Authors:Yu Liu; Chen-dong Xu Pages: 1 - 13 Abstract: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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:Run-zhang Xu; Xing-chang Wang; Shao-hua Chen; Yu Liu; Yan-bing Yang Pages: 389 - 408 Abstract: Abstract In this paper we deal with the initial boundary value problem for two classes of reaction diffusion systems with two source terms in bounded domain. Under some assumptions on the exponents and the initial data, applying the comparison principle, the maximum principle and the supersolution-subsolution method, we prove the global existence and blow up of solutions. We also establish some upper blow up rates. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3136-2 Issue No:Vol. 31, No. 4 (2016)

Authors:Yolanda M. Gómez; Ignacio Vidal Pages: 409 - 424 Abstract: Abstract In this paper we introduce an extension of the half-normal distribution in order to model a great variety of non-negative data. Its hazard rate function can be decreasing or increasing, depending on its parameters. Some properties of this new distribution are presented. For example, we give a general expression for the moments and a stochastic representation. Also, the cumulative distribution function, the hazard rate function, the survival function and the quantile function can be easily evaluated. Maximum likelihood estimators can be computed by using numerical procedures. Finally, a real-life dataset has been presented to illustrate its applicability. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3366-3 Issue No:Vol. 31, No. 4 (2016)

Authors:Wen-hao Gui; Huai-nian Zhang Pages: 425 - 438 Abstract: Abstract In this article, we consider a lifetime distribution, the Weibull-Logarithmic distribution introduced by [6]. We investigate some new statistical characterizations and properties. We develop the maximum likelihood inference using EM algorithm. Asymptotic properties of the MLEs are obtained and extensive simulations are conducted to assess the performance of parameter estimation. A numerical example is used to illustrate the application. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3391-2 Issue No:Vol. 31, No. 4 (2016)

Authors:Yi Wu; Xue-jun Wang; Shu-he Hu Pages: 439 - 457 Abstract: 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:Xiao-yan Ma; Song-liang Qiu; Guo-yan Tu Pages: 458 - 468 Abstract: Abstract In this paper, we study the quotient of hypergeometric functions μ a (r) in the theory of Ramanujan’s generalized modular equation for a ∈ (0, 1/2]. Several new inequalities are given for this and related functions. Our main results complement and generalize some known results in the literature. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3356-5 Issue No:Vol. 31, No. 4 (2016)

Authors:Li-ping Wang; Guo-chun Wen Pages: 469 - 480 Abstract: 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)

Authors:Li-ju Shen; Sha Yao; Guang-ying Zhang; Xin-an Ren Pages: 481 - 490 Abstract: Abstract A local gradient estimate for positive solutions of porous medium equations on complete noncompact Riemannian manifolds under the Ricci flow is derived. Moreover, a global gradient estimate for such equations on compact Riemannian manifolds is also obtained. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3368-1 Issue No:Vol. 31, No. 4 (2016)

Authors:J. Arockia Reeta; J. Vimala Pages: 491 - 502 Abstract: Abstract Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle. PubDate: 2016-12-01 DOI: 10.1007/s11766-016-3411-2 Issue No:Vol. 31, No. 4 (2016)

Authors:Xiao Yu; Hui-hui Zhang; Guo-ping Zhao Pages: 331 - 342 Abstract: Abstract In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of singular integral with a rough kernel on the weighted λ-central Morrey space is also given. PubDate: 2016-09-01 DOI: 10.1007/s11766-016-3348-5 Issue No:Vol. 31, No. 3 (2016)

Authors:Zhong-ping Fan; Di-ming Lu; Xiao-lan Yu Pages: 367 - 378 Abstract: Abstract In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf subalgebra. For a non-cosemisimple Hopf algebra A with the Chevalley property, if its diagram is a Nichols algebra, then the diagram of its maximal pointed Hopf subalgebra is also a Nichols algebra. When A is of finite dimension, we provide a necessary and sufficient condition for A’s diagram equaling the diagram of its maximal pointed Hopf subalgebra. PubDate: 2016-09-01 DOI: 10.1007/s11766-016-3403-2 Issue No:Vol. 31, No. 3 (2016)