Relevant bibliographies by topics / Valued fields

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Valued fields'

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Published: 4 June 2021
Last updated: 28 September 2024

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Journal articles on the topic "Valued fields"

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Harrison-Trainor, Matthew. "Computable valued fields." Archive for Mathematical Logic 57, no. 5-6 (September 15, 2017): 473–95. http://dx.doi.org/10.1007/s00153-017-0589-9.

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Ershov, Yu L. "*-Extremal valued fields." Siberian Mathematical Journal 50, no. 6 (November 2009): 1007–10. http://dx.doi.org/10.1007/s11202-009-0111-7.

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Ershov, Yu L. "Extremal Valued Fields." Algebra and Logic 43, no. 5 (September 2004): 327–30. http://dx.doi.org/10.1023/b:allo.0000044281.72007.d0.

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Ershov, Yu L. "Stable valued fields." Algebra and Logic 46, no. 6 (November 2007): 385–98. http://dx.doi.org/10.1007/s10469-007-0038-7.

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Khanduja, Sudesh K. "On value groups and residue fields of some valued function fields." Proceedings of the Edinburgh Mathematical Society 37, no. 3 (October 1994): 445–54. http://dx.doi.org/10.1017/s0013091500018897.

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Let K = K0(x, y) be a function field of transcendence degree one over a field K0 with x, y satisfying y2 = F(x), F(x) being any polynomial over K0. Let υ0 be a valuation of K0 having a residue field k0 and υ be a prolongation of υ to K with residue field k. In the present paper, it is proved that if G0⊆G are the value groups of υ0 and υ, then either G/G0 is a torsion group or there exists an (explicitly constructible) subgroup G1 of G containing G0 with [G1:G0]<∞ together with an element γ of G such that G is the direct sum of G1 and the cyclic group ℤγ. As regards the residue fields, a method of explicitly determining k has been described in case k/k0 is a non-algebraic extension and char k0≠2. The description leads to an inequality relating the genus of K/K0 with that of k/k0: this inequality is slightly stronger than the one implied by the well-known genus inequality (cf. [Manuscripta Math.65 (1989), 357–376’, [Manuscripta Math.58 (1987), 179–214]).
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Prestel, Alexander, and Cydara C. Ripoll. "Integral-valued rational functions on valued fields." Manuscripta Mathematica 73, no. 1 (December 1991): 437–52. http://dx.doi.org/10.1007/bf02567653.

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Guzy, Nicolas. "0-D-valued fields." Journal of Symbolic Logic 71, no. 2 (June 2006): 639–60. http://dx.doi.org/10.2178/jsl/1146620164.

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AbstractIn [12]. T. Scanlon proved a quantifier elimination result for valued D-fields in a three-sorted language by using angular component functions. Here we prove an analogous theorem in a different language which was introduced by F. Delon in her thesis. This language allows us to lift the quantifier elimination result to a one-sorted language by a process described in the Appendix. As a byproduct, we state and prove a “positivstellensatz” theorem for the differential analogue of the theory of real-series closed fields in the valued D-field setting.
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Pal, Koushik. "Multiplicative valued difference fields." Journal of Symbolic Logic 77, no. 2 (June 2012): 545–79. http://dx.doi.org/10.2178/jsl/1333566637.

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AbstractThe theory of valued difference fields (K, σ, υ,) depends on how the valuation υ interacts with the automorphism σ. Two special cases have already been worked out - the isometric case, where υ(σ(x)) = υ(x) for all x Є K, has been worked out by Luc Belair, Angus Macintyre and Thomas Scanlon; and the contractive case, where υ(σ(x)) > nυ(x) for all x Є K× with υ(x) > 0 and n Є ℕ, has been worked out by Salih Azgin. In this paper we deal with a more general version, the multiplicative case, where υ(σ(x)) = ρ · υ(x), where ρ (> 0) is interpreted as an element of a real-closed field. We give an axiomatization and prove a relative quantifier elimination theorem for this theory.
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JAHNKE, FRANZISKA, PIERRE SIMON, and ERIK WALSBERG. "DP-MINIMAL VALUED FIELDS." Journal of Symbolic Logic 82, no. 1 (March 2017): 151–65. http://dx.doi.org/10.1017/jsl.2016.15.

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Jahnke, Franziska, and Pierre Simon. "NIP henselian valued fields." Archive for Mathematical Logic 59, no. 1-2 (June 29, 2019): 167–78. http://dx.doi.org/10.1007/s00153-019-00685-8.

