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Hidden Properties of Mathematical Physics Equations. Double Solutions. The Realization of Integrable Structures. Emergence of Physical Structures and Observable Formations
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作者 L. I. Petrova 《Journal of Applied Mathematics and Physics》 2020年第7期1255-1262,共8页
With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various... With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms. 展开更多
关键词 Integrability of mathematical physics equations Double Solutions Integrable Structures Discrete Transitions Skew-Symmetric Differential Forms
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New Approaches of Theoretical Astrophysics for Application to Some Astronomical Objects: I. An Application of Non-Classical Equation Mathematical Physics to the Magneto-Hydrodynamic Equilibrium (in Case of Mixed Magnetic Field) of Magnetic Stars
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作者 Mahammad A. Nurmammadov 《Open Journal of Applied Sciences》 2024年第11期3165-3182,共18页
In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the neces... In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the necessary concepts about the equation of non-classical mathematical physics and the possibility of their applicability to astrophysical problems. The conditions of magneto-hydrodynamic equilibrium are determinate, and self-consistence provides the means to derive the corresponding partial differential equations describing this equilibrium in a magnetosphere magnetic star. Namely, this process is to the non-classical equations of mathematical physics in cases of types. Keldysh-Tricomi, a common case equation of non-classical type, is at first introduced by the author. Using the two main physical efficiencies of MHD. A mathematical model of a poloidal-toroidal mixed magnetic field for magnetic stars is constructed, and this model is classified with respect to degenerating case equations. According to Hopf’s theorem, Maxwell’s equation and the magnetic force balance equation constructed equilibrium conditions of the poloidal-toroidal of the magnetic field for a magnetic star. At the same time, the taken example, which is the self-consistency of this model by observation dates, is investigated. At first, in an application, the method of straight lines for recurrent formulas of calculation of magnetic flux and stream functions is used. The physical means, the corresponding singular point of the sonic line, cutoff, and resonance phenomena are considered. In this case, a general solution equation is found, which is interpreted by this phenomenon as a cutoff, resonance. Finally, this obtained solution gives the conditions of magneto-hydrodynamic equilibrium on the magnetosphere of magnetic stars. Methodology and obtained equations are new approaches that are at first considered. 展开更多
关键词 Magnetic Star MHD Equilibrium Keldysh and Tricomi Type Plasma non-classical equations of mathematical physics
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EQUATION OF MATHEMATICAL PHYSICS AND OTHER AREAS OF APPLICATION: A CLASSICAL INTEGRABLE SYSTEM AND THE INVOLUTIVE REPRESENTATION OF SOLUTIONS OF THE HIGHER ORDER KAUP-NEWELL EQUATION
