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Abstract: Descartes’ rule of signs yields an upper bound for the number of positive and negative real roots of a given polynomial. The fundamental theorem of algebra implies a similar property; every real polynomial of degree n ⩾1 has at most n real zeroes. In this paper, we describe axiomatically function families possessing one or another of these properties. The resulting families include, at least, all polynomial functions and sums of exponential functions. As an application of our approach, we consider, among other things, a method for identifying certain type of bases for the Euclidean space. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a strongly damped wave equation with fractional damping on part of its boundary and also with an internal source. Under some appropriate assumptions on the parameters, and with certain initial data, a blow-up result with positive initial energy is established. [Copyright &y& Elsevier]

Abstract: If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with ∣α∣⩽1, ∣β∣⩽1, it is known that. for R ⩾1 and ∣z∣⩾1. The present paper contains a generalization and an improvement of this and some other polynomial inequalities of similar nature. [Copyright &y& Elsevier]

Abstract: Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties of this generating functions are given. By applying this generating function, not only derivative of these polynomials but also recurrence relations of these polynomials are found. Interpolation function of these polynomials is also constructed by Mellin transformation. This function interpolates these polynomials at negative integers which are given explicitly. Moreover, relations between these polynomials, the Stirling numbers of the second kind and Bernoulli polynomials of higher order are given. Furthermore some remarks associated with the Bezier curves are given. [Copyright &y& Elsevier]

Abstract: Determining the cells of an arrangement of hyperplanes is a classical problem in combinatorial geometry. In this paper we present an efficient recursive procedure to solve it. In fact, by considering a connection between the latter problem and optimality conditions of unconstrained quadratic optimization problems in the following form: , with , we can show the proposed algorithm solves problems of the form in polynomial time when the rank of the matrix is fixed and the number of its positive diagonal entries is . [Copyright &y& Elsevier]

Abstract: In this paper we derive an approximation property of four-point interpolatory curve subdivision, based on local cubic polynomial fitting. We show that when the scheme is used to generate a limit curve that interpolates given irregularly spaced points, sampled from a curve in any space dimension with a bounded fourth derivative, and the chosen parameterization is chordal, the accuracy is fourth order as the mesh size goes to zero. In contrast, uniform and centripetal parameterizations yield only second order. [Copyright &y& Elsevier]

Abstract: In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of as , where d is the degree of the polynomial or spline. In this paper we establish, in the important cases , the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polynomial interpolants of degree d. [Copyright &y& Elsevier]

Abstract: There exists a real competition between authors to construct improved iterative methods for solving nonlinear equations. In this paper, by using computer experiment, we study the basins of attraction for some of the iterative methods for solving the equation P(z)=0, where is a complex coefficients polynomial, and this allows us to compare their performances (the area of convergence and theirs speed). The beauty fractal pictures generated by these methods are presented too. [Copyright &y& Elsevier]

Abstract: Frequently in engineering applications, simply structured controllers are required for plants whose dynamics are either not fully known or varies with time. The problem of designing such structurally constrained controllers is known to be NP-hard. This paper presents a method for designing such controllers for both continuous-time and discrete-time uncertain or linear parameter varying (LPV) systems. The method relies on sufficient linear matrix inequalities (LMI) conditions also presented here. These LMIs are used to evaluate performance of a given controller in terms of the worst-case induced -norm for complete operational envelope. The strength of this LMI formulation lies in the fact that the robust performance evaluation condition is less conservative than standard results because it is based on a parameter-dependent Lypunov function and full block multipliers which allows to consider a bound on the rate of change in parameters. The LMI conditions are used in a hybrid evolutionary-LMI algorithm. The proposed algorithm employs evolutionary search to span the solution space and LMI solvers to find the worst case performance. The algorithm is independent of the controller structure, which allows to design simply structured controllers for complex systems in a systematic way. To illustrate the approach, two applications are presented: a distillation column and a spark ignition (SI) engine. For the distillation column, simple PI controllers with first order pre-filters are designed to achieve time and frequency domain control objectives in the presence of 20% input uncertainty. For the SI engine example, gain-scheduled PID controllers are designed and tuned. these examples illustrate that the proposed approach can be used to systematically design simply structured low-order controllers, while satisfying all performance requirements in terms of the worst-case induced -norm. [Copyright &y& Elsevier]