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Dissertations / Theses on the topic "Valued fields"

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Mason, Jonathan W. "Uniform algebras over complete valued fields." Thesis, University of Nottingham, 2012. http://eprints.nottingham.ac.uk/12419/.

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UNIFORM algebras have been extensively investigated because of their importance in the theory of uniform approximation and as examples of complex Banach algebras. An interesting question is whether analogous algebras exist when a complete valued field other than the complex numbers is used as the underlying field of the algebra. In the Archimedean setting, this generalisation is given by the theory of real function algebras introduced by S. H. Kulkarni and B. V. Limaye in the 1980s. This thesis establishes a broader theory accommodating any complete valued field as the underlying field by involving Galois automorphisms and using non-Archimedean analysis. The approach taken keeps close to the original definitions from the Archimedean setting. Basic function algebras are defined and generalise real function algebras to all complete valued fields. Several examples are provided. Each basic function algebra is shown to have a lattice of basic extensions related to the field structure. In the non-Archimedean setting it is shown that certain basic function algebras have residue algebras that are also basic function algebras. A representation theorem is established. Commutative unital Banach F-algebras with square preserving norm and finite basic dimension are shown to be isometrically F-isomorphic to some subalgebra of a Basic function algebra. The theory of non-commutative real function algebras was established by K. Jarosz in 2008. The possibility of their generalisation to the non-Archimedean setting is established in this thesis. In the context of complex uniform algebras, a new proof is given using transfinite induction of the Feinstein-Heath Swiss cheese “Classicalisation” theorem.
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Hossain, Akash. "Forking in valued fields and related structures." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM019.

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Cette thèse est une contribution à la théorie des modèles des corps valués. On étudie la déviation dans les corps valués, ainsi que certains de leurs réduits. On s'intéresse particulièrement aux corps pseudo-locaux, les ultraproduits de caractéristique résiduelle nulle des corps valués p-adiques. Nous considérons d'abord aux groupes des valeurs des corps valués qui nous intéressent, les groupes Abéliens ordonnés réguliers. Nous y établissons description géométrique de la déviation, ainsi qu'une classification détaillée des extensions globales non-déviantes ou invariantes d'un type donné. Nous démontrons ensuite des principes d'Ax-Kochen-Ershov pour la division et la déviation dans la théorie resplendissante des expansions de suites exactes courtes pures de structures Abéliennes, telles qu'étudiées dans l'article sur la distalité d'Aschenbrenner-Chernikov-Gehret-Ziegler. En particulier, nos résultats s'appliquent aux groupes des termes dominants des (expansions de) corps valués. Pour finir, nous donnons diverses conditions suffisantes pour qu'un ensemble de paramètres soit une base d'extension dans un corps valué Hensélien de caractéristique résiduelle nulle. En particulier, nous démontrons que la déviation coïncide avec la division dans les corps pseudo-locaux de caractéristique résiduelle nulle. Nous discutons aussi des résultats de Ealy-Haskell-Simon sur la déviation pour les extensions séparées de corps valués Henséliens de caractéristique résiduelle nulle. Nous contribuons à la question en démontrant que, dans le cas d'une extension Abhyankar, et avec quelques hypothèses supplémentaires, la non-déviation d'un type dans in corps pseudo-local implique l'existence d'une mesure de Keisler globale invariante dont le support contient ce type, à l'instar des corps pseudo-finis
This thesis is a contribution to the model theory of valued fields. We study forking in valued fields and some of their reducts. We focus particularly on pseudo-local fields, the ultraproducts of residue characteristic zero of the p-adic valued fields. First, we look at the value groups of the valued fields we are interested in, the regular ordered Abelian groups. We establish for these ordered groups a geometric description of forking, as well as a full classification of the global extensions of a given type which are non-forking or invariant. Then, we prove an Ax-Kochen-Ershov principle for forking and dividing in expansions of pure short exact sequences of Abelian structures, as studied by Aschenbrenner-Chernikov-Gehret-Ziegler in their article about distality. This setting applies in particular to the leading-term structure of (expansions of) valued fields. Lastly, we give various sufficient conditions for a parameter set in a Henselian valued field of residue characteristic zero to be an extension base. In particular, we show that forking equals dividing in pseudo-local of residue characteristic zero. Additionally, we discuss results by Ealy-Haskell-Simon on forking in separated extensions of Henselian valued fields of residue characteristic zero. We contribute to the question in the setting of Abhyankar extensions, where we show that, with some additional conditions, if a type in a pseudo-local field does not fork, then there exists some global invariant Keisler measure whose support contains that type. This behavior is well-known in pseudo-finite fields
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Touchard, Pierre Verfasser], and Martin [Akademischer Betreuer] [Hils. "On transfer principles in Henselian valued fields / Pierre Touchard ; Betreuer: Martin Hils." Münster : Universitäts- und Landesbibliothek Münster, 2020. http://d-nb.info/122398379X/34.

