Tests for specific nonparametric relations between two distribution functions with applications

Let (X,Y) be a random vector and let G and H be the marginal distributions of X and Y, respectively. In this paper, we propose two tests, one of Kolmogorov‐Smirnov type and the other of Wilcoxon type, for the null hypothesis Ψ(G) = H against the alternative Ψ(G) < H, where Ψ() is a function such that Ψ(G) is a distribution function. The tests are based on the empirical distribution functions of the observations on X and Y, which are dependent. We obtain their asymptotic null distributions. A suspected relationship between the distribution functions of two dependent outcomes can be specified as a hypothesis to be tested in examples like the load sharing models, record values, and auction bidding models. As an application, we consider in detail the problem of testing the effect of load sharing in two component parallel systems.     

On the conjugacy relation in ergodic theory

The set of pairs of transformations on the interval $[0,1]$ can be equipped with a standard Borel structure. We prove that the relation of conjugacy is not a Borel subset of this space, in fact it is complete analytic. Moreover, our construction proves that the two sets, $\{T:T\text{is conjugate of}{T}^{\mathrm{?1}}\}$, and $\{T:\text{the centralizer of}T\text{is non-trivial}\}$ are complete analytic sets. To cite this article: M.D. Foreman et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

87Sr lattice clock with inaccuracy below 10 -15

Aided by ultrahigh resolution spectroscopy, the overall systematic uncertainty of the 1S0-3P0 clock resonance for lattice-confined 87Sr has been characterized to 9 x 10(-16). This uncertainty is at a level similar to the Cs-fountain primary standard, while the potential stability for the lattice clocks exceeds that of Cs. The absolute frequency of the clock transition has been measured to be 429 228 004 229 874.0(1.1) Hz, where the 2.5 x 10(-15) fractional uncertainty represents the most accurate measurement of a neutral-atom-based optical transition frequency to date.     

Systematic study of the 87Srclock transition in an optical lattice

With ultracold 87Srconfined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to date of the 1S0-3P0 optical clock transition with a detailed analysis of systematic shifts (19 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 869 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its hertz-level linewidth characterized by an octave-spanning femtosecond frequency comb.     

Relaxation cross section measurements on NH3 and lower state focussing in a beam maser

Scattering cross for the lower state of the J=3, K=2 inversion doublet of NH₃ were measured using a beam maser spectrometer. The observed relaxation cross sections were the same as those obtained previously for the upper inversion state. These results support previous interpretations of observed relaxation cross sections for coherent superposition states. A coaxial electrostatic focusser state selector for beam maser spectroscopy which provides efficient focussing of states with a negative Stark effect is described.     

Rotational relaxation measurements on OCS using a beam maser

Rotational relaxation cross sections are reported for J = 0, 1 and 2 rotational states of OCS using a variety of polar and non-polar scattering gases. Cross sections are reported for pure states, superposition states and total beam attenuation. Inelastic cross sections for symmetric top scattering molecules are much larger than corresponding cross sections for linear scattering molecules. Upper and lower states for both J = 0 → 1 and J = 1 → 2 transitions were selected using quadrupole or co-axial focusers. These preliminary results show differences in cross sections for different rotational states.     

Strong linear- k valence-band mixing at semiconductor heterojunctions

This paper examines linear- k terms in the gamma(8) valence-band Hamiltonian for heterostructures of zinc-blende-type semiconductors. In bulk crystals such terms are known to be extremely small, due to their origin as relativistic perturbations from d and f orbitals. However, in heterostructures there is a nonvanishing contribution from p orbitals. This contribution is an order of magnitude larger than the corresponding bulk term, and it should give rise to an optical anisotropy comparable to (although smaller than) that seen in recent experiments on the quantum-well Pockels effect.     

Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1x10(-15)

We demonstrate phase and frequency stabilization of a diode laser at the thermal noise limit of a passive optical cavity. The system is compact and exploits a cavity design that reduces vibration sensitivity. The subhertz laser is characterized by comparison with a second independent system with similar fractional frequency stability (1x10(-15) at 1 s). The laser is further characterized by resolving a 2 Hz wide, ultranarrow optical clock transition in ultracold strontium.