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1.
王兴波 《数学学习》2009,12(4):89-92
从对偶矢量入手.在剖析函数微分内在涵义的基础上,由具体至抽象地引入微分1-形式.进而通过外乘法与外微分运算,引进高阶微分形式;通过介绍微分形式的积分转换方法,自然过渡到Stokes定理;最后通过微分形式在矢量分析中的应用,将抽象的理论回归到具体工程计算.由此实现微分形式的教学过程。  相似文献   

2.
本文考虑具有不等式约束条件不可微优化问题,假定目标函数和约束函数既是Lipschitz的也是拟可微的.证明了该问题拟微分形式下的FritzJohn点必是Clarke广义梯度形式下的FritzJohn点.另外,还给出了拟微分和Clarke广义梯度之间的关系.  相似文献   

3.
高岩 《运筹学学报》1999,3(4):47-54
讨论了不等式约束优化问题中拟微分形式下Fritz John必要条件与 Clarke广义梯度形式下Fritz John必要条件的关系.在较弱条件下给出了具有等式与不等式约束条件的两个Lagrange乘子形式的最优性必要条件,在这两个条件中等式约束函数的拟微分和Clarke广义梯度分别被使用。  相似文献   

4.
中心焦点判定的形式积分因子方法   总被引:4,自引:1,他引:3  
杜乃林  陈士华 《数学杂志》1997,17(2):231-239
本文从积分因子的角度探讨了焦点量的计算方法,给出了形式积分因子的存在性和形式积分因子的系数与焦点量的等价关系,从而给出计算焦点量的简捷算法。  相似文献   

5.
小波尺度函数计算的广义高斯积分法及其应用   总被引:7,自引:0,他引:7  
对于小波尺度函数变换的分解系数的积分运算建立了以尺度函数为权的广义高斯积分方法的运算格式.借助于样条函数,证明了其广义高斯积分随小波分解水平(resolutionlevel)指标的上升而收敛.在此基础上给出了以小波尺度函数变换重构或逼近任一函数的显式解析式,并对具有函数算子、微分或积分算子的运算给出了变换规则.这对于求解复杂非线性方程(组)是一种强有力的工具.最后给出了用该文方法求解非线性二点边值问题的算例.  相似文献   

6.
用微分形式的吴方法讨论了广义KdV—Burgers方程不同系数情况下的势对称,并且利用这些对称求得了相应的不变解,这些解对进一步研究广义KdV—Burgers方程所描述的物理现象具有重要意义.  相似文献   

7.
粱洪亮 《数学学习》2004,7(4):46-47,49
将等价关系应用于求极限和判定无穷积分、无穷级数的敛散性 ,可极大地方便问题求解  相似文献   

8.
广义混合似变分不等式组的两步迭代算法   总被引:1,自引:0,他引:1  
对H ilbert空间中一类广义混合似变分不等式组进行了研究;利用次微分算子的预解式技术,建立了广义混合似变分不等式组与不动点问题之间的等价关系;给出了一个求解这种广义混合似变分不等式组的显式两步迭代算法;并证明了该算法在适当的条件下收敛.  相似文献   

9.
本文给出了Heisenberg方程的无穷守恒律,并具体给出了其前三个守恒律,特别得到了铁磁链方程无穷多个微分形式与积分形式的守恒律。  相似文献   

10.
王文友 《数学进展》2005,34(5):569-583
本文基于Mellin变换法求解复杂更一般形式的对偶积分方程组.通过积分变换,由实数域化成复数域上的方程组,引入未知函数的积分变换,移动积分路径,应用Cauchy积分定理,实现退耦正则化为Cauchy奇异积分方程组,由此给出一般性解,并严格证明了对偶积分方程组退耦正则化为Cauchy奇异积分方程组与原对偶积分方程组等价性,以及对偶积分方程组解的存在性和唯一性.给出的解法和理论解,作为求解复杂对偶积分方程组一种有效解法,可供求解复杂的数学、物理、力学中的混合边值问题应用.  相似文献   

11.
Existence of a diagonal form under unimodular equivalence is proved for matrices with entries from the Hurwitz ring of integral quaternions. The diagonal elements satisfy certain divisibility relations with an unexpected character, and these force a degree of uniqueness to the diagonal form. Connections between the so obtained invariant factors of a full matrix and those of a submatrix are then established.  相似文献   

