Mathematical Notes最新文献

Abstract

The chief factor (H/K) of a group (G) is said to be (mathfrak{F})-central if

The (mathfrak{F})-hypercenter of a group (G) is defined to be a maximal normal subgroup of (G) such that all (G)-composition factors below it are (mathfrak{F})-central in (G). In 1995, at the Gomel algebraic seminar, L. A. Shemetkov formulated the problem of describing formations of finite groups (mathfrak{F}) for which, in any group, the intersection of (mathfrak{F})-maximal subgroups coincides with the (mathfrak{F})-hypercenter. In the present paper, new properties of such formations are obtained. In particular, a series of hereditary nonsaturated formations of soluble groups is constructed, which answer Shemetkov’s problem.

Abstract

The aim of this paper is to study weighted estimates of the fractional type Marcinkiewicz integral and its commutator. By producing Guliyev type local pointwise estimates, we prove the boundedness of the fractional type Marcinkiewicz integral on the weighted Morrey–Guliyev spaces. Meanwhile, we also consider the corresponding weighted estimates of the commutators generated by a Lipschitz function and a BMO function.

Abstract

We study the complexity of recognizing (A)-distance graphs in (mathbb{R}^d) and prove that for all finite sets (A) such that any two elements of the set differ by a factor (ge2), the recognition problem for (A)-distance graphs is (mathrm{NP})-hard for any (d geq 3).

Abstract

The main purpose of this article is to show that every commuting Jordan derivation on triangular rings (unital or not) is identically zero. Using this result, we prove that if (mathcal{A}) is a (2)-torsion free ring that is either semiprime or satisfies Condition (P), then, under certain conditions, every commuting Jordan derivation of (mathcal{A}) into itself is identically zero.

Abstract

A matching of a graph is a set of its edges that pairwise do not have common vertices. An important parameter of graphs, which is used in mathematical chemistry, is the Hosoya index, defined as the number of their matchings. Previously, the problems of maximizing this index were considered and completely solved for (n)-vertex trees with two, three and four leaves for any sufficiently large (n). In the present paper, a similar problem is completely solved for 5-leaved trees with (ngeq 20) and for 6-leaved trees with (ngeq 26).

Abstract

Let (M(x)) be the length of the largest subinterval of ([1,x]) which does not contain any sums of two squareful numbers. We prove a lower bound

for all (xgeq 3). The proof relies on properties of random subsets of the prime numbers.

Abstract

We investigate the local dynamics of a system of oscillators with a large number of elements and with diffusion-type couplings containing a large delay. We isolate critical cases in the stability problem for the zero equilibrium state and show that all of them are infinite-dimensional. Using special infinite normalization methods, we construct quasinormal forms, that is, nonlinear boundary value problems of parabolic type whose nonlocal dynamics determines the behavior of solutions of the original system in a small neighborhood of the equilibrium state. These quasinormal forms contain either two or three spatial variables, which emphasizes the complexity of dynamic properties of the original problem.

Abstract

Let (X) be a compact complex space in Fujiki’s class (mathcal{C}). In this paper, we show that (X) admits a compact Kähler model ({tilde X}), that is, there exists a projective bimeromorphic map (sigmacolontilde{X}to X) from a compact Kähler manifold (tilde{X}) such that the automorphism group (operatorname{Aut}(X)) lifts holomorphically and uniquely to a subgroup of (operatorname{Aut}({tilde X})). As a consequence, we also give a few applications to the Jordan property, the finiteness of torsion groups, and arbitrary large finite abelian subgroups for compact complex spaces in Fujiki’s class ({mathcal C}).

Abstract

We consider a random walk with zero mean and finite variance whose steps are arithmetic. The arcsine law for the time the walk reaches its maximum is well known. In this paper, we consider the distribution of the moment of reaching the maximum under the assumption that the maximum value itself is fixed. We show that, in the case of a moderate deviation of the maximum, the distribution of the moment of the maximum with appropriate normalization converges to the chi-square distribution with one degree of freedom. Similar results are obtained in the nonlattice case.

Abstract

Suppose that a sequence ({X_n}_{nge 0}) of random variables is a homogeneous irreducible Markov chain with finite set of states. Let (xi_n), (ninmathbb{N}), be random variables defined on the chain transitions.

The renewal function

where (S_0:=0) and (S_n:=xi_1+dots + xi_n), (ninmathbb{N}), is introduced. It is shown that this function converges to its limit at an exponential rate, and an explicit description of the exponent is given.