Abstract: In this paper, the higher-order tangent numbers and higher-order secant numbers, and , have been studied in detail. Several known results regarding and have been brought together along with many new results and insights and they all have been proved in a simple and unified manner. In particular, it is shown that the higher-order tangent numbers constitute a special class of the partial multivariate Bell polynomials and that can be computed from the knowledge of . In addition, a simple explicit formula involving a double finite sum is deduced for the numbers and it is shown that are linear combinations of the classical tangent numbers . [Copyright &y& Elsevier]

Abstract: In this paper we consider a family of generalized Fibonacci-type polynomials. These polynomials have a lot of similar properties to the generalized Jacobsthal-type polynomials. As an extension of the work of Djordjević [G.B. Djordjević, Mixed convolutions of the Jacobsthal type, Appl. Math. Comput. 186 (2007) 646–651], we give some recurrence relations and identities involving the generalized Fibonacci-type polynomials. [Copyright &y& Elsevier]

Abstract: Let be a graph of order and the Laplacian characteristic polynomial of . Zhou and Gutman proved that among all trees of order , the th coefficient is largest when the tree is a path and is smallest for a star. In this paper, for two given positive integers and , we characterize the trees with a given bipartition which have the minimal and second minimal Laplacian coefficients. [Copyright &y& Elsevier]

Abstract: A -clique-coloring of a graph is an assignment of colors to the vertices of such that every maximal (i.e., not extendable) clique of contains two vertices with different colors. We show that deciding whether a graph has a -clique-coloring is -complete for every . The complexity of two related problems are also considered. A graph is -clique-choosable, if for every -list-assignment on the vertices, there is a clique coloring where each vertex receives a color from its list. This problem turns out to be -complete for every . A graph is hereditary -clique-colorable if every induced subgraph of is -clique-colorable. We prove that deciding hereditary -clique-colorability is also -complete for every . Therefore, for all the problems considered in the paper, the obvious upper bound on the complexity turns out to be the exact class where the problem belongs. [Copyright &y& Elsevier]

Abstract: This paper explores the problems of generalized center conditions and integrability of resonant infinity for a complex polynomial differential system. The method is based on converting resonant infinity into an elementary singular point by a homeomorphic transformation. The calculation of generalized singular point quantities is an effective way of finding necessary conditions for integrable systems. A new recursive algorithm for computing generalized singular point quantities at the origin of the transformed system is derived. At the same time, a necessary and sufficient condition for resonant infinity to be a generalized complex center is presented. As an application of the new recursive algorithm, the generalized center conditions for resonant infinity for a class of cubic systems are discussed. To the best of our knowledge, this is the first time that the generalized center problem has been considered for resonant infinity. [Copyright &y& Elsevier]

Abstract: The well-known Faà di Bruno formula for higher derivatives of a composite function plays an important role in combinatorics. In this paper we obtain a unified approach to some recurrence sequences for the complete Bell polynomials by using Faà di Bruno’s formula. Furthermore, we obtain an inverse relation of Lah numbers of two types, and by using this relation we obtain some new and interesting combinatorial identities. [Copyright &y& Elsevier]

Abstract: In this paper we define the relation of analytic equivalence of functions at infinity. We prove that if the Łojasiewicz exponent at infinity of the gradient of a polynomial is greater or equal to , then there exists such that for every polynomial of degree less or equal to k, whose coefficients of monomials of degree k are less or equal ε, the polynomials f and are analytically equivalent at infinity. [Copyright &y& Elsevier]

