Existence of compatible families of proper regular conditional probabilities

Summary Let (, , ) be a perfect probability space with countably generated, and let IB be a family of sub--fields of . Under a countability condition on the family IB, I show that there exists a family {}_IB of regular conditional probabilities which are everywhere compatible. Under a more stringent condition on IB, I show that the can furthermore be chosen to be everywhere proper. It follows that in the Dobrushin-Lanford-Ruelle formulation of the statistical mechanics of classical lattice systems, every (perfect) probability measure is a Gibbs measure for some specification.Research supported in part by NSF PHY-78-23952NSF Predoctoral Fellow (1976–79) and Danforth Fellow (1979–81).     

An Improved Algorithm for the Multi-commodity Location Problem

Distribution systems designs commonly require the optimal location decisions of regional ware-houses or distribution centers which function as intermediate facilities between plants and customers. This paper deals with such a location problem in which the facilities can handle one of several commodities. We term this problem the multi-commodity facility location problem. A branch and bound algorithm is proposed for solving this problem. Improved bounds are developed for increasing the efficiency of the algorithm. Computational results are provided.     

Gravitational Entropy in Cosmological Models

We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI _h models that admit an isotropic singularity. We also briefly discuss other possible gravitational entropy functions, including an appropriate measure of the velocity dependent Bel-Robinson tensor. PACS: 04.20.-q 95.30.Sf 98.80.Jk     

Anomalous bias dependence of spin torque in magnetic tunnel junctions

We predict an anomalous bias dependence of the spin transfer torque parallel to the interface, Tparallel, in magnetic tunnel junctions, which can be selectively tuned by the exchange splitting. It may exhibit a sign reversal without a corresponding sign reversal of the bias or even a quadratic bias dependence. We demonstrate that the underlying mechanism is the interplay of spin currents for the ferromagnetic (antiferromagnetic) configurations, which vary linearly (quadratically) with bias, respectively, due to the symmetric (asymmetric) nature of the barrier. The spin transfer torque perpendicular to interface exhibits a quadratic bias dependence.     

A Computational Study of CIONO2H+: Structure and Vibrations

Two protonated forms of chlorine nitrate, HClONO⁺ ₂ and ClONO₂H⁺, are treated ab initio by the Hartree-Fock and the second order Møller-Plesset perturbation approach with the standard 6–31G* basis set. Both minimum energy structures are planar (C ₃ symmetry) and their structural, energy, and vibrational parameters are reported. The computations conclude that the proton attacks the chlorine nitrate at its central, not end, oxygen atom. The protonation causes a considerable elongation of the central ON bond which becomes most probable place of cleavage. The dissociation should yield the neutral HOCl and NO⁺ ₂. These quantum-chemical findings well agree with the previous experimental indications.

     

Mass of the Bc meson in three-flavor lattice QCD

We use lattice QCD to predict the mass of the Bc meson. We use the MILC Collaboration's ensembles of lattice gauge fields, which have a quark sea with two flavors much lighter than a third. Our final result is mBc = 6304+/-12(+18)(-0) MeV. The first error bar is a sum in quadrature of statistical and systematic uncertainties, and the second is an estimate of heavy-quark discretization effects.     

High-speed addition/subtraction/complement/doubling of quaternary numbers using optical nonlinearities and DQPSK signals

We propose an innovative approach to implementing multiple arithmetic functions of quaternary numbers using optical nonlinearities and differential quadrature phase-shift keying (DQPSK) signals. By adopting 100 Gbit/s DQPSK signals (A, B) and exploiting nondegenerate four-wave mixing (FWM) for addition/subtraction and degenerate FWM for complement and doubling in a single highly nonlinear fiber, we demonstrate 50 Gbaud/s simultaneous quaternary addition (A+B), dual-directional subtraction (A-B, B-A), complement (-A, -B), and doubling (2B). Power penalties less than 4 dB (addition), 3 dB (dual-directional subtraction), 2 dB (complement), and 3.1 dB (doubling) are observed at a bit-error rate of 10(-9).     

Octave-spanning supercontinuum generation of vortices in an As2S3 ring photonic crystal fiber

We propose As(2)S(3) ring photonic crystal fiber (PCF) for supercontinuum generation of optical vortex modes. Due to the large material index contrast between As(2)S(3) and air holes in the designed ring PCF, there is a two-orders-of-magnitude improvement of the difference between the effective refractive indices of different vortex modes compared with regular ring fiber. The design freedom of PCFs enables a low dispersion (<60 ps/nm/km variation in total) over a 522 nm optical bandwidth. Moreover, the vortex mode has a large nonlinear coefficient of 11.7/W/m at 1550 nm with a small confinement loss of <0.03 dB/m up to 2000 nm. An octave-spanning supercontinuum spectrum of the vortex mode is generated from 1196 to 2418 nm at -20 dB by launching a 120 fs pulse with a 60 W peak power at 1710 nm into a 1 cm long As(2)S(3) ring PCF.     

Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs

We propose an approach to efficiently generate and multiplex optical orbital angular momentum (OAM) modes in a fiber with a ring refractive index profile by using multiple coherent inputs from a Gaussian mode. By controlling the phase relationship of the multiple inputs, one can selectively generate OAM modes of different states l. By controlling both the amplitude and phase of the multiple inputs, multiple OAM modes can be generated simultaneously without additional loss coming from multiplexing. We show, by simulation, the generation of OAM modes (OAM state |l|<3) with mode purity greater than 99%. The power loss of generating and multiplexing seven modes is about 35%. A transmitter for an OAM-based mode-division multiplexing system is proposed based on the discrete Fourier transform between the data carried by the multiple inputs and the data carried by the OAM modes. The experimental implementation of the proposed approach could be achieved by integrating ring fiber, multicore fiber, and photonic integrated circuit technology.