Varieties of affine Kac-Moody algebras

In this paper the identities of the complex affine Kac-Moody algebras are studied. It is proved that the identities of twisted affine algebras coincide with those of the corresponding nontwisted algebras. Moreover, in the class of nontwisted affine Kac-Moody algebras, each of these algebras is uniquely defined by its identities. It is shown that the varieties of affine algebras, as well as the varieties defined by finitely generated three-step solvable Lie algebras, have exponential growth. Translated fromMatematicheskie Zametki, Vol. 62 No. 1, pp. 95–102, July 1997. Translated by A. I. Shtern     

Affine Structures on a Ringed Space and Schemes

The author first introduces the notion of affine structures on a ringed space and then obtains several related properties. Affine structures on a ringed space, arising from complex analytical spaces of algebraic schemes, behave like differential structures on a smooth manifold.     

Positive Harris recurrence and exponential ergodicity of the basic affine jump-diffusion

In this article, we find the transition densities of the basic affine jump-diffusion (BAJD), which has been introduced by Duffie and Gârleanu as an extension of the CIR model with jumps. We prove the positive Harris recurrence and exponential ergodicity of the BAJD. Furthermore, we prove that the unique invariant probability measure π of the BAJD is absolutely continuous with respect to the Lebesgue measure and we also derive a closed-form formula for the density function of π.     

一种基于特征点跟踪的电子稳像算法

提出一种基于特征点跟踪的稳像算法。该算法从参考帧图像中提取出一组特征点,然后在后续帧中进行基于Kalman滤波的特征点的跟踪,匹配参考帧图像中特征点的坐标和当前图像中基于Kalman滤波修正后得到的特征点的坐标,并通过仿射模型求出位移量及旋转参数,最后进行反向变换,从而得到稳定的视频图像。实验结果表明:该算法稳像效果好,运算复杂度低,且具有较强的鲁棒性。     

A Non-expensive Homological Helly Theorem

We will discuss the following result: for a topological space X with the property that $H_k(U)=0$ for $k⩾d$ and every open subset U of X, a finite family of open sets in X has nonempty intersection if for any subfamily of size j, $1⩽j⩽d+1$, the ($d-j$)-dimensional reduced homology group of its intersection is zero. We also use this theorem to discuss new results concerning transversal affine planes to families of convex sets.     

机载摄像机快速标定技术研究

针对飞行试验机载摄像机的标定,提出了一种基于光束法平差的高精度像机标定方法。首先,通过在测试目标周围放置带有编码标志点的标定板,拍摄其多种状态,经图像处理,获取标志点的编码以及中心坐标。然后通过相对定向、绝对定向、三维重建、捆绑调整,以及加入标志点之间的距离约束,得到数字摄像机内外方位元素和镜头畸变差参数,实现机载摄像机快速标定。实验结果表明：该标定方法不需要做高精度的现场控制点,重投影误差小于1cm,标定精度满足飞行试验测试要求。     

结合过滤技术的简单界约束优化问题仿射尺度内点信赖域算法

1 引言 简单界约束优化问题:minx∈(R)nf(x),l≤z≤u,其中f二阶可微,f∈((R)∪{-∞})n,u∈((R)∪{-∞})n(l相似文献   

测量层流扩散火焰温度与烟黑浓度分布的实验研究

本文提出了一种通过线性规划中的内点法(仿射变换法)来计算烟黑浓度和温度分布的模型.根据烟黑辐射特性,利用火焰单色辐射强度图像信息采用此模型同时重建轴对称含烟黑火焰的温度与烟黑浓度分布,对层流乙烯扩散火焰的温度与烟黑浓度进行测量,得到了较好的结果.     

Affine planar geodesic immersions with maximal codimension

This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal. Vrancken classified parallel affine immersions in this case and obtained, among others, generalized Veronese submanifolds. In this work it is shown that the immersions with planar geodesics are the same as the parallel ones in the considered case. A geometric interpretation of parallel immersions is also given： The affine immersions with pointwise planar normal sections （with respect to the equiaffine transversal bundle） are parallel. This result is verified for surfaces in R4 and for immersions with the maximal codimension.     

Modeling and analysis of the coupled dynamics of machine degradation and repair processes using piecewise affine stochastic differential equations

This paper introduces an approach to model the coupled dynamics of recurring degradation and restoration processes that take place in real-world systems, such as manufacturing machines, in the form of non-linear (piecewise affine) differential equations. Unlike previous methods, interactions between degradation and repair dynamics that influence downtime distributions in such manufacturing systems can be explicitly considered and dependencies beyond correlations between the time between failures (TBF) and the time to repair (TTR) can be captured. The periodic solutions of the model capture the progressive evolution of long time-scale failure and repair patterns. The distribution of short time-scale failure–repair cycles can be captured by providing a class of random perturbations to certain model parameters. We provide sufficient conditions for the existence and stability of the resulting non-linear stochastic differential equation (n-SDE) model solutions that mimic the breakdown and repair patterns observed in many real-world manufacturing systems, namely, fairly regular (periodic) large breakdown and repair cycles, interspersed with highly right skewed distributions of short cycles. We also define the basin of attraction for the periodic orbit. The n-SDE model was parametrized using real-world data sets acquired from an automotive manufacturing assembly line segment, and the model solutions were compared with actual observations of TBF and TTR patterns, as well as the performance of the process. Our approach reduces the computation time by about 25% when compared to a discrete-event simulation model, which uses conventional TBF and TTR distributions, implemented on a commercial platform. Experimental investigations also suggest that the model can capture the correlations and non-linear coupled dynamics that exist in real-world operations among TBF and TTR, which are typically ignored in traditional approaches.