Greatest Descent Algorithms in Unconstrained Optimization

We show that, for an unconstrained optimization problem, the long-term optimal trajectory consists of a sequence of greatest descent directions and a Newton method in the final iteration. The greatest descent direction can be computed approximately by using a Levenberg-Marquardt like formula. This implies the view that the Newton method approximates a Levenberg-Marquardt like formula at a finite distance from the minimum point, instead of the standard view that the Levenberg-Marquadt formula is a way to approximate the Newton method. With the insight gained from this analysis, we develop a two-dimensional version of a Levenberg-Marquardt like formula. We make use of the two numerically largest components of the gradient vector to define here new search directions. In this way, we avoid the need of inverting a high-dimensional matrix. This reduces also the storage requirements for the full Hessian matrix in problems with a large number of variables. The author thanks Mark Wu, Professors Sanyang Liu, Junmin Li, Shuisheng Zhou and Feng Ye for support and help in this research as well as the referees for helpful comments.     

Synthesis of amphiphilic graft copolymer brush and its use as template film for the preparation of silver nanoparticles

A microphase‐separated, amphiphilic graft copolymer consisting of a poly (vinyl chloride) (PVC) backbone and poly(oxyethylene methacrylate) (POEM) side chains, (PVC‐g‐POEM at 62:38 wt %) was synthesized via atom transfer radical polymerization (ATRP). Nuclear magnetic resonance (¹H NMR), FTIR spectroscopy, and transmission electron microscopy (TEM) clearly revealed that the “grafting from” method using ATRP was successful and that the graft copolymer molecularly self‐assembled into discrete nanophase domains of continuous PVC and isolated POEM regions. The self‐assembled graft copolymer film was used to template the growth of silver nanoparticles in solid state by introducing a AgCF₃SO₃ precursor and a UV irradiation process. The in situ formation of silver nanoparticles in the graft copolymer template film was confirmed by TEM, UV–visible spectroscopy, and wide angle X‐ray scattering. FTIR spectroscopy and X‐ray photoelectron spectroscopy also demonstrated the selective incorporation and in situ formation of silver nanoparticles within the hydrophilic POEM domains, presumably due to strong interactions between the silver and the ether oxygen in POEM. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3911–3918, 2008     

Synthesis of water-tolerant indium homoenolate in aqueous media and its application in the synthesis of 1,4-dicarbonyl compounds via palladium-catalyzed coupling with acid chloride

The first water-tolerant, ketone-type indium homoenolate was synthesized via the oxidative addition of In/InCl(3) to enones. The reaction proceeds exclusively in aqueous media. Both indium and indium(III) chloride are necessary for the smooth conversion of the reaction. Similar results were obtained when InCl or InCl(2) was used in place of In/InCl(3). The synthetic utility of the indium homoenolate was demonstrated through the synthesis of 1,4-dicarbonyl compounds via palladium-catalyzed coupling of indium homoenolate with acid chloride.     

Multilayer graphene nanoribbons exhibit larger capacitance than their few-layer and single-layer graphene counterparts

This article demonstrates that it is not always beneficial to exfoliate graphitic structures to single-layer graphene to achieve maximum electrochemical performance. Using electrochemical impedance spectroscopy, we show that multilayer graphene nanoribbons with cross sections of 100 × 100 nm provide larger capacitance (15.6 F/g) than do few-layer graphene nanoribbons (14.9 F/g) and far larger capacitance than single-layer graphene nanoribbons (10.9 F/g) with the same cross section.     

A stochastic model for risk management in global supply chain networks

With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau–Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives.     

An Algorithm for Non-Linear Network Programming: Implementation,Results and Comparisons

This paper evaluates an algorithm for solving network flow optimization problems with quadratic cost functions. Strategies for fast implementation are discussed and the results of extensive numerical tests are given. The performance of the algorithm measured by CPU time is compared with that of the convex simplex method specialized for quadratic network programming. Performance of the two methods is analysed with respect to network size and density, and other parameters of interest. The algorithm is shown to perform significantly better on the majority of problems. We also show how the algorithm may be used to solve non-linear convex network optimization problems by the use of sequential quadratic programming.     

The maximum degree in a random tree and related problems

Meir and Moon studied the distribution of the maximum degree for simply generated families of trees. We have sharper results for the special case of labelled trees. © 1994 John Wiley & Sons, Inc.     

Investigations of the effects of ultrasound on some metal and nonmetal systems

The effects of power ultrasound on four metal-nonmetal powdered systems: copper-sulphur iron-sulphur, zinc-sulphur and magnesium-sulphur in various solvents, such as hexane and carbon disulphide, are briefly examined here. For each system, a sonication time of 30 min was affected. The sonicated products are analysed by X-ray diffraction, X-ray fluorescence and atomic absorption spectrophotometry to determine their qualitative and quantitative compositions and the percentage yields of the products obtained are then compared and discussed.