다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

Introduction to Wavelets and Wavelet Transforms: A Primer

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

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A course in combinatorics

R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Exactly Solved Models in Statistical Mechanics

The quantum group SU(2)q is discussed by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum Such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose, is developed

https://iopscience.iop.org/article/10.1088/0305-4470/22/21/020/pdf

On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q

Publisher Summary
This chapter discusses two-variable analogues of the classical orthogonal polynomials. Analogues in severable variables of the Jacobi polynomials are be highly nontrivial generalizations of the one-variable case. The chapter describes a number of distinct classes of orthogonal polynomials in two variables, for which many properties hold that are analogous to properties of Jacobi polynomials. The polynomials belonging to these orthogonal systems are eigenfunctions of two algebraically independent partial differential operators. In the Chebyshev cases, these polynomials can be interpreted as quotients of two eigenfunctions of the Laplacian on a two-dimensional torus or sphere, which satisfy symmetry relations with respect to certain reflections. The classical orthogonal polynomials in one variable are the Jacobi polynomials, the Laguerre, and the Hermite polynomials. The chapter also illustrates examples of two-variable analogues of the Jacobi polynomials.

Two-Variable Analogues of the Classical Orthogonal Polynomials

A Jacobi function ${\phi _\lambda }^{\left( {\alpha ,\beta } \right)}\left( {\alpha ,\beta ,\lambda \in C,\alpha \ne - 1, - 2,} \right)$ is defined as the even C∞-function on ℝ which equals 1 at 0 and which satisfies the differential equation 

$$\left( {{d^2}/d{t^2} + \left( {\left( {2\alpha + 1} \right)cotht + \left( {2\beta + 1} \right)tht} \right)d/dt + + {\lambda ^2} + {{\left( {\alpha + \beta + 1} \right)}^2}} \right){f_\lambda }^{\left( {\alpha ,\beta } \right)}\left( t \right) = 0$$

(11)

Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups

This paper introduces a family of Askey-Wilson type orthogonal polynomials in n variables associated with a root system of type BCn. The family depends, apart from q, on 5 parameters. For n = 1 it specializes to the four-parameter family of one-variable Askey-Wilson polynomials. For any n it contains Macdonald’s two three-parameter families of orthogonal polynomials associated with a root system of type BCn as special cases.

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Askey-Wilson polynomials for root systems of type BC

which generalizes the Mehler-Fok transform, was studied by Titchmarsh [23, w 17], Olevskii [21], Braaksma and Meulenbeld [2], Flensted--Jensen [9], [11, w and w and Flensted--Jensen and Koornwinder [12]. Some papers by Ch6bli [3], [4], [5] deal with a larger class of integral transforms which includes the Jacobi transform. An even more general class was considered by Braaksma and De Shoo [24]. In the present paper short proofs will be given of a Paley--Wiener type theorem and the inversion formula for the Jacobi transform. The L2-theory, i.e. the Plancherel theorem, is then an easy consequence. These results were earlier obtained by Flensted--Jensen [9], [11, w and by Ch6bli [5]. However, to prove the Paley-Wiener theorem these two authors needed the L2-theory, which can be obtained as a corollary of the Weyl S t o n e T i t c h m a r s h K o d a i r a theorem about the spectral decomposition of a singular Sturm--Liouville operator (cf. for instance Dunford and Schwartz [6, Chap. 13, w The proofs presented here exploit the properties of Jacobi functions as hypergeometric functions and no general theorem needs to be invoked. Furthermore, it turns out that the Paley--Wiener theorem, which was proved by Flensted---Jensen [11, w for real c~, fi, ~ > 1, holds for all complex values of ~ and ft. The key formula in this paper is a generalized Mehler formula

https://staff.fnwi.uva.nl/t.h.koornwinder/art/1975/PaleyWienerJacobi.pdf

A new proof of a Paley—Wiener type theorem for the Jacobi transform

For H. Exton's q-analogue of the Bessel function (going back to W. Hahn in a special case, but different from F. H. Jackson's q-Bessel functions) we derive Hansen-Lommel type orthogonality relations, which, by a symmetry, turn out to be equivalent to orthogonality relations which are q-analogues of the Hankel integral transform pair. These results are implicit, in the context of quantum groups, in a paper by Vaksman and Korogodskii. As a specialization we get q-cosines and q-sines which admit q-analogues of the Fourier-cosine and Fourier-sine transforms

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Tom H. Koornwinder

Papers

Two-Variable Analogues of the Classical Orthogonal Polynomials

Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups

Askey-Wilson polynomials for root systems of type BC

A new proof of a Paley—Wiener type theorem for the Jacobi transform

On q-analogues of the Fourier and Hankel transforms