In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in B_{∞,∞}^{0}. We show that a smooth solution of the 3D MHD equations with zero kinematic viscosity in the whole space R^{3} breaks down if and only if certain norm of the vorticity blows up at the same time.
In this paper, we consider a risk model in which each main claim may induce a delayed claim, called a by-claim. We assume that the time for the occurrence of a by-claim is random. We investigate the expected discounted penalty function, and derive the defective renewal equation satisfied by it. We obtain some explicit results when the main claim and the by-claim are both exponentially distributed, respectively. We also present some numerical illustrations.
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k, l)- algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid. The finitedimensional and infinite-dimensional dissipativity results of (k, l)-algebraically stable Runge-Kutta methods are obtained.
Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components: model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.
Image denoising is still a challenge of image processing. Buades et al. proposed a nonlocal means (NL-means) approach. This method had a remarkable denoising results at high expense of computational cost. In this paper, We compared several fast non-local means methods, and proposed a new fast algorithm. Numerical experiments showed that our algorithm considerably reduced the computational cost, and obtained visually pleasant images.
In this paper, we prove that the generator g of a class of backward stochastic differential equations (BSDEs) can be represented by the solutions of the corresponding BSDEs at point (t, y, z), when the terminal data is in L^{p} spaces, for 1 < p ≤ 2.
Empirical likelihood is a nonparametric method for constructing confidence intervals and tests, notably in enabling the shape of a confidence region determined by the sample data. This paper presents a new version of the empirical likelihood method for quantiles under kernel regression imputation to adapt missing response data. It eliminates the need to solve nonlinear equations, and it is easy to apply. We also consider exponential empirical likelihood as an alternative method. Numerical results are presented to compare our method with others.
This work studies a proportional hazards model for survival data with “long-term survivors”, in which covariates are subject to linear measurement error. It is well known that the naive estimators from both partial and full likelihood methods are inconsistent under this measurement error model. For measurement error models, methods of unbiased estimating function and corrected likelihood have been proposed in the literature. In this paper, we apply the corrected partial and full likelihood approaches to estimate the model and obtain statistical inference from survival data with long-term survivors. The asymptotic properties of the estimators are established. Simulation results illustrate that the proposed approaches provide useful tools for the models considered.
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained, which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs), neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
In this paper, we focus on studying approximate solutions of damped oscillatory solutions of the compound KdV-Burgers equation and their error estimates. We employ the theory of planar dynamical systems to study traveling wave solutions of the compound KdV-Burgers equation. We obtain some global phase portraits under different parameter conditions as well as the existence of bounded traveling wave solutions. Furthermore, we investigate the relations between the behavior of bounded traveling wave solutions and the dissipation coefficient r of the equation. We obtain two critical values of r, and find that a bounded traveling wave appears as a kink profile solitary wave if |r| is greater than or equal to some critical value, while it appears as a damped oscillatory wave if |r| is less than some critical value. By means of analysis and the undetermined coefficients method, we find that the compound KdV-Burgers equation only has three kinds of bell profile solitary wave solutions without dissipation. Based on the above discussions and according to the evolution relations of orbits in the global phase portraits, we obtain all approximate damped oscillatory solutions by using the undetermined coefficients method. Finally, using the homogenization principle, we establish the integral equations reflecting the relations between exact solutions and approximate solutions of damped oscillatory solutions. Moreover, we also give the error estimates for these approximate solutions.
In this paper, a new conservative finite difference scheme with a parameter θ is proposed for the initial-boundary problem of the Klein-Gordon-Zakharov (KGZ) equations. Convergence of the numerical solutions are proved with order O(h^{2} + τ^{2}) in the energy norm. Numerical results show that the scheme is accurate and efficient.
In this paper, we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-φ-non-expansive mappings and the set of solutions of an equilibrium problem. We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property (K).
In this paper we study the existence of nontrivial solutions for the periodic discrete nonlinear equation Lu_{n} - ωu_{n} = f_{n}(u_{n}),
where Lu_{n} = a_{n+1}u_{n+1} + a_{n-1}u_{n-1} + b_{n}u_{n}
is the discrete Laplacian in one spatial dimension. The given real-valued sequences a_{n}, b_{n} are assumed to be N-periodic in n, i.e., a_{n+N} = a_{n}, b_{n+N} = b_{n}. The nonlinearity f_{n}(t) is N-periodic in n and asymptotically linear at infinity. We show that, if ω is in the spectrum gap of L, there is a nontrivial solution. The proof is based on the strongly indefinite functional critical points theorem developed recently.
In this paper, we obtain the Painlevé-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequence of mappings converging in a real locally convex Hausdorff topological vector spaces.
By employing the empirical likelihood method, confidence regions for the stationary AR(p)-ARCH(q) models are constructed. A self-weighted LAD estimator is proposed under weak moment conditions. An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained. Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy, especially for relative small size of observation.
In this article, the Bayes linear unbiased estimator (BALUE) of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Bayesian Pitman closeness (PC) criterion.
An L(2, 1)-labelling of a graph G is a function from the vertex set V (G) to the set of all nonnegative integers such that |f(u) - f(v)| ≥ 2 if d_{G}(u, v) = 1 and |f(u) - f(v)| ≥ 1 if d_{G}(u, v) = 2. The L(2, 1)-labelling problem is to find the smallest number, denoted by λ(G), such that there exists an L(2, 1)-labelling function with no label greater than it. In this paper, we study this problem for trees. Our results improve the result of Wang [The L(2, 1)-labelling of trees, Discrete Appl. Math. 154 (2006) 598-603].
In this paper, we prove some results concerning blow-up of viscous compressible reactive (selfgravitating) flows when the initial density is compactly supported and the other initial value satisfy proper conditions. It extends the work of Xin and Cho to the case of viscous compressible reactive self-gravitating flows equations. We control the lower bound of second moment by total energy and obtain the precise relationship between the size of the support of initial density and the existence time.
Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations. New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney (BBM) equations are obtained with the aid of computer algebraic system Maple. The method is also valid for other (1+1)-dimensional and higher dimensional systems.