n * be its maximal compact subgroup. ThenG=Sp(n,R)/K n * can be realized as the Siegel domain of type one. The square-integrable representation ofG gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent state. With the Laguerre polynomials, Hermite polynomials and Jacobi polynomials, two kinds of orthogonal bases for AW are given, and they then give orthogonal decompositions ofL 2-space on the Siegel domain of type one ?(? n , |y| *dxdy).
基金Partially supported by the NSF (Grant DMS-9803323)Supported by fondi MIUR Progetto di interesse Nazionale Problemi Matematici Non Lineari di Propagazionee Stabilitd nei Modelli del Continuo Coordinatore T.Ruggeri,by the GNFM-INDAM,and by the Istitut
文摘Abstract In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.
