Authors:Zhi-ting Xu; Dan-xia Chen Pages: 127 - 146 Abstract: The aim of this paper is to study the dynamics of an SIS epidemic model with diffusion. We first study the well-posedness of the model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions connecting the disease-free equilibrium and the endemic equilibrium when R 0 > 1 and c > c*. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R 0 > 1 and c ∈ [0, c*). PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3460-1 Issue No:Vol. 32, No. 2 (2017)

Authors:De-xing Kong; Qi Liu Pages: 147 - 163 Abstract: In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the (1 + n)-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n = 2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem; while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3422-7 Issue No:Vol. 32, No. 2 (2017)

Authors:Yue Zhang; Chun-gang Zhu; Qing-jie Guo Pages: 164 - 182 Abstract: Rational Bézier surface is a widely used surface fitting tool in CAD. When all the weights of a rational Bézier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational Bézier surfaces. In this paper, we study on the degenerations of the rational Bézier surface with weights in the exponential function and indicate the difference of our result and the work of Garc´ıa-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational Bézier surface with weights in the exponential function is defined, which is just the limit of the surface. Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3457-9 Issue No:Vol. 32, No. 2 (2017)

Authors:Asad Khan; Luo Jiang; Wei Li; Li-gang Liu Pages: 183 - 200 Abstract: Color transfer between images uses the statistics information of image effectively. We present a novel approach of local color transfer between images based on the simple statistics and locally linear embedding. A sketching interface is proposed for quickly and easily specifying the color correspondences between target and source image. The user can specify the correspondences of local region using scribes, which more accurately transfers the target color to the source image while smoothly preserving the boundaries, and exhibits more natural output results. Our algorithm is not restricted to one-to-one image color transfer and can make use of more than one target images to transfer the color in different regions in the source image. Moreover, our algorithm does not require to choose the same color style and image size between source and target images. We propose the sub-sampling to reduce the computational load. Comparing with other approaches, our algorithm is much better in color blending in the input data. Our approach preserves the other color details in the source image. Various experimental results show that our approach specifies the correspondences of local color region in source and target images. And it expresses the intention of users and generates more actual and natural results of visual effect. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3447-y Issue No:Vol. 32, No. 2 (2017)

Authors:Xiao-hui Li; Huo-jun Ruan Pages: 201 - 210 Abstract: In this paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket (SG). As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5: Δu = 0 on SG {q 1, q 2, q 3}, and u(q i ) = a i , i = 1, 2, 3, where q i , i = 1, 2, 3, are boundary points of SG. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3482-8 Issue No:Vol. 32, No. 2 (2017)

Authors:Wen-sheng Wang Pages: 211 - 224 Abstract: In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-Itô-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3160-x Issue No:Vol. 32, No. 2 (2017)

Authors:Guo-lin Yu Pages: 225 - 236 Abstract: There are two approaches of defining the solutions of a set-valued optimization problem: vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated (weak) minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3414-7 Issue No:Vol. 32, No. 2 (2017)

Authors:Shu-guang Han; Jiu-ling Guo; Lu-ping Zhang; Jue-liang Hu; Yi-wei Jiang; Di-wei Zhou Pages: 237 - 252 Abstract: This paper investigates the online inventory problem with interrelated prices in which a decision of when and how much to replenish must be made in an online fashion even without concrete knowledge of future prices. Four new online models with different price correlations are proposed in this paper, which are the linear-decrease model, the log-decrease model, the logarithmic model and the exponential model. For the first two models, the online algorithms are developed, and as the performance measure of online algorithm, the upper and lower bounds of competitive ratios of the algorithms are derived respectively. For the exponential and logarithmic models, the online algorithms are proposed by the solution of linear programming and the corresponding competitive ratios are analyzed, respectively. Additionally, the algorithm designed for the exponential model is optimal, and the algorithm for the logarithmic model is optimal only under some certain conditions. Moreover, some numerical examples illustrate that the algorithms based on the dprice-conservative strategy are more suitable when the purchase price fluctuates relatively flat. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3360-4 Issue No:Vol. 32, No. 2 (2017)

