MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES

Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries consisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary dimensions.

Multivariate Rational Response Surface Approximation of Nodal Displacements of Truss Structures

Polynomial-basis response surface method has some shortcomings for truss structures in structural optimization,concluding the low fitting accuracy and the great computational effort. Based on the theory of approximation, a response surface method based on Multivariate Rational Function basis(MRRSM) is proposed. In order to further reduce the computational workload of MRRSM, focusing on the law between the cross-sectional area and the nodal displacements of truss structure, a conjecture that the determinant of the stiffness matrix and the corresponding elements of adjoint matrix involved in displacement determination are polynomials with the same order as their respective matrices, each term of which is the product of cross-sectional areas, is proposed. The conjecture is proved theoretically for statically determinate truss structure, and is shown corrected by a large number of statically indeterminate truss structures. The theoretical analysis and a large number of numerical examples show that MRRSM has a high fitting accuracy and less computational effort. Efficiency of the structural optimization of truss structures would be enhanced.

OVERCONVERGENCE AND ZEROS OF SEQUENCES OF RATIONAL FUNCTIONS

In the present paper we consider sequences of rational functions with a bounded number or free poles con- verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examine the limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our results further extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.

Accuracy improvement of geometric correction for CHRIS data

This paper deals with a new type of multi-angle remotely sensed data--CHRIS(the Compact High Resolution Imaging Spec-trometer),by using rational function models(RFM)and rigorous sensor models(RSM).For ortho-rectifying an image set,a rigorous sen-sor model-Toutin's model was employed and a set of reported parameters including across track angle,along track angle,IFOV,altitude,period,eccentricity and orbit inclination were input,then,the orbit calculation was started and the track information was given to the raw data.The images were ortho-rectified with geocoded ASTER images and digital elevation(DEM)data.Results showed that with 16 ground control points(GCPs),the correction accuracy decreased with view zenith angle,and the RMSE value increased to be over one pixel at 36 degree off-nadir.When the GCPs were approximately chosen as in Toutin's model,a RFM with three coefficients produced the same accuracy trend versus view zenith angle while the RMSEs for all angles were improved and within about one pixel.

Copositive approximation by rational functions with prescribed numerator degree

The paper proves that, if f（x） ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in （-1, 1）,then there exists a real rational function r（x） ∈ Rn^（2μ-1）l which is eopositive with f（x）, such that the following Jackson type estimate ｜｜f-r｜｜p≤Cδl^2μωφ（f,1/n）p holds, where μ is a natural number ≥3/2＋1/p, and Cδ is a positive constant depending only on δ.

New Extended Jacobi Elliptic Function Rational Expansion Method and Its Application

In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the （2＋1）-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations.

Optimization for ASP flooding based on adaptive rationalized Haar function approximation

This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method,the experimental comparison method and control vector parameterization(CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.

AN EDGE CRACK PROBLEM IN A SEMI-INFINITE PLANE SUBJECTED TO CONCENTRATED FORCES

An oblique edge crack problem in a semi-infinite plane is discussed. Re concentrated forces are applied on the edge crack face, or on the line boundary of the cracked semi-infinite plane. The rational mapping function approach is suggested to solve the boundary value problem and a solution in a closed form is obtained. Finally, several numerical examples with the calculated results are given.

PADE APPROXIMANTS AS LIMITS OF RATIONAL FUNCTIONS OF BEST APPROXIMATION IN ORLICZ SPACE

In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.

THE ASYMPTOTIC FORMULA OF THE ORTHOGONAL RATIONAL FUNCTION ON THE UNIT CIRCLE

In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circle with respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.

APPROXIMATION BY FABER-LAURENT RATIONAL FUNCTIONS IN THE MEAN OF FUNCTIONS OF CLASS LP(T) WITH 1

Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabcrpolynomial F k,p (z),the kth p-Faber principle part F k.p (1/z) for Γ , and defined the nth p-Fcber- Laurent rational function Rn.p (f, z) and p- generalized modulus of continuity Ωp(f, t) of a function f of Lp(Γ) We inves-tigate some properties of Fk,p (z) and Fk.p (1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ω (. , t) in the mean of functions of Lp(Γ) by the rational junctions Rn.p (. . z).