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Touchard, Pierre [Verfasser], and Martin [Akademischer Betreuer] Hils. "On transfer principles in Henselian valued fields / Pierre Touchard ; Betreuer: Martin Hils." Münster : Universitäts- und Landesbibliothek Münster, 2020. http://d-nb.info/122398379X/34.

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Lehéricy, Gabriel. "Quasi-orders, C-groups, and the differentiel rank of a differential-valued field." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC130/document.

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Cette thèse a pour objet les ordres, les valuations et les C-relations sur les groupes, ainsi que les corps différentiels valués tels qu’étudiés par Rosenlicht. Elle accomplit trois objectifs principaux. Le premier est d’introduire et d’étudier une notion de quasi-ordre sur les groupes qui a pour but de réunir les ordres et les valuations dans un même cadre. Nous donnons un théorème de structure des groupes munis d’un tel quasi-ordre, ce qui nous permet ensuite de donner un “théorème de plongement de Hahn” pour ces groupes. Le second objectif de cette thèse est de décrire les C-groupes à l’aide des quasi-ordres. Nous donnons un théorème de structure pour les C-groupes, qui énonce que tout C-groupe est un “mélange” de groupes ordonnés et de groupes valués. Nous utilisons ensuite ce résultat pour caractériser les groupes C-minimaux à l’intérieur de la classe des C-groupes. Le troisième objectif de cette thèse est d’introduire et d’étudier une notion de rang différentiel d’un corps différentiel valué. Nous définissons cette notion par analogie avec les notions de rang exponentiel d’un corps exponentiel et de rang de différence d’un corps aux différences. Nous montrons que cette notion de rang n’est pas tout à fait satisfaisante, et introduisons donc une meilleure notion de rang appelée le rang différentiel déployé. Nous donnons ensuite une méthode pour définir une dérivation “de type Hardy” sur un corps de séries formelles généralisées, ce qui nous permet de construire des corps différentiels valués dont le rang différentiel et le rang différentiel déployé ont été arbitrairement choisis
This thesis deals with orders, valuations and C-relations on groups, and with differential-valued fields à la Rosenlicht. It achieves three main objectives. The first one is to introduce and study a notion of quasi-order on groups meant to encompass orders and valuations in a common framework. We give a structure theorem for groups endowed with such a quasi-order, which then allows us to give a “Hahn’s embedding theorem” for these groups. The second objective of this thesis is to describe C-groups via quasi-orders. We give a structure theorem for C-groups, which basically states that any C-group is a “mix” of ordered groups and valued groups. We then use this result to characterize C-minimal groups inside the class of C-groups. The third objective of this thesis is to introduce and study a notion of differential rank for differential-valued fields. We define this notion by analogy with the exponential rank of an exponential field and with the difference rank of a difference field. We show that this notion of rank is not quite satisfactory, so we introduce a better notion of rank called the unfolded differential rank. We then give a method to define “Hardy-type” derivations on fields of generalized power series, which allows us to build differential-valued fields of arbitrary given differential rank and unfolded differential rank
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Rideau, Silvain. "Éliminations dans les corps valués." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112375/document.

