单状态变量的局部对称性分岔问题中内蕴子模的一点注记

本文证明了Itr(^→T，Z2)=(ItrT)．{x}当且仅当ItrT由T中所有单项式生成，这里T是εu，λ中的理想且T=T．{x}在^→εx，λ(Z2)中具有有限Z2余维数，此结果表明，Golubitsky的书中关于最大内蕴理想和最大内蕴子模的关系式是错误的，本文最后给出了反例。     

关于topos中的内蕴Heyting代数对象(英文)

本文研究了在一般topos中内蕴Heyting代数对象的性质.利用范畴的态射及伴随的方法,获得了内蕴Heyting代数对象为内蕴分配格结果,推广了集合范畴中的对应结果.     

具有单边约束的基本分岔问题的新分岔模式

含约束分岔是非线性动力系统周期解分岔研究中遇到的普遍问题,然而现有的奇异性理论关于此类问题的结果还很少。作为探讨和补充,给出余维数不大于3的10种基本分岔在约束情况下的转迁集和摄动保持分岔图的计算结果。可为约束分岔问题的研究提供直接利用的结果。     

一个酶催化反应系统的局部分岔分析

讨论一个酶催化反应系统的局部分岔.首先得到该系统只有1个或2个孤立平衡点,或者一条奇线,并给出了所有平衡点的定性性质.进一步分析了孤立平衡点在非双曲情形下发生的分岔,包括跨临界分岔和Hopf分岔,通过计算Lyapunov量得出该系统中细焦点阶数为1.最后利用数值模拟验证了所得结论.     

约束含参分岔问题的分类

约束边界与分岔参数有关的约束分岔问题,称为约束含参分岔问题．通过引入适当的变换,将约束含参分岔问题转化为新变量的非约束分岔问题,推导出了约束含参分岔问题转迁集的一般形式,结果表明只有约束分岔集受约束含参的影响,其它转迁集与不含参约束分岔的转迁集相同．以含参约束树枝分岔为例分析了此类问题的分岔分类,讨论了约束含参对分岔分类的影响．     

关于循环环的理想、素理想和极大理想

研究了循环环R=的理想、素理想和极大理想的个数和结构,得到了如下结论:1)理想:(1)若|R|=∞,则R共有无穷多个理想:;(2)若|R|=n,设n的正因数个数为T(n),则R共有T(n)个理想:.2)素理想:(1)若|R|=∞,设a^2=ka(k≥0),①当k=0时,R的素理想只有R;②当k>0时,R的素理想共有无穷多个,它们是:{0}、R及;(2)若|R|=n>1,设a^2=ka,0≤k.3)极大理想:(1)若|R|=∞,则R有无限多个极大理想,它们是;(2)若|R|=n>1,设n的互不相同的素因数个数为ψ(n),则R共有ψ(n)个极大理想:(pa|p是n的素因数).     

关于Burgers-Fisher方程平衡解的分岔问题(英文)

当参数λ在临界值λk=k2(k=1,2,…)附近且小于它时,利用Liapunov-Schmidt方法在奇函数空间H1中得到了两个严格的非平凡定态解,在整个空间H1中得到了一个分岔圆.     

关于Guzowska-Luís-Elaydi模型的分岔

本文考虑了一个离散的Logistic竞争模型.为了讨论分岔,给出了不动点的拓扑类型及非双曲的情况.应用中心流行约化定理,证明了跨临界分岔会在三个不动点上发生.本文还证明了在两个不动点处,跳跃分岔会发生,同时稳定的周期2轨会出现.     

单时滞类Lorenz系统的Hopf分岔分析

本文研究单时滞类Lorenz系统的稳定性问题.利用规范型理论,分析该系统在其零平衡点处的稳定性和发生Hopf分岔的条件,并通过数值仿真验证所得结论的正确性.本文的结论可以看做是对文献[5]研究成果的推广.     