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作者 李忠定 《Acta Mathematica Scientia》 SCIE CSCD 1993年第4期449-456,共8页
Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be... Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation. 展开更多
关键词 equatION OF mathematical physics AND OTHER AREAS OF APPLICATION A CLASSICAL INTEGRABLE SYSTEM AND THE INVOLUTIVE REPRESENTATION OF SOLUTIONS OF THE HIGHER ORDER KAUP-NEWELL equatION CTAM AZ
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The Mathematical and Physical Theory of Rational Human Intelligence: Complete Empirical-Digital Properties;Full Electrochemical-Mechanical Model (Part I: Mathematical Foundations)
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作者 Leo Depuydt 《Advances in Pure Mathematics》 2013年第5期491-561,共71页
The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is stric... The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is strictly digital—not quantitative in the manner that what is usually thought of as mathematics is quantitative. It is anticipated at this time that the exclusively digital nature of rational human intelligence exhibits four flavors of digitality, apparently no more, and that each flavor will require a lengthy study in its own right. (For more information,please refer to the PDF.) 展开更多
关键词 Artificial INTELLIGENCE Boolean ALGEBRA Boole’s ALGEBRA Black Box Theories Brain Science Cognition Cognitive Science Digital mathematICS Electricity and Magnetism J.-L. Lagrange and Partial Differential equations J. C. Maxwell’s Theory of Electromagnetism Neuroscience Non-Quantitative and Quantitative mathematICS physics RATIONAL Human INTELLIGENCE COMPLETE Theory of RATIONAL Thought and Language
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Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua 被引量:1
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作者 Karan S. Surana Emilio N. Alverio 《Applied Mathematics》 2020年第7期546-578,共33页
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous... Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper. 展开更多
关键词 Energy Methods Principle of Virtual Work Calculus of Variations Euler’s equation mathematical Model Classical and non-classical Continuum Mechanics
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Mathematical Model to Elaborate the Table of Thermodynamic Properties 被引量:1
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作者 Debrayan Bravo Hidalgo Liliana Del Carmen Morillo Acosta Nancy Del Rocio Flores Hinojosa 《Journal of Applied Mathematics and Physics》 2022年第6期1951-1967,共17页
Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the d... Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the document covers the theoretical principles of integral calculus, such as Theoretical framework and background, Geometric interpretation of the primitive, Primitive existence theorem. Results: Integral calculus and generalized thermodynamic models, and their applications in various thermodynamic analysis contacts such as the Generalized Enthalpy Model, the Generalized Entropy Model, and the Generalized Model applied to gas mixtures and the General Model to elaborate the properties table. Conclusion: The mathematical analysis developed in this document is very useful in engineering and applied physics environments, a fact that supports its common pedagogical practice in university institutions. 展开更多
