In this paper, we consider the problems of hypothesis testing and interval estimation for variance components in general linear mixed model. Exact test and confidence interval for a single variance component corresponding to random effect are developed based on the concepts of generalized p-value and generalized confidence interval. The generalized p-values and generalized confidence intervals we have developed are functions of the minimal sufficient statistics. Exact test and confidence interval are also established for comparing the random-effects variance components in two independent general linear mixed models. Furthermore, we investigate the statistical properties of the resulting tests and confidence intervals. Some simulation results to compare the powers of the proposed test with those of the existing method are reported. The simulation results indicate that new test appears to have significant gain in the power. Finally, the proposed methods are demonstrated by a real example.

Wavelet analysis is a new tool of time-frequency analysis besides Fourier analysis and Gabor analysis. It has been applied in signal processing, image processing and numerical analysis. A basic problem is which pairs of (A,Γ) exist wavelets.In this paper,We have filled a gap using the techniques employed by Speegle, in Ionascu and Yang Wang's proof in the paper concerning the existence of single function wavelets, and settled the question in two-dimensional case.

μ-Invariant measures play an important role in the theory of stochastic processes. At first, an existence theorem for jump process containing one instantaneous state is proved, and furthermore, the theorem can be still found only when there are some restraints on the q-pair. Then, the question that when there is a q-process P(t), such that π which is the μ-invariant measure of a given q-pair containing one instantaneous state is the μ-invariant measure of P(t) is discussed, and a sufficient condition is obtained.

By applying upper and lower solutions method together with maximal principle, the existence and uniqueness of positive solution for a class of fourth-order singular differential equations with integral boundary value problems are investigated. Sufficient conditions for the existence and uniqueness of C²[0,1] positive solution as well as C³[0,1] are given. Our nonlinearity f(t,x) may be singular at x, t=0 and /or t=1.

In this paper, we assume that the standard parameters of backward stochastic differential equations (BSDEs) satisfy weak assumptions. We prove that the generator g of a BSDE can be uniquely determined by the initial values of the corresponding BSDEs with all terminal conditions. The result also confirms and extends Peng's conjecture.

The point spectrum and the residual spectrum are divided into two kinds, respectively, that is σ_p1,σ_p2 and σ_r1,σ_r2. In this paper, let H and K be separable Hilbert spaces. When A∈B(H) and B∈B(K) are given, we get results on perturbation of this four kinds spectrum of M_C, where .

On the K-quasi-additive fuzzy number valued measure space, aim at given the K-quasi-additive fuzzy number-valued integrals, and regard the whole this kind of integrals as a set function taken valued fuzzy numbers on the measurable spaces, we study their pseudo-autocontinuity from above (below), pseudo-uniform autocontinuity from above (below) and pseudo-double-null asymptotic additivity etc. structural characteristics.

In this paper we have successfully characterized two-degree integral subgraph of q-tree and added-vertex q-tree on n vertices by chromatic polynomials only that if the minimum degree of graph G does not equal δ(G)≠q-3, then the graphs with the chromatic polynomial as following P(G;λ)=λ(λ-1) ... (λ-q+2)(λ-q+1)³(λ-q)^n-q-2, n≥q+2, could only be two-degree integral subgraph of q-tree or added-vertex q-tree on n vertices.

In this paper, we consider the risk process with negative risk sums perturbed by diffusion under constant interest force. Integral equations and integro-differential equations for the probability of ruin for the proposed model are derived. We give the the explicit expression for the probability of ruin when the Z_k's are exponential distributions.

In ATM, arrival rate and service rate of customers vary randomly according to changes of the random environment. In the paper, we deal with a multi-server queueing system with random environment. During sojourns in the state i(1≤i≤m), customers arrive to the system according to a Poisson process of rate λ_i. During sojourn intervals in the state i the service rate μ_i prevails. In the system, there are finite waiting positions and infinite positions of retry orbit, the customers who fail to retry will leave the system with a certain probability forever. Using quasi-birth-death (QBD) process, we obtain the necessary and sufficient condition for stability of the system, the conditional indexes and overall means of the queue in every state are obtained Additionally, the affect of various parameters of Rush-hour and other parameters on the system state and busy cycle are illustrated numerically.

Let γ_s^*(G) be the number of the vertex-edge total signed domination of graph. This paper gives the exact value of the vertex-edge total signed domination number of complete graph with even order.

By using the modified CK's direct method, we set up the symmetry group theorem of the coupled KdV equations. Applying our theorem, some new explicit solutions of the coupled KdV equations are obtained by old solutions of the equation. Based on our results of Lie symmetries, we also get conservation laws of the coupled KdV equations.

Let k[x₁,x₂,...,x_n] be a polynomial ring in the variables x₁,x₂,...,x_n with coefficient in K, I be a zero-dimensional ideal in k[x₁,x₂,...,x_n]. In this paper, we investigate relation of regular and in normal position with respect to a variable, and we show equivalent of regular and in normal position with respect to variable x_i in a zero-dimension ideal under some condictions.

