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The numerical solution of advection-diffusion problems using new cubic trigonometric B-splines approach

APPLIED MATHEMATICAL MODELLING 2016年第7-8期40卷 4586-4611页

作者： Nazir, Tahir Abbas, Muhammad Ismail, Ahmad Izani Md Abd Majid, Ahmad Rashid, Abdur Univ Sargodha Dept Math Sargodha 40100 Pakistan Univ Sains Malaysia Sch Math Sci George Town 11800 Malaysia Gomal Univ Dept Math Dera Ismail Khan 29050 Pakistan

A new cubic trigonometric B-spline collocation approach is developed for the numerical solution of the advection-diffusion equation with Dirichlet and Neumann's type boundary conditions. The approach is based on the usual finite difference scheme to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation function in the space dimension with the help of theta-weighted scheme. The present scheme stabilizes the oscillations that are normally displayed by the approximate solution of the transient advective-diffusive equation in the locality of sharp gradients produced by transient loads and boundary layers. The scheme is shown to be stable and the accuracy of the scheme is tested by application to various test problems. The proposed approach is numerically verified to second order and shown to work for the Peclet number <= 5. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Advection-diffusion equation Cubic trigonometric B-spline basis functions Cubic trigonometric B-spline collocation method interpolation function Thomas algorithm

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Interpolating function and Stokes phenomena

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NUCLEAR PHYSICS B 2015年 900卷 533-559页

作者： Honda, Masazumi Jatkar, Dileep P. Harish Chandra Res Inst Allahabad 211019 Uttar Pradesh India

When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional phi(4) theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane. (C) 2015 The Authors. Published by Elsevier B.V.

关键词： interpolation PHENOMENON interpolation function sine-Gordon model parameter space methods

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REDUCED PIECEWISE BIVARIATE HERMITE interpolationS

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NUMERISCHE MATHEMATIK 1972年第4期19卷 326-&页

作者： MELKES, F Research and Development Institute for Rotating Electrical Machines Mostecká 26 Brno Czechoslovakia

The paper presents two methods for a piecewise Hermite interpolation of a sufficiently smooth function. The interpolation function is on each elementary rectangle, into which the given region is divided, determined by all the derivatives of the function under consideration up to a certain predetermined order. The results obtained are utilized in the solution of a general quasi-linear equation and in the solution of a non-linear integral equation.

关键词： Integral Equation Smooth function Mathematical Method interpolation function Predetermined Order

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interpolation IN COMPUTING FORWARD PROJECTIONS IN DIRECT 3-DIMENSIONAL RECONSTRUCTION

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PHYSICS IN MEDICINE AND BIOLOGY 1983年第12期28卷 1419-1427页

作者： HARAUZ, G OTTENSMEYER, FP ONTARIO CANC INST DIV PHYSTORONTO M4X 1K9ONTARIOCANADA

Describes a simple formulation for computing forward projections directly from 3D data that is independent of any special geometries. Two-dimensional interpolation functions are used to weight the contribution of voxels in the 3D reconstruction to pixels in the 2D projection. The authors present a modified bicubic spline interpolation function, which gives better forward projections at all angles than the simpler nearest neighbour and bilinear interpolation schemes. In the authors' application, electron microscopy, a 3D image of a macromolecule or macromolecular complex can be reconstructed from a set of 2D projected images of different, individual macromolecules lying in different orientations with respect to one another. In particular, the 3D orientation of an individual nucleoprotein complex with respect to a set of reference axes can be determined by selective imaging of the nucleic acid component.