关键词 equations Curves of Thermal Processes Thermodynamic Laws physics-mathematics Energy
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Mathematical Modeling of Heat Flux Distribution in Raw Cotton Stored in Bunt
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作者 Karimov Abdusamat Ismonovich Ismanov Muhammadziyo 《Engineering(科研)》 2020年第8期591-599,共9页
The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some im... The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some improvements. Therefore, the mathematical modeling of storage conditions of raw cotton in bunts and the physical and mechanical conditions that occur in it is of great importance. In the developed mathematical model, the main factor influencing the physical and mechanical properties of raw cotton is the change in temperature. Due to the temperature, kinetic and biological processes accumulated in the raw cotton in Bunt, it can spread over a large surface, first in a small-local state, over time with a nonlinear law. As a result, small changes in temperature lead to a qualitative change in physical properties. In determining the law of temperature distribution in the raw cotton in Bunt, Laplace’s differential equation of heat transfer was used. The differential equation of heat transfer in Laplace’s law was replaced by a system of ordinary differential equations by approximation. Conditions are solved in MAPLE-17 program by numerical method. As a result, graphs of temperature changes over time in raw cotton were obtained. In addition, the table shows the changes in density, pressure and mass of cotton, the height of the bun. As the density of the cotton raw material increases from the top layer of the bunt to the bottom layer, an increase in the temperature in it has been observed. This leads to overheating of the bottom layer of cotton and is the main reason for the deterioration of the quality of raw materials. 展开更多
关键词 physical Mechanical Properties The Bunt Parallelepiped The mathematical Model Biological System Heat Processes Temperature Coefficient Experiment The Bulk Density Volumetric Density Humidity FIGURE Coordinate Axes The Laplace Differential equation Transfer Solution Approximate MAPLE
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“复变函数与数理方程”课程思政教学探索
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作者 章权兵 张华永 任爱娣 《教育教学论坛》 2024年第8期89-92,共4页
课程思政是全面提升人才培养质量、落实立德树人根本任务的重要途径。对电子类专业的专业课程“复变函数与数理方程”的思想政治教学进行了探索,并选取课程中的复变函数的积分、傅里叶变换、定解问题等主要教学内容,通过对教学内容的剖... 课程思政是全面提升人才培养质量、落实立德树人根本任务的重要途径。对电子类专业的专业课程“复变函数与数理方程”的思想政治教学进行了探索,并选取课程中的复变函数的积分、傅里叶变换、定解问题等主要教学内容,通过对教学内容的剖析,挖掘知识点中所蕴含的科学元素和思政元素,将思想政治教育融入知识传授中。在激发学生学习兴趣、培养其学习主动性的同时,帮助学生树立正确的世界观、人生观、价值观,以达到教书育人的目的。 展开更多
关键词 课程思政 复变函数与数理方程 复变函数的积分 傅里叶变换 定解问题
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“数学物理方程”课程建设与思政教育融合的设想和实践
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作者 陈小刚 崔继峰 《科教文汇》 2024年第10期57-60,共4页
