Equivariant K-theory of compact Lie groups with involution

For a compact simply connected simple Lie group $G$ with an involution $\alpha$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\Z/2$ acts either by $\alpha$ or by $g\mapsto \alpha(g)^{-1}$. We also give a representation-theoretic interpretation of those groups, as well as of $K_G(G)$.Comment: Accepted for publication in Journal of K-theor

D-structures and derived Koszul duality for unital operad algebras

Generalizing a concept of Lipshitz, Ozsv\'ath and Thurs-ton from Bordered Floer homology, we define $D$-structures on algebras of unital operads, which can also be interpreted as a generalization of a seemingly unrelated concept of Getzler and Jones. This construction gives rise to an equivalence of derived categories, which can be thought of as a unital version of Koszul duality using non-unital Quillen homology. We also discuss a multi-sorted version of the construction, which provides a framework for unifying the known algebraic contexts of Koszul duality.Comment: Accepted for Publication in J. Pure Appl. Al

Laplaza Sets, or How to Select Coherence Diagrams for Pseudo Algebras

We define a general concept of pseudo algebras over theories and 2-theories. A more restrictive such notion was introduced by Hu and Kriz, but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the mistake by introducing a more general concept, allowing more flexibility in selecting coherence diagrams for pseudo algebras.Comment: 21 pages. To appear in the Advances of Mathematics. Exposition improved, notion of operad with degeneracies removed as a simplification, definition of pseudo algebra improved

On Real-oriented Johnson-Wilson cohomology

Answering a question of W. S. Wilson, I introduce a Z/2-equivariant Atiyah-Real analogue of Johnson-Wilson cohomology theory BP, whose coefficient ring is the =< n-chromatic part of Landweber's Real cobordism ring.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-38.abs.htm

Exploring Dynamics and Performance of International Education (IE) and Senior International Officer (SIO) Through a Lens of Complexity and Network Theories

The purpose of this study is to explore the nature of complex adaptive systems (CAS) and network dynamics in international education (IE) programs in a U.S. higher education institution. I analyze the IE programs through a lens of complexity and network theories and ask how measures of engagement in complex networks affect performance in the IE system. This study presumes that today\u27s international education programs in the U.S. higher education institutions are complex adaptive systems and that traditional leadership is no longer adequate to address the overwhelming opportunities and challenges posed by global education. A two-stage quantitative research design is adopted to investigate network structures and interactions within the IE system and to describe how such network measures impact organizational performance. In Stage 1, Dynamic Network Analysis (DNA) is used to calculate agent-level network measures for each participant within the university IE system\u27s bounded networks and to produce optimized simulations of the IE system for use in Stage 2. In Stage 2, Response Surface Methodology (RSM) is used to examine the relationship between independent and dependent measures. In this study, the independent network measures include (a) informal leadership, which is operationalized as betweenness centrality, (b) clique engagement, which is operationalized as clustering coefficient, and (c) social capital, which is operationalized as hub centrality. These independent measures are used to analyze the dependent measure, organizational performance, which is operationalized as task accuracy. A dynamic network framework of international education is proposed as a useful network model and leadership framework for enabling international education functions, senior international officers (SIOs), and their institutions to achieve excellence and succeed in a new era of global education and knowledge producing

Reliability evaluation of electric power system including wind power and energy storage

Global environmental concerns associated with conventional energy generation have led to the rapid growth of wind energy applications in electric power systems. Growing demand for electrical energy and concerns associated with limited reserves of fossil fuels are also responsible for the development and increase in wind energy utilization. Many jurisdictions around the world have set high wind penetration targets in their energy generation mix. The contribution of wind farms to the overall system reliability is limited by the uncertainty in power output from the highly variable energy source. High wind penetration can lead to high risk levels in power system reliability and stability. In order to maintain the system stability, wind energy dispatch is usually restricted and energy storage is considered to smooth out the fluctuations and improve supply continuity. The research work presented in this thesis is focused on developing reliability models for evaluating the benefits associated with wind power and energy storage in electric power generating systems. An interactive method using a sequential Monte Carlo simulation technique that incorporates wind farm and energy storage operating strategies is developed and employed in this research. Different operating strategies are compared and the resulting benefits are evaluated. Important system impacts on the reliability benefits from wind power and energy storage are illustrated. Hydro facilities with energy storage capability can alleviate the impact of wind power fluctuations and also contribute to system adequacy. A simulation technique for an energy limited hydro plant and wind farm coordination is developed considering the chronological variation in the wind, water and the energy demand. The IEEE four-state model is incorporated in the developed technique to recognize the intermittent operation of hydro units. Quantitative assessment of reliability benefits from effective utilization of wind and water resources are conducted through a range of sensitivity studies. The information provided and the examples illustrated in this thesis should prove useful to power system planners and wind developers to assess the reliability benefit from utilizing wind energy and energy storage and the coordination between wind and hydro power in electric power systems