Trace Extensions,Determinant Bundles,and Gauge Group Cocycles

We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.     

About the Notion of Semiring of Sets

We introduce a generalized notion of semiring and prove that all known properties that semirings have according to the old definition are preserved.     

Multipliers of convergence in norm of series with respect to multiplicative systems

We prove analogs of the Telyakovskii-Pochuev criteria for multipliers of uniform convergence and of convergence in the integral metric for multiplicative systems with bounded generating sequence.     

负关联噪声驱动下单模激光的定态分析

研究了负关联的加法和乘法高斯白噪声驱动下单模激光损失模型的定态情况。文中推导了负关联情况下，定态时的激光场幅的几率分布，光强的平均值，光强的协方差以及光强的偏斜率。并和文献〔１，２〕中正关联时的定态分析作了比较，发现了有意义的新现象。     

Modified constructions of binary sequences using multiplicative inverse

Two new families of finite binary sequences are constructed using multiplicative inverse. The sequences are shown to have strong pseudorandom properties by using some estimates of certain exponential sums over finite fields. The constructions can be implemented fast since multiplicative inverse over finite fields can be computed in polynomial time.     

The Upper Semicontinuity of Random Attractors for Non-Autonomous Stochastic Plate Equations with Multiplicative Noise and Nonlinear Damping

Based on the existence of pullback attractors for the non-autonomous stochastic plate equations with multiplicative noise and nonlinear damping defined in the entire space $\mathbb{R}^n$ by Xiaobin Yao in \cite{Yao4}, in the paper, we further investigate the upper semicontinuity of pullback attractors for the problem.     

Nonnormality and stochastic differential equations

A highly nonnormal Jacobian may give rise to large transients. This behaviour has been shown to have implications for (a) the relevance of linearising a nonlinear system and (b) the timestep restrictions required to keep a numerical method stable. Here, we show that nonnormality also manifests itself for stochastic differential equations. We give an example of a family of systems that is stable without noise, but can be made exponentially unstable in mean-square by a noise perturbation that shrinks to zero as the nonnormality increases. We then show via finite-time convergence theory that an Euler approximation shares the same property, giving a discrete analogue of the result. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65C30, 34F05     

一类幂等半环的性质和结构

研究了加法半群为半格的半环类S+l中的乘法带半环和矩形带半环类BR中的乘法带半环;给出了ID半环中乘法带半环的结构定理,即ID∩.■°D=.■z∨.■z∨D.     

The Use of Constituent Spectra and Weighting in Extended Multiplicative Signal Correction in Infrared Spectroscopy

Extended multiplicative signal correction (EMSC) is a widely used preprocessing technique in infrared spectroscopy. EMSC is a model-based method favored for its flexibility and versatility. The model can be extended by adding constituent spectra to explicitly model-known analytes or interferents. This paper addresses the use of constituent spectra and demonstrates common pitfalls. It clarifies the difference between analyte and interferent spectra, and the importance of orthogonality between model spectra. Different normalization approaches are discussed, and the importance of weighting in the EMSC is demonstrated. The paper illustrates how constituent analyte spectra can be estimated, and how they can be used to extract additional information from spectral features. It is shown that the EMSC parameters can be used in both regression tasks and segmentation tasks.