7,383 research outputs found
Nonabelian Cohomology of Compact Lie Groups
No full textGiven a Lie group G with finitely many components and a compact Lie group A which acts on G by automorphisms, we prove that there always exists an A-invariant maximal compact subgroup K of G, and that for every such K, the natural map H(1)(A,K) -> H(1)(A,G) is bijective. This generalizes a classical result of Serre and a recent result of the first and third named authors of the current paper.MathematicsSCI(E)0ARTICLE2231-2361
A note on quasi-Lie and Hom-Lie structures of σ-derivations of C[z<sub>1</sub><sup>±1</sup>, \dots, z<sub>n</sub><sup>±1</sup>]
No full textIn a previous paper we studied the properties of the bracket defined by Hartwig, Larsson and the second author in (J. Algebra 295, 2006) on σ-derivations of Laurent polynomials in one variable. Here we consider the case of several variables, and emphasize on the question of when this bracket defines a hom-Lie structure rather than a quasi-Lie one.</p
Karl Heinrich Hofmann and the structure of compact groups and pro-lie groups
No full textThis article is dedicated to Karl Heinrich Hofmann on his 90th birthday. The first part of the article records some biographical facts about him. The second part focuses on the research papers and books he published with the author of this article over the last 45 years. These results concern the structure of compact groups and pro-Lie groups. © 2023 Heldermann Verlag
Topological Multi-groups and Multi-fields
No full textTopological groups, particularly, Lie groups are very important in differential
geometry, analytic mechanics and theoretical physics. Applying Smarandache multi-spaces, topological spaces, particularly, manifolds and groups were generalized to combinatorial manifolds and multi-groups underlying a combinatorial structure in references. Then whether can one generalizes their combination, i.e., topological group or Lie group to a multiple one? The answer is YES. In this paper, the author shows how to generalize topological groups and the homomorphism theorem for topological groups to multiple ones
Lie algebras
No full textLie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semi-simple Lie algebras and the dependence of structure of semi-simple Lie algebras on root system
Lie groups and Lie algebras
No full textThese are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT in 2020/2021.262 pages, minor corrections and improvements in v
Co-creating an antenatal care information resource in Arabic with re-settled migrant mothers
No full text2026 Lie and Claisse.Introduction: Arabic-speaking women newly settled in the UK have different experiences of healthcare in their original countries which influence their engagement with the NHS. Like other migrant women, they are often unaccustomed to the way health services work. Language, religious and cultural barriers, as well as the lack of family and community supports contribute to inequalities in health and wellbeing outcomes during pregnancy and childbirth. Materials and methods: To address their needs, the ERicar2 project aimed to produce a co-created antenatal care community information resource with a group of these women. Ten participatory workshops over eleven weeks were conducted to listen to the women\u27s stories of their pregnancy journeys, explore publicly available resources, and work together to produce a prototype of an information resource tailored to their community needs. Results: The qualitative findings from the workshops uncovered their experiences of miscarriage, their health seeking behavior, the role of religious belief and digital media, and the importance to them of their reproductive rights. The messages that they had for a newly arrived Arabic speaking woman were incorporated in a letter illustrated with their drawings, addressed to a fictional character “Dila” and containing QR codes to internet sites for pregnancy support. The letter was digitally animated and recorded in English and Arabic by volunteers among the research participants. The ERicar2 online resource is available for use by UK health providers and Arabic-speaking communities. Discussion: Engagement with migrant mothers through participatory co-creative workshops (ERicar) is a model that can be replicated. In a safe community space, women sharing their pregnancy journeys have led to mutual support and research insights for maternal healthcare. Employing bricolage and iterative co-creation methods, women have been able to contribute to an antenatal resource tailored to the needs of an expectant mother recently resettled in the UK
Reduced-rank adaptive least bit-error-rate detection in hybrid direct-sequence time-hopping ultrawide bandwidth systems
No full textDesign of high-efficiency low-complexity detection schemes for ultrawide bandwidth (UWB) systems is highly challenging. This contribution proposes a reduced-rank adaptive multiuser detection (MUD) scheme operated in least bit-errorrate (LBER) principles for the hybrid direct-sequence timehopping UWB (DS-TH UWB) systems. The principal component analysis (PCA)-assisted rank-reduction technique is employed to obtain a detection subspace, where the reduced-rank adaptive LBER-MUD is carried out. The reduced-rank adaptive LBERMUD is free from channel estimation and does not require the knowledge about the number of resolvable multipaths as well as the knowledge about the multipaths’ strength. In this contribution, the BER performance of the hybrid DS-TH UWB systems using the proposed detection scheme is investigated, when assuming communications over UWB channels modeled by the Saleh-Valenzuela (S-V) channel model. Our studies and performance results show that, given a reasonable rank of the detection subspace, the reduced-rank adaptive LBER-MUD is capable of efficiently mitigating the multiuser interference (MUI) and inter-symbol interference (ISI), and achieving the diversity gain promised by the UWB systems
In-flight validation of Aura MLS ozone with CAFS partial ozone columns
No full textA comprehensive data set of partial ozone columns was derived from the charge-coupled device (CCD) Actinic Flux Spectroradiometer (CAFS) measurements taken during the Polar 2005, Houston 2005, and Costa Rica 2006 Aura Validation Experiments (AVE). It was used to validate the colocated daytime Aura Microwave Limb Sounder (MLS) partial ozone columns along the aircraft tracks over diverse geophysical conditions. Results show that the MLS v.1.5 and CAFS ozone columns agree to better than 3% at pressure levels of 100 and 146 hPa, and to better than 5% at 215 hPa level. The partial ozone column differences between the two systems were the largest during the Polar AVE (PAVE) 2005 campaign (polar region, ~250 hPa pressure level), and the smallest during the CRAVE 2006 campaign (tropics, ~100 hPa pressure level). Overall, the averaged bias between the MLS and CAFS partial ozone column is about 2%, and the standard deviation of the differences is about 2%. The v.2.2 update of the MLS data tends to reduce the bias to less than 1%. In addition, the AVE 2005 campaign uncovered an altitude-dependent bias, where the MLS partial ozone columns above 100 and 146 hPa pressure levels were about 1% higher than the CAFS derived columns, while the bias increased to about 3 % in partial columns integrated above 215 hPa. However, the MLS and CAFS data track each other closely over a wide range of atmospheric conditions, and the differences lie within the combined uncertainties of the two data sets
Mellin-Transform-Based Performance Analysis of FFH -ary FSK Using Product Combining for Combatting Partial-Band Noise Jamming
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