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The present paper is devoted to the Cauchy problem of inhomogeneous convolution equations of a fairly general nature. To solve the problems posed here, we apply the operator method proposed in some earlier papers by the author. The solutions of the problems under consideration are found using an effective method in the form of well-convergent vector-valued power series. The proposed method ensures the continuity of the obtained solutions with respect to the initial data and the inhomogeneous term of the equation. [ABSTRACT FROM AUTHOR]

The aim of the paper is to study spaces of multipliers acting from the Bessel potential space H (ℝ) to the other Bessel potential space H (ℝ). We obtain conditions ensuring the equivalence of uniform and standard multiplier norms on the space of multipliers In the case , the space M[ H (ℝ) → H (ℝ) can be described explicitly. Namely, we prove in this paper that the latter space coincides with the space H (ℝ) of uniformly localized Bessel potentials introduced by Strichartz. It is also proved that if both smoothness indices s and t are nonnegative, then such a description is possible only for the given values of the indices. [ABSTRACT FROM AUTHOR]

For rational functions , where is a polynomial of degree at the most and , with we use simple but elegant techniques to strengthen generalizations of certain results which extend some widely known polynomial inequalities of Erdős-Lax and Turán to rational functions . In return these reinforced results, in the limiting case, lead to the corresponding refinements of the said polynomial inequalities. As an illustration and as an application of our results, we obtain some new improvements of the Erdős-Lax and Turán type inequalities for polynomials. These improved results take into account the size of the constant term and the leading coefficient of the given polynomial. As a further factor of consideration, during the course of this paper we will demonstrate how some recently obtained results could have been proved without invoking the results of Dubinin [Distortion theorems for polynomials on the circle, Sb. Math. 191(12) (2000) 1797–1807]. [ABSTRACT FROM AUTHOR]

In the paper by E. M. Apfelbaum and V. S. Vorobiev [1], it was shown that the critical isotherms of real pure gases coincide with the corresponding isotherms of the classical distribution of Bose-Einstein type for fractional dimension (fractional number of degrees of freedom). For isotherms with T < T, this coincidence no longer occurs, and for some gases the discrepancy is considerable. In the paper, the law of preference of cluster formation over passage to liquid state is used to deduce equations that give a good coincidence for these isotherms. [ABSTRACT FROM AUTHOR]

The theorem proved in this paper establishes conditions under which a Banach space X is an Asplund space (i.e., its dual space is a space with the Radon-Nikodym (RN) property). The theorem is formulated in terms of the existence of a supersequentially compact set in ( B( X **), ω *), where B( X **) stands for the unit ball of the second dual of X and ω* for the weak topology on the ball. The example presented in the paper shows that one cannot get rid of some restrictive conditions in the theorem in general. [ABSTRACT FROM AUTHOR]

In the present paper we establish the existence of a phase transition for one-dimensional the countable state p-adic Potts model. To establish such results, we investigate an infinite dimensional nonlinear p-adic operator associated with the model. It turns out that the finding condition does not depend on values of the prime p, and therefore, an analogous fact is not true when the number of spins is finite. [ABSTRACT FROM AUTHOR]

In the paper [1], V. O. Manturov introduced the groups Gkn depending on two natural parameters n > k and naturally related to topology and to the theory of dynamical systems. The group G2n, which is the simplest part of Gkn, is isomorphic to the group of pure free braids on n strands. In the present paper, we study the groups G2n supplied with additional structures-parity and points; these groups are denoted by G2n,p and G2n,d. First,we define the groups G2n,p and G2n,d, then study the relationship between the groups G2n, G2n,p, and G2n,d. Finally, we give an example of a braid on n + 1 strands, which is not the trivial braid on n + 1 strands, by using a braid on n strands with parity. After that, the author discusses links in Sg × S1 that can determine diagrams with points; these points correspond to the factor S1 in the product Sg × S1. [ABSTRACT FROM AUTHOR]

We investigate the Hyers–Ulam–Rassias stability property of a quadratic functional equation. The analysis is done in the context of modular spaces. The type of stability considered here is very general in character which has been considered in various domains of mathematics. The speciality of the functional equation considered here is that it has a geometrical background behind its introduction. We approach the problem by applying a fixed point method for which a version of the contraction mapping principle in modular spaces is utilized. Also the results in this paper are established without using some familiar conditions on modular spaces. [ABSTRACT FROM AUTHOR]

