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Nanocatalytic resonance scattering spectral analysis

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Science China Chemistry 2010年第5期53卷 1048-1053页

作者： Jiang, ZhiLiang Li, JiShun Wen, GuiQing Liu, QingYe Liang, AiHui School of Environment and Resources Guangxi Normal University Guilin 541004 China College of Chemistry and Bioengineering Guilin University of Technology Guilin 541004 China

The resonance scattering spectral technique has been established using the synchronous scanning technique on spectrofluorometry.Because of its advantages of simplicity,rapidity and sensitivity,it has been widely applied to analyses of proteins,nucleic acids and inorganic ions.This paper summarizes the application of immunonanogold and aptamer modified nanogold(AptAu) catalytic resonance scattering spectral technique in combination with the work of our group,citing 53 references.

关键词： antibody aptamer nanocatalysis resonance scattering spectral assay

C1-Conforming Quadrilateral spectral Element Method for Fourth-Order Equations

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Communications on Applied Mathematics and Computation 2019年第3期1卷 403-434页

作者： Huiyuan Li Weikun Shan Zhimin Zhang State Key Laboratory of Computer Science/Laboratory of Parallel Computing Institute of SoftwareChinese Academy of SciencesBeijing 100190China School of Science Henan University of TechnologyZhengzhou 450001HenanChina Beijing Computational Science Research Center Beijing 100193China Department of Mathematics Wayne State UniversityDetroitMI 48202USA

This paper is devoted to Professor Benyu Guo's open question on the C1-conforming quadrilateral spectral element method for fourth-order equations which has been endeavored for years. Starting with generalized Jacobi polynomials on the reference square, we construct the C1-conforming basis functions using the bilinear mapping from the reference square onto each quadrilateral element which fall into three categories-interior modes, edge modes, and vertex modes. In contrast to the triangular element, compulsively compensatory requirements on the global C1-continuity should be imposed for edge and vertex mode basis functions such that their normal derivatives on each common edge are reduced from rational functions to polynomials, which depend on only parameters of the common edge. It is amazing that the C1-conforming basis functions on each quadrilateral element contain polynomials in primitive variables, the completeness is then guaranteed and further confirmed by the numerical results on the Petrov-Galerkin spectral method for the non-homogeneous boundary value problem of fourth-order equations on an arbitrary quadrilateral. Finally, a C1-conforming quadrilateral spectral element method is proposed for the biharmonic eigenvalue problem, and numerical experiments demonstrate the effectiveness and efficiency of our spectral element method.

关键词： Quadrilateral spectral element method Fourth-order equations Mapped polynomials C1-conforming basis Polynomial inclusion Completeness

The Laplacian spectral radii of unicyclic and bicyclic graphs with n vertices and k pendant vertices

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Science China Mathematics 2010年第8期53卷 2135-2142页

作者： GUO JiMing Department of Applied Mathematics,China University of Petroleum,Dongying 257061,China Department of Applied Mathematics China University of Petroleum Dongying China

In this paper,we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices,respectively.

关键词： Laplacian matrix Laplacian spectral radius unicyclic graph bicyclic graph

Exploiting spectral-Energy Efficiency Tradeoff with Fairness in Non-Orthogonal Multiple Access Systems

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Journal of Beijing Institute of Technology 2019年第2期28卷 336-343页

作者： Zhengyu Song Xin Sun School of Electronic and Information Engineering Beijing Jiaotong University

The spectral efficiency(SE)and energy efficiency(EE)tradeoff while ensuring rate fairness among users in non-orthogonal multiple access(NOMA)systems is investigated.In order to characterize the SE-EE tradeoff with rate fairness,a multi-objective optimization(MOO)problem is first formulated,where the rate fairness is represented with theα-fair utility function.Then,the MOO problem is converted into a single-objective optimization(SOO)problem by the weighted sum method.To solve the converted non-convex SOO problem,we apply sequential convex programming,which helps to propose a general power allocation algorithm to realize the SE-EE tradeoff with rate fairness.We prove the convergence of the proposed algorithm and the convergent solution satisfies the KKT conditions.Simulation results demonstrate the proposed power allocation algorithm can achieve various levels of rate fairness,and higher fairness results in degraded performance of SE-EE tradeoff.A pivotal conclusion is reached that NOMA systems significantly outperform orthogonal multiple access systems in terms of SE-EE tradeoff with the same level of rate fairness.

关键词： non-orthogonal multiple access(NOMA) energy efficiency(EE) spectral efficiency(SE) rate fairness power allocation

The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators

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Science China Mathematics 2008年第7期51卷 1232-1242页

作者： YANG YiDu CHEN Zhen School of Mathematics and Computer Sciences Guizhou Normal UniversityGuiyang 550001China

This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.

关键词： self-adjoint completely continuous operator spectral approximation the order-preserving convergence

Coupling, spectral gap and related topics (Ⅱ)

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Chinese Science Bulletin 1997年第18期42卷 1409-1416页

作者： CHEN Muf aDepartment of Mathematics, Beijing Normal University, Beijing 100875, China Department of Mathematics Beijing Normal University Beijing China

THIS is the second one of a series of three reviews. The ideas introduced in the last review are used to study the estimate of spectral gap and four classes of typical eigenvalue problems on manifolds. The comparison ... 详细信息

关键词： diffusions manifold Markov chains spectral gap couplings.

Population dynamics between a prey and a predator using spectral collocation method

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International Journal of Biomathematics 2019年第5期12卷 19-41页

作者： Sagithyn Thirumalai Rajeuwari Seshadri Suayip Yuzbasi Department of Mathematics Pondicherry UniversityIndia Department of Mathematicst Facviiy of Science Akdeniz University Tr-07058AntalyaTurkey

The struggle for the existence of the biological species is a well-known Prey-Predator model study in the literature.In this study,we present an improved model of Jerri [J.Abdul,Introduction to Integral Equations with Applications,Vol.10 (Wiley,New York,1999)] by introducing the intra-species competition term between the same species in additiuu to the existing environmental changeb and lew other factors in the model.The derntmcl from the exiting (limited) retjources arid other requirements induces competition between the same species which may after the survival tactics among themselves.This intra species term provides strength to tho model ns it makes the model moro realistic.The governing equations are a system of two nonlinear delay integro differential pqimtions,which are solved using spectral collocation method.The role of intra-species coefficients denoting the logistic growth/decay of the two species and two other parameters affecting the population dynamics are analyzed with the three basis functions such as Chebyshev,Legendre and Jacobi polynomials.With the help of simple matrix analysis,the governing equations are converted into a system of nonlinear algebraic equations.Detailed error estiination is computed to compare our results witli the existing inethudb.It is shown with the help of tables and figures that the present method is very efficient,has better accuracy and has least computational cost.

关键词： Prey-predator model spectral collocation method Chebyshev, Legendre and Jacobi polynomials error estimation

The application of spectral distribution of product of two random matrices in the factor analysis

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Science China Mathematics 2007年第9期50卷 1303-1315页

作者： Bai-suo JIN Bai-qi MIAO Wu-yi YE Zhen-xiang WU Department of Statistics and Finance University of Science and Technology of ChinaHefei 230026China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080China

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.

关键词： limiting spectral distribution product of random matrices large dimensional random matrices factor number time series

A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations

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Science China Mathematics 2008年第8期51卷 1376-1390页

作者： CHEN YanPing HUANG YunQing YI NianYu School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem is presented.We obtain a posteriori error estimates of the approximated solutions for both the state and the control.

关键词： Legendre Galerkin spectral method optimal control problems parabolic state equations a posteriori error estimates