It has been long conjectured that the crossing number of Cm Ã— Cn is (mâˆ’2)n, for all m,n such that n â‰¥ m â‰¥ 3. In this paper it is shown that if n â‰¥ m(m+1) and m â‰¥ 3, then this conjecture holds. Thatâ€¦ (More)

We prove the existence of small localized stationary solutions for the generalized Swift-Hohenberg equation and find under some assumption a part of a boundary of their existence in the parameterâ€¦ (More)

Recall that a locally compact group G is called unimodular if the left Haar measure on G is equal to the right one. It is proved in this paper that G is unimodular iff it is approximable by finiteâ€¦ (More)

We introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class K. If A is discrete, this concept agrees with the familiarâ€¦ (More)

We introduce a definition of approximation of a topological algebraic system A by systems of a class K and investigate it for the case when the class K consists of finite systems. For the case whenâ€¦ (More)

A (partial) Latin square is a table of multiplication of a (partial) quasigroup. Multiplication of a (partial) quasigroup may be considered as a set of triples. We give a necessary and sufficientâ€¦ (More)

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones asâ€¦ (More)