The paper focuses on the right and left eigenvectors of a network matrix that belong to the largest eigenvalue. It is shown that each of vector entries measures the walk centrality of the corresponding node’s position in the network’s link structure and of the positions of the node’s adjacent nodes; as a result, it indicates to which degree the node can be associated with the structure’s core, i.e., the structural coreness of the node. The relationship between the vectors’ coordinates and the position of the nodes, as well as the actual computation of the coordinates, is based on an iterative computational scheme known as the power method. The paper studies the method’s convergence for networks of different structure. Some possible applications are discussed. The paper also includes a numerical example dealing with a real network of 197 nodes and 780 links. [ABSTRACT FROM AUTHOR]

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk { z : | z| < 1} assuming that the Taylor coefficients of the function log( zf′( z)/ f( z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle | z| = r of the squared modulus of the function zf′( z)/ f( z). [ABSTRACT FROM AUTHOR]

In the present paper, we prove a fixed-point theorem for completely continuous multivalued mappings defined on a bounded convex closed subset X of the Hilbert space H which satisfies the tangential condition $$F(x) \cap (x + T_X (x)) \ne \emptyset$$ , where T X( x) is the cone tangent to the set X at a point x. The proof of this theorem is based on the method of single-valued approximations to multivalued mappings. In this paper, we consider a simple approach for constructing single-valued approximations to multivalued mappings. This approach allows us not only to simplify the proofs of already-known theorems, but also to obtain new statements needed to prove the main theorem in this paper. [ABSTRACT FROM AUTHOR]

The article reports that the Turan problem was stated by mathematician P. Turán in 1970 in connection with possible applications in the number theory. Further progress in the Turán problem was made in the papers of mathematicians D.V. Gorbachev and A.S. Manoshina. They've proved the Popov's conjecture and reduced the Turán problem for a rational "h" to a finite dimensional external problem and evaluated the result for it. In this article the Turán problem is solved for all rational "h" by considering several linear programming problems.

In this paper, we study the behavior of solutions of a semilinear elliptic equation in the exterior of a compact set as $|x|\backslash to\; \backslash nomathbreak\; \backslash infty$. Such equations were considered by many authors (for example, Kondrat'ev, Landis, Oleinik, Veron, etc.). In the present paper, we study the case in which in the equation contains lower terms. The coefficients of the lower terms are arbitrary bounded measurable functions. It is shown that the solutions of the equation tend to zero as $|x|\backslash to\; \backslash nomathbreak\; \backslash infty$. [ABSTRACT FROM AUTHOR]

The first part of this paper is concerned with the proof of a discrete analog of the Poisson summation formula. In the second part, we describe an elementary proof of a functional equation for the function θ(t), based on the summation formula derived in the paper. [ABSTRACT FROM AUTHOR]

The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., 'Remarks on 'Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings',' Math. Comput. Modelling 54, 1467-1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

This paper is devoted to the determination of the optimal arguments in the exact Jackson inequality in the space L on the Euclidean space with power weight equal to the product of the moduli of the coordinates with nonnegative powers. The optimal arguments are studied depending on the geometry of the spectrum of the approximating entire functions and the neighborhood of zero in the definition of the modulus of continuity. The optimal arguments are obtained in the case where the first skew field is a l-ball for 1 ≤ p≤ 2, and the second is a parallelepiped. [ABSTRACT FROM AUTHOR]

Local polynomial models of real submanifolds of complex spaces were constructed and studied in a series of papers. Among the main features of model surfaces, there is the property that the dimension of the local group of holomorphic symmetries of a germ does not exceed that of the same group of the tangent model surface of this germ. In the paper, this assertion is rendered much stronger; namely, it is proved that the connected component of the identity element in the symmetry group of a nondegenerate germ is isomorphic as a Lie group to a subgroup of the symmetry group of its tangent model surface. [ABSTRACT FROM AUTHOR]

In the paper, we propose a method for proving the unconditional basis property of eigen- and associated functions of an integro-differential operator defined on a nondense domain of definition. In particular, we obtain a new simpler proof of the unconditional basis property of eigenand associated functions of the spectral Orr-Sommerfeld problem, well-known in hydromechanics, which reduces to the eigenvalue problem for the operator under study. [ABSTRACT FROM AUTHOR]

Denote by C( X) the partially ordered (PO) set of all continuous epimorphisms of a space X under the natural identification of homeomorphic epimorphisms. The following homeomorphism theorem for bicompacta is implicitly contained in Magill's 1968 paper: two bicompacta X and Y are homeomorphic if and only if the PO sets C( X) and C( Y) are isomorphic. In the present paper, Magill's theorem is extended to the category of mappings in which the role of bicompacta is played by perfect mappings. The results are obtained in two versions, namely, in the category TOP (of triangular commutative diagrams) and in the category MAP (of quadrangular commutative diagrams). [ABSTRACT FROM AUTHOR]

