65 research outputs found
Free product subgroups between Chevalley groups G(Φ,F) and G(Φ,F[t])
No full textAbstractWe investigate subgroups of a Chevalley group G=G(Φ,A) over a ring A, containing its elementary subgroup E=E(Φ,F) over a subring F⊆A. Assume that the root system Φ is simply laced and A=F[t] is a polynomial ring. We show that if G is of adjoint type, then there exists an element g∈E(Φ,A) such that 〈g,E(Φ,F)〉=〈g〉*E(Φ,F), where 〈X〉 denotes the subgroup, generated by a set X, and * stands for the free product.It follows that under the above assumptions the lattice L=L(E,G) is not standard. Moreover, combining the above result with theorems of Nuzhin and the author one obtains a necessary and sufficient condition for L to be standard provided that A and F are fields of characteristic not 2 and Φ≠G2
Free fermion six vertex model: symmetric functions and random domino tilings
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Our work deals with symmetric rational functions and probabilistic models based on the fully inhomogeneous six vertex (ice type) model satisfying the free fermion condition. Two families of symmetric rational functions
F
λ
,
G
λ
are defined as certain partition functions of the six vertex model, with variables corresponding to row rapidities, and the labeling signatures
λ
=
(
λ
1
≥
…
≥
λ
N
)
∈
Z
N
encoding boundary conditions. These symmetric functions generalize Schur symmetric polynomials, as well as some of their variations, such as factorial and supersymmetric Schur polynomials. Cauchy type summation identities for
F
λ
,
G
λ
and their skew counterparts follow from the Yang–Baxter equation. Using algebraic Bethe Ansatz, we obtain a double alternant type formula for
F
λ
and a Sergeev–Pragacz type formula for
G
λ
. In the spirit of the theory of Schur processes, we define probability measures on sequences of signatures with probability weights proportional to products of our symmetric functions. We show that these measures can be viewed as determinantal point processes, and we express their correlation kernels in a double contour integral form. We present two proofs: The first is a direct computation of Eynard–Mehta type, and the second uses non-standard, inhomogeneous versions of fermionic operators in a Fock space coming from the algebraic Bethe Ansatz for the six vertex model. We also interpret our determinantal processes as random domino tilings of a half-strip with inhomogeneous domino weights. In the bulk, we show that the lattice asymptotic behavior of such domino tilings is described by a new determinantal point process on
Z
2
, which can be viewed as an doubly-inhomogeneous generalization of the extended discrete sine process
Multi-agent Planning and Coordination for Automated Aircraft Ground Handling
No full textInspired by the vision of fully autonomous airside operations at Schiphol airport, this study aims to contribute to the short-term goal of automated aircraft ground handling. In this research, we design and evaluate a multi-agent system for planning of automated ground handling. There are two main components in the system, task allocation optimization, and multi-agent path planning. To allocate tasks to ground support equipment (GSE) vehicles, an auction mechanism inspired by temporal sequential single item (TeSSI) auction is proposed. Ground handling tasks scheduling for GSE vehicles is modeled as several single-vehicle pickup and delivery optimization problems (SPDP), and the values of the objective functions are applied to generate bids for GSE vehicle agents in the auction. Moreover, Prioritized Safe Interval Path Planning for large agents (LA-SIPP) is used to plan collision-free paths for GSE vehicle agents in the model to execute tasks. Experimental studies have shown that the system is able to perform task allocation and path planning of ground handling tasks for flights in 3 aircraft stands within a 4-hour time in a reasonable computational time. Moreover, the model is capable to replan the tasks for agents when disruption happens. Applying the lowest possible numbers of vehicles used in the current operation, the model can always reach success allocation and path planning rates higher than 81% and 98%, respectively.Aerospace Engineerin
Mead and Husserl on the Self and Identification of the Subject
Get PDFOut of many different strategies in the philosophy of the early 20th century the author compares
two completely different philosophies: G. H. Mead’s social behaviorism and E. Husserl’s transcendental
phenomenology with respect to the self-arising problem. For Mead, the initial point of his theory is
the social conduct or person’s behavior, whereas for Husserl, the life of the isolated transcendental
Ego is of greatest value. The author emphasizes, though the main ideas of both philosophers have
different methodological grounds, one finds, that the matter of primary importance for them. This is
the question of who is an executor of the social acts (Mead) and the transcendental phenomenological
act (Husserl)? Through an analysis of the main ideas of both philosophers (‘I’ and ‘Me’ as principles
of the subject by Mead, and intentionality, time analysis, and intersubjectivity by Husserl) the author
demonstrates, firstly, how the question of self-identity is solved in both conceptions, and, secondly,
how to argue the advantages of phenomenology. The article leads to the conclusion: methodologically
Mead’s social behaviorism is relativistic, as far as his theory of subjectivity depends on the social
context. Husserl’s method, despite its complexity, offers a clear subject structure and therefore can be
regarded as more productive for the theory of self. Refs 15
Automorphism Groups of Finite Extensions of Fields and the Minimal Ramification Problem
Get PDFWe study the following question: given a global field and finite group , what is the minimal such that there exists a finite extension with that is ramified over exactly places of ? We conjecture that the answer is for any global field and finite group . In the case when is a number field we show that the answer is always . We show that assuming Schinzel\u27s Hypothesis H the answer is always if is a number field. We show unconditionally that the answer is always if is a global function field.
