Loewy series,V-modules and trace ideals

If _R Vis a V-module and (R V W S) is a Morita context in which (S/WV) _s is flat, then the trace ideal WVis left V-module over S. If, in addition_S:(S/WV) is flat and S/WVis a fully left idempotent ring, then Sis also fully left idempotent. The lower (upper) Loewy length of _R Vprovides an upper bound for the corresponding Loewy length of _s(WV).     

Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi–Yau complete intersections

On the one hand, for a general Calabi–Yau complete intersection X$X$, we establish a decomposition, up to rational equivalence, of the small diagonal in X×X×X$X\times X\times X$, from which we deduce that any decomposable 0-cycle of degree 0 is in fact rationally equivalent to 0, up to torsion. On the other hand, we find a similar decomposition of the smallest diagonal in a higher power of a hypersurface, which provides us an analogous result on the multiplicative structure of its Chow ring.     

Prime ends for domains in metric spaces

In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carathéodory and Näkki. Modulus ends and prime ends, defined by means of the p$p$-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.     

Semigroups with apartness

Proving a constructive version of the Spectral Mapping Theorem, Bridges and Havea used a constructive semigroup with inequality in 8 . This motivated us to achieve a little progress in that direction. The starting point is the structure called a semigroup with apartness. Our primary objective is to prove isomorphism theorems for such constructive semigroups. In doing so our main ideas and notions come from 10 .     

GENERALIZED STOCHASTIC PERTURBATION-DEPENDING DIFFERENTIAL EQUATIONS

The paper is devoted to the generalized stochastic differential equations of the Ito? type whose coefficients are additionally perturbed and dependent on a small parameter. Their solutions are compared with the solutions of the corresponding unperturbed equations. We give conditions under which the solutions of these equations are close in the (2m)-th moment sense on finite intervals or on intervals whose length tends to infinity as the small parameter tends to zero. We also give the degree of the closeness of these solutions.     

基于CDMA的布拉格光纤光栅传感系统的仿真分析

讨论了光纤光栅传感系统中常用的复用技术及其限制,阐述了利用CDMA技术实现光纤布拉格光栅阵列波长解调的复用方式,对系统的原理和性能进行了理论分析。在此基础上通过MATLAB做了基于CDMA的光纤光栅传感仿真分析,仿真结果表明该方法能区分反射波长重叠的光栅,从而提高FBG网络复用的频带利用率。     

Robert Leslie Ellisʼs work on philosophy of science and the foundations of probability theory

The goal of this paper is to provide an extensive account of Robert Leslie Ellis?s largely forgotten work on philosophy of science and probability theory. On the one hand, it is suggested that both his ‘idealist’ renovation of the Baconian theory of induction and a ‘realism’ vis-à-vis natural kinds were the result of a complex dialogue with the work of William Whewell. On the other hand, it is shown to what extent the combining of these two positions contributed to Ellis?s reformulation of the metaphysical foundations of traditional probability theory. This parallel is assessed with reference to the disagreement between Ellis and Whewell on the nature of (pure) mathematics and its relation to scientific knowledge.     

The Vlasov Poisson System with Steady Spatial Asymptotics

Abstract

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as |x|→∞ is considered. Hence the total positive charge and the total negative charge are infinite. Smooth solutions with appropriate asymptotic behavior are shown to exist locally in time. Conditions for continuation of these solutions are also established.     

A fractional credit model with long range dependent default rate

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we start with a bivariate fractional Vasicek model for short and default rate, which allows for fairly explicit calculations. We calculate the prices of corresponding defaultable zero-coupon bonds by invoking Wick calculus. Applying a Girsanov theorem we derive today’s prices of European calls and compare our results to the classical Brownian model.