Authors:Qin Li; Zhi-yong Liu Pages: 269 - 276 Abstract: In this paper, a Kansa’s method is designed to solve numerically the Monge-Ampère equation. The primitive Kansa’s method is a meshfree method which applying the combination of some radial basis functions (such as Hardy’s MQ) to approximate the solution of the linear parabolic, hyperbolic and elliptic problems. But this method is deteriorated when is used to solve nonlinear partial differential equations. We approximate the solution in some local triangular subdomains by using the combination of some cubic polynomials. Then the given problems can be computed in each subdomains independently. We prove the stability and convergence of the new method for the elliptic Monge-Ampère equation. Finally, some numerical experiments are presented to demonstrate the theoretical results. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0656-3 Issue No:Vol. 33, No. 2 (2017)

Authors:Martin Bača; Maria Naseem; Ayesha Shabbir Pages: 277 - 286 Abstract: The Klein-bottle fullerene is a finite trivalent graph embedded on the Klein-bottle such that each face is a hexagon. The paper deals with the problem of labeling the vertices, edges and faces of the Klein-bottle fullerene in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face and the weights of all 6-sided faces constitute an arithmetic progression of difference d. In this paper we study the existence of such labelings for several differences d. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0658-1 Issue No:Vol. 33, No. 2 (2017)

Authors:Fei Fang; Zhong Tan Pages: 287 - 296 Abstract: In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13]. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0659-0 Issue No:Vol. 33, No. 2 (2017)

Authors:Eid H. Doha; Ali H. Bhrawy; Ramy M. Hafez Pages: 297 - 310 Abstract: A new spectral Jacobi rational-Gauss collocation (JRC) method is proposed for solving the multi-pantograph delay differential equations on the half-line. The method is based on Jacobi rational functions and Gauss quadrature integration formula. The main idea for obtaining a semi-analytical solution for these equations is essentially developed by reducing the pantograph equations with their initial conditions to systems of algebraic equations in the unknown expansion coefficients. The convergence analysis of the method is analyzed. The method possesses the spectral accuracy. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Indeed, the present method is compared favorably with other methods. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0660-7 Issue No:Vol. 33, No. 2 (2017)

Authors:Shan-shan Wang; Heng-jian Cui Pages: 327 - 344 Abstract: A consistent test via the partial penalized empirical likelihood approach for the parametric hypothesis testing under the sparse case, called the partial penalized empirical likelihood ratio (PPELR) test, is proposed in this paper. Our results are demonstrated for the mean vector in multivariate analysis and regression coefficients in linear models, respectively. And we establish its asymptotic distributions under the null hypothesis and the local alternatives of order n −1/2 under regularity conditions. Meanwhile, the oracle property of the partial penalized empirical likelihood estimator also holds. The proposed PPELR test statistic performs as well as the ordinary empirical likelihood ratio test statistic and outperforms the full penalized empirical likelihood ratio test statistic in term of size and power when the null parameter is zero. Moreover, the proposed method obtains the variable selection as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed method in hypothesis testing and variable selection. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0663-4 Issue No:Vol. 33, No. 2 (2017)

Authors:Shou-feng Shen; Yong-yang Jin Pages: 345 - 362 Abstract: Differential-difference equations of the form u⃛ n = F n (t, u n−1, u n , u n+1, u̇ n−1, u̇ n , u̇ n+1) are classified according to their intrinsic Lie point symmetries, equivalence group and some low-dimensional Lie algebras including the Abelian symmetry algebras, nilpotent nonAbelian symmetry algebras, solvable symmetry algebras with nonAbelian nilradicals, solvable symmetry algebras with Abelian nilradicals and nonsolvable symmetry algebras. Here F n is a nonlinear function of its arguments and the dot over u denotes differentiation with respect to t. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0664-3 Issue No:Vol. 33, No. 2 (2017)

