A theoretical study on calculation of absolute hydration enthalpies for some univalent ions

Using the total radius of alkaline fluorides and sodium halides and their experimental total enthalpy values, absolute hydration enthalpies of sodium and fluoride ions ( and ) were previously calculated. Also, by the help of data of sodium and fluoride ions for all alkaline metal ions and halides absolute hydration enthalpies were determined.

A Counterexample to Dispersive Estimates for Schrödinger Operators in Higher Dimensions

In dimension n > 3 we show the existence of a compactly supported potential in the differentiability class , for which the solutions to the linear Schrödinger equation in,

Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with Finite-Density Initial Data. II. Dark Solitons on Continua

For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation ( NLSE), , with finite-density initial data

Laplace Sequences of Surfaces in Projective Space and Two-Dimensional Toda Equations

We find that the Laplace sequences of surfaces of period n in projective space P _n–1 have two types, while type II occurs only for even n. The integrability condition of the fundamental equations of these two types have the same form

On the Rate of Convergence to Equilibrium of the Andersen Thermostat in Molecular Dynamics

It has been shown in E and Li (Comm. Pure. Appl. Math., 2007, in press) that the Andersen dynamics is uniformly ergodic. Exponential convergence to the invariant measure is established with an error bound of the form

Optimal Eigenvalue Estimate for the Dirac–Witten Operator on Bounded Domains with Smooth Boundary

Eigenvalue estimate for the Dirac–Witten operator is given on bounded domains (with smooth boundary) of spacelike spin hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS and chiral conditions). Roughly speaking, any eigenvalue of the Dirac–Witten operator satisfies

Stability of Two Soliton Collision for Nonintegrable gKdV Equations

We continue our study of the collision of two solitons for the subcritical generalized KdV equations

The Singular Set for the Composite Membrane Problem

In this paper we study the behavior of the singular set

SNA’s in the Quasi-Periodic Quadratic Family

We rigorously show that there can exist Strange Nonchaotic Attractors (SNA) in the quasi-periodically forced quadratic (or logistic) map

Normal ordering and quantum groups

The irreducible R-matrices associated with the quantum Liouville and sine-Gordon equations were classified by the su(2) index l, 2l integer. We find that the associated quantum field theories must have the following equal time operator product expansions in the lattice approximation

Boson Stars as Solitary Waves

We study the nonlinear equation

Maximal Inequalities for CIR Processes

Let X be a Cox—Ingersoll—Ross (CIR) process given by

Levinson's Theorem for the Nonlocal Interaction in One Dimension

The Levinson theorem for the one-dimensional Schrödinger equation with both local and the nonlocal symmetric potentials is established by the Sturm–Liouville theorem. The critical case where the Schro;audinger equation has a finite zero-energy solution is also analyzed. It is shown that the number n ₊ (n _–) of bound states with even (odd) parity is related to the phase shift ₊(0)[_–(0)] of the scattering states with the same parity at zero momentum as

Laser-diode-excited Blue Upconversion in Tm3+/Yb3+-codoped TeO2-Ga2O3-R2O (R=Li, Na, K) Glasses

This paper reports on intense blue upconversion in Tm³⁺/Yb³⁺ codoped TeO₂-Ga₂O₃-R₂O(R=Li, Na, K) glasses upon excitation with commercial available laser diode (LD). Effects of alkali ions on the Raman spectra, thermal stability and spectroscopic properties of the tellurite-gallium glasses have also been investigated. Energy transfer and the involved upconversion mechanisms have been discussed. Intense blue upconversion emission centered at 476 nm along with a weak red emission at 650 nm has been observed upon excitation of 977 nm LD, assigned to the transitions of , and and/or of Tm³⁺, respectively. The blue upconversion intensity has a cubelike dependence on incident pump laser power, indicating a three-photon process. However, a quadratic dependence of the 476 nm upconversion intensity on the incident pump laser power has been observed when samples under excitation of 808 nm LD due to a two-photon absorption process. Enhanced upconversion luminescence have been observed with replacing K⁺ for Na⁺ and Li⁺.     