“数学物理方程”课程的建设旨在培养学生的科学思维、解决实际问题能力及思想政治素养。首先,明确课程目标是“数学物理方程”课程建设的基础。课程目标应既注重学科知识和技能的培养,又注重对学生思想政治素养和社会责任感的培养。其... “数学物理方程”课程的建设旨在培养学生的科学思维、解决实际问题能力及思想政治素养。首先,明确课程目标是“数学物理方程”课程建设的基础。课程目标应既注重学科知识和技能的培养,又注重对学生思想政治素养和社会责任感的培养。其次,课程内容体系的构建是课程建设的关键步骤。内容体系应具有层次性和有机衔接,使学生能够逐步深入学习和理解知识,丰富学生的学习体验,并促进学科间的融合和交叉。教学方法与手段的选择对于课程教学效果和学生学习体验至关重要。教师通过引导学生思考和解决问题、参与实验和实践活动,利用信息技术拓展学习途径,可以培养学生的创新思维、实践能力和综合素养。最后,评估与反馈机制在课程建设中具有重要作用。多样化的评估方式能够全面了解学生的学习情况和能力发展,及时反馈能够帮助学生调整学习策略和提高学习效果。同时,还应注重评估学生的思想品德和社会责任感,培养学生的思想政治素养和社会意识。 展开更多
关键词 数学物理方程 创新思维 思想政治教育 综合素养 社会责任感
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基于Mathematica和Matlab的典型数学物理方程解分布图像制作 被引量:2
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作者 陈殿伟 杨海英 《吉林化工学院学报》 CAS 2012年第7期41-44,共4页
通过计算机辅助软件Mathematica和Matlab,把典型数学物理方程解的空间分布制作成三维图像.
关键词 mathematICA MATLAB 数学物理方程
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“以学生为中心”的数学物理方程课程教学方法探索
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作者 胡赵胜 林珍华 常晶晶 《物理通报》 CAS 2024年第4期13-16,共4页
数学物理方程作为数学与物理的桥梁在理工科本科教育中极为重要,结合实践教学经历,通过分章节式背景知识补充及多平台资源自我学习、引导学生知识体系重构式教学、学生自主讨论式知识运用,以充分调动学生主观能动性,引导学生拓展、重构... 数学物理方程作为数学与物理的桥梁在理工科本科教育中极为重要,结合实践教学经历,通过分章节式背景知识补充及多平台资源自我学习、引导学生知识体系重构式教学、学生自主讨论式知识运用,以充分调动学生主观能动性,引导学生拓展、重构自身知识体系,提升知识灵活运用能力,以实现“学生为中心”的教学理念,提高教学成效. 展开更多
关键词 数学物理方程 以学生为中心 主观能动性 教学改革
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基于BOPPPS教学方法的“数学物理方程”课程建设与实践
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作者 鲍文娣 郭会 乔田田 《科教导刊》 2024年第17期90-92,共3页
文章基于“学生为中心,产出为导向”的教学理念,根据“数学物理方程”课程特点,构建了基于BOPPPS教学法的“线上+线下”混合式教学模式。为适应专业人才培养目标,打造了与混合式教学相适配的“线上资源+专业特色大作业+双创竞赛”一体... 文章基于“学生为中心,产出为导向”的教学理念,根据“数学物理方程”课程特点,构建了基于BOPPPS教学法的“线上+线下”混合式教学模式。为适应专业人才培养目标,打造了与混合式教学相适配的“线上资源+专业特色大作业+双创竞赛”一体化实践教学体系。同时,以立德树人为根本,构建了与混合式教学相适配的课程思政教学体系。实践表明,该课程改革有效激发了学生的学习内驱力,提升了学生的思维能力,促进了“知识传授、能力培养、价值引领”三位一体课程教学目标的达成,教学质量稳步提升。 展开更多
关键词 数学物理方程 专业特色 BOPPPS教学法 课程思政
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基于Mathematica的《数理方程》可视化教学改革探索 被引量:3
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作者 许韬 郭启龙 +1 位作者 戴芊慧 孟得新 《教育教学论坛》 2017年第52期144-146,共3页
《数理方程》素来具有知识点综合性强、数学推导复杂烦琐、学生普遍缺少学习兴趣和耐心等特点。以Mathematica符号计算平台为基础,我们针对弦的振动过程、杆的热量传导、温度(电势)的稳恒分布、行波的传播以及特殊函数的性质等教学环节... 《数理方程》素来具有知识点综合性强、数学推导复杂烦琐、学生普遍缺少学习兴趣和耐心等特点。以Mathematica符号计算平台为基础,我们针对弦的振动过程、杆的热量传导、温度(电势)的稳恒分布、行波的传播以及特殊函数的性质等教学环节设计了一定的图形和动画,将难以描绘的物理现象和抽象的特殊函数向学生进行可视化演示,从而在一定程度上激发了学生的学习兴趣,提高了课堂教学效果。 展开更多
关键词 数理方程 可视化教学 mathematICA软件
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The Utilization of the Generating Function Technique in the Discovery of Solutions for the Three-Dimensional Navier-Stokes Equation System
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作者 Robert Lloyd Jackson 《Open Journal of Fluid Dynamics》 2022年第1期86-95,共10页
The derivation of solutions to the Navier-Stokes (system of) equations (NSEs), in three spatial dimensions, has been an enigma as time can tell. This study wishes to show how to eradicate this problem via the usage of... The derivation of solutions to the Navier-Stokes (system of) equations (NSEs), in three spatial dimensions, has been an enigma as time can tell. This study wishes to show how to eradicate this problem via the usage of a recently proposed method for solving partial differential equations called the Generating Function Technique, or GFT for short. The paper will first quickly define the NSEs with and without an external force, then provide a quick synopsis of the GFT. Next, the study will derive solutions to these two major problems and give an analysis of the data concerning a specific set of criteria established by the Clay Mathematics Institute to determine the smoothness and existence of solutions. Results via GFT will show one can easily prove the existence of solutions to the NSEs with or without the presence of an external force. However, only the solutions to the NSEs will be globally bound. 展开更多