In the present paper, the spinodal is constructed by using the values of the isotherm of a new ideal gas at the point µ = 0 and as µ = −∞ on the ( Z, P)-diagram. For a nonideal gas, a generalization of the type of Bogoliubov-Vlasov self-consistent field is given if the potential of pairwise interaction is known. A 'two-liquid' model of the supercritical region, i.e., a superfluid 'liquid' (molecules-monomers) and a normal 'liquid' (clusters), is constructed. An application to the transport problems is given. [ABSTRACT FROM AUTHOR]

In the paper, quantitative characteristics of identities of group algebras of finite groups are studied. A series of relations connecting the PI-exponents of identities with involution and Lie identities of the group algebra itself and of its Lie subalgebra of skew-symmetric elements are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold. [ABSTRACT FROM AUTHOR]

In the paper, using the Adyan-Lysenok theorem claiming that, for any odd number n ≥ 1003, there is an infinite group each of whose proper subgroups is contained in a cyclic subgroup of order n, it is proved that the set of groups with this property has the cardinality of the continuum (for a given n). Further, it is proved that, for m ≥ k ≥ 2 and for any odd n ≥ 1003, the m-generated free n-periodic group is residually both a group of the above type and a k-generated free n-periodic group, and it does not satisfy the ascending and descending chain conditions for normal subgroups either. [ABSTRACT FROM AUTHOR]

In this paper, we consider algorithms for constructing n-terms approximations with nonnegative coefficients. The convergence theorem is proved for a “positive” analog of the Pure Greedy Algorithm. We establish a condition on the sequence of weakness coefficients which is sufficient for the convergence of the Positive Weak Greedy Algorithm. This condition is also necessary for the class of monotone sequences. [ABSTRACT FROM AUTHOR]

In this paper, we study conditions for the existence of a function satisfying constraints on its value at each point and on its derivative. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Laplacian spectrum of an infinite countable graph in a different way than in the papers by B. Mohar. We prove some basic properties of this type of spectrum. The approach used is in line with our approach to the limiting spectrum of an infinite graph. The technique of the Laplacian spectrum of finite graphs is essential in this approach. [ABSTRACT FROM AUTHOR]

In the paper, the spaces of weakly additive τ-smooth and Radon functionals are investigated. It is proved that the functors of weakly additive τ-smooth and Radon functionals weakly preserve the density of Tychonoff spaces, and the functor of weakly additive τ-smooth functionals forms a monad in the category of Tychonoff spaces and their continuous mappings. Examples and remarks are given showing that these functors fail to satisfy certain Shchepin normality conditions. Problems having positive solutions for normal functors are presented. [ABSTRACT FROM AUTHOR]

The paper deals with averaging problems for parabolic equations. We prove that exponential dichotomy is preserved without any assumption concerning the almost-periodicity of the coefficients. [ABSTRACT FROM AUTHOR]

The theorem proved in this paper gives a congruence for the traces of powers of an algebraic integer for the case in which the exponent of the power is a prime power. The theorem implies a congruence in Gauss’ form for the traces of the sums of powers of algebraic integers, generalizing many familiar versions of Fermat’s little theorem. Applied to the traces of integer matrices, this gives a proof of Arnold’s conjecture about the congruence of the traces of powers of such matrices for the case in which the exponent of the power is a prime power. [ABSTRACT FROM AUTHOR]

Suppose that K is a compact set in the open complex plane. In this paper, we prove an existence criterion for an estimate of Markov-Bernstein type for derivatives of a rational function R( z) at any fixed point z0 ∈ K. We prove that, for a fixed integer s, the estimate of the form | R( s) ( z0)| ≤ C( K, z0, s) n‖ R‖ C( K), where R is an arbitrary rational function of degree n without poles on K and C is a bounded function depending on three arguments K, z0, and s, holds if and only if the supremum over z in the complement of K is finite. Under this assumption, C is less than or equal to const · s!ω( K, z0, s). [ABSTRACT FROM AUTHOR]

In this paper, we construct fast discrete transforms of wavelet type with an arbitrary number of zero moments for nonuniform grids. We obtain explicit formulas for the parameters defining the wavelet transform. [ABSTRACT FROM AUTHOR]

