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 equation For these polynomials we prove an integral representation, a combinatorial formula, Pieri rules, Cauchy identity, and we also show that they do not satisfy any rationalq-difference equation. The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. The inverse conductivity problem to the the elliptic equation ${\rm div}((1+(k-1)\chi_D)\nabla u)=0\ {\rm in }\ \Omega$ is considered. As applications, the wave equation on?+ × ?+ and the heat equation in a semi-infinite rod are considered in detail. Pointwise fourier inversion: A wave equation approach Functions of the Laplace operator F(- Δ) can be synthesized from the solution operator to the wave equation. Schr?dinger equation and oscillatory Hilbert transforms of second degree Balls and quasi-metrics: A space of homogeneous type modeling the real analysis related to the Monge-Ampère equation As an application, starting from the Monge-Ampère setting introduced in [3], we get a space of homogeneous type modeling the real analysis for such an equation. In a much cited article, Yau [5] proved that when the Ricci curvature is bounded uniformly below, then the only bounded solution to the heat equation ?tμ=Δμ on [0, ∞) × M which vanishes at t=0 is the one which vanishes evarywhere. Well-posedness of a semilinear heat equation with weak initial data In the first part the initial value problem (IVP) of the semilinear heat equation with initial data in is studied. We develop here a part of the existence theory for the inhomogeneous refinement equation where a (k) is a finite sequence and F is a compactly supported distribution on ?. For the analogs of the heat and wave equation, we give algorithms for approximating the solution, and display the results of implementing these algorithms. We give strong evidence that the analog of finite propagation for the wave equation does not hold because of inconsistent scaling behavior in space and time. In particular, we find a finite dimensional matrix B, constructed from the coefficientscα of the equation (I-B)q=p, where the vectorp depends on h. In this paper we analyze solutions of the n-scale functional equation Ф(x) = Σk∈?Pk Ф(nx-k), where n≥2 is an integer, the coefficients {Pk} are nonnegative and Σpk = 1. Their relationship with the heat equation and the newly introduced wavelet differential equation is established. Refinable distributions satisfy a refinement equation f(x)=Σk∈Λ ck f(Ax-k), where Λ is a finite subset of Γ, the ck are r×r matrices, and f=(f1,...,fr)T. A partial differential equation from polymer science is shown to be solvable using the operational properties of the Euclidean-group Fourier transform.

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2008 CNKI－中国知网

2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社