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.

     

Stacking of triphenylene: characterization of the potential energy surface

The interaction potential energy of triphenylene dimer has been calculated with Møller–Plesset second-order perturbation theory for various geometrical configurations. Different types of geometrical perturbations such as rotation, displacements and their combinations are studied in terms of their effects on the stability of the dimer. Minimum energy conformers for face to face, rotated, parallel displaced and T-shape structures are obtained. For the unsubstituted triphenylene, the 35° rotation of one of the monomers results in the global minimum. However, the dimer is still very flexible in terms of displacements. A helical structure seems to be the most stable form for the trimer. For large stacked clusters, the two body forces dominate the interactions while at small monomer–monomer separation, three body terms behave like z ^?9 where z is the vertical distance between two adjacent monomers.     

Interferometry with entangled atoms

A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser beam. The laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two, motion-sensitive, phase shifts, which allow the measurement of the average acceleration of each ensemble, and, via simple differencing, of the acceleration gradient. Here we propose entangling the quantum states of atoms from the two ensembles prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase which can be measured directly, with no need for differencing. Received 6 June 2002 / Received in final form 25 October 2002 Published online 28 January 2003     

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.     

Comments on “A more precise statement of Hamilton's principle”

Among the problems C. D. Bailey has questioned in a recent paper (Ref. 1) are a precise and general formulation of Hamilton's variational principle and the establishment of a sufficiency criterion for this to be a minimum principle. In this paper, we will try to answer these questions using the geometric theory of classical mechanics.     

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.