Abstract For a one-dimensional semilinear wave equation, a mixed problem with nonlinear boundary condition is considered. The uniqueness and the local and global solvability of the problem under consideration are studied depending on the type of nonlinearities in the equation and in the boundary conditions. The cases of nonexistence of a solution not only globally but even locally are considered, as

Abstract We construct a family of flat isotropic nonhomogeneous tori in \(\mathbb{H}^n\) and \(\mathbb{C}\mathrm{P}^{2n+1}\) and find necessary and sufficient conditions for their Hamiltonian minimality.

Abstract A lattice of definability subspaces in the order of rational numbers is described. It is proved that this lattice consists of five subspaces defined in the paper that are generated by the following relations: “equality,” “less,” “between,” “cycle,” and “linkage.” For each of the subspaces, its width (the minimum number of arguments of a generating relation) is found and a convenient description

Abstract A logistic delay equation with diffusion, which is important in applications, is studied. It is assumed that all of its coefficients, as well as the coefficients in the boundary conditions, are rapidly oscillating functions of time. An averaged equation is constructed, and the relation between its solutions and the solutions of the original equation is studied. A result on the stability of

Abstract The initial boundary-value problem for systems of fourth-order partial differential equations with two independent variables is considered. By using a new unknown eigenfunction, the problem under consideration is reduced to an equivalent nonlocal problem for a system of second-order hyperbolic-type integro-differential equations with integral conditions. An algorithm for finding an approximate

Abstract A hypergraph \(H=(V,E)\) has property \(B_k\) if there exists a 2-coloring of the set \(V\) such that each edge contains at least \(k\) vertices of each color. We let \(m_{k,g}(n)\) and \(m_{k,b}(n)\), respectively, denote the least number of edges of an \(n\)-homogeneous hypergraph without property \(B_k\) which contains either no cycles of length at least \(g\) or no two edges intersecting

Abstract The paper deals with the construction of a multivalued solution of the Cauchy problem for the Hamilton–Jacobi equation with discontinuous Hamiltonian with respect to the phase variable. The constructed multivalued solution is approximated by a sequence of continuous solutions of auxiliary Cauchy problems of the Hamilton–Jacobi equation with Hamiltonian which is Lipschitz with respect to the

Abstract It is established that, among all continuously differentiable homeomorphic changes of variable, the absolute convergence of Fourier series in the Haar wavelet system is preserved by only those for which \(\varphi^{-1}(0)\) is binary-rational and \(\varphi'(x)=\pm 2^m\), where \(m\) is an integer and \(x\in\mathbb R\). It is also established that this condition is necessary for a continuously

Abstract Properties of the approximate rotation of vector fields generated by multivalued maps of monotone type are studied. Analogs of the Hopf theorems on the extension of multivalued maps without singular points and homotopy classification of the corresponding vector fields are proved. Applications to variational inequalities and operator inclusions are outlines.

Abstract The first example of a Banach space with the approximation property but without the bounded approximation property was given by Figiel and Johnson in 1973. We give the first example of a Banach lattice with the approximation property but without the bounded approximation property. As a consequence, we prove the existence of an integral operator (in the sense of Grothendieck) on a Banach lattice

Abstract Let \(G\) be a finite group, let \(M\) be a maximal subgroup of \(G\), and let \(\mathfrak F\) be a hereditary formation consisting of solvable groups. The metanilpotency of the \(\mathfrak F\)-residual \(G^\mathfrak F\) is established under the assumption that all subgroups maximal in \(M\) are \(\mathfrak F\)-subnormal in \(G\), and the nilpotency of \(G^\mathfrak F\) is established in the

Abstract An ordered topological vector space has the countable dominated extension property if any linear operator ranging in this space, defined on a subspace of a separable metrizable topological vector space, and dominated there by a continuous sublinear operator admits extension to the entire space with preservation of linearity and domination. Our main result is that the strong \(\sigma\)-interpolation

Abstract Questions related to the homogenization of the Dirichlet problem for nondivergence elliptic equations of second order with rapidly oscillating \(\varepsilon\)-periodic coefficients are studied. Error estimates of homogenization in the Sobolev spaces of order \(\sqrt\varepsilon\) are obtained. Asymptotic homogenization methods are applied.

Abstract Let \(\Lambda\) be a class of Abelian groups. A group \(A\in\Lambda\) is said to be determined by its endomorphism semigroup \(E^\star(A)\) in the class \(\Lambda\) if every isomorphism \(E^\star(A)\cong E^\star(B)\), where \(B\in\Lambda\), implies the isomorphism \(A\cong B\). The paper describes those Abelian groups in the class \(\mathscr Q\mathscr D_{\mathrm{cd}}\) of completely decomposable

Abstract Let \(f(x)\) be a function belonging to the Lebesgue class \(L^p({\mathbb R}_+)\) on the semiaxis \({\mathbb R}_+=[0,+\infty)\), \(1\le p\le 2\), and let \(\widehat{f}\) be the Fourier–Walsh transform of the function \(f\). In this paper, we give the solution of the following problem: if the function \(f\) belongs to the dyadic Dini–Lipschitz class \(\operatorname{DLip}_\oplus(\alpha,\beta

In my paper, it is necessary to make the following corrections on p. 382. In Example 3 (line 6 from below), the equality bk = µ-k must be replaced by bk = µ-k P(Zk < 0)

The class of generalized bounded variation is considered. For functions from this class, the deviation of the generalized Cesáro means of negative order in the norm of Lr, (1 ≤ r ≤ ∞) is estimated.

A finite set A = {a1 < …

The present paper is devoted to estimating the codimensions cn for the variety of associative algebras given by the identity [x1, …, xl] = 0 for odd l. The characteristic of the ground field is different from 2 and 3. The construction of the so-called extended Grassmann algebra is applied very effectively.

The problem of estimating the distance between two bodies of volume e inside an n-dimensional ball U of unit volume as n → ∞ is considered.

A sharp integral inequality is proved and used to obtain a Sobolev interpolation inequality. Further, a new proof of a Gross-Sobolev logarithmic inequality is constructed on the basis of the Sobolev interpolation inequality.

We show that a comparison of the capacities of suitable condensers gives an inequality for the Schwarzian derivatives of a holomorphic p-valent function defined on the unit disk and ranging in a given domain of the complex plane. If that domain is a disk as well and the function is univalent, then this inequality essentially coincides with the classical Nehari inequality. The cases of equality in the

A logistic equation with state- and parameter-dependent delay is considered. The existence of a nonlocal relaxation periodic solution of this equation is proved for sufficiently large parameter values. The proof is carried out by using the large parameter method. For large parameter values, asymptotic estimates of the main characteristics of this solution are also constructed.

In the present paper, the notion of (additive) local multiplier on the ring of matrices over an arbitrary unital associative ring is introduced and investigated. It is proved that every local left multiplier on the matrix ring over a division ring is a left multiplier. Also, in the present paper, the notion of (additive) local Jordan multiplier on a Jordan ring of symmetric matrices is introduced and

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.