Symmetric Ideals

Polynomials appear in many different fields such as statistics, physics and optimization. However, when the degrees or the number of variables are high, it generally becomes quite difficult to solve polynomials or to optimize polynomial functions. An approach that can often be helpful to reduce the complexity of such problems is to study symmetries in the problems. A relatively new field, that has gained a lot of traction in the last fifteen years, is the study of symmetry in polynomial rings in increasingly many variables. By considering the action of the symmetric groups on these polynomial rings, one can for instance show that certain sequences of symmetric ideals in increasingly larger polynomial rings are finitely generated up to orbits. In this thesis we will investigate some properties of such sequences. In particular the Hilbert Series and Gröbner bases of Specht ideals, a class of ideals arising from the representation theory of the symmetric group. We prove a conjectured Gröbner basis for Specht ideals of shape (n−k, 1^k) and give two different criteria for verifying the conjecture for other Specht ideals. We also build on a result from the representation theory of the symmetric group by showing that the leading monomials of the standard Specht polynomials span the vector space of leading monomials of Specht polynomials

Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems, part 1

The proceedings of the workshop are presented. Some areas of discussion are as follows: modeling, systems identification, and control of flexible aircraft, spacecraft, and robotic systems

Space Generic Open Avionics Architecture (SGOAA) reference model technical guide

This report presents a full description of the Space Generic Open Avionics Architecture (SGOAA). The SGOAA consists of a generic system architecture for the entities in spacecraft avionics, a generic processing architecture, and a six class model of interfaces in a hardware/software system. The purpose of the SGOAA is to provide an umbrella set of requirements for applying the generic architecture interface model to the design of specific avionics hardware/software systems. The SGOAA defines a generic set of system interface points to facilitate identification of critical interfaces and establishes the requirements for applying appropriate low level detailed implementation standards to those interface points. The generic core avionics system and processing architecture models provided herein are robustly tailorable to specific system applications and provide a platform upon which the interface model is to be applied

Fracture and shakedown of pavements under repeated traffic loads

Thesis (Ph.D.) University of Alaska Fairbanks, 1998Under repeated external loads, engineering structures or objects may fail by large plastic deformation or fatigue. Shakedown will occur when the accumulation of plastic deformation ceases under repeated loads; the response of the system is then purely elastic. Fatigue and shakedown have been individually studied for decades and no attempt has been made to couple these two mechanisms in the mechanics analysis. In this study, an attempt is made to couple shakedown and fatigue in pavement mechanics analysis using numerical simulation. The study covers three main areas: fatigue, static shakedown, and kinematic shakedown analysis. A numerical approach to fatigue analysis is proposed based on elastic-plastic fracture mechanics. The amount of the crack growth during each load cycle is determined by using the J-integral curve and \rm R\sb{-}curve. Crack propagation is simulated by shifting the \rm R\sb{-}curve along the crack growth direction. Fatigue life is predicted based on numerically estabiished fatigue equation. The numerical results indicate that the algorithm can be applied to fatigue analyses of different materials. A numerical algorithm based on the finite element method coupled with the nonlinear programming is proposed in static shakedown analysis. In this algorithm, both the inequality and equality constraints are included in the pseudo-objective function. These constraints are normalized by the material yield stress and the reference load, respectively. A multidirectional search algorithm is used in the optimization process. The influence of finite element mesh on shakedown loads is investigated. An algorithm that utilizes eigen-mode to construct the arbitrary admissible plastic deformation path is proposed in kinematic shakedown analysis. This algorithm converts the shakedown theorem into a convex optimization problem and can be solved by using a multidirectional search algorithm. Fatigue behavior of a two-layer full-depth pavement system of asphalt concrete is analyzed using the proposed numerical algorithm. Fatigue crack growth rate is estimated and fatigue life is predicted for the system. Shakedown analyses are also carried out for the same pavement system. The comparison between the shakedown load and the fatigue failure load with respect to the same crack length indicates that the shakedown dominates the response of the pavement system under traffic load

GRASP/Ada (Graphical Representations of Algorithms, Structures, and Processes for Ada): The development of a program analysis environment for Ada. Reverse engineering tools for Ada, task 1, phase 2

The study, formulation, and generation of structures for Ada (GRASP/Ada) are discussed in this second phase report of a three phase effort. Various graphical representations that can be extracted or generated from source code are described and categorized with focus on reverse engineering. The overall goal is to provide the foundation for a CASE (computer-aided software design) environment in which reverse engineering and forward engineering (development) are tightly coupled. Emphasis is on a subset of architectural diagrams that can be generated automatically from source code with the control structure diagram (CSD) included for completeness

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth

The Sixth Copper Mountain Conference on Multigrid Methods, part 2

The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Workshop on Squeezed States and Uncertainty Relations

The proceedings from the workshop are presented, and the focus was on the application of squeezed states. There are many who say that the potential for industrial applications is enormous, as the history of the conventional laser suggests. All those who worked so hard to produce squeezed states of light are continuing their efforts to construct more efficient squeezed-state lasers. Quite naturally, they are looking for new experiments using these lasers. The physical basis of squeezed states is the uncertainty relation in Fock space, which is also the basis for the creation and annihilation of particles in quantum field theory. Indeed, squeezed states provide a unique opportunity for field theoreticians to develop a measurement theory for quantum field theory