A note on “Efficient feasibility testing for dial-a-ride problems”

Hunsaker and Savelsbergh [B. Hunsaker, M.W.P. Savelsbergh, Efficient feasibility testing for dial-a-ride problems, Operations Research Letters 30 (2002) 169-173.] developed a linear-time algorithm to verify the feasibility for dial-a-ride problems. However, this algorithm may incorrectly declare infeasibility due to ride time constraints in some cases. We propose a revised procedure to address this flaw, but in an O(n²) worst-case time.     

The fully Sinc‐Galerkin method for time‐dependent boundary conditions

The fully Sinc‐Galerkin method is developed for a family of complex‐valued partial differential equations with time‐dependent boundary conditions. The Sinc‐Galerkin discrete system is formulated and represented by a Kronecker product form of those equations. The numerical solution is efficiently calculated and the method exhibits an exponential convergence rate. Several examples, some with a real‐valued solution and some with a complex‐valued solution, are used to demonstrate the performance of this method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

Blow‐up phenomena for a pseudo‐parabolic equation

By the means of a differential inequality technique, we obtain a lower bound for blow‐up time if p and the initial value satisfy some conditions. Also, we establish a blow‐up criterion and an upper bound for blow‐up time under some conditions as well as a nonblow‐up and exponential decay under some other conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Exponential stabilization and L2‐gain for uncertain switched nonlinear systems with interval time‐varying delay

This paper is concerned with the exponential stabilization and L₂‐gain for a class of uncertain switched nonlinear systems with interval time‐varying delay. Based on Lyapunov–Krasovskii functional method, novel delay‐dependent sufficient conditions of exponential stabilization for a class of uncertain switched nonlinear delay systems are developed under an average dwell time scheme. Then, novel criteria to ensure the exponential stabilization with weighted L₂‐gain performance for a class of uncertain switched nonlinear delay systems are established. Furthermore, an effective method is proposed for the designing of a stabilizing feedback controller with L₂‐gain performance. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Commutativity of quaternion‐matrix–valued functions and quaternion matrix dynamic equations on time scales

In this paper, we obtain some basic results of quaternion algorithms and quaternion calculus on time scales. Based on this, a Liouville formula and some related properties are derived for quaternion dynamic equations on time scales through conjugate transposed matrix algorithms. Moreover, we introduce the quaternion matrix exponential function by homogeneous quaternion matrix dynamic equations. Also a corresponding existence and uniqueness theorem is proved. In addition, the commutativity of quaternion‐matrix–valued functions is investigated and some sufficient and necessary conditions of commutativity and noncommutativity are established on time scales. Also the fundamental solution matrices of some basic quaternion matrix dynamic equations are obtained. Examples are provided to illustrate the results, which are completely new on hybrid domains particularly when the time scales are the quantum case and the discrete case ; , both of which are significant for the study of quaternion q‐dynamic equations and quaternion difference dynamic equations. Finally, we present several applications including multidimensional rotations and transformations of the submarine, the gyroscope, and the planet whose dynamical behaviors are depicted by quaternion dynamics on time scales and the corresponding iteration numerical solution for homogeneous quaternion dynamic equations are provided on various time scales.     

Blow-up solutions to the nonlinear Schrödinger equation with oscillating nonlinearities

In this article we investigate the possibility of finite time blow-up in H¹(R²) for solutions to critical and supercritical nonlinear Schrödinger equations with an oscillating nonlinearity. We prove that despite the oscillations some solutions blow up in finite time. Conversely, we observe that for a given initial data oscillations can extend the local existence time of the corresponding solution.     

Optimal (r,N)‐policy for discrete‐time Geo ∕ G ∕ 1 queue with different input rate and setup time

This paper presents a queue‐length analysis of Geo ∕ G ∕ 1 queue with ( r , N )‐policy and different input rate. Using a different method, the recursive expressions of queue‐length distribution at different epochs are obtained. Furthermore, some performance measures are also investigated. Finally, the Tabu search algorithm is used to search the joint optimum value of ( r , N ), which minimizes the state‐dependent operating cost. Copyright © 2014 John Wiley & Sons, Ltd.     

