The traveling purchaser problem with stochastic prices: Exact and approximate algorithms

The paper formulates an extension of the traveling purchaser problem where multiple types of commodities are sold at spatially distributed locations with stochastic prices (each following a known probability distribution). A purchaser’s goal is to find the optimal routing and purchasing strategies that minimize the expected total travel and purchasing costs needed to purchase one unit of each commodity. The purchaser reveals the actual commodity price at a seller upon arrival, and then either purchases the commodity at the offered price, or rejects the price and visits a next seller. In this paper, we propose an exact solution algorithm based on dynamic programming, an iterative approximate algorithm that yields bounds for the minimum total expected cost, and a greedy heuristic for fast solutions to large-scale applications. We analyze the characteristics of the problem and test the computational performance of the proposed algorithms. The numerical results show that the approximate and heuristic algorithms yield near-optimum strategies and very good estimates of the minimum total cost.     

Preparation of hierarchical polyaniline nanotubes based on self‐assembly and its electrochemical capacitance

This article reports the preparation and self‐assembly of polyaniline (PANI) nanotubes, which were chemically synthesized by using in situ doping polymerization in the presence of ammonium persulfate (APS; (NH₄)S₂O₈) as the oxidant without the use of an external template. The synthesized hierarchically nanotubes with a shape of a single nanotube with a length of 0.6 to 0.8 µm and an average with of 100 nm assembled from nanoparticles. The effects of the [salicylic acid]/[aniline] ratio on the size and capacitance of PANI nanotubes were studied. The specific capacitance behavior of the PANI nanotubes was also investigated by using cyclic voltammogram and galvanostatic charge–discharge tests. A maximum discharge‐specific capacitance of 422.5 F/g could be achieved, suggesting its potential application in electrode material for electrochemical capacitors. Copyright © 2011 John Wiley & Sons, Ltd.     

Synthesis and properties of phenothiazylene vinylene‐based polymers: New organic semiconductors for field‐effect transistors and solar cells

A series of new phenothiazylene vinylene‐based semiconducting polymers, poly[3,7‐(4′‐dodecyloxyphenyl)phenothiazylene vinylene] ( P1 ), poly[3,7‐(4′‐dodecyloxyphenyl)phenothiazylene vinylene‐alt‐1,4‐phenylene vinylene] ( P2 ), and poly[3,7‐(4′‐dodecyloxyphenyl)phenothiazylene vinylene‐alt‐2,5‐thienylene vinylene] ( P3 ), have been synthesized via a Horner‐Emmons reaction. FTIR and ¹H NMR spectroscopies confirmed that the configurations of the vinylene groups in the polymers were all‐trans (E). The weight‐averaged molecular weights (M_w) of P1 , P2 , and P3 were found to be 27,000, 22,000, and 29,000, with polydispersity indices of 1.91, 2.05, and 2.25, respectively. The thermograms for P1 , P2 , and P3 each contained only a broad glass transition, at 129, 167, and 155 °C, respectively, without the observation of melting features. UV–visible absorption spectra of the polymers showed two strong absorption bands in the ranges 315–370 nm and 450–500 nm, which arose from absorptions of the phenothiazine segments and the conjugated main chains. Solution‐processed field‐effect transistors fabricated from these polymers showed p‐type organic thin‐film transistor characteristics. The field‐effect mobilities of P1 , P2 , and P3 were measured to be 1.0 × 10^?4, 3.6 × 10^?5, and 1.0 × 10^?3 cm² V^?1 s^?1, respectively, and the on/off ratios were in the order of 10² for P1 and P2 , and 10³ for P3 . Atomic force microscopy and X‐ray diffraction analysis of thin films of the polymers show that they have amorphous structures. A photovoltaic device in which a P3 /PC₇₁BM (1/5) blend film was used as the active layer exhibited an open‐circuit voltage (V_OC) of 0.42 V, a short circuit current (J_SC) of 5.17 mA cm^?2, a fill factor of 0.35, and a power conversion efficiency of 0.76% under AM 1.5 G (100 mW cm^?2) illumination. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 635–646, 2010     

