Distribution results for lattices in SL(2,ℚ p )

In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚ_p) on ℚ_p × ℚ_p and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually associated to GL(2,ℚ_p)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension of the geodesic flow.     

The Livsic Cocycle Equation for Compact Lie Group Extensions of Hyperbolic Systems

In this article we extend well-known results of Livsic on theregularity of measurable solutions to the cocycle equation.Livsic proved a regularity result for real valued cocycles,but for compact Lie group valued cocycles his result was restrictedto coboundaries (that is, trivial or constant cocycles). Inthis article we prove the complete result. We present several useful applications of these results.     

Outflow refreshment angiography: A bright blood, bright static tissue technique

A new “bright blood” strategy, outflow refreshment imaging, is introduced in which a number of overlapping slices are excited in rapid succession. Flowing spins that refresh each overlapped slice portion contribute a bright signal. Additionally, static tissue in each non-overlapped slice portion also yields a bright signal. However, the flow/static contrast is comparable to that produced in inflow refreshment images, and angiograms can be generated by conventional maximum intensity projection processing. The dual ability to visualize angiograms and static tissue images is a major benefit of the strategy. Computer simulations of flow sensitivities and in vivo results are presented which compare the outflow and inflow refreshment imaging strategies.     

Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

A gauge-covariant bimetric tetrad theory of gravitation and electromagnetism

In order to get to a geometrically based theory of gravitation and electromagnetism, a gauge covariant bimetric tetrad space-time is introduced. The Weylian connection vector is derived from the tetrads and it is identified with the electromagnetic potential vector. The formalism is simplified by the use of gauge-invariant quantities. The theory contains a contorsion tensor that is connected with spinning properties of matter. The electromagnetic field may be induced by conventional sources and by spinning matter. In absence of spinning matter, the equations are identical with those of the gauge-covariant bimetric theory.⁽²³⁾     

High-throughput characterization of local conductivity of Nd0.9Ca0.1Ba2Cu3O7−δ thin film by the low-temperature scanning microwave microscope

We developed a scanning microwave microscope (SμM) designed for high-throughput electric-property screening as well as for rapid construction of electronic phase diagrams at low temperatures. As a sensor probe, we used a high-Qλ/4 coaxial cavity resonator to which a thin needle with ball-tip end was attached. The sensor module was mounted on the low-temperature XYZ stage, which allowed us to map out the change of resonance frequency and quality factor due to the local tip-sample interaction at low temperatures. From the measurements of combinatorial thin films, such as Ti_1−xCo_xO_2−δ and Nd_0.9Ca_0.1Ba₂Cu₃O_7−δ (NCBCO), it was demonstrated that this SμM system has enough performance for the high-throughput characterization of sample conductance under variable temperature conditions.