Authors:Hee-Jin Moon; Chang-Ho Han; Yong-Kab Choi Pages: 363 - 372 Abstract: In this paper we establish asymptotic results and a generalized uniform law of the iterated logarithm (LIL) for the increments of a strictly stationary random process, whose results are proved by separating linearly positive quadrant dependent (LPQD) random process and linearly negative quadrant dependent (LNQD) one, respectively. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0665-2 Issue No:Vol. 33, No. 2 (2017)

Authors:Dan Wu Pages: 389 - 400 Abstract: In this paper, we consider the nonlinear fractional Schrödinger equations with Hartree type nonlinearity in mass-supercritical and energy-subcritical case. By sharp Hardy-Littlewood-Sobolev inequality and the Pohozaev identity, we established a threshold condition, which leads to a global existence of solutions in energy space. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0668-z Issue No:Vol. 33, No. 2 (2017)

Authors:Amir Peyravi Pages: 401 - 408 Abstract: In this article, we study the weak dissipative Kirchhoff equation \({u_{tt}} - M\left( {\left\ {\nabla u} \right\ _2^2} \right)\Delta u + b\left( x \right){u_t} + f\left( u \right) = 0\) , under nonlinear damping on the boundary \(\frac{{\partial u}}{{\partial v}} + \alpha \left( t \right)g\left( {{u_t}} \right) = 0\) . We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping. Our result extends and improves some results in the literature such as the work by Zhang and Miao (2010) in which only exponential energy decay is considered and the work by Zhang and Huang (2014) where the energy decay has been not considered. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0669-y Issue No:Vol. 33, No. 2 (2017)

Authors:Yan-jie Zhou; Fei Teng; Zhen-dong Luo Pages: 409 - 416 Abstract: In this study, a time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element (SCNMFE) formulation based on two local Gauss integrals and parameterfree with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0670-5 Issue No:Vol. 33, No. 2 (2017)

Authors:Ji-xiu Wang Pages: 417 - 434 Abstract: In this paper, we study the existence of semiclassical states for some p-Laplacian equation. Under given conditions and minimax methods, we show that this problem has at least one positive solution provided that ε ≤ E; for any m ∈ ℕ, it has m pairs solutions if ε ≤ E m , where E, E m are sufficiently small positive numbers. Moreover, these solutions are closed to zero in W 1,p (ℝ N ) as ε → 0. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0671-4 Issue No:Vol. 33, No. 2 (2017)

Authors:Juan Chen; Lu-ming Zhang Pages: 435 - 450 Abstract: In this article, a compact finite difference scheme for the coupled nonlinear Schrödinger equations is studied. The scheme is proved to conserve the original conservative properties. Unconditional stability and convergence in maximum norm with order O(τ 2 + h 4) are also proved by the discrete energy method. Finally, numerical results are provided to verify the theoretical analysis. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0672-3 Issue No:Vol. 33, No. 2 (2017)

Authors:Xiao Han; Chen-chen Zou; Xiang-zhong Fang Pages: 463 - 474 Abstract: The mortality of ovarian cancer is higher than any other female genital malignant tumors, while there exists a strong correlation between early-stage detection and cure for it. CA125 and HE4 are two most common and effective serum markers in recent screening research of ovarian cancer. This paper derives a sequential screening strategy for ovarian cancer by jointly modeling the longitudinal profiles of CA125 and HE4. We construct a Bayesian hierarchical mixture model with changepoint, and propose two approaches for diagnosis: the risk of cancer index and the hypothesis test on the true incidence time. We simulated a 7-year sequential screening research and compared with the standard approach based on a fixed cutoff level. Our approach achieves a 15% higher sensitivity for a fixed specificity, indicating that the sequential strategy combining multiple markers is more effective in the early-stage detection of ovarian cancer. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0674-1 Issue No:Vol. 33, No. 2 (2017)

