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On the values of representation functions 被引量:1
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作者 CHEN YongGao 《Science China Mathematics》 SCIE 2011年第7期1317-1331,共15页
For a set A of nonnegative integers, the representation functions R2(A,n) and R3(A,n) are defined as the numbers of solutions to the equation n = a + a′ with a,a′∈ A, a < a′ and a a′, respectively. Let N be th... For a set A of nonnegative integers, the representation functions R2(A,n) and R3(A,n) are defined as the numbers of solutions to the equation n = a + a′ with a,a′∈ A, a < a′ and a a′, respectively. Let N be the set of nonnegative integers. Given n0 > 0, it is known that there exist A,A′■ N such that R2(A′,n) = R2(N \ A′,n) and R3(A,n) = R3(N \ A,n) for all n n0. We obtain several related results. For example, we prove that: If A ■ N such that R3(A,n) = R3(N \ A,n) for all n n0, then (1) for any n n0 we have R3(A,n) = R3(N \ A,n) > c1n - c2, where c1,c2 are two positive constants depending only on n0; (2) for any α < 116, the set of integers n with R3(A,n) > αn has the density one. The answers to the four problems in Chen-Tang (2009) are affirmative. We also pose two open problems for further research. 展开更多
关键词 PARTITION representation function binary representation Sárkzy’s problem
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From the Green's Function in Tight-Binding Representation to Interatomic Many-body Potentials 被引量:1
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作者 Shaojun LIU(Department of physics, Beijing Normal University, Beijing 100875, China)Xiaobo WEI(Department of Physics, Liuzhou College of Education, Liuzhou 545005, China)Zhaodou CHEN Jun CAI and Benkun MA(Department of Physics, Beijing Normal University, 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 1999年第4期315-319,共5页
In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hoppin... In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method. 展开更多
关键词 REV Li Chen From the Green’s function in Tight-Binding representation to Interatomic Many-body Potentials body
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THE PROBABILISTIC REPRESENTATION FORMULAE FOR COSINE OPERATOR FUNCTIONS
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作者 周密 陈文忠 《Analysis in Theory and Applications》 1993年第1期42-52,共11页
In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special c... In this paper we obtained general representation formulae for strongly continuous cosine operator functions via probabilistic approach,which include Webb's[1]and Shaw's[2]formulae and some new one as special cases.We also give the quantitative estimations for the general formulae. 展开更多
关键词 TH THE PROBABILISTIC representation FORMULAE FOR COSINE OPERATOR functionS
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State Representation Methodology (SRM) for Bridge Condition Assessment in SHM 被引量:2
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《Journal of Civil Engineering and Architecture》 2012年第4期433-443,共11页
This paper introduces a new concept of "State Representation Methodology (SRM)" which is a kind of bridge condition assessment method for structural health monitoring system (SHM). There are many methods for sys... This paper introduces a new concept of "State Representation Methodology (SRM)" which is a kind of bridge condition assessment method for structural health monitoring system (SHM). There are many methods for system identification from the simplicity comparison of damage index to the complicated statistical pattern recognition algorithms in SHM. In these methods, modal analysis and parameters identification or many defined indices are common-used for extracting the dynamic or static characteristics of a system. However, there is a common problem: due to the complexity of a large size system with high-order nonlinear characteristics and severe environment interference, it is impossible to extract and quantify exactly these modal parameters or system parameters or indices as the feature vectors of a system in damage detection in an easy way. The SRM considered a more general theory for the non-parametric description of system state. 展开更多
关键词 BRIDGE damage detection system state representation methodology (SRM) structural health monitoring (SHM) state representation function (SRF) SRM Tool Kernel function.
