scholarly journals A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere

1992 ◽  
Vol 27 (2) ◽  
pp. 246-252 ◽  
Author(s):  
Craig D. Hodgson ◽  
Igor Rivin ◽  
Warren D. Smith
Keyword(s):  
Convex Polyhedra ◽  
Hyperbolic Polyhedra

scholarly journals Greedy systems of linear inequalities and lexicographically optimal solutions

2019 ◽  
Vol 53 (5) ◽  
pp. 1929-1935
Author(s):  
Satoru Fujishige
Keyword(s):  
Convex Functions ◽  
Linear Inequalities ◽  
Convex Polyhedra ◽  
Optimal Solutions ◽  
Integral Points ◽  
System Of Linear Inequalities ◽  
Discrete Convexity ◽  
The Greedy Algorithm

The present note reveals the role of the concept of greedy system of linear inequalities played in connection with lexicographically optimal solutions on convex polyhedra and discrete convexity. The lexicographically optimal solutions on convex polyhedra represented by a greedy system of linear inequalities can be obtained by a greedy procedure, a special form of which is the greedy algorithm of J. Edmonds for polymatroids. We also examine when the lexicographically optimal solutions become integral. By means of the Fourier–Motzkin elimination Murota and Tamura have recently shown the existence of integral points in a polyhedron arising as a subdifferential of an integer-valued, integrally convex function due to Favati and Tardella [Murota and Tamura, Integrality of subgradients and biconjugates of integrally convex functions. Preprint arXiv:1806.00992v1 (2018)], which can be explained by our present result. A characterization of integrally convex functions is also given.

On the Topological Characterization of 3-D Polyhedral Microstrutures

2007 ◽  
Vol 537-538 ◽  
pp. 563-570 ◽  
Author(s):  
Tamás Réti ◽  
Agnes Csizmazia ◽  
Imre Felde
Keyword(s):  
Single Phase ◽  
Cellular Systems ◽  
Convex Polyhedra ◽  
Quantitative Characterization ◽  
Topological Characterization ◽  
Shape Factors ◽  
3 Dimensional ◽  
Cellular Models ◽  
Finite Set

To characterize topologically the polycrystalline microstructure of single-phase alloys computer simulations are performed on 3-dimensional cellular models. These infinite periodic cellular systems are constructed from a finite set of space filling convex polyhedra (grains). It is shown that the appropriately selected topological shape factors can be successfully used for the quantitative characterization of computer-simulated microstructures of various types.

ON ARCHIMEDEAN LINK COMPLEMENTS

2002 ◽  
Vol 11 (06) ◽  
pp. 833-868 ◽  
Author(s):  
IAIN R. AITCHISON ◽  
LAWRENCE D. REEVES
Keyword(s):  
Hyperbolic Metric ◽  
Archimedean Solids ◽  
Link Complements ◽  
Hyperbolic Polyhedra ◽  
Figure Eight Knot ◽  
Alternating Links

We study a subclass of alternating links for which the complete hyperbolic metric can be realised directly by pairwise identification of faces of two ideal hyperbolic polyhedra. Our main result is a characterization of these links: essentially, the corresponding polyhedra are exactly the Archimedean solids with trivalent vertices. Furthermore, we show that the only knots which arise are the two dodecahedral knots, and the figure eight knot.

scholarly journals A Lipschitzian characterization of convex polyhedra

1969 ◽  
Vol 23 (1) ◽  
pp. 167-167 ◽  
Author(s):  
David W. Walkup ◽  
Roger J.-B. Wets
Keyword(s):  
Convex Polyhedra

scholarly journals Piecewise Linear Sheaves

2019 ◽  
Author(s):  
Masaki Kashiwara ◽  
Pierre Schapira
Keyword(s):  
Vector Space ◽  
Piecewise Linear ◽  
Building Blocks ◽  
Convex Polyhedra ◽  
Triangulated Category ◽  
Real Vector ◽  
Proper Cone ◽  
Finite Dimensional ◽  
Higher Dimensional

Abstract On a finite-dimensional real vector space, we give a microlocal characterization of (derived) piecewise linear sheaves (PL sheaves) and prove that the triangulated category of such sheaves is generated by sheaves associated with convex polyhedra. We then give a similar theorem for PL $\gamma $-sheaves, that is, PL sheaves associated with the $\gamma $-topology, for a closed convex polyhedral proper cone $\gamma $. Our motivation is that convex polyhedra may be considered as building blocks for higher dimensional barcodes.

A characterization of compact convex polyhedra in hyperbolic 3-space

1993 ◽  
Vol 111 (1) ◽  
pp. 77-111 ◽  
Author(s):  
Craig D. Hodgson ◽  
Igor Rivin
Keyword(s):  
Compact Convex ◽  
Convex Polyhedra

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

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