The electronic states of carbon monofluoride: Rydberg states

Hartree-Fock and multiconfiguration Hartree-Fock calculations are reported on some low-lying Rydberg states of CF and the ground state of CF⁺. For the CF⁺ ground state, ¹Σ⁺, the calculations give a bond length of 1.55 Å, a fundamental frequency of 1821 cm^?1, and a dissociation energy of 6.9 eV. Many interactions between the valence and Rydberg state manifolds are revealed. Also a strong mixing of the 3dσ and 4sσ components due to an accidental degeneracy is described.     

Separation of rhodium and iridium by multiple fractional extraction

Mixtures of the chloro complexes of rhodium(III) and iridium(IV) were resolved by a nine stage multiple extraction technique. The solutes are partitioned in a hydrochloric acid-tributyl phosphate system. Rhodium is concentrated in the raffinate while iridium is concentrated in the extractant. 99% of the rhodium and 94% of the iridium are recovered free of the other metal. Experimental results agree reasonably well with the results predicted by a theoretical treatment of the distribution data.     

A Chebotarev Theorem for finite homogeneous extensions of shifts

We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form :X×G/H→X×G/H where (x,gH)=(σx, α(x)gH), for some finite groupG and subgroupH. Given a σ-closed orbit τ, the periods of the -closed orbits covering τ define a partition of the integer |G/H|. The theorem then gives us an asymptotic formula for the number of closed orbits with respect to the various partitions of the integer |G/H|. We apply our theorem to the case of a finite extension and of an automorphism extension of shifts of finite type. We also give a further application to ‘automorphism extensions’ of hyperbolic toral automorphisms. Financially supported by Universiti Kebangsaan Malaysia     

Convergence rate estimate for a domain decomposition method

Summary We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ². We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.This author was supported by the National Science Foundation under contract numbers DCR-8521451 and ECS-8957475, by the IBM Corporation, and by the 3M Company, while in residence at Yale UniversityThis author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under Contract W-31-109-Eng-38This author was supported by the National Science Foundation under contract number ECS-8957475, by the IBM Corporation, and by the 3M Company     

Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

Ramsey partitions of integers and pair divisions

Ifk ₁ andk ₂ are positive integers, the partitionP = (₁,₂,..., _n ) ofk ₁+k ₂ is said to be a Ramsey partition for the pairk ₁,k ₂ if for any sublistL ofP, either there is a sublist ofL which sums tok ₁ or a sublist ofP –L which sums tok ₂. Properties of Ramsey partitions are discussed. In particular it is shown that there is a unique Ramsey partition fork ₁,k ₂ having the smallest numbern of terms, and in this casen is one more than the sum of the quotients in the Euclidean algorithm fork ₁ andk ₂.An application of Ramsey partitions to the following fair division problem is also discussed: Suppose two persons are to divide a cake fairly in the ratiok ₁k ₂. This can be done trivially usingk ₁+k ₂-1 cuts. However, every Ramsey partition ofk ₁+k ₂ also yields a fair division algorithm. This method yields fewer cuts except whenk ₁=1 andk ₂=1, 2 or 4.     

Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

An SIS waveguide heterodyne receiver for 600 HGz-635 GHz

A waveguide SIS heterodyne receiver using a Nb/AlO_X/Nb junction has been built for astronomical observations of molecular transitions in the frequency range 600 GHz - 635 GHz, and has been successfully used at the Caltech Submillimeter Observatory (CSO). We report double sideband (DSB) receiver noise temperatures as low as 245 K at 600 GHz -610 GHz, and near 300 K over the rest of the bandwidth. These results confirm that SIS quasiparticle mixers work well at submillimeter-wave frequencies corresponding to photon energies of at least 90% of the superconductor energy gap. In addition, we have systematically investigated the effect on the receiver performance of the overlap between first-order and second-order photon steps of opposite sign at these frequencies. The receiver noise increases by as much as 40% in the region of overlap. We infer potential limitations for operating submillimeter-wave Nb/AlO_x/Nb mixers.     

MR imaging findings in recurrent primary osseous Ewing sarcoma

The objective of this study was to determine the value of magnetic resonance (MR) imaging in diagnosing local recurrence of Ewing sarcoma. We retrospectively reviewed radiographs, Tc^99m-methylene diphosphonate (MDP) skeletal scintigraphy, computed tomography scans, and MR studies of 11 patients who had local recurrences of osseous Ewing sarcoma following initial responses to chemotherapy and local radiation. The MR images were compared to those of a control group of nine patients who had no evidence of relapse. T₁- and T₂-weighted MR images identified 9 of the 11 recurrences. Computed tomography was diagnostic in 4 of 6 cases evaluated, Tc^99m-MDP bone scintigraphy in 4 of 11 cases, and plain radiographs in 2 of 10. MR findings at relapse included changes in signal intensity, increased extent of abnormal marrow signal on T₁- and T₂-weighted images, and identification of a new soft tissue mass. These findings suggest that MR imaging is valuable in the routine follow-up of parimary osseous Ewing sarcoma.     

Small Transitive Families of Subspaces

A family of subspaces of a complex separable Hilbert space is transitive if every bounded operator which leaves each of its members invariant is scalar. This article surveys some results concerning transitive families of small cardinality, and adds some new ones. The minimum cardinality of a transitive family in finite dimensions (greater than 2) is 4. In infinite dimensions a transitive pair of linear manifolds exists but the minimum cardinality of a transitive family of dense operator ranges or norm-closed subspaces is not known. However, a transitive family of dense operator ranges with 5 elements can be found, and so can a transitive family of norm-closed subspaces with 4 elements. In finite dimensions (> 1) three nest algebras (corresponding to maximal nests) can intersect in the scalar operators, but two cannot. It is not known if this is the case in infinite dimensions for maximal nests of type ω + 1. Four such nest algebras can intersect in the scalar operators. Received June 15, 2002, Accepted November 27, 2002