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How to find Representation of Functions as Power Series
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作者 梁宇学 《中学生数学(高中版)》 2019年第2期40-41,共2页
关键词 How to find representation of functions as Power Series
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Trajectory online optimization for unmanned combat aerial vehicle using combined strategy 被引量:1
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作者 Kangsheng Dong Hanqiao Huang +1 位作者 Changqiang Huang Zhuoran Zhang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第5期963-970,共8页
This paper presents a combined strategy to solve the trajectory online optimization problem for unmanned combat aerial vehicle (UCAV). Firstly, as trajectory directly optimizing is quite time costing, an online trajec... This paper presents a combined strategy to solve the trajectory online optimization problem for unmanned combat aerial vehicle (UCAV). Firstly, as trajectory directly optimizing is quite time costing, an online trajectory functional representation method is proposed. Considering the practical requirement of online trajectory, the 4-order polynomial function is used to represent the trajectory, and which can be determined by two independent parameters with the trajectory terminal conditions; thus, the trajectory online optimization problem is converted into the optimization of the two parameters, which largely lowers the complexity of the optimization problem. Furthermore, the scopes of the two parameters have been assessed into small ranges using the golden section ratio method. Secondly, a multi-population rotation strategy differential evolution approach (MPRDE) is designed to optimize the two parameters; in which, 'current-to-best/1/bin', 'current-to-rand/1/bin' and 'rand/2/bin' strategies with fixed parameter settings are designed, these strategies are rotationally used by three subpopulations. Thirdly, the rolling optimization method is applied to model the online trajectory optimization process. Finally, simulation results demonstrate the efficiency and real-time calculation capability of the designed combined strategy for UCAV trajectory online optimizing under dynamic and complicated environments. 展开更多
关键词 unmanned combat aerial vehicle (UCAV) trajectory online optimization functional representation parameter optimization rolling optimization differential evolution
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Erratum to “The Riemann Hypothesis-Millennium Prize Problem” [Advances in Pure Mathematics 6 (2016) 915-920] 被引量:4
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作者 A. A. Durmagambetov 《Advances in Pure Mathematics》 2016年第13期1053-1056,共4页
The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mist... The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mistake. The author wishes to correct the errors in Theorem 2 of the result part. 展开更多
关键词 Euler CHEBYSHEV DIRICHLET RIEMANN Hypothesis Zeta function Muntz function Complex Numbers Regular function Integral function representation Millennium Prize Problem
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Generator,multiquadric generator,quasi-interpolation and multiquadric quasi-interpolation
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作者 WU Zong-min MA Li-min 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第4期390-400,共11页
The aim of this survey paper is to propose a new concept "generator". In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than ba... The aim of this survey paper is to propose a new concept "generator". In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than basis. Various properties of generator are also discussed. Moreover, a special generator named multiquadric function is introduced. Based on the multiquadric generator, the multiquadric quasi-interpolation scheme is constructed, and furthermore, the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives. 展开更多
关键词 GENERATOR function representation approximation numerical differentiation multiquadric quasi-interpolation
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Inhomogeneous Cauchy-Riemann equation in Octonion space
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作者 GONG Ding-dong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第4期447-452,共6页
The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the ... The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed. 展开更多
关键词 OCTONION integral representation of differentiable functions inhoraogeneous Cauchy-RiemannEquation Cousin problem.
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Functional Knowledge Representation Based on Problem Reduction
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作者 高济 《Journal of Computer Science & Technology》 SCIE EI CSCD 1992年第2期105-113,共9页
This paper proposes an approach for functional knowledge representation based on problem reduction,which represents the organization of problem-solving activities in two levels:reduction and reasoning.The former makes... This paper proposes an approach for functional knowledge representation based on problem reduction,which represents the organization of problem-solving activities in two levels:reduction and reasoning.The former makes the functional plans for problem-solving while the latter constructs functional units, called handlers,for executing subproblems designated by these plans.This approach emphasizes that the representation of domain knowledge should be closely combined with(rather than separated from)its use therefore provides a set of reasoning-level primitives to construct handlers and formulate the control strate- gies for executing them.As reduction-level primitives,handlers are used to construct handler-associative networks,which become the executable representation of problem-reduction graphs,in order to realize the problem-solving methods suited to domain features.Besides,handlers and their control slots can be used to focus the attention of knowledge acquisition and reasoning control. 展开更多
关键词 In high functional Knowledge representation Based on Problem Reduction MODE
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REPRESENTATION OF MARTINGALE ADDITIVE FUNCTIONALS 0N BANACH SPACES
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作者 凡汝宗 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1990年第1期74-80,共7页
Assume that B is a separable real Banach space and X(t) is a diffusion process on B. In thispaper, we will establish the representation theorem of martingale additive functionals of X(t).
