A class of optimal solutions of the matrix Nehari-extension problem

1991 ◽  
Vol 1 (1) ◽  
pp. 7-31 ◽  
Author(s):  
G. D. Halikias
Keyword(s):  
Extension Problem ◽  
Optimal Solutions ◽  
The Matrix

Contractive analogs

2011 ◽  
Author(s):  
Mihály Bakonyi ◽  
Hugo J. Woerdeman
Keyword(s):  
Extension Problem ◽  
Operator Matrix ◽  
Model Matching ◽  
Schmidt Norm ◽  
The Matrix ◽  
Completion Problems ◽  
Linearly Constrained ◽  
Contractive Operator ◽  
Pick Problem ◽  
Partial Contraction

This chapter deals with contractive completions of partial operator matrices. Since the norm of a submatrix is always less or equal to the norm of the matrix itself, every partial matrix which admits a contractive completion has to be partially contractive (or a partial contraction), that is, all its fully specified submatrices are contractions. The discussions cover contractive operator-matrix completions; linearly constrained completion problems; the operator-valued Nehari and Carathéodory problems; Nehari's problem in two variables; Nehari and Carathéodory problems for functions on compact groups; the Nevanlinna–Pick problem; the operator Corona problem; joint operator/Hilbert–Schmidt norm control extensions; an L1 extension problem for polynomials; superoptimal completions and approximations of analytic functions; and model matching. Exercises and notes are provided at the end of the chapter.

scholarly journals An algorithm for constructing multidimensional biorthogonal periodic multiwavelets

2000 ◽  
Vol 43 (3) ◽  
pp. 633-649 ◽  
Author(s):  
Say Song Goh ◽  
K. M. Teo
Keyword(s):  
Entire Function ◽  
Function Space ◽  
Sufficient Conditions ◽  
Riesz Bases ◽  
Extension Problem ◽  
The Matrix ◽  
Matrix Extension

AbstractThis paper deals with the problem of constructing multidimensional biorthogonal periodic multiwavelets from a given pair of biorthogonal periodic multiresolutions. Biorthogonal polyphase splines introduced to reduce the problem to a matrix extension problem, and an algorithm for solving the matrix extension problem is derived. Sufficient conditions for collections of periodic multiwavelets to form a pair of biorthogonal Riesz bases of the entire function space are also obtained.

scholarly journals Sparse Solutions of a Class of Constrained Optimization Problems

2021 ◽  
Author(s):  
Lei Yang ◽  
Xiaojun Chen ◽  
Shuhuang Xiang
Keyword(s):  
Optimization Problems ◽  
Linear Equations ◽  
Solution Set ◽  
Optimal Solutions ◽  
Constrained Optimization Problems ◽  
Infinity Norm ◽  
Underdetermined System ◽  
The Matrix ◽  
Sparse Solutions ◽  
Theoretical Results

In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing [Formula: see text] subject to [Formula: see text] for given [Formula: see text] and [Formula: see text]. We then study various properties of the optimal solutions of this problem. Specifically, without any condition on the matrix A, we provide upper bounds in cardinality and infinity norm for the optimal solutions and show that all optimal solutions must be on the boundary of the feasible set when [Formula: see text]. Moreover, for [Formula: see text], we show that the problem with [Formula: see text] has a finite number of optimal solutions and prove that there exists [Formula: see text] such that the solution set of the problem with any [Formula: see text] is contained in the solution set of the problem with p = 0, and there further exists [Formula: see text] such that the solution set of the problem with any [Formula: see text] remains unchanged. An estimation of such [Formula: see text] is also provided. In addition, to solve the constrained nonconvex non-Lipschitz Lp-L1 problem ([Formula: see text] and q = 1), we propose a smoothing penalty method and show that, under some mild conditions, any cluster point of the sequence generated is a stationary point of our problem. Some numerical examples are given to implicitly illustrate the theoretical results and show the efficiency of the proposed algorithm for the constrained Lp-L1 problem under different noises.

scholarly journals Improving Construction Productivity by Integrating the Lean Concept and the Clancey Heuristic Model

2019 ◽  
Vol 11 (17) ◽  
pp. 4535
Author(s):  
Svetlana Besklubova ◽  
Xueqing Zhang
Keyword(s):  
Decision Making ◽  
Construction Projects ◽  
Heuristic Model ◽  
Optimal Solutions ◽  
Productivity Improvement ◽  
Cost Overruns ◽  
Main Thrust ◽  
Construction Productivity ◽  
The Matrix ◽  
Lean Tools

The profitability of most construction projects critically depends on construction productivity, which can lead to project cost overruns and schedule delays if not fully addressed. Although a literature review provides numerous worldwide examples of construction productivity improvement by mitigating and eliminating influencing disruptions through lean tool implementation, those studies considered a limited number of productivity disruptions in which the choice of lean tools was not clearly justified. This gap has significantly hampered the required improvements in construction productivity due to the limitations in selecting optimal solutions to fully overcome relevant disruptions and prevent their consequences. Hence, as a response to the aforementioned shortcomings, the present study develops the lean-Clancy-based decision-making matrix (LCDMM) that combines two different methods—the “Clancey heuristic model” and “lean construction”—with the goal of determining optimal and beneficial solutions to eliminate disruptions. The main thrust towards the adaptation of the matrix is based on its potential to link disruptions with solutions based on lean tools. In order to assess the practicality of LCDMM, the proposed solutions for two disruptions, as examples, are compared to existing practical solutions. Ultimately, it is clear that LCDMM, as a reusable tool, can assist scholars and practitioners in assembling the analysis of disruption waste and in selecting solutions for productivity improvement.

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.

Organisation in the Structure of the Cytoplasmic Ground Substance

1978 ◽  
Vol 36 (3) ◽  
pp. 627-639
Author(s):  
K.R. Porter
Keyword(s):  
Endoplasmic Reticulum ◽  
Golgi Complex ◽  
Random Distribution ◽  
Ground Substance ◽  
The Matrix ◽  
Cell Processes ◽  
Cytoplasmic Ground Substance

Most types of cells are known from their structure and overall form to possess a characteristic organization. In some instances this is evident in the non-random disposition of organelles and such system subunits as cisternae of the endoplasmic reticulum or the Golgi complex. In others it appears in the distribution and orientation of cytoplasmic fibrils. And in yet others the organization finds expression in the non-random distribution and orientation of microtubules, especially as found in highly anisometric cells and cell processes. The impression is unavoidable that in none of these cases is the organization achieved without the involvement of the cytoplasmic ground substance (CGS) or matrix. This impression is based on the fact that a matrix is present and that in all instances these formed structures, whether membranelimited or filamentous, are suspended in it. In some well-known instances, as in arrays of microtubules which make up axonemes and axostyles, the matrix resolves itself into bridges (and spokes) between the microtubules, bridges which are in some cases very regularly disposed and uniform in size (Mcintosh, 1973; Bloodgood and Miller, 1974; Warner and Satir, 1974).

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