The Description and Characterization of Symmetric Frames and Gabor Frames and Applications in Material Engineering

2013 ◽  
Vol 712-715 ◽  
pp. 2458-2463
Author(s):  
Qing Jiang Chen ◽  
Xiao Ting Lei ◽  
Jian Feng Zhou
Keyword(s):  
Legendre Polynomials ◽  
Materials Science ◽  
Tight Frame ◽  
Simple Approach ◽  
Gabor Frames ◽  
Wavelet Frames ◽  
Science And Engineering ◽  
Interdisciplinary Field ◽  
Frame Wavelets

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, we discuss a new set of symmetric tight frame wave-lets with the associated filterbanks outputs downsampled by several generators. The frames consist of several generators obtained from the lowpass filter using spectral factorization, with lowpass fil-ter via a simple approach using Legendre polynomials. The filters are feasible to be designed and offer smooth scaling functions and frame wavelets. We shall give an example to demonstrste that so -me examples of symmetric tight wavelet frames with three compactly supported real-valued sym- metric generators will be presented to illustrate the results.

The Characters of Multiple Tight Multivariate Wavelet Frames and Application in Quantum Physics

2012 ◽  
Vol 459 ◽  
pp. 271-274
Author(s):  
De Lin Hua ◽  
Qing Bin Lu
Keyword(s):  
Quantum Physics ◽  
Materials Science ◽  
Constructive Method ◽  
Tight Frames ◽  
Wavelet Frames ◽  
Science And Engineering ◽  
Interdisciplinary Field

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This paper is devoted to the study and construction of finitely supported tight multivariate frames of multivariate multi-wavelets. Inparticular, a necessary conditi- on for their existence is obtained to present some feasible idea for designing such MRA tight frames. The characteristics of binary multiscale pseudoframes for subspaces is investigated. The constructi- on of a GMS of Paley-Wiener subspace of is studied. A constructive method for affine multivariate frames based on such a GMS is established.

The Characteristics of a Pair of Dual Binary Canonical Frames Generated by Refinable Functions

2012 ◽  
Vol 461 ◽  
pp. 864-867
Author(s):  
Zhong Yin Chen ◽  
Jian Tang Zhao
Keyword(s):  
Materials Science ◽  
Refinable Functions ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Science And Engineering ◽  
Binary Function ◽  
The Past ◽  
Interdisciplinary Field ◽  
Popular Subject ◽  
Compactly Supported Functions

Materials science is an interdisciplinary field applyingthe properties of matter to various areas of science and engineering. Wavelet analysis has become a popular subject in researching into materials science during the past twenty years. Nowadays, it has been developed a mathematical br- anch. In this paper, we show that there exist binary wavelet frames generated by several compactly supported functions which have good dual binary wavelet frames, but for which the canonical dual binary wavelet frame does not consist of wavelets. That is to say, the canonical dual binary wavelet frame cannot be generated by the translations and dilations of a single binary function.

The Description of the Semi-Local Hardy Space by Gabor Frames

2013 ◽  
Vol 321-324 ◽  
pp. 2380-2384
Author(s):  
Jin Shun Feng
Keyword(s):  
Hardy Space ◽  
Materials Science ◽  
Gabor Frames ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Science And Engineering ◽  
Decomposition Scheme ◽  
Interdisciplinary Field ◽  
Local Hardy Space ◽  
Affine Frames

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, the notion of the binary generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of binary multiscale pseudo- -frames for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of L^2(R^2) is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of L^2(R^2) based on a BGMS is established.

The Traits of Nontensor Five-Variant Wavelet Packs and Applications in Management Science and Materials Science

2012 ◽  
Vol 461 ◽  
pp. 868-871 ◽  
Author(s):  
Qing Ge Zhang
Keyword(s):  
Functional Analysis ◽  
Materials Science ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Orthogonal Wavelet ◽  
Science And Engineering ◽  
Interdisciplinary Field ◽  
Novel Approach ◽  
Generalized Multiresolution Analysis

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this article, the notion of orthogonal nonseparable five-variant wavelet packages is presented. A novel approach for constructing them is presented by iteration method and functional analysis method. A feasible approach for constructing two-directional orthogonal wavelet packs is developed. The orthogonality property of five-variant wavelet packs is discussed. Three orthogonality formulas concerning these wavelet packs are estabished. A constructive method for affine frames of is proposed. The sufficient condition for the existence of a class of affine pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis.