关键词 representation OF MARTINGALE ADDITIVE functionALS 0N BANACH SPACES DE
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The Riemann Hypothesis-Millennium Prize Problem
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作者 A. A. Durmagambetov 《Advances in Pure Mathematics》 2016年第12期915-920,共6页
This work is dedicated to the promotion of the results C. Muntz obtained modifying zeta functions. The properties of zeta functions are studied;these properties lead to new regularities of zeta functions. The choice o... This work is dedicated to the promotion of the results C. Muntz obtained modifying zeta functions. The properties of zeta functions are studied;these properties lead to new regularities of zeta functions. The choice of a special type of modified zeta functions allows estimating the Riemann’s zeta function and solving Riemann Problem-Millennium Prize Problem. 展开更多
关键词 Euler CHEBYSHEV DIRICHLET RIEMANN Hypothesis Zeta function Muntz function Complex Numbers Regular function Integral function representation Millennium Prize Problem
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Spectral representation of correspondence of multi-valued logical functions
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作者 冯登国 肖国镇 《Chinese Science Bulletin》 SCIE EI CAS 1995年第5期439-440,共2页
In cryptology, it is an important topic to study the best affine approach of functions. The best affine approach of Boolean functions has been discussed in ref. [1] by using the Walsh spectrum, of which the key proble... In cryptology, it is an important topic to study the best affine approach of functions. The best affine approach of Boolean functions has been discussed in ref. [1] by using the Walsh spectrum, of which the key problem is how to represent the correspondence of Boolean functions by using Walsh spectrum. For the multi-valued logical functions so far, the spectral representation of their correspondence has not been presented yet. This let- 展开更多
关键词 Spectral representation of correspondence of multi-valued logical functions
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DECOMPOSITION OF A CLASS OF FUNCTIONALS AND THE PREDICTABLE REPRESENTATION THEOREM ON BANACH SPACES
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作者 凡汝宗 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1992年第2期153-167,共15页
Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a r... Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t). 展开更多
关键词 DECOMPOSITION OF A CLASS OF functionALS AND THE PREDICTABLE representation THEOREM ON BANACH SPACES
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SIMULATION OF FABRIC DRAPE USING A THIN PLATE ELEMENT WITH FINITE ROTATION 被引量:1
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作者 陈明祥 孙庆平 袁铭辉 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1998年第3期239-247,共9页
The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representatio... The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs. 展开更多
关键词 nonlinear finite element cloth draping flexible thin plate finite rotation tensor function representation theory conjugate gradient
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Continuous representation of human portraits and natural scenery in human ventral temporal cortex: evidence from functional magnetic resonance imaging
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作者 肖壮伟 林冲宇 +5 位作者 罗小景 黄芳梅 庄伟端 李俊雄 翁旭初 吴仁华 《Chinese Medical Journal》 SCIE CAS CSCD 2004年第9期1309-1312,共4页
Background Functional magnetic resonance imaging (fMRI) has become a powerful tool for tracking human brain activity in vivo. This technique is mainly based on blood oxygenation level dependence (BOLD) contrast. In t... Background Functional magnetic resonance imaging (fMRI) has become a powerful tool for tracking human brain activity in vivo. This technique is mainly based on blood oxygenation level dependence (BOLD) contrast. In the present study, we employed this newly developed technique to characterize the neural representations of human portraits and natural sceneries in the human brain.Methods Nine subjects were scanned with a 1.5 T magnetic resonance imaging (MRI) scanner using gradient-recalled echo and echo-planar imaging (GRE-EPI) pulse sequence while they were visually presented with 3 types of white-black photographs: natural scenery, human portraits, and scrambled nonsense pictures. Multiple linear regression was used to identify brain regions responding preferentially to each type of stimulus and common regions for both human portraits and natural scenery. The relative contributions of each type of stimulus to activation in these regions were examined using linear combinations of a general linear test.Results Multiple linear regression analysis revealed two distinct but adjacent regions in both sides of the ventral temporal cortex. The medial region preferentially responded to natural scenery, whereas the lateral one preferentially responded to the human portraits. The general linear test further revealed a distribution gradient such that a change from portraits to scenes shifted areas of activation from lateral to medial.Conclusions The boundary between portrait-associated and scenery-associated areas is not as clear as previously demonstrated. The representations of portraits and scenes in ventral temporal cortex appear to be continuous and overlap. 展开更多
关键词 functional magnetic resonance imaging · brain · cognition · representation
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