A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization

 In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The algorithm's distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according to the factorization X=RR ^T . The rank of the factorization, i.e., the number of columns of R, is chosen minimally so as to enhance computational speed while maintaining equivalence with the SDP. Fundamental results concerning the convergence of the algorithm are derived, and encouraging computational results on some large-scale test problems are also presented. Received: March 22, 2001 / Accepted: August 30, 2002 Published online: December 9, 2002 Key Words. semidefinite programming – low-rank factorization – nonlinear programming – augmented Lagrangian – limited memory BFGS This research was supported in part by the National Science Foundation under grants CCR-9902010, INT-9910084, CCR-0203426 and CCR-0203113     

Modeling the Adsorption of CO on Small Pt,Fe and Co Clusters for the Fischer–Tropsch Synthesis

The adsorption of CO on Fe, Pt and Co clusters was modeled by the DFT approach using the B3LYP and the BPW91 functionals together with the LANL2DZ and the 6-31G(d) basis set. These calculations show that although CO adsorbs more strongly on Pt than on either Fe or Co, the dissociation energy on Fe and on Co is lower than the corresponding dissociation energy on Pt. Therefore, the activation energy for dissociation is not determined by the adsorption energy. Additionaly, the CO bond distances also do not show any correlation to the adsorption energy.     

Synthesis of linear and 4‐arm star block copolymers of poly(methyl acrylate‐b‐solketal acrylate) by SET‐LRP at 25 °C

The new SET‐LRP (using Cu(0) powder for organic synthesis) was successfully used to produce well‐defined linear and star homo‐ and diblock‐copolymers of PMA, PSA, and P(MA‐b‐GA)_n (where n = 1 or 4). The kinetic data showed that all SET‐LRP were first order and reached high conversions in a short period of time. The other advantage of using such a system is that the copper can easily be removed through filtration, allowing the production of highly pure polymer. The molecular weight distributions were well controlled with polydispersity indexes below 1.1 and the number‐average molecular weight close to theory, especially upon the addition of Cu(II)Br₂/Me₆‐TREN complex. The linear and star block copolymers were then hydrolyzed to produce the biocompatible amphiphilic P(MA‐b‐GA)_n, where the glycerol side‐groups make the outer block hydrophilic. These blocks were micellized into water and found to have a R_g/R_H equal to 0.8 and 1.59 for the liner and star blocks, respectively. This together with the TEM's supported that the linear blocks formed the classical core‐shell micelles, where as, the star blocks formed vesicles. We found direct support for the vesicle structure from a TEM where one vesicle squashed a second vesicle consistent with a hollow structure. Such vesicle structures have potential applications as delivery nanoscaled devices for drugs and other important biomolecules. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6346–6357, 2008     

Algèbres de Boole monadiques libres

Sans résumé Presented by A. Horn.     

Optical and spectroscopic properties of germanotellurite glasses

In this work, new glass compositions in the TeO₂-GeO₂-Nb₂O₅-K₂O system have been prepared and studied. The germanotellurite glasses were prepared by melt-quenching and their density, refractive index and characteristic temperatures have been determined. The structure of these glasses has been studied by infrared and Raman spectroscopies.The progressive replacement of TeO₂ by GeO₂ led to an increase of the glass transition and crystallisation temperatures of the glasses and a simultaneous decrease of their density and refractive index. Typical density and refractive index values of these glasses ranged from 4.98 to 3.85 g cm^− 3 and 2.08 to 1.79, respectively, with increasing GeO₂ content. The infrared spectra are dominated by a band ~ 640 cm^− 1 in the tellurite glass and ~ 800 cm^− 1 in the germanate glass. The Raman spectra of the germanotellurite glasses present an intense boson peak between ~ 34 and 47 cm^− 1, together with high frequency peaks at ~ 670 cm^− 1 and ~ 470 cm^− 1 for high tellurite and high germanate glass compositions, respectively. The vibrational spectra of these germanotellurite glasses indicate that the glass network consists basically of TeO₄ and [TeO₃]/[TeO_3 + 1] units, mixed with GeO₄ and NbO₆ polyhedra.     

Black hole particle emission in higher-dimensional spacetimes

In models with extra dimensions, a black hole evaporates both in the bulk and on the visible brane, where standard model fields live. The exact emissivities of each particle species are needed to determine how the black hole decay proceeds. We compute and discuss the absorption cross sections, the relative emissivities, and the total power output of all known fields in the evaporation phase. Graviton emissivity is highly enhanced as the spacetime dimensionality increases. Therefore, a black hole loses a significant fraction of its mass in the bulk. This result has important consequences for the phenomenology of black holes in models with extra dimensions and black hole detection in particle colliders.     

Catalytic properties of the dioxomolybdenum siloxide MoO2(OSiPh3)2 and its 2,2'-bipyridine adduct MoO2(OSiPh3)2(bpy)

The tetrahedral triphenylsiloxy complex MoO(2)(OSiPh(3))(2) (1) and its Lewis base adduct with 2,2'-bipyridine, MoO(2)(OSiPh(3))(2)(bpy) (2), were prepared and characterised by IR/Raman spectroscopy, and thermogravimetric analysis. Both compounds catalyse the epoxidation of cis-cyclooctene at 55 degrees C using tert-butylhydroperoxide (t-BuOOH) is decane as the oxidant, giving 1,2-epoxycyclooctane as the only product. The best results were obtained in the absence of a co-solvent (other than the decane) or in the presence of 1,2-dichloroethane, while much lower activities were obtained when hexane or acetonitrile were added. With no co-solvent, catalyst 1 (initial activity 272 mol x molMo(-1) x h(-1)for a catalyst:substrate: oxidant molar ratio of 1:100:150) is much more active than 2(initial activity 12 mol x molMo(-1) x h(-1)). The initial reaction rates showed first order dependence with respect to the initial concentration of olefin. With respect to the initial amount of oxidant, the rate order dependence for 1 (1.9) was higher than that for 2 (1.6).The dependence of the initial reaction rate on reaction temperature and initial amount of catalyst was also studied for both catalysts. The lower apparent activation energy of 1 (11 kcal x mol(-1)) as compared with 2 (20 kcal x mol(-1)) is in accordance with the higher activity of the former.     

A synthetic entry to furo[2,3-b]pyridin-4(1H)-ones and related furoquinolinones via iodocyclization

[reaction: see text] N-Methyl-4-alkoxy-3-alkynylpyridin-2(1H)-ones readily undergo iodine-promoted 5-endo-heteroannulation under mild conditions to 3-iodofuropyridinium triiodide salts in moderate to good yields. The latter may be dealkylated in situ upon exposure to an iodide anion to provide the corresponding 3-iodofuro[2,3-b]pyridin-4(1H)-ones. The same strategy applies to the formation of furo[2,3-b]quinolin-4(9H)-ones.     

Black hole bombs and explosions: from astrophysics to particle physics

Black holes are the elementary particles of gravity, the final state of sufficiently massive stars and of energetic collisions. With a 40-year long history, black hole physics is a fully-blossomed field which promises to embrace several branches of theoretical physics. Here I review the main developments in highly dynamical black holes with an emphasis on high energy black hole collisions and probes of particle physics via superradiance. This write-up, rather than being a collection of well known results, is intended to highlight open issues and the most intriguing results.