scholarly journals Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Jianjun Sun ◽  
Bin Huang ◽  
Xiaodong Chen ◽  
Lihong Cui
Keyword(s):  
Wavelet Frames ◽  
Symmetric Extension ◽  
The Matrix ◽  
Polyphase Matrix ◽  
Necessary Constraints ◽  
Sobolev Exponent

A construction approach for the 3-band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the parameterizations of 3-band tight wavelet frames with3N+1filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.

scholarly journals Polyphase matrix characterization of framelets on local fields of positive characteristic

2017 ◽  
Vol 9 (1) ◽  
pp. 248-259
Author(s):  
F. A. Shah ◽  
M. Y. Bhat
Keyword(s):  
Positive Characteristic ◽  
Local Fields ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension ◽  
Polyphase Matrix

AbstractAn important tool for the construction of framelets on local fields of positive characteristic using unitary extension principle was presented by Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293-307]. In this article, we continue the study of framelets on local fields and present a polyphase matrix characterization of framelets generated by the extension principle.

A PAIR OF ORTHOGONAL WAVELET FRAMES IN L2(ℝd)

2014 ◽  
Vol 12 (02) ◽  
pp. 1450011 ◽  
Author(s):  
GHANSHYAM BHATT
Keyword(s):  
Dimensional Case ◽  
Extension Principle ◽  
Higher Dimension ◽  
Wavelet Frames ◽  
Orthogonal Wavelet ◽  
Extra Condition ◽  
Simple Method ◽  
One Dimensional ◽  
Unitary Extension ◽  
Polyphase Matrix

A simple method of construction of a pair of orthogonal wavelet frames in L2(ℝd) is presented. This is a generalization of one-dimensional case to higher dimension. The construction is based on the well-known Unitary Extension Principle (UEP). The presented method produces the polyphase components of the filters of the wavelet functions, and hence the filters. A pair of orthogonal wavelet frames can be constructed with an extra condition. In the construction, the polyphase matrix is used as opposed to the modulation matrix. This is less restrictive and yields a fewer wavelet functions in the system than in the previously known constructions.

Parameterization of Masks for Tight Wavelet Frames and Multiple Pseudoframes and Applications in Mechanical Engineering

2014 ◽  
Vol 915-916 ◽  
pp. 1448-1451
Author(s):  
Yu Min Yu
Keyword(s):  
Mechanical Engineering ◽  
Materials Science ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Wavelet Frames ◽  
Decomposition Scheme ◽  
Symmetric Extension ◽  
Analysis Design ◽  
Affine Frames ◽  
Resolution Structure

Mechanical engineering is a discipline of engineering that applies the principles of engine ering, physics and materials science for analysis, design, manufacturing, and maintenance of mecha nical systems. In this work, the construction of 4-band tight wavelet frames with symmetric proper-ties using symmetric extension and parameterization of the paraunitary matrix. The notion of an 4-band generalized multiresolution structure of subspace is proposed. The characteristics of affine pseudoframes for subspaces is investigated. The construction of a generalized multiresolution structure of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obta-ined based on such a generalized multiresolution structure and a sufficient condition for its exist-ence is presented. A constructive method for affine frames of based on a generalized multi-resolution structure is presented.

TIGHT FRAME CHARACTERIZATION OF MULTIWAVELET VECTOR FUNCTIONS IN TERMS OF THE POLYPHASE MATRIX

2009 ◽  
Vol 07 (01) ◽  
pp. 9-21 ◽  
Author(s):  
JENS KROMMWEH
Keyword(s):  
Tight Frame ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension ◽  
Directional Wavelets ◽  
Extension Principles ◽  
Polyphase Matrix ◽  
Common Extension ◽  
Polyphase Representation

The extension principles play an important role in characterizing and constructing of wavelet frames. The common extension principles, the unitary extension principle (UEP) or the oblique extension principle (OEP), are based on the unitarity of the modulation matrix. In this paper, we state the UEP and OEP for refinable function vectors in the polyphase representation. Finally, we apply our results to directional wavelets on triangles which we have constructed in a previous work. We will show that the wavelet system generates a tight frame for L2(ℝ2).

Crystalloid Inclusions in Hepatocyte Mitochondria and Their Similarity to Cytoplasmic Crystalloids

1974 ◽  
Vol 32 ◽  
pp. 198-199
Author(s):  
Odell T. Minick ◽  
Hidejiro Yokoo
Keyword(s):  
Liver Disease ◽  
Alcoholic Liver Disease ◽  
Special Interest ◽  
Structural Variations ◽  
Mitochondrial Alterations ◽  
The Matrix ◽  
Crystalloid Inclusions ◽  
Liver Biopsies

Mitochondrial alterations were studied in 25 liver biopsies from patients with alcoholic liver disease. Of special interest were the morphologic resemblance of certain fine structural variations in mitochondria and crystalloid inclusions. Four types of alterations within mitochondria were found that seemed to relate to cytoplasmic crystalloids.Type 1 alteration consisted of localized groups of cristae, usually oriented in the long direction of the organelle (Fig. 1A). In this plane they appeared serrated at the periphery with blind endings in the matrix. Other sections revealed a system of equally-spaced diagonal lines lengthwise in the mitochondrion with cristae protruding from both ends (Fig. 1B). Profiles of this inclusion were not unlike tangential cuts of a crystalloid structure frequently seen in enlarged mitochondria described below.