We also show that for a broader class of fields than previously known, every finite group can be realized as the automorphism group of a finite extension (without restriction on the ramification).
An important new tool used in this work is a recent result of the author and C. Tsang, which says that for any finite group there exists a natural number and a subgroup of the symmetric group such that .v2: added conditional results proving Conj 1.1 and r_F(S_n)<=1 assuming Schinzel\u27s Hypothesis
Advisory System for MDO Architecture Selection in the MDO System Formulation Stage
No full textOne of the challenges in executing an MDO system is the selection of the best performing MDO architecture in terms of computational effort for a given MDO problem. To address this, several comparative studies have been created, which analyze the relative performance of MDO architectures with respect to internal features of MDO problems, such as the number of design variables and nature of interdisciplinary coupling. However, the existing research is limited in applicability. An inclusive prediction model, that can recommend the best MDO architecture for any MDO problem is not found yet in literature. In this thesis, the intention is to conduct a thorough comparison of two commonly used MDO architectures with respect to a database of sequentially generated MDO problems, having a range of internal features. Following this, a prediction model of MDO architecture is to be developed by applying a suitable machine learning algorithm on the generated database.Aerospace Engineerin
Multi-agent planning and coordination for automated aircraft ground handling
No full textInspired by the vision of fully autonomous airside operations at Schiphol airport, this study aims to contribute to the short-term goal of automated aircraft ground handling. In this research, we design and evaluate a multi-agent system for planning of automated ground handling. There are two main components in the system: task allocation optimization and multi-agent path planning. To allocate tasks to ground support equipment (GSE) vehicles, an auction mechanism inspired by temporal sequential single item (TeSSI) auction is proposed. Ground handling tasks scheduling for GSE vehicles is modeled as several single-vehicle pickup and delivery optimization problems (SPDP), and the values of the objective functions are used to generate bids for GSE vehicle agents in the auction. Prioritized safe interval path planning for large agents (LA-SIPP) is used to plan collision-free paths for GSE vehicle agents in the model to execute tasks. The aim is to increase the success rates of allocating tasks and finding collision free paths without causing flight delays, given the limited resources such as a small number of available GSE vehicles, time windows constraints and conflicting interests of different agents. Due to the results, even for the instances with frequent flights and the most limited resources, the success rates of allocation and path planning were higher than 81% and 98%, respectively. Furthermore, periodic task allocation and path planning of the ground handling tasks for flights in three aircraft stands during a planning time window of the day, as well as replanning in case of disruptions were performed in a short CPU time. There is a lack of research dealing with the complete process of ground handling, since existing studies concerning the automation of ground handling operations involve fleet assignment or task scheduling models without an integration of detailed path planning. Our main contribution is to present a framework that combines task allocation and path planning for automation of ground handling operations and provides solutions using a multi-agent perspective.Air Transport & Operation
Relative commutator calculus in Chevalley groups
No full textWe revisit localisation and patching method in the setting of Chevalley groups. Introducing certain subgroups of relative elementary Chevalley groups, we develop relative versions of the conjugation calculus and the commutator calculus in Chevalley groups G(ɸ, R), rk(ɸ) ≥ 2, which are both more general, and substantially easier than the ones available in the literature. For classical groups such relative commutator calculus has been recently developed by the authors in Hazrat, Zhang (2011) [34], Hazrat et al. (2011) [33]. As an application we prove the mixed commutator formula,. [E(ɸ,R,a),G(ɸ,R,b)]=[E(ɸ,R,a),E(ɸ,R,b)], for two ideals a,b⊴R. This answers a problem posed in a paper by Alexei Stepanov and the second author
BOOKS ARE KEYS TO THE WORLD. Co-active “complex cultural work” and “differential consciousness work” for a “transversal culture of consciousness” – also a matter of books, book places, “bibliotopes”. Some personal comments on dominants (A.A. Ukhtomskij)
