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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]

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 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]

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]

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]

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]

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 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 purpose of this paper is to formulate and prove an L- L analog of Miyachi's theorem for connected nilpotent Lie groups with noncompact center for 2 ≤ p, q ≤ +∞. This allows us to solve the sharpness problem in both Hardy's and Cowling-Price's uncertainty principles. When G is of compact center, we show that the aforementioned uncertainty principles fail to hold. Our results extend those of [1], where G is further assumed to be simply connected, p = 2, and q = +∞. When G is more generally exponential solvable, such a principle also holds provided that the center of G is not trivial. Representation theory and a localized Plancherel formula play an important role in the proofs. [ABSTRACT FROM AUTHOR]

The optimal control of the solutions of the initial-finish problem for Sobolev-type equations is studied. The abstract results obtained in the paper are applied to the linear Hoff model on graphs. [ABSTRACT FROM AUTHOR]

It is proved in the paper that the multiplication operation on an arbitrary E-algebra can be extended to an E-algebra A-morphism. As a corollary, it is proved that every May algebra defined by an E-algebra is a Cartan object in the category of May algebras. [ABSTRACT FROM AUTHOR]

The Hoffman-Singleton graph is the unique strongly regular graph with parameters (50, 7, 0, 1). A well-known hypothesis states that a distance-regular graph in which the neighborhood of each vertex is isomorphic to the Hoffman-Singleton graph has intersection array {50, 42, 1; 1, 2, 50} or {50, 42, 9; 1, 2, 42}. In the present paper, we prove this hypothesis under the assumption that a distance-regular graph is a Terwilliger graph and the graph diameter is at most 5. [ABSTRACT FROM AUTHOR]

In the paper, an analog of the Engel theorem for graded algebras admitting a Lie-type module is proved. Moreover, it is shown that every semisimple algebra of associative type with ordered grading and one-dimensional grading subspaces is the direct sum of two-sided ideals that are simple algebras. [ABSTRACT FROM AUTHOR]

In this paper, we mainly introduce the concept of weak relative [ C, H]-Hopf modules and give the fundamental theorem of weak relative right [ C, H]-Hopf modules. [ABSTRACT FROM AUTHOR]

The main result of this paper is the fact that the fraction of primes p ≤ x satisfying the condition that p − 1 has a prime divisor q > exp(ln x/ln ln x) and the number of prime divisors of q − 1 essentially differ from ln ln( x/n), where n = ( p − 1)/ q, tends to zero as x increases. [ABSTRACT FROM AUTHOR]

The paper is concerned with the problem of inverting block matrices to which the well-known Frobenius— Schur formulas are not applicable. These can be square matrices with four noninvertible square or rectangular blocks as well as square or rectangular matrices with two blocks. With regard to rectangular matrices, the results obtained are a further step in the development of the canonization method, which is used for solving arbitrary matrix equations. [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]

In the paper, the notions of radical of an ideal and radical of a submodule are generalized and described. [ABSTRACT FROM AUTHOR]

In this paper, we study the Darboux transformation of the Darboux-Treibich-Verdier equation. On the basis of this transformation, we construct a generalization of the Darboux transformation to the case of the Heun equation and to other linear ordinary differential equations of second order. Examples are given. [ABSTRACT FROM AUTHOR]

We consider finite groups only. Let ω be a nonempty subset of the set P of all primes, and let f : ω ∪ {ω′} → {formations of groups} and δ : P → {nonempty Fitting formations of groups} be some functions. The formation consisting of all groups G such that $${G \mathord{\left/ {\vphantom {G O}} \right. \kern-\nulldelimiterspace} O}_\omega (G) \in f(\omega ')$$ and $${G \mathord{\left/ {\vphantom {G G}} \right. \kern-\nulldelimiterspace} G}_{\delta (p)} \in f(p)$$ for any p ∈ ω ∩ π ( G) is referred to as an ω-fan formation with direction δ. Let ℌ be some class of groups; an ω-fan formation $$\mathfrak{F}$$ with direction δ is said to be an ℌωδ-critical formation if $$\mathfrak{F}\not \subseteq \mathfrak{H}$$ and any proper ω-fan subformation with direction δ in $$\mathfrak{F}$$ is contained in the class ℌ. In the paper, a description of the structure of the ℌωδ-critical formations is presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider two problems of linear discrete games of pursuit. In each of them, the terms of the sequence defining the pursuer’s control are bounded by some positive number. In the first problem, the terms of the sequence defining the quarry’s control are bounded by some positive number and, in the second problem, the sum of the pth powers of the terms of this sequence is bounded by a given number. For each problem, we obtain a necessary and sufficient condition for the termination of pursuit from all points in space. [ABSTRACT FROM AUTHOR]

This paper is devoted to the proof of the existence of a solution of the Cauchy problem for a system of equations of ultraparabolic type. [ABSTRACT FROM AUTHOR]

In classifying and studying holomorphic automorphisms of surfaces, it is often convenient to pass to tangent model surfaces. This method is well developed for surfaces of type $(n,K)$, where $K\backslash le\; n^2$; for such surfaces, tangent quadrics (i.e., surfaces determined by equations of degree $2$) with a number of useful properties have been constructed. In recent years, for surfaces of higher codimensions, tangent model surfaces of degrees $3$ and $4$ with similar properties were constructed. However, this construction imposes new constraints on the codimension. In this paper, the same method is applied to surfaces of even higher codimension. Model surfaces of the fifth degree are constructed. It is shown that all the basic useful properties of model surfaces are preserved, in spite of a number of technical difficulties. [ABSTRACT FROM AUTHOR]

In this paper, we study singular parabolic equations with “quadratic nonlinearity.” We consider questions of unique solvability, of stabilization of solutions at infinity, and of the presence of positive solutions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain two-sided estimates with sharp constants of the sums of sine series with a convex sequence of coefficients tending to zero. [ABSTRACT FROM AUTHOR]

Let $\backslash frak\; B$ ($\backslash frak\; D$) be the variety of associative (special Jordan, respectively) algebras over an infinite field of characteristic 2 defined by the identity $((((x\_1,x\_2),x\_3),\; ((x\_4,x\_5),x\_6)),$$(x\_7,x\_8))=\backslash nomathbreak\; 0$ ($((x\_1x\_2\backslash cdot\; x\_3)(x\_4x\_5\backslash cdot\; x\_6))(x\_7x\_8)=\backslash nomathbreak\; 0$, respectively). In this paper, we construct infinite independent systems of identities in the variety $\backslash frak\; B$ ($\backslash frak\; D$, respectively). This implies that the set of distinct nonfinitely based subvarieties of the variety $\backslash frak\; B$ ($\backslash frak\; D$) has the cardinality of the continuum and that there are algebras in $\backslash frak\; B$ ($\backslash frak\; D$) with undecidable word problem. [ABSTRACT FROM AUTHOR]

In this paper, we study necessary and sufficient conditions for functions to be approximated uniformly on plane compact sets by polynomial solutions to second-order homogeneous elliptic equations with constant coefficients. Sufficient conditions for approximability are of reductive character, i.e., the possibility of approximating on some (simpler) parts of the compact set implies approximability on the entire compact set. [ABSTRACT FROM AUTHOR]