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Cette thèse est une contribution à la théorie des modèles des corps valués. Les principaux résultats de ce texte sont des résultats d’éliminations des quantificateurs et des imaginaires. Le premier chapitre contient une étude des imaginaires dans les extensions finies de Qp. On y démontre que ces corps ainsi que leurs ultraproduits éliminent les imaginaires dans le langage géométrique. On en déduit un résultat de rationalité uniforme pour les fonctions zêta associées aux familles de relations d’équivalences définissables dans les extensions finies de Qp. La motivation première du deuxième chapitre est l’étude de W(F_p^alg) en tant que corps valué analytique de différence. Plus généralement, on démontre un théorème d’élimination des quantificateurs de corps dans le langage RV pour les corps valués analytiques -Henséliens de caractéristique nulle. On donne aussi une axiomatisation de la théorie de W(F_p^alg) ainsi qu’une preuve qu’elle est NIP. Dans le troisième chapitre, on prouve la densité des types définissables dans certains enrichissements d’ACVF. On en déduit un critère pour l’élimination des imaginaires et la propriété d’extension invariante. Ce chapitre contient aussi des résultats abstraits sur les ensembles extérieurement définissables dans les théories NIP. Dans le dernier chapitre, les résultats du chapitre précédent sont appliqués à VDF, la modèle complétion des corps valués munis d’une dérivation qui préserve la valuation, pour obtenir l’élimination des imaginaires dans le langage géométrique ainsi que la densité des types définissables et la propriété d’extension invariante. Ce chapitre contient aussi des considérations sur les fonctions définissables, les types et les groupes définissables dans VDF
This thesis is about the model theory of valued fields. The main results in this text are eliminationsof quantifiers and imaginaries. The first chapter is concerned with imaginaries in finite extensions of Qp. I show that these fields and their ultraproducts eliminate imaginaries in the geometric language. As a corollary, I obtain the uniform rationality of zeta functions associated to families of equivalence relations that aredefinable in finite extensions of Qp.The motivation for the second chapter is to study W(F_p^alg) as an analytic difference valued field. More generally, I show a field quantifier elimination theorem in the RV-language for -Henselian characteristic zero valued fields with an analytic structure. I also axiomatise the theory of W(F_p^alg) and I show that this theory is NIP.In the third chapter, I prove the density of definable types in certain enrichments of ACVF. From this result, I deduce a criterion for the elimination of imaginaries and the invariant property. This chapter also contains abstract results on externally definable sets in NIP theories. In the last chapter, the previous chapter is applied to VDF, the model completion of valued fields with a valuation preserving derivation, to obtain the elimination of imaginaries in the geometric language, as well as the density of definable types and the invariant extension property. This chapter also contains considerations about definable functions, types and definable groupes in VDF
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Forey, Arthur. "Invariants motiviques dans les corps valués." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066557/document.

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Cette thèse est consacrée à définir et étudier des invariants motiviques associés aux ensembles semi-algébriques dans les corps valués. Ceux-ci sont les combinaisons booléennes d'ensembles définis par des inégalités valuatives. L'outil principal que nous utilisons est l'intégration motivique, une forme de théorie de la mesure à valeurs dans le groupe de Grothendieck des variétés définies sur le corps résiduel. Dans une première partie, on définit la notion de densité locale motivique. C'est un analogue valuatif du nombre de Lelong complexe, de la densité réelle de Kurdyka-Raby et de la densité p-adique de Cluckers-Comte-Loeser. C'est un invariant métrique à valeurs dans un localisé du groupe de Grothendieck des variétés. Notre résultat principal est que cet invariant se calcule sur le cône tangent muni de multiplicités motiviques. On établit un analogue de la formule de Cauchy-Crofton locale. On montre enfin que dans le cas d'une courbe plane, la densité motivique est égale à la somme des inverses des multiplicités des branches. L'objet de la seconde partie est de définir un morphisme d'anneau du groupe de Grothendieck des ensembles semi-algébriques sur un corps valué K vers le groupe de Grothendieck de la catégorie d'Ayoub des motifs rigides analytiques sur K. On montre qu'il étend le morphisme qui envoie la classe d'une variété algébrique sur la classe de son motif cohomologique à support compact. Cela fournit donc une notion virtuelle de motif cohomologique à support compact pour les variétés rigides analytiques. On montre également un théorème de dualité permettant de comparer le motif cohomologique de la fibre de Milnor analytique avec la fibre de Milnor motivique
This thesis is devoted to define and study some motivic invariants associated to semialgebraic sets in valued fields. They are boolean combinations of sets defined by valuative inequalities. Our main tool is the theory of motivic integration, which is a kind of measure theory with values in the Grothendieck group of varieties defined over the residue field. In the first part, we define the notion of motivic local density. It is a valuative analog of complex Lelong number, Kurdyka-Raby real density and p-adic density of Cluckers- Comte-Loeser. It is a metric invariant with values in a localization of the Grothendieck group of varieties. Our main result is that it can be computed on the tangent cone with motivic multiplicities. We also establish an analog of the local Cauchy-Crofton formula. We finally show that the density of a germ of plane curve defined over the residue field is equal to the sum of the inverses of the multiplicities of the formal branches of the curve. The goal of the second part is to define a ring morphism from the Grothendieck group of semi-algebraic sets defined over a valued field K to the Grothendieck group of Ayoub’s categoryof rigid analytic motives over K. We show that it extends the morphism sending the class of an algebraic variety to the class of its cohomological motive with compact support. This gives a notion of virtual cohomological motive with compact support for rigid analytic varieties. We also show a duality theorem allowing us to compare the cohomological motive of the analytic Milnor fiber with the motivic Milnor fiber
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Stroder, Miriam Elizabeth. "Effects of Culturally Responsive Teaching Practices on the Literacy Learning of Latino Students." TopSCHOLAR®, 2008. http://digitalcommons.wku.edu/cgi/query.cgi?field_1=lname&value_1=Stroder&field_2=fname&value_2=Miriam&field_3=institution&value_3=Western%20Kentucky%20University&advanced=1.