A Complete Field of Meromorphic Function

In any completely close complex field C, generalized transcendental meromorphic functions may have some new properties. It is well known that a meromorphic function of characteristic zero is a rational function. This paper introduced some mathematical properties of the transcendental meromorphic function, which is generalized to the meromorphic function by multiplying and differentiating the generalized meromorphic function. The analysis shows that the difference between any non-zero constant and the derivative of the general meromorphic function has an infinite zero. In addition, for any natural number n, there are no practically exceptional values for the multiplication of the general meromorphic function and its derivative to the power of n.

RATIONAL FUNCTIONS OF BEST UNIFORM APPROXIMATION AND HOLOMORPHIC CONTINUATION OF FUNCTIONS

Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zera capacity.As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of fare given.

Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to （2＋1）-Dimensional Stochastic Dispersive Long Wave System

In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the （2＋ 1）-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

Polynomial Functions Composed of Terms with Non-Integer Powers

Polynomial functions containing terms with non-integer powers are studied to disclose possible approaches for obtaining their roots as well as employing them for curve-fitting purposes. Several special cases representing equations from different categories are investigated for their roots. Curve-fitting applications to physically meaningful data by the use of fractional functions are worked out in detail. Relevance of this rarely worked subject to solutions of fractional differential equations is pointed out and existing potential in related future work is emphasized.

Jellyfish bio-inspired Fe@CNT@CuNC derived from ZIF-8 for cathodic oxygen reduction

Biomimetics provides guidance to design and synthesize advanced catalysts for oxygen reduction reaction in microbial fuel cells(MFCs).Herein,jellyfish-inspired Fe clusters on carbon nanotubes connected with CuNC(Fe@CNT@CuNC)were designed and prepared by using zeolitic imidazolate framework(ZIF)-8 precursors to imitate the organic texture and function of jellyfish.The antibacterial effect of Cu^(+)ions depressed the growth of cathode biofilm to ensure rapid mass transport.Fe clusters and CuNC connected by CNTs accelerated the electron transfer from Fe to CuNC.The optimization of oxygen adsorption was caused by electron redistribution between sites of Fe and Cu.Jellyfish-like catalysts achieved a half-wave potential of 0.86 V and onset potential of 0.95 V vs.reversible hydrogen electrode(RHE).MFCs gained the maximum power density of 1600 mW·m^(-2) after 500 h measurement.This work provides insights into the special design of advanced catalysts based on bio-inspiration and biomimetics.

Approximation Properties of Newman Type Interpolation Rational Functions with Fewer Nodes

In the present note,we consider the problem:how many interpolation nodes can be deleted from the Newman-type rational function such that the convergence rate still achieve.

A new method of frequency-dependent network equivalence for power system

Electromagnetic transient simulation for large-scale power system is a time-consuming problem.A new frequency-dependent equivalence method is presented in the paper,which might significantly accelerate power system electromagnetic transient simulation.In the method,an effective algorithm is designed to directly transfer the port admittance determinant of external system's mixing matrix into admittance rational function;and the step-by-step strategy for the equivalence of actual large system is put forward,which further reduces the calculation quantities needed.Moreover,the study of multiple real root pole characteristics of admittance transfer function of two-port network is performed and a proposition is achieved.Based on the proposition and residue theorem,the equivalence system for external system corresponding to the admittance rational function is obtained.The computation complexity of the step-by-step equivalence method is about o(┌n/np×T┐)(┌┐ is upper integral operation,n is the total buses number of external system,N P is the total buses number of single step equivalence network,T is single step equivalence time),which indicates that the computation complexity of the method proposed has nearly linear relationship with the buses number of external system,and the method proposed has satisfactory computation speed.Since the mixing matrix of external system includes all the information of external system,therefore,port admittance rational function derived from it can reflect its full frequency characteristic and the equivalence network achieved has high equivalence precision.Moreover,since the port rational function is gained at the condition of the external system without source,which equals stable passive network,it could not show any unstable pole and need not extra measure to make the equivalence system stable.The test results of the samples and comparison with other methods demonstrate that the new method proposed is valid and effective.

On Reed-Solomon Codes

The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estimate,Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small.In the first part,the result of Li and Wan is improved.On the other hand,one of the important parameters of an error-correcting code is the dimension.In most cases,one can only get bounds for the dimension.In the second part,a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained.

Some Recent Advances on SpectralMethods for Unbounded Domains

We present in this paper a unified framework for analyzing the spectral methods in unbounded domains using mapped Jacobi,Laguerre and Hermite functions.A detailed comparison of the convergence rates of these spectral methods for solutions with typical decay behaviors is carried out,both theoretically and computationally.A brief review on some of the recent advances in the spectral methods for unbounded domains is also presented.