The Bivariate Minimum-Energy Tight Wavelet Frames and Applications in Economics and Management

2014 ◽  
Vol 915-916 ◽  
pp. 1412-1417
Author(s):  
Jian Guo Shen
Keyword(s):  
Multiresolution Analysis ◽  
Material Science ◽  
Minimum Energy ◽  
Research Field ◽  
Wavelet Frames ◽  
Science And Engineering ◽  
Interdisciplinary Field ◽  
Existence Criterion ◽  
Generalized Multiresolution Analysis ◽  
Active Research

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. Frames have become the focus of active research field, both in the-ory and in applications. In the article, the binary minimum-energy wavelet frames and frame multi-resolution resolution are introduced. A precise existence criterion for minimum-energy frames in terms of an ineqity condition on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient condi tion for the existence of tight wavelet frames is obtained by virtue of a generalized multiresolution analysis.

Semi-orthogonal wavelet frames on local fields

Analysis ◽  
2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Firdous A. Shah ◽  
M. Younus Bhat
Keyword(s):  
Finite Number ◽  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
Orthogonal Wavelet ◽  
Basic Equations ◽  
Frame Multiresolution Analysis ◽  
Frame Wavelets ◽  
Equivalent Conditions

AbstractWe investigate semi-orthogonal wavelet frames on local fields of positive characteristic and provide a characterization of frame wavelets by means of some basic equations in the frequency domain. The theory of frame multiresolution analysis recently proposed by Shah [J. Operators (2015), Article ID 216060] on local fields is used to establish equivalent conditions for a finite number of functions

The Characterization of Two-Direction Vector-Valued Wavelets and its Applications in Material Engineering

2013 ◽  
Vol 457-458 ◽  
pp. 36-39
Author(s):  
Qing Jiang Chen ◽  
Huan Chen ◽  
Hong Wei Gao
Keyword(s):  
Matrix Theory ◽  
Direction Vector ◽  
Analysis Method ◽  
Science And Engineering ◽  
Time Frequency ◽  
Multi Scale ◽  
Interdisciplinary Field ◽  
The Matrix ◽  
Vector Valued

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this work, we study construction and properties of orthogonal two-direction vector-valued wavelet with poly-scale. Firstly, the concepts concerning two-direct-ional vector-valued waelets and wavelet wraps with multi-scale are provided. Secondly, we prop ose a construction algorim for compactly supported orthogonal two-directional vector-valued wave lets. Lastly, properties of a sort of orthogonal two-directional vector-valued wavelet wraps are char acterized by virtue of the matrix theory and the time-frequency analysis method.

Non-Destructive Techniques for the Characterization of Structural Materials: Materials Science & Engineering Curriculum for the Education of an Innovative Model

2002 ◽  
Vol 760 ◽  
Author(s):  
Antonia Moropoulou ◽  
Eleni Aggelakopoulou ◽  
Nicolas P. Avdelidis ◽  
Maria Koui
Keyword(s):  
Engineering Students ◽  
Chemical Engineering ◽  
Materials Science ◽  
Engineering Curriculum ◽  
Science And Engineering ◽  
Course Content ◽  
Materials Science And Engineering ◽  
Undergraduate Programme ◽  
Non Destructive

ABSTRACTIn this paper, the example of the Materials Science and Engineering (MSE) Curriculum that exists as a scientific direction in the undergraduate programme of the Chemical Engineering School, in the National Technical University of Athens (NTUA), in Greece, is presented. The course content includes several tools, such as theoretical lessons, laboratory modules - nondestructive testing (NDT) and instrumental techniques - semi industrial scale devices, fieldworks and a dissertation thesis. The presented curriculum can be regarded as an innovative educational model for chemical engineering students that choose to become involved in the field of MSE.

The Research of Dual Quarternary Pseudoframes for Hardy Space and Applications in Engineering Materials

2014 ◽  
Vol 977 ◽  
pp. 19-24
Author(s):  
Chun Yi Jiao ◽  
Shi Heng Wang
Keyword(s):  
Hardy Space ◽  
Materials Science ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Science And Engineering ◽  
Decomposition Scheme ◽  
Interdisciplinary Field ◽  
Affine Frames ◽  
Engineering Materials

Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering.. In this work, the notion of the quarternary generalized multiresol- ution structure (TGMS) of subspace is proposed. The characteristics of quarternary affine pseudoframes for subspaces is investigated. Construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a TGMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a TGMS is established.

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