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CLASS NUMBER FORMULAS FOR CERTAIN BIQUADRATIC FIELDS
No full textWe consider the class numbers of imaginary quadratic extensions , for certain primes , of totally real quadratic fields which have class number one. Using seminal work of Shintani, we obtain two elementary class number formulas for many such fields. The first expresses the class number as an alternating sum of terms that we generate from the coefficients of the power series expansions of two simple rational functions that depend on the arithmetic of and . The second makes use of expansions of , where is a prime such that and remains inert in . More precisely, for a generator of the totally positive unit group of , the base- expansion of has period length , and our second class number formula expresses the class number as a finite sum over disjoint cosets of size
Etale descent obstruction and anabelian geometry of curves over finite fields
No full textLet and be smooth, proper and geometrically integral curves over afinite field . Any morphism from to induces a morphism of their\'etale fundamental groups. The anabelian philosophy proposed by Grothendiecksuggests that, when has genus at least , all open homomorphisms betweenthe \'etale fundamental groups should arise in this way from a nonconstantmorphism of curves. We relate this expectation to the arithmetic of the curve over the global function field . Specifically, we show thatthere is a bijection between the set of conjugacy classes of well-behavedmorphism of fundamental groups and locally constant adelic points of thatsurvive \'etale descent. We use this to provide further evidence for theanabelian conjecture by relating it to another recent conjecture by Sutherlandand the second author
Les carrières de trachyte de la chaîne des Puys (Massif central, France). Production et diffusion des sarcophages au premier Moyen Âge (Ve–IXe s.)
No full textDans le cadre d’un Programme collectif de recherche (PCR), une équipe pluridisciplinaire étudie les conditions d’exploitation, d’utilisation et de diffusion d’une lave, extraite des volcans auvergnats, le trachyte. Au sein de ce collectif, l’étude archéologique de trois carrières de sarcophages du premier Moyen Âge a permis de faire le lien entre les lieux de fabrication et les nécropoles grâce à une signature géologique discriminante entre les carrières. Cette approche renouvelle les problématiques et montre l’exploitation conjointe de plusieurs carrières, dont ont été extraits plusieurs milliers de sarcophages retrouvés en Auvergne mais aussi en Limousin. Leur répartition spatiale montre la proximité des lieux de diffusion avec les anciennes voies romaines, suggérant l’insertion du schéma économique des sarcophages en trachyte dans un réseau déjà en place, soit qu’il ait été réactivé, soit qu’il n’ait jamais réellement disparu
On Rotation Distance of Rank Bounded Trees
No full textComputing the rotation distance between two binary trees with internalnodes efficiently (in time) is a long standing open question in thestudy of height balancing in tree data structures. In this paper, we initiatethe study of this problem bounding the rank of the trees given at the input(defined by Ehrenfeucht and Haussler (1989) in the context of decision trees).We define the rank-bounded rotation distance between two given binary trees and (with internal nodes) of rank at most , denoted by, as the length of the shortest sequence of rotations thattransforms to with the restriction that the intermediate trees mustbe of rank at most . We show that the rotation distance problem reduces inpolynomial time to the rank bounded rotation distance problem. This motivatesthe study of the problem in the combinatorial and algorithmic frontiers.Observing that trees with rank coincide exactly with skew trees (binarytrees where every internal node has at least one leaf as a child), we show thefollowing results in this frontier : We present an time algorithm for computing . That is,when the given trees are skew trees (we call this variant as skew rotationdistance problem) - where the intermediate trees are restricted to be skew aswell. In particular, our techniques imply that for any two skew trees. We show the following upper bound : for any two trees and of rankat most and respectively, we have that: where . This bound is asymptoticallytight for . En route our proof of the above theorems, we associate binary trees topermutations and bivariate polynomials, and prove several characterizations inthe case of skew trees.Comment: 28 pages, 2 figures, Abstract shortened to meet arxiv requirements, accepted journal versio
Simulations for Event-Clock Automata
No full textEvent-clock automata (ECA) are a well-known semantic subclass of timedautomata (TA) which enjoy admirable theoretical properties, e.g.,determinizability, and are practically useful to capture timed specifications.However, unlike for timed automata, there exist no implementations for checkingnon-emptiness of event-clock automata. As ECAs contain special prophecy clocksthat guess and maintain the time to the next occurrence of specific events,they cannot be seen as a syntactic subclass of TA. Therefore, implementationsfor TA cannot be directly used for ECAs, and moreover the translation of an ECAto a semantically equivalent TA is expensive. Another reason for the lack ofECA implementations is the difficulty in adapting zone-based algorithms,critical in the timed automata setting, to the event-clock automata setting.This difficulty was studied by Geeraerts et al. in 2011, where the authorsproposed a zone enumeration procedure that uses zone extrapolations forfiniteness. In this article, we propose a different zone-based algorithm tosolve the reachability problem for event-clock automata, using simulations forfiniteness. A surprising consequence of our result is that for event-predictingautomata, the subclass of event-clock automata that only use prophecy clocks,we obtain finiteness even without any simulations. For general event-clockautomata, our new algorithm exploits the G-simulation framework, which is thecoarsest known simulation relation in timed automata literature, and has beenrecently used for advances in other extensions of timed automata