It follows from results of A. Yudin, V. Yudin, E. Belinskii, and I. Liflyand that if $m\backslash ge\; \backslash nomathbreak\; 2$ and a $2\backslash pi$-periodic (in each variable) function $f(\backslash boldkey\; x)\backslash in\; C(T^m)$ belongs to the Nikol'skii class $h\_\backslash infty^\{(m-1)/2\}(T^m)$, then its multiple Fourier series is uniformly convergent over hyperbolic crosses. In this paper, we establish the finality of this result. More precisely, there exists a function in the class $H\_\backslash infty^\{(m-1)/2\}(T^m)$ whose Fourier series is divergent over hyperbolic crosses at some point. [ABSTRACT FROM AUTHOR]

In this paper, we consider the linear space of minimal differential operators with constant coefficients which are dominated by systems of minimal operators acting in spaces with uniform norm. In terms of domination conditions, we prove the quasiellipticity test for a given operator; this criterion generalizes a similar result of De Leeuw and Mirkil to elliptic operators. [ABSTRACT FROM AUTHOR]

Interpretation of logical connectives as operations on sets of binary strings is considered; the complexity of a set is defined as the minimum of Kolmogorov complexities of its elements. It is readily seen that the complexity of a set obtained by the application of logical operations does not exceed the complexity of the conjunction of their arguments (up to an additive constant). In this paper, it is shown that the complexity of a set obtained by a formula $\backslash Phi$ is small (bounded by a constant) if $\backslash Phi$ is deducible in the logic of weak excluded middle, and attains the specified upper bound otherwise. [ABSTRACT FROM AUTHOR]

Let $G$ be a group, let $A$ be an Abelian group, and let $n$ be an integer such that $n\backslash ge\; -1$. In the paper, the sets $\backslash Phi\_n(G,A)$ of functions from $G$ into $A$ of degree not greater than $n$ are studied. In essence, these sets were introduced by Logachev, Sal'nikov, and Yashchenko. We describe all cases in which any function from $G$ into $A$ is of bounded (or not necessarily bounded) finite degree. Moreover, it is shown that if $G$ is finite, then the study of the set $\backslash Phi\_n(G,A)$ is reduced to that of the set $\backslash Phi\_n(G/O^p(G),A\_p)$ for primes $p$ dividing $|G/G\text{'}|$. Here $O^p(G)$ stands for the $p$-coradical of the group $G$, $A\_p$ for the $p$-component of $A$, and $G\text{'}$ for the commutator subgroup of $G$. [ABSTRACT FROM AUTHOR]

Let $C$ be an Abelian group. An Abelian group $A$ in some class $\backslash Cal\; X$ of Abelian groups is said to be $\backslash sideset\_C\backslash and\backslash to\; H$-definable in the class $\backslash Cal\; X$ if, for any group $B\backslash in\; \backslash Cal\; X$, it follows from the existence of an isomorphism $\backslash operatorname\{Hom\}(C,A)\backslash cong\backslash operatorname\{Hom\}(C,B)$ that there is an isomorphism $A\backslash cong\; B$. If every group in $\backslash Cal\; X$ is $\{\}\_CH$-definable in $\backslash Cal\; X$, then the class $\backslash Cal\; X$ is called an $\{\}\_CH$-class. In the paper, conditions are studied under which a class of completely decomposable torsion-free Abelian groups is a $\backslash sideset\_C\backslash and\backslash to\; H$-class, where $C$ is a completely decomposable torsion-free Abelian group. [ABSTRACT FROM AUTHOR]

In this paper, we consider equations of the form $\backslash ddot\; x+B\backslash dot\; x+Ax=\backslash nomathbreak\; 0$, where $x=x(t)$ is a function with values in the Hilbert space $\backslash Cal\; H$, the operator $B$ is symmetric, and the operator $A$ is uniformly positive and self-adjoint in $\backslash Cal\; H$. The linear operator $\backslash Cal\; T$ generating the $C\_0$-semigroup in the energy space $\backslash Cal\; H\_1\backslash times\; \backslash Cal\; H$ is associated with this equation. We prove that this semigroup is exponentially stable if the operator $B$ is uniformly positive and the operator $A$ dominates $B$ in the sense of quadratic forms. [ABSTRACT FROM AUTHOR]

The notions of "tropical mathematics" and "subtropical mathematics" are studied. The main principles of tropical analysis and examples of their application to various problems are considered. [ABSTRACT FROM AUTHOR]

In this paper, some converses of Jessen's inequality, in terms of the time scale calculus, are proved. The obtained results are used to derive new converse inequalities for generalized means, power means and Hölder's inequality. [ABSTRACT FROM AUTHOR]

