Maximum Density Space Packing with Parallel Strings of Spheres.
Displaying 81 – 100 of 235
Mean Projections and Finite Packings of Convex Bodies.
Károly, Jr. Böröczky (1994)
Monatshefte für Mathematik
Mehrfache gitterförmige Kreis- und Kugelanordnungen.
A. Florian, G. Fejes Tóth (1975)
Monatshefte für Mathematik
Metric Entropy of Homogeneous Spaces
Stanisław Szarek (1998)
Banach Center Publications
For a precompact subset K of a metric space and ε > 0, the covering number N(K,ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In this paper we give asymptotically correct estimates for covering numbers for a large class of homogeneous...
Minimum Area of Circumscribed Polygons.
G.D. Chakerian (1973)
Elemente der Mathematik
...-Morphic Sets of Prototiles.
P. Schmitt (1987)
Discrete & computational geometry
Multiple Lattice Packings and Coverings of Spheres.
L.J. Yang (1980)
Monatshefte für Mathematik
Multiple tilings by cubes with no shared faces.
Sándor Szabó (1982)
Aequationes mathematicae
Multiple Tilings of n-Dimensional Space by Unit Cubes.
Raphael M. Robinson (1979)
Mathematische Zeitschrift
New conjectural lower bounds on the optimal density of sphere packings.
Stillinger, F.H., Torquato, S. (2006)
Experimental Mathematics
New Upper Bounds for Some Spherical Codes
Boyvalenkov, Peter, Kazakov, Peter (1995)
Serdica Mathematical Journal
The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases...
New upper bounds on sphere packings. II.
Cohn, Henry (2002)
Geometry & Topology
Non-integer lattice tilings by (k, n) truncated crosses.
S. Szabó (1983)
Aequationes mathematicae
Nontiles and nonfacets for the Euclidean space, spherical complexes and convex polytopes.
Egon Schulte (1984)
Journal für die reine und angewandte Mathematik
Note on Packing of 19 Equal Circles on a Sphere.
Tibor Tarnai (1984)
Elemente der Mathematik
Note to a paper of Bambah, Rogers and Zassenhaus
G. Fejes Tóth (1988)
Acta Arithmetica
Notions of denseness.
Kuperberg, Greg (2000)
Geometry & Topology
O ukladaní kociek a iných objektov
Vojtech Bálint, Zuzana Sedliačková, Peter Adamko (2020)
Pokroky matematiky, fyziky a astronomie
Uvedieme históriu a prehľad výsledkov o ukladaní kociek do kvádra s minimálnym objemom a pridáme aj hlavné myšlienky niektorých dôkazov. V závere sa veľmi stručne zmienime o iných ukladacích problémoch.
On a generalization of Craig lattices
Hao Chen (2013)
Journal de Théorie des Nombres de Bordeaux
In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range . We also construct some dense lattices of dimensions in the range . Finally we also obtain some new lattices of moderate dimensions such as , which are denser than the...
On a Problem About Covering Lines by Squares.
W. Kern, A. Wanka (1990)
Discrete & computational geometry