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GOMEZ-CALDERON, JAVIER. "POLYNOMIALS WITH SMALL VALUE SET OVER FINITE FIELDS." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183933.

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Let K(q) be the finite field with q elements and characteristic p. Let f(x) be a monic polynomial of degree d with coefficients in K(q). Let C(f) denote the number of distinct values of f(x) as x ranges over K(q). It is easy to show that C(f) ≤ [|(q - 1)/d|] + 1. Now, there is a characterization of polynomials of degree d < √q for which C(f) = [|(q - 1)/d|] +1. The main object of this work is to give a characterization for polynomials of degree d < ⁴√q for which C(f) < 2q/d. Using two well known theorems: Hurwitz genus formula and Andre Weil's theorem, the Riemann Hypothesis for Algebraic Function Fields, it is shown that if d < ⁴√q and C(f) < 2q/d then f(x) - f(y) factors into at least d/2 absolutely irreducible factors and f(x) has one of the following forms: (UNFORMATTED TABLE FOLLOWS) f(x - λ) = D(d,a)(x) + c, d|(q² - 1), f(x - λ) = D(r,a)(∙ ∙ ∙ ((x²+b₁)²+b₂)²+ ∙ ∙ ∙ +b(m)), d|(q² - 1), d=2ᵐ∙r, and (2,r) = 1 f(x - λ) = (x² + a)ᵈ/² + b, d/2|(q - 1), f(x - λ) = (∙ ∙ ∙((x²+b₁)²+b₂)² + ∙ ∙ ∙ +b(m))ʳ+c, d|(q - 1), d=2ᵐ∙r, f(x - λ) = xᵈ + a, d|(q - 1), f(x - λ) = x(x³ + ax + b) + c, f(x - λ) = x(x³ + ax + b) (x² + a) + e, f(x - λ) = D₃,ₐ(x² + c), c² ≠ 4a, f(x - λ) = (x³ + a)ⁱ + b, i = 1, 2, 3, or 4, f(x - λ) = x³(x³ + a)³ +b, f(x - λ) = x⁴(x⁴ + a)² +b or f(x - λ) = (x⁴ + a) ⁱ + b, i = 1,2 or 3, where D(d,a)(x) denotes the Dickson’s polynomial of degree d. Finally to show other polynomials with small value set, the following equation is obtained C((fᵐ + b)ⁿ) = αq/d + O(√q) where α = (1 – (1 – 1/m)ⁿ)m and the constant implied in O(√q) is independent of q.
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Ai, Xiaohua. "Arithmetic of values of L-functions and generalized multiple zeta values over number fields." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066394/document.

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L'objectif principal de cette thèse est de généraliser les multizetas au cas où le corps de base Q est remplacé par un corps de nombres quelconque. La motivation derrière cette construction vient des travaux de A. Goncharov sur les corrélateurs de Hodge et de la philosophie plectique de J. Nekovar et A. Scholl. On commence par la construction des fonctions de Green plectiques supérieures. Hecke a prouvé que l'intégration d'une série d'Eisenstein appropriée sur le groupe de classes des idèles du corps de nombres donné, multipliée par un caractère du groupe des classes des idèles, est équale à la fonction L associée à ce caractère. Remplacant la série d'Eisenstein par les fonctions de Green plectiques supérieures, une intégration similaire donne des nouveaux résultats, qui généralisent les multizetas classiques et les multi-polylogarithmes. D'après le principe plectique, un sous-groupe de l'anneau des entiers du corps de nombres donné joue un rôle essentiel dans ces travaux
The principal objective of this thesis is to generalize multiple zeta values to the case when the ground field Q is replaced by an arbitrary number field. The motivation behind the construction comes from the work of A. Goncharov on Hodge correlators and the plectic philosophy of J. Nekovar and A. Scholl. We start by constructing the higher plectic Green functions. Hecke once proved that the integral of the restriction of a suitable Eisenstein series over $\mathbb{Q}$ to the idele class group of a given number field multipled an idele class character of finite order is equal to the L-function of this charator. By replacing Eisenstein seris with our higher plectic Green functions, a similar integration gives new results, which give the generalization of classical multiple zeta values and multiple polyloarithms. According to the plectic principle, a non-trivial subgroup of the ring of integers of a given number field plays an essential role in this work
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Books on the topic "Valued fields"

