Stability and convergence of modified Ishikawa iterative sequences with errors in Banach spaces

Summary Some stability and convergence theorems of the modified Ishikawa iterative sequences with errors for asymptotically nonexpansive mapping in the intermediate sense and asymptotically pseudo contractive and uniformly Lipschitzian mappings in Banach spaces are obtained.     

New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.     

Normalization and noise-reduction algorithm for fringe patterns

This paper presents a fringe pattern normalization and noise-reduction algorithm. Locally the background noise is suppressed, the modulation normalized and the noise smoothed. An expression to calculate the cosine-only term is formulated. It is related to the directional derivatives of the intensity fringes. Two-dimensional Fourier series are used to calculate the parameters needed for the algorithm. Experimental work is presented using diffraction and ESPI images. The programming is relatively simple and involves mainly local convolutions. The processing time using a 2 GHz computer to normalize an image of 256 × 256 pixels is approximately one second.     

双频超声交替强化超临界流体萃取装置的设计与应用

本文针对超临界流体萃取（SFE）系统设备的特点，设计丁可用于强化SFE过程的双频超声波交替强化装置。以香椿叶中黄酮类化合物为提取对象，对超声强化USFE过程的影响因素及强化效果进行了实验研究，结果表明；低频超声利于提取，频率为20kHz的超声强化的萃取率最大，38kHz的超声最小，两者交替的居于中间。     

Modelling of composting of food waste in a column reactor

The composting of organic solid waste, the mixture of fruit and vegetable leftovers enriched with night soil, was investigated in a closed thermally insulated reactor. It was found that 80.9 % of the original substrate biodegraded after 14 days. A mathematical model of the column reactor was proposed where the biodegradation rate of the organic solid waste was described using simple n-thorder kinetics. A good prediction of process performance was obtained using the proposed kinetics and experimentally obtained reaction heat. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Equality and inequality constrained optimization algorithms with convergent stepsizes

In this paper, we consider two algorithms for nonlinear equality and inequality constrained optimization. Both algorithms utilize stepsize strategies based on differentiable penalty functions and quadratic programming subproblems. The essential difference between the algorithms is in the stepsize strategies used. The objective function in the quadratic subproblem includes a linear term that is dependent on the penalty functions. The quadratic objective function utilizes an approximate Hessian of the Lagrangian augmented by the penalty functions. In this approximation, it is possible to ignore the second-derivative terms arising from the constraints in the penalty functions.The penalty parameter is determined using a strategy, slightly different for each algorithm, that ensures boundedness as well as a descent property. In particular, the boundedness follows as the strategy is always satisfied for finite values of the parameter.These properties are utilized to establish global convergence and the condition under which unit stepsizes are achieved. There is also a compatibility between the quadratic objective function and the stepsize strategy to ensure the consistency of the properties for unit steps and subsequent convergence rates.This research was funded by SERC and ESRC research contracts. The author is grateful to Professors Laurence Dixon and David Mayne for their comments. The numerical results in the paper were obtained using a program written by Mr. Robin Becker.     

Two methods for semi-automated quantification of changes in ventricular volume and their use in schizophrenia

Two semi-automated methods for quantification of ventricular volume change from baseline and follow-up magnetic resonance imaging scans have been developed. Technique 1 employs direct segmentation of the ventricles from both the scans using thresholding and contour extraction. Technique 2 operates on difference images produced by voxel based intensity subtraction of the baseline from the registered follow-up images. Here, all voxels with intensities above a noise threshold and in a restricted area are monitored to compute volumetric changes. In phantom measurements the first technique was accurate to 0.0046%, the second to 0.167% of the phantom volume. Results from normal volunteers was that the average ventricular volume changed by 1.52% and 1.54% for images acquired within 9 months using techniques 1 and 2, respectively. With schizophrenic patients mean change of 10.78% and 9.43% were found employing the first and second procedures, respectively. All measurements agreed with a radiologist’s visual grading of the changes. Robust, objective, fast, easy-to-use, and fairly accurate procedures have been developed and validated to quantify volumetric changes.     

Application of extraction disks in dissolution tests of clenbuterol and levothyroxine tablets by capillary electrophoresis

Sample preparation procedures using octadecyl (C₁₈) extraction disks were developed to obtain accurate and reproducible results for determinations of clenbuterol (20 μg per dose) and levothyroxine (100 μg per dose) in dissolution media of solid oral dosage forms. Preconcentration of samples allowed final concentrations of 1.1 μg/ml of clenbuterol and 4.0 μg/ml of levothyroxine to be reached prior to CE analysis. The results obtained by CE were in good agreement with those of HPLC. The precision of the migration time, peak area, peak height and accuracy were determined in both intea-day (n = 6) and inter-day (n =18) assays. Linearity was demonstrated over the ranges 0.5–80.0 μg/ml of clenbuterol and 1.0–30.0 μg/ml of levothyroxine. The mean recoveries were higher than 94.0%, ranging from 50 to 125% levels with respect to dose potencies. The proposed methodology may be generally applied to determine drugs at ng/ml concentrations.     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.