Coherency loss in γ' precipitates in nickel-base superalloy

1983 ◽  
Vol 41 ◽  
pp. 244-245
Author(s):  
R. A. Ricks ◽  
Angus J. Porter
Keyword(s):  
Lattice Mismatch ◽  
Lattice Parameter ◽  
Nickel Base Superalloy ◽  
Large Size ◽  
The Matrix ◽  
Nimonic 80A ◽  
Interfacial Dislocations ◽  
Nickel Base ◽  
Coherency Loss ◽  
Nimonic 115

During a recent investigation concerning the growth of γ' precipitates in nickel-base superalloys it was observed that the sign of the lattice mismatch between the coherent particles and the matrix (γ) was important in determining the ease with which matrix dislocations could be incorporated into the interface to relieve coherency strains. Thus alloys with a negative misfit (ie. the γ' lattice parameter was smaller than the matrix) could lose coherency easily and γ/γ' interfaces would exhibit regularly spaced networks of dislocations, as shown in figure 1 for the case of Nimonic 115 (misfit = -0.15%). In contrast, γ' particles in alloys with a positive misfit could grow to a large size and not show any such dislocation arrangements in the interface, thus indicating that coherency had not been lost. Figure 2 depicts a large γ' precipitate in Nimonic 80A (misfit = +0.32%) showing few interfacial dislocations.

Influence of Heat Treatments on Microstructures in an Fe-Co-V Alloy

1974 ◽  
Vol 32 ◽  
pp. 512-513
Author(s):  
S. Mahajan ◽  
M. R. Pinnel ◽  
J. E. Bennett
Keyword(s):  
Single Phase ◽  
Alloy Composition ◽  
Supersaturated Solid Solution ◽  
Cell Formation ◽  
Heat Treatments ◽  
Air Cooling ◽  
Iced Brine ◽  
Transmission Electron ◽  
The Matrix ◽  
Bcc Structure

The microstructural changes in an Fe-Co-V alloy (composition by wt.%: 2.97 V, 48.70 Co, 47.34 Fe and balance impurities, such as C, P and Ni) resulting from different heat treatments have been evaluated by optical metallography and transmission electron microscopy. Results indicate that, on air cooling or quenching into iced-brine from the high temperature single phase ϒ (fcc) field, vanadium can be retained in a supersaturated solid solution (α2) which has bcc structure. For the range of cooling rates employed, a portion of the material appears to undergo the γ-α2 transformation massively and the remainder martensitically. Figure 1 shows dislocation topology in a region that may have transformed martensitically. Dislocations are homogeneously distributed throughout the matrix, and there is no evidence for cell formation. The majority of the dislocations project along the projections of <111> vectors onto the (111) plane, implying that they are predominantly of screw character.

Heterogeneity of Size and Distribution of Intramembrane Particles in the Plasma Membrane of Yeast

1977 ◽  
Vol 35 ◽  
pp. 596-597
Author(s):  
E. Keyhani
Keyword(s):  
Plasma Membrane ◽  
Candida Utilis ◽  
Synthetic Medium ◽  
Freeze Fracture ◽  
Translational Diffusion ◽  
Yeast Cells ◽  
Distilled Water ◽  
Intramembrane Particles ◽  
The Matrix ◽  
Water Cell

The matrix of biological membranes consists of a lipid bilayer into which proteins or protein aggregates are intercalated. Freeze-fracture techni- ques permit these proteins, perhaps in association with lipids, to be visualized in the hydrophobic regions of the membrane. Thus, numerous intramembrane particles (IMP) have been found on the fracture faces of membranes from a wide variety of cells (1-3). A recognized property of IMP is their tendency to form aggregates in response to changes in experi- mental conditions (4,5), perhaps as a result of translational diffusion through the viscous plane of the membrane. The purpose of this communica- tion is to describe the distribution and size of IMP in the plasma membrane of yeast (Candida utilis).Yeast cells (ATCC 8205) were grown in synthetic medium (6), and then harvested after 16 hours of culture, and washed twice in distilled water. Cell pellets were suspended in growth medium supplemented with 30% glycerol and incubated for 30 minutes at 0°C, centrifuged, and prepared for freeze-fracture, as described earlier (2,3).

Electron microscopy and diffraction studies of polyimides

1983 ◽  
Vol 41 ◽  
pp. 28-29
Author(s):  
O.C. de Hodgins ◽  
K. R. Lawless ◽  
R. Anderson
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Structural Features ◽  
Inert Atmosphere ◽  
Polyimide Films ◽  
Resolution Electron ◽  
The Matrix ◽  
High Resolution Electron Microscope ◽  
Diffraction Patterns ◽  
Polymeric Samples

Commercial polyimide films have shown to be homogeneous on a scale of 5 to 200 nm. The observation of Skybond (SKB) 705 and PI5878 was carried out by using a Philips 400, 120 KeV STEM. The objective was to elucidate the structural features of the polymeric samples. The specimens were spun and cured at stepped temperatures in an inert atmosphere and cooled slowly for eight hours. TEM micrographs showed heterogeneities (or nodular structures) generally on a scale of 100 nm for PI5878 and approximately 40 nm for SKB 705, present in large volume fractions of both specimens. See Figures 1 and 2. It is possible that the nodulus observed may be associated with surface effects and the structure of the polymers be regarded as random amorphous arrays. Diffraction patterns of the matrix and the nodular areas showed different amorphous ring patterns in both materials. The specimens were viewed in both bright and dark fields using a high resolution electron microscope which provided magnifications of 100,000X or more on the photographic plates if desired.

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