1

Ershov, Yuri L. Multi-Valued Fields. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1307-0.

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Hendricus, Schikhof Wilhelmus, ed. Locally convex spaces over non-Archimedean valued fields. Cambridge, UK: Cambridge University Press, 2010.

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Jean-Pierre, Fouque, Hochberg Kenneth J, and Merzbach Ely, eds. Stochastic analysis: Random fields and measure-valued processes. Ramat-Gan, Israel: Gelbart Research Institute for Mathematical Sciences and the Emmy Noether Research Institute of Mathematics, Bar-Ilan University, 1996.

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Perez-Garcia, C. Locally convex spaces over non-Archimedean valued fields. New York: Cambridge University Press, 2009.

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1959-, Hrushovski Ehud, and Macpherson Dugald, eds. Stable domination and independence in algebraically closed valued fields. Cambridge: Cambridge University Press, 2008.

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Valéry, Covachev, ed. Complex vector functional equations. Singapore: World Scientific, 2001.

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Esposito, Giampiero. Euclidean quantum gravity on manifolds with boundary. Dordrecht: Kluwer Academic Publishers, 1997.

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Wijers, Jean Paul, Isabel Amaral, William Hanson, Bengt-Arne Hulleman, and Diana Mather. Protocol to Manage Relationships Today. NL Amsterdam: Amsterdam University Press, 2020. http://dx.doi.org/10.5117/9789463724159.

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Protocol to Manage Relationships Today explains the contemporary value of protocol, not only for monarchies or diplomatic institutes, but for any non-profit or for-profit organisation. This book presents modern protocol as a tool to build strong, authentic networks of reciprocal relationships. When used effectively protocol can: - Increase the effect of the networking activities of an organisation. Protocol gives a professional structure to relationship management, to achieve access to the 'right' networks and a reciprocal relationship with the most valued stakeholders. - Deepen relationships. In our world there is so much focus on pragmatism in building relationships - protocol focuses on the common ground to gain value. - Be used as a valuable tool in a post COVID-19 era, where the need for space and time to build real and authentic relationships is well understood. The book defines how tested values perfectly fit in today's society, where modern organisations want to build effective relationships and communities. This book is focused on developing an increasingly vital expertise for professionals who deal with complex relationship management issues on a strategic and tactical operational level. They come from different fields, such as government institutions, non-profit organisations and commercial environments. This book also gives protocol officers a contemporary approach towards the application of protocol. It is not designed as a complete guide to all the rules of protocol, but it describes how to translate the context into a tailor-made protocol for each meeting or event. The book explains protocol as a flexible method to handle unique situations. Protocol is presented on four levels: the 'why' of protocol; the strategic and tactical level; the practical implementation; and the execution of protocol. Protocol to Manage Relationships Today is written by Europe's foremost protocol experts with collective years of experience with the management of networking meetings and events at the highest level.
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South Africa. Dept. of Agriculture., ed. Field crops market value chain profiles. Pretoria: Department of Agriculture, 2007.

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Esposito, Giampiero. Euclidean Quantum Gravity on Manifolds with Boundary. Dordrecht: Springer Netherlands, 1997.

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Book chapters on the topic "Valued fields"

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Ershov, Yuri L. "Multi-Valued Fields." In Multi-Valued Fields, 85–140. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1307-0_2.

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Ershov, Yuri L. "Valuation Rings." In Multi-Valued Fields, 1–84. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1307-0_1.

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Ershov, Yuri L. "Local-Global Properties of Near Boolean Families." In Multi-Valued Fields, 141–94. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1307-0_3.

