Quotient rings and Fountain-Gould left orders by the local approach

We study Fountain-Gould left orders in semiprime rings coinciding with their socles by means of local rings at elements.     

Stable subsets of modules and the existence of a unit in associative rings

We obtain criteria for the existence of a (left) unit in rings (arbitrary, Artinian, Noetherian, prime, and so on) that are based on the systematic study of properties of stable subsets of modules and their stabilizers that generalize the technique of idempotents. We study a class of quasiunitary rings that is a natural extension of classes of rings with unit and of von Neumann (weakly) regular rings, which inherits may properties of these classes. Some quasiunitary radicals of arbitrary rings are constructed, and the size of these radicals “measures the probability” of the existence of a unit. Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 596–611, April, 1997. Translated by A. I. Shtern     

On Left Regular Ordered Semigroups

The main result of the paper is a decomposition theorem of the left regular ordered semigroups into left regular and left simple semigroups.     

无挠左（右）Artin环是拟Frobenius环

无挠左（右）Ａｒｔｉｎ环是拟Ｆｒｏｂｅｎｉｕｓ环乌成伟（吉林工学院基础部，长春１３００１２）关键词内积，左（右）内零化子，自内射环．分类号ＡＭＳ（１９９１）１６Ｄ５０／ＣＣＬＯ１５３．３设Ｒ为有１的左（右）Ａｒｔｉｎ环，如果对于任一整数洲与ｒ∈Ｒ，ｍ...     

The G-Ellipticity for the Sub-Laplacian on Two Step Stratified Lie Groups

This paper reveals that the sub-Laplacian L₀ on two step stratified Lie groups has a similar behavior like elliptic operators on the Euclidean space, that is, the sub - Laplacian satisfies a group-elliptic estimate, called the G- elliptic estimate (or the L^p regularity), and the general left Invariant operator L_λ has such a behavior if and only if λ is admissible.     

L-spaces and S-spaces in P(ω)

We show that CH implies that $\text{P}\text{(ω)}$, when equipped with the Vietoris topology, has a subspace which is an L-space and a subspace which is an S-space. This is an immediate consequence of the following purely combinatorial result: CH implies the existence of an ω₁-sequence 〈x_α: α < ω₁〉 in $\text{P}\text{(ω)}$ such that (1) if α<β<ω₁, then $\text{X}{}_{\mathrm{\beta }}\text{?}{}^1\text{X}{}_{\mathrm{\alpha }}$; (2) if I ?ω₁ is unaccountable, then there are distinct α, β ∈ I with X_β ?X_α.     

Dynamic spanning without probabilities

The paper presents a non-probabilistic approach to continuous-time trading where, in analogy to the binomial option-pricing model, terminal payoffs resulting from a given trading strategy are meaningful ‘state-by-state’, i.e., path-by-path. In particular, we obtain results of the form: “If a certain trading strategy is applied and if the realized price trajectory satisfies a certain analytical property, then the terminal payoff is.…” This way, derivation of the Black and Scholes formula and its extension become an exercise in the analysis of a certain class of real functions. While results of the above forms are of great interest if the analytical property in question is believed to be satisfied for almost all realized price trajectories (for example, if the price is believed to follow a certain stochastic process which has this property with probability 1), they are valid regardless of the stochastic process which presumably generates the possible price trajectories or the probability assigned to the set of all paths having this analytical property.     

Groups associated with minimal flows

Let S be topological semigroup, we consider an appropriate semigroup compactification of S. In this paper we study the connection between subgroups of a maximal group in a minimal left ideal of , which arise as equivalence classes of some closed left congruence, and the minimal ow characterized by the left congruence. A particular topology is defined on a maximal group and it is shown that a closed subgroup under this topology is precisely the intersection of an equivalence class with the maximal group for some left congruence on .     

具有电与磁非线性效应超常介质中光束的聚焦特性

基于Drude模型,采用解析法与数值模拟法研究了具有电与磁非线性效应超常介质中光束的聚焦特性。结果表明超常材料中光束聚焦现象不但可以发生在自聚焦非线性介质中(正折射区)而且可以发生在自散焦非线性介质中(负折射区),且光束中心频率离介质的等离子频率越近,其聚焦效应越明显。特别是当电与磁非线性极化率为异号时,超常介质的非线性符号可以通过调控电与磁等离子频率的相对大小控制,这为主动操控光束的传输提供一种新的自由度。     

关于光学实验中望远镜与光杠杆的调节探讨

在关于望远镜的光杠杆调节中通常只给出了对光杠杆及望远镜的上下位置的调节,而忽视了望远镜和光杠杆的左右调节。给出了望远镜和光杠杆的调节中左右位置的调节原理和调节操作方法,从而使望远镜和光杠杆的调节更具有目的性,使实验进行的更加快速和准确。