Multivariate design

In multivariate data analysis such as principal components analysis (PCA) and projections to latent structures (PLS), it is essential that the training set systems (objects) are selected to provide data with substantial information for model parametrization, and to represent properly any future situations where the multilvariate model is used for predictions. In the framework of multivariate projections (PCA, SIMCA and PLS), elementary concepts of statistical design (fractional factorials and composite designs) can be used with the latent variables (PC or PLS scores) as design variables. The plan of action thus becomes: (1) problem formulation (specify aim and model, make a conceptual division of the investigated system into subsystems); (2) collection of multivariate data for each type of subsystems; (3) estimation of the practical dimensionality of the data for each type of subsystems by PC or PLS analysis; (4) use of the PC or PLS scores (t) as design variables in the combination of subsystems to systems in the training set; (5) measurement of responses (Y); (6) analysis of data by PCA or PLS; (7) interpretation of results with possible feedback to steps 1, 2 or 3. The procedures are illustrated by two problems: a structure/activity relationship for a family of peptides, and optimization of an organic synthesis with respect to system variables (solvent, substrate, co-reactant_) and process variables (temperature, reactant concentrations).     

Charged particle multiplicity distributions at 200 and 900 GeV c.m. energy

Multiplicity distributions of charged particles produced in non single-diffractive collisions between protons and antiprotons at centre of mass energies of 200 and 900 GeV are presented. The data were recorded in the UA5 streamer chambers at the CERN Collider, which was operated in a pulsed mode between the two energies. A new method to correct for acceptance limitations and inefficiencies based on the principle of maximum entropy has been used. Multiplicity distributions in full phase space and in intervals of pseudorapidity are presented in tabular form. The violation of KNO scaling in full phase space found by the UA5 group at an energy of 546 GeV is confirmed also at 200 and 900 GeV. The shape of the 900 GeV distribution in full phase space is narrower in the peak region than at 200 GeV but exhibits a pronounced high multiplicity tail. The negative binomial distribution fits data at 200 GeV in all pseudorapidity intervals and in small intervals at 900 GeV. In large intervals at 900 GeV, however, the negative binomial distribution. Fits to the partially coherent laser distribution are also presented as well as comparisons with predictions of the Dual Parton, the Fritiof and the Pythia models.     

On the existence of catching-up optimal solutions for Lagrange problems defined on unbounded intervals

In this paper, we are concerned with the question of the existence of optimal solutions for infinite-horizon optimal control problems of Lagrange type. In such problems, the objective or cost functional is described by an improper integral. As dictated by applications arising in mathematical economics, we do nota priori assume that this improper integral converges. This leads us to consider a weaker type of optimality, known as catching-up optimality. The results presented here utilize the classical convexity and seminormality conditions typically imposed in the existence theory for the case of finite intervals. These conditions are significantly weaker than those imposed by other authors; as a consequence, their existence results are contained as special cases of the results presented here. The method of proof utilizes the Carathéodory-Hamilton-Jacobi theory previously developed by the author for infinite-horizon optimal control problems.This research forms part of the author's doctoral dissertation written at the University of Delaware, Newark, Delaware under the supervision of Professor T. S. Angell.     

Force-Free States, Relative Strain, and Soft Elasticity in Nematic Elastomers

The remarkable ability of nematic elastomers to exhibit large deformations under small applied forces is known as soft elasticity. The recently proposed neo-classical free-energy density for nematic elastomers, derived by molecular-statistical arguments, has been used to model soft elasticity. In particular, the neo-classical free-energy density allows for a continuous spectrum of equilibria, which implies that deformations may occur in the complete absence of force and energy cost. Here we study the notion of force-free states in the context of a continuum theory of nematic elastomers that allows for isotropy, uniaxiality, and biaxiality of the polymer microstructure. Within that theory, the neo-classical free-energy density is an example of a free-energy density function that depends on the deformation gradient only through a nonlinear strain measure associated with the deformation of the polymer microstructure relative to the macroscopic continuum. Among the force-free states for a nematic elastomer described by the neo-classical free energy density, there is, in particular, a continuous spectrum of states parameterized by a pair of tensors that allows for soft deformations. In these force-free states the polymer microstructure is material in the sense that it stretches and rotates with the macroscopic continuum. Limitations of and possible improvements upon the neo-classical model are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A dimeric aluminium hydroxide supported by a new disiloxide ligand

The synthesis and structure of a dimeric aluminium hydroxide complex containing the novel chelating 1,4-disiloxide ligand [CH(2){Me(Me(3)Si)(2)Si}(2)SiO](2)(2-) (2)-2H is reported. [CH(2){Me(Me(3)Si)(2)Si}(2)SiO](2)AlOH (4) was prepared by careful hydrolysis of [CH(2){Me(Me(3)Si)(2)Si}(2)SiO](2)AlMe·THF (3).     

Intracavity ionization and pulse formation in femtosecond enhancement cavities

We experimentally and numerically investigate the intracavity ionization of a dilute gas target by an ultrashort pulse inside a femtosecond enhancement cavity. Numerical simulations detail how the dynamic ionization of the gas target limits the achievable peak intensity of the evolving intracavity pulse beyond that of linear cavity losses, setting a constraint on the strength of the nonlinear interaction that can be sustained in such optical cavities. Experimental measurements combined with numerical simulations predict ionization levels in a femtosecond enhancement cavity for the first time. We demonstrate how the resonant response of the femtosecond enhancement cavity can itself be used as a sensitive probe of optical nonlinearities at high intensities.     

Stress-energy tensor for a massless spin 1/2 field in static black hole spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static nonrotating black holes, corresponding to the Schwarzschild, Reissner-Nordstr?m, and extreme Reissner-Nordstr?m solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress energy differs even in sign from the analytic approximation. For the Reissner-Nordstr?m and extreme Reissner-Nordstr?m solutions, divergences predicted by the analytic approximations are shown not to exist.     

Day-side auroral signatures based on simultaneous, coordinatedobservations at Svalbard and Greenland

The height distribution of the dayside cusp aurora and the relation between optical emissions and net downward electron energy flux are discussed. These two important characteristics of day-side cusp aurora are still unknown. It is instructive to compare particle flux and optical luminosity because these two quantities should be proportional if the cusp aurora is caused by electron impact, as has been found for nighttime aurora in the oval. Furthermore, there should then be a direct relation between auroral altitudes and particle energy. Based on coordinated auroral observations at Svalbard and Greenland, together with simultaneous, overhead F-9 satellite measurements, these quantities have been evaluated