Spectroscopic studies of CO2 trapped in rare gas matrices

Low temperature (5 K) high resolution (0.15 and 0.03 cm⁻¹) absorption spectra of ¹³CO₂ have been recorded in neon, argon, krypton, and xenon matrices, in the ν₃ and ν₂ regions. Diffusion experiments have been performed in krypton and xenon in order to identify vibrational traps which could be responsible for the decrease and shortening of the emission observed after laser excitation: high-frequency structures in the ν₃ region are assigned to dimers and a doubling of the monomer line is due to a site effect. In neon, only a double substitutional site, with a splitting of the degenerate ν₂ vibration, is observed. In argon, as previously reported, a single and a double site are characterized. In krypton and xenon, where ν₂ is not split, only single sites would be predicted. As one of them exhibits a ν₃ line highly sensitive to temperature, we expect a large coupling with the lattice and a fast vibrational relaxation. This site is very likely the vibrational trap we are looking for.     

Nested regular polygon solutions for planar 2N-body problems

In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.     

A language-driven generalized numerical database translator

Numerical databases arise in many scientific applications to keep track of large dense and sparse matrices, residing on secondary devices in matrix compact data representation. This paper describes a language-driven generalized data translator for translating any numerical database from one matrix compact data representation to another. Our approach is to describe any matrix compact data representation by a physical schema and any numerical database and its mapping to storage by data language facilities. The languages are processed by a Generalized Syntax-Directed Translation Scheme (GSDTS) to automatically generate FORTRAN conversion programs which become the major modules of the translator.     

A constructive characterization ofQ o-matrices with nonnegative principal minors

In [2] we characterized the class of matrices with nonnegative principla minors for which the linear-complementarity problem always has a solution. That class is contained in the one we study here. Our main result gives a finitely testable set of necessary and sufficient conditions under which a matrix with nonnegative principal minors has the property that if a corresponding linear complementarity problem is feasible then it is solvable. In short, we constructively characterize the matrix class known asQ _o ∩P _o . Research partially supported by the National Science Foundation Grant DMS-8420623 and U.S. Department of Energy Contract DE-AA03-76SF00326, PA # DE-AS03-76ER72018.     

Structural properties and recognition of restricted and strongly unimodular matrices

A (0, ±1) matrix A is restricted unimodular if every matrix obtained from A by setting to zero any subset of its entries is totally unimodular. Restricted unimodular matrices are also known as matrices without odd cycles. They have been studied by Commoner and recently Yannakakis has given a polynomial algorithm to recognize when a matrix belongs to this class. A matrix A is strongly unimodular if any matrix obtained from A by setting at most one of its entries to zero is totally unimodular. Crama et al. have shown that (0,1) matrix A is strongly unimodular if and only if any basis of (A, 1) is triangular, whereI is an identity matrix of suitable dimensions. In this paper we give a very simple algorithm to test whether a matrix is restricted unimodular and we show that all strongly unimodular matrices can be obtained by composing restricted unimodular matrices with a simple operation. Partially supported by a New York University Research Challenge Fund Grant.     

Eigenfunctions of expected value operators in the Wishart distribution,II

Let V = (v_ij) denote the k × k symmetric scatter matrix following the Wishart distribution W(k, n, Σ). The problem posed is to characterize the eigenfunctions of the expectation operators of the Wishart distribution, i.e., those scalar-valued functions f(V) such that (E_nf)(V) = λ_n,kf(V). A finite sequence of polynomial eigenspaces, EP spaces, exists whose direct sum is the space of all homogeneous polynomials. These EP subspaces are invariant and irreducible under the action of the congruence transformation V → T′VT. Each of these EP subspaces contains an orthogonally invariant subspace of dimension one. The number of EP subspaces is determined and eigenvalues are computed. Bi-linear expansions of $\text{|I + VA|}{}^{\mathrm{<mtext>?n</mtext><mtext>2</mtext>}}$ and (tr VA)^r into eigenfunctions are given. When f(V) is an EP polynomial, then f(V^?1) is an EP function. These EP subspaces are identical to the more abstractly defined polynomial subspaces studied by James.     

Jacobi matrices for measures modified by a rational factor

This paper describes how, given the Jacobi matrixJ for the measure d(t), it is possible to produce the Jacobi matrix for the measurer(t)d(t) wherer(t) is a quotient of polynomials. The method uses a new factoring algorithm to generate the Jacobi matrices associated with the partial fraction decomposition ofr(t) and then applies a previously developed summing technique to merge these Jacobi matrices. The factoring method performs best just where Gautschi's minimal solution method for this problem is weakest and vice versa. This suggests a hybrid strategy which is believed to be the most powerful yet for solving this problem. The method is demonstrated on a simple example and some numerical tests illustrate its performance characteristics.     

Performance analysis of a hybrid switching system where voice messages can be queued

In the classical model of a hybrid switching system with movable boundary it is assumed that blocked voice messages are lost and do not affect the further functioning of the system. We describe a more realistic model where blocked voice messages are queued and then are served once a channel becomes free. The main mathematical difficulty in the analysis of such models lies in the fact that the underlying stochastic process has as state space the whole quadrant ₊ ² . We reduce the problem to a set of equations defined over the lattice semi-strip {1,...,N} × ₊. This in turn allows us to use available general mathematical theories.     

Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit time-stepping applied to preconditioned Euler equations. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed.The work reported was performed in the framework of the BRITE-EURAM Aeronautics R&D Programme of the European Communities (Contract No. AER2-CT92-0040). The work was started during the second author's visit to CWI in 1993.     

Nonlinear coordinate representations of smooth optimization problems

Nonlinear coordinate representations of smooth optimization problems are investigated from the point of view of variable metric algorithms. In other words, nonlinear coordinate systems, in the sense of differential geometry, are studied by taking into consideration the structure of smooth optimization problems and variable metric methods.Both the unconstrained and constrained cases are discussed. The present approach is based on the fact that the nonlinear coordinate transformation of an optimization problem can be replaced by a suitable Riemannian metric belonging to the Euclidean metric class. In the case of equality and inequality constraints, these questions are related closely to the right inverses of full-rank matrices; therefore, their characterization is a starting point of the present analysis. The main results concern a new subclass of nonlinear transformations in connection with the common supply of coordinates to two Riemannian manifolds, one immersed in the other one. This situation corresponds to the differentiable manifold structure of nonlinear optimization problems and improves the insight into the theoretical background of variable metric algorithms. For a wide class of variable metric methods, a convergence theorem in invariant form (not depending on coordinate representations) is proved. Finally, a problem of convexification by nonlinear coordinate transformations and image representations is studied.This research was supported by the Hungarian National Research Foundation, Grant Nos. OTKA-2568 and OTKA-2116, and by the Project Trasporti of the Italian National Research Council (CNR).