Group Theoretic Properties of the Group of Computable Automorphisms of a Countable Dense Linear Order

We compare Aut(Q), the classical automorphism group of a countable dense linear order, with Aut _c (Q), the group of all computable automorphisms of such an order. They have a number of similarities, including the facts that every element of each group is a commutator and each group has exactly three nontrivial normal subgroups. However, the standard proofs of these facts in Aut(Q) do not work for Aut _c (Q). Also, Aut(Q) has three fundamental properties which fail in Aut _c (Q): it is divisible, every element is a commutator of itself with some other element, and two elements are conjugate if and only if they have isomorphic orbital structures.     

Critical phenomena and relativistic gravitational collapse

Recent calculations have shown the existence of critical phenomena in general relativity associated with the collapse of wavepackets of massless fields that are near, in parameter space, the onset of black hole formation (the critical point). Two physically distinct systems have been explored: collapse of spherically-symmetric massless scalar field and collapse of vacuum, axisymmetric gravitational waves. Nonlinear effects dominate near the critical point. Black-hole mass serves as an order parameter and has a power-law dependence on critical separation in the supercritical region of parameter space. Remarkably, the values of the critical exponent of the power law are nearly identical in the two systems. The nonlinearity induces the fields to oscillate. Each successive oscillation is an echo, obeying a spatial and temporal scaling relation.     

On the initial time behavior of spatial derivatives for solutions of the parabolic Cauchy problem

The continuity of the spatial derivatives for solutions of the parabolic Cauchy problem is established down to the initial time under the assumption that the initial data and coefficients are sufficiently smooth.     

Simple thermometric appratus for the estimation of carbon monoxide in air

A simple, inexpensive apparatus is described for estimating the amount of carbon monoxide in air over a range of concentration from 0.01 to 0.1% or higher, with an accuracy of 0.005 to 0.01%. Thc carbon monoxide is oxidised by passing through a layer of Hopcalite catalyst at room temperature, and the rise in temperature of the air stream due to the heat of combustion is measured with a thermometer. About 60% of the theoretically possible temperature rise is actually observed with the apparatus. By means of a calibration chart, the concentration of carbon monoxide present is read as a function of the temperature increase.     

Equilibrium structure of hydrogen-bonded polymer blends

Deuterium-labeled polystyrene modified by random distributions of the comonomer p-(1,1,1,3,3,3-hexaflouro-2-hydroxyisopropyl)-α-methyl-styrene [DPS(OH)] has been blended with poly(butyl methacrylate) (PBMA) and studied with small-angle neutron scattering (SANS). Miscibility is induced via hydrogen bonding between the DPS(OH) hydroxyl group and PBMA carbonyl groups. The data suggest that the nature of the miscible-phase structure in these blends differs from that of the usual homopolymer blends at small scattering angles, which we attribute to the short-range site specific nature of the hydrogen bond interaction. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2745–2750, 1998     

A general solution to unsteady, coupled magnetohydrodynamic couette flow

A general solution to nonsteady coupled magnetohydrodynamic plane Couette flow by the method of Fourier series expansion is presented in this paper. Two particular examples of the utility of the solution are included: 1) an impulsive start of the wall, and 2) a wall velocity proportional to (1 − exp(− αt)). For the case of an impulsive start of the wall it is found that flow is apparently accelerated by the presence of the magnetic field, a situation opposite to that which occurs when no induced magnetic field is allowed.     

Crystal structure of the methanol solvate of (η5-cyclopentadienyl)[1,2-bis(diphenylphosphino)ethane] nitroruthunium(II) Ru(η5-C5H5)dppe)(NO2)·CH3OH

The title complex crystallizes in the centrosymmetric monoclinic space group C2/c (No. 15) withZ=8. The structure was refined toR=4.49% for those 2745 independent reflections with 2=5–50^o and |F |>6(F). Ruthenium-ligand distances are as follows: Ru-P=2.284(2) and 2.286(2) Å, Ru-NO₂=2.049(6) Å and Ru-C(Cp)=2.210(10)-2.246(9) Å. Bond lengths within the nitro ligand are N(1)-O(1)=1.226(10) Å and N(1)-O(2)=1.244(10) Å. The methanol of solvation is ordered but is subject to large thermal vibrational motions.     

The construction of stationary two-dimensional Markoff fields with an application to quantum field theory

It is shown that if φ(f)  ∝_R^dφ(y) f(y) dy is a Markoff random field and X_α are multiplicative functionals of φ (with E(X_α) = 1) which converge locally in L₁, then there exists a locally Markoff random field $\text{φ}{}_1$ such that $\text{E(exp(iφ}{}_1\text{(f))) =}\text{lim}{}_{\mathrm{\alpha }}\text{E(X}{}_{\mathrm{<mtext>\alpha </mtext>}}\text{exp}\text{(iφ(φ)))}$. We choose φ to be the two-dimensional generalization of the Ornstein-Uhlenbeck velocity process and take X_α proportional to exp(?λ∝_R² : P(φ(y)) : g_α(y) dy), where: P(φ(y)) : is a regularized even degree polynomial in φ(y). It is then proved that for an appropriate choice of g_α → 1 and small λ, {X_α} does converge locally in L₁ and that the corresponding $\text{φ}{}_1$ is stationary.