7,185 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
Full text linkTopological 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
Full text linkThese 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
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
Mellin-Transform-Based Performance Analysis of FFH -ary FSK Using Product Combining for Combatting Partial-Band Noise Jamming
No full textReceiver Multiuser Diversity Aided Multi-Stage MMSE Multiuser Detection for DS-CDMA and SDMA Systems Employing I-Q Modulation
Full text linkThe so-called receiver multiuser diversity aided multistage minimum mean-square error multiuser detector (RMD/MS-MMSE MUD), which was proposed previously by the author, is investigated in the context of the direct-sequence code-division multiple-access (DS- CDMA) and space-division multiple-access (SDMA) systems that employ in- and quadrature-phase (I-Q) modulation schemes. A detection scheme is studied, which is operated in real domain in the principles of successive interference cancellation (SIC). The concept of noise recognition factor (NRF) is proposed for explaining the efficiency of SIC-type detectors and also for motivating to design other high-efficiency detectors. The achievable bit error rate (BER) performance of the RMD/MS-MMSE MUD is investigated for DS-CDMA and SDMA systems of either full-load or overload, when communicating over Rayleigh fading channels for the SDMA and over either additive white Gaussian noise (AWGN) or Rayleigh fading channels for the DS-CDMA. The studies and performance results show that the RMD/MS-MMSE MUD is a highly promising MUD. It has low implementation complexity and good error performance. Furthermore, it is a high-flexibility detector suitable for various communication systems operated in different communication environments
A study of Lie Xian Zhuan and Lie Yi Zhuan
No full textLie Xian Zhuan is representatives of the early story of Immortals class; Lie Yi Zhuan is Wei-Jin and South & North Dynasties\ue2s early Zhiguai's Novels. This thesis is focused on Research the books's author , Year of publication and table of contents ,discuss about the witchcraft from Pre-Qin Dynasty to the Wei Jin Dynasty. By research Lie Xian Zhuan and Lie Yi Zhuan 's contents, can probe the differences between both's background and witchcraft
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