7,441 research outputs found
Vanishing integrals for Hall-Littlewood polynomials
It is well known that if one integrates a Schur function indexed by a
partition over the symplectic (resp. orthogonal) group, the integral
vanishes unless all parts of have even multiplicity (resp. all parts
of are even). In a recent paper of Rains and Vazirani, Macdonald
polynomial generalizations of these identities and several others were
developed and proved using Hecke algebra techniques. However at (the
Hall-Littlewood level), these approaches do not work, although one can obtain
the results by taking the appropriate limit. In this paper, we develop a direct
approach for dealing with this special case. This technique allows us to prove
some identities that were not amenable to the Hecke algebra approach, as well
as to explicitly control the nonzero values. Moreover, we are able to
generalize some of the identities by introducing extra parameters. This leads
us to a finite-dimensional analog of a recent result of Warnaar, which uses the
Rogers-Szeg\"o polynomials to unify some existing summation type formulas for
Hall-Littlewood functions.Comment: 31 page
Reading Responses To Journal Articles, Computational Emulation Of Published Research
Students responded to sets of journal articles in computational optics and imaging every week. Articles investigated scientific questions, visualization of scientific data, ethical questions, and international collaborative projects (such as the Event Horizon Telescope). Students also completed labs to gain proficiency in computational tools
Reliability growth models for NASA applications
The objective of any reliability growth study is prediction of reliability at some future instant. Another objective is statistical inference, estimation of reliability for reliability demonstration. A cause of concern for the development engineer and management is that reliability demands an excessive number of tests for reliability demonstration. For example, the Space Transportation Main Engine (STME) program requirements call for .99 reliability at 90 pct. confidence for demonstration. This requires running 230 tests with zero failure if a classical binomial model is used. It is therefore also an objective to explore the reliability growth models for reliability demonstration and tracking and their applicability to NASA programs. A reliability growth model is an analytical tool used to monitor the reliability progress during the development program and to establish a test plan to demonstrate an acceptable system reliability
Reliability evaluation methodology for NASA applications
Liquid rocket engine technology has been characterized by the development of complex systems containing large number of subsystems, components, and parts. The trend to even larger and more complex system is continuing. The liquid rocket engineers have been focusing mainly on performance driven designs to increase payload delivery of a launch vehicle for a given mission. In otherwords, although the failure of a single inexpensive part or component may cause the failure of the system, reliability in general has not been considered as one of the system parameters like cost or performance. Up till now, quantification of reliability has not been a consideration during system design and development in the liquid rocket industry. Engineers and managers have long been aware of the fact that the reliability of the system increases during development, but no serious attempts have been made to quantify reliability. As a result, a method to quantify reliability during design and development is needed. This includes application of probabilistic models which utilize both engineering analysis and test data. Classical methods require the use of operating data for reliability demonstration. In contrast, the method described in this paper is based on similarity, analysis, and testing combined with Bayesian statistical analysis
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