Thermoelectric power of YBa2Cu3Ox in equilibrium with gas phases

Thermoelectric power (TP) and electrical conductivity (EC) measurements were performed for YEa₂Cu₃O_x at 1128 K under controlled oxygen partial pressure varying between 50 and 10⁵ Pa. Three regimes are observed for the electrical properties. At low both TP and EC remain constant with . In the medium range sharp changes of both electrical parameters occur; TP changes sign from positive above 4×10² Pa to negative below this value. In the high region (>7.6×10³ Pa) TP vs log exhibits two slopes; 5.1 below 1.5×10⁴ Pa and 8.4 above this value. The slopes can be discussed in terms of the defect structure involving singly and doubly ionized oxygen vacancies below and above 7.6×10³ Pa, respectively.     

Monitoring structural transformation of hydroxy-sulphate green rust in the presence of sulphate reducing bacteria

The activities of bacterial consortia enable organisms to maximize their metabolic capabilities. This article assesses the synergetic relationship between iron reducing bacteria (IRB), Shewanella putrefaciens and sulphate reducing bacteria (SRB) Desulfovibrio alaskensis. Thus, the aim of this study was first to form a biogenic hydroxy-sulpahte green rust GR2( $ {\text{SO}}_{{\text{4}}} ^{{2 - }} The activities of bacterial consortia enable organisms to maximize their metabolic capabilities. This article assesses the synergetic relationship between iron reducing bacteria (IRB), Shewanella putrefaciens and sulphate reducing bacteria (SRB) Desulfovibrio alaskensis. Thus, the aim of this study was first to form a biogenic hydroxy-sulpahte green rust GR2() through the bioreduction of lepidocrocite by S. putrefaciens and secondly to investigate if sulfate anions intercalated in the biogenic GR2() could serve as final electron acceptor for a sulfate reducing bacterium, D. alaskensis. The results indicate that the IRB lead to the formation of GR2() and this mineral serve as an electron acceptor for SRB. GR2() precipitation and its transformation was demonstrated by using X-ray diffraction (DRX), M?ssbauer spectroscopy (TMS) and transmission electron spectroscopy (TEM). These observations point out the possible acceleration of steel corrosion in marine environment in presence of IRB/SRB consortia.     

Energy dependence of the charge exchange reaction from muonic hydrogen to oxygen

The charge exchange reaction of negative muons from the atom to oxygen has been measured in gaseous mixtures of H₂ + O₂. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of , describing the transfer from the ground state of thermalized atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate =3.9 10¹¹ s^-1 in the energy interval 0.12–0.22 eV. The analysis with the model of Two components shows that all measured time spectra can be reproduced with the same set of parameters.     

On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator

A Complete Set of Riemann Invariants

There are at most 14 independent real algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space. In the general case, these invariants can be written in terms of four different types of quantities: R , the real curvature scalar, two complex invariants I and J formed from the Weyl spinor, three real invariants I₆, I₇ and I₈ formed from the trace-free Ricci spinor and three complex mixed invariants K, L and M. Carminati and McLenaghan [5] give some geometrical interpretations of the role played by the mixed invariants in Einstein-Maxwell and perfect fluid cases. They show that 16 invariants are needed to cover certain degenerate cases such as Einstein-Maxwell and perfect fluid and show that previously known sets fail to be complete in the perfect fluid case. In the general case, the invariants I and J essentially determine the components of the Weyl spinor in a canonical tetrad frame; likewise the invariants I₆, I₇ and I₈ essentially determine the components of the trace-free Ricci spinor in a (in general different) canonical tetrad frame. These mixed invariants then give the orientation between the frames of these two spinors. The six real pieces of information in K, L and M are precisely the information needed to do this. A table is given of invariants which give a complete set for each Petrov type of the Weyl spinor and for each Segre type of the trace-free Ricci spinor This table involves 17 real invariants, including one real invariant and one complex invariant involving , and in some degenerate cases.