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, Theory of Comp. Systems , 43 ( 1 ) ( 2008 ) 38 - 55 . [6] Januszewski , J. and Lassak , M. , On-line packing sequences of cubes in the

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Abstract  

We present a very short survey of known results and many new estimates and results on the maximum number of points that can be chosen in the n-dimensional unit cube so that every distance between them is at least 1.

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numbers 1965 Hua, L. K. , On the representations of a number as the sum of two cubes, Math. Z. , 44

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It is shown that each separable metric, not totally disconnected, topological space admits a superextension homeomorphic to the Hilbert cube. Moreover, for simple spaces, such as the closed unit interval or then-spheresS n, we give easily described subbases for which the corresponding superextension is homeomorphic to the Hilbert cube.

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References [1] Vörös L. Two new space-filling mosaics based on a symmetric 3D model of the 10D cube , Pollack

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Assis , F.R. , Morais , R.M.S.C. & Morais , A.M.M.B. ( 2017 a): Mathematical modelling of osmotic dehydration kinetics of apple cubes . J. Food Process. Pres. , 41 ( 3 ), doi:10.1111/jfpp.12895

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L. Two-and three-dimensional tilings based on a model of the six-dimensional cube , KoG Scientific and Professional Journal of the Croatian Society for Geometry and Graphics , No. 10 , 2006 , pp. 19 – 25

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Abstract  

We prove that almost all integers N satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 5; 6; 7; 8, i.e., N = p 1 3 + ... + p j 3 with |p i − (N/j)1/3| ≦

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$N^{1/3 - \delta _j + \varepsilon }$$ \end{document}
(1 ≦ ij), for δ j = 1/45; 1/30; 1/25; 2/45, respectively.

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1 1 14 Sárközy, A. , On lattice-cubes in the three-space (in Hungarian), Matematikai Lapok (1961).

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Abstract  

We give a very short survey of the results on placing of points into the unit n-dimensional cube with mutual distances at least one. The main result is that into the 5-dimensional unit cube there can be placed no more than 40 points.

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