Legendre wavelets method for constrained optimal control problems

A numerical method for solving non‐linear optimal control problems with inequality constraints is presented in this paper. The method is based upon Legendre wavelet approximations. The properties of Legendre wavelets are first presented. The operational matrix of integration and the Gauss method are then utilized to reduce the optimal control problem to the solution of algebraic equations. The inequality constraints are converted to a system of algebraic equalities; these equalities are then collocated at the Gauss nodes. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2002 John Wiley & Sons, Ltd.     

An analytical solution of the diffusion- convection equation over a finite domain

Numerical solutions to the diffusion-convection equation are usually evaluated through comparison with analytical solutions in one dimension. Literature survey indicates the most frequently used analytical solution is one derived for asemi-infinite domain. This paper presents an analytical solution to this problem over a finite domain. Comparison is made with a solution to a mathematically similar problem in heat conduction with radiation.     

Hyaluronic Acid (HA)‐Based Silk Fibroin/Zinc Oxide Core–Shell Electrospun Dressing for Burn Wound Management

Burn injuries represent a major life‐threatening event that impacts the quality of life of patients, and places enormous demands on the global healthcare systems. This study introduces the fabrication and characterization of a novel wound dressing made of core–shell hyaluronic acid–silk fibroin/zinc oxide (ZO) nanofibers for treatment of burn injuries. The core–shell configuration enables loading ZO—an antibacterial agent—in the core of nanofibers, which in return improves the sustained release of the drug and maintains its bioactivity. Successful formation of core–shell nanofibers and loading of zinc oxide are confirmed by transmission electron microscopy, Fourier‐transform infrared spectroscopy, and energy dispersive X‐ray. The antibacterial activity of the dressings are examined against Escherichia coli and Staphylococcus aureus and it is shown that addition of ZO improves the antibacterial property of the dressing in a dose‐dependent fashion. However, in vitro cytotoxicity studies show that high concentration of ZO (>3 wt%) is toxic to the cells. In vivo studies indicate that the wound dressings loaded with ZO (3 wt%) substantially improves the wound healing procedure and significantly reduces the inflammatory response at the wound site. Overall, the dressing introduced herein holds great promise for the management of burn injuries.     

Synthetic approaches towards the sulfonamide substituted‐4,5‐diaryl‐4H‐1,2,4‐triazole‐3‐thiones

A new series of 3‐alkylthio‐4,5‐diaryl‐4H‐1,2,4‐triazoles having a SO₂NH₂ substituent in the para‐position on one of the aryl rings ( 19/25 ) were prepared starting from the appropriate benzoic acid hydrazides ( 15/21 ). Reaction of the corresponding hydrazides with the appropriate isothiocyanates yielded 16/22 , which were cyclized in basic media to give 4,5‐diaryl‐2,4‐dihydro‐3H‐1,2,4‐triazole‐3‐thiones 17/23 . Alkylation of 17/23 afforded the alkylthio compounds 18/24 . Final debenzylation was achieved with concentrated sulfuric acid to give the target sulfonamides 19/25 .     

On Operator-Valued Semicircular Random Variables

In this paper, we discuss some special properties of operator-valued semicircular random variables including representation of the Cauchy transform of a compactly supported probability measure in terms of their operator-valued Cauchy transforms and existence of nonzero discrete part of their associated distributions.     

Direct limits of Cohen–Macaulay rings

Let A be a direct limit of a direct system of Cohen–Macaulay rings. In this paper, we describe the Cohen–Macaulay property of A. Our results indicate that A is not necessarily Cohen–Macaulay. We show A is Cohen–Macaulay under various assumptions. As an application, we study Cohen–Macaulayness of non-affine normal semigroup rings.     

Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation

Current methods of estimating the Brillouin frequency shift in Brillouin optical time domain analysis sensors are based on curve-fitting techniques. These techniques apply the same weight to all portions of the curve and dutifully fit into the peak and noisy ends of the curve. This makes them very sensitive to noise, initialization of fitting parameters, symmetry, and start and stop frequencies. We introduce a method based on the cross-correlation technique to estimate the central frequency of noisy Lorentzian curves, which is more robust to noise and free from initial settings of fitting parameters.