Uniformly convex operators and martingale type

The concept of uniform convexity of a Banach space was generalized to linear operators between Banach spaces and studied by Beauzamy [1976]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map I_X is. Pisier showed that uniformly convex Banach spaces have martingale type p for some p>1. We show that this fact is in general not true for linear operators. To remedy the situation, we introduce the new concept of martingale subtype and show, that it is equivalent, also in the operator case, to the existence of an equivalent uniformly convex norm on X. In the case of identity maps it is also equivalent to having martingale type p for some p>1. Our main method is to use sequences of ideal norms defined on the class of all linear operators and to study the factorization of the finite summation operators. There is a certain analogy with the theory of Rademacher type.Comment: 15 pages, to be published in Revista Matematica Iberoamerican

Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

Assimilation of Earth rotation parameters into a global ocean model: excitation of polar motion

The oceanic contribution to Earth rotation anomalies can be manifold. Possible causes are a change of total ocean mass, changes in current speed or location and changes in mass distribution. To derive the governing physical mechanisms of oceanic Earth rotation excitation we assimilate Earth rotation observations with a global circulation ocean model. Before assimilation, observations of length of day and polar motion were transformed into estimates of ocean angular momentum. By using the adjoint 4D-VAR assimilation method we were able to reproduce these estimated time series. Although length of day was assimilated simultaneously the analysis in this paper focuses on the oceanic polar motion generation. Our results show that changes in mass distribution and currents contribute to oceanic polar motion generation. Both contributions are highly correlated and show similar amplitudes. The changes in the model done by the assimilation procedure could be related to changes in the atmospheric forcing. Since for geometrical reasons the change of total ocean mass does not project on polar motion, we conclude that the polar motion is mainly generated by a geostrophic response to atmospheric momentum forcing. In geostrophic currents mass displacement and current speed entail each other. This way the large similarity of mass and current generated ocean angular momentum can be explained

Correlations of a bound interface over a random substrate

The correlation function of a one-dimensional interface over a random substrate, bound to the substrate by a pressure term, is studied by Monte-Carlo simulation. It is found that the height correlation , averaged over the substrate disorder, fits a form exp(-(j/b)^c) to a surprising precision in the full range of j where the correlation is non-negligible. The exponent c increases from 1.0 to 1.5 when the interface tension is taken larger and larger.Comment: 7 pages, 5 figure

Analysis of dynamic inlet distortion applied to a parallel compressor model

An investigation of surge was conducted by using a parallel compressor model of the J85-13 compressor implement on an analog computer. Surges were initiated by various types of dynamic disturbances in inlet pressure. The compressor model was less sensitive to disturbances of short duration, high frequency, and long duration where the compressor discharge pressure could react. Adding steady distortion to dynamic disturbances reduced the amount of dynamic disturbance required to effect surge. Steady and unsteady distortions combined linearly to reduce surge margin

Deflection of a Viscoelastic Cantilever under a Uniform Surface Stress: Applications to Static-mode Microcantilever Sensors Undergoing Adsorption

The equation governing the curvature of a viscoelastic microcantilever beam loaded with a uniform surface stress is derived. The present model is applicable to static-mode microcantilever sensors made with a rigid polymer, such as SU-8. An analytical solution to the differential equation governing the curvature is given for a specific surface stress representing adsorption of analyte onto the viscoelastic beam’s surface. The solution for the bending of the microcantilever shows that, in many cases, the use of Stoney’s equation to analyze stress-induced deflection of viscoelastic microcantilevers (in the present case due to surface analyte adsorption) can lead to poor predictions of the beam’s response. It is shown that using a viscoelastic substrate can greatly increase sensitivity (due to a lower modulus), but at the cost of a longer response time due to viscoelasticcreep in the microcantilever. In addition, the effects of a coating on the cantilever are considered. By defining effective moduli for the coated-beam case, the analytical solution for the uncoated case can still be used. It is found that, unlike the case of a silicon microcantilever, the stress in the coating due to bending of a polymer cantilever can be significant, especially for metalcoatings. The theoretical results presented here can also be used to extract time-domain viscoelasticproperties of the polymermaterial from beam response data

Performance of a J85-13 compressor with clean and distorted inlet flow

The results presented are of a series of experimental tests in which a J85-13 turbojet engine was subjected to both distorted and undistorted inlet total pressure conditions. A distinctive feature of the data base obtained is that it includes compressor interstage information not previously recorded for a J85-13 engine. Each of the eight compressor stages was instrumented to obtain the characteristics of the individual stages for undistorted inlet conditions, and these data are documented in the report along with the undistorted compressor overall performance. Also included in the report is the overall performance of the compressor exposed to 14 different distorted-inlet conditions - 10 circumferential patterns and 4 radial patterns. The distortion patterns were introduced using screens that spoiled from 8 to 50 percent of the compressor face area; the distortion screen density, or the area blocked by the screen wire per unit area of screen, varied from 26 to 69 percent

Experimental program for the evaluation of turbofan/turboshaft c conversion technology

A TF34 turbofan engine is being modified to produce shaft power from an output coupling on the fan disk when variable inlet guide vanes are closed to reduce fan airflow. The engine, called a convertible engine, could be used on advanced rotorcraft such as X-wing, ABC (Advanced Blade Concept), and Folding Tilt Rotor, and on V/STOL craft in which two engines are cross-coupled. The engine will be tested on an outdoor static test stand at NASA Lewis Research Center. Steady-state tests will be made to measure performance in turbofan, turboshaft, and combined power output modes. Transient tests will be made to determine the response to the engine and a new digital engine control system for several types of rapid changes in thrust and shaft loads. The paper describes the engine modifications, the test facility equipment, proposed testing techniques for several types of tests, and typical test results predicted from engine performance computer programs