Treshchev, D. V. Shkalikov, A. A.
Published in
Mathematical Notes

Conditions for the operator differential equation x˙=Ax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot x = Ax$$\end{document} possessing a quadratic first integral...

Luyen, D. T.
Published in
Mathematical Notes

In this paper, we study the existence of multiple solutions for the boundary-value problem Δγu+f(x,u)=0inΩ,u=0on∂Ω,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Del...

Perov, A. I. Kostrub, I. D.
Published in
Mathematical Notes

In this paper, both well-known and new properties of the spectral abscissa and the logarithmic norm are described. In addition to well-known formulas for the norm of a matrix and for its logarithmic norm in cubic, octahedral, spherical norms, various estimates for these quantities in an arbitrary Ho¨ lder norm are proved.

Baskakov, A. G. Kharitonov, V. D.
Published in
Mathematical Notes

The study of the spectral properties of operator polynomials is reduced to the study of the spectral properties of the operator specified by the operator matrix. The results obtained are applied to higher-order difference operators. Conditions for their invertibility and for them to be Fredholm, as well as the asymptotic representation for bounded ...

Chung, Y.–B.
Published in
Mathematical Notes

We construct an orthonormal basis for the class of square integrable functions on bounded domains in the plane in terms of the classical kernel functions in potential theory. Then we generalize the results of Brown and Halmos about algebraic properties of Toeplitz operators and Laurent operators on the unit disc to general bounded domains. This is ...

Shcherbakov, V. I.
Published in
Mathematical Notes

In this paper, we obtain five tests (three of which are symmetric) of pointwise convergence of Fourier series with respect to generalized Haar systems; the tests are similar to the Dini convergence tests. It is shown that the Dini convergence tests for Price systems are also valid for generalized Haar systems. It is also shown that the classicalDin...

Mao, L. X.
Published in
Mathematical Notes

In this paper, we investigate the homological properties of the functor categories (mod−R, Ab) and ((mod−R)op, Ab). Some new homological dimensions in these functor categories such as FP-projecive dimensions and cotorsion dimensions for functors and functor categories are introduced and studied. We also characterize functor categories of homologica...

Lyubimtsev, O. V.
Published in
Mathematical Notes

A ring K is a unique addition ring (a UA-ring) if its multiplicative semigroup (K, · ) can be equipped with a unique binary operation + transforming this semigroup to a ring (K, ·, +). An Abelian group is called an End-UA-group if its endomorphism ring is a UA-ring. In the paper, we find End-UA-groups in the class of nonreduced Abelian groups.

Shen, Z. Zhang, J. Chen, G. Chen, Y.
Published in
Mathematical Notes

A subgroup H of a group G is said to be S-quasinormally embedded in G if for every Sylow subgroup P of H, there is an S-quasinormal subgroup K in G such that P is also a Sylow subgroup of K. Groups with certain S-quasinormally embedded subgroups of prime power order are studied. We prove Theorems 1.4, 1.5 and 1.6 of [10] remain valid if we omit the...

Maslov, V. P.
Published in
Mathematical Notes

In this article, we study, from the mathematical point of view, the analogies between language and multi-particle systems in thermodynamics. We attempt to introduce an appropriate mathematical apparatus and the technical tools of statistical physics to descriptions of language. In particular, we apply the notions of number of degrees of freedom, Bo...