This paper proposes a method of estimating computational complexity of problem through analyzing its input condition for N-vehicle exploration problem. The N-vehicle problem is firstly formulated to determine the optimal replacement in the set of permutations of 1 to N. The complexity of the problem is factorial of N (input scale of problem). To balance accuracy and efficiency of general algorithms, this paper mentions a new systematic algorithm design and discusses correspondence between complexity of problem and its input condition, other than just putting forward a uniform approximation algorithm as usual. This is a new technique for analyzing computation of NP problems. The method of corresponding is then presented. We finally carry out a simulation to verify the advantages of the method: 1) to decrease computation in enumeration; 2) to efficiently obtain computational complexity for any N-vehicle case; 3) to guide an algorithm design for any N-vehicle case according to its complexity estimated by the method.

A wide range of applications for wireless ad hoc networks are time-critical and impose stringent requirement on the communication latency. One of the key communication operations is to broadcast a message from a source node. This paper studies the minimum latency broadcast scheduling problem in wireless ad hoc networks under collision-free transmission model. The previously best known algorithm for this NP-hard problem produces a broadcast schedule whose latency is at least 648(r_max/r_min)² times that of the optimal schedule, where r_max and r_min are the maximum and minimum transmission ranges of nodes in a network, respectively. We significantly improve this result by proposing a new scheduling algorithm whose approximation performance ratio is at most (1 + 2r_max/r_min)² + 32. Moreover, under the proposed scheduling each node just needs to forward a message at most once.

Given a real (finite-dimensional or infinite-dimensional) Hilbert space H with a Jordan product, we introduce the concepts of w-unique and w-P properties for linear transformations on H, and investigate some interconnections among these concepts. In particular, we discuss the w-unique and w-P properties for Lyapunov-like transformations on H. The properties of the Jordan product and the Lorentz cone in the Hilbert space play important roles in our analysis.

In this paper we introduce a minimax model for network connection problems with interval parameters. We consider how to connect given nodes in a network with a path or a spanning tree under a given budget, where each link is associated with an interval and can be established at a cost of any value in the interval. The quality of an individual link (or the risk of link failure, etc.) depends on its construction cost and associated interval. To achieve fairness of the network connection, our model aims at the minimization of the maximum risk over all links used. We propose two algorithms that find optimal paths and spanning trees in polynomial time, respectively. The polynomial solvability indicates salient difference between our minimax model and the model of robust deviation criterion for network connection with interval data, which gives rise to NP-hard optimization problems.

We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions are known. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand may be lost. Our objective is to minimize the total discounted cost over the problem horizon by choosing an optimal replenishment and discretionary sales policy. We obtain the structure of the optimal replenishment and discretionary sales policy and show that the optimal policy for finite horizon problem converges to that of the infinite horizon problem. Moreover, we compare the optimal policy under random yield with that under certain yield, and show that the optimal order quantity (sales quantity) under random yield is more (less) than that under certain yield.

The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov’s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order averaging method and Melinikov’s method, we give the conditions for the existence of chaos in an averaged system under quasi-periodic perturbations for Ω = nω + εν, n = 1 - 4, where ν is not rational to ω. We are not able to prove the existence of chaos for n = 5 - 15, but show the chaotic behavior for n = 5 by numerical simulation. By numerical simulation we check on our theoretical analysis and further exhibit the complex dynamical behavior, including the bifurcation and reverse bifurcation from period-one to period-two orbits; the onset of chaos, the entire chaotic region without periodic windows, chaotic regions with complex periodic windows or with complex quasi-periodic windows; chaotic behaviors suddenly disappearing, or converting to period-one orbit which means that the system can be stabilized to periodic motion by adjusting bifurcation parameters α, δ, f₀ and Ω; and the onset of invariant torus or quasi-periodic behaviors, the entire invariant torus region or quasi-periodic region without periodic window, quasi-periodic behaviors or invariant torus behaviors suddenly disappearing or converting to periodic orbit; and the jumping behaviors which including from periodone orbit to anther period-one orbit, from quasi-periodic set to another quasi-periodic set; and the interleaving occurrence of chaotic behaviors and invariant torus behaviors or quasi-periodic behaviors; and the interior crisis; and the symmetry breaking of period-one orbit; and the different nice chaotic attractors. However, we haven’t find the cascades of period-doubling bifurcations under the quasi-periodic perturbations and show the differences of dynamical behaviors and technics of research between the periodic perturbations and quasi-periodic perturbations.

