13,496 research outputs found
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
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
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
Frequency response of an axial-flow compressor exposed to inlet pressure perturbations
Experimental results of a series of engine tests designed to obtain the stage dynamics of an eight-stage axial-flow compressor over the frequency range of 0.5 to 200 hertz are presented. The total pressure at the compressor face was varied by means of a secondary air jet system installed in the engine inlet and positioned to oppose the primary airflow. Total-pressure probes located at each compressor stage were used to obtain the frequency response of each compressor-stage total pressure to the average compressor-inlet total pressure. The engine operating conditions were chosen to illustrate the effects of changing the rotor speed, changing the exhaust nozzle area, and isolating the compressor discharge pressure perturbations from the fuel control and hence, the fuel flow
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
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
- …