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基于数学模型的实际问题解决——以“几何问题”为例
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作者 周琪 《数学之友》 2024年第20期59-61,共3页
在小学数学教学中,几何学习占有重要地位.它不仅培养学生的空间想象能力,还为学生今后学习更高级的数学知识奠定基础.研究表明,基于数学模型的教学方法能有效提高学生的空间想象能力、逻辑思维能力和问题解决能力,为小学数学教学实践提... 在小学数学教学中,几何学习占有重要地位.它不仅培养学生的空间想象能力,还为学生今后学习更高级的数学知识奠定基础.研究表明,基于数学模型的教学方法能有效提高学生的空间想象能力、逻辑思维能力和问题解决能力,为小学数学教学实践提供了新的思路和方法. 展开更多
关键词 数学模型 “几何问题” 问题解决
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A New Rational Algebraic Approach to Find Exact Analytical Solutions to a (2+1)-Dimensional System 被引量:7
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作者 BAI Cheng-Jie ZHAO Hong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第5X期801-810,共10页
In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and othe... In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on (2+1)-dimensional dispersive long-wave equation. 展开更多
关键词 rational algebraic approach (2+1)-dimensional dispersive long-wave equation exact solutions
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Stress on Ballast-Bed and Deterioration of Geometry in a Railway Track
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作者 Konstantinos Giannakos 《Journal of Civil Engineering and Architecture》 2010年第6期27-42,共16页
In Greece extended cracking of twin-block concrete sleepers (ties) and fouling of the ballast-bed were observed with implied problems of gauge widening and deterioration of track's geometry. This led to a ten-year ... In Greece extended cracking of twin-block concrete sleepers (ties) and fouling of the ballast-bed were observed with implied problems of gauge widening and deterioration of track's geometry. This led to a ten-year investigation program, during which a new method was developed for the estimation of actions on track panel as well as of the pressures / stresses that develop under the seating surface of the sleeper on the ballast-bed. Results from the tests performed on the ballast used in the Greek network are also presented, conducted in laboratories in France, Austria, and Greece. The influence of the actions -static and mainly dynamic- on the track response and the stress and strain of the ballast-bed are also discussed as derived from the tests and theoretical analysis. 展开更多
关键词 Railway ballast ballast hardness actions on track mean stress on ballast bed cracked concrete ties.
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Some Open Problems in Geometric Topologyof Low Dimensions
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作者 Alberto CAVICCHIOLI(Department Of Mathematics,University of Modena,Via Campi 213/B, 41100 Modena, Italy )Dusan REPOVS(Institute for Mathematics, Physics and Mechanics,University of Ljubljana,P. O. Box 64, Ljubljana 61111,Slovenia 《Chinese Quarterly Journal of Mathematics》 CSCD 1995年第4期8-14,共7页
SomeOpenProblemsinGeometricTopologyofLowDimensions¥AlbertoCAVICCHIOLI(DepartmentOfMathematics,UniversityofMo... SomeOpenProblemsinGeometricTopologyofLowDimensions¥AlbertoCAVICCHIOLI(DepartmentOfMathematics,UniversityofModena,ViaCampi213/... 展开更多
关键词 approximation by embeddings ISOTOPY knot space SPINE s-cobordism homotopytype smooth manifolds: crystallization genus homotopy sphere open problems
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DKP Oscillator in a Noncommutative Space
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作者 M.Falek M.Merad 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第9期587-592,共6页
We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein Gordon oscillator type, the wave functions are then deduced and compared with th... We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter. 展开更多
关键词 noncommutative geometry DKP oscillator
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ON THE HEILBRONN NUMBER OF n-NONCOLINEAR POINTS IN THE PLANE
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作者 于剑 《Journal of China University of Mining and Technology》 1996年第2期99-103,共5页
In this article,we have given the definition of the Heilbronn number of n-noncollinear points in the plane. By this, we got the exact value of H5 which is the exact upper bound of H5 (K), where H5 (K) is any Heilbronn... In this article,we have given the definition of the Heilbronn number of n-noncollinear points in the plane. By this, we got the exact value of H5 which is the exact upper bound of H5 (K), where H5 (K) is any Heilbronn number in common sense. 展开更多
关键词 Heilbronn number Heilbronn arrangement convex hull
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Fast image matching algorithm based on affine invariants
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作者 张毅 卢凯 高颖慧 《Journal of Central South University》 SCIE EI CAS 2014年第5期1907-1918,共12页
Feature-based image matching algorithms play an indispensable role in automatic target recognition (ATR). In this work, a fast image matching algorithm (FIMA) is proposed which utilizes the geometry feature of ext... Feature-based image matching algorithms play an indispensable role in automatic target recognition (ATR). In this work, a fast image matching algorithm (FIMA) is proposed which utilizes the geometry feature of extended centroid (EC) to build affine invariants. Based on at-fine invariants of the length ratio of two parallel line segments, FIMA overcomes the invalidation problem of the state-of-the-art algorithms based on affine geometry features, and increases the feature diversity of different targets, thus reducing misjudgment rate during recognizing targets. However, it is found that FIMA suffers from the parallelogram contour problem and the coincidence invalidation. An advanced FIMA is designed to cope with these problems. Experiments prove that the proposed algorithms have better robustness for Gaussian noise, gray-scale change, contrast change, illumination and small three-dimensional rotation. Compared with the latest fast image matching algorithms based on geometry features, FIMA reaches the speedup of approximate 1.75 times. Thus, FIMA would be more suitable for actual ATR applications. 展开更多
关键词 affine invariants image matching extended centroid ROBUSTNESS PERFORMANCE
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Duality of Unary Convex Functions Programming
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作者 朱德通 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第4期32-39,共8页
