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325  Articles
1 of 33 pages  |  10  records  |  more records»
Extremal lattices are lattices maximal in size with respect to the number n of their join-irreducible elements with bounded Vapnik-Chervonekis dimension k. It is natural, however, to estimate the size of a lattice also with respect to the number of its me... see more

The Sauer-Shelah lemma provides an exact upper bound on the size of set families with bounded Vapnik-Chervonekis dimension. When applied to lattices represented as closure systems, this lemma outlines a class of extremal lattices obtaining this bound. Her... see more

We show that the subgroup lattice of any finite group satisfies Frankl’s Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common technical result... see more

We consider the problem of fast zeta and Möbius transforms in finite posets, particularly in lattices. It has previously been shown that for a certain family of lattices, zeta and Möbius transforms can be computed in O(e)O(e) elementary arithmetic operati... see more

An extremal graph for a graph HH on nn vertices is a graph on nn vertices with maximum number of edges that does not contain HH as a subgraph. Let Tn,rT_{n,r} be the Turán graph, which is the complete rr-partite graph on nn vertices with part sizes that d... see more

This article reviews the development in our laboratory of magnetic lattices comprising periodic arrays of magnetic microtraps created by patterned magnetic films to trap periodic arrays of ultracold atoms. Recent achievements include the realisation of mu... see more

The paper concerns the application of the extremal energy efficient control for two pumps connected in parallel. One of the pumps is with the controlled induction motor drive. The extremal control algorithm description, its mathematical model and the syst... see more

On the basis of analysis of scientific achievements in the field of correlation-extremal systems of piloted aircraft and the peculiarities of their application are discussed exist-ing problems and ways to enable high-precision guidance of aircraft.

We construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine extended Coxeter groups W(A3) and W(B3)=Aut(A3). It is naturally expected that these rank-3 Coxeter-Weyl... see more

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