No full textAngeregt durch eine Arbeit zu kreativer Poesietherapie in ihrem Buchladen (Helga Mitterhauser-Dubian 2023) hat H. Petzold einen Text geschrieben, der sich mit der Wirkung von Büchern und mit dem Lesen in Büchern und an Bücherorten (Bibliotheken, Archiven, Buchhandlungen – „Bibliotopen“) befasst, wie sich der Autor in seiner persönlichen Biographie, seinem Elternhaus und dem komplexen kulturellen Milieu in Kindheit und Jugend erlebt hat, aber auch in seinem wissenschaftlichen „Werkleben“ über die Lebensspanne hin. Er beschreibt prägende Erfahrungen als fokusbildende Arbeitsprinzipien, die mit dem Konzept der „Dominante“, des „beherrschenden Prinzips/Fokus“ des Neurophysiologen Alexei Uchtomskijs erklärt werden. Das Training von solchen „Dominanten“, heute als „Förderung des Konnektoms“ verstanden, entwickelt die Ausbildung einer „differentiellen Bewusstseinsarbeit“ und „starker Mentalisierungen“ und hat zu den späteren integrativen Ideen für eine „transversalen Bewusstseinskultur“ und für „komplexe Kulturarbeit“ in einer „unipluralen Welt“ beigetragen. Neben einer prägenden „Ökologisation“, dem Einfluss persönlicher Out-door-Naturerfahrung seit Kinderzeiten, die dominante Interessen an Lebendigem ausgebildet haben, waren es Erfahrungen mit Büchern, Buchläden, Bibliotheken, die einen sehr starken Einfluss auf das Lebenswerk der BegründerInnen der Integrativen Therapie und auf seine theoretischen Rahmenkonzepte ausgeübt haben. Dieser Umstand biographischer In-door-Erfahrung wurde bislang von Petzold et al. noch kaum thematisiert. Er war zu „selbstverständlich“ gewesen. Wichtige Rahmenkonzepte werden hier kurz beleuchtet, mit Integrativen Theoriekonzepten erläutert, in biographischen Erfahrungen des Begründers verortet und in ihrer Bedeutung für eine „integrative Kulturarbeit“ für die Aufgaben des 21. Jahrhunderts dargestellt. Der Text will deutlich machen: Neue Aspekte von Selbst-Kenntnis und Weltverstehen können immer wieder neu gewonnen werden, bis ins hohe Alter.Inspired by a work on creative poetry therapy in her bookstore (Helga Mitterhauser-Dubian 2023) H. Petzold wrote a text that deals with the effect of books and with reading in books and in book places (libraries, archives, bookstores – „bibliotopes“ ). He reports how the author experienced these places in his personal biography, his parents‘ home and the complex cultural milieu in childhood and youth, but also in his scientific „work life“ over the course of his life. He describes formative experiences as focus-forming working principles, which are explained with the concept of the “dominant”, the “ruling principle/focus” of the neurophysiologist Alexei Uchtomskijs. The training of such “dominants”, today understood as “promoting the connectome”, develops the training of “differential consciousness work” and “strong mentalizations” and has led to the later integrative ideas for a “transversal culture of consciousness” and for “complex cultural work”, contributing to a “uniplural world”. In addition to a formative „ecologization“, the influence of personal out-door nature experiences since childhood, which developed dominant interests in living things, it was experiences with books, bookstores, libraries that had a very strong influence on the life’s work of the founders of integrative therapy and on itss theoretical framework concepts. This circumstance of biographical in-door experience has so far been barely discussed yet by Petzold et al. – It had been too “natural”. Important framework concepts are briefly highlighted here, explained with integrative theoretical concepts, located in the biographical experiences of the founder and presented in its importance for “integrative cultural work” for the tasks of the 21st century. The text wants to make it clear: New aspects of self-knowledge and understanding of the world can be gained again and again, even into old age.https://www.fpi-publikation.de/polyloge/25-2023-petzold-h-g-2023e-buecher-sind-schluessel-zur-welt-ko-aktive-komplexe-kulturarbeit-und-differentielle-bewusstseinsarbeit-fuer-eine-t/peerReviewedpublishedVersio
Subring subgroups in Chevalley groups with doubly laced root systems
No full textAbstractWe study the lattice L of subgroups of a Chevalley group G(Φ,A) over a ring A, containing its elementary subgroup E(Φ,S) over a subring S⊆A. The standard description asserts that for any H∈L there exists a unique subring R⊇S of A such that H contains E(Φ,R) as a normal subgroup.The standard description was obtained by Ya. Nuzhin for algebraic field extensions. On the other hand, it was expected that the standard description does not hold for transcendental extensions. This was recently proved by the author for simply laced root systems.Now, suppose that Φ is doubly laced, i.e. Φ=Bl, Cl or F4, and that 2 is invertible in S. In the article we prove that in these settings the standard description of L holds for an arbitrary pair of rings S⊆A
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