交错群A_5与二面体群D_6直积的整群环的挠单位

本文利用Luthar-Passi方法,研究了五次交错群A_5与六阶二面体群D_6直积的整群环的挠单位,得到了该群的Zassenhaus猜想成立.     

Wedge Operations and Doubling Operations of Real Toric Manifolds

This paper deals with two things.First,the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G.Second,the author focuses on a specific canonical extensions called doublings and presents their various properties.They include existence of infinitely many real topological toric manifolds admitting complex structures,and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups.Moreover,some questions about real topological toric manifolds related to Halperin's toral rank conjecture are presented.     

代数的张量积的同调满同态的构造

利用已知的代数的同调满同态来构造其张量积代数的同调满同态.设A,B,C,D是域k上的有限维代数,如果环同态f:A→C和g:B→D是环的同调满同态,则fg:AB→CD也是环的同调满同态.     

Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.     

On realization of fusion rings from generalized Cartan matrices

The Casimir element of a fusion ring (R, B) gives rise to the so called Casimir matrix C of (R, B). This enables us to construct a generalized Cartan matrix D-C in the sense of Kac for a suitable diagonal matrix D. In this paper, we study some elementary properties of the Casimir matrix C and use them to realize certain fusion rings from the generalized Cartan matrix D-C of finite (resp. affine) type. It turns out that there exists a fusion ring with D-C being of finite (resp. affine) type if and only if D-C has only the form A₂ (resp. A₁⁽¹⁾. We also realize all fusion rings with D-C being a particular generalized Cartan matrix of indefinite type.     

Multiplicative Jordan Decomposition in Integral Group Ring of Group K_8×C_5

In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper "The multiplicative Jordan decomposition in group rings II.     

关于半clean群环

环$R$称为是半clean的, 是指环中的每个元素都是一个单位与一个周期元的和. clean环是半clean的. 刻画半clean群环的一般情形是不容易的. 我们的目的是考虑如下问题：若$G$ 是局部有限群或者是阶是3的循环群, 群环$RG$何时是semiclean的. clean群环上的一些已有结果被推广.     

Ion transmission in an electrospray ionization-mass spectrometry interface using an S-lens

We present the design and performance of an in-house built electrospray ionization-mass spectrometry (ESI-MS) interface equipped with an S-lens ion guide. The ion source was designed specifically for our ion beam experiments to investigate the chemical reactivity and deposition of the clusters and nanoparticles. It includes standard ESI-MS interface components, such as nanoelectrospray, ion transfer capillary, and the S-lens. A custom design enables systematic optimization of all relevant factors influencing ion formation and transfer through the interface. By varying the ESI voltage and flow rate, we determined the optimal operating conditions for selected silica emitters. A comparison of the pulled silica emitters with different tip inner diameters reveals that the total ion current is highest for the largest tip, whereas a tip with the smallest diameter exhibited the highest transmission efficiency through the ESI-MS interface. Ion transmission through the transfer capillary is strongly limited by its length, but the loss of ions can be reduced by increasing the capillary voltage and temperature. The S-lens was characterized over a wide range of RF frequencies and amplitudes. Maximum ion current was detected at RF amplitudes greater than 50 V peak-to-peak (p/p) and frequencies above 750 kHz, with a stable ion transmission region of about 20%. A factor of 2.6 increase in total ion current is observed for 650 kHz as RF amplitudes reach 400 V p/p. Higher RF amplitudes also focus the ions into a narrow beam, which mitigates their losses when passing through the ion guide.