On the convergence of a class of derivative-free minimization algorithms

A convergence analysis is presented for a general class of derivative-free algorithms for minimizing a functionf(x) for which the analytic form of the gradient and the Hessian is impractical to obtain. The class of algorithms accepts finite-difference approximation to the gradient, with stepsizes chosen in such a way that the length of the stepsize must meet two conditions involving the previous stepsize and the distance from the last estimate of the solution to the current estimate. The algorithms also maintain an approximation to the second-derivative matrix and require that the change inx made at each iteration be subject to a bound that is also revised automatically. The convergence theorems have the features that the starting pointx ¹ need not be close to the true solution andf(x) need not be convex. Furthermore, despite the fact that the second-derivative approximation may not converge to the true Hessian at the solution, the rate of convergence is still Q-superlinear. The theorry is also shown to be applicable to a modification of Powell's dog-leg algorithm.     

Properties of an exact crystalline many-body ground state

A new quantum many-body Hamiltonian is introduced, for which the exact ground state is a Jastrow-type product. This Hamiltonian is interpreted as a one-component |x|-potential Coulomb system in free boundary conditions, and by explicit calculation it is shown that the ground state is crystalline. The generaln-body density matrix is calculated, and is related to then-body density matrix calculated in periodic boundary conditions.     

Hölder Regularity of Integrated Density of States for the Almost Mathieu Operator in a Perturbative Regime

Consider the Almost Mathieu operator H = cos 2(k +)+ on the lattice. It is shown that for large , the integrated density of states is Hölder continuous of exponent < . This result gives a precise version in the perturbative regime of recent work by M. Goldstein and W. Schlag on Hölder regularity of the integrated density of states for 1D quasi-periodic lattice Schrödinger operators, assuming positivity of the Lyapunov exponent (and proven by different means). Our approach provides also a new way to control Green's functions, in the spirit of the author's work in KAM theory. It is by no means restricted to the cosine-potential and extends to band operators.     

Statistical Properties of Stimulated Raman Scattering in a Nonlinear Regime

Statistical properties of the Raman scattering of an intense step pulse are investigated by numerical solution of the equations of a semi-classical theory with assignment of a random Gaussian distribution of the initial polarization over the sample. The probability density functions of the intensity, energy, delay time, and width of a Stokes pulse and also of the position, height, and width of the spectral peaks of the first incidental Stokes component with the preservation of the phase memory of scattering centers are calculated. The influence of collisional dephasing on the fluctuation of these characteristics is considered.     

Identification of non-minimum phase transfer function using higher-order spectrum

The present paper treats the identification of parametric nonminimum phase transfer function. We propose a method of identification based on the inner outer factorization of stable transfer function. It consists of identifying the outer and inner parts of a transfer function separately. The outer part is identified by the use of the second-order spectral estimate from the observed linear process, while the inner part is identified by the use of a higher-order cumulant spectral estimate from the observed process. Respective parameter estimators are determined in the light of asymptotic efficiency. In order to estimate the order of the inner part of a transfer function, a criterion is proposed. It is introduced based on the same principle as in the case of Akaike's AIC.     

The Wigner Function as Distribution Function

Some entangled states have nonnegative Wigner representative function. The latter allow being viewed as a distribution function of local hidden variables. It is argued herewith that the interpretation of expectation values using such distribution functions as local hidden variable theory requires restrictions pertaining to the observables under study. The reasoning lead to support the view that violation of Bell’s inequalities that is always possible for entangled states hinges not only on the states involved but also whether the dynamical variables have their values defined even when they cannot be measured.     

水稻糙米粗蛋白近红外光谱定量分析模型的优化研究

筛选有代表性的191份糙米样品为试材,其中42份来自国家稻种资源库、149份来自水旱稻杂交产生的DH系,蛋白质含量变幅5.90％～14.50％,采用偏最小二乘法(PLS)建立模型,并构造模型的评价参数——目标函数[R/(1+RMSECV)], 同时借助校正集和验证集两个载荷向量得分二维空间投影图,对近红外定量模型进行评价和优化。结果表明: 在5 000～9 000 cm-1范围内,预处理方法为一阶导数,校正模型和外部检验的目标函数值分别为0.701和0.687;两载荷向量得分直观分布图显示样品的聚类结果与目标函数筛选结果一致,也进一步验证了目标函数是模型评价和优化的有效指标。     

Water absorption kinetics in different wettability conditions studied at pore and sample scales in porous media by NMR with portable single-sided and laboratory imaging devices

NMR relaxation time distributions of water (1)H obtained by a portable single-sided surface device have been compared with MRI internal images obtained with a laboratory imaging apparatus on the same biocalcarenite (Lecce Stone) samples during capillary water uptake. The aim of this work was to check the ability of NMR methods to quantitatively follow the absorption phenomenon under different wettability conditions of the internal pore surfaces. Stone wettability changes were obtained by capillary absorption of a chloroform solution of Paraloid PB72, a hydrophobic acrylic resin frequently used to protect monuments and buildings, through one face of each sample. Both relaxation and imaging data have been found in good quantitative agreement each other and with masses of water determined by weighing the samples. In particular the Washburn model of water capillary rise applied to the imaging data allowed us to quantify the sorptivity in both treated and untreated samples. Combining relaxation and imaging data, a synergetic improvement of our understanding of the water absorption kinetics at both pore and sample scales is obtained. Since relaxation data have been taken over the course of time without interrupting the absorption process, simply by keeping the portable device on the surface opposite to the absorption, the results show that the single-sided NMR technique is a powerful tool for in situ evaluation of water-repellent treatments frequently used for consolidation and/or protection of stone artifacts.     

Two-Dimensional Rossby Waves: Exact Solutions to Petviashvili Equation

The two-dimensional (2D) nonlinear Rossby waves described by the Petviashvili equation, which has been invoked as an ageostrophic extension of the barotropic quasi-geostrophic potential vorticity equation, can be investigated through the exact periodic-wave solutions for the Petviashvili equation, while the exact analytical periodic-wave solutions to the Petviashvili equation are obtained by using the Jacobi elliptic function expansion method. It is shown that periodic-wave 2D Rossby solutions can be obtained by this method, and in the limit cases, the 2D Rossby soliton solutions are also obtained.     

On the Capability of the Generalized Gamma Function to Represent Spray Drop‐Size Distribution

The three‐parameter, Generalized Gamma function solution of a recent MEF formulation used to derive liquid spray drop‐size distribution, is applied to sprays resulting from three different atomization processes. The objectives of these applications are to determine the sign of the parameters for which this function reports a more reliable fit and to further understand the parameter stability problem reported elsewhere. It is found that the lack of stability of the parameters is related to a characteristic feature of the mathematical function and appears for a series of spray drop‐size distributions with constant shape. For each situation analyzed in the present study, the Generalized Gamma function provides a very good fit with parameters that are either constant or correlated to the working conditions. As far as the sign of the parameters is concerned, the results show that the best formulation is a function of the spray and that it is impossible to know, a priori, which parameter sign will report the best fit. Finally, for one situation, it is found that the Generalized Gamma function allows extrapolation of drop sizes outside the measured values. All of the results converge to conclude that the three‐parameter Generalized Gamma function, which is identical to the well‐known Nukiyama‐Tanasawa distribution, accumulates valuable attributes to represent liquid spray drop‐size distributions.