Most nonliner programming problems consist of functions which are sums of unary,convex functions of linear fuctions.In this paper.we derive the duality forms of the unary oonvex optimization, and these technuqucs are ... Most nonliner programming problems consist of functions which are sums of unary,convex functions of linear fuctions.In this paper.we derive the duality forms of the unary oonvex optimization, and these technuqucs are applied to the geometric programming and minimum discrimination information problems. 展开更多
关键词 unary convex optimization duality form conjugate transform
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On Simultaneous Exact Controllability
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作者 Gustavo Perla Menzala Boris Kapitonov 《Journal of Mathematics and System Science》 2013年第12期655-658,共4页
We consider a mixed problem for a system describing the evolution of sound in a compressible fluid. We describe how to treat a simultaneous exact boundary controllability problem in the sense proposed by J.L. Lions as... We consider a mixed problem for a system describing the evolution of sound in a compressible fluid. We describe how to treat a simultaneous exact boundary controllability problem in the sense proposed by J.L. Lions as well as D. Russell. By using convenient modified multipliers we obtain an observability inequality provided suitable geometric condition on the domain is valid and the speed velocity of the models are related. 展开更多
关键词 Exact controllability multipliers technique Hilbert uniqueness method.
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A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides 被引量:13
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作者 LUO WenYu YANG ChunMei +1 位作者 QIN JiXing ZHANG RenHe 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2012年第4期572-588,共17页
In this paper,a stepwise coupled-mode model with the use of the direct global matrix approach is proposed.This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry ... In this paper,a stepwise coupled-mode model with the use of the direct global matrix approach is proposed.This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry.With the use of the direct global matrix approach,this method is numerically stable.In addition,by introducing appropriately normalized range solutions,this model is free from the numerical overflow problem.Furthermore,we put forward source conditions appropriate for the line-source problem in plane geometry.As a result,this method is capable of addressing the scenario with a line source on top of a sloping bottom.Closed-form expressions for coupling matrices are derived and applied in this paper for handling problems with pressure-release boundaries and a homogeneous water column.The numerical simulations indicate that the proposed model is accurate,efficient,and numerically stable.Consequently,this model can serve as a benchmark model in range-dependent propagation modeling.Although this method is verified by an ideal wedge problem in this paper,the formulation applies to realistic problems as well. 展开更多
关键词 coupled-mode theory range-dependent waveguide direct global matrix approach
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On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus
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作者 Chunhe LI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2013年第3期435-454,共20页
In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the 'solvability of a relevant linearized Darboux equation... In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the 'solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov's positive annulus in R^3. 展开更多
关键词 Alexandrov's positive annulus Darboux equation Gauss-Codazzi system SOLVABILITY
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Global Geometry of 3-Body Motions with Vanishing Angular MomentumⅠ
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作者 Wu-Yi HSIANG Eldar STRAUME 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2008年第1期1-54,共54页
Following Jacobi's geometrization of Lagrange's least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is t... Following Jacobi's geometrization of Lagrange's least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor (U + h), where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^*≌S^2 (1/2). In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve (which only records the change of shape) in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems. 展开更多
关键词 3-Body problem Kinematic geometry REDUCTION Shape curves
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The Cauchy problem of generalized Landau-Lifshitz equation into S^n 被引量:2
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作者 SONG Chong YU Jie 《Science China Mathematics》 SCIE 2013年第2期283-300,共18页
In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geom... In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geometric form and applying the geometric energy method with a forth-order perturbation,we show the global well-posedness of the Cauchy problem in suitable Sobolev spaces. 展开更多
关键词 generalized Landau-Lifshitz geometric energy method
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Efficient design of rotary traveling wave oscillator array via geometric programming
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作者 Li-jia CHEN Hua-feng ZHANG +1 位作者 Jin-fang ZHOU Kang-sheng CHEN 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2009年第12期1815-1823,共9页
This paper presents an efficient method for globally optimizing and automating component sizing for rotary traveling wave oscillator arrays. The lumped equivalent model of transmission lines loaded by inverter pairs i... This paper presents an efficient method for globally optimizing and automating component sizing for rotary traveling wave oscillator arrays. The lumped equivalent model of transmission lines loaded by inverter pairs is evaluated and posynomial functions for oscillation frequency, power dissipation, phase noise, etc. are formulated using transmission line theory. The re- sulting design problem can be posed as a geometric programJning problem, which can be efficiently solved with a convex opti- mization solver. The proposed method can compute the global optima more efficiently than the traditional iterative scheme and various design problems can be solved with the same circuit model. The globally optimal trade-off curves between competing objectives are also computed to carry out robust designs and quickly explore the design space. 展开更多
关键词 Rotary traveling wave oscillator array (RTWOA) Clock distribution Transmission line resonator Global optimi-zation Geometric programming (GP)
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