Authors:Yu Liu; Chen-dong Xu Pages: 1 - 13 Abstract: A new method for approximation of conic section by quartic Bézier curve is presented, based on the quartic Bézier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G 2 continuous spline approximation of conic section when using the subdivision scheme, and the effectiveness of this method is demonstrated by some numerical examples. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3434-3 Issue No:Vol. 32, No. 1 (2017)

Authors:Cai-yun Li; Chun-gang Zhu Pages: 14 - 26 Abstract: Parametric polynomial surface is a fundamental element in CAD systems. Since the most of the classic minimal surfaces are represented by non-parametric polynomial, it is interesting to study the minimal surfaces represented in parametric polynomial form. Recently, Ganchev presented the canonical principal parameters for minimal surfaces. The normal curvature of a minimal surface expressed in these parameters determines completely the surface up to a position in the space. Based on this result, in this paper, we study the bi-quintic isothermal minimal surfaces. According to the condition that any minimal isothermal surface is harmonic, we can acquire the relationship of some control points must satisfy. Follow up, we obtain two holomorphic functions f(z) and g(z) which give the Weierstrass representation of the minimal surface. Under the constrains that the minimal surface is bi-quintic, f(z) and g(z) can be divided into two cases. One case is that f(z) is a constant and g(z) is a quadratic polynomial, and another case is that the degree of f(z) and g(z) are 2 and 1 respectively. For these two cases, we transfer the isothermal parameter to canonical principal parameter, and then compute their normal curvatures and analyze the properties of the corresponding minimal surfaces. Moreover, we study some geometric properties of the bi-quintic harmonic surfaces based on the Bézier representation. Finally, some numerical examples are demonstrated to verify our results. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3451-2 Issue No:Vol. 32, No. 1 (2017)

Authors:Fei-wei Qin; Shu-ming Gao; Xiao-ling Yang; Jing Bai; Qu-hong Zhao Pages: 27 - 52 Abstract: During the new product development process, reusing the existing CAD models could avoid designing from scratch and decrease human cost. With the advent of big data, how to rapidly and efficiently find out suitable 3D CAD models for design reuse is taken more attention. Currently the sketch-based retrieval approach makes search more convenient, but its accuracy is not high enough; on the other hand, the semantic-based retrieval approach fully utilizes high level semantic information, and makes search much closer to engineers’ intent. However, effectively extracting and representing semantic information from data sets is difficult. Aiming at these problems, we proposed a sketch-based semantic retrieval approach for reusing 3D CAD models. Firstly a fine granularity semantic descriptor is designed for representing 3D CAD models; Secondly, several heuristic rules are adopted to recognize 3D features from 2D sketch, and the correspondences between 3D feature and 2D loops are built; Finally, semantic and shape similarity measurements are combined together to match the input sketch to 3D CAD models. Hence the retrieval accuracy is improved. A sketch-based prototype system is developed. Experimental results validate the feasibility and effectiveness of our proposed approach. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3450-3 Issue No:Vol. 32, No. 1 (2017)

Authors:Fan Zhang; Xue-ying Qin; Xue-mei Li; Fu-hua Cheng Pages: 53 - 67 Abstract: For a given set of data points in the plane, a new method is presented for computing a parameter value (knot) for each data point. Associated with each data point, a quadratic polynomial curve passing through three adjacent consecutive data points is constructed. The curve has one degree of freedom which can be used to optimize the shape of the curve. To obtain a better shape of the curve, the degree of freedom is determined by optimizing the bending and stretching energies of the curve so that variation of the curve is as small as possible. Between each pair of adjacent data points, two local knot intervals are constructed, and the final knot interval corresponding to these two points is determined by a combination of the two local knot intervals. Experiments show that the curves constructed using the knots by the new method generally have better interpolation precision than the ones constructed using the knots by the existing local methods. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3338-2 Issue No:Vol. 32, No. 1 (2017)

