Density functionals for exchange and correlation energies: Exact conditions and comparison of approximations

A set of exact conditions is compiled for the purpose of developing and testing approximations for the exchange-correlation energy as a functional of the electron density. Special emphasis is placed upon recently developed density-scaling relationships. Commonly used generalized gradient approximations are compared against several of these conditions. A direct tabular comparison of these functionals (not of calculated properties) with one another is also made. © 1994 John Wiley & Sons, Inc.     

A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.     

Clifford Analysis Techniques for Spherical PDE

For a ? R\alpha \in \mathbf{R}, the class of a-\alpha -order spherical harmonic functions in an open set W í\Omega \subseteq S^n-1\mathbf{S}^{n-1}, H^a(W)H^{\alpha }(\Omega ) is defined as the C²-C^{2}-solutions of D_au=0\Delta _{\alpha }u=0; where D_a=D_s+a(n+a-2)\Delta _{\alpha }=\Delta _{s}+\alpha (n+\alpha -2) is the spherical Laplace--Beltrami operator of order a\alpha and D_s\Delta _{s} is the radially independent part of the Laplace operator. We obtain a Green's integral formula for the functions in H^a(W)H^{\alpha }(\Omega ) with kernel expressed as a Gegenbauer function. As generalizations, higher order spherical iterated Dirac operators are defined in a polynomial form. Integral representations of the null solutions to these operators and an intertwining formula relating these operators on the sphere and their analogues in Euclidean space are presented.     

Derivation of fluorine-containing pyridine dicarboxylates. II. Elaboration at the 4-position

In response to the bio-activity found in fluorine-containing 4-alkyl-3, 5-pyridinedicarboxylates, a series of novel 4-substituted derivatives, not directly available by Hantzsch sequences, were prepared. Starting 4-alkylpyridines, 1 , were converted via enamine 2 to materials 3–8 . Derivatives 9–16 in turn were derived from aldehyde 3 , while acid derivatives 28–36 were prepared from 14 . Addition of oxygen, sulfur, and carbenoids effected conversion of 4-allylpyridine 16 to epoxy and cyclopropyl derivative 16–22 . A number of neighboring group effects were noted, including those forming the fused-ring systems 23-27 .     

cos πρ theorems for δ-subharmonic functions

For ϕ a δ-subharmonic function, sharp results are obtained that connectA(r, ϕ), B(r, ϕ) andT(r, ϕ), whereA(r, ϕ)=inf_|z|=r ϕ(z),B(r, ϕ)=sup_|z|=r ϕ(z), andT(r, ϕ) is the Nevanlinna characteristics.     

2‐Amino‐4‐chloro‐6‐[N‐methyl‐N‐(4‐methylphenyl)amino]pyrimidine: formation versus fragmentation of hydrogen‐bonded chains of edge‐fused R22(8) rings in 4,6‐disubstituted 2‐aminopyrimidines

Molecules of the title compound, C₁₂H₁₃ClN₄, are linked by two independent N—H...N hydrogen bonds into a chain of edge‐fused R₂²(8) rings. The significance of this study lies in its attempt to rationalize the patterns of supramolecular aggregation in the title compound and in a range of analogous 4,6‐disubstituted 2‐aminopyrimidines.     

Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder

This paper presents a numerical study of a two‐dimensional time‐dependent flow around a cylinder. Its main objective is to provide accurate reference values for the maximal drag and lift coefficient at the cylinder and for the pressure difference between the front and the back of the cylinder at the final time. In addition, the accuracy of these values obtained with different time stepping schemes and different finite element methods is studied. Copyright © 2004 John Wiley & Sons, Ltd.     

High‐order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high‐order accurate, finite‐difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier–Stokes equations. Fourth‐ or sixth‐order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth‐order accurate, centred finite differences. Implicit time marching is performed for both steady‐state and time‐accurate numerical solutions. High‐order, spectral‐type, low‐pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non‐linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright © 2004 John Wiley & Sons, Ltd.