Bases for some reciprocity algebras II

We construct bases for the stable branching algebras for the symmetric pairs (GL_n,O_n), (O_n+m,O_n×O_m) and (Sp_2n,GL_n).     

Design of a tunnel-entrance hood with multiple windows and variable cross-section

A theory is proposed for the design of a uniform tunnel-entrance hood whose cross-sectional area exceeds the tunnel area . A train entering the tunnel produces a low-frequency compression wave that can be subject to nonlinear steepening in a long tunnel. An optimized hood of length ℓ_h increases the initial thickness of the compression wave front from R/M to ℓ_h/M, where Rℓ_h is the nominal radius of the tunnel and M is the train Mach number. In addition, the pressure rise should be linear across the wave front to obtain an overall minimum value of the subjectively important pressure gradient. This is achieved in a uniform hood by distributing windows along the hood wall to vent away high-pressure air displaced by the train. We consider the problem of determining the distribution and sizes of these windows and the magnitude of the area ratio to ensure that the hood behaves optimally at low-train Mach numbers (M<0.2), when the hood can be regarded as being acoustically compact. At the projected higher Mach numbers of advanced high-speed trains (0.4, say) recent analysis for hoods of uniform cross-section by Howe in 2003 indicates that a hood optimized for low Mach number operations continues to produce an essentially linear pressure rise across a compression wave of thickness ℓ_h/M except for a low-amplitude oscillation at the very front of the wave.     

The rôle of surface shear stress fluctuations in the generation of boundary layer noise

The influence of unsteady wall shear stress on boundary layer noise and wall pressure fluctuations is discussed. It is argued that in the acoustic analogy theory of boundary layer noise the surface shear stress “dipole” characterizes acoustic propagation and not generation. Analytical results are presented in support of this view which, in addition, indicate that the effect of the surface dipole is to dininish rather than enhance boundary layer radiation at low Mach numbers.     

Superactions

We present a general formalism for constructing super-invariants by integrating over even-dimensional submanifolds of superspace, valid for all N. This result includes all previous action formulae, without central changes, and we use it to derive the on-shell N=4 super-Yang-Mills action and a manifestly SU(8) invariant linearized three-loop counterterm for N=8 supergravity. We also present a compact diagrammatic technique that replaces index manipulation involving spinor derivatives.     

Application of energy conservation to the solution of radiation problems involving uniformly convected source distributions

This paper describes a technique for determining the mean square asymptotic properties of the radiation fields of uniformly convecting multipole source distributions which avoids the usual asymptotic far field analysis of the integral representation of the wave field. The method is based on the principle of conservation of energy and is illustrated here by a consideration of the acoustic field radiated by convected sources located in free space and within a semi-infinite jet flow.     

Studies of potassium ferrite K1+xFe11O17. I. Electronic conductivity and defect structure

The electronic conductivity of the nonstoichiometric potassium ferrite phase (with the β-alumina structure) has been measured as a function of temperature and potassium ion concentration. The latter was varied by coulometric titration using the cell: K_11q/K-β-alumina/K_1+xFe₁₁O₁₇. At 523°K the conductivity increased nearly linearly as x was increased from 0.09 to 0.65 while the activation energy for conduction decreased from 0.1 to 0.07 eV. The cell emf was completely reversible. The results are consistent with the view that the excess potassium ions are charge compensated by reduction of Fe³⁺ to Fe²⁺, and a comparison with results in the literature for some ironcontaining spinels suggests that a similar small polaron electron hopping mechanism operates.     

The systematics of h112 proton alignment in 157, 158, 159Er

Rotational bands have been observed in ^{157, 158, 159}Er to very high spin ($\text{J ～ 41}\text{h}\text{?}$). Upbends are found, due to the alignment of two h_{$\text{11}\text{2}$} protons at $\text{0.40 ?}\text{h}\text{?}\text{ω ? 0.46}\text{MeV}$ in all bands. A systematic shift with neutron number of the band-crossing frequency is observed and is related to a change in quadrupole deformation ?₂.     

On some results of Strichartz and of Rallis and Schiffman

Let (i, H, E) and (j, K, F) be abstract Wiener spaces and let α be a reasonable norm on E ? F. We are interested in the following problem: is ($\text{i ? j, H}\text{}\text{?}\text{bo}{}_2\text{K, E}\text{}\text{?}\text{bo}{}_{\mathrm{\alpha F}}$) an abstract Wiener space ? The first thing we do is to prove that the setting of the problem is meaningfull: namely, i ? j is always a continuous one to one map from $\text{H}\text{}\text{?}\text{bo}{}_2\text{K}$ into $\text{E}\text{}\text{?}\text{bo}{}_{\mathrm{\alpha }}\text{F}$. Then we exhibit an example which shows that the answer cannot be positive in full generality. Finally we prove that if F=L^p(X,$\text{X}$,λ) for some σ-finite measure λ ? 0 then $\text{(i?j, H}\text{?}{}_2\text{K,L}{}^{\mathrm{p}}$(X,$\text{X}$,λ) is an abstract Wiener space. By-products are some new results on γ-radonifying operators, and new examples of Banach spaces and cross norms for which the answer is affirmative (in particular α = π the projective norm, and F=L¹(X,$\text{X}$,λ)).