Multiple and Polynomial Recurrence for Abelian Actions in Infinite Measure

The (C,F)-construction from a previous paper of the first authoris applied to produce a number of funny rank one infinite measurepreserving actions of discrete countable Abelian groups G with‘unusual’ multiple recurrence properties. In particular,the following are constructed for each p N{}:

1. a p-recurrent actionT=(T_g)_gG such that (if p) no one transformationT_g is (p+1)-recurrentfor every element g of infinite order;
2. an action T=(T_g)_gGsuch that for every finite sequence g1,...,g_rGwithout torsionthe transformation T_g1x...x T_gr is ergodic,p-recurrent but(if p) not (p+1)-recurrent;
3. a p-polynomially recurrent (C,F)-transformationwhich (if p)is not (p+1)-recurrent.

-recurrence here meansmultiple recurrence. Moreover, it is shown that there existsa (C,F)-transformation which is rigid (and hence multiply recurrent)but not polynomially recurrent. Nevertheless, the subset ofpolynomially recurrent transformations is generic in the groupof infinite measure preserving transformations endowed withthe weak topology.     

Variational Principles for Eigenvalues of Self-adjoint Operator Functions

Variational principles for eigenvalues of certain functions whose values are possibly unbounded self-adjoint operators T() are proved. A generalised Rayleigh functional is used that assigns to a vector x a zero of the function T()x, x), where it is assumed that there exists at most one zero. Since there need not exist a zero for all x, an index shift may occur. Using this variational principle, eigenvalues of linear and quadratic polynomials and eigenvalues of block operator matrices in a gap of the essential spectrum are characterised. Moreover, applications are given to an elliptic eigenvalue problem with degenerate weight, Dirac operators, strings in a medium with a viscous friction, and a Sturm-Liouville problem that is rational in the eigenvalue parameter.     

Global simulation for laser-driven MeV electrons in fast ignition

A comprehensive examination of the interaction of a picosecond-long ignition pulse on high-density (40 times critical density) pellets using a two-dimensional particle-in-cell model is described. The global geometry consists of a 50 mum diameter pellet surrounded by a corona which is isolated by a vacuum region from the boundary. For cone-attached targets, as much as 67% of the incident laser energy is absorbed with 12% sent forward as fast electrons in a 23 degrees cone. The current filaments are driven by the Weibel instability of the forward-going fast electron flux and its return current with the ions playing an important role of neutralizing the space charge. No global current filament coalescence has been observed. The electron distribution function obeys a power law, which begins at E approximately 0.2 MeV and falls off as E-(2-3).     

Equivariant local Epsilon Constants and Etale Cohomology

A conjecture is formulated which relates the equivariant localepsilon constant of a Galois extension of p-adic fields to anatural algebraic invariant coming from étale cohomology.Some evidence for the conjecture is provided and its relationto a conjecture for the equivariant global epsilon constantof an extension of number fields formulated by Bley and Burnsis established.     

Schopenhauer's Prolegomenon to Fuzziness

Prolegomenon means something said in advance of something else. In this study, we posit that part of the work by Arthur Schopenhauer (1788–1860) can be thought of as a prolegomenon to the existing concept of fuzziness. His epistemic framework offers a comprehensive and surprisingly modern framework to study individual decision making and suggests a bridgeway from the Kantian program into the concept of fuzziness, which may have had its second prolegomenon in the work by Frege, Russell, Wittgenstein, Peirce and Black. In this context, Zadeh's seminal contribution can be regarded as the logical consequence of the Kant-Schopenhauer representation framework.     

Classification of Material <Emphasis Type="Italic">G</Emphasis>-Structures

A geometrical interpretation of the G-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtained.     

High-speed horizontal-path atmospheric turbulence correction with a large-actuator-number microelectromechanical system spatial light modulator in an interferometric phase-conjugation engine

Results of atmospheric propagation for a high-speed, large-actuator-number adaptive optics system are presented. The system uses a microelectromechanical system- (MEMS-) based spatial light modulator correction device with 1024 actuators. Tests over a 1.35-km path achieved correction speeds in excess of 800 Hz and Strehl ratios close to 0.5. The wave-front sensor was based on a quadrature interferometer that directly measures phase. This technique does not require global wave-front reconstruction, making it relatively insensitive to scintillation and phase residues. The results demonstrate the potential of large-actuator-number MEMS-based spatial light modulators to replace conventional deformable mirrors.     

Novel pulsed switched power supply for a fast field cycling NMR spectrometer

In this paper, we outline the operating principles of a pulsed switched power supply for a fast field-cycling nuclear magnetic resonance spectrometer. The power supply uses a variant of a four-quadrant chopper with a duty cycle that defines the average output current. With this topology only two semiconductors are necessary to drive hundreds of amperes with an output power of several kilowatts. The output current ripple has a well-defined shape that can be reduced to acceptable values by a careful design of the semiconductors' controlling circuits and drivers. A power supply prototype was tested with a home build air-core magnet operating with fields between 0 and 0.21 T. The system is computer controlled using pulse generator and data acquisition PC cards, and specific user-friendly home-developed software. A comparative proton relaxometry study in two well-known liquid crystal compounds 5CB and MBBA was performed to check the reproducibility of the T1 measurements.     

Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik's coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.     

Asymptotic properties of two interacting maps

In this paper we consider a system whose state x changes to (x) if a perturbation occurs at the time t, for . Moreover, the state x changes to the new state (x) at time t, for . It is assumed that the number of perturbations in an interval (0, t) is a Poisson process. Here and are measurable maps from a measure space into itself. We give conditions for the existence of a stationary distribution of the system when the maps and commute, and we prove that any stationary distribution is an invariant measure of these maps.