The traveling salesman problem: A duality approach

In this study we formulate the dual of the traveling salesman problem, which extends in a natural way the dual problem of Held and Karp to the nonsymmetric case. The dual problem is solved by a subgradient optimization technique. A branch and bound scheme with stepped fathoming is then used to find optimal and suboptimal tours. Computational experience for the algorithm is presented.This author's work was partially supported by NSF Grant #GK-38337.     

2-Aroylbenzoic acids—VIII: The synthesis and some reactions of 2-aroylbenzoic acids from m-chlorophenol

The syntheses of the novel 2-(4′-chloro-2′-hydroxybenzoyl) benzoic acid 1 and 2-(2′-chloro-4′-hydroxybenzoyl)benzoic acid 2 are described and some of their reactions are given.     

Predicting the nonlinear tensile behavior of carbon nanotubes using finite element simulation

Carbon nanotubes (CNTs) possess extremely high mechanical properties and could be the ultimate reinforcing materials for the development of nanocomposites. In this work, a Finite Element (FE) model based on the molecular mechanics theory was developed to evaluate tensile properties of single-walled carbon nanotubes (SWCNTs). The deformation and fracture of carbon nanotubes under tensile strain conditions were studied by common FE software, Ansys. In this model, individual carbon nanotube was simulated as a frame-like structure, and the primary bonds between two nearest-neighboring atoms were treated as beam elements. The beam element properties were determined via the concept of energy equivalence between molecular dynamics and structural mechanics. So far, several researches have studied the elastic behavior of CNTs, and its nonlinearity is not well understood. The novelty of the model lies on the use of nonlinear beam elements to evaluate SWNTs tensile failure. The obtained calculated mechanical properties show good agreement with existing numerical and experimental results.     

Existence and asymptotic stability of a viscoelastic wave equation with a delay

In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem

Can an Amine Be a Stronger Acid than a Carboxylic Acid? The Surprisingly High Acidity of Amine–Borane Complexes

The gas‐phase acidity of a series of amine–borane complexes has been investigated through the use of electrospray mass spectrometry (ESI‐MS), with the application of the extended Cooks kinetic method, and high‐level G4 ab initio calculations. The most significant finding is that typical nitrogen bases, such as aniline, react with BH₃ to give amine–borane complexes, which, in the gas phase, have acidities as high as those of either phosphoric, oxalic, or salicylic acid; their acidity is higher than many carboxylic acids, such as formic, acetic, and propanoic acid. Indeed the complexation of different amines with BH₃ leads to a substantial increase (from 167 to 195 kJ mol^?1) in the intrinsic acidity of the system; in terms of ionization constants, this increase implies an increase as large as fifteen orders of magnitude. Interestingly, this increase in acidity is almost twice as large as that observed for the corresponding phosphine–borane analogues. The agreement between the experimental and the G4‐based calculated values is excellent. The analysis of the electron‐density rearrangements of the amine and the borane moieties indicates that the dative bond is significantly stronger in the N‐deprotonated anion than in the corresponding neutral amine–borane complex, because the deprotonated amine is a much better electron donor than the neutral amine. On the top of that, the newly created lone pair on the nitrogen atom in the deprotonated species, conjugates with the BN bonding pair. The dispersion of the extra electron density into the BH₃ group also contributes to the increased stability of the deprotonated species.     

Réactivité de l’acide déhydroacétique hydrogené en c5-c6 : obtention des pyrano-1,5-benzodiazépines différemment substituées et de la structure enaminone

A number of 1,5-benzodiazepines derivatives 4 were obtained via the interaction of dehydroacetic acid hydrogenated at C₅-C₆, orthophenylenediamines and aromatic aldehydes. The interpretation of the results is enriched by a study of the electronic effects of the DHA hydrogenated at C₅-C₆. Accordingly, it leads us to obtain the original structure cynnamoyle 5.     

A thienoquinoxaline and a styryl-quinoxaline as new fluorescent probes for amyloid-β fibrils

Simple and easy to prepare quinoxaline derivatives proved able to stain amyloid fibers such as aggregated lysozyme and Aβ(1-40)-peptide by a fluorescence “turn on” mechanism. Thienoquinoxaline 1 allowed the detection of lysozyme and Aβ(1-40) fibers at λ = 555 and 532 nm, respectively, with excitation at λ = 450 nm. Styryl-quinoxaline 2 stained lysozyme and Aβ(1-40) fibers with fluorescence at λ = 579 and 567 nm, respectively, upon excitation at λ = 453 nm. The apparent K_d values for Aβ(1-40) fibers were 77 and 294 nM for 1 and 2, respectively. The sensitivity of the aggregates detection assay with these new dyes was higher than that of thioflavin T. Considering their unique fluorescence properties compared to other dyes reported in the field, they can be considered as additional staining tools for the detection and studies of peptide/protein aggregation.     

Iterative algorithm for solving a class of general Sylvester-conjugate matrix equation \sum_{i = 1}^{s} A_{i}V + \sum_{j = 1}^{t} B_{j}W = \sum_{l = 1}^{m} E_{l}\overline{V}F_{l} + C

This paper is concerned with iterative solution to general Sylvester-conjugate matrix equation of the form $\sum_{i = 1}^{s} A_{i}V + \sum_{j = 1}^{t} B_{j}W = \sum_{l = 1}^{m} E_{l}\overline{V}F_{l} + C$ . An iterative algorithm is established to solve this matrix equation. When this matrix equation is consistent, for any initial matrices, the solutions can be obtained within finite iterative steps in the absence of round off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.     

Global bounds of solutions for a strongly coupled system of reaction-diffusion equations

Boundedness results for a strongly coupled system of reaction-diffusion equations on spatially bounded region are proved.     

Degradation and toxicity reduction of textile wastewater using immobilized titania nanophotocatalysis

The feasibility and performance of photocatalytic degradation and toxicity reduction of textile dye (Acid Blue 25) have been studied at pilot scale in an immobilized titania nanoparticle photocatalytic reactor. UV-Vis, Ion Chromatography (IC) and chemical oxygen demand (COD) analyses were employed to obtain the details of the photocatalytic dye degradation. The effects of operational parameters such as H2O2, pH and dye concentration on the photocatalytic degradation of Acid Blue 25 were investigated. The aliphatic carboxylic acid intermediates and inorganic anions generated during the dye degradation process were analyzed. Daphnia magna bioassay has been used to test the progress of toxicity during the treatment process. Total disappearance of dye was attained. During the photocatalytic treatment process, the residual acute toxicity was reduced. The results showed that immobilized titania nanophotocatalysis capable to degradation and toxicity reduction of acid dye textile wastewater.