Condensations of projective sets onto compacta

For a coanalytic-complete or -complete subspace of a Polish space we prove that there exists a continuous bijection of onto the Hilbert cube . This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen.

Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.

     

Effects of Cs treatment on field emission properties of capped carbon nanotubes

Within the methodology [M. Khazaei, A.A. Farajian, Y. Kawazoe, Phys. Rev. Lett. 95 (2005) 177602] based on first-principles electronic structure calculations, the effects of Cs treatment on current emissions and emission patterns of capped carbon nanotubes are considered at low deposition densities when the nanotubes are under an electric field 0.2 V/Å. The results show that the current emission from the cap with one adsorbed Cs is 3.4 times larger than the cap without any Cs. It is 9.6 times larger in the cap with two adsorbed Cs atoms. After Cs deposition the emission patterns become asymmetric (current emission from the carbon atoms located at the topmost pentagon ring close to Cs atoms is larger than the other atomic sites). There are very few localized states on Cs atoms. Hence, although the tunneling probability of electron emission from Cs atoms is significant, there is no current from Cs atoms. In addition, the effect of Cs on work function reduction of nanotubes is explained in terms of Cs deposition densities and the surface dipole moments.     

Neural network applied to reconstruction of complex objects based on fringe projection

The neural network has been introduced into the reconstruction of the complex object based on fringe projection. In this method, the neural network with powerful property of approximation is used to get the continuous approximate function of a discrete fringe pattern captured by an image frame grabber. The depth-related phase of the measured object modulated into the fringe pattern can be demodulated by dealing with the approximate function. Compared with the Fourier transform profilometry (FTP), in the network method, one deformed fringe pattern is needed to reconstruct the tested object, and a high spatial resolution is maintained for no filtering process. Therefore, this method performs better than FTP in the measurement of the complex object. Moreover, the network method is capable of demodulating more depth-related phase even in the case that the local shadow exists in the fringe pattern. Computer simulations and experiments validate the feasibility of this method.     

几周期余弦-高斯激光脉冲的时间重心

研究了几周期超短余弦-高斯脉冲的时间重心与绝对相位以及与余弦函数参量之间的关系．给出了几周期超短余弦-高斯脉冲时间重心的解析表达式和模拟图形．结果表明，余弦-高斯脉冲的时间重心随着绝对相位的变化而发生漂移，并且脉冲宽度对余弦-高斯脉冲时间重心的漂移量也有一定的影响．余弦函数的参量在一定取值范围内对余弦-高斯脉冲也有较大的影响，它可能导致几周期余弦-高斯脉冲的时间重心有较大的漂移．     

Arbitrage valuation and bounds for sinking-fund bonds with multiple sinking-fund dates

The paper tackles the problem of pricing, under interest-rate risk, a default-free sinking-fund bond which allows its issuer to recurrently retire part of the issue by (a) a lottery call at par, or (b) an open market repurchase. By directly modelling zero-coupon bonds as diffusions driven by a single-dimensional Brownian motion, a pricing formula is supplied for the sinking-fund bond based on a backward induction procedure which exploits, at each step, the martingale approach to the valuation of contingent-claims. With more than one sinking-fund date, however, the pricing formula is not in closed form, not even for simple parametrizations of the process for zerocoupon bonds, so that a numerical approach is needed. Since the computational complexity increases exponentially with the number of sinking-fund dates, arbitrage-based lower and upper bounds are provided for the sinking-fund bond price. The computation of these bounds is almost effortless when zero-coupon bonds are as described by Cox, Ingersoll and Ross. Numerical comparisons between the price of the sinking-fund bond obtained via Monte Carlo simulation and these lower and upper bounds are illustrated for different choices of parameters.     

Alternative Synthesis and the Determination of Absolute Configuration of Docetaxel,an Anticancer Drug

Abstract

A simple, efficient, and alternative synthetic route for docetaxel with better control on the protection–deprotection sequence has been developed. The process is easily scalable and commercially viable, and critical impurities can be controlled efficiently. For the first time, absolute configuration of docetaxel was determined unambiguously by single-crystal x-ray diffraction.     

Imaginary quadratic function fields

In Bautista-Ancona and Diaz-Vargas (2006) [B-D] a characterization and complete listing is given of the imaginary quadratic extensions K of k(x), where k is a finite field, in which the ideal class group has exponent two and the infinite prime of k(x) ramifies. The objective of this work is to give a characterization and list of these kind of extensions but now considering the case in which the infinite prime of k(x) is inert in K. Thus, we get all the imaginary quadratic extensions of k(x), in which the ideal class group has exponent two.     

Conditional VaR estimation using Pearson’s type IV distribution

This paper presents a new value at risk (VaR) estimation model for equity returns time series and tests it extensively on Stock Indices of 14 countries. Two most important stylized facts of such series are volatility clustering, and non-normality as a result of fat tails of the return distribution. While volatility clustering has been extensively studied using the GARCH model and its various extensions, the phenomenon of non-normality has not been comprehensively explored, at least in the context of VaR estimation. A combination of extreme value theory (EVT) and GARCH has been explored to analyze financial data showing non-normal behavior. This paper proposes a combination of the Pearson’s Type IV distribution and the GARCH (1, 1) approach to furnish a new method with superior predictive abilities. The approach is back tested for the entire sample as well as for a holdout sample using rolling windows.     

Generalized absolute Cesaro summability of a Fourier series

In an attempt to study the scope of a theorem due to Pati, the authors have established that φ(t) logK|t∈B _u V in (0,π)⟹ΣA _n (x) is |C, 0,β| forβ>1, at the pointt = x.     

Alan Walsh and the absolute analysis project

The significance of Walsh’s idea of the absolute method of analysis for the development of electrothermal atomic absorption spectrometry and, in particular, the absolute analysis project is discussed.