Let G be a group and Aut(G) be its automorphism group. An automorphism α of G is called a commuting automorphism if α(x)x = xα(x) for all x ∈ G. The set of all commuting automorphisms of G is denoted by A(G). We find some cases when A(G) is a subgroup of Aut(G).

In this paper, we propose a class of hybrid control strategy with time-varying delay in order to guarantee the global uniform exponential practical stabilization of nonlinear continuous system in the presence of a disturbing term and multiple bounded time-varying delays. Moreover, a numerical example is worked out to verify the effectiveness of the theoretical result.

An Abelian group on which every nonzero ring is isomorphic to the ring of endomorphisms of this group is called an RE-group. In the present paper, the RE-groups are described in some classes of Abelian groups, including periodic, divisible, unreduced, and torsion-free rank-1 groups. It is shown that there are no RE-groups in the class of completely decomposable torsion-free Abelian groups.

Using an integral construction based on symmetrized polynomials, we obtain a new estimate for the irrationality measure of the number In 7. This estimate improves a result due to Wu, which was proved in 2002.

The problem of representing Boolean functions by two-pole contact circuits that are irredundant and admit short fault detection or diagnostic tests of closures of at most k contacts for a given positive integer k is considered. The following assertions are proved: for almost every Boolean function of n variables, the minimal length of a fault detection (diagnostic) test is equal to 2 (does not exceed

Suppose that A and B are C*-algebras, A is separable, and B is stable. The elements of the group E1(A, B) in Connes—Higson E-theory are represented by *-homomorphisms from the suspension of A to the asymptotic algebra 21B. In the paper, an endofunctor M in the category of C* -algebras is constructed and a set of special homotopy classes of *-homomorphisms from A to MUB is defined so that this set endowed

Let φ: ℝn × [0, ∞) → [0, ∞) satisfy that φ(x, ·), for any given x ∈ Rn, is an Orlicz function and φ(·, t) is a Muckenhoupt A∞ weight uniformly in t ∈ (0, ∞). The Musielak–Orlicz Hardy space Hφ(ℝn) is defined to be the space of all tempered distributions whose grand maximal functions belong to the Musielak–Orlicz space Lφ(ℝn). In this paper, the authors establish the boundedness of maximal Bochner–Riesz

The interconnection between an optimal control problem and its convexification in the sense of Gamkrelidze and Bogolyubov is studied. Bogolyubov’s classical result for the simplest problem of variational calculus is obtained as a corollary.

The present paper is devoted to the study of predual spaces of JBW-algebras. It is proved that the predual space of a JBW-algebra is a strongly facially symmetric space if and only if this algebra is the direct sum of an Abelian algebra and an algebra of type I2.

A subgroup H of a finite group G is said to be F(G)-subnormal if it is subnormal in HF(G), where F(G) is the Fitting subgroup of G. In the paper, the problem of whether or not a formation β contains products of F(G)-subnormal β-subgroups of finite solvable groups is studied. In particular, solvable saturated formations β with this property are described. Formation properties of groups having three

Variational principles for functionals on the space C(X) of continuous functions that can be written as a representation of a functional in the form of the Legendre transform of the dual functional are considered. The formula of the Legendre transform determines a functional on wider sets of functions, and this functional is called the extended Legendre transform. Functionals that can be represented

The application of the collocation method to the boundary integral equation of the exterior Dirichlet boundary-value problem for the Helmholtz equation is justified. In addition, a new method for constructing cubature formulas for surface singular integrals is proposed.