Triatomic Vibrational Energies

The generator coordinate approximation theory isformally applied to H ₃ ⁺ . Asecular equation with an eigenvector ofthree dimensions and matrix elements ofsix dimensions results. Numerical solutions of this equation are thevibrational energy levels ofH ₃ ⁺ .     

Double exchange model for magnetic hexaborides

A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu1-xCaxB6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as the Hall effect, magnetoresistance, frequency dependent conductivity, and dc resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature T(C) as a function of the plasma frequency omega(p).     

Phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field

In this paper we study the critical behavior of the two-dimensional antiferromagnetic Ising model in both uniform longitudinal (H$H$) and transverse (Ω$\Omega$) magnetic fields. Using the effective-field theory (EFT) with correlation in single site clusters we calculate the phase diagrams in the H−T$H-T$ and Ω−T$\Omega -T$ planes for the square lattice. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.     

Frobenius theorem for foliations on singular varieties

We generalize Frobenius singular theorem due to Malgrange, for a large class of codimension one holomorphic foliations on singular analytic subsets of ℂ ^N . This research was partially supported by Pronex.     

A constraint generation algorithm for large scale linear programs using multiple-points separation

In order to solve linear programs with a large number of constraints, constraint generation techniques are often used. In these algorithms, a relaxation of the formulation containing only a subset of the constraints is first solved. Then a separation procedure is called which adds to the relaxation any inequality of the formulation that is violated by the current solution. The process is iterated until no violated inequality can be found. In this paper, we present a separation procedure that uses several points to generate violated constraints. The complexity of this separation procedure and of some related problems is studied. Also, preliminary computational results about the advantages of using multiple-points separation procedures over traditional separation procedures are given for random linear programs and survivable network design. They illustrate that, for some specific families of linear programs, multiple-points separation can be computationally effective.