用安培环路定理求载流无限长螺线管磁场

本文区别一般教材中毕奥一萨伐尔定律与安培环路定理相结合的方法，仅用安培环路定理求出载流无限长螺线管磁场分布，突显了安培环路定理在磁场分布方面的作用与意义，加深对安培环路定理的理解。     

关于刚体弹性碰撞的一个定理

讨论一类刚体的弹性碰撞，从而得到一个定理，该定理的结论与理论力学中质点弹性碰撞的相应结论类似。     

陈子定理产生的时代:日冬至在牵牛

“陈子定理”是指“勾股定理”名下广泛内容中一部分已明确的内容，即勾股术的普遍公式，它出自《周髀算经》卷上“荣方问于陈子”一节，根据该书上的句子“日冬至在牵牛”测算，陈子定理产生的年代应为公元前700年．而约公元前550年，希腊人Pythagoras发现了与陈子定理相同的规律，现称为Pythagoras定理。     

带电体定轴转动的磁矩计算

带电体定轴转动的磁矩计算与刚体定轴转动的转动惯量计算想仿，平行轴定理和正交轴定理有助于磁矩的计算。     

超声波电发生器的最大输出功率和效率

本文从电路理论中的最大功率传输定理出发，分析了超声波电发生器与普通电源的异同，提出了最大功率传输定理的扩展条件，从而将一般电源的匹配和超声波发生器的匹配这两种概念统一起来。文章应用扩展后的最大功率传输定理，从一个新的角度对超声波电发生器的最大输出功率和效率进行了分析，得到与图解法等其他方法相同的结果。     

对质点动量定理与角动量定理等价性的探讨

论证了质点动量定理与质点对某一固定点的角动量定理并不等价，但它与质点对任意固定点的角动量定理等价的。     

从陈子定理看经典力学

从陈子定理可以演绎出描写质点运动的各种表示方式，从陈子定理可以推导出质点动力学的基本定理，包括牛顿运动三定律，动能定理，质心运动定理。     

对磁路定理的改进

应用电磁学理论，对传统的磁路定理进行了改进，改进后的磁路定理不但适用于稳恒磁路，而且适用于交变磁路，对变压器的实验证明了该磁路定理的合理性。     

质心和质心运动定理应用一例

质心和质心运动定理应用一例南京金陵职业大学工程技术系柳涛南京师范大学物理系吴秀芳质心和质心运动定理是力学教学中的一个难点．通过下面对下落弹簧运动规律的分析与研究，不仅５ｆ使初学者较深ｋ７）地理解和掌握质心和质心运动定理，而且提供了一道运用数学知识处理...     

特勒根定理的证明及应用

本文用回路电流法证明了特勒根定理，并用该定理证明了弥尔曼定理和互易定理。     

THE TRANSFORMATION BETWEEN THE AKNS HIERARCHY AND THE KN HIERARCHY WITH SELF-CONSISTENT SOURCES

It is shown that the AKNS hierarchy with self-consistent sources can transform to KN hierarchy with self-consistent sources through a transformation operator and gauge transformation. Besides, there exists transformation in their conservation laws and Hamiltonian structures.     

碰撞中动量守恒定律和能量守恒定律的相对论协变性

以两个小球碰撞为例,验证了动量守恒定律和能量守恒定律在洛仑兹变换下的形式不变性     

SEMIDISCRETE INTEGRABLE NONLINEAR SYSTEMS GENERATED BY THE NEW FOURTH-ORDER SPECTRAL OPERATOR: LOCAL CONSERVATION LAWS

Starting with the semidiscrete integrable nonlinear Schrödinger system on a zigzag-runged ladder lattice we have presented the generalization and an essentially off-diagonal enlargement of its spectral operator which in the framework of zero-curvature equation allows to generate at least two new types of semidiscrete integrable nonlinear systems. The two types of evolutionary operators consistent with the extended spectral operator are proposed. In order to fix arbitrary sampling functions in each type of evolution operators we have to rely upon a restricted collection of lowest local conservation laws whose local densities are independent on the type of admissible evolution operators. For this purpose the modified procedure of seeking the infinite hierarchy of local conservation laws based upon several distinct generating functions has been developed and some lowest local conservation laws have been explicitly obtained.     

不同惯性系中的力学规律

由力学相对性原理可知，在不同惯性系中，一切力学规律（如牛顿运动定律、动量定理、动量守恒定律、角动量定理等）的形式都相同．但在一个惯性系中机械能（或角动量）守恒，在另一惯性系中观察机械能（或角动量）却不一定守恒．     

约束系统的对称变换

对于用非独立态函数描述的受约束系统,在对称变换下将导致推广的Noether定理,一般说,此时不产生Noether定理的守恒量,在有限约束下内部对称变换的推广Noether定理,就化为通常Noether定理的结果。 关键词：     

Symmetries and Two Types of Non-Noether Conservation Laws of Birkhoffian System with Unilateral Constraints

The symmetries and non-Noether conservation laws of Birkhoffian system with unilateral constraints are studied. The differential equations of motion of the system are established, and the criterions of Noether symmetry, Lie symmetry and Mei symmetry of the system are given. Two types of new conservation laws, called the Hojman conservation law and the Mei conservation law respectively, are obtained, and the intrinsic relations among the symmetries and the new conservation laws are researched. At the end of the paper, an example is given to illustrate the application of the results.     

Generalized Noether identities and application to Yang-Mills field theory

We derive generalized Noether identities for a system with noninvariant action integral under an infinite continuous group and deduce the string conservation laws of the system. We give a preliminary application to field theory and discuss the strong conservation laws for the BRS transformation and the weak conservation laws of Yang-Mills fields. The Dirac constraint of the system is examined.     

A DIRECT PROCEDURE ON THE INTEGRABILITY OF NONISOSPECTRAL AND VARIABLE-COEFFICIENT MKdV EQUATION

An elementary and systematic method based on binary Bell polynomials is applied to nonisospectral and variable-coefficient MKdV (vcMKdV) equation. The bilinear representation, bilinear Bäcklund transformation, Lax pair and infinite local conservation laws are obtained step by step, without too much clever guesswork.     

Further Study on the Conservation Laws of?Energy-Momentum Tensor Density for a Gravitational System

The various methods to derive Einstein conservation laws and the relevant definitions of energy-momentum tensor density for gravitational fields are studied in greater detail. It is shown that these methods are all equivalent. The study on the identical and different characteristics between Lorentz and Levi-Civita conservation laws and Einstein conservation laws is thoroughly explored. Whether gravitational waves carry the energy-momentum is discussed and some new interpretations for the energy exchanges in the gravitational systems are given.     

On symmetries,conservation laws and exact solutions of the nonlinear Schrödinger–Hirota equation

In this paper, conservation laws and exact solution are found for nonlinear Schrödinger–Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger–Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.