An elementary approach to containment relations between symbolic and ordinary powers of certain monomial ideals

We provide an elementary explanation of a surprising result of Ein–Lazarsfeld–Smith and Hochster–Huneke on the containment between symbolic and ordinary powers of ideals for a certain class of simple monomial ideals.     

Prime Ideals in Birational Extensions of Two-Dimensional Power Series Rings

In this article we consider simple birational extensions of power series rings in one variable over one-dimensional Noetherian domains having infinitely many maximal ideals. For these rings we describe the partially ordered sets that arise as prime spectra. We characterize the prime spectra in the case that the coefficient rings are countable Dedekind domains. The prime spectra over Dedekind domains are the same as the prime spectra that arise for simple birational extensions of power series rings over the integers and the same as the prime spectra of simple birational extensions of k[[x]][z], where k is a countable field and x and z are indeterminates.     

On the Automorphism Group of the First Weyl Algebra

Let A ₁: = 𝕜[t, ?] be the first algebra over a field 𝕜 of characteristic zero. Let Aut_𝕜(A ₁) be the automorphism group of the ring A ₁. One can associate to each right ideal I of A ₁ a subgroup of Aut_𝕜(A ₁) called the isomorphism subgroup of I. In this article, we show that each such isomorphism subgroup is equal to its normalizer. For that, we study when the isomorphism subgroup of a right ideal of A ₁ contains a given isomorphism subgroup.     

Rings Over which the Krull Dimension and the Noetherian Dimension of All Modules Coincide

We denote by 𝒜(R) the class of all Artinian R-modules and by 𝒩(R) the class of all Noetherian R-modules. It is shown that 𝒜(R) ? 𝒩(R) (𝒩(R) ? 𝒜(R)) if and only if 𝒜(R/P) ? 𝒩(R/P) (𝒩(R/P) ? 𝒜(R/P)), for all centrally prime ideals P (i.e., ab ∈ P, a or b in the center of R, then a ∈ P or b ∈ P). Equivalently, if and only if 𝒜(R/P) ? 𝒩(R/P) (𝒩(R/P) ? 𝒜(R/P)) for all normal prime ideals P of R (i.e., ab ∈ P, a, b normalize R, then a ∈ P or b ∈ P). We observe that finitely embedded modules and Artinian modules coincide over Noetherian duo rings. Consequently, 𝒜(R) ? 𝒩(R) implies that 𝒩(R) = 𝒜(R), where R is a duo ring. For a ring R, we prove that 𝒩(R) = 𝒜(R) if and only if the coincidence in the title occurs. Finally, if Q is the quotient field of a discrete valuation domain R, it is shown that Q is the only R-module which is both α-atomic and β-critical for some ordinals α,β ≥ 1 and in fact α = β = 1.     

微流控双稳振荡器光开关

针对光开关集成化、微型化、低能耗的要求,设计了一种微流控双稳振荡器1×2型光开关,其两个输出端口的插入损耗分别为1.03dB和0.18dB.微流控双稳振荡器由对称级联的两个常闭阀构成,光开关由三段嵌入在振荡器输出端的光纤波导构成,通过改变注射泵驱动微器件中液体流动的速率可以控制光开关的开关周期.利用有限元分析软件对影响开关周期的因素进行了仿真研究.结果表明,当液体的注入流速从0.2mm/s增大到1.0mm/s时,开关周期从1.25s减小到0.26s,周期占空比约为0.5,阀的阈值与开关时间常量呈线性关系.随着常闭阀阀座的增宽,开关周期变长;阀的宽长比增大,开关周期减小;振荡器的不对称设计可以调节周期的占空比.通过调节入口流速和阀的阈值特性,可以设计特定频率的光开关,这为单入多出、多入多出光开关的后续研究提供了依据.     

关于有界闭凸集上的弱滴性质的注记

证明了“若K是Banach空间X中的有界闭凸集,0∈intK,则K有弱滴性质当且仅当K⁰有(WS)性质.”从而证明了文[1]中提出的一个问题.     

Computing polynomial univariate representations of zero-dimensional ideals by Grbner basis

Rational Univariate Representation(RUR) of zero-dimensional ideals is used to describe the zeros of zero-dimensional ideals and RUR has been studied extensively.In 1999,Roullier proposed an efficient algorithm to compute RUR of zero-dimensional ideals.In this paper,we will present a new algorithm to compute Polynomial Univariate Representation(PUR) of zero-dimensional ideals.The new algorithm is based on some interesting properties of Grbner basis.The new algorithm also provides a method for testing separating elements.     

Conditioning of BPM pickup signals for operations of the Duke storage ring with a wide range of single-bunch current

The Duke storage ring is a dedicated driver for the storage ring based oscillator free-electron lasers（FELs）, and the High Intensity Gamma-ray Source（HIGS）. It is operated with a beam current ranging from about1 mA to 100 mA per bunch for various operations and accelerator physics studies. High performance operations of the FEL and γ-ray source require a stable electron beam orbit, which has been realized by the global orbit feedback system. As a critical part of the orbit feedback system, the electron beam position monitors（BPMs） are required to be able to precisely measure the electron beam orbit in a wide range of the single-bunch current. However, the high peak voltage of the BPM pickups associated with high single-bunch current degrades the performance of the BPM electronics, and can potentially damage the BPM electronics. A signal conditioning method using low pass filters is developed to reduce the peak voltage to protect the BPM electronics, and to make the BPMs capable of working with a wide range of single-bunch current. Simulations and electron beam based tests are performed. The results show that the Duke storage ring BPM system is capable of providing precise orbit measurements to ensure highly stable FEL and HIGS operations.     

Banach空间中Cauchy初值问题解的存在性

在研灾Banach空间常微分方程Cauchy 问题解的存在性问题时,人们常常使用一个 很难验证且一般情况下难以达到的条件──一致连续性条件,本文完全不使用一致连续性条 件,仅利用紧型条件,获得了Banach空间Cauchy问题解的存在性定理,从而改进和推广了已 知的有关结果,     

一种辩识多输入多输出振动系统参数的方法

本文讨论的是多输入、多输出串联振动系统传递函数的辩识问题.本文表明:从系统结构来看,多输入、多输出串联振动系统可以化成为多重交叉闭环系统.本文将这类振动系统的传递函数分解成多个二阶子系统.从系统辩识的角度出发,提出了一种通过辩识子系统传递函数,实现对整个系统传递函数辩识的新方法.仿真结果及模型实验结果表明:这种方法是可行的,且具有较高的精度.