Table of Content

01 January 2009, Volume 30 Issue 1

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Articles

System of set-valued mixed quasi-variational-like inclusions
involving H-η-monotone operators in Banach spaces

Xie-ping DING;Zhong-bao WANG

2009, 30(1):  1-12 .  doi:10.1007/s10483-009-0101-z

Abstract ( 1604 )   PDF (162KB) ( 847 )  

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A new system of the set-valued mixed quasi-variational-like inclusions (SSMQVLI) involving H_η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H_η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.

3D analysis of functionally graded material plates with complex shapes and various holes

Zhi-yuan CAO;Shougao TANG;Guohua CHENG

2009, 30(1):  13-18 .  doi:10.1007/s10483-009-0102-9

Abstract ( 1540 )   PDF (122KB) ( 777 )  

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In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with the parameters of a given FGM plate, problems of FGM plate under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, which is proven to be an effective numerical method for the mechanical analyses of FGM structures. Examples of FGM plates with complex shapes and various holes are presented.

An open-plus-closed-loop control for chaotic Mathieu-Duffing oscillator

Jian-he SHEN;Shu-hui CHEN

2009, 30(1):  19-27 .  doi:10.1007/s10483-009-0103-z

Abstract ( 1489 )   PDF (662KB) ( 1084 )  

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By using the idea of open-plus-closed-loop(OPCL) control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to verify the theoretical results.

Optimal error estimates for Fourier spectral approximation of the generalized KdV equation

Zhen-guo DENG;He-ping MA

2009, 30(1):  29-38 .  doi:10.1007/s10483-009-0104-1

Abstract ( 1726 )   PDF (141KB) ( 821 )  

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A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L²-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.

Elastodynamics of axi-symmetric deformation in magneto-micropolar generalized thermoelastic medium

Rajneesh Kumar;Rupender

2009, 30(1):  39-48 .  doi:10.1007/s10483-009-0105-6

Abstract ( 1454 )   PDF (335KB) ( 831 )  

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The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transform techniques are used to solve the problem. Various types of sources are taken to illustrate the utility of the approach. Integral transforms are inverted by using a numerical technique to obtain the components of stresses, temperature distribution, and induced electric and magnetic fields. The expressions of these quantities are illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i.e., Lord and Shulman (L-S theory) and Green and Lindsay (G-L theory). Some particular interesting cases are also deduced from the present investigation.

An efficient FEM for pressure analysis of oil film in a piston pump

Tadeusz Zloto;Arkadiusz Nagorka

2009, 30(1):  49-61 .  doi:10.1007/s10483-009-0106-z

Abstract ( 1421 )   PDF (4436KB) ( 1108 )  

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The paper concerns numerical analysis of pressure distribution of an oil film on the valve plate in the variable height gap of an axial piston pump. The analysis employs the finite element method. For determination of oil pressure variations in the gap, the Reynolds equation, commonly applied in the theory of lubrication, is applied. The equation is solved numerically with the use of self-developed program based on the finite element method. In order to obtain high accuracy of the results, an adaptive mesh refinement based on residual estimations of solution errors is applied. The calculation results are represented as dependent on the geometric and working parameters of the pump.

Exact analytical solution to three-dimensional phase change heat transfer
problems in biological tissues subject to freezing

Fang-fang LI;Jing LIU;Kai YUE

2009, 30(1):  63-72 .  doi:10.1007/s10483-009-0107-x

Abstract ( 1911 )   PDF (152KB) ( 1060 )  

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Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.

A parametric type of KKM theorem in FC-spaces with applications

Lei DENG;Xiao-yan ZANG

2009, 30(1):  73-79 .  doi:10.1007/s10483-009-0108-x

Abstract ( 1592 )   PDF (124KB) ( 609 )  

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The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then
established in noncompact $FC$-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures.

Three positive doubly periodic solutions of a nonlinear telegraph system

Fang-lei WANG;Yu-kun AN

2009, 30(1):  81-88 .  doi:10.1007/s10483-009-0109-z

Abstract ( 1911 )   PDF (111KB) ( 764 )  

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This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.

CCH-based geometric algorithms for SVM and applications

Xin-jun PENG;Yi-fei WANG

2009, 30(1):  89-100 .  doi:10.1007/s10483-009-0110-6

Abstract ( 1570 )   PDF (205KB) ( 888 )  

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The support vector machine (SVM) is a novel machine learning tool in data mining. In this paper, the geometric approach based on the compressed convex hull (CCH) with a mathematical framework is introduced to solve SVM classification problems. Compared with the reduced convex hull (RCH), CCH preserves the shape of geometric solids for data sets; meanwhile, it is easy to give the necessary and sufficient condition for determining its extreme points. As practical applications of CCH, spare and probabilistic speed-up geometric algorithms are developed. Results of numerical experiments show that the proposed algorithms can reduce kernel calculations and display nice performances.

Free vibration and transverse stresses of viscoelastic laminated plates

Ming-yong HU;An-wen WANG

2009, 30(1):  101-108 .  doi:10.1007/s10483-009-0111-y

Abstract ( 1643 )   PDF (318KB) ( 993 )  

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Based on Reddy's layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of
simply supported viscoelastic sandwich plate, showing good agreement
with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lower-frequency free vibration, and the transverse normal stress is the main one in higher-frequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress's maximum value and the in-plane stress's maximum-value is obtained.
The results show that the proposed method, and the adopted equations
and programs are reliable.

Spectral properties and geometric interpretation of R-filters

Tuo LENG

2009, 30(1):  109-120 .  doi:10.1007/s10483-009-0112-2

Abstract ( 1510 )   PDF (136KB) ( 733 )  

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By applying the Fourier analysis, we study the spectral properties of R-filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation of R-filters.

An iterative modified kernel based on training data

Zhi-xiang ZHOU;Feng-qing HAN

2009, 30(1):  121-128 .  doi:10.1007/s10483-009-0113-x

Abstract ( 1515 )   PDF (175KB) ( 919 )  

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To improve performance of a support vector regression, a new method for a modified kernel function is proposed. In this method, information of all samples is included in the kernel function with conformal mapping. Thus the kernel function is data-dependent. With a random initial parameter, the kernel function is modified repeatedly until a satisfactory result is achieved. Compared with the conventional model, the improved approach does not need to select parameters of the kernel function. Simulation is carried out for the one-dimension continuous function and a case of strong earthquakes. The results show that the improved approach has better learning ability and forecasting precision than the traditional model. With the increase of the iteration number, the figure of merit decreases and converges. The speed of convergence depends on the parameters used in the algorithm.