Distributed Receding Horizon Control with Application to Multi-Vehicle Formation Stabilization

We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled non-separably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed optimal control problems for each subsystem and establish that the distributed receding horizon implementation is asymptotically stabilizing. The communication requirements between subsystems with coupling in the cost function are that each subsystem obtain the previous optimal control trajectory of those subsystems at each receding horizon update. The key requirements for stability are that each distributed optimal control not deviate too far from the previous optimal control, and that the receding horizon updates happen sufficiently fast. The theory is applied in simulation for stabilization of a formation of vehicles

Computer model for refinery operations with emphasis on jet fuel production. Volume 1: Program description

A FORTRAN computer program is described for predicting the flow streams and material, energy, and economic balances of a typical petroleum refinery, with particular emphasis on production of aviation turbine fuel of varying end point and hydrogen content specifications. The program has provision for shale oil and coal oil in addition to petroleum crudes. A case study feature permits dependent cases to be run for parametric or optimization studies by input of only the variables which are changed from the base case

Obtaining One-loop Gravity Amplitudes Using Spurious Singularities

The decomposition of a one-loop scattering amplitude into elementary functions with rational coefficients introduces spurious singularities which afflict individual coefficients but cancel in the complete amplitude. These cancellations create a web of interactions between the various terms. We explore the extent to which entire one-loop amplitudes can be determined from these relationships starting with a relatively small input of initial information, typically the coefficients of the scalar integral functions as these are readily determined. In the context of one-loop gravity amplitudes, of which relatively little is known, we find that some amplitudes with a small number of legs can be completely determined from their box coefficients. For increasing numbers of legs, ambiguities appear which can be determined from the physical singularity structure of the amplitude. We illustrate this with the four-point and N=1,4 five-point (super)gravity one-loop amplitudes.Comment: Minor corrections. Appendix adde

Perturbative expansion of N<8 Supergravity

We characterise the one-loop amplitudes for N=6 and N=4 supergravity in four dimensions. For N=6 we find that the one-loop n-point amplitudes can be expanded in terms of scalar box and triangle functions only. This simplification is consistent with a loop momentum power count of n-3, which we would interpret as being n+4 for gravity with a further -7 from the N=6 superalgebra. For N=4 we find that the amplitude is consistent with a loop momentum power count of n, which we would interpret as being n+4 for gravity with a further -4 from the N=4 superalgebra. Specifically the N=4 amplitudes contain non-cut-constructible rational terms.Comment: 13 pages. v2 adds analytic expression for rational parts of 5-pt 1-loop N=4 SUGRA amplitude; v3 normalisations clarifie

The n-point MHV one-loop Amplitude in N=4 Supergravity

We present an explicit formula for the n-point MHV one-loop amplitude in a N=4 supergravity theory. This formula is derived from the soft and collinear factorisations of the amplitude.Comment: 8 pages; v2 References added. Minor changes to tex

Finding Their Way: A Critical Ethnography of Five African American Women Educators\u27 Early Experiences to Develop Into Culturally Relevant Pedagogues

ABSTRACT FINDING THEIR WAY: A CRITICAL ETHNOGRAPHY OF FIVE OF AFRICAN AMERICAN WOMEN EDUCATORS’ EARLY EXPERIENCES TO DEVELOP INTO CULTURALLY RELEVANT PEGAGOGUES by Rachel Beatrice Dunbar Teacher education programs have been charged with the responsibility to equip all teachers to work successfully in increasingly diverse elementary classrooms around the nation (NCES, 1996). However, the composition of the nation’s teaching force has not kept pace with these changes. Additionally, there is concern that many Pre-service teachers are ill prepared to work with culturally diverse students, partly because teacher education programs (TEPs) often adopt a monocultural, one-size-fits-all approach to preparation, ignoring race, class, and gender considerations (King & Castnell, 2001). African American women who seek preparation are greatly impacted by this singular approach to teacher education, which influences the way in which they experience their training. Consequently, they are often underserved in TEPs (Cozart & Price, 2005). It has been argued that TEPs will have to broaden their approaches to preparation by using a culturally relevant approach to teaching (Gay & Kirkland, 2003). Given the necessity for teachers to be equipped to meet the needs of culturally diverse learners in the classroom, it is imperative that TEPs are designed to cultivate culturally appropriate practices within Pre-service teachers. The purpose of this qualitative study was to explore the nature of the diversity preparation of five African American women and their teaching experiences following the completion of their teacher education training. The critical ethnographic case studies that developed were theoretically framed in Culturally Relevant Pedagogy (Ladson-Billings, 1995), Black Feminist Thought (Collins, 1990), and Womanism (Phillips, 2006). Data were collected from classroom observations, individual, and group interviews. Using a system of open coding (Strauss & Corbin, 1998), data analysis resulted in the emergence of three overarching themes: a) the formal diversity preparation offered by the university, b) the women’s individual perspectives of cultural relevance, and c) the ways in which the women incorporated their perspectives into their classroom practices. The experiences the young women encountered significantly influenced their understandings of culture and its impact on learning for diverse student populations. The results of this study suggest the need for teacher educators to reconsider how TEPs are structured to better prepare minority Pre-service teachers in the future to teach culturally diverse students

Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation

Soft and collinear factorisations can be used to construct expressions for amplitudes in theories of gravity. We generalise the "half-soft" functions used previously to "soft-lifting" functions and use these to generate tree and one-loop amplitudes. In particular we construct expressions for MHV tree amplitudes and the rational terms in one-loop amplitudes in the specific context of N=4 supergravity. To completely determine the rational terms collinear factorisation must also be used. The rational terms for N=4 have a remarkable diagrammatic interpretation as arising from algebraic link diagrams.Comment: 18 pages, axodraw, Proof of eq. 4.3 adde