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Ershov, Yuri L. "Model-Theoretic Properties of Multi-Valued Fields." In Multi-Valued Fields, 195–258. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1307-0_4.

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Diagana, Toka, and François Ramaroson. "Non-Archimedean Valued Fields." In SpringerBriefs in Mathematics, 1–39. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27323-5_1.

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Ribenboim, Paulo. "Polynomials and Henselian Valued Fields." In Springer Monographs in Mathematics, 79–105. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0551-7_4.

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Fresnel, Jean, and Marius van der Put. "Valued Fields and Normed Spaces." In Rigid Analytic Geometry and Its Applications, 1–11. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0041-3_1.

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Sarbadhikari, Haimanti, and Shashi Mohan Srivastava. "Model Theory of Valued Fields." In A Course on Basic Model Theory, 193–207. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5098-5_7.

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Mathiak, Karl. "Valued vector spaces." In Valuations of Skew Fields and Projective Hjelmslev Spaces, 51–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0074656.

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Efrat, Ido. "𝐾-rings of wild valued fields." In Mathematical Surveys and Monographs, 247–52. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/surv/124/27.

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Conference papers on the topic "Valued fields"

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Wang, Xiao, Ni Chen, Chengyu Wang, Johannes Froech, Arka Majumdar, and David J. Brady. "Metalens-based snapshot ptychography." In Imaging Systems and Applications, FD1.5. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/isa.2024.fd1.5.

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We demonstrate a wavefront camera using a metalens. The metalens consists of a 5 by 5 array of overlapping focal apertures. We use a hybrid neural phase retrieval algorithm to image remote complex valued fields.
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Wang, Xiao, Ni Chen, Chengyu Wang, Johannes Froech, Arka Majumdar, and David J. Brady. "Metalens-based snapshot ptychography." In Propagation Through and Characterization of Atmospheric and Oceanic Phenomena, FD1.5. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/pcaop.2024.fd1.5.

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We demonstrate a wavefront camera using a metalens. The metalens consists of a 5 by 5 array of overlapping focal apertures. We use a hybrid neural phase retrieval algorithm to image remote complex valued fields.
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Wang, Xiao, Ni Chen, Chengyu Wang, Johannes Froech, Arka Majumdar, and David J. Brady. "Metalens-based snapshot ptychography." In Computational Optical Sensing and Imaging, FD1.5. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cosi.2024.fd1.5.

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We demonstrate a wavefront camera using a metalens. The metalens consists of a 5 by 5 array of overlapping focal apertures. We use a hybrid neural phase retrieval algorithm to image remote complex valued fields.
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Wang, Xiao, Ni Chen, Chengyu Wang, Johannes Froech, Arka Majumdar, and David J. Brady. "Metalens-based snapshot ptychography." In Adaptive Optics: Methods, Analysis and Applications, FD1.5. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/aopt.2024.fd1.5.

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We demonstrate a wavefront camera using a metalens. The metalens consists of a 5 by 5 array of overlapping focal apertures. We use a hybrid neural phase retrieval algorithm to image remote complex valued fields.
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Wang, Xiao, Ni Chen, Chengyu Wang, Johannes Froech, Arka Majumdar, and David J. Brady. "Metalens-based snapshot ptychography." In 3D Image Acquisition and Display: Technology, Perception and Applications, FD1.5. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/3d.2024.fd1.5.

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We demonstrate a wavefront camera using a metalens. The metalens consists of a 5 by 5 array of overlapping focal apertures. We use a hybrid neural phase retrieval algorithm to image remote complex valued fields.
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Malyarenko, Anatoliy. "Spectral expansions of tensor-valued random fields." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972687.

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Sugawara, Yukihiro, Rei Ueno, Naofumi Homma, and Takafumi Aoki. "System for Automatic Generation of Parallel Multipliers over Galois Fields." In 2015 IEEE International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2015. http://dx.doi.org/10.1109/ismvl.2015.15.

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HRISTOV, Milen J. "VECTOR-VALUED LAPLACE TRANSFORMATION APPLIED TO RATIONAL BÉZIER CURVES." In 4th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814719780_0016.

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Aktas, Omer, and Bekir Z. Yuksek. "Real valued TM fields in arbitrary cross section waveguide." In 2016 IEEE International Conference on Mathematical Methods in Electromagnetic Theory (MMET). IEEE, 2016. http://dx.doi.org/10.1109/mmet.2016.7544064.

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Weigle, Chris, and David C. Banks. "Extracting iso-valued features in 4-dimensional scalar fields." In the 1998 IEEE symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/288126.288175.