周期分岔解的鲁棒控制

根据C-L方法,可以得到非线性动力系统的分岔方程和拓扑分岔图．根据得到的分岔图,结合控制理论,提出了周期解的鲁棒控制方法．该方法将运动模式控制到目标模式．由于该方法对控制器的参数没有严格的控制,所以在设计和制造控制器方面是很方便的．数值研究验证了该方法的有效性．     

On Canonical Ideals of One-Dimensional Local Analytically Irreducible Rings

A characterization is given for certain canonical ideals of local one-dimensional commutative rings with identity under the assumption of analytical irreducibility. This extends both a known result characterizing the case when the ring itself is a canonical ideal (i.e., it is a Gorenstein ring), and another one which is a general characterization of canonical ideals but under the further assumption of residual rationality.     

Adjacent Ideals to Simple Complete Ideals in Two-Dimensional Regular Local Rings

Let R be a two-dimensional regular local ring with infinite residue field, and ? be a simple complete residually rational ideal of R of order r which determines R _h . Let 𝒯 be the set of quadratic transforms T of R _h with [T: R _h ] = 1, and 𝒮 the set of simple complete ideals of R of order r which are adjacent to ? from below. If R _h is free respectively a satellite, then there exist T* ∈ 𝒯 respectively T*, T** ∈ 𝒯 and a bijective map between the set 𝒮 and the set 𝒯?{T*} respectively 𝒯?{T*, T**}.     

On the Number of Integral Ideals in Two Different Quadratic Number Fields

Let K be an algebraic number field of finite degree over the rational field Q,and a K(n) the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of a K(n),Σn≤x a K(n)~l, l = 1, 2, 3, ···.This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sum Σn≤x aK_1(n~j)~laK_2(n~j)~l, j = 1, 2, l = 2, 3, ···,where K_1 and K_2 are two different quadratic fields.     

常数激励对局部分岔的影响

用奇异性理论讨论了常数激励对1/2内共振系统周期解局部分岔的影响．研究表明,常数激励项能否产生影响关键取决于低频振子中是否存在某些非线性项．常数激励, 一方面起主分岔参数的作用, 另一方面,与系统中某些非线性项的系数一起确定分岔解基本类型、 影响开折参数．在非退化条件下,可不考虑三次非线性项的影响．     

Full Ideals

Contractedness of 𝔪-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, 𝔪). In such rings, the contracted 𝔪-primary ideals are known to be characterized by the property that I: 𝔪 = I: x for some x ∈ 𝔪 ?𝔪². We call the ideals with this property full ideals and compare this class of ideals with the classes of 𝔪-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The 𝔪-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be 𝔪-full. We also show the equivalence of the properties full, 𝔪-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full.     

高维同宿分支问题

本文通过应用指数二分性和将关于周期系统的Floquet方法推广到非周期系统，来构造适当的局部坐标系以建立Poincare映射，并用以解决各类余维为1和2的同宿分支问题．文中还给出了分支图和分支曲线．     

The Rees Valuations of Complete Ideals in a Regular Local Ring

Let I be a complete m-primary ideal of a regular local ring (R, m) of dimension d ≥ 2. In the case of dimension two, the beautiful theory developed by Zariski implies that I factors uniquely as a product of powers of simple complete ideals and each of the simple complete factors of I has a unique Rees valuation. In the higher dimensional case, a simple complete ideal of R often has more than one Rees valuation, and a complete m-primary ideal I may have finitely many or infinitely many base points. For the ideals having finitely many base points Lipman proves a unique factorization involving special *-simple complete ideals and possibly negative exponents of the factors. Let T be an infinitely near point to R with dim R = dim T and R/m = T/m _T . We prove that the special *-simple complete ideal P _RT has a unique Rees valuation if and only if either dim R = 2 or there is no change of direction in the unique finite sequence of local quadratic transformations from R to T. We also examine conditions for a complete ideal to be projectively full.