关键词 physics and mathematics Fluid Mechanics Partial Differential equations
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基于创新能力培养的数理方程课程的改革与实践 被引量:1
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作者 刘志明 黄建华 王晓 《高等数学研究》 2023年第4期85-88,共4页
本文对数理方程教学过程中存在的问题进行分析,通过比较上海交大、北航、国防科大的数理方程课程的教学学时、教学内容、考核方式和教学要求,从融入建模思想、增加实践环节、融入课程思政、注重过程评价等方面进行教学改革,以期提高数... 本文对数理方程教学过程中存在的问题进行分析,通过比较上海交大、北航、国防科大的数理方程课程的教学学时、教学内容、考核方式和教学要求,从融入建模思想、增加实践环节、融入课程思政、注重过程评价等方面进行教学改革,以期提高数理方程课程的教学效果. 展开更多
关键词 数理方程 创新能力 教学改革
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数学物理方程中定解问题案例教学研究
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作者 姜春华 张援农 《现代信息科技》 2023年第21期187-190,共4页
数学物理方程是理工科专业的一门重要的基础专业课程,是数学和实际物理问题之间重要的重要桥梁。在教学实践中,该课程烦琐的数学公式推导,同时涉及一些物理背景知识,导致学生对本课程的学习性不高。案例教学是提高学生学习兴趣的重要方... 数学物理方程是理工科专业的一门重要的基础专业课程,是数学和实际物理问题之间重要的重要桥梁。在教学实践中,该课程烦琐的数学公式推导,同时涉及一些物理背景知识,导致学生对本课程的学习性不高。案例教学是提高学生学习兴趣的重要方式之一,通过对地球物理学空间物理专业的一个物理问题进行提炼,导出了相应的定解问题,并数值模拟该定解问题的解,对模拟结果实现了可视化,使学生对其物理机制有了进一步的了解,形成一个有价值的案例,有效提升学生对该课程学习的积极性和课程教学效果。 展开更多
关键词 数学物理方程 定解问题 案例教学 可视化
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积分变换在数理方程中的应用
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作者 杜玲珑 王珂 《大学数学》 2023年第5期76-80,共5页
积分变换是研究数理方程的重要工具.利用Fourier变换或Laplace变换,可以求得一些数理方程的显式解.事实上,对于一些半无界问题的数理方程如热传导方程,可以进行Fourier-Laplace变换,通过寻求半无界问题的Green函数和全空间问题热核的关... 积分变换是研究数理方程的重要工具.利用Fourier变换或Laplace变换,可以求得一些数理方程的显式解.事实上,对于一些半无界问题的数理方程如热传导方程,可以进行Fourier-Laplace变换,通过寻求半无界问题的Green函数和全空间问题热核的关系,给出半无界问题解的表达式. 展开更多
关键词 半无界热传导方程 Fourier-Laplace积分变换 数理方程
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“偏微分方程”课程中的高阶学习探索
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作者 于灏 杨云龙 《科技风》 2023年第11期14-16,共3页
本文以本科“偏微分方程”教学中涉及的格林公式与高斯公式为出发点,通过复数乘积的几何解释,将格林公式与高斯公式在积分形式上统一为无空间维数要求的散度定理。进而引入一般的分部积分公式,使学生对抽象积分有一个初步的了解,达到在... 本文以本科“偏微分方程”教学中涉及的格林公式与高斯公式为出发点,通过复数乘积的几何解释,将格林公式与高斯公式在积分形式上统一为无空间维数要求的散度定理。进而引入一般的分部积分公式,使学生对抽象积分有一个初步的了解,达到在“偏微分方程”课程中进行高阶学习探索的目的。 展开更多
关键词 偏微分方程 数学物理方程 高阶学习
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齐次平衡原则与BTs 被引量:19
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作者 王明亮 白雪 《兰州大学学报(自然科学版)》 CAS CSCD 北大核心 2000年第3期12-17,共6页
用齐次平衡原则导出了 Thomas方程、Burgers方程、Kd V方程和 Boussinesq方程的新型BT.它们的著名非线性变换 ,可作为这里导出的新型
关键词 非线性数学物理方程 齐次平衡原则 BTS
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基于GIS的LL-Ⅱ分布式降雨径流模型的结构 被引量:28
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作者 李兰 钟名军 《水电能源科学》 2003年第4期35-38,共4页
主要讨论了LILAN- 分布水文模型的结构。该模型结构是为水文过程模拟和预报而设计的,它提出了变动生态产流模式,耦合了一维坡面流、一维壤中流、一维地下水流、一维河川径流和二维土壤含水量方程组。通过实际检验,该模型能够明显改善模... 主要讨论了LILAN- 分布水文模型的结构。该模型结构是为水文过程模拟和预报而设计的,它提出了变动生态产流模式,耦合了一维坡面流、一维壤中流、一维地下水流、一维河川径流和二维土壤含水量方程组。通过实际检验,该模型能够明显改善模拟预报精度、增强数值计算稳定性、提高参数优选的运行速度和减少存储空间,能够适合不同水文特征地区的产汇流计算,可以提供流域内任意空间网格的水文计算过程。 展开更多
关键词 数学物理方程 DEM LILAN—Ⅱ分布水文模型 产流 汇流 降雨径流模型 GIS
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