Results 251 to 260 of about 62,542 (292)

Short wavelets and matrix dilation equations

IEEE Transactions on Signal Processing, 1995
Scaling functions and orthogonal wavelets are created from the coefficients of a lowpass and highpass filter (in a two-band orthogonal filter bank). For "multifilters" those coefficients are matrices. This gives a new block structure for the filter bank, and leads to multiple scaling functions and wavelets.
G. Strang, V. Strela
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Sobolev Characterization of Solutions of Dilation Equations

SIAM Journal on Mathematical Analysis, 1992
A technique of positive operators is applied to the study of the regularity (or smoothness) of the solutions of the two-scale (or ``refinement'' or ``dilation'') equations in the formulation of a multiresolution analysis. The sharp limit of the Sobolev exponent of the solution is given in terms of the spectral radius of a corresponding finite ...
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Dilation symmetries and equations on the lattice

Journal of Physics A: Mathematical and General, 1999
For nearest neighbour coupled systems on the one dimensional lattice with dilation symmetry \(u_{n,\tau}=tu_{n,t}+h_n(u_{n+1},u_n,u_{n-1})\) the authors establish an essentially equivalent, linearizable reduced system. Hence, for equations of this type the dilation symmetry implies linearizablility.
LEVI, Decio, Yamilov R.
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ANALYZING DUCTILE FRACTURE USING DUAL DILATIONAL CONSTITUTIVE EQUATIONS

Fatigue & Fracture of Engineering Materials & Structures, 1994
Abstract— By adopting a suggestion made by Thomason, a new failure criterion for the Gurson‐Tvergaard model has been recently introduced by the authors. In this study, a method based on the Gurson‐Tvergaard constitutive model and the new failure criterion is applied to the analysis of ductile fracture.
Z. L. Zhang, E. Niemi
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Dilations and the Equation of a Line

Mathematics Teaching in the Middle School, 2016
Track students' understanding of proportional reasoning by combining transformational geometry, similar-triangle reasoning, and linear relationships.
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Wavelets and Dilation Equations: A Brief Introduction

SIAM Review, 1989
Wavelets are new families of basis functions that yield the representation $f(x) = \sum {b_{jk} W(2^j x - k)} $. Their construction begins with the solution $\phi (x)$ to a dilation equation with coefficients $c_k $. Then W comes from $\phi $, and the basis comes by translation and dilation of W.
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A canonical dilation of the Schrödinger equation

Russian Journal of Mathematical Physics, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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L p –Solutions of Vector Refinement Equations with General Dilation Matrix

Acta Mathematica Sinica, English Series, 2005
The purpose of this paper is to investigate the solutions of refinement equations of the form \[ \varphi(x)= \sum_{\alpha\in\mathbb{Z}^s}a(\alpha)\,\varphi(Mx-\alpha),\quad x\in\mathbb{R}^s, \] where the vector of functions \(\varphi= (\varphi_1,\dots,\varphi_r)^T\) is in \((L_p(\mathbb{R}^s))^r ...
Li, Song, Hu, Rueifang, Wang, Xiangqing
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Wheeler–DeWitt Equation with a Screened-Coulomb Dilation Potential

Few-Body Systems, 2013
Wheeler–DeWitt equation for anisotropically expanding homogeneous high-dimension spaces is approximately solved under a screened-coulomb dilation potential via an appropriate approximation. The wave function is reported in terms of the Jacobi polynomials and eigenvalues and eigenfunctions are reported via the Nikiforov–Uvarov technique.
S. Zarrinkamar, H. Hassanabadi, A. A. Rajabi   +2 more
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A characterization of dilatations and a functional equation

Journal of Geometry, 1984
Verf. beweist: Es sei \(\sigma:{\mathbb{R}}^ 2\to {\mathbb{R}}^ 2\) eine Abbildung mit (1) Für alle \(p,q\in {\mathbb{R}}^ 2\) mit \((p-q)^ 2=1\) sind p-q und \(\sigma(p)-\sigma(q)\) linear abhängig. (2) Es gibt \(p_ 0\in {\mathbb{R}}^ 2\), so daß \(\sigma\) in \(p_ 0\) stetig ist. Dann ist \(\sigma\) eine Dilatation; d.h.
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