An edge-of-the-wedge theorem for hypersurface CR functions

The classical edge-of-the-wedge theorem for holomorphic functions is generally false for CR functions. However, it is true on Levi-indefinite hypersurfaces for wedges pointing in null directions.     

On Affine Normal Forms and a Classification of Homogeneous Surfaces in Affine Three-Space

We classify homogeneous surfaces in real and complex affine three-space. This is achieved by choosing affine coordinates so that the surface is defined by a function whose Taylor series is in a preferred normal form.     

What is Q-Curvature?

Branson’s Q-curvature is now recognized as a fundamental quantity in conformal geometry. We outline its construction and present its basic properties.     

Extreme Value Asymptotics for Multivariate Renewal Processes

For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results are established for thed-dimensional renewal process. Similar theorems for the estimated version of this process are also derived. These results are suggested to serve as simultaneous asymptotic testing devices for detecting changes in the multivariate setting.     

Experimental comparison of Jψ production by π±, K±, p and p̄ beams at 39.5 GeV/c

Measurements have been made of relative production cross sections of the $\text{J}\text{ψ}$ by π^±, K^±, p and p? at 39.5 GeV/c incident on copper. $\text{J}\text{ψ}$ production rates from π^?, K^? and p? are similar. The $\text{J}\text{ψ}$ relative particle/anti-particle production cross sections for x>0 are $\text{σ(π}{}^{\mathrm{+}}\text{)}\text{σ(π}{}^{\mathrm{?}}\text{)=(0.87±0.14)}$, σ(K⁺)/σ(K^?)=(0.85±0.5) and $\text{σ(}\text{p}\text{)}\text{σ(}\text{p}\text{?}\text{)=(0.15 ±0.08)}$. The small p/p? cross section ratio disagrees with models of J/ψ production by gluon amalgamation.     

Large-eddy simulations of chevron jet flows with noise predictions

Hybrid large-eddy type simulations for chevron nozzle jet flows are performed at Mach 0.9 and Re = 1.03 × 10⁶. Without using any subgrid scale model (SGS), the numerical approach applied in the present study is essentially implicit large-eddy simulation (ILES). However, a Reynolds-averaged Navier–Stokes (RANS) solution is patched into the near wall region. This makes the overall solution strategy hybrid RANS–ILES. The disparate turbulence length scales, implied by these different modeling approaches, are matched using a Hamilton–Jacobi equation. The complex geometry features of the chevron nozzles are fully meshed. With numerical fidelity in mind, high quality, hexahedral multi-block meshes of 12.5 × 10⁶ cells are used. Despite the modest meshes, the novel RANS–ILES approach shows encouraging performance. Computed mean and second-order fluctuating quantities of the turbulent near field compare favorably with measurements. The radiated far-field sound is predicted using the Ffowcs Williams and Hawkings (FW–H) surface integral method. Encouraging agreement of the predicted far-field sound directivity and spectra with measurements is obtained.     

Measured and modeled enhancement of transition metal emissions in the d.c. plasma jet

Enhancement of sensitive transition metal lines by a sodium matrix is measured in a 3-electrode d.c. plasma jet. Spiking with 0.43 M NaCI causes enhancement by factors of 1.85–2.92 in ionic lines and of 1.22–1.99 in atomic lines for eight of the structurally related analyte elements, but suppresses Zn I and Zn II emissions by about 25 %. Emission response to NaCI of lines within the same spectrum, or between different spectra of like ionization stage, can be simulated to 15 % and 20–25 %, respectively, by approximations linear in energy differences. For ionic lines these differences are the absolute value of the line excitation potential minus the energy of the ion state most readily pumped by Penning ionization by argon. For atomic lines it is the difference between emitting state excitation potential and the first ionization potential. Analyses of the experimental data strongly suggest that: (1) Na acts mainly to pertub radiative transfer rather than collisional redistribution processes; (2) population pumping of excited analyte states is largely driven by Penning ionization; (3) accelerated radiative cooling due to Na is manifested in a lowering of local kinetic temperature; (4) to a first-order of approximation, ambipolar diffusion, analyte-Na collisions of the second kind, and analyte ground state spin, do not influence emission line enhancement by easily ionized elements (EIE). Approximations are developed for predicting transition metal enhancements by arbitrary Na doping concentrations, and means are sketched for extending the method to other analyte group/EIE combinations. Practical implications of the work are noted.