scholarly journals A proof of the matrix version of Baker's conjecture in Diophantine approximation

2018 ◽  
Vol 167 (01) ◽  
pp. 159-169
Author(s):  
TUSHAR DAS ◽  
DAVID SIMMONS
Keyword(s):  
Diophantine Approximation ◽  
Matrix Version ◽  
The Matrix

AbstractWe prove that the matrix analogue of the Veronese curve is strongly extremal in the sense of Diophantine approximation, thereby resolving a question posed by Beresnevich, Kleinbock and Margulis (2015) in the affirmative.

Hybrid Complex Numbers: The Matrix Version

2018 ◽  
Vol 28 (3) ◽  
Author(s):  
G. Dattoli ◽  
S. Licciardi ◽  
R. M. Pidatella ◽  
E. Sabia
Keyword(s):  
Complex Numbers ◽  
Matrix Version ◽  
Hybrid Complex ◽  
The Matrix

The matrix version of Hamburger’s theorem

2012 ◽  
Vol 91 (3-4) ◽  
pp. 493-499 ◽  
Author(s):  
Yu. M. Dyukarev ◽  
A. E. Choque Rivero
Keyword(s):  
Matrix Version ◽  
The Matrix

scholarly journals The matrix version for the multivariable Humbert polynomials

2012 ◽  
Vol 13 (2) ◽  
pp. 197 ◽  
Author(s):  
Rabia Aktaş ◽  
Bayram Çekim ◽  
Recep Şahin
Keyword(s):  
Matrix Version ◽  
The Matrix ◽  
Humbert Polynomials

A NOTE ON MATRIX APPROXIMATION IN THE THEORY OF MULTIPLICATIVE DIOPHANTINE APPROXIMATION

2019 ◽  
Vol 100 (3) ◽  
pp. 372-377
Author(s):  
YUAN ZHANG
Keyword(s):  
Number Theory ◽  
Diophantine Approximation ◽  
Hausdorff Measure ◽  
Matrix Form ◽  
Matrix Approximation ◽  
The Matrix ◽  
Closing The Gap

We prove the Hausdorff measure version of the matrix form of Gallagher’s theorem in the inhomogeneous setting, thereby proving a conjecture posed by Hussain and Simmons [‘The Hausdorff measure version of Gallagher’s theorem—closing the gap and beyond’, J. Number Theory186 (2018), 211–225].

scholarly journals Program Linier Parametrik

2019 ◽  
Vol 2 (1) ◽  
pp. 69-76
Author(s):  
Adolf T Simatupang
Keyword(s):  
Objective Function ◽  
Optimal Solution ◽  
Critical Value ◽  
Critical Values ◽  
Linear Program ◽  
Linear Programs ◽  
Program Problem ◽  
Matrix Version ◽  
Linear Program Problem ◽  
The Matrix

This study aims to discuss a linear program problem where its constants can change, If a constant for a linear program problem is changed, then we don't need to count from the beginning again. Next, we will examine the properties of the objective function as a result of changes in these constants. In this discussion determine the non-negative "critical value" which provides the optimal solution to the problem of parametric linear programs. Searching for critical values in parametric linear programs is done by the matrix version method.

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.

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