Gegenbauer spectral method for time‐fractional convection–diffusion equations with variable coefficients

In this paper, we study the numerical solution to time‐fractional partial differential equations with variable coefficients that involve temporal Caputo derivative. A spectral method based on Gegenbauer polynomials is taken for approximating the solution of the given time‐fractional partial differential equation in time and a collocation method in space. The suggested method reduces this type of equation to the solution of a linear algebraic system. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Eigenvalue problems for nonlinear third‐order m‐point p‐Laplacian dynamic equations on time scales

This work deals with the existence and uniqueness of a nontrivial solution for the third‐order p‐Laplacian m‐point eigenvalue problems on time scales. We find several sufficient conditions of the existence and uniqueness of nontrivial solution of eigenvalue problems when λ is in some interval. The proofs are based on the nonlinear alternative of Leray–Schauder. To illustrate the results, some examples are included. Copyright © 2014 John Wiley & Sons, Ltd.     

Minimum time‐step criteria for the Galerkin finite element methods applied to one‐dimensional parabolic partial differential equations

The finite element method has been well established for numerically solving parabolic partial differential equations (PDEs). Also it is well known that a too large time step should not be chosen in order to obtain a stable and accurate numerical solution. In this article, accuracy analysis shows that a too small time step should not be chosen either for some time‐stepping schemes. Otherwise, the accuracy of the numerical solution cannot be improved or can even be worsened in some cases. Furthermore, the so‐called minimum time step criteria are established for the Crank‐Nicolson scheme, the Galerkin‐time scheme, and the backward‐difference scheme used in the temporal discretization. For the forward‐difference scheme, no minimum time step exists as far as the accuracy is concerned. In the accuracy analysis, no specific initial and boundary conditions are invoked so that such established criteria can be applied to the parabolic PDEs subject to any initial and boundary conditions. These minimum time step criteria are verified in a series of numerical experiments for a one‐dimensional transient field problem with a known analytical solution. The minimum time step criteria developed in this study are useful for choosing appropriate time steps in numerical simulations of practical engineering problems. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

A STATE‐SPACE MODEL FOR UNIVARIATE ORDINAL‐VALUED TIME SERIES

Abstract A state‐space model was developed to analyze a univariate time series of ordinal‐valued flower phenology data. Flower abundance, recorded as either “none,”“some,” or “much,” was observed each month on trees in a lowland Costa Rican rain forest to investigate flowering patterns of different species. Data from a single Capparis pittieri and daily rain measurements are used to demonstrate the model. A method to obtain maximum likelihood estimates of the parameters and the use of predicted probability differences to assess goodness of fit are described. Opportunities for improving the model are also discussed.     

The discrete‐time Kolmogorov systems with historic behavior

The main aim of this paper is to discuss some feature so‐called historic behavior of a discrete‐time Kolmogorov system of predator–prey interactions, which causes the nonexistence of the time averages.     

Non‐Abelian homomorphism testing,and distributions close to their self‐convolutions

In this paper, we study two questions related to the problem of testing whether a function is close to a homomorphism. For two finite groups G,H (not necessarily Abelian), an arbitrary map f : G,H, and a parameter 0 < ε < 1, say that f is ε‐close to a homomorphism if there is some homomorphism g such that g and f differ on at most ε | G | elements of G, and say that f is ε‐far otherwise. For a given f and ε, a homomorphism tester should distinguish whether f is a homomorphism, or if f is ε‐far from a homomorphism. When G is Abelian, it was known that the test which picks O(1/ε) random pairs x,y and tests that f(x) + f(y) = f(x + y) gives a homomorphism tester. Our first result shows that such a test works for all groups G. Next, we consider functions that are close to their self‐convolutions. Let A = {a_g | g ε G} be a distribution on G. The self‐convolution of A, A^′ = {a | g ε G}, is defined by It is known that A= A^′ exactly when A is the uniform distribution over a subgroup of G. We show that there is a sense in which this characterization is robust—that is, if A is close in statistical distance to A^′, then A must be close to uniform over some subgroup of G. Finally, we show a relationship between the question of testing whether a function is close to a homomorphism via the above test and the question of characterizing functions that are close to their self‐convolutions. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Improved H∞ performance analysis of uncertain Markovian jump systems with overlapping time‐varying delays

