面向近原子尺度制造的光学测量精度极限分析

纳米级乃至更高精度的测量是原子及近原子尺度制造技术发展的基础和保障.光学测量具有精度高、测量范围广、测量直观等优点,其对单个成像光斑中心的定位可达远超衍射极限的精度.但由于光本身散粒噪声、探测器暗电流噪声等随机性的存在,光学测量存在精度极限.本文基于克拉美罗下界理论发展了可适用于任意强度分布像斑的精度极限计算方法,并以典型艾里斑为例,分析了成像过程中反映信噪比、能量集中度、计算方式的参数对定位精度极限的影响规律并给出提高精度的建议和结论.对实验所得像斑进行了精度极限计算,验证了所得结论对类似艾里斑的像斑的适用性.研究为原子及近原子尺度制造过程中光学测量的应用和优化提供了分析方法和理论指导.     

Acoustic frequency and optimum sonochemical production at single and multi-bubble scales: A modeling answer to the scaling dilemma

The present work consists of an innovative approach aiming to address the scalability dilemma of the sonochemical activity dependency of acoustic frequency. The study originates from the discordance of observations between the theoretical investigations of the sonochemical activity of the single acoustic cavitation bubble in function of the acoustic frequency, in one hand, and the experimental findings regarding the optimal frequency condition, mainly in terms of pollutant degradation, in the other hand. A single bubble and an up-scaled model of the sonochemical activity are suggested and simulations were conducted based on both of them over the frequencies 20, 200, 300, 360, 443, 500, 600 and 800 kHz under an oxygen atmosphere. The results reveal that the sonochemical production at single bubble scale is monotonously decreasing with the increase of frequency, while all the products demonstrate an absolute optimum of sonochemical production at 200 kHz, except HO^• that attains its maximum molar yield under 300 kHz. Besides, the production of the predominant species, namely HO₂^•, HO^• and O₃, manifests a clear rebound at 500 kHz. All the present results were compared to and confirmed by experimental findings, while the scalability of the concentrations of sonochemically produced species was discussed using a parameter we introduced as “the mass focusing factor”.     

On a bivariate copula with both upper and lower full-range tail dependence

Copula functions can be useful in accounting for various dependence patterns appearing in joint tails of data. We propose a new two-parameter bivariate copula family that possesses the following features. First, both upper and lower tails are able to explain full-range tail dependence. That is, the dependence in each tail can range among quadrant tail independence, intermediate tail dependence, and usual tail dependence. Second, it can capture upper and lower tail dependence patterns that are either the same or different. We first prove the full-range tail dependence property, and then we obtain the corresponding extreme value copula. There are two applications based on the proposed copula. The first one is modeling pairwise dependence between financial markets. The second one is modeling dynamic tail dependence patterns that appear in upper and lower tails of a loss-and-expense data.     

Addendum to Pontryagin’s maximum principle for dynamic systems on time scales

This note is an addendum to [L. Bourdin and E. Trélat, SIAM J. Cont. Optim., 2013] and [M. Bohner, K. Kenzhebaev, O. Lavrova and O. Stanzhytskyi, J. Differ. Equ. Appl., 2017], pointing out the differences between these papers and raising open questions.     

Numerical solution to a linear equation with tensor product structure

We consider the numerical solution of a c‐stable linear equation in the tensor product space , arising from a discretized elliptic partial differential equation in . Utilizing the stability, we produce an equivalent d‐stable generalized Stein‐like equation, which can be solved iteratively. For large‐scale problems defined by sparse and structured matrices, the methods can be modified for further efficiency, producing algorithms of computational complexity, under appropriate assumptions (with n_s being the flop count for solving a linear system associated with ). Illustrative numerical examples will be presented.     

基于Curvelet域高斯尺度混合模型的地震信号降噪方法

结合曲波变换和高斯尺度混合模型提出地震信号随机噪声压制方法.该方法首先运用曲波变换对含有随机噪声的地震信号进行分解,然后对各小波子带系数分别建立高斯尺度混合模型估计出原始地震信号所对应的小波系数,最后经曲波逆变换重构获得降噪处理后的地震信号.仿真地震信号和实际地震信号的实验结果均表明本文方法能够有效压制地震信号中的随机噪声干扰,较多地保留了有效信号.     

Kinetic energy density for orbital‐free density functional calculations by axiomatic approach

An axiomatic approach is herein used to determine the physically acceptable forms for general D‐dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one‐point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large‐scale orbital free density functional theory calculations.     

Preparation of fluorescent polyaspartic acid and evaluation of its scale inhibition for CaCO3 and CaSO4

Polysuccinimide was synthesized from maleic anhydride and urea. A polyaspartic acid derivative (PASP‐Try‐SEA) was synthesized from the polysuccinimide with 2 ‐aminoethanesulfonic acid and tryptophan. The products were characterized by UV, FTIR,¹H NMR, TGA and PL, respectively. The results showed that the fluorescent chromophore‐indolyl groups were successfully incorporated into PASP. The relationship between the fluorescence intensity and the concentration of fluorescent polyaspartic acid (FPASP) is linear with the excitation wavelength of 366 nm and 422 nm. FPASP also showed excellent scale inhibition properties with a scale inhibition rate of 78% achieved for CaCO₃ with a dosage of 9 mg/L and a significantly enhanced scale inhibition effect for CaSO₄, achieving an inhibition rate of 98%, which were determined using the static scale inhibition method. When FPASP was added to the solution, CaCO₃ and CaSO₄ deposits showed flower patterns with floppy accumulation by scanning electron microscopy. Copyright © 2016 John Wiley & Sons, Ltd.     

On the absolute convergence of multiple fourier series

Let f: R ^N → C be a periodic function with period 2π in each variable. We prove suffcient conditions for the absolute convergence of the multiple Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to multiple Fourier series. This research was started while the first author was a visiting professor at the Department of Mathematics, Texas A&M University, College Station during the fall semester in 2005; and it was also supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192.