A universal continuum of weight

We prove that every continuum of weight  is a continuous image of the Cech-Stone-remainder  of the real line. It follows that under  the remainder of the half line is universal among the continua of weight  -- universal in the `mapping onto' sense.

We complement this result by showing that 1) under  every continuum of weight less than  is a continuous image of , 2) in the Cohen model the long segment of length  is not a continuous image of , and 3)  implies that is not a continuous image of , whenever  is a -saturated ultrafilter.

We also show that a universal continuum can be gotten from a -saturated ultrafilter on , and that it is consistent that there is no universal continuum of weight  .

     

Modeling of multimaterial interfaces in the finite difference method

This work develops a procedure for representing multimaterial interfaces in finite difference models. The boundary separating the two materials can be on or between a row of nodes. The development is validated by embedding the boundary between two regions in a single, larger region and comparing the results. The development is facilitated by the use of a physically based notation that represents the displacement approximations in terms of rigid-body rotations and strain gradient quantities that produce the displacements. Four example problems are presented.     

Core excitons in SixGe1-x alloys

The Hjalmarson et al. theory of Frenkel core excitons is applied to the Si and Ge p core excitons in Si_xGe_1-x alloys. The Si 2p and Ge 3p Frenkel excitons' “binding energies” with respect to the conduction-band edge are found to be strong functions of x, with nearly zero binding energies for both excitons near x=0 or 1, and with binding energies of order tenths of eV for compositions x near x=0.2.     

Search for quadrupole strength in the electroexcitation of the delta+(1232)

High-precision 1H(e,e'p)pi(0) measurements at Q2 = 0.126 (GeV/c)2 are reported, which allow the determination of quadrupole amplitudes in the gamma*N-->Delta transition; they simultaneously test the reliability of electroproduction models. The derived quadrupole-to-dipole ( I = 3/2) amplitude ratios, R(SM) = (-6.5+/-0.2(stat+sys)+/-2.5(mod))% and R(EM) = (-2.1+/-0.2(stat+sys)+/-2.0(mod))%, are dominated by model error. Previous R(SM) and R(EM) results should be reconsidered after the model uncertainties associated with the method of their extraction are taken into account.     

-Measurement of the proton's electric to magnetic form factor ratio from 1H(over -->)(e(over -->),e'p)

We report the first precision measurement of the proton electric to magnetic form factor ratio from spin-dependent elastic scattering of longitudinally polarized electrons from a polarized hydrogen internal gas target. The measurement was performed at the MIT-Bates South Hall Ring over a range of four-momentum transfer squared Q2 from 0.15 to 0.65 (GeV/c)(2). Significantly improved results on the proton electric and magnetic form factors are obtained in combination with existing cross-section data on elastic electron-proton scattering in the same Q2 region.     

Ordinal remainders of ψ-spaces

We consider which ordinals, with the order topology, can be Stone-?ech remainders of which spaces of the form ψ(κ,M), where ω?κ is a cardinal number and M⊂ω[κ] is a maximal almost disjoint family of countable subsets of κ (MADF). The cardinality of the continuum, denoted c, and its successor cardinal, c⁺, play important roles. We show that if κ>c⁺, then no ψ(κ,M) has any ordinal as a Stone-?ech remainder. If κ?c then for every ordinal δ<κ⁺ there exists Mδ⊂ω[κ], a MADF, such that βψ(κ,Mδ)?ψ(κ,Mδ) is homeomorphic to δ+1. For κ=c⁺, βψ(κ,Mδ)?ψ(κ,Mδ) is homeomorphic to δ+1 if and only if c⁺?δ<c⁺⋅ω.     

Guiding synchrotron X‐ray diffraction by multimodal video‐rate protein crystal imaging

Synchronous digitization, in which an optical sensor is probed synchronously with the firing of an ultrafast laser, was integrated into an optical imaging station for macromolecular crystal positioning prior to synchrotron X‐ray diffraction. Using the synchronous digitization instrument, second‐harmonic generation, two‐photon‐excited fluorescence and bright field by laser transmittance were all acquired simultaneously with perfect image registry at up to video‐rate (15 frames s^?1). A simple change in the incident wavelength enabled simultaneous imaging by two‐photon‐excited ultraviolet fluorescence, one‐photon‐excited visible fluorescence and laser transmittance. Development of an analytical model for the signal‐to‐noise enhancement afforded by synchronous digitization suggests a 15.6‐fold improvement over previous photon‐counting techniques. This improvement in turn allowed acquisition on nearly an order of magnitude more pixels than the preceding generation of instrumentation and reductions of well over an order of magnitude in image acquisition times. These improvements have allowed detection of protein crystals on the order of 1 µm in thickness under cryogenic conditions in the beamline. These capabilities are well suited to support serial crystallography of crystals approaching 1 µm or less in dimension.