In this paper, the nonlinear regression models with right censored data are considered, an ajusted empirical log-likelihood ratio is proposed for the vector of regression parameter. Under certain conditions, it is shown that the proposed statistics have the chi-squared limiting distribution, which enables us to construct the confidence regions of the parameters of interest. In the simulation study, we have compared the performance of the finite sample for the classical empirical likelihood, the adjusted empirical likelihood and the nonlinear least squares methods. An illustration is given by using chloride transport data.

The basic properties of randomized similarity and randomized logic pseudo-metric are given in R₀ three-valued propositional logic system. After that, the randomized divergence degree of theories is introduced in randomized logic metric space. It is proved that the set of atomic formulas is not totally divergent in randomized logic metric space. It is divergent or not is decided by the randomized number sequence.

In this paper, the concept of globally proper efficient subdifferential is introduced for a set-valued mapping. The necessary optimality conditions of the constraintset-valued optimization problem for globlly proper efficient solutions are established in terms of support function of set-valed mapping and Lagrange multiplier by using the concept of globally proper efficient subdifferential for set-valued mapping.

In this paper, the partial cooperative game on mesh-like directed graph has been researched, by defining the cooperative function on each state node of the directed graph and applying the concept of strategy in graph-game constructed by Berge C. During the process of the game, players take partial cooperative behavior instead of the complete cooperative one. The main character of partial cooperative game is that each player's behavior is a combination of cooperative one and individual one. In this paper, players are permitted to leave the coalition after joining it. Also, on directed graph, the value of partial cooperative games, the algorithm for constructing the optimal path, and some illustrations are given.

In this paper, by using the method of lower solution and topology degree theorem, we study the existence of positive solution for a class of singular second-order four-point boundary value problem with sign changing nonlinearity. The associated Green's function for the above problem is given. As an application, we also give an example to demonstrate our result. The results of this paper are new and extend previously known results.

In this paper, we consider the M/M/1 queue with multiple vacation policy and the vacation time follows T-SPH distribution. Based on the QBD process and operator-geometric method, we get the stochastic decomposition structures for the stationary queue length and waiting time for the model, and also we give PGF for the additional queue length and the LST for additional delay.

By using the method of Picard-Fuchs equation and the Riccati equation method, we give a linear estimate of the number of zeros of Abelian integrals for the quadratic reversible systems under polynomial perturbations of arbitrary degree n. The upper bound is 4[2n/3]+2[(2n+1)/3]+[(2n+2)/3]+16 when n > 3.

The existence and successive iteration of positive solutions for some impulsive boundary value problems with p-Laplacian on half line are investigated in this paper and the corresponding iterative schemes for approximating the solutions are also given.

In this paper, the constrained sequential max-min problems are considered. The objective function and partial constraint functions are smoothed by using aggregate function, then the existence of the generalized K-K-T point under quasi-normal cone condition is constructively proved based on the homotopy method. For almost all the interior points in the feasible region, the homotopy path generated with aggregated homotopy interior point method converges to the generalized K-K-T point.

In experimental design, optimal design and uniform design are two important types of designs. They have different advantages and shortcomings. In this paper, the threshold accepting algorithm is considered to construct the multi-dimension D-optimal design. And based on the D-optimal design and uniform design, a new type of design, constructed by a new algorithm, is considered. Numerical results show that this type of design has a trade-off between the $D$-efficiency and robustness.

A new space L²(T) on time scales T is defined in this paper. With the aid of theory of Weyl circle, we investigate the classification of limit circle and limit point for the following second-order dynamic equation on time scales Ly=-[p(t)y^Δ]^Δ+q(t)y^σ=λy^σ where p(t)∈C^'_rd, q(t)∈C_rd, q(t)>0, λ∈C₀. The problem of limit circle with bounded perturbation for the dynamic equations Ly=λy^σ is also involved, and the invariability under the bounded perturbation is obtained.

The dynamics of a delayed Nicholson blowflies equation with delay-dependent parameters are investigated. We prove geometrically that a finite number of Hopf bifurcations occur between two critical values of time delay τ. By using the perturbation approach, an approximation to the bifurcating periodic solution and the formulas for determining the direction and stability of the Hopf bifurcations are derived. Finally, some numerical examples supporting our theoretical predictions are also given.

Let G=(V,E) be a graph, a function f: E →{-1,1} is said to be a inverse signed edge dominating function of G, if holds for every edge e∈E(G). The inverse signed edge domination number of G, denoted as , equals is a inverse signed edge dominating function ofG}. On the basis of the inverse signed edge domination number of a graph G defined, some upper bounds of for general graphs are obtained.

