scholarly journals Wavelets associated with nonuniform multiresolution analyses and one-dimensional spectral pairs

2006 ◽  
Vol 323 (2) ◽  
pp. 798-817 ◽  
Author(s):  
Jean-Pierre Gabardo ◽  
Xiaojiang Yu
Keyword(s):  
One Dimensional ◽  
Spectral Pairs

scholarly journals Nonuniform wavelets and wavelet sets related to one-dimensional spectral pairs

2007 ◽  
Vol 145 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Xiaojiang Yu ◽  
Jean-Pierre Gabardo
Keyword(s):  
Wavelet Sets ◽  
One Dimensional ◽  
Spectral Pairs

scholarly journals Dual wavelets associated with nonuniform MRA

2018 ◽  
Vol 50 (2) ◽  
pp. 119-132
Author(s):  
Mohd Younus Bhat
Keyword(s):  
Positive Integer ◽  
Multiresolution Analysis ◽  
Discrete Subgroup ◽  
Scaling Functions ◽  
One Dimensional ◽  
Spectral Pair ◽  
Spectral Pairs ◽  
The Given

A generalization of Mallats classical multiresolution analysis, based on thetheory of spectral pairs, was considered in two articles by Gabardo and Nashed. In thissetting, the associated translation set is no longer a discrete subgroup of R but a spectrumassociated with a certain one-dimensional spectral pair and the associated dilation is aneven positive integer related to the given spectral pair. In this paper, we construct dualwavelets which are associated with Nonuniform Multiresolution Analysis. We show thatif the translates of the scaling functions of two multiresolution analyses are biorthogonal,then the associated wavelet families are also biorthogonal. Under mild assumptions onthe scaling functions and the wavelets, we also show that the wavelets generate Rieszbases

scholarly journals Inequalities for nonuniform wavelet frames

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Firdous A. Shah
Keyword(s):  
Fourier Transforms ◽  
Sufficient Conditions ◽  
Discrete Subgroup ◽  
Wavelet Frames ◽  
Wavelet System ◽  
One Dimensional ◽  
Spectral Pair ◽  
Spectral Pairs

Abstract Gabardo and Nashed studied nonuniform wavelets by using the theory of spectral pairs for which the translation set {\Lambda=\{0,r/N\}+2\mathbb{Z}} is no longer a discrete subgroup of {\mathbb{R}} but a spectrum associated with a certain one-dimensional spectral pair. In this paper, we establish three sufficient conditions for the nonuniform wavelet system {\{\psi_{j,\lambda}(x)=(2N)^{j/2}\psi((2N)^{j}x-\lambda),\,j\in\mathbb{Z},\,% \lambda\in\Lambda\}} to be a frame for {L^{2}(\mathbb{R})} . The proposed inequalities are stated in terms of Fourier transforms and hold without any decay assumptions on the generator of such a system.

scholarly journals Scaling functions on the spectrum

2018 ◽  
Vol 10 (2) ◽  
pp. 340-346
Author(s):  
◽  
Firdous A. Shah
Keyword(s):  
Multiresolution Analysis ◽  
Short Communication ◽  
Discrete Subgroup ◽  
Scaling Functions ◽  
Fourier Domain ◽  
One Dimensional ◽  
Spectral Pair ◽  
Classic Theory ◽  
Spectral Pairs ◽  
Fundamental Equations

Abstract A generalization of Mallat’s classic theory of multiresolution analysis based on the theory of spectral pairs was considered by Gabardo and Nashed [4] for which the translation set Λ = {0, r/N}+2 ℤ is no longer a discrete subgroup of ℝ but a spectrum associated with a certain one-dimensional spectral pair. In this short communication, we characterize the scaling functions associated with such a nonuniform multiresolution analysis by means of some fundamental equations in the Fourier domain.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Intergrowth of modulated structures in high Tc Bi-Sr-Ca-Cu-O superconductors

1990 ◽  
Vol 48 (4) ◽  
pp. 76-77
Author(s):  
A.Q. He ◽  
G.W. Qiao ◽  
J. Zhu ◽  
H.Q. Ye
Keyword(s):  
Twin Structure ◽  
Modulated Structure ◽  
High Tc ◽  
One Dimensional ◽  
Lattice Constants ◽  
Superconducting Phases ◽  
Modulated Structures ◽  
Layer Structures

Since the first discovery of high Tc Bi-Sr-Ca-Cu-O superconductor by Maeda et al, many EM works have been done on it. The results show that the superconducting phases have a type of ordered layer structures similar to that in Y-Ba-Cu-O system formulated in Bi2Sr2Can−1CunO2n+4 (n=1,2,3) (simply called 22(n-1) phase) with lattice constants of a=0.358, b=0.382nm but the length of c being different according to the different value of n in the formulate. Unlike the twin structure observed in the Y-Ba-Cu-O system, there is an incommensurate modulated structure in the superconducting phases of Bi system superconductors. Modulated wavelengths of both 1.3 and 2.7 nm have been observed in the 2212 phase. This communication mainly presents the intergrowth of these two kinds of one-dimensional modulated structures in 2212 phase.

Electronic structure studies of conducting polymers by electron energy-loss spectroscopy

1996 ◽  
Vol 54 ◽  
pp. 160-161
Author(s):  
J. Fink
Keyword(s):  
Electronic Structure ◽  
Conducting Polymers ◽  
Conjugated Polymers ◽  
Electron Acceptors ◽  
Electron Donors ◽  
Light Emitting ◽  
One Dimensional ◽  
New Class ◽  
Electrical Conductivities ◽  
Electron Energy Loss

Conducting polymers comprises a new class of materials achieving electrical conductivities which rival those of the best metals. The parent compounds (conjugated polymers) are quasi-one-dimensional semiconductors. These polymers can be doped by electron acceptors or electron donors. The prototype of these materials is polyacetylene (PA). There are various other conjugated polymers such as polyparaphenylene, polyphenylenevinylene, polypoyrrole or polythiophene. The doped systems, i.e. the conducting polymers, have intersting potential technological applications such as replacement of conventional metals in electronic shielding and antistatic equipment, rechargable batteries, and flexible light emitting diodes.Although these systems have been investigated almost 20 years, the electronic structure of the doped metallic systems is not clear and even the reason for the gap in undoped semiconducting systems is under discussion.

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