Comparison of Two Reformulation-Linearization Technique Based Linear Programming Relaxations for Polynomial Programming Problems

In this paper, we compare two strategies for constructing linear programmingrelaxations for polynomial programming problems using aReformulation-Linearization Technique (RLT). RLT involves an automaticreformulation of the problem via the addition of certain nonlinear impliedconstraints that are generated by using the products of the simple boundingrestrictions (among other products), and a subsequent linearization based onvariable redefinitions. We prove that applying RLT directly to the originalpolynomial program produces a bound that dominates in the sense of being atleast as tight as the value obtained when RLT is applied to the jointcollection of all equivalent quadratic problems that could be constructed byrecursively defining additional variables as suggested by Shor.     

The synthesis and fluorescence properties of novel chromenone-crown ethers

o-Dihyroxy-3-phenylchromenone derivatives, namely, 6,7-dihydroxy-3-(3′,4′-dimethoxyphenyl)chromenone and 6,7-dimethoxy-3-(3′,4′-dihydroxyphenyl)chromenone, were obtained from 2,4,5-trihydroxybenzaldehyde/3,4-dimethoxyphenylacetic acid and 2-hydroxy-4,5-dimethoxybenzaldehyde/3,4-dihydroxyphenylacetic acid, respectively, in the presence of acetic anhydride and sodium acetate under an inert atmosphere, after treatment with MeOH/HCl(aq). The chromenone-crown ethers were prepared from cyclic condensation of o-dihydroxy-3-phenylchromenones with poly(ethylene glycol) ditosylates in the presence of CH₃CN/alkali metal carbonates. The chromatographically purified novel chromenone-crown ethers were identified by ¹H NMR, MALDI-TOF mass spectrometry and elemental analysis. The fluorescence and UV–vis spectroscopic properties of the obtained chromenone-crown ethers and their complexes with Li⁺, Na⁺ and K⁺ perchlorate salts were estimated in acetonitrile. The quantum yields of novel chromenone-crown ethers were determined by the comparative method.

     

A string-like self-dual solution of Yang-Mills theory

We attempt to obtain Nielsen-Olesen strings in pure Yang-Mills theory without Higgs scalars. This is inspired by recent work interpreting the Prasad-Sommerfield monopole as a static self-dual Yang-Mills solution in which A₄^a plays the role of the Higgs field. In similar fashion, we make A₃^aA₄^a serve as the two required isovector fields in an ansatz independent of x₃ and x₄. The condition of self-duality results in a single Painlevé equation of the third kind (or equivalently, a radial sinh-Gordon equation in 2 + 0 dimensions), the solution of which determines A_μ^a. We make use of the extensive analysis of the former equation carried out by Wu, McCoy and collaborators in the context of the scaling limit of the two-dimensional Ising model. Their simplest solution yields a flux value of ?2π/e just as in the Nielsen-Olesen model and flux is quantized in multiples of this unit. The string tension (action per unit time per unit distance) diverges as r^?2 (In r)^?2 as r → 0 for the same Wu-McCoy solution.     

Solutions to euclidean gravity for infinitely many instantons

Self-dual solutions to euclidean Einstein equations are obtained by integrating over various configurations of an infinite number of Hawking-Gibbons multi-instantons. The resulting metrics are all stationary and of Bianchi type II (euclidean version). They may be previously unknown solutions. In the weak field approximation one finds related spatially increasing potentials reminiscent of confinement. Following Eguchi and Hanson, self-dual Maxwell fields for the coupled Maxwell-Einstein system are also constructed.     

Theoretical calculations of high-pressure phases of NiF<Subscript>2</Subscript>: An ab initio constant-pressure study

We have studied the structural properties of the antiferromagnetic NiF₂ tetragonal structure with P4₂/mnm symmetry using density functional theory (DFT) under rapid hydrostatic pressure up to 400 GPa. For the exchange correlation energy we used the local density approximation (LDA) of Ceperley and Alder (CA). Two phase transformations are successfully observed through the simulations. The structures of XF₂-type compounds crystallize in rutile-type structure. NiF₂ undergoes phase transformations from the tetragonal rutile-type structure with space group P4₂/mnm to orthorhombic CaCl₂-type structure with space group Pnnm and from this orthorhombic phase to monoclinic structure with space group C2/m at 152 GPa and 360 GPa, respectively. These phase changes are also studied by total energy and enthalpy calculations. According to these calculations, we perdict these phase transformations at about 1.85 and 30 GPa.     

