We give a unified description of the modular and quasi-modular functions used in Viazovska's proof best packing bounds dimension 8 by Cohn, Kumar, Miller, Radchenko, Viazovska bound 24. show that necessarily forms have to be obtain these results. extend constructions arbitrary dimensions divisible 4.

Non thermal plasma (NTP) reactors packed with non-catalytic or catalytic packing material have been widely used for the abatement of volatile organic compounds such as toluene, benzene, etc. Packed bed reactors are single stage reactors where the packing material is placed directly in the plasma discharge region. The presence of packing material can alter the physical (such as discharge charact...

In this paper, we consider the maximum weight ({K1,K2},k,l)-packing problem in a graph. This generalizes number of well-known problems, for example: induced matching, k-separated connected independent set, dissociating k-packing. We show that class cographs, ({K1,K2},k,l)- packing can be computed O(n + m) time. Let Γ graphs and Γ* all simple (with respect to modular decomposition) subgraphs fro...

a modular $k$-coloring, $kge 2,$ of a graph $g$ without isolated vertices is a coloring of the vertices of $g$ with the elements in $mathbb{z}_k$ having the property that for every two adjacent vertices of $g,$ the sums of the colors of the neighbors are different in $mathbb{z}_k.$ the minimum $k$ for which $g$ has a modular $k-$coloring is the modular chromatic number of $g.$ except for some s...

INTRODUCTION. What is the effect of maldistribution on the mass transfer efficiency of a distillation column containing structured packing?. The column of structured packing is considered to consist of a set of unit cells. Each pair of sheets gives a two-dimensional set of " elementary " cells: