The Newton Bracketing Method for Convex Minimization

An iterative method for the minimization of convex functions f :ⁿ , called a Newton Bracketing (NB) method, is presented. The NB method proceeds by using Newton iterations to improve upper and lower bounds on the minimum value. The NB method is valid for n = 1, and in some cases for n > 1 (sufficient conditions given here). The NB method is applied to large scale Fermat–Weber location problems.     

Sonochemical preparation of GaSb nanoparticles

A room temperature sonochemical method for the preparation of GaSb nanoparticles using less hazardous Ga and antimony chloride (SbCl(3)) as the precursors has been described. The formation of GaSb has been confirmed by means of XRD, EDAX, and XPS characterization. TEM and SAED results show that the as-prepared solid consists of nanosized GaSb crystals with sizes in the range 20-30 nm. The photoacoustic spectrum result reveals that the GaSb nanoparticles have a direct band gap of about 1.21 eV. On the basis of the control experiments and the extreme conditions produced by ultrasound, an ultrasound-assisted in-situ reduction/combination mechanism has been proposed to explain the reaction.     

Release of nitrosating species in the course of reduction of benzo-1,2,3,4-tetrazine 1,3-dioxides

[reaction: see text] The reduction of benzo-1,2,3,4-tetrazine 1,3-dioxides (BTDOs) 1 with Na(2)S(2)O(4) or SnCl(2) is suggested to proceed via intermediate N-nitrosobenzotriazoles 3 to afford benzotriazoles 2. The (15)N-labeling experiments exhibit that the N-3 atom of the tetrazine ring is incorporated into the nitroso group of 3 that is ultimately released into solution. It is possible that the biological activity of BTDOs is due to their ability to release nitrosating species, i.e., N-nitrosotriazol 3 or HNO(2), in the course of reduction.     

Universal scaling in transient creep

We present experimental evidence that pressure solution creep does not establish a steady-state interface microstructure as previously thought. Conversely, pressure solution controlled strain and the characteristic length scale of interface microstructures grow as the cubic root of time. Transient creep with the same scaling is known in metallurgy (Andrade creep). The apparent universal scaling of pressure solution transient creep is explained using an analogy with spinodal dewetting.     

Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

The phase diagram of a polydisperse mixture of uniaxial rodlike and platelike hard parallelepipeds is determined for aspect ratios kappa=5 and 15. All particles have equal volume, and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for kappa=15, but to be unstable against demixing into two uniaxial nematics for kappa=5. The phase diagram for kappa=15 is qualitatively similar to that of the binary mixture, regardless of the amount of polydispersity, while for kappa=5 a sufficient amount of polydispersity stabilizes the biaxial phase. This provides clues for designing an experiment to observe this long searched biaxial phase.     

Self-written waveguides in photopolymerizable resins

We study the optically induced growth and interaction of self-written waveguides in a photopolymerizable resin. We investigate experimentally how the interaction depends on the mutual coherence and the relative power of the input beams and suggest an improved analytical model that describes the growth of single waveguides and the main features of their interaction in photosensitive materials.     

Classical Limits of Euclidean Gibbs States for Quantum Lattice Models

Models of quantum and classical particles on a lattice ^d are considered. The classical model is obtained from the corresponding quantum model when the reduced mass of the particle m = / #x210F;² tends to infinity. For these models, the convergence of the Euclidean Gibbs states, when m + , is described in terms of the weak convergence of local Gibbs specifications, determined by conditional Gibbs measures. In fact, it is shown that all conditional Gibbs measures of the quantum model weakly converge to the conditional Gibbs measures of the classical model. A similar convergence of the periodic Gibbs measures and, as a result, of the order parameters, for such models with pair interactions possessing the translation invariance, has also been shown.     

Pi-envelopes of Lie superalgebras

In this paper we find necessary and sufficient conditions on a finite-dimensional Lie superalgebra under which any associative PI-envelope of is finite-dimensional. We also extend M. Scheunert's result which enables one to pass from color Lie superalgebras to the ordinary ones, to the case of gradings by an arbitrary abelian group.