A classification of orbits admitting a unique invariant measure

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_{\infty }$-invariant and concentrated on a single isomorphism class must be zero, or one, or continuum. Further, such an isomorphism class admits a unique $S_{\infty }$-invariant probability measure precisely when the structure is highly homogeneous; by a result of Peter J. Cameron, these are the structures that are interdefinable with one of the five reducts of the rational linear order $(\mathbb{Q},<)$.     

Bimodules in crossed products of von Neumann algebras

In this paper, we study bimodules over a von Neumann algebra M   in the context of an inclusion M⊆M_?αG$M\subseteq M{?}_{\alpha }G$, where G is a discrete group acting on a factor M by outer ?-automorphisms. We characterize the M  -bimodules X⊆M_?αG$X\subseteq M{?}_{\alpha }G$ that are closed in the Bures topology in terms of the subsets of G  . We show that this characterization also holds for w^?$w^{?}$-closed bimodules when G has the approximation property (AP  ), a class of groups that includes all amenable and weakly amenable ones. As an application, we prove a version of Mercer's extension theorem for certain w^?$w^{?}$-continuous surjective isometric maps on X.     

What is a design? How should we classify them?

Design theory crosses the boundary between mathematics and statistics, and includes a wide range of disparate types of design. In this paper we present a classification scheme which aims to include as many important types as possible, based on a balance among concept, representation and use.     

Anomalous pulse-width narrowing with first-order compensation of polarization mode dispersion

We present analytical and experimental results to demonstrate the narrowing of pulses transmitted through optical fibers, with polarization mode dispersion compensated for to first order in frequency. The compensation technique splits the optical signal at the fiber output into polarization components that are aligned with the output principal states of polarization, and only one of the two components is subsequently detected. It is shown that it is possible with this compensation technique to have output pulses that are narrower than the input pulses. Pulse narrowing can also be found when the optical signal is split into orthogonal polarization components that are not principal states of polarization.     

Stories about groups and sequences

The main theme of this article is that counting orbits of an infinite permutation group on finite subsets or tuples is very closely related to combinatorial enumeration; this point of view ties together various disparate stories. Among these are reconstruction problems, the relation between connected and arbitrary graphs, the enumeration of N-free posets, and some of the combinatorics of Stirling numbers.Dedicated to Hanfried Lenz on the occasion of his 80th birthday.     

High-power optical parametric chirped-pulse amplifier system with a 1.55 microm signal and a 1.064 microm pump

We have designed and built a chirped-pulse parametric-amplifier system that utilizes a 10 Hz, 300 ps, Nd:YAG pump laser system; a 1.575 microm fiber oscillator and amplifier as the signal source; and rubidium titanyl phosphate and potassium titanyl arsenate nonlinear crystals. We obtained 260 fs, 30 mJ pulses centered at 1.550 microm, representing a gain of > 10(9) and a peak power of 100 GW. To our knowledge, these are the highest energy and peak power pulses ever produced in the 1.5-2.0 microm region     

Electron density and temperature contour plots from alaser-produced plasma using collective ultraviolet Thomson scattering

Temporally integrated ultraviolet collective Thomson scattering measurements were performed with frequency-quadrupled Nd:YAG laser radiation on an underdense long-scalelength aluminum plasma (n_c ~10²¹ cm^-3, Z≈7, T_e≈T_i ⩾50 eV, L⩾100 μm). The plasma was preformed by an Nd:YAG fundamental beam (1.06 μm) with focusable intensities of 10 ¹¹ W/cm². Color images of two-dimensional (2-D) spatially resolved (30 μm) electron density and electron temperature were obtained. These are the shortest wavelength Thomson scattering measurements on a plasma to date     

Field Measurements of Polarization Mode Dispersion

Polarization mode dispersion (PMD) measurements are presented for a sample of installed optical fibers. High PMD values are fairly common, with 9 of the 71 fibers having PMD coefficients above 0.3 ps km1 2. The results are analyzed in terms of the age of the fibers and the type of cabling. Measurements are presented for a number of concatenated fiber links, and the results show that the PMD value of the link is approximately equal to the square root of the sum of the squares of the PMD values of the individual fibers.