Spectroscopic and Computational Insight into the Intermolecular Interactions between Zwitter‐Type Ionic Liquids and Water Molecules

Geometric and conformational changes of zwitter‐type ionic liquids (ZILs) due to hydrogen‐bonding interactions with water molecules are investigated by density functional theory (DFT), two‐dimensional IR correlation spectroscopy (2D IR COS), and pulsed‐gradient spin‐echo NMR (PGSE NMR). Simulation results indicate that molecular structures in the optimized states are strongly influenced by hydrogen bonding of water molecules with the sulfonate group or imidazolium and pyrrolidinium rings of 3‐(1‐methyl‐3‐imidazolio)propanesulfonate ( 1 ) and 3‐(1‐methyl‐1‐pyrrolidinio)propanesulfonate ( 2 ), respectively. Concentration‐dependent 2D IR COS reveals kinetic conformational changes of the two ZIL–H₂O systems attributable to intermolecular interactions, as well as the interactions of sulfonate groups and imidazolium or pyrrolidinium rings with water molecules. The dramatic changes in the ¹H self‐diffusion coefficients elucidate the formation of proton‐conduction pathways consisting of ZIL networks. In ZIL domains, protons are transferred by a Grotthuss‐type mechanism through formation, breaking, and restructuring of bonds between ZILs and H₂O, leading to an energetically favorable state. The simulation and experimental investigations delineated herein provide a perspective to understanding the interactions with water from an academic point of view as well as to designing ILs with desired properties from the viewpoint of applications.     

Hyponormal Toeplitz Operators with Matrix-Valued Circulant Symbols

In this paper we are concerned with the hyponormality of Toeplitz operators with matrix-valued circulant symbols. We establish a necessary and sufficient condition for Toeplitz operators with matrix-valued partially circulant symbols to be hyponormal and also provide a rank formula for the self-commutator.     

Cu(I)-catalyzed cascade reaction of N-tosylhydrazones with 3-butyn-1-ol: A new synthesis of tetrahydrofurans

The Cu(I)-catalyzed cascade coupling/cyclization reaction of N-tosylhydrazones with 3-butyn-1-ol has been explored. This new strategy represents a simple platform for the synthesis of tetrahydrofurans in moderate to good yields.     

Term rank preservers of Boolean matrices

We obtain some characterizations of linear operators that preserve the term rank of Boolean matrices. That is, a linear operator over Boolean matrices preserves the term rank if and only if it preserves the term ranks 1 and k(≠1) if and only if it preserves the term ranks 2 and l(≠2). Other characterizations of term rank preservers are given.     

Synthesis of a benzoxazine with precisely two phenolic OH linkages and the properties of its high‐performance copolymers

A phenolic OH‐containing benzoxazine ( F‐ap ), which cannot be directly synthesized from the condensation of bisphenol F, aminophenol, and formaldehyde by traditional procedures, has been successfully prepared in our alternative synthetic approach. F‐ap was prepared by three steps including (a) condensation of 4‐aminophenol and 5,5'‐methylenebis(2‐hydroxybenzaldehyde) (1) , (b) reduction of the resulting imine linkage by sodium borohydride, and (c) ring closure condensation by formaldehyde. The key starting material, (1) , was prepared from 2‐hydroxybenzaldehyde and s‐trioxane in the presence of sulfuric acid. F‐ap is structurally similar to bis(3,4‐dihydro‐2H‐3‐phenyl‐1,3‐benzoxazinyl)methane ( F‐a, a commercial benzoxazine based on bisphenol F/aniline/formaldehyde) except for two phenolic OHs. The phenolic OHs can provide reaction sites with epoxy and 1,1'‐(methylenedi‐p‐phenylene)bismaleimide (BMI). The structure–property relationships between the thermosets of F‐ap /epoxy, F‐a /epoxy, F‐ap /BMI, and F‐a /BMI were discussed. Experimental data showed that thermosets based on F‐ap /epoxy and F‐ap /BMI provided much better thermal properties than those based on F‐a /epoxy and F‐a /BMI. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2686–2694