It is proved that the maximum possible volume of a parallelotope contained in ad-dimensional simplexSis equal to(d!/dd) vol(S). A description of all the parallelotopes of maximum volume contained in… (More)

We estimate the number and ratio of negative homothetic copies of a d-dimensional convex body C sufficient for the covering of C. If the number of those copies is not very large, then our estimates… (More)

We prove that in Euclidean d-space every sequence of cubes with total volume 2 + 3 is able to cover on-line the unit cube. The proof is based on an on-line q-adic method of covering the unit segment… (More)

The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean n-space En is at most n+2. We obtain this estimate as an immediate consequence of our theorem which says that for… (More)

The paper deals with approaches in modeling of a complex electro-hydro-mechanical system. The proposed system is a fuel metering device that is a non-linear system with hysteresis and transport… (More)

We present efficient algorithms for the on-line q-adic covering of the unit interval by sequences of segments. The basic method guarantees covering provided the total length of segments is at least 1… (More)

Let M be a planar centrally symmetric convex body. If H is an a‰ne regular hexagon of the smallest (the largest) possible area inscribed in M, then M contains (respectively, the interior of M does… (More)

A convex body R in a normed d-dimensional space M is called reduced if the M-thickness ∆(K) of each convex body K ⊂ R different from R is smaller than ∆(R). We present two characterizations of… (More)