Abstract: In this paper, we propose an analytical solution to a nonlinear second-order boundary value problem using the Homotopy Perturbation Method (HPM) and the 4q-Boubaker Polynomials Expansion Scheme (BPES). Both methods have been applied to a particular differential problem. The results are plotted, and compared with exact solutions proposed elsewhere, in order to evaluate accuracy. [Copyright &y& Elsevier]

Abstract: In this paper, we show the applicability of the first integral method, which is based on the ring theory of commutative algebra, to the regularized long-wave Burgers equation and the Gilson–Pickering equation under a parameter condition. Our method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are derived in a concise manner. [Copyright &y& Elsevier]

Abstract: In this paper we consider identical parallel machines scheduling problems with a deteriorating maintenance activity. In this model, each machine has a deteriorating maintenance activity, that is, delaying the maintenance increases the time required to perform it. We need to make a decision on when to schedule the rate-modifying activities and the sequence of jobs to minimize some objective function. We concentrate on two goals separately, namely, minimizing the total absolute differences in completion times (TADC) and the total absolute differences in waiting times (TADW). We show that the problems remain polynomially solvable under the proposed model. [Copyright &y& Elsevier]

Abstract: In this paper a new version of the Modified Quadrature Element Method (MQEM) is proposed. Like MQEM, the proposed method overcomes the drawback of the distance δ of the Quadrature Element Method (QEM) without introducing further degrees of freedom at the ends of the element as in the Differential Quadrature Element Method (DQEM), but it makes the computational cost of the stiffness matrix (and the mass matrix) lighter and uses a general procedure to generate the sampling points distribution. The method here presented has been applied to compute the fundamental frequencies of some structures. [Copyright &y& Elsevier]

Abstract: Let be the lollipop graph obtained by appending a g-cycle to a pendant vertex of a path on vertices. In 2002, Fallat, Kirkland and Pati proved that for and , . In this paper, we prove that for , for all n, where is the algebraic connectivity of . [Copyright &y& Elsevier]

Abstract: In this paper, the notion of Birkhoff–James approximate orthogonality sets is introduced for rectangular matrices and matrix polynomials. The proposed definition yields a natural generalization of standard numerical range and q-numerical range (and also of recent extensions), sharing with them several geometric properties. [Copyright &y& Elsevier]

Abstract: In our previous work, we investigated detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) detectability, strong detectability, (weak) periodic detectability, and strong periodic detectability. In this paper, we extend our results in three aspects. (1) We extend detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong detectability. The previous algorithms are based on an observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called a detector. (3) We extend detectability to D-detectability. While detectability requires determining the exact state of a system, D-detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on detectability of discrete event systems becomes more applicable in solving many practical problems. [Copyright &y& Elsevier]

Abstract: In this paper we are concerned with the problem of the dimension of the higher secant variety of the Segre variety (-times, and ). In order to determine the dimensions of these varieties we construct a specific subscheme of which is a generic configuration of the union of linear subspaces of dimension and double points, and then we compute the value of Hilbert function of this scheme at degree . We show that has the expected Hilbert function at degree , except possibly for certain values of . [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose two new operators for complex polynomial matrices. One is the conjugate product and the other is the Sylvester-conjugate sum. Then some important properties for these operators are proved. Based on these derived results, we propose a unified approach to solving a general class of Sylvester-polynomial-conjugate matrix equations, which include the Yakubovich-conjugate matrix equation as a special case. The complete solution of the Sylvester-polynomial-conjugate matrix equation is obtained in terms of the Sylvester-conjugate sum, and such a proposed solution can provide all the degrees of freedom with an arbitrarily chosen parameter matrix. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of single and multiple degree elevation and reduction for DP curves and surfaces is considered and expressed in matrix representations. Using monomial matrix representations of the univariate DP polynomials, single and multiple degree elevation matrices can be derived by minor extension of this monomial matrix. Given this result, matrices of constrained single and multiple degree reduction can be readily obtained. Finally, important and sufficient conditions for degree reduction can also be found from these resulting matrices. [Copyright &y& Elsevier]