Authors:M. Sh. Dahaghin; Sh. Eskandari Pages: 68 - 78 Abstract: In this paper, we present a numerical method for solving two-dimensional Volterra-Fredholm integral equations of the second kind (2DV-FK2). Our method is based on approximating unknown function with Bernstein polynomials. We obtain an error bound for this method and employ the method on some numerical tests to show the efficiency of the method. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3352-4 Issue No:Vol. 32, No. 1 (2017)

Authors:Jun Zhao; Yi Zhang Pages: 79 - 92 Abstract: Portfolio selection is an important issue in finance and it involves the balance between risk and return. This paper investigates portfolio selection under Mean-CVaR model in a nonparametric framework with α-mixing data as financial data tends to be dependent. Many works have provided some insight into the performance of portfolio selection from the aspects of data and simulation while in this paper we concentrate on the asymptotic behaviors of the optimal solutions and risk estimation in theory. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3472-x Issue No:Vol. 32, No. 1 (2017)

Authors:Xiao-feng Yang; Jin-ping Yu Pages: 93 - 107 Abstract: Under the assumption that the dynamic assets price follows the variance gamma process, we establish a new bilateral pricing model of interest rate swap by integrating the reduced form model for swap pricing and the structural model for default risk measurement. Our pricing model preserves the simplicity of the reduced form model and also considers the dynamic evolution of the counterparty assets price by incorporating with the structural model for default risk measurement. We divide the swap pricing framework into two parts, simplifying the pricing model relatively. Simulation results show that, for a one year interest rate swap, a bond spread of one hundred basis points implies a swap credit spread about 0.1054 basis point. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3290-1 Issue No:Vol. 32, No. 1 (2017)

Authors:Man-jun Ma; Hui Li; Mei-yan Gao; Ji-cheng Tao; Ya-zhou Han Pages: 108 - 116 Abstract: In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3409-4 Issue No:Vol. 32, No. 1 (2017)

Authors:Yi-fen Ke; Chang-feng Ma Pages: 117 - 126 Abstract: In this paper, we propose and analyze an accelerated augmented Lagrangian method (denoted by AALM) for solving the linearly constrained convex programming. We show that the convergence rate of AALM is O(1/k 2) while the convergence rate of the classical augmented Lagrangian method (ALM) is O(1/k). Numerical experiments on the linearly constrained l 1−l 2 minimization problem are presented to demonstrate the effectiveness of AALM. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3381-z Issue No:Vol. 32, No. 1 (2017)

Authors:Dong-mei Liu; You-shan Tao Pages: 379 - 388 Abstract: This work deals with the zero-Neumann boundary problem to a fully parabolic chemotaxis system with a nonlinear signal production function f(s) fulfilling 0 ≤ f(s) ≤ Ks α for all s ≥ 0, where K and α are positive parameters. It is shown that whenever 0 < α < \(\frac{2}{n}\) (where n denotes the spatial dimension) and under suitable assumptions on the initial data, this problem admits a unique global classical solution that is uniformly-in-time bounded in any spatial dimension. The proof is based on some a priori estimate techniques. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3386-z Issue No:Vol. 31, No. 4 (2016)

Authors:Yi Wu; Xue-jun Wang; Shu-he Hu Pages: 439 - 457 Abstract: In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent (NSD, in short) random variables is established. By using the exponential inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3406-z Issue No:Vol. 31, No. 4 (2016)

Authors:Li-ping Wang; Guo-chun Wen Pages: 469 - 480 Abstract: Firstly, the Riemann boundary value problem for a kind of degenerate elliptic system of the first order equations in R 4 is proposed. Then, with the help of the one-to-one correspondence between the theory of Clifford valued generalized regular functions and that of the degenerate elliptic system’s solution, the boundary value problem as stated above is transformed into a boundary value problem related to the generalized regular functions in Clifford analysis. Moreover, the solution of the Riemann boundary value problem for the degenerate elliptic system is explicitly described by using a kind of singular integral operator. Finally, the conditions for the existence of solutions of the oblique derivative problem for another kind of degenerate elliptic system of the first order equations in R 4 are derived. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3285-3 Issue No:Vol. 31, No. 4 (2016)