Weighted Discrepancy and High-Dimensional Numerical Integration

The concept of weighted discrepancy of sequences was introduced by Sloan and Woniakowski when they proved a general form of a Koksma–Hlawka inequality for the numerical integration of functions. This version takes imbalances in the importance of the projections of the integrand into account.In this paper we give estimates for the weighted discrepancy of several important point sets. Further we carry out various (high-dimensional) numerical integration experiments and we compare the results with the error bounds provided by the generalized Koksma–Hlawka inequality and by the estimates for the weighted discrepancy. Finally we discuss various consequences.     

Untersuchungen zur Quellung und Lösung von Cellulose in aminhaltigen Flüssigkeitsgemischen. 1. Mitt. Untersuchungen zum Verhalten von Cellulose in Gemischen von SO2 und Diäthylamin mit einer organischen Flüssigkeit

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Nuclear Quadrupole Interactions in Nuclear Quadrupole Resonance Detection of Energetic and Controlled Materials: Theoretical Study

There has been a growing interest in nuclear quadrupole resonance (NQR) techniques useful for the detection of explosives and drugs in solid state systems. This paper uses the first-principles one-electron Hartree?CFock theoretical method to study the nuclear quadrupole interaction parameters e ² qQ and ?? for the ¹⁴N nuclei in the explosives RDX and ??-HMX as well as the drugs cocaine and heroin. It has been found in our earlier published investigations reviewed here that there is very good agreement for our calculated e ² qQ and ?? for ¹⁴N, for all these four systems, and experiment. We also present our unpublished theoretical results for cocaine with an HCl molecule attached. We successfully explain quantitatively the drastic decrease in e ² qQ in going to cocaine-HCl from cocaine-free base as well as the observed substantial increase in ?? and discuss the implications of these dramatic changes for NQR detection in general.     

First-Principles Theory of Muon and Muonium Trapping in the Protein Chain of Cytochrome c and Associated Hyperfine Interactions

The microscopic details of the electron transfer in cytochrome c (cyt c) are being investigated by the Muon Spin Relaxation (μSR) technique. We are using the Hartree–Fock Cluster Procedure to determine the most likely trapping sites for μ⁺ and muonium (Mu) in the protein chain, and have performed extensive calculations in single amino acid molecules of the protein chain of cyt c. The double-bonded oxygen atom of the carboxyl group was identified as the trapping site for both μ⁺ and Mu. Utilizing the wave functions we obtained from the Hartree–Fock calculations, we have determined the hyperfine field that the μ⁺ in Mu experiences while the latter is trapped at the oxygen. This revised version was published online in September 2006 with corrections to the Cover Date.     

Theory for Relative Strengths of Trapping of He+ Ions in Solid, Liquid and Gaseous Hydrogen

The study of trapping of He⁺ ion in solid hydrogen is important both as a problem in solid state physics and also as an applied physics problem in the field of muon catalyzed fusion (μCF). In μCF, He⁺ ion acts as a trap for μ⁻, interrupting the chain reaction aspect of the catalytic role of μ⁻ in producing fusion of deuteron and triton and of triton and triton in solid hydrogen composed of ²H–³H and ³H–³H molecules, respectively. Using the Hartree–Fock procedure, combined with procedures for including many-body effects, as well as relaxation effects associated with the He⁺–H₂ distances and the adjustment of the H–H separation, we have investigated the trapping of He⁺ in gaseous and solid state environments. For the former, the environment of He⁺ is simulated by a single hydrogen molecule and for the solid by clusters appropriately chosen to represent the hexagonal close-packed structure. Our results for the gaseous state indicate that the trapping is rather strong with a binding energy of 8.5 eV, with almost equal binding energy in the linear and triangular configurations with respect to the H–H direction. For the solid, both the likely sites for He⁺ trapping, namely the tetrahedral and octahedral interstitial sites, are also found to provide deep traps (8.6 eV) of almost equal strength, independent of the orientations of the neighboring molecules, showing that the trapping is not influenced by the orientational disorder in the surrounding hydrogen molecules. Further, the influence of next nearest neighbor hydrogen molecules is found to enhance the trapping energy for He⁺ substantially, by 0.6 eV, with the incorporation of the third nearest neighbors having a much smaller added effect, demonstrating the convergence of our results with respect to the size of the cluster chosen to simulate the solid. The substantial influence on the He⁺ trapping energy found for the neighbors beyond the nearest ones provides an explanation of the greater accumulation of helium in the solid state of hydrogen in μCF experiments as compared to the liquid. Suggestions are made regarding the possible reasons for the almost negligible accumulation of helium in the liquid state. This revised version was published online in August 2006 with corrections to the Cover Date.     

Theoretical Study of Trapping Sites for Muon in the Heme Group of Cytochrome c and Associated Shifts in Muon Spin Relaxation Frequencies

Muon Spin Relaxation (μSR) experiments are currently being conducted on the important electron transfer molecule cytochrome c (cyt c) with the goal to find out about microscopic details of the path the moving electron is taking. Simultaneously we are using the Unrestricted Hartree–Fock Cluster Procedure to determine the trapping sites for muon (μ⁺) and muonium (Mu) in the heme unit of cyt c and the associated hyperfine interactions. For the trapping sites with the highest binding energies for μ⁺, namely the nitrogen and the carbon of the pyrrole rings, we have used the available magnetic susceptibility data together with our calculated hyperfine fields to predict the Knight-shifts. At room-temperature we found 88.4 ppm and 79.0 ppm for the most attractive N- and adjacent C-site, respectively. At 150 K, these shifts increase to 172.7 ppm for the N-site and 153.7 ppm for the C-site. This revised version was published online in September 2006 with corrections to the Cover Date.     

Internal vibrations of the Li(NH3)4+ complex analyzed from ab initio, density functional theory, and the classical spring network model

We report our theoretical findings regarding internal vibrations of the Li(NH 3) 4 (+) complex which have been studied using three different methods, namely, a classical spring network model, density functional theory, and ab initio Hartree-Fock plus M?ller-Plesset correlation energy correction truncated at second-order. The equilibrium Li...N and N...N distances are found to be 2.12 and 3.47 A, respectively, in good agreement with the experimental data. The theoretically determined vibrational frequencies of the lowest modes are in good agreement with those extracted from inelastic X-ray scattering measurements. From group theory considerations, the internal vibrations of Li(NH 3) 4 (+) complexes resemble those of a tetrahedral object. Further experimental investigation is suggested.