Authors:Li-hua You; Fang Chen; Jian Shen; Bo Zhou Pages: 475 - 484 Abstract: For any positive integers k and m, the k-step m-competition graph C m k (D) of a digraph D has the same set of vertices as D and there is an edge between vertices x and y if and only if there are distinct m vertices v 1, v 2, · · ·, v m in D such that there are directed walks of length k from x to v i and from y to v i for all 1 ≤ i ≤ m. The m-competition index of a primitive digraph D is the smallest positive integer k such that C m k (D) is a complete graph. In this paper, we obtained some sharp upper bounds for the m-competition indices of various classes of primitive digraphs. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0675-0 Issue No:Vol. 33, No. 2 (2017)

Authors:Fan-qun Li; Xin-sheng Zhang Pages: 485 - 496 Abstract: In this paper, we consider the problem of estimating a high dimensional precision matrix of Gaussian graphical model. Taking advantage of the connection between multivariate linear regression and entries of the precision matrix, we propose Bayesian Lasso together with neighborhood regression estimate for Gaussian graphical model. This method can obtain parameter estimation and model selection simultaneously. Moreover, the proposed method can provide symmetric confidence intervals of all entries of the precision matrix. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0676-z Issue No:Vol. 33, No. 2 (2017)

Authors:Jing-fu Zhao; Hong-tao Zhang; Jing Yang Pages: 497 - 504 Abstract: This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion can create non-constant positive steady states even though the corresponding model without cross-diffusion fails. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0677-y Issue No:Vol. 33, No. 2 (2017)

Authors:Feng Wang; Jian-xing Zhao; Chao-qian Li Pages: 505 - 514 Abstract: For the Hadamard product of an M-matrix and its inverse, some new lower bounds on the minimum eigenvalue are given. These bounds can improve considerably some previous results. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0678-x Issue No:Vol. 33, No. 2 (2017)

Authors:Shu Liu Pages: 529 - 550 Abstract: We consider a longitudinal data additive varying coefficient regression model, in which the coefficients of some factors (covariates) are additive functions of other factors, so that the interactions between different factors can be taken into account effectively. By considering within-subject correlation among repeated measurements over time and additive structure, we propose a feasible weighted two-stage local quasi-likelihood estimation. In the first stage, we construct initial estimators of the additive component functions by B-spline series approximation. With the initial estimators, we transform the additive varying coefficients regression model into a varying coefficients regression model and further apply the local weighted quasi-likelihood method to estimate the varying coefficient functions in the second stage. The resulting second stage estimators are computationally expedient and intuitively appealing. They also have the advantages of higher asymptotic efficiency than those neglecting the correlation structure, and an oracle property in the sense that the asymptotic property of each additive component is the same as if the other components were known with certainty. Simulation studies are conducted to demonstrate finite sample behaviors of the proposed estimators, and a real data example is given to illustrate the usefulness of the proposed methodology. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0681-2 Issue No:Vol. 33, No. 2 (2017)

Authors:Huai-yu Zhou; Su-fang Tang Pages: 551 - 560 Abstract: We discuss the properties of solutions for the following elliptic partial differential equations system in R n , $$\begin{cases}(-\triangle)^{\frac{\alpha}{2}} u&= u^{p_{1}} v^{p_{2}}\\(-\triangle)^{\frac{\alpha}{2}} v &= u^{q_{1}} v^{q_{2}}\end{cases}$$ where 0 < α < n, p i and q i (i = 1, 2) satisfy some suitable assumptions. Due to equivalence between the PDEs system and a given integral system, we prove the radial symmetry and regularity of positive solutions to the PDEs system via the method of moving plane in integral forms and Regularity Lifting Lemma. For the special case, when p 1 + p 2 = q 1 + q 2 = \(\frac{n+\alpha}{n-\alpha}\) , we classify the solutions of the PDEs system. PubDate: 2017-04-01 DOI: 10.1007/s10255-017-0662-5 Issue No:Vol. 33, No. 2 (2017)