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.

A Study of Binary Minimum-Energy Shortly Supported Wavelet Frames Associated with a Scaling Function

2011 ◽  
Vol 219-220 ◽  
pp. 500-503
Author(s):  
Qing Jiang Chen ◽  
Gai Hu
Keyword(s):  
Explicit Formula ◽  
Multiresolution Analysis ◽  
Scaling Function ◽  
Minimum Energy ◽  
Research Field ◽  
Sufficient Condition ◽  
Wavelet Frames ◽  
Existence Criterion ◽  
Generalized Multiresolution Analysis ◽  
Active Research

Frames have become the focus of active research field, both in theory and in applications. In the article, the binary minimum-energy wavelet frames and frame multiresolution resolution are introduced. A precise existence criterion for minimum-energy frames in terms of an ineqity conditi- -on 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 condition for the existence of affine pseudoframes is obtained by virtue of a generalized multiresolution analysis. The pyramid de -composition scheme is established based on such a generalized multiresolution structure.

The Research of Bivariate Minimum-Energy Wavelet Frames and Pseudoframes

2010 ◽  
Vol 159 ◽  
pp. 1-6
Author(s):  
Ping An Wang
Keyword(s):  
Explicit Formula ◽  
Multiresolution Analysis ◽  
Minimum Energy ◽  
Laurent Polynomial ◽  
Sufficient Condition ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Existence Criterion ◽  
Generalized Multiresolution Analysis ◽  
Active Research

Frames have become the focus of active research, both in theory and in applications. In the article, the notion of bivariate minimum-energy wavelet frames is introduced. A precise existence criterion for minimum-energy frames in terms of an inequality condition on the Laurent polynomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also establish- ed. 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 pyramid decomposition scheme is established based on such a generalized multiresol- -ution structure.

The Research of Bivariate Minimum-Energy Frames and Frames of Subspace and Application in Particle Physics

2012 ◽  
Vol 459 ◽  
pp. 280-283
Author(s):  
Yan Hui Lv
Keyword(s):  
Particle Physics ◽  
Materials Science ◽  
Minimum Energy ◽  
Research Field ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Generalized Multiresolution Analysis ◽  
Properties Of Materials ◽  
Active Research ◽  
The Relationship

Materials science is an applied science concerned with the relationship between the struc- ture and properties of materials. 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 are introduced. A precise exist-ence 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 con-dition for the existence of affine pseudoframes is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresolution structure.

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.

scholarly journals A Short Note on Wavelet Frames Based on FMRA on Local Fields

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
M. Younus Bhat
Keyword(s):  
Multiresolution Analysis ◽  
Positive Characteristic ◽  
Minimum Energy ◽  
Short Note ◽  
Explicit Construction ◽  
Local Fields ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Frame Multiresolution Analysis ◽  
Field Of Positive Characteristic

The concept of frame multiresolution analysis (FMRA) on local fields of positive characteristic was given by Shah in his paper, Frame Multiresolution Analysis on Local Fields published by Journal of Operators. The author has studied the concept of minimum-energy wavelet frames on these prime characteristic fields. We continued the studies based on frame multiresolution analysis and minimum-energy wavelet frames on local fields of positive characteristic. In this paper, we introduce the notion of the construction of minimum-energy wavelet frames based on FMRA on local fields of positive characteristic. We provide a constructive algorithm for the existence of the minimum-energy wavelet frame on the local field of positive characteristic. An explicit construction of the frames and bases is given. In the end, we exhibit an example to illustrate our algorithm.

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 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.

A Review on the Glass Transition of Polymer on Surface and in the Thin Film

2014 ◽  
Vol 1002 ◽  
pp. 17-22
Author(s):  
Ran Huang
Keyword(s):  
Thin Film ◽  
Glass Transition ◽  
Materials Science ◽  
Research Field ◽  
Science And Engineering ◽  
Chain Mobility ◽  
Geometric Confinement ◽  
Materials Science And Engineering ◽  
Active Research ◽  
Bulk Behavior

Since the first paper by Keddie et al. published on 1994 [21], the glass transition of polymer systems on surface/thin film has been an active research field and attracted many groups interests. Numerous works have been done, in both experimental and computation approaches, to investigate this subject. In this paper we reviewed the milestone findings in the last twenty years. Generally with only minor disagreements in the mechanism all the mainstream works are consistent in the conclusions that: 1) Geometric confinement in thin film or on surface reduces the glass transition temperatureTgcomparing to the bulk behavior; 2) For supported film the substrate-film interaction is critical and its effect may surpass the geometry effects and rise increase onTg; 3) Chain mobility and molecular weight are critical but the detailed phenomena vary with systems. Notwithstanding the achievement has been made, due to the controversy of glass transition itself and technology limitation on characterization on glass transitions on thin film, the research in this field is still a long-marching effort and breakthrough findings are expected for the development in materials science and engineering and feedback knowledge to understand the glass transition on the theoretical base.

scholarly journals Next-Generation Wearable Biosensors Developed with Flexible Bio-Chips

Micromachines ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 64
Author(s):  
Dahyun Nam ◽  
Jae Min Cha ◽  
Kiwon Park
Keyword(s):  
Data Collection ◽  
Real Time ◽  
Health Monitoring ◽  
Material Science ◽  
Academic Research ◽  
Research Field ◽  
Health Conditions ◽  
Science And Engineering ◽  
Laboratory Equipment ◽  
Daily Lives

The development of biosensors that measure various biosignals from our body is an indispensable research field for health monitoring. In recent years, as the demand to monitor the health conditions of individuals in real time have increased, wearable-type biosensors have received more attention as an alternative to laboratory equipment. These biosensors have been embedded into smart watches, clothes, and accessories to collect various biosignals in real time. Although wearable biosensors attached to the human body can conveniently collect biosignals, there are reliability issues due to noise generated in data collection. In order for wearable biosensors to be more widely used, the reliability of collected data should be improved. Research on flexible bio-chips in the field of material science and engineering might help develop new types of biosensors that resolve the issues of conventional wearable biosensors. Flexible bio-chips with higher precision can be used to collect various human data in academic research and in our daily lives. In this review, we present various types of conventional biosensors that have been used and discuss associated issues such as noise and inaccuracy. We then introduce recent studies on flexible bio-chips as a solution to these issues.

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