Abstract: In this paper, we first consider the problem of determining the robust positivity of a real function as the real vector varies over a box . We show that, it is sufficient to check a finite number of specially constructed points. This is accomplished by using some results on sign-definite decomposition. We then apply this result to determine the robust Hurwitz stability of a family of complex polynomials whose coefficients are polynomial functions of the parameters of interest. We develop an eight polynomial vertex stability test that is a sufficient condition of Hurwitz stability of the family. This test reduces to Kharitonov’s well known result for the special case where the parameters are just the polynomial coefficients. In this case, the result is tight. This test can be recursively and modularly used to construct an approximation of arbitrary accuracy to the actual stabilizing set. The result is illustrated by examples. [Copyright &y& Elsevier]

Abstract: Work on solving the second order linear oscillation defined by Eq. , with continuous and positive coefficient that satisfies Lipschitz’s condition on semi-axis and the divergence of , had started since the 1830s with Sturm’s theorems. This paper presents generalizations as well as a simplification of classical Sturm’s theorems on the location and the position of zero oscillations, which have not been included in Amrein et al. (2005) . Besides, according to results from Dimitrovski and Mijatović (1997) , Dimitrovski et al. (2007)  and Dimitrovski et al. (2007) , we add some ideas and supplements (Theorems 2.4–2.8, 2.10 and 2.11) to the classical Sturm’s theory of oscillations. [Copyright &y& Elsevier]

Abstract: For a simple graph , let denote the complement of relative to the complete graph and let where denotes the adjacency matrix of . The complete product of two simple graphs and is the graph obtained from and by joining every vertex of to every vertex of . In is represented in terms of , , and . In this paper we extend the notion of complete product of simple graphs to that of generalized complete product of matrices and obtain their characteristic polynomials. [ABSTRACT FROM AUTHOR]

Abstract: This paper is dedicated to the stability analysis of a class of uncertain distributed delay systems, the kernel of which can be modeled as a polynomial function of the delay. The results are constructed by rewriting the system as an uncertain interconnected model. Appropriate robust control tools, i.e. quadratic separation, are then used to address the stability issue. To this end, some relations that highlight relevant characteristics of the delayed term are added to the interconnected model leading then to the conservatism reduction. Finally, numerical examples show the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper we consider parallel identical machines scheduling problems with deteriorating jobs. In this model, job processing times are defined by functions of their starting times. We concentrate on two goals separately, namely, minimizing the total absolute differences in completion times (TADC) and the total absolute differences in waiting times (TADW). We show that the problems remains polynomially solvable under the proposed model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the algebra endowed with the involution induced by the transposition superinvolution of the superalgebra of -matrices over the field . We study the -polynomial identities for this algebra in the case of characteristic zero. We describe a finite set generating the ideal of its -identities. We also consider , the algebra of matrices over the Grassmann algebra . We prove that for a large class of involutions defined on it any -polynomial identity is indeed a polynomial identity. A similar result holds for the verbally prime algebra . [ABSTRACT FROM AUTHOR]

Abstract: A recent breakthrough in the theory of (type ) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. The inversion statistic, which is the more intricate one, suffices for specializing a closely related formula to one for the type Hall–Littlewood -polynomials (spherical functions on -adic groups). An apparently unrelated development, at the level of arbitrary finite root systems, led to Schwer’s formula (rephrased and rederived by Ram) for the Hall–Littlewood -polynomials of arbitrary type. The latter formula is in terms of so-called alcove walks, which originate in the work of Gaussent–Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by deriving a Haglund–Haiman–Loehr type formula for the Hall–Littlewood -polynomials of type from Ram’s version of Schwer’s formula via a “compression” procedure. [Copyright &y& Elsevier]

Abstract: In this paper we study the von Kármán plate model with long-range memory and we show the general decay of the solution as time goes to infinity. This result generalizes and improves on earlier ones in the literature because it allows certain relaxation functions which are not necessarily of exponential or polynomial decay. [Copyright &y& Elsevier]

