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Abstract: We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials. [Copyright &y& Elsevier]

In a recent paper [1] a number of numerical schemes for the shallow water equations based on a conservative linearization are analyzed. In particular, it is established that the schemes are related through the use of a source term. In this paper this technique is applied to the Euler equations, and further analysis suggests a new formulation of an existing scheme having the same key properties. [Copyright &y& Elsevier]

Abstract: In this paper, we shall study the uniqueness problems of meromorphic functions sharing a small function. Our results improve or generalize many previous results on value sharing of meromorphic functions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a scheduling problem for automated guided vehicles in container terminals is defined and formulated as a Minimum Cost Flow model. This problem is then solved by a novel algorithm, NSA+, which extended the standard Network Simplex Algorithm (NSA). Like NSA, NSA+ is a complete algorithm, which means that it guarantees optimality of the solution if it finds one within the time available. To complement NSA+, an incomplete algorithm Greedy Vehicle Search (GVS) is designed and implemented. The NSA+ and GVS are compared and contrasted to evaluate their relative strength and weakness. With polynomial time complexity, NSA+ can be used to solve very large problems, as verified in our experiments. Should the problem be too large for NSA+, or the time available for computation is too short (as it would be in dynamic scheduling), GVS complements NSA+. [ABSTRACT FROM AUTHOR]

Abstract: The Wiener index of a connected graph is defined as the sum of distances between all pairs of vertices. The Wiener polynomial has the property that its first derivative evaluated at equals the Wiener index, i.e. . The hyper-Wiener polynomial satisfies the condition , the hyper-Wiener index of . In this paper we introduce a new generalization of the Wiener index and of the Wiener polynomial. One of the advantages of our definitions is that one can handle the Wiener and hyper-Wiener index (respectively polynomial) with the same formula, i.e. , , and . [Copyright &y& Elsevier]

Abstract: Imposing constraints is a way to incorporate information into the sequence alignment procedure. In this paper, a general model for constrained alignment is proposed so that analyses admitted are more flexible and that different pattern definitions can be treated in a simple unified way. We give a polynomial time algorithm for pairwise constrained alignment for the generalized formulation, and prove the inapproximability of the problem when the number of sequences can be arbitrary. In addition, previous works deal only with the case that the patterns in the constraint have to occur in the output alignment in the same order as that specified by the input. It is of both theoretical and practical interest to investigate the case when the order is no longer limited. We show that the problem is not approximable even when the number of sequences is two. We also give the NPO-completeness results for the problems with bounds imposed on the objective function value. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to derive quadrature formulae of Gauss type based on Euler identities. First, we derive quadrature formulae where the integral over [0,1] is approximated by values of the function in three points: and . As special cases, the Gauss 2-point formula, Simpson’s formula, dual Simpson’s formula and Maclaurin’s formula are obtained. Next, corrected Gauss 2-point formulae are derived and finally, the Gauss 3-point formulae and the corrected Gauss 3-point formulae are considered. We call “corrected” such quadrature formulae where the integral is approximated both with the values of the integrand in certain points and the values of its first derivative in the end points of the interval. Corrected formulae have a degree of exactness higher than the adjoint original formulae. [Copyright &y& Elsevier]

This paper develops and demonstrates a guaranteed a-priori error bound for the Taylor polynomial approximation of any degree to the solution of initial value ordinary differential equations. The error bound is explicit and does not require upper bounds on the potentially complicated and intrinsically unknown right-hand side nor on any of its higher-order derivatives as with existing bounds, and thus it provides a valuable tool for the numerous applications in which initial value ode problems arise and for which approximate solutions must be sought. [Copyright &y& Elsevier]

Abstract: In this paper we investigate the polynomial identities of an important subalgebra of the PI-algebra UT 3 of 3×3 upper triangular matrices in characteristic zero. Moreover we prove that the five algebras which were used in Giambruno and La Mattina [A. Giambruno, D. La Mattina, PI-algebras with slow codimension growth, J. Algebra 284 (2005) 371–391] to classify (up to PI-equivalence) the algebras whose sequence of codimensions is bounded by a linear function generate the only five minimal varieties of quadratic growth. [Copyright &y& Elsevier]

Abstract: In this paper we study the multigraded Hilbert and Poincaré–Betti series of , where is the ring of polynomials in indeterminates divided by the monomial ideal . There is a conjecture about the multigraded Poincaré–Betti series by Charalambous and Reeves which they proved in the case where the Taylor resolution is minimal. We introduce a conjecture about the minimal -free resolution of the residue class field and show that this conjecture implies the conjecture of Charalambous and Reeves and, in addition, gives a formula for the Hilbert series. Using Algebraic Discrete Morse theory, we prove that the homology of the Koszul complex of with respect to is isomorphic to a graded commutative ring of polynomials over certain sets in the Taylor resolution divided by an ideal of relations. This leads to a proof of our conjecture for some classes of algebras . We also give an approach for the proof of our conjecture via Algebraic Discrete Morse theory in the general case. The conjecture implies that is Golod if and only if the product (i.e. the first Massey operation) on the Koszul homology is trivial. Under the assumption of the conjecture we finally prove that a very simple purely combinatorial condition on the minimal monomial generating system of implies Golodness for . [Copyright &y& Elsevier]