12.
新的正交关系被推广到正交各向异性三维弹性力学· 将弹性力学新正交关系中构造对偶向量的思路推广到正交各向异性问题· 将弹性力学求解辛体系的对偶向量重新排序后,提出了一种新的对偶向量· 由混合变量求解法直接得到对偶微分方程· 所导出的对偶微分矩阵具有主对角子矩阵为零矩阵的特点· 由于对偶微分矩阵的这一特点,对于正交各向异性三维弹性力学发现了2个独立的、对称的正交关系· 采用分离变量法求解对偶微分方程· 从正交各向异性弹性力学求解体系的积分形式出发,利用一些恒等式证明了新的正交关系· 新的正交关系不但包含原有的辛正交关系,而且比原有的关系简洁· 新正交关系的物理意义是对偶方程的解关于z坐标的对称性的体现· 辛正交关系是一个广义关系,但辛正交关系可以在一定的条件下以狭义的强形式出现· 新的研究成果将为研究正交各向异性三维弹性力学的解析解和有限元解提供新的有效工具·  相似文献   

13.
We consider a nonlocal problem with integral conditions of the 1st kind. The main goal is to prove the unique solvability of this problem under the assumption that kernels of nonlocal conditions depend both on spatial and time variables. To this end we propose a technique based on the proved equivalence between the nonlocal problem with integral conditions of the 1st kind and a nonlocal problem with integral conditions of the 2nd kind in a special form. We formulate requirements to the initial data guaranteeing the unique existence of a generalized solution to the stated problem.  相似文献   

14.
A (positive definite integral) quadratic form is called diagonally 2-universal if it represents all positive definite integral binary diagonal quadratic forms. In this article, we show that, up to equivalence, there are exactly 18 (positive definite integral) quinary diagonal quadratic forms that are diagonally 2-universal. Furthermore, we provide a “diagonally 2-universal criterion” for diagonal quadratic forms, which is similar to “15-Theorem” proved by Conway and Schneeberger.  相似文献   

15.
We describe a natural isomorphism between the set of equivalence classes of pseudocycles and the integral homology groups of a smooth manifold. Our arguments generalize to settings well-suited for applications in enumerative algebraic geometry and for construction of the virtual fundamental class in the Gromov-Witten theory.

  相似文献   


16.
New compactness results on the velocity functions and shear stress functions of the well-known Falkner-Skan equation are obtained. The methodology is to utilize the equivalence between the Falkner-Skan equation and a singular integral equation established recently by Lan and Yang.  相似文献   

17.
The scalar problem of plane wave diffraction by a system of bodies and infinitely thin screens is considered in a quasi-classical formulation. The solution is sought in the classical sense but is defined not in the entire space ?3 but rather everywhere except for the screen edges. The original boundary value problem for the Helmholtz equation is reduced to a system of weakly singular integral equations in the regions occupied by the bodies and on the screen surfaces. The equivalence of the integral and differential formulations is proven, and the solvability of the system in the Sobolev spaces is established. The integral equations are approximately solved by the Bubnov-Galerkin method. The convergence of the method is proved, its software implementation is described, and numerical results are presented.  相似文献   

18.
The paper deals with the three‐dimensional Dirichlet boundary value problem (BVP) for a second‐order strongly elliptic self‐adjoint system of partial differential equations in the divergence form with variable coefficients and develops the integral potential method based on a localized parametrix. Using Green's representation formula and properties of the localized layer and volume potentials, we reduce the Dirichlet BVP to a system of localized boundary‐domain integral equations. The equivalence between the Dirichlet BVP and the corresponding localized boundary‐domain integral equation system is studied. We establish that the obtained localized boundary‐domain integral operator belongs to the Boutet de Monvel algebra. With the help of the Wiener–Hopf factorization method, we investigate corresponding Fredholm properties and prove invertibility of the localized operator in appropriate Sobolev (Bessel potential) spaces. Copyright © 2016 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons, Ltd.  相似文献   

19.
分数阶微分方程的比较定理   总被引:3,自引:0,他引:3  
本文给出了非线性Riemann—Liouville分数阶微分方程和Caputo分数阶微分方程与相应的非线性Volterra积分方程的等价性,并在此基础上建立了分数阶微分方程的比较定理.  相似文献   

20.
郭国安  宋洪雪 《大学数学》2017,33(2):101-107
运用复分析方法,首次给出了一类由三角函数、指数函数与幂函数乘积的线性组合产生的函数在某个区间上恒为零的充分必要条件证明,建立了此类函数积分计算的理论基础,结合微分和线性代数思想,系统讨论了待定系数法在一类含有三角函数的积分计算中的应用.  相似文献   

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