Equivalent rotations associated with the permutation inversion group revisited: symmetry projection of the rovibrational functions of methane

In this work the analysis of the equivalent rotations from the permutation inversion group formalism is revisited. We emphasize that explicit knowledge of changes in the Euler angles are not required in order to determine the transformation that a given symmetry operation causes to the rotational functions when dealing with the permutation inversion group formalism. Indeed, matrix elements of the equivalent rotations are provided by a single Wigner's D ^(j)(R) function. Taking advantage of this, we propose a symmetry projection approach to build the rovibrational functions of methane. This approach focuses on the relevance of the isomorphism between permutations and equivalent rotations. In our method, symmetry adapted functions are obtained by simultaneous diagonalization of a set of commuting operators, whose representation is given in terms of direct products of Wigner's D functions and vibrational matrix representations provided by a local scheme. The proposed approach is general and permits us to obtain in a systematic fashion an orthonormal set of symmetry-projected functions, with good total angular momentum, and carrying the irreducible representations of the molecular symmetry group.     

A model for viscosity coefficients of gases with potentials differing in form

A recent theory of non-conformal interactions has been very succesful in providing effective spherical potentials for the pressure of more than 40 real gases and many of their binary mixtures. Here, this theory is applied to deal with low-density viscosity coefficients. In its simplest form, the approximate non-conformal (ANC) theory introduces, besides the usual corresponding states parameters-energy ? and distance r_m-a softness parameter s to account for the form of a particular potential function. We investigate the effects of the potential form on the temperature behaviour of the viscosisty coefficient η. It is shown that the softer potentials, with wider attractive wells, have larger viscosities and an explicit expression for η (T, ?, r_m, s) is obtained. The ANC potentials are tested in their capacity to reproduce the temperature dependence of η for the heavier noble gases (Ar, Kr and Xe), diatomics (H₂, N₂, O₂ and CI₂) and a dozen small polyatomics. It is found that the ANC model η (T, ?, r_m, s), with only three substance-dependent parameters, reproduces experimental 7 data within their estimated error.     

Environmental Applications of Excitation-Emission Spectrofluorimetry: An In-Depth Review II

Abstract: This part is devoted to the environmental applications of excitation-emission spectrofluorimetry (EES): Characterization of chromophoric dissolved organic matter (CDOM) in drinking waters, rivers, fog waters, lakes, oceans, leachates, wastewaters, sluge, bioreactor membrane foulants, and soils; characterization of extracellular polymeric substances in sludges; study of interactions between CDOM and organic pollutants in soils; and quantification of organic pollutants in waters and soils. This part includes the pretreatment of samples, and the environmental applications of the technique are discussed, including its application to bioremediation of wastewaters.

More than 200 references (focusing mainly on the last 10 years) from all kinds of journals (environment, analytical chemistry, biotechnology) have been carefully revised and included in this part of the article.     

Pressure induced anisotropic magnetovolume phenomena in Lu2Fe17 Intermetallics

Magnetisation and magnetic susceptibility of a Lu₂Fe₁₇ single crystal have been studied under hydrostatic pressure up to 1.2 GPa at temperatures down to 5 K using a SQUID magnetometer. The ferromagnetic phase of Lu₂Fe₁₇ is suppressed rapidly above a critical pressure P _C = 0.4 GPa in the whole temperature range below the critical temperature T _C . A magnetic phase diagram of Lu₂Fe₁₇ has been constructed using results of the magnetic susceptibility measurements under pressure. A pressure induced incommensurate antiferromagnetic phase exhibits metamagnetic transitions with the increasing critical magnetic field H _C under pressure. Taking into account recent neutron diffraction data, the pressure induced anisotropic changes of the lattice parameters of the Lu₂Fe₁₇ are discussed.     

Liquid Sorption and Nanoparticle Intercalation in Layer-Structured Materials

Abstract

Alkylammonium intercalated graphite oxides (R-GO), palladium intercalated alumina-pillared montmorillonites (Pd/Al₂O₃-PILC) and titania-pillared montmorillonites (TiO₂-PILC) have been prepared and the intercalation materials have been characterized by BET surface area analysis, UV/VIS spectroscopy, ICP-AES, DTG-DTA, XRD and TEM measurements. R-GO particles were prepared by oxidation of natural graphite followed by organophilization with cationic surfactants. For TiO₂-PILC and Pd/Al₂O₃-PILC the synthesis included the interlamellar adsorption of precursor species (polyaluminium-hydroxide, Pd-acetate and tetraethyl orthotitanate) from dilute solutions and subsequent chemical reactions at the montmorillonite/solution interface.     

Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality

This paper presents a mean‐reverting jump diffusion model for the electricity spot price and derives the corresponding forward price in closed‐form. Based on historical spot data and forward data from England and Wales the model is calibrated and months, quarters, and seasons–ahead forward surfaces are presented.     

Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit

The time of operation of an adiabatic quantum computer must be less than the decoherence time, otherwise the computer would be nonoperative. So far, the nonadiabatic corrections to an adiabatic quantum computer are merely theoretical considerations. By the above reason, we consider the particular case of a quantum-dot-confined electron spin qubit working adiabatically in the nanoscale regime (e.g., in the MeV range of energies) and include nonadiabatic corrections in it. If the decoherence times of a quantum dot computer are ～100 ns [J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998)] then the predicted number of one qubit gate (primitive) operations of the Loss–DiVincenzo quantum computer in such an interval of time must be >10 ¹⁰. However, if the quantum-dot-confined electron spin qubit is very excited (i.e., the semiclassical limit) the number of operations of such a computer would be approximately the same as that of a classical computer. Our results suggest that for an adiabatic quantum computer to operate successfully within the decoherence times, it is necessary to take into account nonadiabatic corrections.     

Smoothing of Commutators for a Hörmander Class of Bilinear Pseudodifferential Operators

Commutators of bilinear pseudodifferential operators with symbols in the Hörmander class $BS_{1, 0}^{1}$ and multiplication by Lipschitz functions are shown to be bilinear Calderón-Zygmund operators. A connection with a notion of compactness in the bilinear setting for the iteration of the commutators is also made.     

Preservation of reliability classes under the formation of coherent systems

The preservation of reliability aging classes under the formation of coherent systems is a relevant topic in reliability theory. Thus, it is well known that the new better than used class is preserved under the formation of coherent systems with independent components. However, surprisingly, the increasing failure rate class is not preserved in the independent and identically distributed case, that is, the components may have the (negative) aging increasing failure rate property, but the system does not have this property. In this paper, we study conditions for the preservation of the main reliability classes under the formation of general coherent systems. These results can be applied both for systems with independent or dependent components. We consider both the case of systems with identically distributed components and the case of systems with components having different distributions. Copyright © 2013 John Wiley & Sons, Ltd.     

On a Sum of Modified Bessel Functions

In this paper we consider a sum of modified Bessel functions of the first kind of which particular case is used in the study of Kanter’s sharp modified Bessel function bound for concentrations of some sums of independent symmetric random vectors. We present some monotonicity and convexity properties for that sum of modified Bessel functions of the first kind, as well as some Turán type inequalities, lower and upper bounds. Moreover, we point out an error in Kanter’s paper (J Multivariate Anal 6:222–236, 1976).