The Cartesian Closedness of the Category CDL and Function Spaces on Topological CDL''''s

ＴｈｅＣａｒｔｅｓｉａｎＣｌｏｓｅｄｎｅｓｓｏｆｔｈｅＣａｔｅｇｏｒｙＣＤＬａｎｄＦｕｎｃｔｉｏｎＳｐａｃｅｓｏｎＴｏｐｏｌｏｇｉｃａｌＣＤＬ＇ｓＹａｎｇＺｈｏｎｇｑｉａｎｇ（杨忠强）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａａｎｘｉＮ...     

The Problem of Periodic Solutions for a Class of Dynamical Systems（Ⅰ

ＴｈｅＰｒｏｂｌｅｍｏｆＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｆｏｒａＣｌａｓｓｏｆＤｙｎａｍｉｃａｌＳｙｓｔｅｍｓ（Ⅰ）ＺｈａｎｇＺｈｉｐｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ，４７５００...     

Atoms of Lattices of Supernilpotent and Special Radicals

ＡｔｏｍｓｏｆＬａｔｔｉｃｅｓｏｆＳｕｐｅｒｎｉｌｐｏｔｅｎｔａｎｄＳｐｅｃｉａｌＲａｄｉｃａｌｓＺｈｏｎｇＤｅｑｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＣｏｕｒｓｅｓ，ＺｈｕｚｈｏｕＥｎｇｉｎｅｅｒｉｎｇＩｎｓｔｉｔｕｔｅ）Ａｂｓｔｒａｃｔ：Ｉ...     

Dynamical Behavior in Behavior in Simple and Coupled Systems of Continuous Josephson－Junctions

ＤｙｎａｍｉｃａｌＢｅｈａｖｉｏｒｉｎＢｅｈａｖｉｏｒｉｎＳｉｍｐｌｅａｎｄＣｏｕｐｌｅｄＳｙｓｔｅｍｓｏｆＣｏｎｔｉｎｕｏｕｓＪｏｓｅｐｈｓｏｎ－ＪｕｎｃｔｉｏｎｓＱｉａｎＭｉｎ（钱敏）ＺｈｏｕＳｈｅｎｇｆａｎ（周盛凡）（ＤｅｐａｒｔｍｅｎｏｆＭａ...     

The Structure of Hypergroup on the Cyclical Group

ＴｈｅＳｔｒｕｃｔｕｒｅｏｆＨｙｐｅｒｇｒｏｕｐｏｎｔｈｅＣｙｃｌｉｃａｌＧｒｏｕｐ￥ＺｈｏｎｇＹｕｂｉｎ（Ｄｅｐａｒｔｍｅｎｔｏｆｍａｔｈｅｍａｔｉｃｓ，ＧｕａｎｇｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ）Ａｂｓｔｒａｃｔ：Ｓｉｎｃｅｔｈｅｈｙｐｅｒ...     

Strong-principal Bimodules of Jacobson Radical of CSL Algebras

Ｓｔｒｏｎｇ－ｐｒｉｎｃｉｐａｌＢｉｍｏｄｕｌｅｓｏｆＪａｃｏｂｓｏｎＲａｄｉｃａｌ　ｏｆＣＳＬＡｌｇｅｂｒａｓＺｈｕＪｕｎ（朱军）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｂｅｉＩｎｓｔｉｔｕｔｅｆｏｒＭａｔｉｏｎａｌｉｔｉｅｓ，Ｅｎｓ...     

Nontrivial Solutions of Semilinear Elliptic Equations Involving Critical Sobolev Exponents

ＮｏｎｔｒｉｖｉａｌＳｏｌｕｔｉｏｎｓｏｆＳｅｍｉｌｉｎｅａｒＥｌｌｉｐｔｉｃＥｑｕａｔｉｏｎｓＩｎｖｏｌｖｉｎｇＣｒｉｔｉｃａｌＳｏｂｏｌｅｖＥｘｐｏｎｅｎｔｓＨａｎＪｉａｎｌｏｎｇ（韩建龙）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｔｉａ...     

The Range Set of Meromorphic Derivatives

ＴｈｅＲａｎｇｅＳｅｔｏｆＭｅｒｏｍｏｒｐｈｉｃＤｅｒｉｖａｔｉｖｅｓＩｎｄｒａｊｉｔＬａｈｉｒｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪａｄａｖｐｕｒＵｎｉｖｅｒｓｉｔｙ，Ｃａｌｃｕｔａ－７０００３２，Ｉｎｄｉａ）ＡｂｓｔｒａｃｔＩｎｔ...     

Jordan Canonical Form of a Matrix over the Quaternion Field

ＪｏｒｄａｎＣａｎｏｎｉｃａｌＦｏｒｍｏｆａＭａｔｒｉｘｏｖｅｒｔｈｅＱｕａｔｅｒｎｉｏｎＦｉｅｌｄＨｕａｎｇＬｉｐｉｎｇ（黄礼平）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＳｃｉｅｎｃｅｓ，ＸｉａｎｇｔａｎＭｉｎｉｎｇＩｎｓｔｉｔｕｔｅ，Ｘｉａｎｇｔａｎ...     

