University of Wisconsin–Milwaukee

About: University of Wisconsin–Milwaukee is a education organization based out in Milwaukee, Wisconsin, United States. It is known for research contribution in the topics: Population & Gravitational wave. The organization has 11839 authors who have published 28034 publications receiving 936438 citations. The organization is also known as: UWM & University of Wisconsin-Milwaukee.

Lie Superalgebras and Enveloping Algebras

Abstract: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.

Feynman propagator in curved spacetime: A momentum-space representation

Abstract: We obtain a momentum-space representation of the Feynman propagator $G(x,{x}^{\ensuremath{'}})$ for scalar and spin-\textonehalf{} fields propagating in arbitrary curved spacetimes. The construction uses Riemann normal coordinates with origin at the point ${x}^{\ensuremath{'}}$ and is therefore only valid for points $x$ lying in a normal neighborhood of ${x}^{\ensuremath{'}}$. We show that the resulting momentum-space representation is equivalent to the DeWitt-Schwinger propertime representation. Our momentum-space representation permits one to apply momentum-space techniques used in Minkowski space to arbitrary curved spacetimes. The usefulness of this representation in discussing the renormalizability of interacting field theories in curved spacetime is illustrated by an explicit renormalization, to second order in the coupling constant, of a quartically self-interacting scalar field theory in an arbitrary spacetime.

Three-dimensional graphene-based composites for energy applications

Abstract: Three-dimensional (3D) graphene-based composites have drawn increasing attention for energy applications due to their unique structures and properties. By combining the merits of 3D graphene (3DG), e.g., a porous and interconnected network, a high electrical conductivity, a large accessible surface area, and excellent mechanical strength and thermal stability, with the high chemical/electrochemical activities of active materials, 3DG-based composites show great promise as high-performance electrode materials in various energy devices. This article reviews recent progress in 3DG-based composites and their applications in energy storage/conversion devices, i.e., supercapacitors, lithium-ion batteries, dye-sensitized solar cells, and fuel cells.

Concept maps in medical education: an analytical literature review

Abstract: OBJECTIVES As the medical profession continues to change, so do the educational methods by which medical students are taught. Various authors have acknowledged the need for alternative teaching and learning strategies that will enable medical students to retain vast amounts of information, integrate critical thinking skills and solve a range of complex clinical problems. Previous research has indicated that concept maps may be one such teaching and learning strategy. This article aims to: (i) review the current research on concept maps as a potential pedagogical approach to medical student learning, and (ii) discuss implications for medical student teaching and learning, as well as directions for future research. METHODS The literature included in this review was obtained by searching library databases including ACADEMIC SEARCH, ERIC, EBSCOHost, PsychINFO, PsychARTICLES, PubMed/MEDLINE, CINAHL and EMBASE. This literature review is a summary of both conceptual and empirically published literature on the uses of concept mapping in medical education. RESULTS The 35 studies reviewed here indicate that concept maps function in four main ways: (i) by promoting meaningful learning; (ii) by providing an additional resource for learning; (iii) by enabling instructors to provide feedback to students, and (iv) by conducting assessment of learning and performance. CONCLUSIONS This review provides ideas for medical school faculty staff on the use of concept maps in teaching and learning. Strategies such as fostering critical thinking and clinical reasoning, incorporating concept mapping within problem-based learning, and using concept mapping in group and collaborative learning are identified. New developments in medical education include the use of serial concept maps, concept maps as a methodology to assist learners with lower cognitive competence, and the combination of group concept maps with structured feedback.