非齐次线性递归方程的特解公式

提出了非齐次线性递归方程的降阶公式,并由此导出了常系数非齐次线性递归方程的特解公式．     

算子法求常系数多元线性非齐次递归公式的通项

本文引入算子Ｄ的方法，先对一无线性非齐次递归公式进行研究，然后把多元线性非齐次递归公式归结到一元线性非齐次递归公式。     

非齐次线性递归方程的特解公式

提出了非齐次线性递归方程的降阶公式,并由此导出了常系数非齐次线性递归方程的特解公式.     

一类二阶变系数非齐次线性微分方程的通解

通过在二阶变系数非齐次线性微分方程两边同乘以某个积分因子将该方程转化为常系数非齐次线性微分方程,进而得出二阶变系数非齐次线性微分方程的通解公式.     

二阶常系数非齐次线性微分方程一特解的积分求法

本文给出二阶常系数非齐次线性微分方程的一个特解的积分公式．并给出证明。     

常系数非齐次线性微分方程特解的另一种求法

将常系数线性微分方程转化为一阶常系数线性微分方程组,并利用线性微分方程组的基解矩阵的性质和矩阵指数的性质以及非齐次线性微分方程组的常数变易公式,得到了常系数非齐次线性微分方程的积分形式的特解公式,并通过实例说明所得结论的有用性.     

特殊类型二阶变系数非齐次线性微分方程通解公式

本给出了二阶变系数非齐次线性微分方程的系数满足某些特殊条件时的通解公式．     

一阶非齐次拟线性双曲组的柯西问题整体经典解的存在性

本文考察了弱线性退化的一阶非齐次拟线性严格双曲组具有小初值的柯西问题.在非齐次项满足匹配条件的假设下,给出了精细的波的分解公式,利用这些公式,证明了整体C1解的存在唯一性和稳定性.     

关于一类差分方程的特解求法

使用一阶常系数线性非齐次差分方程的通解公式,讨论二阶常系数线性非齐次差分方程yx+2+ayx+1+byx=f(x)特解的一种求法,给出计算特解的一个公式.     

用齐次化原理解线性非齐次微分方程

齐次化原理是求解线性非齐次偏微分方程的一种方法。本文利用这种方法求解线性非齐次常微分方程,并推导出解的一般公式。     

EIN NEUER BEWEIS UND EINE VERSCHÄRFUNG FÜR DEN REDUKTIONSTYP ∀∃∀∞(0, 1) MIT EINER ANWENDUNG AUF DIE SPEKTRALE DARSTELLUNG VON PRÄDIKATEN

A simultaneous semantical and syntactical reduction is given for the satisfiability respectively finite satisfiability of first order formulas. We choose ???∞(0, 1) as conservative reduction class and allow only formulas out of ???∞(0, 1) having a simple set theoretical model if they are satisfiable at all. With the same method we get a spectral representation of any ?-ary enumerable respectively coenumerable predicate by a formula out of ???∞(?, 1).     

On families of quadrature formulas based on Euler identities

A family consisting of quadrature formulas which are exact for all polynomials of order ?5 is studied. Changing the coefficients, a second family of quadrature formulas, with the degree of exactness higher than that of the formulas from the first family, is produced. These formulas contain values of the first derivative at the end points of the interval and are sometimes called “corrected”.     

基于泰勒级数展开的一点超前差分公式的推导

传统的数值微分公式有前向差分、后向差分和中心差分公式.所谓一点超前差分公式,就是后向差分公式在形式上"前移"一点来计算一阶导数的公式.该公式有效地弥补了传统差分公式的不足之处.不同于以前研究中使用拉格朗日公式来推导一点超前公式的做法,给出了基于泰勒级数展开的对该组公式及其截断误差的推导,从另一个角度验证了一点超前公式,使其更为完善.     

A note on the area and coarea formulas for general volume densities and some applications

We present the area and coarea formulas for Lipschitz maps, valid for general volume densities. We apply these formulas to derive an anisotropic tube formula for hypersurfaces in \({{\mathbb{R}}^n}\) and to give a short euclidean proof of the anisotropic Sobolev inequality. A discussion about the first variation of the anisotropic area is also included.     

On the weak control of slowly damped systems : PMM vol. 42, no. 6, 1978. pp. 1000–1005

Asymptotic formulas are obtained which make it possible to derive the first approximation solution of the Riccati matrix algebraic equation of special form. Method is based on Bass' formulas [1] and the theory of perturbations [2], The problem of control of a slowly damped oscillator is investigated in detail. Formulation of the problem in this paper differs substantially from that in [3] (no assumption is made about single-frequency oscillations, and only a stationary system is considered over an infinite time interval).     

关于复函数的中值公式及“中间点”的渐近性

讨论几个复函数徽分中值公式的“中间点”渐近性，所得渐近估计式推广了有关文献中相应的结论，然后，建立复函数的积分中值公式及“中间点”的渐近性质，得到与实积分相类似的结果．     

Bifurcation of limit cycles from a heteroclinic loop with two cusps

In this paper, we study the expansion of the first Melnikov function for general near-Hamiltonian systems near a heteroclinic loop with two cusps of order 1 or 2, obtain the formulas for the first coefficients appearing in the expansion, and establish some bifurcation theorems on the number of limit cycles. We also give some application examples.     

Arrangements of planes in space

This paper presents a variety of formulas for the number of cells, faces, and edges, bounded and unbounded, that are formed by an arbitrary set of planes in $\text{R}$³. Using an elegant geometric method described in 1966 by Brousseau, we first prove a version in $\text{R}$³ of the general partition formulas established algebraically by Zaslavsky in 1975. From these formulas we deduce two families of inclusion–exclusion formulas for the counters, the first similar to formulas outlined by Roberts in 1889, the second related to formulas given by Steiner in 1826. We conclude with some non-trivial new bounds for the counters of an arbitrary arrangement in $\text{R}$³ and two specific examples.     

Estimates for the Remainders of Certain Quadrature Formulas

Estimates of the remainders of certain quadrature formulas are obtained, in particular, of quadrature formulas with nodes that are the zeros of Chebyshev polynomials of the first kind in classes of differentiable functions characterized by a generalized modulus of continuity.     

Sub-Riemannian calculus on hypersurfaces in Carnot groups

We develop a sub-Riemannian calculus for hypersurfaces in graded nilpotent Lie groups. We introduce an appropriate geometric framework, such as horizontal Levi-Civita connection, second fundamental form, and horizontal Laplace-Beltrami operator. We analyze the relevant minimal surfaces and prove some basic integration by parts formulas. Using the latter we establish general first and second variation formulas for the horizontal perimeter in the Heisenberg group. Such formulas play a fundamental role in the sub-Riemannian Bernstein problem.