关键词： PROJECTION macromolecules pixel set bilinear interpolation Computerized tomography, 3 dimensional reconstruction Three-Dimensional Images Angle reference axes three-dimensional displays solidification interpolation function interpolation

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An efficient memetic algorithm using approximation scheme for solving nonlinear integer bilevel programming problems

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INTERNATIONAL JOURNAL OF COMPUTATIONAL SCIENCE AND ENGINEERING 2020年第1期23卷 63-73页

作者： Liu, Yuhui Li, Hecheng Chen, Huafei Huang, Jing Qinghai Normal Univ Sch Comp Sci & Technol Xining 810016 Peoples R China Qinghai Univ Dept Fundamental Courses Xining 810016 Peoples R China Qinghai Normal Univ Sch Math & Stat Xining 810016 Peoples R China Sichuan Univ Sci & Engn Sch Math & Stat Zigong 643000 Peoples R China

Nonlinear integer bilevel programming problems (NIBLPPs) are mathematical models with hierarchical structure, which are known as strongly NP-hard problems. In general, it is extremely hard to solve this kind of problem because they are always non-convex and non-differentiable, especially when integer constraints are involved. In this manuscript, based on a simplified branch and bound method as well as interpolation technique, a memetic algorithm is developed to solveNIBLPPs. Firstly, the leader's variable values are taken as individuals in populations, for each individual in the initial population, a simplified branch and bound method is adopted to obtain the follower's optimal solutions. Then, in order to reduce the computation cost in frequently solving the follower's problems for lots of offspring generated in evolution, the interpolation method is applied to approximate the solutions to the follower's problem for each individuals in populations. In addition, among these approximated points, only potential better points can be chosen to endure further optimisation procedure, so as to obtain precise optimal solutions to the follower's problems. The simulation results show that the proposed memetic algorithm is efficient in dealing withNIBLPPs.

关键词： nonlinear integer bilevel programming problem NIBLPP memetic algorithm branch and bound method interpolation function optimal solutions

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Derivation of a Formula for Inductance Gradient Using Intelligent Estimation Method

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IEEE TRANSACTIONS ON MAGNETICS 2009年第1期45卷 305-308页

作者： Keshtkar, Asghar Bayati, Sadjad Keshtkar, Ahmad Univ Tabriz Fac Elect & Comp Engn Tabriz *** Iran Imam Khomeini Int Univ Fac Engn & Technol Ghazvin Iran Univ Tabriz Fac Elect & Comp Engn Field & Wave Res Lab Tabriz 51664 Iran Tabriz Univ Med Sci Dept Med Phys Tabriz *** Iran

The efficiency of a railgun can be defined as the exchanged transferred electrical energy to the kinetic energy of the armature. According to the good relation beween the applied force to the armature and the inductance gradient (L'), the importance of this parameter calculation is obviously clear. There are several researchers who calculated L' using different numerical and analytical methods in these years. The analytical method to solve the simple problems is suitable, and numerical methods include sufficient coding time and programmer performance time. A method will be introduced in this paper to extract a formula or formulas of L' using structural railgun parameters which can cause the results similar to the results of the numerical methods. This method has not any time problem, and so, there is a good accuracy of data analysis. In this technique, which is called intelligent estimation method, according to the behavior of the railgun magnetism and its geometrical structure, an equation with unknown multiplications for L' formula is defined. Then, by applying the reported data in different studies for L', these equations can be found. Finally, the proposed method introduces a closed formula for a given structure of railgun. A rectangular configuration is investigated as a case study in this paper.

关键词： Formula inductance gradient intelligent estimation method (IEM) interpolation function railgun

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BANDWIDTH AND SIGNAL-DATA COMPRESSION USING MAXIMUM SPECIFIED ERROR AS CONTROL

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ELECTRONICS LETTERS 1985年第16期21卷 673-674页

作者： SANDMAN, AM Centre for Information Engineering City University London UK

A technique for bandwidth compression is described which is based on the principle of having an interpolation function between `important points?? and ensuring that the maximum error between the original function and the interpolation function is closely approached but never exceeded. The maximum error controls the placing of the `important points??.