The Jacobson and Brown—McCoy Radicals of Certain Group Rings

ＴｈｅＪａｃｏｂｓｏｎａｎｄＢｒｏｗｎ－ＭｃＣｏｙＲａｄｉｃａｌｓｏｆＣｅｒｔａｉｎ　Ｇｒｏｕｐ　ＲｉｎｇｓＺｈｏｕＹｏｎｇｘｉｎ（周永新）（Ｍａｔｈ．Ｄｅｐｔ．，ＨｅｂｅｉＴｅａｃｈｅｒｓ＇Ｕｎｉｖｅｒｓｉｔｙ，Ｓｈｉｊｉａｚｈｕａｎｇ，０５００１...     

Preservation of Sahlqvist fixed point equations in completions of relativized fixed point Boolean algebras with operators

We define Sahlqvist fixed point equations and relativized fixed point Boolean algebras with operators (relativized fixed point BAOs). We show that every Sahlqvist fixed point equation is preserved under completions of conjugated relativized fixed point BAOs. This extends the result of Givant and Venema (1999) to the setting of relativized fixed point BAOs.     

一些连续统的孤立链回归点

对树或图上的连续自映射,本文证明了孤立链回归点是终周期点,如孤立边回归不在临界点的轨道中且它的轨道中也不含有临界点,则它还是周期点,我们还证明了上述性质可以扩张到一类特殊的λ－dendroid上。     

一类面积函数的最小值点的特性

本文运用Ｒｉｅｍａｎｎ－Ｓｔｉｅｌｊｅｏ积分的基本性质讨论了一类由连续单调函数所确定的面积函数的最小值问题，得到了该问题的最小值点恰为区问的中点。其变形问题的最小值点的函数值与函数在两端点的函数值的均值相等。     

Leray-Schauder不动点定理的一个新证明

给出Leray-Schauder不动点定理的一个新证明.我们首先给出集值映射的焊接引理,利用集值映射的焊接引理和Kakutani不动点定理证明Leray-Schauder不动点定理,并证明Leray-Schauder不动点定理与Brouwer不动点定理等价.     

On the stability of the vertical rotation of a solid suspended on a rod

The problem of the motion of a dynamically symmetric solid suspended from a fixed point by a weightless rod and two ball and socket joints one of which is fixed at the fixed point O', and the other is on the body axis of symmetry at the point O is considered. The question of the stability of the uniform body rotation when points O' and O, and the body centre of inertia C lie on the same vertical, and at the same time point O may be either above or below point O', and point C either above or below point O, is discussed. An analysis of the necessary and sufficient conditions for stability is given. The set of all the system's parameters is reduced to three independent dimensionless parameters L, Ω and β, and in the plane (L, Ω), for fixed values of β, the regions for which the unperturbed rotation is steady, or steady to a first approximation, or non-steady are indicated. The regions for which the body rotation is steady to a first approximation when the point O is situated higher than the point O', and the point C lies higher or lower than the point O are determined.

The sufficient conditions for the vertical rotation of a dynamically symmetric body suspended on a filament were obtained in /1/ and investigated for the cases where in non-perturbed motion the point C is below point O, when points C and O coincide, and when the length of the filament is zero (Lagrange gyroscope). In /2/ an analysis is given of the sufficient conditions for stability obtained in /1/, and also the necessary conditions for the cases where in a non-perturbed motion point C is located above point O.     

On farthest points of sets

For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set.     

向量对策理想-Nash平衡点的存在性

本文采用向量优化问题中理想解的概念,定义向量对策理想-Nash平衡点,并证明这一平衡点的存在性．这一结果一方面体现了向量对策Pareto-Nash平衡点和弱Pareto-Nash平衡点的存在性,同时,还给出了特殊的Pareto-Nash平衡点的存在性．     

一类五次多项式系统的奇点量与极限环分支

该文研究一类五次多项式微分系统在高次奇点与无穷远点的极限环分支问题. 该系统的原点是高次奇点, 赤道环上没有实奇点. 首先推导出计算高次奇点与无穷远点奇点量的代数递推公式,并用之计算系统原点、无穷远点的奇点量，然后分别讨论了系统原点、无穷远点中心判据. 给出了多项式系统在高次奇点分支出5个极限环同时在无穷远点分支出2个极限环的实例. 这是首次在同步扰动的条件下讨论高次奇点与无穷远点分支出极限环的问题.     

一阶自回归模型参数变点的假设检验

本文讨论一阶自回归模型自回归参数$\phi$的变点问题. 对于一阶自回归模型, 在模型的白噪声序列的方差$\sigma^2$已知和未知的条件下, 利用最大似然方法, 我们分别讨论了模型自回归参数$\phi$的Abrupt Change-Point 和Gradual Change-Point的检测问题.     

Least number of periodic points of self-maps of Lie groups

There are two algebraic lower bounds of the number of n-periodic points of a self-map f :M → M of a compact smooth manifold of dimension at least 3:N Fn(f) = min{#Fix(gn); g ～f; g is continuous} and N J Dn(f) = min{#Fix(gn); g ～ f; g is smooth}.In general,N J Dn(f) may be much greater than N Fn(f).If M is a torus,then the invariants are equal.We show that for a self-map of a nonabelian compact Lie group,with free fundamental group,the equality holds  all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.