Abstract: Let the space be divided into unit squares where a polyomino is a finite, connected set of unit squares. In this paper, we give a necessary and sufficient condition on tessellating polyominos by observing an unexpected relation between such tessellations and systems of arithmetic progressions. [Copyright &y& Elsevier]

Abstract: In this paper, the authors establish some explicit formulas and representations for the Nörlund polynomial B n (χ) and b n (χ) Several identities involving Bernoulli numbers, Nörlund numbers, Stirling numbers and the associated Stirling numbers are also presented. [Copyright &y& Elsevier]

Abstract: In this paper we consider polynomials orthogonal with respect to an oscillatory weight function on , where is an integer. The existence of such polynomials as well as several of their properties (three-term recurrence relation, differential equation, etc.) are proved. We also consider related quadrature rules and give applications of such quadrature rules to some classes of integrals involving highly oscillatory integrands. [Copyright &y& Elsevier]

Abstract: We establish Mehler–Heine-type formulas for orthogonal polynomials related to rational modifications of Hermite weight on the real line and for Hermite–Sobolev orthogonal polynomials. These formulas give us the asymptotic behaviour of the smallest zeros of the corresponding orthogonal polynomials. Furthermore, we solve a conjecture posed in a previous paper about the asymptotics of the smallest zeros of the Hermite–Sobolev polynomials as well as an open problem concerning the asymptotics of these Sobolev orthogonal polynomials. [Copyright &y& Elsevier]

Abstract: This paper deals with the classes of strong distribution functions defined on the interval , , where . The classification is such that the distribution function has a (reciprocal) symmetry, depending on , about the point . We consider properties of the L-orthogonal polynomials associated with . Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some . [Copyright &y& Elsevier]

Abstract: Starting from the coefficients of the power expansions for the Dawson''s integral both around the origin and infinity, a linear functional acting on the space of Laurent polynomials is defined. In this paper, properties of this functional are studied in connection with certain sequences of orthogonal Laurent polynomials and two-point Padé approximants. [Copyright &y& Elsevier]

Abstract: In (simple) Pál-type interpolation the problem consists of finding a polynomial of degree that has prescribed values at, say, n pairwise distinct points and prescribed values for the rth derivative at (another) set of m distinct points. The problem is named regular if it has a unique solution for any set of data; this is equivalent to the homogeneous problem (all prescribed values are 0) having the trivial solution only. In this paper the effect of interchanging the value-nodes and the derivative-nodes on the regularity of the problem is studied for several sets of nodes. [Copyright &y& Elsevier]

Abstract: Let R be a ring and be a polynomial in noncommutative indeterminates with coefficients from and zero constant. The ring R is said to be an f-ring if for all of R and a virtually f-ring if for every n infinite subsets (not necessarily distinct) of R, there exist n elements such that . Let be the ‘smallest’ ring (in some sense) with identity containing R such that . Then denote by the subring generated by the identity of and denote by the image of f in (the ring of polynomials with coefficients in in commutative indeterminates ). In this paper, we show that if R is a left primitive virtually f-ring such that , then R is finite. Using this result, we prove that an infinite semisimple virtually f-ring R is an f-ring, if the subring of generated by the coefficients of is equal to ; and we also prove that if , where , then every infinite virtually f-ring with identity is a commutative f-ring. Finally we show that a commutative Noetherian virtually f-ring R with identity is finite if the subring generated by the coefficients of is . [Copyright &y& Elsevier]

Systems of algebraic equations with interval coefficients are very common in several areas of engineering sciences. The computation of the solution of such systems is a central problem when the characterization of the variables related by such systems is desired.In this paper we characterize the solution of systems of algebraic equations with real interval coefficients. The characterization is obtained considering the approach introduced in J. Comput. Appl. Math. 136 (2001) 271. [Copyright &y& Elsevier]

Let K be a field of characteristic zero, let A, B be K-algebras with polynomial identity and let M be a free (A,B)-bimodule. The algebra R=A/0 M/B can be endowed with a natural Z2-grading. In this paper, we compute the graded cocharacter sequence, the graded codimension sequence and the superexponent of R. As a consequence of these results, we also study the above PI-invariants in the setting of upper triangular matrices. In particular, we completely classify the algebra of 3×3 upper triangular matrices endowed with all possible Z2-gradings. [Copyright &y& Elsevier]

In this paper, we analyse the stability of parallel algorithms for the evaluation of polynomials written as a finite series of orthogonal polynomials. The basic part of the computation is the solution of a triangular tridiagonal linear system. This fact allows us to present a more detailed analysis. The theoretical results show that the parallel algorithms are almost as stable as their sequential counterparts for practical applications. Extensive numerical experiments confirm the theoretical conclusions. [Copyright &y& Elsevier]

This paper is concerned with oscillation of self-adjoint second-order vector difference equations with respect to a parameter. Properties of zeros and monotonicity of matrix-valued solutions are studied. The oscillation of two consecutive polynomials for vector-valued solutions is discussed. A separation theorem for matrix-valued solutions is also obtained. [Copyright &y& Elsevier]