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Showing 1 to 15 of 15 for “"INTEGRAL TRANSFORMS"”.
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Curvature Detection by Integral Transforms
In various fields of image analysis, determining the precise geometry of occurrent edges, e.g. the contour of an object, is a crucial task. Especially the curvature of an edge is of great practical relevance. In this thesis, we develop different methods to detect a variety of edge features, among …
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Generalized integral transforms related to the theory of potential and stokes flow
… is focused on the derivation of novel integral formulation for simple problems. This alternative integral representations display a rapid decay as the complex parameter involved tends to infinity and are therefore suitable for numerical computations and for the study of the asymptotic …
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Efficient numerical methods based on integral transforms to solve option pricing problems
… implement a class of numerical methods (based on integral transforms) to solve PDEs for pricing a variety of financial derivatives. Our approach is based on spectral discretization of the spatial (asset) derivatives and the use of inverse Laplace transforms to solve the resulting problem in time. …
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Partial Cosine-Funk Transforms at Poles of the Cosine-λ Transform on Grassmann Manifolds
… transform, denoted C<sup>λ</sup>, is a family of integral transforms we can define on the sphere and on the Grassmannian manifolds of p-dimensional subspaces in K<sup>n</sup> where K is R, C or the skew field H of quaternions. We treat the Grassmannians as the symmetric spaces SO(n)/S(O(p) × …
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Hydroelastic waves and their interaction with fixed structures
… the linear problems, selection of appropriate integral transforms leads to explicit analytical solutions in terms of integral quadratures. For the nonlinear case, the numerical solution is found by application of Green’s second identity combined with a boundary element method. The resulting …
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Hadwiger Integration of Definable Functions
… extend these valuations, which we call Hadwiger integrals, to denable functionals on R^n, and present some important properties of the valuations. With the appropriate topologies on the set of denable functionals, we obtain dual classication theorems for general valuations on such functionals. We …
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Smooth Test and Its Applications in Economics and Finance
… in formulating tests based on the probability integral transforms. In case of parametric applications of density forecast evaluation we have to account for the effect of parameter estimation and dependent data in the implementation of the smooth test. In the non-parametric case of comparing two …
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Applications of a generalized integral transform to vibrations of continuous media
A finite generalized integral transform was applied to three general classes of problems in the vibrations of continuous media. For its kernel the eigenfunction of an associated eigenvalue problem was used and the result was denoted the eigentransform. The eigentransform was applied to (1) …
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A Study of Radiofrequency Cardiac Ablation Using Analytical and Numerical Techniques
… The solution, which was obtained using integral transforms, has the form of a surface integral nested within another surface integral. An integration routine capable of evaluating such integrals was developed and a C program was written to implement this routine. The surface integration …
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On orthogonal polynomials and related discrete integrable systems
… this approach. Chapter 3 considers a singular integral transform that is related to the Gel’fand-Levitan equation, which provides the inverse part of the inverse scattering method (a solution method of integrable systems). These singular integral transforms constitute a dressing method between …
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Mathematical Study on the Expressive Power of Machine Learning and Applications in Optimal Filtering Problems
… deep neural networks (DNNs) are replaced with integral transforms, with a finite-rank parameterization of the weight integral kernels. The GAT maps the input vector into the function space by treating the input vector as coefficients of the input basis function, performing activation on the …
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Local behavior of distributions and applications
… theory, summability of divergent series and integrals, and number theory. In Chapter 2 we give two new proofs of the Prime Number Theory based on ideas from asymptotic analysis on spaces of distributions. Several inverse problems in Fourier analysis and summability theory are studied in …
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ΣΥΜΒΟΛΗ ΣΤΗΝ ΑΝΤΙΜΕΤΩΠΙΣΗ ΠΡΟΒΛΗΜΑΤΩΝ ΤΗΣ ΖΕΥΓΜΕΝΗΣ ΚΑΙ ΓΕΝΙΚΕΥΜΕΝΗΣ ΘΕΡΜΟΕΛΑΣΤΙΚΟΤΗΤΑΣ
… X2 [- , ], X3 FINITE) HAVE BEEN STUDIED BY USING INTEGRAL AND FINITE FOURIER TRANSFORMS. THE GENERALIZED THEORY OF LORD AND SHULMAN HAS BEEN USED TO STUDY THE CHARACTERISTICS OF THE WAVE MOTION IN A THIN PLATE OF INFINITE LENGTH UNDER PLANE STRESS STATE. FINALLY THE THREE-DIMENSIONAL GENERALIZED …