The effect of hydrocarbon chain length and end-capping on the liquid chromatographic properties of stationary phases containing bonded nitrile groups

Summary Stationary phases containing bonded nitrile groups have been synthesized. The effect of the n-alkyl chain length connecting the nitrile groups to the surface and of the end-capping on the chromatographic properties was studied. The synthesized material was compared with commercial nitrile phases in the separation of isomeric cresols and xylenols.     

Linear quantum Enskog equation. I. Homogeneous quantum fluids

The quantum-statistical generalization of the well-known classical, linear revised Enskog equation is derived for spatially uniform systems. This new quantum kinetic equation allows the study of equilibrium time correlation functions and their associated transport coefficients of normal quantum fluids where static correlations and degeneracy effects due to particle statistics (both are treated exactly) are important. Furthermore, we derive the quantum-statistical analog of the classical ring operator. These microscopic and systematic derivations are based on a recently developed superoperator formalism (including cluster expansion techniques) that, as a main feature, allows a clear distinction between static and dynamic correlations, which is crucial in the discussion of the Enskog approximation.     

Mathematical Relationships Between Bond-Bending Force Fields

Molecular mechanics softwares adopt various set of force field functions. In some cases, reliable data from one set of force field parameters cannot be used in a software that adopts another set of force field. Using mathematical approach, exact relationships between parameters from three bond-bending force fields, namely the (i) harmonic cosine angle, (ii) polynomial series, and (iii) Fourier series, are herein developed. Parameters from these three potential functions are further related to the approximate form, the harmonic angle function, which is valid for small change in chemical bond angle.     

On the Uniform Convergence of Walsh-Fourier Series

We study the uniform convergence of Walsh-Fourier series of functions on the generalized Wiener class BV (p(n)↑∞) This revised version was published online in June 2006 with corrections to the Cover Date.     

WEAK CONVERGENCE OF SOME DIRICHLET SERIES

1 Besicovitch Inner ProductIll this paper, we consider Dirichlet serie8where an, tL = 1, 2,' ', are complex nunlbers. They are Besicovitch almost periodic functionsWe see the 8ystenl {e.(t); e.(t) = e--it Iog 1l, 71 = l, 2,' .} fOrnis a1l orthollor11la1 systelll witl1respect to tI1e BesicovitcI1 iIl1ler productThell we call fOrm the gelleralized trigouolnetrical polynolIlialsAccording to tl1e idea developed il1 [l],[2], auy Dirichlet seriesis weakly convergent over K witll respect to …     

A method for minimizing the sum of a convex function and a continuously differentiable function

This paper presents a method for minimizing the sum of a possibly nonsmooth convex function and a continuously differentiable function. As in the convex case developed by the author, the algorithm is a descent method which generates successive search directions by solving quadratic programming subproblems. An inexact line search ensures global convergence of the method to stationary points.     

Relationship between retention and molecular structure of pyrimidine bases

Summary The influence of the type and position of CH₃, NH₂ and OH groups in the pyrimidine ring, the eluent composition and the surface chemistry of the stationary phase on the retention of pyrimidine bases in reversed-phase liquid chromatography was investigated. On the basis of the hypothesis about the additivity of the adsorption energy the contribution of various structural groups on retention has been established.     

Diffraction of sound waves by a rigid cylindrical cavity of finite length with an internal impedance surface

A rigorous solution is presented for the problem of diffraction of plane harmonic sound waves by a cavity formed by a terminated rigid cylindrical waveguide of finite length whose interior surface is lined by an acoustically absorbent material. The solution is obtained by a modification of the Wiener-Hopf technique and involve an infinite series of unknowns, which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem and their effects on the diffraction phenomenon are shown graphically.Received: December 12, 2001     

The energy of Einstein-Maxwell dilation-axion black hole in the teleparallel geometry

The energy of the stationary axisymmetric Einstein-Maxwell dilation-axion （EMDA） black hole is studied in the context of the Hamiltonian formulation of the teleparallel equivalence of general relativity （TEGR）. The energy expression for the finite and arbitrary space-like two spheres is exactly computed by means of the integral form of the constraint equations of the formalism naturally without any restriction on the metric parameters. We also show that our results give the same values obtained by other methods for some special cases.