Global differential geometry: An introduction for control engineers

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control

Optical spectroscopy of IRAS sources with infrared emission bands. 1: IRAS 21282+5050 and the diffuse interstellar bands

Spectroscopy of the starlike optical counterpart to IRAS 21282+5050, a source with the hydrocarbon infrared emission band spectrum, shows an 07(f)-(WC11) planetary nebula nucleus suffering an extinction of 5.7 mag. Emission line widths in the WC spectrum are only approx. 100 km/s, indicating a very slow stellar wind. Optical diffuse interstellar bands (DIBs) are prominent. Five DIBs are strongly enhanced, namely lamda lamda 5797, 6196, 6203, 6283, and 6613. The presence of circumstellar hydrocarbon molecules may explain both the infrared emission bands and the enhanced DIBs

Report of the Fourth District Economists' Roundtable

A summary of the 1994 forecasts for real output and inflation presented by 15 members of the Fourth District Economists' Roundtable at their January 1994 meeting, highlighting the measurement of service sector prices and the role of small businesses in creating jobs.Federal Reserve District, 4th

Enhancing Care Transitions for Older People through Interprofessional Simulation: A Mixed Method Evaluation

Introduction: The educational needs of the health and social care workforce for delivering effective integrated care are important. This paper reports on the development, pilot and evaluation of an interprofessional simulation course, which aimed to support integrated care models for care transitions for older people from hospital to home. Theory and methods: The course development was informed by a literature review and a scoping exercise with the health and social care workforce. The course ran six times and was attended by health and social care professionals from hospital and community (n=49). The evaluation aimed to elicit staff perceptions of their learning about care transfers of older people and to explore application of learning into practice and perceived outcomes. The study used a sequential mixed method design with questionnaires completed pre (n=44) and post (n=47) course and interviews (n=9) 2-5 months later. Results:Participants evaluated interprofessional simulation as a successful strategy. Post-course, participants identified learning points and at the interviews, similar themes with examples of application in practice were: Understanding individual needs and empathy; Communicating with patients and families; Interprofessional working; Working across settings to achieve effective care transitions. Conclusions and discussion:An interprofessional simulation course successfully brought together health and social care professionals across settings to develop integrated care skills and improve care transitions for older people with complex needs from hospital to home

Midyear report of the Fourth District Economists' Roundtable

A summation of the May 20, 1994 meeting of the Fourth District Economists' Roundtable, at which participants offered their views on the current and prospective state of the economy and discussed the limitations of describing the U.S. business cycle.Federal Reserve District, 4th

Multifractality and intermediate statistics in quantum maps

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical computations and provide analytical arguments showing that the generalized fractal dimensions are directly related to the parameter of the underlying classical map, and thus to other properties such as spectral statistics. Our results could be relevant for Anderson and quantum Hall transitions, where wave functions also show multifractality.Comment: 4 pages, 4 figure

Quantum Non-Markovianity: Characterization, Quantification and Detection

We present a comprehensive and up to date review on the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.Comment: Review article. Close to published versio