It was a question of Taibleson, open for a long time that the almost everywhere convergence of Fejér (or ( C, 1)) means of Fourier series of integrable functions with respect the character system of the group of 2-adic integers. This question was answered by Gá t in 1997. The aim of this paper is to investigate the maximal operator of the sup |σ|. Among other things, we prove that this operator is bounded from the Hardy space H to the Lebesgue space L if and only if 1/2 < p < ∞. The two-dimensional maximal operator is also discussed. [ABSTRACT FROM AUTHOR]

Earlier, for odd n, the author described unitary n × n matrices U with the following property: if H is a Hankel matrix, then U* HU is a Hankel matrix as well. In the present paper, it is shown that this description also holds for even n starting from n = 4. [ABSTRACT FROM AUTHOR]

Formulas for the regularized trace of the one-dimensional non-self-adjoint Dirac operator with L-potential are obtained. The cases of periodic and antiperiodic boundary conditions as well as of the Dirichlet boundary conditions are considered. The formulas are obtained by using the method of similar operators on the basis of results from the papers [1] and [2]. [ABSTRACT FROM AUTHOR]

In the general case, the order of a finite nonidentity group G is substantially larger than the squared degree of every irreducible character Θ of G, i.e., Θ(1)< G. In the present paper, we study finite groups with an irreducible character Θ such that . [ABSTRACT FROM AUTHOR]

This paper deals with the asymptotic behavior of the integral (here the minimum is taken over integers q and ∥·∥ denotes the distance to the nearest integer). [ABSTRACT FROM AUTHOR]

The problem of enumerating and denumerating words generated by Dyck grammars arises in the work of compilers for high-level programming languages and a number of other applications. The present paper proposes an algorithm for the fast enumeration and denumeration of words of Dyck languages; the complexity of this algorithm per one symbol of enumerated words is O(log n log log n) bit operations, provided that the Schönhage-Strassen multiplication and division algorithmis used. The well-knownmethods applied earlier possess complexity O( n) per one symbol of enumerated words. The construction of the proposed algorithm is based on the Ryabko method. [ABSTRACT FROM AUTHOR]

In the paper,we study algebras having n bilinearmultiplication operations [InlineMediaObject not available: see fulltext.]: A× A → A, s = 1, ..., n, such that ( a[InlineMediaObject not available: see fulltext.] b) [InlineMediaObject not available: see fulltext.] c = a[InlineMediaObject not available: see fulltext.] ( b[InlineMediaObject not available: see fulltext.] c), s, r = 1,..., n, a, b, c ∈ A. The radical of such an algebra is defined as the intersection of the annihilators of irreducible A-modules, and it is proved that the radical coincides with the intersection of the maximal right ideals each of which is s-regular for some operation [InlineMediaObject not available: see fulltext.]. This implies that the quotient algebra by the radical is semisimple. If an n-tuple algebra is Artinian, then the radical is nilpotent, and the semisimple Artinian n-tuple algebra is the direct sum of two-sided ideals each of which is a simple algebra. Moreover, in terms of sandwich algebras, we describe a finite-dimensional n-tuple algebra A, over an algebraically closed field, which is a simple A-module. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of global asymptotic stability of the zero solution of a system of autonomous differential equations. A proposed method for studying this problem is based on the use of an auxiliary positive definite function whose derivative can be sign-alternating along solutions of the system. [ABSTRACT FROM AUTHOR]

Open discrete annular Q-mappings with respect to the p-modulus in ℝ, n ≥ 2, are considered in this paper. It is established that such mappings are finite Lipschitz for n − 1 < p < n if the integral mean value of the function Q( x) over all infinitesimal balls B( x, ɛ) is finite everywhere. [ABSTRACT FROM AUTHOR]

It is well known that the supercritical state of a gas has great dissolving capacity. In this paper, the mathematical reason for this phenomenon is studied in great detail. [ABSTRACT FROM AUTHOR]

Let A, K, and H be subgroups of a group G and K ≤ H. Then we say that A covers the pair ( K, H) if AH = AK and avoids the pair ( K, H) if A ∩ H = A ∩ K. A pair ( K, H) in G is said to be maximal if K is a maximal subgroup of H. In the present paper, we study finite groups in which some subgroups cover or avoid distinguished systems of maximal pairs of these groups. In particular, generalizations of a series of known results on (partial) CAP-subgroups are obtained. [ABSTRACT FROM AUTHOR]