一种评价CCOS抛光工艺误差抑制能力的方法

结合光学加工中材料去除的卷积模型和功率谱密度函数,建立了描述CCOS抛光工艺抑制不同频段误差能力的数学模型——平滑谱函数.利用Rigid Conformal磨盘抛光620mm口径微晶平面玻璃,通过计算平滑谱函数曲线,将CCOS抛光工艺抑制不同频段误差的能力表示为归一化且无量纲的频谱曲线.计算结果表明平滑谱函数曲线能以数值大小评价CCOS抛光工艺对不同频率误差的抑制能力.     

半马尔科夫下电场可修系统可靠性分析

众所周知,在马尔科夫模型下,在每个状态下的逗留时间服从指数分布,这经常太受限制,尤其是在电场可修系统中,不太适合操作数据要求.因此,提出了利用半马尔科夫过程去研究电场可修系统,而且,利用了马尔科夫更新理论和概率分析方法讨论了电场系统的稳态可用度.最后,通过一个数值例子陈述了获得的结果.     

Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space

In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.     

Support vector machine with a Pearson VII function kernel for discriminating halophilic and non-halophilic proteins

Understanding of proteins adaptive to hypersaline environment and identifying them is a challenging task and would help to design stable proteins. Here, we have systematically analyzed the normalized amino acid compositions of 2121 halophilic and 2400 non-halophilic proteins. The results showed that halophilic protein contained more Asp at the expense of Lys, Ile, Cys and Met, fewer small and hydrophobic residues, and showed a large excess of acidic over basic amino acids. Then, we introduce a support vector machine method to discriminate the halophilic and non-halophilic proteins, by using a novel Pearson VII universal function based kernel. In the three validation check methods, it achieved an overall accuracy of 97.7%, 91.7% and 86.9% and outperformed other machine learning algorithms. We also address the influence of protein size on prediction accuracy and found the worse performance for small size proteins might be some significant residues (Cys and Lys) were missing in the proteins.     

Conditional parameter identification with different losses of under- and overestimation

In many scientific and practical tasks, the classical concepts for parameter identification are satisfactory and generally applied with success, although many specialized problems necessitate the use of methods created with specifically defined assumptions and conditions. This paper investigates the method of parameter identification for the case where losses resulting from estimation errors can be described in polynomial form with additional asymmetry representing different results of under- and overestimation. Most importantly, the method presented here considers the conditionality of this parameter, which in practice means its significant dependence on other quantities whose values can be obtained metrologically. To solve a problem in this form the Bayes approach was used, allowing a minimum expected value of losses to be achieved. The methodology was based on the nonparametric technique of statistical kernel estimators, which freed the investigated procedure from forms of probability distributions characterizing both the parameter under investigation and conditioning quantities. As a result an algorithm is presented, ready for direct use without further intensive research and calculations.     

A novel approach to the rapid assignment of 13C NMR spectra of major components of vegetable oils such as avocado,mango kernel and macadamia nut oils

Assignment of ¹³C nuclear magnetic resonance (NMR) spectra of major fatty acid components of South African produced vegetable oils was attempted using a method in which the vegetable oil was spiked with a standard triacylglycerol. This proved to be inadequate and therefore a new rapid and potentially generic graphical linear correlation method is proposed for assignment of the ¹³C NMR spectra of major fatty acid components of apricot kernel, avocado pear, grapeseed, macadamia nut, mango kernel and marula vegetable oils. In this graphical correlation method, chemical shifts of fatty acids present in a known standard triacylglycerol is plotted against the corresponding chemical shifts of fatty acids present in the vegetable oils. This new approach (under carefully defined conditions and concentrations) was found especially useful for spectrally crowded regions where significant peak overlap occurs and was validated with the well‐known ¹³C NMR spectrum of olive oil which has been extensively reported in the literature. In this way, a full assignment of the ¹³C{1H} NMR spectra of the vegetable oils, as well as tripalmitolein was readily achieved and the resonances belonging to the palmitoleic acid component of the triacylglycerols in the case of macadamia nut and avocado pear oil resonances were also assigned for the first time in the ¹³C NMR spectra of these oils. Copyright © 2009 John Wiley & Sons, Ltd.     

A Wiener-Tauberian and a Pompeiu type theorems on the Laguerre hypergroup

A Wiener-Tauberian theorem is proven on the Laguerre hypergroup [M.M. Nessibi, K. Trimèche, Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets, J. Math. Anal. Appl. 208 (1997) 337-363]. As consequence of this theorem we establish a Pompeiu type-theorem and we study some of its applications.     

Solvability of partial differential equations by meshless kernel methods

This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well-posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy. The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 101205). Robert Schaback’s research in Hong Kong was sponsored by DFG and City University of Hong Kong.     

The best constant of Sobolev inequality on a bounded interval

The best constants Cm,j of Sobolev embedding of Hm(0,a) into Cj[0,a](0?j?m−1) are obtained. Especially, when a=∞, these constants can be represented in a closed form.