Line transect sampling is a very useful method in survey of wildlife population. Confident interval estimation for density D of a biological population is proposed based on a sequential design. The survey area is occupied by the population whose size is unknown. A stopping rule is proposed by a kernel-based estimator of density function of the perpendicular data at a distance. With this stopping rule, we construct several confidence intervals for D by difference procedures. Some bias reduction techniques are used to modify the confidence intervals. These intervals provide the desired coverage probability as the bandwidth in the stopping rule approaches zero. A simulation study is also given to illustrate the performance of this proposed sequential kernel procedure.

We study the soft-capacitated facility location game which is an extension of the facility location game of P′al and Tardös. We propose a 6-approximate cross-monotonic cost-sharing method. Numerical tests indicate that the method is effective.

This paper gets some necessary conditions for the existence of some kinds of clear 4^m2ⁿ compromise plans which allow estimation of all main effects and some specified two-factor interactions without assuming the remaining two-factor interactions being negligible. Some methods for constructing clear 4^m2ⁿ compromise plans are introduced.

A restricted signed r-set is a pair (A, f), where A ⊆ [n] = {1, 2, · · · , n} is an r-set and f is a map from A to [n] with f(i) ≠ i for all i ∈ A. For two restricted signed sets (A, f) and (B, g), we define an order as (A, f) ≤ (B, g) if A ⊆ B and g|A = f. A family A of restricted signed sets on [n] is an intersecting antichain if for any (A, f), (B, g)∈ A, they are incomparable and there exists x ∈ A ∩ B such that f(x) = g(x). In this paper, we first give a LYM-type inequality for any intersecting antichain A of restricted signed sets, from which we then obtain |A| ≤ (_r-1 ^n-1)(n-1)^r-1 if A consists of restricted signed r-sets on [n]. Unless r = n = 3, equality holds if and only if A consists of all restricted signed r-sets (A, f) such that x₀ ∈ A and f(x₀) = ε₀ for some fixed x₀ ∈ [n], ε₀ ∈ [n] \ {x₀}.

This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem in cones. The paper extends some previous results and reports some new results about impulsive differential equations.

Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.

In this paper, we investigate the blow-up behavior of solutions of a parabolic equation with localized reactions. We completely classify blow-up solutions into the total blow-up case and the single point blow-up case, and give the blow-up rates of solutions near the blow-up time which improve or extend previous results of several authors. Our proofs rely on the maximum principle, a variant of the eigenfunction method and an initial data construction method.

In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order derivative, the multiplicity result of three positive solutions are obtained.

In this paper, we study the problem of a variety of nonlinear time series model X_n+1 = T_Zn+1(X(n), · · ·,X(n - Z_n+1), _en+1(Z_n+1)) in which {Z_n} is a Markov chain with finite state space, and for every state i of the Markov chain, {e_n(i)} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {X_n} defined by the above model is investigated. Some new novel results on the underlying models are presented.

Integral self-affine tiling of Bandt’s model is a generalization of the integral self-affine tiling. Using ergodic theory, we show that the Lebesgue measure of the tile is a rational number where the denominator equals to the order of the associate symmetry group. We apply the result to the study of the Levy Dragon.

In this paper, the estimation of variance components in the linear mixed model with two random effects is investigated. The class of combination estimates based on the quadratic invariant statistics and consistent nonnegative estimates are obtained. Furthermore, it is shown that the consistent nonnegative estimate dominates ANOVA estimate under some conditions.

This paper addresses the simultaneous determination of pricing and inventory replenishment strategies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts: the deterministic component, which is influenced by the price, and the stochastic component (perturbation). The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of (s,S,p)-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost (these costs are all state-dependent) is convex.

In this paper, three numerical schemes with high accuracy for the coupled Schrödinger equations are studied. The conservative properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable.

In this paper, the linear stability of symplectic methods for Hamiltonian systems is studied. In particular, three classes of symplectic methods are considered: symplectic Runge-Kutta (SRK) methods, symplectic partitioned Runge-Kutta (SPRK) methods and the composition methods based on SRK or SPRK methods. It is shown that the SRK methods and their compositions preserve the ellipticity of equilibrium points unconditionally, whereas the SPRK methods and their compositions have some restrictions on the time-step.