A kind of rational cubic spline with parameters is constructed, which is the extension of the standard cubic spline. Selecting proper parameters, the given spline can more approximate the interpolated curve than the standard cubic spline. The shape of the interpolating curve can be adjusted by parameters locally, which is convenient for user to restrict the interpolating curves. How to constrain the interpolating curve to be in the given region is studied. The sufficient conditions for the interpolating curves to be above, below or between the given piecewise quadratic curves are derived. Two examples are given in this paper.

In this paper, we systematically study the sufficient and necessary conditions of stability, asymptotical stability,uniform stability and unstability of the equilibrium solution x=0 to dynamic equation on time scale x^Δ=f(t,x), (t,x)∈T×Rⁿ. In the proof, sufficient conditions are proved mainly by properties of function of Class K and continuation of Lyapunov function; in necessary proof,we separately structure Lyapunov functions which satisfy the conditions of the theorems, such that the results establish.

In this paper, we discuss the left-definite boundary conditions of a class of fourth-order differential operators, and we study the left-definite problems by the positive definiteness of the self-adjoint extension. Besides, we give the necessary and sufficient conditions of left-defined problem by means of the cofficient of self-adjoint differential operators, the endpoints of interval and boundary conditions. Moreover, we correspondingly obtain all of the left-defined boundary matrix of fourth-order self-adjoint differential operators.

A hybrid iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of a family of quasi-φ-asymptotically nonexpansive mappings in a Banach space is induced. Under suitable conditions the strong convergence theorems are proved. The results presented in the paper extend and improve the corresponding results announced by many others.

In this paper, Newton-KKT interior-point methods for indefinite quadratic programming is extended and applied to some special linear complementarity problems. Global and local quadratic convergence properties of the extended method are analyzed under nondegeneracy assumptions. Numerical results show that the proposed method is practical.

When the tail of the claim size distribution is consistently varying, the precise large deviations for the risk process of the model based on the policy entrance process (LIG) are derived in this paper.

In this article, we consider the nonlinear cell division model with proliferating phase and quiescent phase. The trait of the model is that the cell division rate and cell-stage transition rates are dependent of the age and the total cell population. By using the Banach fixed point theorem, we prove the existence and uniqueness of a global solution for this problem.

In this paper, we consider the problem of determining the potential and the boundary conditions by three spectra. That is to prove that the potential on [0,1] can be uniquely determined by a full spectrum on [0,1] and two partial spectra on [0,a] and [a,1] (0 < a < 1) respectively. On both of these two subinterval, any one of the eigenvalues can be missed in each interval respectively. After these two eigenvalues missed, the potential can also be uniquely determined.

In this paper, an alternating projection method is proposed for solving nonlinear saddle point problems, and the convergence property of the proposed method is proved. Some primary numerical results in comparion with the preconditioned Arrow-Hurwicz method show that the proposed method is applicable and efficient.

In this paper, a high accuracy numerical simulative method is studied for heat conduction equations with discontinuous diffusion coefficient on large fluid distortion grids. This method applies a so-called "twin-fitting" approximate method proposed in this paper to the calculation of fluxes on edges, then improves calculational accuracy of fluxes on edges with discontinuous diffusion coefficient, at last is given some related error analysis. In two dimension case, an adaptive and high accuracy method is constructed to calculate fluxes on edges, here the "adaptive" means to determine the stencils and the weights adaptively. Numerical experiments show that this method can be accommodated to large fluid distortion grids and the difficult case of discontinuous diffusion coefficient.

The Shapley value of n-person cooperative games with interval coalition worth is investigated. In this paper, by means of operation rules of interval numbers, the axiom system is set up. We prove the existence and uniqueness of a solution concept for n-person games with interval coalition worth, which is called the Shapley value. And an explicit formula and some properties of the Shapley value are given. Finally, an illustrative example is provided to verify its feasibility and practicality.

In this paper, some tests are investigated for conditional heteroscedasticity of dynamic panel data models. For the dynamic panel data models with fixed effects when both n and T are large, by first-order difference of the residuals, some artificial autoregressive models are considered and some tests are constructed on the basis of the ordinary least squares (OLS) estimators of the coefficients of the artificial autoregressive models. The results show that the tests are asymptotically distributed as Χ² and easy to implement. The small sample properties of the tests are investigated by means of Monte Carlo experiments. The evidence shows that the tests perform well.

This paper deals with the upper-bound estimates of ruin probability in the compound Pascal risk Model with random interest under stochastic environment. For the Pascal risk Model in which the interest rates and premium rates change separately based on two markov environment, we give the inequalities for ruin probabilities.

In this paper, two classes of new descent methods with variable parameters are proposed to solve unconstrained optimization problems. And, under Wolfe line search conditions, we proved their global convergence without the given sufficient descent condition. Many numerical experiments show that they are efficient and robust, and they can be widely used in scientific computation.