关键词： interpolation function maximum specified error as control data compression bandwidth compression pulse-code modulation PCM Information theory signal-data compression Signal processing and detection Modulation and coding methods

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Contact analysis for solids based on linearly conforming radial point interpolation method

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COMPUTATIONAL MECHANICS 2007年第4期39卷 537-554页

作者： Li, Y. Liu, G. R. Luan, M. T. Dai, K. Y. Zhong, Z. H. Li, G. Y. Han, X. Natl Univ Singapore Ctr Adv Computat Engn Sci Dept Mech Engn Singapore 119260 Singapore Dalian Univ Technol Sch Civil & Hydraul Engn Dalian 116024 Peoples R China Huanan Univ Key Lab Adv Technol Vehicle Body Design & Manufac MOE Changsha 410082 Peoples R China

To simulate the contact nonlinearity in 2D solid problems, a contact analysis approach is formulated using incremental form of the subdomain parametric variational principle (SPVP). The formulation is based on a linearly conforming radial point interpolation method (LC-RPIM) using nodal integration technique. Contact interface equations are also presented using a modified Coulomb frictional contact model and discretized by contact point-pairs. In the present approach, the global discretized system equations are transformed into a standard linear complementarity problem (LCP) that can be solved readily using the Lemke method. The present approach can simulate various contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is performed to validate the proposed method via comparison with the ABAQUS(R) and to investigate the effects of the various parameters used in computations. These parameters include normal and tangential adhesions, frictional coefficient, nodal density, the dimension of local nodal support domain, nodal irregularity, shape parameters used in the radial basis function and the external load. The numerical results have demonstrated that the present approach is accurate and stable for contact analysis of 2D solids.

关键词： frictional contact contact interface model meshfree method interpolation function gradient smoothing parametric variational principle

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IMPLEMENTATION OF AN INTELLIGENT INSTRUMENT FOR PASSIVE RECOGNITION AND 2-DIMENSIONAL LOCATION ESTIMATION OF ACOUSTIC TARGETS

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 1992年第6期41卷 885-890页

作者： PAPADOPOULOS, G EFSTATHIOU, K LI, YQ DELIS, A Department of Electrical Engineering University of Patras Patras Greece

This paper is concerned with the development of an intelligent instrument for real-time recognition and location of sound broadband sources. The performance of this instrument was evaluated in an anechoic chamber. The necessary software and hardware implementation is explained. Very fast hardware is used to achieve real-time processing. The timing is the critical parameter of the system performance. Some advanced software techniques are used for the detection, recognition and position estimation of the source target. The method of cross-correlation with a suitable interpolation function is examined for the estimation of the source position. Some experimental results are cited which provide a more quantitative study of the system performance for recognition and position estimation of a source.

关键词： critical parameter Recognition (Psychology) position estimation Cross correlation interpolation function System performance intelligent instrument

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Some solutions to the matrix equation for three point Nevanlinna-Pick interpolation on the bidisc

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LINEAR ALGEBRA AND ITS APPLICATIONS 1997年第0期254卷 467-484页

作者： Patton, LJ Department of Mathematics California Polytechnic State University San Luis Obispo California 93407 USA

Some explicit solutions to the 3 x 3 case of Agler's matrix equation for Nevanlinna-Pick interpolation on the bidisc are provided. Agler showed there exists a holomorphic function bounded by 1 on the bidisc D-2 which maps n prescribed points in D-2 to n prescribed points in D if and only if there exists a pair of n x n positive semidefinite matrices satisfying a certain matrix equation. We show there exists a solution to Agler's equation in which one matrix has a row and column of zeros if and only if an explicit set of inequalities that depend on the data are satisfied. A solution of this form is also equivalent to the existence of an interpolating function which is constant with respect to one coordinate of one bidisc data point. The best possible bounds on diagonal elements of solutions to Agler's 2 x 2 matrix equation are also provided. (C) Elsevier Science Inc., 1997.

关键词： inequalities interpolation Zero If and only if There exists interpolation function Analytic functions Explicit Solution

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