This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator (MQLE) in quasi-likelihood nonlinear models (QLNM) with random regressors. The asymptotic results of generalized linear models (GLM) with random regressors are generalized to QLNM with random regressors.

This paper deals with the output feedback H^∞ control problem for a class of nonlinear stochastic systems. Based on the latest developed theory of stochastic dissipation, a notable result about the nonlinear H^∞ output feedback control of deterministic system is generalized to the stochastic case. Finally, in the cases of state feedback and output feedback, two families of controllers are provided respectively.

The singularly perturbed boundary value problem of scalar integro-differential equations has been studied extensively by the differential inequality method . However, it does not seem possible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore , for n-dimensional vector integro-differential equations the problem has not been solved fully. Here, we study this nonlinear vector problem and obtain some results. The approach in this paper is to transform the appropriate integro-differential equations into a canonical or diagonalized system of two first-order equations.

By constructing auxiliary differential equations, we obtain peaked solitary wave solutions of the generalized Camassa-Holm equation, including periodic cusp waves expressed in terms of elliptic functions.

The exact parametric representations of the traveling wave solutions for a nonlinear elastic rod equation are considered. By using the method of planar dynamical systems, in di?erent parameter regions, the phase portraits of the corresponding traveling wave system are given. Exact explicit kink wave solutions, periodic wave solutions and some unbounded wave solutions are obtained.

In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on E_c (the set consisting of continuous equilibria of τ) implies the strong one.

In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.

The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market. We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper. A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time. We also consider a special case when the asset price follows GBM (Geometric Brownian Motion) and interest rate follows Vasicek’s model.

In this paper we study reflected and doubly reflected backward stochastic differential equations (BSDEs, for short) driven by Teugels martingales associated with Lévy process satisfying some moment conditions and by an independent Brownian motion. For BSDEs with one reflecting barrier, we obtain a comparison theorem using the Tanaka-Meyer formula. For BSDEs with two reflecting barriers, we first prove the existence and uniqueness of the solutions under the Mokobodski’s condition by using the Snell envelope theory and then we obtain a comparison result.

This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Gerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.

A bulk-arrival single server queueing system with second multi-optional service and unreliable server is studied in this paper. Customers arrive in batches according to a homogeneous Poisson process, all customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. The first service time and the second service all have general distribution and they are independent. We assume that the server has a service-phase dependent, exponentially distributed life time as well as a servicephase dependent, generally distributed repair time. Using a supplementary variable method, we obtain the transient and the steady-state solutions for both queueing and reliability measures of interest.

In this paper, we propose a new time-dependent model for solving total variation (TV) minimization problems in image restoration. The main idea is applying a priori smoothness on the solution image. Five di?erent BCs are introduced and analyzed. 2D numerical experimental results by explicit numerical schemes are discussed.

With a Hölder type inequality in Besov spaces, we show that every strong solution θ(t, x) on

In this paper we apply the (variant) fountain theorems to study the symmetric nonlinear Kirchhoff nonlocal problems. Under the Ambrosetti-Rabinowitz’s 4-superlinearity condition, or no Ambrosetti- Rabinowitz’s 4-superlinearity condition, we present two results of existence of infinitely many large energy solutions, respectively.

In this paper we consider the bifurcation problem -divA(x,▽u) = λa(x)|u|^p-2u + f(x, u, λ) in Ω with p > 1.Under some proper assumptions on A(x, ξ),a(x) and f(x, u, λ), we show that the existence of an unbounded branch of positive solutions bifurcating from the principal eigenvalue of the problem -divA(x,▽u) =λa(x)|u|^p-2u.

In this paper, we continue the discussion of [12] to establish the Hermite pseudospectral method with weight ω(x) ≡ 1. As an application, we consider the pseudospectral approximation of the reaction-diffusion equation on the whole line, we prove the existence of the approximate attractor and give the error estimate for the approximate solution.

In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coefficient μ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when μ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when μ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented.

This paper deals with the standing waves for a class of coupled nonlinear Klein-Gordon equations with space dimension By using the variational calculus and scaling argument, we establish the existence of standing waves with ground state, discuss the behavior of standing waves as a function of the frequency ω and give the sufficient conditions of the stability of the standing waves with the least energy for the equations under study.

The state 0 of a birth and death process with state space E = {0, 1, 2, · · ·} is a barrier which can be classified into four kinds: reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.

A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.