Sparsity in sums of squares of polynomials

Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and semidefinite programming (SDP) relaxation of polynomial optimization problems. We discuss effective methods to obtain a simpler representation of a sparse polynomial as a sum of squares of sparse polynomials by eliminating redundancy.A considerable part of this work was conducted while this author was visiting Tokyo Institute of Technology. Research supported by Kosef R004-000-2001-00200Mathematics Subject Classification (1991): 90C22, 90C26, 90C30     

Determination of sulphate in natural water by flow-injection analysis

Summary Sulphate was determined in natural water samples by flow-injection analysis using dimethylsulphonazo-III as reagent. The interference by Ca was eliminated by a cation-exchanger column inserted directly after the sample injection valve. In order to ensure high sensitivity and reproducibility it was necessary to saturate the carrier solution with barium sulphate and to fill the reaction coil with ethanol-water (11) when not in use. Standard deviations were 0.94–1.2% for 6–10mg/l sulphate. The limit of detection was about 0.2mg/l. The calibration graph was linear up to 14mg/l Mg²⁺, NH ₄ ⁺ , Na⁺, K⁺, Cl^–, NO ₃ ^– , PO ₄ ^3– , HCO ₃ ^– and SiO ₃ ^2– did not interfere in the normally occurring concentrations.

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Sulfatbestimmung in natürlichem Wasser durch Flow-Injection-Analyse

Zusammenfassung Als Reagens dient Dimethylsulfonazo-III. Die Störung durch Calcium bei dieser Bestimmung wird durch eine Kationenaustauschersäule eliminiert, die direkt nach dem Probeinjektions-Ventil angeordnet ist. Zur Erhöhung der Empfindlichkeit und Reproduzierbarkeit ist es notwendig, die Trägerlösung mit Bariumsulfat zu sättigen sowie bei Nichtbenutzung des Systems den Reaktionsteil mit Ethanol-Wasser (11) zu füllen. Mit dem so modifizierten Verfahren ergaben sich Standardabweichungen von 0,94–1,2% für 6–10 mg/l Sulfat, die Nachweisgrenze liegt bei 0,2 mg/l. Die Eichkurve ist bis 14 mg/l linear. Mg²⁺, NH ₄ ⁺ , Na⁺, K⁺, Cl^–, NO ₃ ^– , PO ₄ ^3– , HCO ₃ ^– und SiO ₃ ^2– stören in den normalerweise vorkommenden Konzentrationen nicht.

     

On a functional integral approach to the Dixon-Israel theory of covariant superfluid mechanics

We have found a functional expression foe the pressure of a non-relativistic superfluid, which supports the equation of state given by Israel.     

Nondegenerate -biresolving textile systems and expansive automorphisms of onesided full shifts

We study nondegenerate, -biresolving textile systems and using properties of them, we prove a conjecture of Boyle and Maass on arithmetic constraints for expansive automorphisms of onesided full shifts and positively expansive endomorphisms of mixing topological Markov shifts. A similar result is also obtained for expansive leftmost-permutive endomorphisms of onesided full shifts.

     

Green polymers from Geobacillus thermodenitrificans DSM465--candidates for molecularly imprinted materials

Novel molecular recognition materials were prepared from water soluble proteins from thermophile G. thermodenitrificans DSM465 by an alternative molecular imprinting method. Water soluble proteins from G. thermodenitrificans DSM465 were converted into the molecularly imprinted materials by adopting 9-EA as a print molecule. The molecularly imprinted protein membranes recognized As in preference to Gs. The adsorption isotherms led to the conclusion that molecular recognition sites toward As were constructed by the presence of 9-EA during the membrane preparation process. The affinity constant between As and the molecular recognition site thus constructed was determined to be 1.75 x 10(5) mol(-1) dm(3). The results obtained in the present study suggest that water soluble proteins from G. thermodenitrificans DSM465 is one of environmentally-friendly 'green' polymers to be converted into molecular recognition materials by applying an alternative molecular imprinting method.     

Picosecond IR-UV pump-probe study on the vibrational relaxation of phenol-ethylene hydrogen-bonded cluster: difference of relaxation route/rate between the donor and the acceptor site excitations

Picosecond time-resolved IR-UV pump-probe spectroscopy has been performed to study intracluster vibrational energy redistribution (ICVR) and vibrational predissociation (VP) for the OH and CH stretch vibrations of phenol-ethylene hydrogen-bonded cluster. The transient UV spectra after the picosecond IR pulse excitation of these modes were observed by 1+1 REMPI via S(1) with a picosecond UV pulse. We have focused on the difference of the energy flow routes and their rates between the donor (phenol) and the acceptor (ethylene) site. Though the transient UV spectra showed a similar broad feature for all the vibrations examined, the time profiles exhibited a remarkable site dependence, as well as substantial mode dependence. Especially, we found a large difference in the early stage of the IVR evolution and the rates, whereas the VP rates were very similar.     

Collision-energy-resolved penning ionization electron spectroscopy of phenylacetylene and diphenylacetylene by collision with He*(2(3)s) metastable atoms

Penning ionization of phenylacetylene and diphenylacetylene upon collision with metastable He*(2(3)S) atoms was studied by collision-energy-/electron-energy-resolved two-dimensional Penning ionization electron spectroscopy (2D-PIES). On the basis of the collision energy dependence of partial ionization cross-sections (CEDPICS) obtained from 2D-PIES as well as ab initio molecular orbital calculations for the approach of a metastable atom to the target molecule, anisotropy of interaction between the target molecule and He*(2(3)S) was investigated. For the calculations of interaction potential, a Li(2(2)S) atom was used in place of He*(2(3)S) metastable atom because of its well-known interaction behavior with various targets. The results indicate that attractive potentials localize in the pi regions of the phenyl groups as well as in the pi-conjugated regions of the acetylene group. Although similar attractive interactions were also found by the observation of CEDPICS for ionization of all pi MOs localized at the C[triple bond]C bond, the in-plane regions have repulsive potentials. Rotation of the phenyl groups about the C[triple bond]C bond can be observed for diphenylacetylene because of a low torsion barrier. So the examination of measured PIES was performed taking into consideration the change of ionization energies for conjugated molecular orbitals.     

Integral averaging technique for oscillation of damped half-linear oscillators

This paper is concerned with the oscillatory behavior of the damped half-linear oscillator (a(t)?_p(x′))′ + b(t)?_p(x′) + c(t)?_p(x) = 0, where ?p(x) = |x|^p?1 sgn x for x ∈ ? and p > 1. A sufficient condition is established for oscillation of all nontrivial solutions of the damped half-linear oscillator under the integral averaging conditions. The main result can be given by using a generalized Young’s inequality and the Riccati type technique. Some examples are included to illustrate the result. Especially, an example which asserts that all nontrivial solutions are oscillatory if and only if p ≠ 2 is presented.     

Solving polynomial least squares problems via semidefinite programming relaxations

A polynomial optimization problem whose objective function is represented as a sum of positive and even powers of polynomials, called a polynomial least squares problem, is considered. Methods to transform a polynomial least square problem to polynomial semidefinite programs to reduce degrees of the polynomials are discussed. Computational efficiency of solving the original polynomial least squares problem and the transformed polynomial semidefinite programs is compared. Numerical results on selected polynomial least square problems show better computational performance of a transformed polynomial semidefinite program, especially when degrees of the polynomials are larger.