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Cyclicity of the 2-class group of the first Hilbert 2-class field of some number fields
No full textLet \mathds{k} be a real quadratic number field. Denote by\mathrm{Cl}_2(\mathds{k}) its -class group and by \mathds{k}_2^{(1)}(resp. \mathds{k}_2^{(2)}) its first (resp. second) Hilbert -class field.The aim of this paper is to study, for a real quadratic number field whosediscriminant is divisible by one prime number congruent to modulo 4, themetacyclicity of G=\mathrm{Gal}(\mathds{k}_2^{(2)}/\mathds{k}) and thecyclicity of \mathrm{Gal}(\mathds{k}_2^{(2)}/\mathds{k}_2^{(1)}) whenever therank of \mathrm{Cl}_2(\mathds{k}) is , and the -rank of\mathrm{Cl}_2(\mathds{k}) is
Gradient estimates for a nonlinear elliptic equation on a smooth metric measure space
No full textLet (M, g, e −f dv) be a smooth metric measure space. We consider local gradient estimates for positive solutions to the following elliptic equation ∆ f u + au log u + bu = 0 where a, b are two real constants and f be a smooth function defined on M. As an application, we obtain a Liouville type result for such equation in the case a < 0 under the m-dimensions Bakry-Émery Ricci curvature
A probabilistic model for fast-to-evaluate 2D crack path prediction in heterogeneous materials
No full textThis paper is devoted to the construction of a new fast-to-evaluate model for the prediction of 2D crack paths in concrete-like microstructures. The model generates piecewise linear cracks paths with segmentation points selected using a Markov chain model. The Markov chain kernel involves local indicators of mechanical interest and its parameters are learnt from numerical full-field 2D simulations of cracking using a cohesive-volumetric finite element solver called XPER. This model does not include any mechanical elements. It is the database, derived from the XPER crack, that contains the mechanical information and optimizes the probabilistic model. The resulting model exhibits a drastic improvement of CPU time in comparison to simulations from XPER
A numerical technique for solving variable order time fractional differential-integro equations
No full textIn this manuscripts, we consider the coupled differential-integral equations including the variable-order Caputo fractional operator. To solve numerically these type of equations, we apply the shifted Jacobi-Gauss collocation scheme. Using this numerical method a system of algebraic equations is constructed. We solve this system with a recursive method in the nonlinear case and we solve it in linear case with algebraic formulas. Finally, for the high performance of the suggested method three Examples are illustrated
Series acceleration formulas obtained from experimentally discovered hypergeometric recursions
No full textIn 2010, Kh. Hessami Pilehrood and T. Hessami Pilehrood introduced generating function identities used to obtain series accelerations for values of Dirichlet's function, via the Markov--Wilf--Zeilberger method. Inspired by these past results, together with related results introduced by Chu et al., we introduce a variety of hypergeometric recurrences. We prove these recurrences using the WZ method, and we apply these recurrences to obtain series acceleration identities. We introduce a family of summations generalizing a Ramanujan-type series for due to Guillera, and a family of summations generalizing an accelerated series for Catalan's constant due to Lupa\c{s}, and many related results
Les moulins seigneuriaux à Annecy: Un premier regard sur les dynamiques d'occupation des bords du Thiou aux XIVe et XVe siècles
No full textL'étude de l'implantation et du déplacement des moulins comtaux de la ville d'Annecy sous le règne d'Amédée III de Genève est ici utilisée pour proposer une restitution du développement urbain de la ville médiévale. À partir de données extraites de l'étude approfondie des vingt-huit Comptes de Châtellenie conservés pour cette période (1325-1366) et complétées par le reste de notre corpus de thèse, nous cherchons à souligner les dynamiques de transformation de l'espace urbain tout en documentant la construction de ces édifices. Les moulins installés au bord du Thiou sont construits et entretenus, loués et vendus, par l'administration comtale qui en tire des bénéfices figurant en première page de chaque Compte de Châtellenie. Le niveau de détail varie selon les auteurs mais les données qui peuvent être extraites sont précieuses par leur régularité alors qu'aucun vestige archéologique n'est conservé sur le territoire
Inversion sequences avoiding 021 and another pattern of length four
No full textWe study the enumeration of inversion sequences that avoid the pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions. We introduce the concept of dregular generating trees and conjecture that for any 021-avoiding pattern τ , the generating tree T ({021, τ }) is d-regular for some integer d
Answer Counting under Guarded TGDs
No full textWe study the complexity of answer counting for ontology-mediated queries andfor querying under constraints, considering conjunctive queries and unionsthereof (UCQs) as the query language and guarded TGDs as the ontology andconstraint language, respectively. Our main result is a classificationaccording to whether answer counting is fixed-parameter tractable (FPT),W[1]-equivalent, #W[1]-equivalent, #W[2]-hard, or #A[2]-equivalent, lifting arecent classification for UCQs without ontologies and constraints due to Dellet al. The classification pertains to various structural measures, namelytreewidth, contract treewidth, starsize, and linked matching number. Our results rest on the assumption that the arity of relation symbols isbounded by a constant and, in the case of ontology-mediated querying, that allsymbols from the ontology and query can occur in the data (so-called full dataschema). We also study the meta-problems for the mentioned structural measures, thatis, to decide whether a given ontology-mediated query or constraint-queryspecification is equivalent to one for which the structural measure is bounded
Making first order linear logic a generating grammar
No full textIt is known that different categorial grammars have surface representation ina fragment of first order multiplicative linear logic (MLL1). We show that thefragment of interest is equivalent to the recently introduced extended tensortype calculus (ETTC). ETTC is a calculus of specific typed terms, whichrepresent tuples of strings, more precisely bipartite graphs decorated withstrings. Types are derived from linear logic formulas, and rules correspond toconcrete operations on these string-labeled graphs, so that they can beconveniently visualized. This provides the above mentioned fragment of MLL1that is relevant for language modeling not only with some alternative syntaxand intuitive geometric representation, but also with an intrinsic deductivesystem, which has been absent. In this work we consider a non-trivial notationally enriched variation of thepreviously introduced ETTC, which allows more concise and transparentcomputations. We present both a cut-free sequent calculus and a naturaldeduction formalism
Good-for-games -Pushdown Automata
No full textWe introduce good-for-games -pushdown automata (-GFG-PDA).These are automata whose nondeterminism can be resolved based on the inputprocessed so far. Good-for-gameness enables automata to be composed with games,trees, and other automata, applications which otherwise require deterministicautomata. Our main results are that -GFG-PDA are more expressive thandeterministic - pushdown automata and that solving infinite games withwinning conditions specified by -GFG-PDA is EXPTIME-complete. Thus, wehave identified a new class of -contextfree winning conditions forwhich solving games is decidable. It follows that the universality problem for-GFG-PDA is in EXPTIME as well. Moreover, we study closure propertiesof the class of languages recognized by -GFG- PDA and decidability ofgood-for-gameness of -pushdown automata and languages. Finally, wecompare -GFG-PDA to -visibly PDA, study the resources necessaryto resolve the nondeterminism in -GFG-PDA, and prove that the parityindex hierarchy for -GFG-PDA is infinite. This is a corrected version of the paper arXiv:2001.04392v6 publishedoriginally on January 7, 2022