A simple low-vacuum environmental cell.

The environmental cell device discussed in this paper provides a modest low-vacuum scanning electron microscopy (SEM) capability to a standard SEM without requiring additional pumping. This environmental cell confines a volume of low vacuum in contact with the sample surface using a container that has an aperture for admitting the primary electron beam. The aperture is large enough to permit a limited field of view of the sample, and small enough to limit the outflow of gas into the SEM chamber to that which can be accommodated by the standard SEM pumping system. This environmental cell also functions as a gaseous detector device.     

A new Löwenheim-Skolem theorem

This paper establishes a refinement of the classical Löwenheim-Skolem theorem. The main result shows that any first order structure has a countable elementary substructure with strong second order properties. Several consequences for Singular Cardinals Combinatorics are deduced from this.

     

Comparison of XYZ Model Fitting Functions for 111Cd in In3La

The XYZ model describes the interaction between nuclear probes and an electric field gradient that fluctuates among three orthogonal directions. The model presents a means to calculate the perturbation function that represents spectra obtained using perturbed angular correlation spectroscopy. Three analytic approximations of the perturbation function have been developed previously, and they are evaluated in the present paper in the context of Cd jumping among In-lattice sites in In₃La.     

Ihara zeta functions of digraphs

After defining and exploring some of the properties of Ihara zeta functions of digraphs, we improve upon Kotani and Sunada’s bounds on the poles of Ihara zeta functions of undirected graphs by considering digraphs whose adjacency matrices are directed edge matrices.     

On the torsion of Jacobians of principal modular curves of level 3<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3ⁿ) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the second uses the moduli interpretation. Received: 30 September 2005     

Aryl pyrrolidinones via radical 1,4-aryl migration and 5-endo-trig cyclisation of N-(2-bromoallyl)arylcarboxamides

Radical reaction of a series of N-(2-bromoallyl)arylcarboxamides led to the production of 4-arylpyrrolidin-2-ones and directly reduced materials in comparable yields. A cascade process, involving sequential 5-exo-trig spirocyclisation, β-scission, and 5-endo-trig cyclisation of the resulting acyl radical, is proposed to explain the pyrrolidinone products.     

Properties of polystyrene-poly(methylmethacrylate) random and diblock copolymers in dilute and semidilute solutions

Solution properties for random and diblock copolymers of polystyrene (PS) and poly(methyl methacrylate) (PMMA) have been measured by dynamic and total intensity light scattering in solvents of differing quality. The results are compared with the corresponding properties for PS and PMMA homopolymers of similar molecular weight, in order to determine if interactions between unlike monomers are significant. The hydrodynamic radius (R_h) and diffusion second virial coefficient (k_d) for the random copolymer are found to be larger than the corresponding values for the homopolymers in a solvent which is near-theta for the two homopolymers, whereas no such effect is observed for the block copolymer. This suggests that most intrachain interactions occur a relatively short distance along the chain backbone. In a mutual good solvent R_h and k_d of the random copolymer are comparable to the average of the values for the homopolymers, indicating that in a good solvent monomer/solvent interactions dominate over monomer/monomer interactions. For an isolated diblock copolymer in a mutual good solvent, there is no evidence that interactions between unlike monomers lead to additional expansion of the entire molecule, as measured by R_h, nor expansion of the individual blocks as probed by light scattering with one block optically masked. However, at low but finite concentration there is evidence (the coefficients of the binary interaction terms in the viscosity and the mutual diffusion coefficient, and the second and third virial coefficients) that a weak ordering effect may exist in block copolymer solutions, far from the conditions where microphase separation occurs. Finally, measurements of ternary polymer-polymer-solvent solutions show no dependence on monomer composition or monomer distribution for the tracer diffusion of probe PS-PMMA copolymers in a PMMA/toluene matrix. This indicate that the frictional interaction is largely unaffected by interactions between unlike monomers. However, there is evidence that the thermodynamic interaction is more unfavorable between a random copolymer and the homopolymer matrix than between a diblock and the matrix. © 1994 John Wiley & Sons, Inc.