Determination of molecular structure in solution using vibrational circular dichroism spectroscopy: the supramolecular tetramer of S-2,2'-dimethyl-biphenyl-6,6'-dicarboxylic acid

The infrared (IR) and vibrational circular dichroism (VCD) spectra of S-2,2'-dimethyl-biphenyl-6,6'-dicarboxylic acid, S-1, in CDCl(3) solution are concentration-dependent, showing that oligomerization occurs with increasing concentration. DFT calculations support the conclusion that the oligomer formed is the cyclic tetramer (S-1)(4), in which S-1 monomers are linked by hydrogen(H)-bonded (COOH)(2) moieties. Due to the existence of two inequivalent tautomeric conformations of each (COOH)(2) moiety, six inequivalent conformations of (S-1)(4) are possible. B3LYP/6-31G* DFT calculations predict that the conformation "aaab", possessing three equivalent (COOH)(2) conformations, a, and one tautomeric conformation, b, has the lowest free energy. B3LYP/6-31G* IR and VCD spectra vary substantially with conformation. The B3LYP/6-31G* IR and VCD spectra of the C=O stretch modes of "aaab" are in excellent agreement with the experimental spectra, while those of all other conformations exhibit poor agreement, confirming the prediction that the "aaab" conformation is the predominant conformation. Comparison of the calculated IR and VCD spectra of the six conformations to the experimental spectra in the range 1100-1600 cm(-1) further supports this conclusion. The study is the first to use VCD spectroscopy to determine the structure of a supramolecular species.     

A parameter-uniform Schwarz method for a coupled system of reaction–diffusion equations

We consider an arbitrarily sized coupled system of one-dimensional reaction–diffusion problems that are singularly perturbed in nature. We describe an algorithm that uses a discrete Schwarz method on three overlapping subdomains, extending the method in [H. MacMullen, J.J.H. Miller, E. O’Riordan, G.I. Shishkin, A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers, J. Comput. Appl. Math. 130 (2001) 231–244] to a coupled system. On each subdomain we use a standard finite difference operator on a uniform mesh. We prove that when appropriate subdomains are used the method produces ε-uniform results. Furthermore we improve upon the analysis of the above-mentioned reference to show that, for small ε, just one iteration is required to achieve the expected accuracy.     

Microsoft Excel as a supplement in a high school statistics course

This study was conducted in the spring of 2002 at Arlington High School in a Probability and Statistics course for junior and senior level students. Two sections of the class were compared with respect to the use/non-use of EXCEL in the course. The experimental group (the one using EXCEL) outperformed the control group on five of the six teacher-created unit tests and on both of the criterion referenced assessments used by the district; however, the differences were not statistically significant at the 0.05 level. Furthermore, the experimental group expressed very positive feelings towards the use of the software in a survey administered at the conclusion of the course.     

Large volume growth and finite topological type

It is shown in this paper that a complete noncompact -dimensional Riemannian manifold with nonnegative Ricci curvature, sectional curvature bounded from below, and large volume growth is of finite topological type provided that the volume growth rate of the complement of the cone of rays from a fixed base point is less than .

     

Numerical methods for reaction-diffusion problems with non-differentiable kinetics

Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.Dedicated to Ivo Babuka on his sixtieth birthdayResearch partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant Number AFOSR 85-0322     

Spin correlation in t&tmacr; production from p&pmacr; collisions at radicals = 1.8 TeV

The D0 collaboration has performed a study of spin correlation in t&tmacr; production for the process t&tmacr;-->bW(+)&bmacr;W-, where the W bosons decay to enu or &mgr;nu. A sample of six events was collected during an exposure of the D0 detector to an integrated luminosity of approximately 125 pb(-1) of sqrt[s] = 1.8 TeV p&pmacr; collisions. The standard model (SM) predicts that the short lifetime of the top quark ensures the transmission of any spin information at production to the t&tmacr; decay products. The degree of spin correlation is characterized by a correlation coefficient kappa. We find that kappa>-0.25 at the 68% confidence level, in agreement with the SM prediction of kappa = 0.88.     

Cross section for b-Jet production in &pmacr;p collisions at radicals = 1.8 TeV

Bottom-quark production in &pmacr;p collisions at sqrt[s] = 1.8 TeV is studied with 5 pb(-1) of data collected in 1995 by the D0 detector at the Fermilab Tevatron Collider. The differential production cross section for b jets in the central rapidity region ( | y(b)|<1) as a function of jet transverse energy is extracted from a muon-tagged jet sample. Within experimental and theoretical uncertainties, D0 results are found to be higher than, but compatible with, next-to-leading-order QCD predictions.     

An estimate of the secondary-proton spectrum at small atmospheric depths

Summary We have calculated the energy spectrum of secondary protons produced in the atmosphere as a function of the atmospheric depth and zenith angles at a location with zero geomagnetic cut-off. In this calculation, we have included all relevant energy losses and production processes. It is shown that the protons produced from the target nuclei through recoil and evaporation processes dominate the spectrum below 350 MeV. These calculations have been carried out over an energy region from 20 MeV to 40 GeV and up to a depth of 40 g/cm² of the atmosphere over a latitude with zero geomagnetic cut-off for both the periods of minimum and maximum solar modulation.