Abstract: In this paper, we prove a more general result concerning the location of the zeros of a polynomial in a ring shaped region involving binomial coefficients and t-Fibonacci numbers. We include not only some known results as special cases, but also improve the results due to Daiz-Barrero and Egozcue as a particular case. [ABSTRACT FROM AUTHOR]

Abstract: A family of square matrices of the same order is called a quasi-commuting family if for all where need not be distinct. Let , be polynomials in the indeterminates with coefficients in the complex field , and let be matrices over which are not necessarily distinct. Let and let . In this paper, we prove that, for matrices over , if is a quasi-commuting family, then implies that . [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses a new and efficient linearization technique to solve mixed 0–1 polynomial problems to achieve a global optimal solution. Given a mixed 0–1 polynomial term , where are binary (0–1) variables and is a continuous variable. Also, can be either a positive or a negative parameter. We transform into a set of auxiliary constraints which are linear and can be solved by exact methods such as branch and bound algorithms. For this purpose, we will introduce a method in which the number of additional constraints is decreased significantly rather than the previous methods proposed in the literature. As is known in any operations research problem decreasing the number of constraints leads to decreasing the mathematical computations, extensively. Thus, research on the reducing number of constraints in mathematical problems in complicated situations have high priority for decision makers. In this method, each -auxiliary constraints proposed in the last method in the literature for the linearization problem will be replaced by only 3 novel constraints. In other words, previous methods were dependent on the number of 0–1 variables and therefore, one auxiliary constraint was considered per 0–1 variable, but this method is completely independent of the number of 0–1 variables and this illustrates the high performance of this method in computation considerations. The analysis of this method illustrates the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: Logical filtering is the process of updating a belief state (set of possible world states) after a sequence of executed actions and perceived observations. In general, it is intractable in dynamic domains that include many objects and relationships. Still, potential applications for such domains (e.g., semantic web, autonomous agents, and partial-knowledge games) encourage research beyond intractability results. In this paper we present polynomial-time algorithms for filtering belief states that are encoded as First-Order Logic (FOL) formulas. Our algorithms are exact in many cases of interest. They accept belief states in FOL without functions, permitting arbitrary arity for predicates, infinite universes of elements, and equality. They enable natural representation with explicit references to unidentified objects and partially known relationships, still maintaining tractable computation. Previous results focus on more general cases that are intractable or permit only imprecise filtering. Our algorithms guarantee that belief-state representation remains compact for STRIPS actions (among others) with unbounded-size domains. This guarantees tractable exact filtering indefinitely for those domains. The rest of our results apply to expressive modeling languages, such as partial databases and belief revision in FOL. [ABSTRACT FROM AUTHOR]

Abstract: Fourth root metrics are a special and important class of Finsler metrics, which have been applied to physics. In this paper, we study invariant fourth root Finsler metrics on the Grassmannian manifolds . By using the results from the theory of invariant polynomials of Lie groups, we obtain a complete classification of such metrics. Further, some invariant -th root Finsler metrics are also given. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents an algebraic approach, using polynomial and rational models over an arbitrary field, to tangential interpolation problems, both by polynomial as well as rational matrix functions. Appropriate extensions of scalar problems, associated with the names of Lagrange (first order), Hermite (high order) and Newton (recursive) are derived. The relation of interpolation problems to the matrix Chinese remainder theorem are clarified. Some two sided interpolation problems are discussed, using the theory of tensored functional models. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a class of polynomial interior-point algorithms for the Cartesian second-order cone linear complementarity problem based on a parametric kernel function, with parameters and , are presented. The proposed parametric kernel function is used both for determining the search directions and for measuring the distance between the given iterate and the -center for the algorithms. Moreover, the currently best known iteration bounds for the large- and small-update methods, namely, and , are obtained, respectively, which reduce the gap between the practical behavior of the algorithms and its theoretical performance results. [ABSTRACT FROM AUTHOR]

