Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order M?ller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.     

Über Borel's Verallgemeinerung des Grenzbegriffes

Ohne Zusammenfassung     

Über die Beziehungen zwischen der Darstellung eines eindeutigen Zweiges einer monogenen Function durch Herrn Mittag-Leffler,der Methode der Mittelwerte des Herrn Borel und der Transformation des Herrn Lindelöf

Ohne Zusammenfassung     

Magnetic support near a charged rotating black hole

Three equilibrium conditions for magnetic trapping are applied to a charged black hole whose axis of rotation is aligned with an asymptotically uniform weak magnetic field.     

Enhanced memory performance by tailoring the microstructural evolution of (ZrO2)0.6(SiO2)0.4 charge trapping layer in the nanocrystallites-based charge trap flash memory cells

ZrO₂ nanocrystallites based charge trap memory cells by incorporating a (ZrO₂)_0.6(SiO₂)_0.4 film as a charge trapping layer and amorphous Al₂O₃ as tunneling and blocking layer were prepared and investigated. The precipitation reaction in charge trapping layer forming ZrO₂ nanocrystallites during rapid thermal annealing was investigated by transmission electron microscopy. The density and size of ZrO₂ nanocrystallites are the critical factors for controlling the charge storage characteristics. The ZrO₂ nanocrystallites based memory cells after postannealing at 800 ^°C for 60 s exhibit the best electrical characteristics and a low charge loss ～5 % after 10⁵ write/erase cycles operation.     

A novel assignment method in the 13C NMR spectroscopy of coumarins and furocoumarins

The signal shifts caused by replacing the carbonyl oxygen by sulphur represent a valuable method of assignment of the ¹³C NMR signals in coumarins and furocoumarins substituted at the benzoic and furanoic rings.     

New Class of Kirchhoff Type Equations with Kelvin-Voigt Damping and General Nonlinearity: Local Existence and Blow-up in Solutions

In this paper, we consider a class of Kirchhoff equation, in the presence of a Kelvin-Voigt type damping and a source term of general nonlinearity forms. Where the studied equation is given as follows\begin{equation*}u_{tt} -\mathcal{K}\left( \mathcal{N}u(t)\right)\left[ \Delta_{p(x)}u +\Delta_{r(x)}u_{t}\right]=\mathcal{F}(x, t, u).\end{equation*}Here, $\mathcal{K}\left( \mathcal{N}u(t)\right)$ is a Kirchhoff function, $\Delta_{r(x)}u_{t}$ represent a Kelvin-Voigt strong damping term, and $\mathcal{F}(x, t, u)$ is a source term. According to an appropriate assumption, we obtain the local existence of the weak solutions by applying the Galerkin's approximation method. Furthermore, we prove a non-global existence result for certain solutions with negative/positive initial energy. More precisely, our aim is to find a sufficient conditions for $p(x), q(x), r(x), \mathcal{F}(x,t,u)$ and the initial data for which the blow-up occurs.     

Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe

Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic (129)Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an "NMR force field". By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T(1). The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T(1). Persistent dimers Xe(2) are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings.     

Gyration in the ergosphere of a black hole

A covariant definition of gyration is proposed and used to refute a previous demonstration that gyration is impossible in the equatorial plane of an ergosphere. We show that reasonable charge to mass ratios and magnetic field strengths can induce gyration and consider implications for the observation of collapsed objects.