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## Analytic Function (analytic + function)
## Selected Abstracts## Implicit Surface Modelling with a Globally Regularised Basis of Compact Support COMPUTER GRAPHICS FORUM, Issue 3 2006C. WalderWe consider the problem of constructing a globally smooth analytic function that represents a surface implicitly by way of its zero set, given sample points with surface normal vectors. The contributions of the paper include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable interpolation properties previously only associated with fully supported bases. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem lying at the core of kernel-based machine learning methods. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data and four-dimensional interpolation between three-dimensional shapes. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations [source] ## Numerical evaluation of eigenvalues in notch problems using a region searching method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2006Y. Z. ChenAbstract This paper presents a method for finding the eigenvalues of some equations, or the zeros of analytic functions. There are two steps in the method. In the first step, integration along the edges of rectangle for an analytic function is performed. From the result of integration, one can know whether the zero exists in the rectangle or not. If the zero of an analytic function exists in the rectangle, we can perform the second step. In the second step, the zero is obtained by iteration. Therefore, the method is called a region searching method. Particular advantage of the suggested method is that the process for finding zero can be visualized. For example, one can clearly indicate the rectangles, which contain the zeros of an analytic function. Three numerical examples are presented. The obtained results are satisfactory even for a complicated case, for example, for finding eigenvalues of a composed wedge of dissimilar materials. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Carathéodory,Julia type conditions and symmetries of boundary asymptotics for analytic functions on the unit disk MATHEMATISCHE NACHRICHTEN, Issue 11 2009Vladimir BolotnikovAbstract It is shown that the following conditions are equivalent for the generalized Schur class functions at a boundary point t0 , ,,: 1) Carathéodory,Julia type condition of order n; 2) agreeing of asymptotics of the original function from inside and of its continuation by reflection from outside of the unit disk ,, up to order 2n + 1; 3) t0 -isometry of the coefficients ofthe boundary asymptotics; 4) a certain structured matrix , constructed from these coefficients being Hermitian. It is also shown that for an arbitrary analytic function, properties 2), 3), 4) are still equivalent to each other and imply 1) (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## On the complex oscillation theory of f , + A (z)f = 0 where A (z) is analytic in the unit disc MATHEMATISCHE NACHRICHTEN, Issue 6 2009Ting-Bin CaoAbstract In this paper, we investigate the complex oscillation theory of the second order linear differential equation f , + A (z)f = 0, where the coefficient A (z) is an analytic function in the unit disc , = {z: |z | < 1} (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Numerical evaluation of eigenvalues in notch problems using a region searching method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2006Y. Z. ChenAbstract This paper presents a method for finding the eigenvalues of some equations, or the zeros of analytic functions. There are two steps in the method. In the first step, integration along the edges of rectangle for an analytic function is performed. From the result of integration, one can know whether the zero exists in the rectangle or not. If the zero of an analytic function exists in the rectangle, we can perform the second step. In the second step, the zero is obtained by iteration. Therefore, the method is called a region searching method. Particular advantage of the suggested method is that the process for finding zero can be visualized. For example, one can clearly indicate the rectangles, which contain the zeros of an analytic function. Three numerical examples are presented. The obtained results are satisfactory even for a complicated case, for example, for finding eigenvalues of a composed wedge of dissimilar materials. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A transmission problem with imperfect contact for an unbounded multiply connected domain MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2010L. P. CastroAbstract An analysis of the flux of certain unbounded doubly periodic multiply connected domains with circle disjoint components is performed. This is done under generalized non-ideal contact conditions on the boundary between domain components, which include analytic given data. A formula for the flux that depends on the conductivity of components, their radii, centers, the conductivity of the matrix, and also certain values of special Eisenstein functions is derived. Existence and uniqueness of solution to the problem are obtained by using a transmission problem with imperfect contact for analytic functions in corresponding Hardy spaces. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Carathéodory,Julia type conditions and symmetries of boundary asymptotics for analytic functions on the unit disk MATHEMATISCHE NACHRICHTEN, Issue 11 2009Vladimir BolotnikovAbstract It is shown that the following conditions are equivalent for the generalized Schur class functions at a boundary point t0 , ,,: 1) Carathéodory,Julia type condition of order n; 2) agreeing of asymptotics of the original function from inside and of its continuation by reflection from outside of the unit disk ,, up to order 2n + 1; 3) t0 -isometry of the coefficients ofthe boundary asymptotics; 4) a certain structured matrix , constructed from these coefficients being Hermitian. It is also shown that for an arbitrary analytic function, properties 2), 3), 4) are still equivalent to each other and imply 1) (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Generalization of a class of nonlinear averaging integral operators MATHEMATISCHE NACHRICHTEN, Issue 1-2 2005Teodor BulboacAbstract Let H(U) be the space of all analytic functions in the unit disk U, and let coE denote the convex hull of the set E , ,. If K , H(U) then the operator I : K , H(U) is said to be an averaging operator if For a function h , A , H(U) we will determine simple sufficient conditions on h such that for all f , ,,1/,, where and ,,1/, represents the class of 1/, -convex functions (not necessarily normalized). As an application, we will give sufficient conditions on h to insure that the operators Ih;,,, are averaging operators on certain subsets of H(U), in order to generalize the result of [5]. In addition, some particular cases of this result obtained for appropriate choices of the function h will also be given. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] |