The 2D Boussinesq equations with vertical viscosity and vertical diffusivity

This paper aims at the global regularity of classical solutions to the 2D Boussinesq equations with vertical dissipation and vertical thermal diffusion. We prove that the Lr-norm of the vertical velocity v for any 1<r<∞ is globally bounded and that the L^∞-norm of v controls any possible breakdown of classical solutions. In addition, we show that an extra thermal diffusion given by the fractional Laplace δ(−Δ) for δ>0 would guarantee the global regularity of classical solutions.     

Structured eigenvalue condition numbers and linearizations for matrix polynomials

This work is concerned with eigenvalue problems for structured matrix polynomials, including complex symmetric, Hermitian, even, odd, palindromic, and anti-palindromic matrix polynomials. Most numerical approaches to solving such eigenvalue problems proceed by linearizing the matrix polynomial into a matrix pencil of larger size. Recently, linearizations have been classified for which the pencil reflects the structure of the original polynomial. A question of practical importance is whether this process of linearization significantly increases the eigenvalue sensitivity with respect to structured perturbations. For all structures under consideration, we show that this cannot happen if the matrix polynomial is well scaled: there is always a structured linearization for which the structured eigenvalue condition number does not differ much. This implies, for example, that a structure-preserving algorithm applied to the linearization fully benefits from a potentially low structured eigenvalue condition number of the original matrix polynomial.     

Absence of Cooper-type bound states in three- and few-electron systems

It is shown that the appearance of a fixed-point singularity in the kernel of the two-electron Cooper problem is responsible for the formation of the Cooper pair for an arbitrarily weak attractive interaction between two electrons. This singularity is absent in the problem of three and few superconducting electrons at zero temperature on the full Fermi sea. Consequently, such three- and few-electron systems on the full Fermi sea do not form Cooper-type bound states for an arbitrarily weak attractive pair interaction. Received: 9 February 1998 / Revised and Accepted: 13 May 1998     

Amperometric determination of 2-benzothiazole sulphenamide accelerators

A simple method for the amperometric estimation of N-cyclohexyl-2-benzothiazole sulphenamide, N-dicyclohexyl-2-benzothiazole sulphenamide, 2-(morpholinothio)benzothiazole and N-tert.-butyl-2-benzothiazole sulphenamide is reported. The results are obtained within 5 min and are correct within +/- 2.0%.     

Vector space of linearizations for the quadratic two-parameter matrix polynomial

Given a quadratic two-parameter matrix polynomial Q(λ,?μ), we develop a systematic approach to generating a vector space of linear two-parameter matrix polynomials. The purpose for constructing this vector space is that potential linearizations of Q(λ,?μ) lie in it. Then, we identify a set of linearizations and describe their constructions. Finally, we determine a class of linearizations for a quadratic two-parameter eigenvalue problem.     

The adiabatic‐to‐diabatic transformation angle and the berry phase for coupled jahn–teller/renner–teller systems: The F + H2 as a case study

The approach to calculate improved, two‐state, adiabatic‐to‐diabatic transformation angles (also known as mixing angles), presented before (see Das et al., J Chem Phys 2010, 133, 084107), was used here while studying the F + H₂ system. However, this study is characterized by two new features: (a) it is the first of its kind in which is studied the interplay between Renner–Teller (RT) and Jahn–Teller (JT) nonadiabatic coupling terms (NACT); (b) it is the first of its kind in which is reported the effect of an upper singular RT‐NACT on a lower two‐state (JT) mixing angle. The fact that the upper NACT is singular (it is shown to be a quasi‐Dirac δ‐function) enables a semi‐analytical solution for this perturbed mixing angle. The present treatment, performed for the F + H₂ system, revealed the existence of a novel parameter, η, the Jahn–Renner coupling parameter (JRCP), which yields, in an unambiguous way, the right intensity of the RT coupling (as resembled, in this case, by the quasi‐Dirac δ‐function) responsible for the fact that the final end‐of‐the contour angle (identified with the Berry phase) is properly quantized. This study implies that the numerical value of this parameter is a pure number (independent of the molecular system): η = $ 2\sqrt 2 /\pi $ (= 0.9003) and that there is a good possibility that this value is a novel characteristic molecular constant for a certain class of tri‐atomic systems. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011