Sensitivity analysis of the greatest eigenvalue of a symmetric matrix via the ɛ-subdifferential of the associated convex quadratic form

LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR ^m , and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper.     

Constrained minimax approximation and optimal preconditioned for Toeplitz matrices

A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented.     

Droplet dynamics for asymmetric Ising model

Nucleation from a metastable state is studied for an anisotropic Ising model at very low temperatures. It turns out that the critical nucleus as well as configurations on a typical path to it differ from the Wulff shape of an equilibrium droplet.     

High-performance liquid chromatography with continuous gradient elution in screening for unknown metabolites of butoprozine directly in dog bile

This paper describes the screening for metabolites of butoprozine, a new anti-anginal drug, in dog bile by means of reverse-phase HPLC. Although it does involve a simple clean-up step to remove a substantial amount of endogenous bile compounds, this screening method nevertheless avoids extraction of metabolites and thus allows all metabolites to be introduced into the chromatographic system. A single run of 100 minutes from 100% water to 100% methanol in a linear gradient effects adequate separation of the great majority of metabolites without interference from remaining endogenous compounds. Two methods of differentiating between metabolite peaks and endogenous peaks have been worked out. The first one makes use of ¹⁴C-labeled butoprozine by measuring the amount of radioactivity in the column effluent while simultaneously recording the UV absorbance. The second method compares continuous gradient chromatograms of bile recorded before and after butoprozine administration under very similar conditions. The latter method can be applied to both radioactive and non-radioactive materials.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.     

2-Cyanoacrylates in the conjugate addition of trifluoroacetic acid and nucleophilic reagents

In the presence of trifluoroacetic acid, ethyl 2-cyanoacrylate readily reacts with nucleophilic reagents, such as 2-chloro-1,3,2-benzodioxaphosphole, (EtO)₃P, (EtO)₂PCl, Ph₂PCl, Ph₃P, and thiourea. In these reactions the acid proton enters position 2 of the cyanoacrylate, whereas the nucleophilic component enters position 3, in accordance with the electron density distribution in the acrylate. In the absence of trifluoroacetic acid the above reagents, except 2-chloro-1,3,2-benzodioxaphosphole, cause ethyl 2-cyanoacrylate polymerization. The interaction of ethyl 2-cyanoacrylate with 2-chloro-1,3,2-benzodioxaphosphole and trifluoroacetic acid is the first example of a 2-cyanoacrylate taking part in the acid-initiated electrophilic conjugate addition of a weak nucleophile.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1245–1247, July, 1993.     

Nondifferential optimization via adaptive smoothing

The problem of minimizing a nondifferential functionx f(x) (subject, possibly, to nondifferential constraints) is considered. Conventional algorithms are employed for minimizing a differential approximationf off (subject to differentiable approximations ofg). The parameter is adaptively reduced in such a way as to ensure convergence to points satisfying necessary conditions of optimality for the original problem.This research was supported by the UK Science and Engineering Research Council, the National Science Foundation under Grant No. ECS-8121149, and the Joint Services Electronics Program, Contract No. F49620-79-C-0178.     

Optimization of upper semidifferentiable functions

In this paper, we present an implementable algorithm to minimize a nonconvex, nondifferentiable function in ^m . The method generalizes Wolfe's algorithm for convex functions and Mifflin's algorithm for semismooth functions to a broader class of functions, so-called upper semidifferentiable. With this objective, we define a new enlargement of Clarke's generalized gradient that recovers, in special cases, the enlargement proposed by Goldstein. We analyze the convergence of the method and discuss some numerical experiments.The author would like to thank J. B. Hiriart-Urruty (Toulouse) for having provided him with Definition 2.1 and the referees for their constructive remarks about a first version of the paper.     

A quantitative method for dual‐pass electrostatic force microscopy phase measurements

Electrostatic force microscopy (EFM) has become a powerful tool for investigating charges on surfaces. The use of phase measurement in EFM is a direct and fast way to detect electrostatic force gradients, but only qualitatively. With the dual‐pass scheme, the phase signal at lifted height is often assumed to exclude any influences from the topography, but it does not. We report the collection of both topography and phase data by EFM on charged, micron‐sized metal wires. In order to quantify the electrostatic force, a cone model and finite element analysis are provided to integrate the force gradient from the phase signal. Copyright © 2007 John Wiley & Sons, Ltd.     

氟的离子选择电极瞬时电位法测定

研究了氟离子选择电极瞬时电位分析法，其检出限和Nernst响应下限均低于传统电位分析法，空白液切换到试液时瞬时电位达到稳定的峰电位Vp比传统电位法的响应快得多，可以实现小体积试液的快速准确分析；用该法测定了自来水和矿泉水中氟的含量；利用校正曲线的截距和检出限计算了LaF3的溶度积，在0.1mol/L KNO3介质中Ksp(LaF3)=10^-28.45，在0.001mol/L柠檬酸钠＋HAc-NaAc缓冲液（pH=5.50，离子强度I＝0.10mol/L)介质中溶度积K′sp(LaF3)=10^-26.26；据此，计算得柠檬酸与La^3 络合物的稳定常数K1=10^5.46和K2=10^3.99；用离子水合吉氏自由能ΔGh(F^-,g)解释了不同浓度F^-试液瞬时电位的跃迁时间。