Misclassification minimization

The problem of minimizing the number of misclassified points by a plane, attempting to separate two point sets with intersecting convex hulls inn-dimensional real space, is formulated as a linear program with equilibrium constraints (LPEC). This general LPEC can be converted to an exact penalty problem with a quadratic objective and linear constraints. A Frank-Wolfe-type algorithm is proposed for the penalty problem that terminates at a stationary point or a global solution. Novel aspects of the approach include: (i) A linear complementarity formulation of the step function that counts misclassifications, (ii) Exact penalty formulation without boundedness, nondegeneracy or constraint qualification assumptions, (iii) An exact solution extraction from the sequence of minimizers of the penalty function for a finite value of the penalty parameter for the general LPEC and an explicitly exact solution for the LPEC with uncoupled constraints, and (iv) A parametric quadratic programming formulation of the LPEC associated with the misclassification minimization problem.This material is based on research supported by Air Force Office of Scientific Research Grant F49620-94-1-0036 and National Science Foundation Grants CCR-9101801 and CDA-9024618.     

The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

On pasting -weights

Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.

     

C 1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsP _i in a domainD of thex–y plane andn real numbersf _i, consider the problem of computing a bivariate functionf(x, y) of classC ¹ inD whose values inP _i are exactlyf _i,i=1,,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ _l inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.Work supported by MURST Project of Computational Mathematics, Italy.     

In situ FTIR diagnostics of the radio-frequency plasma decomposition of N2O

The decomposition of N₂O in a 13.56-MHz parallel-plate system was studied usingin situ Fourier transform infrared (FTIR) spectroscopy. Areas of two infrared absorption bands of N₂O recorded at 8 cm^–1 resolution were used to estimate relative gas-phase dissociation as a function of rf power and flow rate at 500 mT. Flow rate was found to strongly affect band areas over the range of powers investigated (10–90 W). The effect of rf power on band areas diminished above 40 W, probably due to poor plasma confinement. Distortion of the band shapes by the plasma permitted rotational temperatures to be estimated. Rotational temperature increased essentially linearly with power at constant flow rate, reaching 450 K at 80 W, but was independent of flow rate at constant power. Rotational temperatures were also found to depend on the temperature of the electrodes, which were heated by plasma exposure. No infrared-active product species were observed even under batch conditions where all N₂O was irreversibly dissociated. This lack of detectable products and a 50% pressure rise observed in a batch study suggest that N₂ and O₂ are the primary stable discharge products.     

Analyzing electrochemical noise with Chebyshev’s discrete polynomials

The principles underlying a novel method intended for analyzing experimental data obtained when studying fluctuation processes are considered. The method in question is Chebyshev’s spectroscopy. The application of this method allows one to determine statistic characteristics of steady-state electrochemical noise against the background of severe deterministic interference without invoking the procedure of the fitting of the initial data. The potentialities of this novel method, which is intended for treating noise experiment, are demonstrated by examining model examples and analyzing the electrochemical noise generated by a lithium electrode placed in an aprotic organic electrolyte.     

傅里叶变换红外光谱和傅里叶变换拉曼光谱法无损鉴别药材的真伪

利用傅里叶变换红外（FT-IR）和近红外傅里叶变换拉曼（NIR FT-aman）光谱法对大黄（西宁大黄）与伪品大黄（华北大黄、山大黄、水根大黄）进行了无损快速的鉴别。结果表明：尽管正品大黄与伪品大黄差别较小，有大部分的化学成分有很大的相同之处，但在红外、拉曼谱图中各自的特征峰较突出，根据谱峰的强度和位置可容易地将它们区别开来。红外和拉曼光谱法相互印证，相互补充，具有快速、准确、操作简单、重复性好、不需对样品进行分离提取，可直接鉴别等特点。     

Quality control of Metamitron in agrochemicals using Fourier transform infrared spectroscopy in the middle and near range

Two vibrational spectrometry-based methodologies were developed for Metamitron determination in pesticide formulations. Fourier transform-middle infrared (FT-MIR) procedure was based on the extraction of Metamitron by CHCl₃ and latter determination by peak area measurement between 1556 and 1533 cm⁻¹, corrected with a two points baseline established from 1572 to 1514 cm⁻¹. Fourier transform-near infrared (FT-NIR) determination was made after the extraction of Metamitron in acetonitrile and measuring the peak area between 6434 and 6394 cm⁻¹ corrected using a two points baseline defined between 6555 and 6228 cm⁻¹. Repeatability, as relative standard deviation, of 5 independent measurements at mg g⁻¹ concentration level, of 0.16% and 0.07% for MIR and NIR and a limit of detection of 0.03 and 0.004 mg g⁻¹ were obtained for MIR and NIR, respectively.NIR determination provides a sample frequency of 120 h⁻¹, higher than that found by MIR and liquid chromatographic methods (60 and 15 h⁻¹, respectively). On the other hand, the NIR method reduces the solvent consumption and waste generation, to only 1 ml acetonitrile per sample as compared with 3.4 ml chloroform required for the MIR determination and 60 ml acetonitrile used in the chromatographic reference procedure. So, vibrational procedures can be considered serious alternatives to long and time consuming chromatographic methods usually recommended for quality control of commercially available pesticide formulations.     

红外光谱法在双亲性化合物水溶液体系研究中的应用

浓度，温度，压力，体系组分及不同分子间相互作用等因素对双亲性化合物分子在水溶液体系中的聚集状态及相变过程均有影响。本文综述了富里叶变换红外光谱方法在这一研究领域内应用十余年间的研究进展。     

On assignment of fundamental vibrational modes of hypophosphite anion and its deuterated analogue

Results of ab initio and density functional theory calculations on the structure and vibrational frequencies of hypophosphite anion indicate earlier experimental assignments of the fundamental vibrational modes are correct while the recent reassignments of several modes proposed by Bickley et al. are inconsistent with the calculated results.