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Abstract: In this paper, we formulate a new robust two-species nonautonomous predator–prey model with multi-delays and impulsive effects and perform a systematic mathematical and ecological study. Our results in this paper indicate that under the appropriate linear periodic impulsive perturbations, the system is permanent and has a unique positive globally attractive semi-trivial periodic solution. By using the Brouwer fixed point theorem, we prove that if the periodic system is permanent, then there is at least one positive periodic solution of the system. We show that the conditions for global attractivity of the positive semi-trivial periodic solution and permanence of the population of the model depend on time delay, so, we call it “profitless”. In this paper, the main feature is that we introduce multi-delays and impulses into the predator–prey model, exhibit a new modeling method which is applied to investigate multi-species impulsive multi-delays differential equations. [Copyright &y& Elsevier]

Abstract: Modeling of multibody systems is an important though demanding field of application for interval arithmetic. Interval modeling of dynamics is particularly challenging, not least because of the differential equations which have to be solved in the process. Most modeling tools transform these equations into a (non-autonomous) initial value problem, interval algorithms for solving of which are known. The challenge then consists in finding interfaces between these algorithms and the modeling tools. This includes choosing between “symbolic” and “numerical” modeling environments, transforming the usually non-autonomous resulting system into an autonomous one, ensuring conformity of the new interval version to the old numerical, etc. In this paper, we focus on modeling multibody systems’ dynamics with the interval extension of the “numerical” environment MOBILE, discuss the techniques which make the uniform treatment of interval and non-interval modeling easier, comment on the wrapping effect, and give reasons for our choice of MOBILE by comparing the results achieved with its help with those obtained by analogous symbolic tools. [Copyright &y& Elsevier]

Abstract: We developed an algorithm in Kıymaz and Mirasyedioğlu [O. Kıymaz and Ş. Mirasyedioğlu, An algorithmic approach to exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients, Appl. Math. Comp. 139 (1) (2003) 165–178] for computing exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients, near a point x = x 0. In this paper we present a symbolic algorithm to compute the exact power series solutions of nth order linear homogeneous differential equations with polynomial coefficients, near an ordinary point. [Copyright &y& Elsevier]

The Lai-Chen algorithm, an extended feedback control scheme of the original Chen- Lai algorithm, was proposed to gradually make an arbitrarily given discrete-time dynamical system chaotic in terms of possessing positive Lyapunov exponents with uniformly bounded orbits. In this paper, based on the Monte Carlo method, we further study the distribution of the controlled Lyapunov exponents generated by the Lai-Chen algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, MPEC problems with linear complementarity constraints are considered. By means of Fischer–Burmeister function, the linear complementarity condition is transformed into a nonsmooth equation. Then, during the iteration, a corresponding smooth system approximates the nonsmooth equation. The smooth optimization is solved by SQP algorithm for standard constrained optimization. Global convergence and superlinear convergence rate are established under some suitable assumptions. Moreover, we conclude that the current iterate point is an exact stationary point of the MPEC problem when the proposed algorithm stops in finite iteration. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematics analysis and computer algebra, a reliable algorithm for solving high-order nonlinear Volterra–Fredholm integro-differential equations was established, and a new Maple procedure voltfredproc was established too. The results of the examples indicated that the procedure voltfredproc of Taylor polynomial method is simple and effective, and could provide an accuracy approximate solution or exact solution of the high-order nonlinear Volterra–Fredholm integro-differential equation. This would be useful for solving integro-differential equation, integral equations and ordinary differential equation. [Copyright &y& Elsevier]

Abstract: This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent differences such that are positive integers and . All algebraic transformations of these Gauss hypergeometric functions are considered. We show that apart from classical transformations of degree 2, 3, 4, 6 there are several other transformations of degree 6, 8, 9, 10, 12, 18, 24. Besides, we present an algorithm to compute relevant Belyi functions explicitly. [Copyright &y& Elsevier]

Abstract: This paper proposes a second-order scheme of precision integration for dynamic analysis with respect to long-term integration. Rather than transforming into first-order equations, a recursive scheme is presented in detail for direct solution of the homogeneous part of second-order algebraic and differential equations. The sine and cosine matrices involved in the scheme are calculated using the so-called 2 N algorithm. Numerical tests show that both the efficiency and the accuracy of homogeneous equations can be improved considerably with the second-order scheme. The corresponding particular solution is also presented, incorporated with the second-order scheme where the excitation vector is approximated by the truncated Taylor series. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the existence of solutions for first- and second-order nonresonance impulsive functional differential inclusions with variable moments. The proofs make use of the Martelli fixed-point theorem for condensing multivalued maps. [Copyright &y& Elsevier]

Abstract: In this paper, we address the problem of the guaranteed cost stabilization for a class of neutral delay-differential systems with a given quadratic cost function. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be easily solved by various efficient optimization algorithms. [Copyright &y& Elsevier]

We give a general result on the average-case performance of certain greedy algorithms. These are derived from algorithms in which the possible operations performed at each step are prioritised. This type of prioritisation has occurred in previously studied heuristics for finding large subgraphs with special properties in random regular graphs, such as maximum independent sets and minimum dominating sets. The approach in this paper eliminates some of the complications caused by prioritisation. The main results apply in general to random graphs with a given degree sequence. [Copyright &y& Elsevier]

This paper considers discrete processes governed by difference rather than differential equations for the state transformation. The basic question asked is if and when Hamiltonian canonical structures are possible in optimal discrete systems. Considering constrained discrete control, general optimization algorithms are derived that constitute suitable theoretical and computational tools when evaluating extremum properties of constrained physical models. The mathematical basis of the general theory is the Bellman method of dynamic programming (DP) and its extension in the form of the so-called Carathe´odory-Boltyanski (CB) stage criterion which allows a variation of the terminal state that is otherwise fixed in the Bellman's method. Two relatively unknown, powerful optimization algorithms are obtained: an unconventional discrete formalism of optimization based on a Hamiltonian for multistage systems with unconstrained intervals of holdup time, and the time interval constrained extension of the formalism. These results are general; namely, one arrives at: the discrete canonical Hamilton equations, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory along with all basic results of variational calculus. Vast spectrum of applications of the theory is briefly discussed. [Copyright &y& Elsevier]