Estimates of generalized Chebyshev function on GL m

In this paper, we study the generalized Chebyshev function related to automorphic L-functions of $GL_m \left( {\mathbb{A}_\mathbb{Q} } \right)$ , and estimate its asymptotic behavior with respect to the parameters of the original automorphic objects.     

A formal theory of generalized intermediate syllogisms

In this paper, we continue developing the formal theory of intermediate quantifiers (expressions such as most, few, almost all, a lot of, many, a great deal of, a large part of, a small part of). The theory is a fuzzy-logic formalization of the concept introduced by Peterson in his book. We will syntactically prove that 105 generalized Aristotle's syllogisms introduced in this book are valid in our theory. At the same time, we will also prove that syllogisms listed there as invalid are invalid also in our theory. Therefore, we believe that our theory provides a reasonable mathematical model of the generalized syllogistics.     

Numerical technique based on generalized Laguerre and shifted Chebyshev polynomials

In this study, we present a numerical scheme for solving a class of fractional partial differential equations. First, we introduce psi -Laguerre polynomials like psi-shifted Chebyshev polynomials and employ these newly introduced polynomials for the solution of space-time fractional differential equations. In our approach, we project these polynomials to develop operational matrices of fractional integration. The use of these orthogonal polynomials converts the problem under consideration into a system of algebraic equations. The solution of this system provide us the desired results. The convergence of the proposed method is analyzed. Finally, some illustrative examples are included to observe the validity and applicability of the proposed method.     

N-symmetric Chebyshev polynomials in a composite model of a generalized oscillator

We continue to study a composite model of a generalized oscillator generated by an N-periodic Jacobi matrix. The foundation of the model is a system of orthogonal polynomials connected to this matrix for N = 3, 4, 5. We show that such polynomials do not exist for N ?? 6.     

Shape preserving properties of generalized Bernstein operators on Extended Chebyshev spaces

We study the existence and shape preserving properties of a generalized Bernstein operator B _n fixing a strictly positive function f ₀, and a second function f ₁ such that f ₁/f ₀ is strictly increasing, within the framework of extended Chebyshev spaces U _n . The first main result gives an inductive criterion for existence: suppose there exists a Bernstein operator B _n : C[a, b] → U _n with strictly increasing nodes, fixing f₀, f₁ ? U_n{f_{0}, f_{1} \in U_{n}} . If U_n ì U_{n + 1}{U_{n} \subset U_{n + 1}} and U _n+1 has a non-negative Bernstein basis, then there exists a Bernstein operator B _n+1 : C[a, b] → U _n+1 with strictly increasing nodes, fixing f ₀ and f ₁. In particular, if f ₀, f ₁, . . . , f _n is a basis of U _n such that the linear span of f ₀, . . . , f _k is an extended Chebyshev space over [a, b] for each k = 0, . . . , n, then there exists a Bernstein operator B _n with increasing nodes fixing f ₀ and f ₁. The second main result says that under the above assumptions the following inequalities hold

A generalized central limit theorem in infinite ergodic theory

We prove a generalized central limit theorem for dynamical systems with an infinite ergodic measure which induce a Gibbs–Markov map on some subset, provided the return time to this subset has regularly varying tails. We adapt a method designed by Csáki and Földes for observables of random walks to show that the partial sums of some functions of the system—the return time and the observable—are asymptotically independent. Some applications to random walks and Pomeau–Manneville maps are discussed.     

A new generalized Wick theorem in conformal field theory

We describe a new generalized Wick theorem for interacting fields in two-dimensional conformal field theory and briefly discuss its relation to the Borcherds identity and its derivation by an analytic method. We give examples of calculating operator product expansions using the generalized Wick theorem including fermionic fields.     

Chebyshev Wavelet collocation method for solving generalized Burgers–Huxley equation

In this paper, new and efficient numerical method, called as Chebyshev wavelet collocation method, is proposed for the solutions of generalized Burgers–Huxley equation. This method is based on the approximation by the truncated Chebyshev wavelet series. By using the Chebyshev collocation points, algebraic equation system has been obtained and solved. Approximate solutions of the generalized Burgers–Huxley equation are compared with exact solutions. These calculations demonstrate that the accuracy of the Chebyshev wavelet collocation solutions is quite high even in the case of a small number of grid points. Copyright © 2015 John Wiley & Sons, Ltd.     

A vector Chebyshev algorithm

We consider polynomials orthogonal relative to a sequence of vectors and derive their recurrence relations within the framework of Clifford algebras. We state sufficient conditions for the existence of a system of such polynomials. The coefficients in the above relations may be computed using a cross-rule which is linked to a vector version of the quotient-difference algorithm, both of which are proved here using designants. An alternative route is to employ a vector variant of the Chebyshev algorithm. This algorithm is established and an implementation presented which does not require general Clifford elements. Finally, we comment on the connection with vector Padé approximants. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the generalized Chebyshev polynomials corresponding to plane trees of diameter 4

The combinatorial classification of plane trees by the number of realizations of their valency sets has distinguished some special classes of plane trees. One of them, the plane trees of diameter 4, turned out to be a very interesting object of investigation from the Galois action point of view. In this paper, we present equation sets for some subclasses of trees of diameter 4, calculate discriminants of the corresponding generalized Chebyshev polynomials, some related polynomials, and their fields of definitions, and use this to get some information about the Galois action on plane trees. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 6, pp. 19–33, 2007.     

Toward a generalized computability theory

Translated fromAlgebra i Logika, Vol. 32, No. 4, pp. 349–386, July–August, 1993.     

A unified theory of generalized closed sets in weak structures

A new kind of sets called generalized w-closed (briefly gw-closed) sets is introduced and studied in a topological space by using the concept of weak structures introduced by á.?Császár in?[6]. The class of all gw-closed sets is strictly larger than the class of all w-closed sets. Furthermore, g-closed sets (in the sense of N.?Levine?[17]) is a special type of gw-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of w-regular and w-normal spaces have been given.     

A counterexample to uniqueness of generalized characteristics in Hamilton-Jacobi theory

The notion of generalized characteristics plays a pivotal role in the study of propagation of singularities for Hamilton-Jacobi equations. This note gives an example of nonuniqueness of forward generalized characteristics emanating from a given point.