Convergence of an Exact Quantization Scheme

It has been shown by Voros [V1] that the spectrum of the one-dimensional homogeneous anharmonic oscillator (Schrödinger operator with potential q^2M, M=2,3,...) is a fixed point of an explicit non-linear transformation. We show that this fixed point is globally and exponentially attractive in spaces of properly normalized sequences.Partially supported by Faperj and CNPq, BrazilCurrent address:Laboratoire de Probabilités et Modéles aléatoires, Université Pierre et Marie Curie–Boi te courrier 188, 75252–Paris Cedex 05, France. E-mail: artur@ccr.jussieu.fr     

State selective production of molecules in optical lattices

We demonstrate quantum control over both internal and external quantum degrees of freedom in a high number of identical "chemical reactions," carried out in an array of microtraps in a 3D optical lattice. Starting from a Mott insulating phase of an ultracold atomic quantum gas, we use two-photon Raman transitions to create molecules on lattice sites occupied by two atoms. In the atom-molecule conversion process, we can control both the internal rovibronic and external center of mass quantum state of the molecules. The lattice isolates the microscopic chemical reactions from each other, thereby allowing photoassociation spectra without collisional broadening even at high densities of up to 2 x 10(15) cm(-3).     

Does the Boltzmann Principle Need a Dynamical Correction?

In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived (M. Bianucci, R. Mannella, B. J. West and P. Grigolini, Phys. Rev. E 51: 3002 (1995)) which differs from the one that follows from the Boltzmann principle S = kln(E) via the thermodynamic relation 1/T=S / E by additional terms of dynamical character, which are argued to correct and generalize the Boltzmann principle for small systems (here (E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker–Planck formalism of Bianucci et al., is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the volume entropy S = k ln (E) via the thermodynamic relation above for systems of any number of degrees of freedom ((E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al., and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain (N~10) of quartic oscillators are also provided to further illustrate these facts.     

Two countably compact topological groups: One of size and the other of weight without non-trivial convergent sequences

E. K. van Douwen asked in 1980 whether the cardinality of a countably compact group must have uncountable cofinality in . He had shown that this was true under GCH. We answer his question in the negative. V. I. Malykhin and L. B. Shapiro showed in 1985 that under GCH the weight of a pseudocompact group without non-trivial convergent sequences cannot have countable cofinality and showed that there is a forcing model in which there exists a pseudocompact group without non-trivial convergent sequences whose weight is . We show that it is consistent that there exists a countably compact group without non-trivial convergent sequences whose weight is .

     

Structural and surface analysis of thin-film ZnTe formed with pulsed-laser deposition

Nanosecond pulses of a Nd:YAG laser have been employed to deposit thin-film zinc telluride (ZnTe) on silicon (Si) and glass without heating these substrates. We present and discuss the structural and surface properties of films deposited at 1064 nm and 532 nm. X-ray diffraction and analysis of the surface roughness with atomic force microscopy reveal that the material texture and surface morphology depend on the ablation laser line used rather than on the substrate. The observations contribute to improved understanding of pulsed-laser deposition and provide tools to optimize the optoelectronic and photonic properties of ZnTe thin-films as well as their incorporation into Si-based technologies in order to fabricate cost-effective and functional optoelectronic devices and all-optical laser digitizer.     

Interpolating Blaschke products solving Pick-Nevanlinna problems

We study when a Pick-Nevanlinna problem with more than one solution can be solved by an interpolating Blaschke product. Supported in part by the grant PB85-0374 of the CYCIT, Ministerio de Educación y Ciencia, Spain.     

Closures of finitely generated ideals in Hardy spaces

LetH ^∞ be the algebra of bounded analytic functions in the unit diskD. LetI=I(f ₁,...,f _N) be the ideal generated byf ₁,...,f _N∈H ^∞ andJ=J(f ₁,...,f _N) the ideal of the functionsf∈H ^∞ for which there exists a constantC=C(f) such that |f(z)|≤C(|f ₁ (z)|+...;+|f _N (z)|),z∈D. It is clear that , but an example due to J. Bourgain shows thatJ is not, in general, in the norm closure ofI. Our first result asserts thatJ is included in the norm closure ofI ifI contains a Carleson-Newman Blaschke product, or equivalently, if there existss>0 such that

Impact of the interaction with the positive charge in adsorption of benzene and other organic compounds from aqueous solutions on carbons

We present the results of benzene adsorption at the acidic pH level determined on the series of chemically modified activated carbons and at three temperatures. The influence of carbon surface chemical composition on benzene adsorption is discussed. It is shown that the decrease in the pH level from 7 up to 1.5 increases benzene adsorption and the only exception is carbon modified with gaseous ammonia. Basing on the results of current work and those published previously (for phenol, paracetamol, acetanilide and aniline) and using the results of quantum chemistry calculations (DFT, Gaussian 98) we show, that the value of the energy of interaction with unit positive charge is crucial during the analysis of the influence of pH level on adsorption. Obtained results allow to predict the changes in adsorption of aromatics on carbons with the decrease in the pH level.     

Salmon (Salmo salar) Cooking: Achieving Optimal Quality on Select Nutritional and Microbiological Safety Characteristics for Ready-to-Eat and Stored Products

This study was performed in order to assess technological characteristics, proximate composition, fatty acids profile, and microbiological safety of sous-vide processed salmon in comparison with steaming and roasting. The cooking loss was lower in the sous-vide method (6.3–9.1%) than in conventional methods (11.6–16.2%). The preparation of salmon using sous-vide was more time- and energy-consuming than steaming. The dry matter content of the salmon fillets was higher in conventionally processed samples than sous-vide due to the evaporation of water, and it was connected with total protein (r = 0.85) and lipid content (r = 0.73). Analysis of the fatty acids profile only revealed significant differences in six fatty acids. All of the heat treatment methods ensured microbiological safety with regard to coagulase-positive Staphylococcus, E. coli, Listeria monocytogenes, and Salmonella spp. However, in sous-vide (57 °C, 20 min) and steamed samples after storage Enterobacteriaceae bacteria (<10⁴) was detected. Summing up, high parameters of sous-vide salmon cooking, when considering both technological parameters, nutritional value, and microbiological status should be recommended.