Projective representations and spin characters of complex reflection groups G(m,p,n)G(m, p, n) and G(m,p,∞)G(m, p, \infty), III

This paper is a continuation of two previous papers in MSJ Memoirs, Vol.\,29 (Math. Soc. Japan, 2013) with the same title and numbered as I and II. Based on the hereditary property given there, from mother groups $G(m,1,n)$, the generalized symmetric groups, to child groups $G(m,p,n)$, the complex reflection groups, we study in detail classification and construction of irreducible projective representations (= spin representations) and their characters of $G(m,1,n)$ for $n$ finite. Then, taking limits as $n$ tends to infinity, we obtain spin characters of the inductive limit groups $G(m,1,\infty)$. By the heredity studied further, this gives the main kernel of the results for $G(m,p,\infty)$ with $p|m, p>1$.Comment: 88 pages, typos corrected, references correcte

HARMONIC FUNCTIONS ON THE BRANCHING GRAPH ASSOCIATED WITH THE INFINITE WREATH PRODUCT OF A COMPACT GROUP

Detailed study of the characters of S∞(T)S∞(T), the wreath product of compact group T with the infinite symmetric group S∞, is indispensable for harmonic analysis on this big group. In preceding works, we investigated limiting behavior of characters of the finite wreath product Sn(T) as n→∞ and its connection with characters of S∞(T). This paper takes a dual approach to these problems. We study harmonic functions on Y(Tˆ), the branching graph of the inductive system of Sn(T)'s, and give a classification of the minimal nonnegative harmonic functions on it. This immediately implies a classification of the characters of S∞(T), which is a logically independent proof of the one obtained in earlier works. We obtain explicit formulas for minimal nonnegative harmonic functions on Y(Tˆ) and Martin integral expressions for harmonic functions

Introductory Lectures on Group Representations

Part I. Takeshi Hirai, Atomosphere in the theory of group representations [1]Part II. Nobuhiko Tatsuuma, General theory of unitary representation of locally compact groups [37

On Inductive Limits of Topological Algebraic Structures in relation to the Product Topologies

This is the proceedings of the 2nd Japanese-German Symposium on Infinite Dimensional Harmonic Analysis held from September 20th to September 24th 1999 at the Department of Mathematics of Kyoto University.この論文集は, 1999年9月20日から9月24日の日程で京都大学理学研究科数学教室において開催された第2回日独セミナー「無限次元調和解祈」の成果をもとに編集されたものである.編集 : ハーバート・ハイヤー, 平井 武, 尾畑 信明Editors: Herbert Heyer, Takeshi Hirai, Nobuaki Obata #enIn infinite-dimensional harmonic analysis, we encounter naturally inductive limits of certain topological algebraic objects, such as Lie groups, Banach algebras, topological semigroups and so on. In such cases, the inductive limit algebraic structures are not necessarily consistent with the inductive limit topologies, contrary to the affirmative statement in [Enc, Article 210]. This phenomenon is studied in [TSH] in the case of topological groups. We study in this paper similar situations for other categories of topological algebraic structures. Further, in relation to this, we study certain properties of general topological spaces for the 'commutativity' of (1) taking direct products and (2) taking inductive limits

Stochastic Geometry-Based Throughput Analysis of User-Specific Power-Level-Constrained GF-NOMA

Hirai T., Ueda Y., Wakamiya N.. Stochastic Geometry-Based Throughput Analysis of User-Specific Power-Level-Constrained GF-NOMA. IEEE Internet of Things Journal, (2024); https://doi.org/10.1109/JIOT.2024.3409698.This paper proposes a stochastic geometry-based analytical framework for the throughput of the grant-free power-domain non-orthogonal multiple access (GF-NOMA) with user-specific constraints of selectable power levels and analyzes the achievable throughput. Our analytical framework uses stochastic geometry to reflect selectable power levels constrained by the maximum transmission power and channel of each user to an inhomogeneous offered load per level. This key idea enables our framework to analyze the throughput bounded by the geographical user distribution and derive a suitable selection strategy of power levels under the constraint more accurately than the existing models. Our analytical results showed that our framework analyzed the throughput with only an analysis error of 0.1% compared with the Monte Carlo simulations, although the existing model overestimated 58% higher throughput. By using the proposed analytical model, our results presented decreasing the achievable throughput with increasing the coverage range. This paper also proposes a heuristic method based on our proposed analytical model to derive a suitable selection strategy of power levels. Our results highlight that the derived selection strategy on our analytical framework achieved 20 higher throughput than the baseline strategy, where each user randomly selects a power level under the power level constraint

Power-Level-Design-Aware Scalable Framework for Throughput Analysis of GF-NOMA in mMTC

Hirai T., Oda R., Wakamiya N.. Power-Level-Design-Aware Scalable Framework for Throughput Analysis of GF-NOMA in mMTC. IEEE Internet of Things Journal , (2024); https://doi.org/10.1109/JIOT.2024.3400996.This paper proposes a scalable framework to analyze the throughput of the grant-free power-domain nonorthogonal multiple access (GF-NOMA) and presents the achievable performance in the optimized offered load at each power level (called per-level offered load) by using our framework. Our analytical model reflects packet errors caused by power collisions, characterized by GF-NOMA, based on the power level design guaranteeing the required signal-to-interference-and-noise ratio (SINR). This key idea enables analyzing the throughput of a large-scale GF-NOMA system more accurately than the existing analytical models. Also, this key idea enables optimizing the per-level offered load rather than a uniform one in typical optimization problems related to the throughput: the throughput maximization or energy minimization problem with a throughput condition. Our analytical results highlight some key insights into designing future access control methods in GF-NOMA. First, our analytical model achieves an approximation error of only 0.4% for the exact throughput obtained by the exhaustive search at five power levels; the existing analytical model provides an approximation error of 25%. Next, our proposed framework highlights that the optimal per-level offered load restrictively improves the throughput above the optimally uniform per-level offered load. Finally, our proposed framework discovers a 27 more energy-efficient per-level offered load than the existing framework at five power levels while providing higher throughput than the optimally uniform per-level offered load

Hydrothermal metallurgy for recycling of slag and glass

Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd

Mechanistic insights into cAMP-mediated presynaptic potentiation at hippocampal mossy fiber synapses

Presynaptic plasticity is an activity-dependent change in the neurotransmitter release and plays a key role in dynamic modulation of synaptic strength. Particularly, presynaptic potentiation mediated by cyclic adenosine monophosphate (cAMP) is widely seen across the animals and thought to contribute to learning and memory. Hippocampal mossy fiber-CA3 pyramidal cell synapses have been used as a model because of robust presynaptic potentiation in short- and long-term forms. Moreover, direct presynaptic recordings from large mossy fiber terminals allow one to dissect the potentiation mechanisms. Recently, super-resolution microscopy and flash-and-freeze electron microscopy have revealed the localizations of release site molecules and synaptic vesicles during the potentiation at a nanoscale, identifying the molecular mechanisms of the potentiation. Incorporating these growing knowledges, we try to present plausible mechanisms underlying the cAMP-mediated presynaptic potentiation