Abstract: IDR() is now recognized as one of the most effective methods, often superior to other Krylov subspace methods, for large nonsymmetric linear systems of equations. In this paper we propose an improvement upon IDR() by incorporating a higher-order stabilization polynomial into IDR(). The proposed algorithm, named GBi-CGSTAB(), shares desirable features with both IDR() and Bi-CGSTAB(). [ABSTRACT FROM AUTHOR]

Abstract: This paper presents algorithms for decomposing any zero-dimensional polynomial set into simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a key ingredient of these algorithms, we generalize the squarefree decomposition approach for univariate polynomials over a finite field to that over the field product determined by a simple set. As a subprocedure of the generalized squarefree decomposition approach, a method is proposed to extract the th root of any element in the field product. Experiments with a preliminary implementation show the effectiveness of our algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, quintic parametric polynomial minimal surface and their properties are discussed. We first propose the sufficient condition of quintic harmonic polynomial parametric surface being a minimal surface. Then several new models of minimal surfaces with shape parameters are derived from this condition. We also study the properties of new minimal surfaces, such as symmetry, self-intersection on symmetric planes and containing straight lines. Two one-parameter families of isometric minimal surfaces are also constructed by specifying some proper shape parameters. [ABSTRACT FROM AUTHOR]

Abstract: In [G. Lunardon, Semifields and linear sets of , Quad. Mat., Dept. Math., Seconda Univ. Napoli, Caserta (in press)], G. Lunardon has exhibited a construction method yielding a theoretical family of semifields of order and odd, with left nucleus , middle and right nuclei both and center . When this method gives an alternative construction of a family of semifields described in [N.L. Johnson, G. Marino, O. Polverino, R. Trombetti, On a generalization of cyclic semifields, J. Algebraic Combin. 26 (2009), 1–34], which generalizes the family of cyclic semifields obtained by Jha and Johnson in [V. Jha, N.L. Johnson, Translation planes of large dimension admitting non-solvable groups, J. Geom. 45 (1992), 87–104]. For , no example of a semifield belonging to this family is known. In this paper we first prove that, when , any semifield belonging to the family introduced in the second work cited above is not isotopic to any semifield of the family constructed in the former. Then we construct, with the aid of a computer, a semifield of order 210 belonging to the family introduced by Lunardon, which turns out to be non-isotopic to any other known semifield. [Copyright &y& Elsevier]

Abstract: In the present paper, we utilize the general q-exponential operators to derive several Carlitz type bivariate generating functions for Rogers–Szegö polynomials. Moreover, we give an equivalent expansion formula of a certain bivariate generating functions for Rogers–Szegö polynomials and propose an open problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we give direct approximation theorems for a general family of truncated operators. We discuss the linear and nonlinear cases. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for the complex genuine Durrmeyer polynomials attached to analytic functions on compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for the genuine Durrmeyer polynomials, namely the extensions of the approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane. [ABSTRACT FROM AUTHOR]

Abstract: A non-linear structure preserving matrix method for the computation of a structured low rank approximation of the Sylvester resultant matrix of two inexact polynomials and is considered in this paper. It is shown that considerably improved results are obtained when and are processed prior to the computation of , and that these preprocessing operations introduce two parameters. These parameters can either be held constant during the computation of , which leads to a linear structure preserving matrix method, or they can be incremented during the computation of , which leads to a non-linear structure preserving matrix method. It is shown that the non-linear method yields a better structured low rank approximation of and that the assignment of and is important because may be a good structured low rank approximation of , but may be a poor structured low rank approximation of because its numerical rank is not defined. Examples that illustrate the differences between the linear and non-linear structure preserving matrix methods, and the importance of the assignment of and , are shown. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the uniqueness problems of difference polynomials of meromorphic functions that share a value or a fixed point. We also obtain several results concerning the shifts of meromorphic functions and the sufficient conditions for periodicity which improve some recent results in Heittokangas et al. (2009) and Liu (2009) . [ABSTRACT FROM AUTHOR]