An implicit function theorem for the stream calculus
No full textIn the context of the stream calculus, we present an Implicit FunctionTheorem (IFT) for polynomial systems, and discuss its relations with theclassical IFT from calculus. In particular, we demonstrate the advantages ofthe stream IFT from a computational point of view, and provide a few exampleapplications where its use turns out to be valuable
Applying computational approaches to energy discourse: a comparative methodological study of rule-based and large language model qualitative content analysis
No full textComposing dynamic programming tree-decomposition-based algorithms
No full textGiven two integers and as well as graph classes, the problems, \break, and ask, given graph as input, whether , , respectively can be partitionedinto sets such that, for each between and, , , respectively. Moreover in , we request that the number of edges withendpoints in different sets of the partition is bounded by . We show that ifthere exist dynamic programming tree-decomposition-based algorithms forrecognizing the graph classes , for each , then we canconstructively create a dynamic programming tree-decomposition-based algorithmsfor ,, and. We apply thisapproach to known problems. For well-studied problems, like VERTEX COVER andGRAPH -COLORING, we obtain running times that are comparable to those of thebest known problem-specific algorithms. For an exotic problem frombioinformatics, called DISPLAYGRAPH, this approach improves the known algorithmparameterized by treewidth
Les ports secondaires rouliers et ferries en France: Le tournant ferroviaire des pré- et post-acheminements de remorques non-accompagnées
No full textThis article is a contribution to the work about pre- and post-shipments to/from seaports, and on the place of secondary ports in the organization of trade. It develops an argument based on the analysis of generic and regionalized factors in the understanding of transport strategies. It also mobilizes the study of the interplay of actors to shed light on the processes at work in the territories. Empirical and qualitative in scope, it is based on a series of semi-structured interviews that reinforce the grey literature. This article analyses the recent boom (2016-2023) of rail pre- and post-shipments services for unaccompanied trailers to/from French roll-on/roll-off and ferries’ ports on the Channel/North Sea and Mediterranean coasts. It provides an annotated list of factors facilitating and dampening the demand for unaccompanied trailer transport by sea and rail; and drawing on the case of the United Kingdom's exit from the European Union (Brexit), it highlights the importance of regional contexts in the dynamics of the evolution of this demand. Finally, this article provides an overview of unaccompanied trailer rail services, in order to highlight the underlying interplay of actors, which shows the extent to which the phenomenon is driven by a small number of maritime, port and rail operators who adopt a cooperative and competitive approach. In the course of this evolution, a new competitive landscape, based on the emergence of a small number of secondary roll-on/roll-off and ferries ports, structuring the rail and maritime offer, appears in France.Cet article est une contribution aux travaux sur les pré- et post-acheminements maritimes et sur la place des ports secondaires dans l’organisation des échanges. Il développe un argumentaire fondé sur l’analyse des facteurs d‘évolution génériques et des facteurs régionalisés dans la compréhension des stratégies de transports. Il mobilise également l’étude des jeux d’acteurs pour éclairer les processus à l’œuvre sur les territoires. De visée empirique et qualitative, il est basé sur une série d’entretiens semi-directifs confortant l’état de l’art. Cet article analyse l’essor récent (2016-2023) des services de pré- et post-acheminements ferroviaires de remorques non-accompagnées de/vers les ports rouliers et ferries français des façades Manche / mer du Nord et Méditerranée. Il établit une liste commentée des facteurs facilitant, et des facteurs freinant la demande de transport maritime et ferroviaire de remorques non-accompagnées ; et en s’appuyant sur le cas de la sortie du Royaume-Uni de l’Union européenne (Brexit), il met en évidence l’importance des contextes régionaux dans la dynamique d’évolution de cette demande. Enfin, cet article dresse un état des lieux des services ferroviaires de remorques non-accompagnées, afin de mettre en exergue le jeu d’acteurs sous-jacent, qui montre à quel point le phénomène est porté par un petit nombre d’opérateurs maritimes, portuaires et ferroviaires qui adoptent une démarche autant coopérative que concurrentielle. Au fil de cette évolution, un nouveau paysage concurrentiel, basé sur l’émergence d’un petit nombre de ports rouliers et ferries secondaires, structurant l’offre ferroviaire et maritime, apparaît en France
On -generated axial algebras of Jordan type
No full textAxial algebras of Jordan type are a special type of commutativenon-associative algebras. They are generated by idempotents whose adjointoperators have the minimal polynomial dividing , where is a fixed value that is not equal to or . These algebras haverestrictive multiplication rules that generalize the Peirce decomposition foridempotents in Jordan algebras. A universal -generated algebra of Jordan type as an algebrawith parameters was constructed by I. Gorshkov and A. Staroletov. Dependingon the value of the parameter, the universal algebra may contain a non-trivialform radical. In this paper, we describe all semisimple -generated algebrasof Jordan type over a quadratically closed field.Comment: 12 page