Synthesis and complexation of a novel soluble vic-dioxime with hydroxyethyl pendant arms

A new soluble vic-dioxime ligand namely 1,4-bis(2′-hydroxyethyl)-2,3-bis(hydroxyimino)-5,6-diphenylpiperazine, (LH₂) containing optically active centers has been prepared as a mixture of isomers from (CNO)₂ and N,N-bis(2-hydroxyethyl)stilbendiamine (1) which has been made by the reduction of the condensation of the product of benzaldehyde and 2-aminoethanol in the presence of aluminum amalgam. N,N-coordinated planar metal complexes of this ligand have been synthesized with Ni^II, Cu^II, Co^II, Pd^II and U^VIO₂. Oxidation of (LH)₂Co in the presence of a base, such as pyridine, leads to an octahedral complex (LH)₂CopyCl containing pyridine and chloride as axial ligands in addition to vic-dioxime ligands. The structures of the ligand and its complexes are proposed on the basis of elemental analysis, ¹H-n.m.r., mass, i.r. and u.v.–vis. spectral data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Matrix Summability and Positive Linear Operators

In the present paper we prove a Korovkin type approximation theorem for a sequence of positive linear operators acting from a weighted space C_ρ1 into a weighted space B_ρ2 with the use of a matrix summability method which includes both convergence and almost convergence. We also study the rates of convergence of these operators.     

Electrochemical Determination of Copper(II) in Water Samples Using a Novel Ion-Selective Electrode Based on a Graphite Oxide–Imprinted Polymer Composite

A novel copper(II)-selective electrode based on graphite oxide/imprinted polymer composite was developed for the electrochemical monitoring of copper(II) (Cu²⁺) ions. The electrode exhibited highly selective potentiometric response to Cu²⁺ with respect to common alkaline, alkaline earth and heavy metal cations. The composite composition studies indicated that the most suitable composite composition performing the most promising potentiometric properties was 20.0% ionophore (Cu²⁺-ion imprinted polymer), 10.0% paraffin oil, 5.0% multiwalled carbon nanotubes, and 65.0% graphite oxide. The fabricated electrode exhibited a linear response to Cu²⁺ over the concentration range of 1.0?×?10^??6–1.0?×?10^??1?M (correlation coefficient of 0.9998) with a sensitivity of 26.1?±?0.9?mV decade^??1. The detection limit of the fabricated electrode was determined to be 4.0?×?10^??7?M. The electrode worked well in the pH range of 4.0–8.0. The electrode had stable, reversible and fast potentiometric response (3?s). In addition, the electrode had a lifetime of more than 1 year. The analytical applications of the proposed electrode were performed using as an indicator electrode for the potentiometric titration of Cu²⁺ with ethylene diamine tetraacetic acid solution and for the determination of Cu²⁺ of spiked river, dam, and tap water samples. The obtained results for potentiometric titration and water samples were satisfactory.     

4‐Amino‐3,5‐diethyl‐4H‐1,2,4‐triazole at 100 K: chains of edge‐fused R44(10) and R44(20) rings

The title compound, C₆H₁₂N₄, has four crystallographically independent molecules in the asymmetric unit. Intermolecular N—H...N hydrogen bonds involving amino groups and triazole N atoms form a three‐dimensional framework involving R₄⁴(10) and R₄⁴(20) rings. The hydrogen bonding is supported by weak C—H...π interactions.     

The performance assessment of a refrigeration system which exists on a cargo vessel influenced by seawater-intake temperature

Journal of Thermal Analysis and Calorimetry - The effects of the seawater-intake temperature on the performance of the refrigeration system which exists on a cargo vessel were introduced in this...