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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]

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]

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]

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]

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]

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]

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]

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]

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]

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,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 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]

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]