On the theory of electron capture and loss in collisions of accelerated ions

Based on the stationary multichannel scattering theory, the processes of one-electron charge exchange in collisions of multiply charged ions have been considered for the range of high energies of the colliding particles in view of the Coulomb interaction of the nuclei. Numerical calculations have been performed to find the cross-section for electron capture in scattering of high-energy hydrogen-like ions in atomic hydrogen. It has been shown that the Coulomb interaction of nuclei substantially increases the capture cross-section compared to the result predicted by the Brinkmann-Kramers approximation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 77–81, March, 2008.     

Error bounds for minimal energy bivariate polynomial splines

Summary. We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. Received March 28, 2000 / Revised version received June 23, 2000 / Published online March 8, 2002 RID="*" ID="*" Supported by the National Science Foundation under grant DMS-9870187 RID="**" ID="**" Supported by the National Science Foundation under grant DMS-9803340 and by the Army Research Office under grant DAAD-19-99-1-0160     

The first total synthesis of lipid II: the final monomeric intermediate in bacterial cell wall biosynthesis

Bacterial peptidoglycan is composed of a network of beta-[1,4]-linked glyan strands that are cross-linked through pendant peptide chains. The final product, the murein sacculus, is a single, covalently closed macromolecule that precisely defines the size and shape of the bacterial cell. The recent increase in bacterial resistance to cell wall active agents has led to a resurgence of activity directed toward improving our understanding of the resistance mechanisms at the molecular level. The biosynthetic enzymes and their natural substrates can be invaluable tools in this endeavor. While modern experimental techniques have led to isolation and purification of the biosynthetic enzymes utilized in peptidoglycan biosynthesis, securing useful quantities of their requisite substrates from natural substrates has remained problematic. In an effort to address this issue, we report the first total synthesis of lipid II (4), the final monomeric intermediate utilized by Gram positive bacteria for peptidoglycan biosynthesis.     

Test of pressure-dependent SCC theories of impurity spectra using a combined SCC and CF model

Two recent theories of pressure dependent impurity optical spectra are tested by constraining the configurational coordinate parameters using crystal field theory. It is found that the theory of Drickamer, Frank and Slichter is more consistent with crystal field behavior and with experimental evidence than that of Curie, Berry and Williams.     

Scheduling programs with repetitive projects: A comparison of a simulated annealing,a genetic and a pair-wise swap algorithm

We address the problem of scheduling in programs involving the production of multiple units of the same product. Our study was motivated by a construction program for fast naval patrol boats. Other applications of this problem include procurement of multiple copies of aircraft, spacecraft, and weapon systems. In this problem we must decide how many units of the product to assign to each of a number of available crews (individuals, teams, subcontractors, etc.). These types of problems are characterized by two potentially conflicting considerations: 1) the need to complete each unit by its contractual due date, and 2) learning effects. Because of the first consideration, there is a tendency to use multiple crews for simultaneous production, so that meeting due dates is assured. However, the second consideration encourages assigning many units to a single crew so that learning effects are maximized. We study this scheduling problem with two different penalty cost structures and develop models for both versions. The models trade-off the penalty associated with late deliveries and the savings due to learning (and possibly incentive payments for early completion). We discuss different heuristic algorithms — simulated annealing, a genetic algorithm, and a pair-wise swap heuristic — as well as an exhaustive search to determine a baseline for comparisons. Our computational results show that the pair-wise swap algorithm is the most efficient solution procedure for these models.     

EPR and saturation transfer EPR spectra at high microwave field intensities

The eight unique EPR signals at the first and second harmonies of the Zeeman modulation are sensitive to the very slow rotational diffusion of spin labeled biomolecules when these signals are recorded under conditions of microwave saturation and finite Zeeman modulation frequencies and amplitudes. Such saturation transfer sensitive spectra have been employed to study contractile proteins, hemoproteins, enzymes, etc. When these species or their supramolecular complexes are characterized by correlation times in the range 10^?8 to 10^?3 s. Published computer simulation reproduce quite well spectra at the longer correlation times and the general sensitivity of spectra to changing rotational correlation time; however, agreement between experimental and calculated spectral shapes is poor for rotational correlation time on the order of 10^?7 s and the dependence of experimental spectra upon microwave field intensity is not reproduced. In the present communication we show that the previously reported discrepancy between experimental and calculated spectra is due to the neglect of higher order cou magnetic interactions modulated by the molecular motion and involving the spin-microwave field interaction. When these “pseudodiagonal” terms of the spin density equation are explicitly included, experimental spectral lineshapes, spectral line positions, and the ratios of amplitudes of the various signal components are quantitatively reproduced. Plots of the ratios of the heights of the high and low field spectral extrema suggest a procedure for calibrating microwave field intensities as these ratios are found experimentally and theoretically to be nearly a linear function of microwave field intensity for intensities in the range 0.15 to 0.5 G. The separation of low and high field extrema was observed to increase with increasing microwave field intensity, suggesting the need to carefully consider saturation effects when determining rotational correlation times from this separation.     

Transition moment closure tests for ethylene

The completeness of a basis set for ethylene is examined relative to its ability to describe transition moments. The double zeta (Dunning contraction) plus polarization plus Rydberg Cartesian Gaussian set does much better for length than for velocity moments. An attempt is made to interpret the transition moment sums for the occupied orbitals.     

Unimodular quadratic forms over global function fields

The isometry problem is studied for unimodular quadratic forms over the Hasse domains of global function fields. Over the polynomial ring k[x] the problem reduces to classification of forms over k; but examples are provided showing that in general no such reduction occurs, even when the underlying ring is Euclidean. Connections with the structure of the ideal class group are given, and a complete invariant for the isometry class is found in the ternary isotropic case.     

Measurement of multiplet intensities and noble gas-broadened line widths in the V3-fundamental of methane

Integrated intensity data at 300°K for J-multiplets between P(11)and R(11) in the _{V3-fundamental of ¹²CH4} are presented, along with the intensity of the entire Q-branch, which also encompasses the Q-branch of the _{V3-fundamental of ¹³CH4}. These data, together with theoretical estimates for the intensities of J-multiplets of J > 11, sum up to a value of S_band= 284±14cm^?2atm^?1 at 300°K. This results is in excellent agreement with most of the previously published values for this parameter. Within experimental error, the intensities of the J-multiplets in the _{V3-fundamental do not seem to exhibit the strong anamolies that were characteristic of lines in the 2V3}-band.Line widths have been measured at 100°K, 130°K, 190°K, 250°K, and 300°K for R(0), R(1), and R(2) broadened by He, Ne and Ar. The temperature dependence of the line width is discussed for the three cases of broadening. In neon broadening at 300°K, the ‘effective mean line widths’ for multiplets R(3) through R(11) have also been obtained experimentally; their J-dependence is interpreted using Gordon's theory of line shapes in multiplet spectra.