二阶微分方程的Mather集和拟周期解

考虑了二阶非线性微分方程ｘ↑．．＋ｘ＾２ｎ＋１＋∑↑ｌ↓ｊ＝０ｘ＾ｊｐｊ（ｔ）＝０，ｘ∈Ｒ＾１，其中ｐｉ（ｔ）是周期为１的函数，１≤ｉ≤ｌ≤２ｎ。证明了：如ｐｊ∈Ｃ＾２（Ｓ＾１），方程有Ｍａｔｈｅｒ集存在；对方程的一些特殊情形，证明了相应的Ｍａｔｈｅｒ集确是不变闭曲线，从而得到解的有界性。     

一类P—Laplace方程解的有界性研究

研究二阶微分方程（Фp（x^1））^1＋x^2n＋1＋∑^2nj=0x^jpj（t）=0,n≥1,x∈（-∞,∞）解的有界性。     

一类半线性Duffing方程解的有界性

借助一个非线性变换,在一定的假设下,利用Moser小扭转定理重新证明方程x^″＋n^2x＋φ（x）=p（t）所有解都是有界的,这一方法可极大地简化文献【1】中定理1的证明．     

关于一类非多项式位势的Littlewood问题(英文)

本文证明了方程+x²ⁿ⁺¹+P_x（x,t）=0所有解的有界性,其中n≥1,P（x,t）是关于两个变量x与t都是光滑的1-周期函数.     

一类非对称Duffing方程的不变环面

证明了一类Duffing方程:(x¨) g(x)=e(t).的不变环面的存在性,从而得出所有的解都是有界的,其中e(t)是以1为周期的函数,函数g:R→R具有性质:当x≥d0时,g(x)是次线性的,当x≤-d0时,g(x)是半线性的,d0为一正常数.     

Attraction and stability for neutral stochastic functional differential equations

The main aim of this paper is to establish several new criteria on the attractor for the solutions of neutral stochastic functional differential equations. A kind of ψ-function is introduced to our discussion, and some results on the attractor for the product of the ψ-function and the solutions are obtained. As a byproduct, a number of new criteria on asymptotic stability are also shown. Biography: CEN Liqun(1975–), female, Ph.D. candidate, research direction: theory and applications of stochastic differential equations.     

高维小扭转映射不变环面的存在性

考虑角度变量和作用变量具有不同维数的高维近可积小扭转映射不变环面的存在性, 通过构造KAM迭代的方法, 证明高维近可积小扭转映射在满足Rüssmann非退化条件及相交性条件下存在一族不变环面.     

一类带不变号权函数二阶超线性方程的周期碰撞解

运用相平面定性分析方法, 研究一类带不变号权函数二阶微分方程的碰撞问题. 通过坐标变换将碰撞问题转化为与之等价的定义在全平面上的问题, 在某种超线性条件下对解的动态行为进行分析, 得到了大振幅解的动态行为. 结果表明, Poincaré映射在充分大的圆环边界上具有扭转性, 并通过反复运用推广的Poincaré Birkhoff扭转定理, 得到了无穷多个ω- 周期碰撞解的存在性.     

Y_CΩ_(2n)are easy terms

For any natural number n≥1, Y CΩ 2n is an easy term; that is, for any λ term M, λβ+Y-CΩ 2n =M is consistent, where Y C is Curry fixed point combinator, Ω 2n ≡ω 2n ω 2n and ω 2n ≡λx.xx...x (there are 2n occurrences of x after λx ). This result is a partial solution to Jacopini's conjecture: Y CΩ n is an easy term for any natural number n≥2.     

Solution of Cauchy’s problem for wave equations in higher space dimensions by means of D’Alembert’s formula

A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown. Foundation item: Supported by the Natural Science Foundation of Hubei Province (992P0307) and the National Natural Science Foundation of China (39970203) Biography: YAO Duan-zheng (1946-), female, Professor, Research direction: mathematical physics and nonlinear optics.     

A generalization of Esseen’s inequality for NA random variables

The generalization of Esseen’ s inequality for NA random variables under the relatively general conditions is discussed. These results are about the same as those of the independent variables.     

