scholarly journals A stability result using the matrix norm to bound the permanent

2018 ◽  
Vol 224 (1) ◽  
pp. 437-454
Author(s):  
Ross Berkowitz ◽  
Pat Devlin
Keyword(s):  
Stability Result ◽  
Matrix Norm ◽  
The Matrix

On the Matrix Norm Subordinate to the Holder Norm

1999 ◽  
Vol 18 (2) ◽  
pp. 175-182 ◽  
Author(s):  
J. Albrecht ◽  
P.P. Klein
Keyword(s):  
Matrix Norm ◽  
Hölder Norm ◽  
The Matrix

scholarly journals A hypothesis of state covariance decorrelation effects to partial observability SLAM

2019 ◽  
Vol 14 (2) ◽  
pp. 588 ◽  
Author(s):  
H Ahmad ◽  
N.A Othman ◽  
M M Saari ◽  
M S Ramli ◽  
M M Mazlan ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Matrix Inversion ◽  
Matrix Norm ◽  
Main Element ◽  
Partial Observability ◽  
Localization And Mapping ◽  
The Matrix ◽  
Simulation Results ◽  
Partially Observable

<span>This paper analyze the performance of partial observability in simultaneous localization and mapping(SLAM) problem. The study focuses mainly on the effect of having a decorrelation technique known as Covariance Inflation to the estimation. The matrix inversion will be the main element to be investigated through two conditions with respect to some defined environment namely as unstable partially observable SLAM and partially observable SLAM via matrix norm analysis. For assessment purposes, the Extended Kalman Filter estimation is referred as the estimator to understand how the conditions can influence the results. The simulation results depicted that, the matrix norm is able to determine the efficiency of estimation and is proportional to the uncertainties of the system.</span>

The norm of a Möbius transformation

1984 ◽  
Vol 96 (2) ◽  
pp. 301-308 ◽  
Author(s):  
A. F. Beardon ◽  
J. B. Wilker
Keyword(s):  
Conformal Transformation ◽  
Riemann Sphere ◽  
Matrix Norm ◽  
Hyperbolic Distance ◽  
Möbius Transformation ◽  
The Matrix ◽  
Mobius Transformation ◽  
Image Position

A Möbius transformation z → (az + b)/(cz + d), ad — bc = 1, acts as a conformal transformation of the Riemann sphere , and its Poincaré extension acts as an isometry of hyperbolic 3-space modelled in the ball < 1. The size of this transformation can be measured by the matrix normor by the hyperbolic distance ρ through which its extension moves the point (0, 0, 0).

scholarly journals Repeated Columns and an Old Chestnut

10.37236/3345 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
R. P. Anstee ◽  
Linyuan Lu
Keyword(s):  
Stability Result ◽  
Strong Stability ◽  
Inductive Proof ◽  
T Subsets ◽  
The Matrix ◽  
Disjoint Sets

Let $t\ge 1$ be a given integer. Let ${\cal F}$ be a family of subsets of $[m]=\{1,2,\ldots ,m\}$. Assume that for every pair of disjoint sets $S,T\subset [m]$ with $|S|=|T|=k$, there do not exist $2t$ sets in ${\cal F}$ where $t$ subsets of ${\cal F}$ contain $S$ and are disjoint from $T$ and $t$ subsets of ${\cal F}$ contain $T$ and are disjoint from $S$. We show that $|{\cal F}|$ is $O(m^{k})$. Our main new ingredient is allowing, during the inductive proof, multisets of subsets of $[m]$ where the multiplicity of a given set is bounded by $t-1$. We use a strong stability result of Anstee and Keevash. This is further evidence for a conjecture of Anstee and Sali. These problems can be stated in the language of matrices. Let $t\cdot M$ denote $t$ copies of the matrix $M$ concatenated together. We have established the conjecture for those configurations $t\cdot F$ for any $k\times 2$ (0,1)-matrix $F$.

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).

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