The extended Koopmans' theorem Fock operator and the generalized overlap amplitude one-electron operator

The wave function of a system may be expanded in terms of eigenfunctions of the N −1 electron Hamiltonian times one-particle functions known as generalized overlap amplitudes (GOAS). The one-electron operator whose eigenfunctions are the GOAS is presented, without using an energy-dependent term as in the one-particle Green function or propagator approach. It is shown that this operator and the extended Koopmans' theorem (EKT) one-electron operator are of similar form, but perform complementary roles. The GOA operator begins with one-electron densities and total energies of N −1 electron states to generate the two-matrix and total energy of an N-electron state. The EKT operator begins with the two-matrix of an N-electron state to generate one-electron densities and ionization potentials (or approximations thereto) for N −1 electron states. However, whereas the EKT orbitals must be linearly independent, no such restriction applies to the GOAS. © 1996 John Wiley & Sons, Inc.     

Analysis of chemical bonding in C2 using Dyson orbitals

Multireference configuration interaction wave functions with single and double excitations were calculated for the ¹Σ⁺_g ground state of the C₂ molecule and the excited states of C⁺₂ with symmetries ²Σ⁺_g, ²Σ^-_u, ²Π_u, and ²Π_g. The corresponding σ_g, σ_u, π_u, and π_g valence Dyson orbitals were calculated. Most of the density due to the valence electrons is accounted for by three σ_g, one σ_u, and one degenerate pair of π_u Dyson orbitals. Electron correlation plays an important role in the bond strength of C₂ by increasing the occupation of the σ_g valence orbitals and decreasing the occupation of the σ_u and π_u valence orbitals. © 1996 John Wiley & Sons, Inc.     

Versatile host for metallo anions and cations

The crystal structures of two metallo oxides, perrhenate and dichromate, are reported with a diprotonated tetraamido/diamino-based macrocycle, L, in which the floppy ligand assumes a folded conformation. When the four amides are deprotonated, this same ligand binds transition-metal ions in its tetraanionic form, H-4L. For the divalent metal ions Cu2+ and Ni2+, H-4L again folds and dinuclear complexes are formed. With trivalent metal ions Co3+ and Fe3+, the ligand wraps about the metal ions, resulting in mononuclear complexes.     

Capillary electrophoresis: An integrated system with a unique split-flow sample introduction mechanism

The performance of an integrated capillary electrophoresis system with a novel split-flow sample injection mechanism and special high sensitivity UV absorbance detector is described. Sample introduction into the capillary is accomplished with a standard HPLC-type microliter syringe. The injected sample is divided proportionally between the separation capillary and an adjustable splitvent. The volume of sample introduced into the capillary can be manipulated by varying the length or the i.d. of the splitvent tubing; or the volume of sample injected. Data are presented showing reproducibility of retention time, peak height, and peak area; minimum detectability; and operation at short UV wavelengths.     

Inherent Ethyl Acetate Selectivity in a Trianglimine Molecular Solid

Ethyl acetate is an important chemical raw material and solvent. It is also a key volatile organic compound in the brewing industry and a marker for lung cancer. Materials that are highly selective toward ethyl acetate are needed for its separation and detection. Here, we report a trianglimine macrocycle ( TAMC ) that selectively adsorbs ethyl acetate by forming a solvate. Crystal structure prediction showed this to be the lowest energy solvate structure available. This solvate leaves a metastable, “templated” cavity after solvent removal. Adsorption and breakthrough experiments confirmed that TAMC has adequate adsorption kinetics to separate ethyl acetate from azeotropic mixtures with ethanol, which is a challenging and energy-intensive industrial separation.     

Convex Komlós sets in Banach function spaces

In 1967 Komlós proved that for any sequence n{fn} in L₁(μ), with ‖fn‖?M<∞ (where μ is a probability measure), there exists a subsequence n{gn} of n{fn} and a function g∈L₁(μ) such that for any further subsequence n{hn} of n{gn},

     

A new 11 point degree 6 cubature formula for the triangle

We present a new cubature formula in the triangle which exactly integrates polynomials up to degree 6, using only 11 points. The formula was computed by starting with a 12 point cubature formula and applying the reduced basis method to drive one of the weights to zero, resulting in an 11 point formula with positive weights and no points outside the triangle. This improves upon the previously best known positive inside formulas, which have 12 or more points. The lower bound on the number of points for a degree 6 cubature formula in the triangle is 10, which to date has only been obtained by allowing some of the points to be outside the triangle. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust Optimal Service Analysis of Single-Server Re-Entrant Queues

We generalize the analysis of J.A. Ball, M.V. Day, and P. Kachroo (Mathematics of Control, Signals, and Systems, vol. 12, pp. 307–345, 1999) to a fluid model of a single server re-entrant queue. The approach is to solve the Hamilton-Jacobi-Isaacs equation associated with optimal robust control of the system. The method of staged characteristics is generalized from Ball et al. (1999) to construct the solution explicitly. Formulas are developed allowing explicit calculations for the Skorokhod problem involved in the system equations. Such formulas are particularly important for numerical verification of conditions on the boundary of the nonnegative orthant. The optimal control (server) strategy is shown to be of linear-index type. Dai-type stability properties are discussed. A modification of the model in which new customers are allowed only at a specified entry queue is considered in 2 dimensions. The same optimal strategy is found in that case as well.