Turchin模型动力学行为研究

实验室采集的数据都是离散的,且自然界中很多食植动物都是非叠代繁殖的。为了准确解释种群密度的周期振荡现象,Turchin提出离散时间模型。本文利用非线性微分方程的理论知识对Turchin模型的动力学行为进行详尽的分析,探讨解的有界性,得出解的存在范围,从而得到正向不变集;求出边界平衡点并讨论其稳定性;给出内部平衡点的存在条件及其局部渐近稳定的充要条件,为进一步解释种群的动态规律提供理论依据。     

泰勒定理论证函数性态的教学研究①

该文从一个新的角度研究了高等数学中泰勒定理的本质,通过典型实例阐述了泰勒公式对函数及其各阶导数之间有机联系的深入刻画及运用其论证函数性态的要点,进而帮助学生更深入地理解并掌握泰勒定理这一教学重点和难点。     

On the asymmetric distribution of heat loss from the Earth’s interior

Mean heat flows and heat Josses of the Northern and Southern hemispheres are calculated using degree 12 spherical harmonic representation of the global heat flow field (Pollacket al., 1993). Mean heat flows and heat losses of 0° hemisphere and 180° hemisphere, with median lines being 0° longitude and 180° longitude, are also calculated. The mean heat flow of the Southern Hemisphere is 99.3 mW·m^¨, significantly higher than that of the Northern Hemisphere (74.0 mW·m^¨). The mean heat flow of 0° hemisphere (94. 1 mW·m²) is also higher than the value of 180° hemisphere (79. 3 mW·m²). The mantle heat loss from the Southern Hemisphere is 22.1 × 10¹² W, as twice as that from the Northern Hemisphere (10.8 × 10¹² W). The 16.9 × 10¹² W mantle heat loss from 0° hemisphere is close to 16.0 × 10¹² W from 180° hemisphere. The hemispherical asymmetry of global heat loss is originated by the asymmetry of geographic distribution of continents and oceans. The asymmetric distribution of heat loss is a long-term phenomenon in the geological history.     

Ouyang型非线性积分不等式的推广

对Pachpane BC(1995)、Yang Enhao(1998)和李文荣(2000)给出的推广的Ouyang积分不等式作进一步研究,给出了两个更广泛的Ouyang型非线性不等式及其应用．     

一类立方非线性型八阶常微分方程周期解的多重存在性

本文运用极小化定理和Clark定理研究了满足边界条件u（0）=u″（0）=u（iv）（0）=u（vi）（0）=0和u（L）=u″（L）=u（iv）（L）=u（vi）（L）=0的一类立方非线性型八阶常微分方程u（viii）＋Au（vi）＋Bu（iv）＋Cu″＋Du-u3=0多重非平凡周期解的存在性.     

“Double dawn” eclipse andthe rotational variation of the earth

A record of “double dawn” at State Zheng in the first year of the reign of King Yi in Western Zhou Dynasty in the chronicle “Bamboo Annals” (Zhushu Jinian) is discussed. We think that it may be a record of an annular solar eclipse happening in 899 BC. The record and the †T, which describes the secular variation of the earth’s rotation, are analyzed and discussed.     

一类次二次四阶半线性微分方程两个非平凡周期解的存在性研究

这篇文章应用临界点理论中的Brezis-Nirenberg型环绕定理,证明了一类四阶半线性次二次微分方程u(4)-Au″-Bu-Vu(t,u)=0(1),两个非平凡2T-周期解的存在性.其中A0,B0,Aπ2BT2,V(t,u)∈C1([0,T]×R,R)满足条件2V(t,u)-uV(t,u)→∞,|u|→∞,t∈[0,T].     

Implicational lattices and generalization of Stone’s representation theorem

Let F(S) be the free algebra of type (,∨,→) generated by the non_empty set S, it is proved that the logical equivalent relation defined by means of R 0_semantics is a congruence relation on F(S) and the corresponding quotient algebra is said to be the R 0_semantic Lindenbaum algebra. Taking R 0_semantic Lindenbaum algebra as a prototype, the concepts of implicational lattices and regular implicational lattices which are generalizations of the concept of Boolean algebras are introduced. Besides, the concept of fuzzy implicational spaces is introduced and the representation theorem of regular implicational lattices is obtained by means of fuzzy implicational spaces. In case of Boolean algebras, the corresponding fuzzy implicational spaces are zero_dimensional compact Hausdorff spaces and herefrom it is proved that the famous Stone's representation theorem of Boolean algebras is a corollary of the representation theorem of regular implicational lattices.