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.

     

Synthesis, characterization, and biological evaluation of new oxime-phosphazenes

Hexachlorocylotriphosphazene (1) was reacted with 4-hydroxy-3-methoxybenzaldehyde to give hexakis[(4-formyl-2-methoxy)phenoxy]cyclotriphosphazene (2). Hexakis[(4-(hydroxyimino)2-methoxy)phenoxy]cyclotriphosphazene (3) was synthesized by reaction of 2 with hydroxlamine hydrochloride in pyridine. Compound 3 was reacted with benzyl chloride, acetyl chloride, allyl bromide, benzoyl chloride, propanoyl chloride, 4-methoxybenzoyl chloride, 2-chlorobenzoyl chloride, chloroacetyl chloride, methyl iodide, and thiophene-2-carbonyl chloride. From these reactions, full or partially substituted compounds were obtained, usually in high yields. Pure or defined products could not be obtained from reaction of 3 with methacryloyl chloride and O-acetylsalicyloyl chloride. The structures of the compounds were determined by elemental analysis, and IR, ¹H, ¹³C, and ³¹P NMR spectroscopy. The synthesized compounds were screened for in-vitro antimicrobial activity against two Gram-positive bacteria (Staphylococcus aureus and Enterococcus faecalis), two gram-negative bacteria (Escherichia coli and Klebsiella pneumonia), and fungal strains (Aspergillus niger, and Candida albicans) by the agar well diffusion method. Few compounds had significant activity against both Gram-positive and Gram-negative bacteria. None of the compounds had antifungal activity except compounds 7 and 9, which had moderate activity.     

Identification of radiation‐induced radical structure in azocalix[4]arene: an EPR study

A macrocyclic azocalix[4]arene (1) based ester derivative was synthesized. The single crystals of azocalix[4]arene were produced by slow evaporation of concentrated ethyl acetate solutions. These single crystals were exposed to ⁶⁰Co gamma rays with a dose rate of 0.980 kGy h^‐1 for 48 and 72 h to produce a stable free radical. Electron paramagnetic resonance (EPR) measurements were performed in three mutually perpendicular planes of the single crystal in the magnetic field, in addition, temperature dependence of the EPR signal was studied between 120 K and 450 K. The spectra were found to be temperature and angular dependent. Analysis based on the spectra recorded showed that a free radical was formed by fission of a C–H bond. This radical is described as ^?C_aHC_bH₃ The averages of the principal values of the hyperfine parameters and g‐factor are: g = 2.0034, A_Ha = 1.28 mT, A_H1=H2 = 1.00 mT, and A_H3 = 0.49 mT. Copyright © 2013 John Wiley & Sons, Ltd.     

Quantum chemical computational studies on 5-(4-bromophenylamino)-2-methylsulfanylmethyl-2H-1,2,3-triazol-4-carboxylic acid ethyl ester

The optimized molecular geometry, vibrational frequencies, and gauge including atomic orbital (GIAO) (1)H and (13)C NMR shift values of 5-(4-bromophenylamino)-2-methylsulfanylmethyl-2H-1,2,3-triazol-4-carboxylic acid ethyl ester have been calculated by using Hartree-Fock (HF) and density functional method (DFT/B3LYP) with 6-31G(d), 6-31G(d,p) and LANL2DZ basis sets. The optimized molecular geometric parameters were presented and compared with the data obtained from X-ray diffraction. In order to fit the calculated harmonic wavenumbers to the experimentally observed ones, scaled quantum mechanics force field (SQM FF) methodology was proceeded. Correlation factors between the experimental and calculated (1)H chemical shift values of the title compound in vacuum and in CHCl(3) solution by using the conductor-like screening continuum solvation model (COSMO) were reported. The calculated results showed that the optimized geometry well reproduces the crystal structure. The theoretical vibrational frequencies and chemical shifts are in very good agreement with the experimental data. In solvent media the energetic behavior of the title compound was also examined by using the B3LYP method with the 6-31G(d) basis set, applying the COSMO model. The obtained results indicated that the total energy of the title compound decreases with increasing polarity of the solvent. Furthermore, molecular electrostatic potential (MEP), natural bond orbital (NBO) and frontier molecular orbitals (FMOs) of the title compound were performed by the B3LYP/LANL2DZ method, and also thermodynamic parameters for the title compound were calculated at all the HF and B3LYP levels.     

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.     

Complete mapping of the morphologies of some linear and graft fluorinated co-oligomers in an aprotic solvent by dissipative particle dynamics

The mesoscopic morphologies of linear and graft fluorinated block copolymers of ABCBA and C:BA types, respectively, have been investigated by using dissipative particle dynamics method. Self-assembly in a selective solvent has been examined by the introduction of dimethylformamide as the choice of solvent. By comparing the solubility parameters calculated using atomistic simulations, fluorine-containing segments are found to be immiscible both with other segments of the polymer and with the solvent. Morphologies of the pure linear and graft copolymers were lamellar and cylindrical, respectively. Interfacial tension versus concentration curves have been used to explain the self-assembly behavior of copolymers in solution, as well as to predict the kinetic mechanisms responsible for this behavior.     

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.