In this article, we study the problem of robust H_∞ performance analysis for a class of uncertain Markovian jump systems with mixed overlapping delays. Our aim is to present a new delay‐dependent approach such that the resulting closed‐loop system is stochastically stable and satisfies a prescribed H_∞ performance level χ. The jumping parameters are modeled as a continuous‐time, finite‐state Markov chain. By constructing new Lyapunov‐Krasovskii functionals, some novel sufficient conditions are derived to guarantee the stochastic stability of the equilibrium point in the mean‐square. Numerical examples show that the obtained results in this article is less conservative and more effective. The results are also compared with the existing results to show its conservativeness. © 2016 Wiley Periodicals, Inc. Complexity 21: 460–477, 2016     

POSITIVE SOLUTIONS FOR p-LAPLACIAN DYNAMIC EQUATIONS ON TIME SCALES

The three-point boundary value problems of p-Laplacian dynamic equations on time scales are investigated. By using Krasnosel＇skii＇s fixed-point theorem and fixed-point index theorem, criteria are achieved for the existence of at least one, two or 2n positive solutions. Furthermore, some examples are included to illustrate the main theorems.     

Asymptotic expansions for the conditional sojourn time distribution in the <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">M</Emphasis>/1-PS queue

We consider the M/M/1 queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer’s service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison (SIAM J. Appl. Math. 45:152–167, [1985]) and Flatto (Ann. Appl. Probab. 7:382–409, [1997]). This work was partly supported by NSF grant DMS 05-03745.     

THE MITRA‐WAN FORESTRY MODEL: A DISCRETE‐TIME OPTIMAL CONTROL PROBLEM

In this paper, we present some new properties of the Mitra‐Wan forestry model written as a discrete‐time optimal control problem. For this problem, the set of stationary states is characterized. For the optimal long‐run management, we consider the following optimality criteria: average optimality, good control policies, bias optimality, and overtaking optimality. We establish relationships between these criteria and show that the value of average optimal policies is constant and equals the value in the optimal stationary state.     

Synchronization of memristor‐based delayed BAM neural networks with fractional‐order derivatives

This article deals with the problem of synchronization of fractional‐order memristor‐based BAM neural networks (FMBNNs) with time‐delay. We investigate the sufficient conditions for adaptive synchronization of FMBNNs with fractional‐order 0 < α < 1. The analysis is based on suitable Lyapunov functional, differential inclusions theory, and master‐slave synchronization setup. We extend the analysis to provide some useful criteria to ensure the finite‐time synchronization of FMBNNs with fractional‐order 1 < α < 2, using Mittag‐Leffler functions, Laplace transform, and linear feedback control techniques. Numerical simulations with two numerical examples are given to validate our theoretical results. Presence of time‐delay and fractional‐order in the model shows interesting dynamics. © 2016 Wiley Periodicals, Inc. Complexity 21: 412–426, 2016     

Expected hitting and cover times of random walks on some special graphs

We give general bounds (and in some cases exact values) for the expected hitting and cover times of the simple random walk on some special undirected connected graphs using symmetry and properties of electrical networks. In particular we give easy proofs for an N–1H_N-1 lower bound and an N² upper bound for the cover time of symmetric graphs and for the fact that the cover time of the unit cube is Φ(NlogN). We giver a counterexample to a conjecture of Freidland about a general bound for hitting times. Using the electric approach, we provide some genral upper and lower bounds for the expected cover times in terms of the diameter of the graph. These bounds are tight in many instances, particularly when the graph is a tree. © 1994 John Wiley & Sons, Inc.     

Finite‐time synchronization of memristive neural networks with time‐varying delays via two control methods

In this paper, on the basis of the Lyapunov stability theory and finite‐time stability lemma, the finite‐time synchronization problem for memristive neural networks with time‐varying delays is studied by two control methods. First, the discontinuous state‐feedback control rule containing integral part for square sum of the synchronization error and the discontinuous adaptive control rule are designed for realizing synchronization of drive‐response memristive neural networks in finite time, respectively. Then, by using some important inequalities and defining suitable Lyapunov functions, some algebraic sufficient criteria guaranteeing finite‐time synchronization are deduced for drive‐response memristive neural networks in finite time. Furthermore, we give the estimation of the upper bounds of the settling time of finite‐time synchronization. Lastly, the effectiveness of the obtained sufficient criteria guaranteeing finite‐time synchronization is validated by simulation.