Remarks on Nonlinear Schrödinger Equations with Harmonic Potential

Bose-Einstein condensation is usually modeled by nonlinear Schrödinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For the global problem, we establish an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schrödinger equation. With this evolution law, we give wave collapse criteria, as well as an upper bound for the blow up time. Taking the physical scales into account, we finally give a lower bound for the breaking time. This study relies on two explicit operators, suited to nonlinear Schrödinger equations with harmonic potential, already known in the linear setting.     

On the Brownian-directed polymer in a Gaussian random environment

In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong disorder regime under some reasonable assumptions on the spatial covariance of the environment. Some further developments, concerning some concentration inequalities for the partition function, are given for the weak disorder regime.     

Reflection and transmission mid-infrared spectroscopy for rapid determination of coal properties by multivariate analysis

In the present paper, the influence of different acquisition techniques (transmission, diffuse reflectance infrared Fourier transform and attenuated total reflectance) in the determination of nine coal properties related to combustion power plants has been studied. Raw coal samples of different origins were pooled for developing a correlation between the resultant spectra and the corresponding coal properties by multivariate analysis techniques. Thus, the existent collinearity in mid-infrared coal spectra led to the application of partial least squares regression (PLS), studying simultaneously the influence of different spectroscopic units as well as several spectral data mathematical pre-treatments. On the other hand, a principal component analysis (PCA) revealed a relationship between principal components and coal composition in both transmission and reflection techniques. Although the best accuracy and precision results were obtained for coal properties related to organic matter, the system was also able to differentiate coal samples attending to the presence of a specific mineral matter, kaolinite.     

A combined experimental and theoretical study of the molecular inclusion of organometallic sandwich complexes in a cavitand receptor

We describe herein a detailed study of the inclusion processes of several positively charged organometallic sandwich complexes inside the aromatic cavity of the self-folding octaamide cavitand 1. In all cases, the binding process produces aggregates with a simple 1:1 stoichiometry. The resulting inclusion complexes are not only thermodynamically stable, but also kinetically stable on the (1)H NMR spectroscopy timescale. The binding constants for the inclusion complexes were determined by different titration techniques. We have also investigated the kinetics of the binding process and the motion of the metallocenes included in the aromatic cavity of the host. Using DFT-based calculations, we have evaluated the energies of a diverse range of potential binding geometries for the complexes. We then computed the proton chemical shifts of the included guest in each one of the binding geometries. The agreement between the averaged computed values and the experimentally determined chemical shifts clearly supports the proposed binding geometries that we assigned to the inclusion complexes formed in solution. The combination of experimental and theoretical results has allowed us to elucidate the origins of the distinct features detected in the complexation process of the different guests, as well as their different motions inside the host.     

Does Förster theory predict the rate of electronic energy transfer for a model dyad at low temperature?

The use of the F?rster model to predict the dynamics of resonant electronic energy transfer (RET) in a model donor-acceptor dyad (a terphenyl-bridged perylene diimide (PDI)-terrylene diimide (TDI) dyad molecule) embedded at low temperature in a PMMA matrix is tested against experiment. The relevant ingredients involved in the F?rster rate for RET, namely electronic coupling, spectral overlap, and screening effects, are accounted for in a quantitative manner. Electronic couplings are obtained from time-dependent density functional theory calculations, and the effect of the PMMA environment is included both on the transition densities and on their interaction through the IEFPCM model. We find that the presence of the terphenyl bridge induces a slight delocalization of the PDI and TDI transition densities over the bridge originating in a 56% increase in the coupling and in the breakdown of the dipole-dipole approximation. The spectral overlap is determined on the basis of a detailed simulation of the homogeneously broadened donor emission and acceptor absorption line shapes determined by fitting the single molecule spectra measured at 1.2 K. The corresponding distribution of spectral overlap throughout the ensemble is then estimated by assuming an uncorrelated inhomogeneous line broadening for the donor and acceptor. Combining the calculated electronic couplings and spectral overlaps sampled from Monte Carlo realizations of the energetic disorder, we obtain a mean RET time (approximately 8 ps) and a distribution in reasonable agreement with experiment.     

Polynuclear Gold [AuI]4, [AuI]8, and Bimetallic [AuI4AgI] Complexes: C−H Functionalization of Carbonyl Compounds and Homogeneous Carbonylation of Amines

The synthesis of tetranuclear gold complexes, a structurally unprecedented octanuclear complex with a planar [Au^I₈] core, and pentanuclear [Au^I₄M^I] (M=Cu, Ag) complexes is presented. The linear [Au^I₄] complex undergoes C?H functionalization of carbonyl compounds under mild reaction conditions. In addition, [Au^I₄Ag^I] catalyzes the carbonylation of primary amines to form ureas under homogeneous conditions with efficiencies higher than those achieved by gold nanoparticles.     

Dehalogenation of 1,3-diiodotricyclo[3.3.0.0(3,7)]octane: generation of 1,3-dehydrotricyclo[3.3.0.0(3,7)]octane, a 2,5-methano-bridged [2.2.1]propellane

Compounds isolated from the reaction of (+/-)-1,3-diiodotricyclo[3.3.0.0(3,7)]octane with molten sodium or tBuLi suggest the intermediate formation of (+/-)-1,3-dehydrotricyclo[3.3.0.0(3,7)]octane. Worthy of note is the formation of stereoisomeric bi(5-methylenebicyclo[2.2.1]hept-2-ylidene) derivatives, probably by coupling of two units of (+/-)-1,3-dehydrotricyclo[3.3.0.0(3,7)]octane of the same or different absolute configuration followed by fragmentation, processes that have been studied by theoretical calculations.     

Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems

In this paper, we analyze the semilocal convergence of k-steps Newton’s method with frozen first derivative in Banach spaces. The method reaches order of convergence k + 1. By imposing only the assumption that the Fréchet derivative satisfies the Lipschitz continuity, we define appropriate recurrence relations for obtaining the domains of convergence and uniqueness. We also define the accessibility regions for this iterative process in order to guarantee the semilocal convergence and perform a complete study of their efficiency. Our final aim is to apply these theoretical results to solve a special kind of conservative systems.     

Evidence of a broad structure at an invariant mass of 4.32 GeV/c2 in the reaction e+e- --> pi+pi-psi(2S) measured at BABAR

We present a measurement of the cross section of the process e(+)e(-)-->pi(+)pi(-)psi(2S) from threshold up to 8 GeV center-of-mass energy using events containing initial-state radiation, produced at the SLAC PEP-II e(+)e(-) storage rings. The study is based on 298 fb(-1) of data recorded with the BABAR detector. A structure is observed in the cross section not far above threshold, near 4.32 GeV. We also investigate the compatibility of this structure with the Y(4260) previously reported by this experiment.