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Reports on the topic "Valued fields"

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Wøien Meijer, Mari, Elin Cedergren, and Hjördís Guðmundsdóttir. From Fields to Futures: 40 action points for rural revitalisation - Nordic Rural Youth Panel 2023. Nordregio, November 2023. http://dx.doi.org/10.6027/r2023:131403-2503.

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The Nordic Rural Youth Panel has synthesized a report outlining 40 actionable recommendations for making rural areas in the Nordic region more attractive for young people. This paper addresses the ongoing trend of young people moving to cities, highlighting the need for better public transportation, a variety of housing options, and education that connects to local job markets in rural areas. The panel wants to change the common view that success and a good life can only be found in cities, showing instead that rural areas have a lot to offer. The report expands on several key areas: - Transportation: Young people in rural areas need easy and affordable access to public transit and various local travel options to support a fair transition to green transport. - Housing: There's a need for affordable and diverse housing, ensuring young people have good options for both renting and buying that meet their needs, and are linked to local services and community activities. - Education and employment: Young people need access to education at all levels in rural areas, with clear paths from education to local jobs, including options for remote work. - Health and recreation: There should be safe spaces for discussions about mental and physical health, as well as access to places for sports and other activities. - Community and social life: Funding is needed for public spaces and activities that bring people together, helping to create strong community ties. - Inclusion: Policies and discussions need to be accessible and relevant to young people, using their language and platforms to ensure they can actively participate and feel valued. Developed with input from 25 young people across the whole Nordic region, the panel’s recommendations provide a direct and valuable perspective for policymakers. It serves as a guide for creating appealing, dynamic, and sustainable rural communities, ensuring young people are at the centre of these efforts.
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Nottingham, M. Structured Field Values for HTTP. RFC Editor, February 2021. http://dx.doi.org/10.17487/rfc8941.

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Sparks, R. Multiple SIP Reason Header Field Values. RFC Editor, March 2023. http://dx.doi.org/10.17487/rfc9366.

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Trainor-Guitton, W. Value of Information Evaluation using Field Data. Office of Scientific and Technical Information (OSTI), June 2015. http://dx.doi.org/10.2172/1229846.

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Trainor-Guitton, W. Value of Information Evaluation using Field Data. Office of Scientific and Technical Information (OSTI), December 2014. http://dx.doi.org/10.2172/1179122.

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He, Haoran, David Neumark, and Qian Weng. Do Workers Value Flexible Jobs? A Field Experiment. Cambridge, MA: National Bureau of Economic Research, January 2019. http://dx.doi.org/10.3386/w25423.

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Keränen, A., and C. Bormann. Sensor Measurement Lists (SenML) Fields for Indicating Data Value Content-Format. RFC Editor, June 2022. http://dx.doi.org/10.17487/rfc9193.

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Steven Wesnousky, S. John Caskey, and John W. Bell. Recency of Faulting and Neotechtonic Framework in the Dixie Valley Geothermal Field and Other Geothermal Fields of the Basin and Range. Office of Scientific and Technical Information (OSTI), February 2003. http://dx.doi.org/10.2172/808727.

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Kozachenko, Nadiia. AGM cognitive actions as modal operators of three-valued logic: presentation. Ruhr-Universität Bochum, July 2022. http://dx.doi.org/10.31812/123456789/6687.

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AGM is designed so that its principles can be applied to the development of belief dynamics models, regardless of the field of application. The main idea of this work is to see how we can to represent cognitive actions considered in AGM within a certain three-valued logic, and check what interesting properties can be discovered in this way. To do this, we will consider the basic concepts and principles of AGM. Then we interpret them in a logical schema. And then we see what information about them we can get in the resulting system.
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Alhasan, Ahmad, Brian Moon, Doug Steele, Hyung Lee, and Abu Sufian. Chip Seal Quality Assurance Using Percent Embedment. Illinois Center for Transportation, December 2023. http://dx.doi.org/10.36501/0197-9191/23-029.

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This study investigates the use of macrotexture as an indicator of the percent embedment (PE) of aggregate in a chip seal and ultimately, as a quality assurance tool for chip seals. The study included an extensive field- and controlled-testing program from 24 chip seal sections constructed in Illinois. Surface texture measurements were acquired using a high-speed texture profiler and a stationary laser texture device. The analysis showed that stationary texture measurements were more consistent and reliable for estimating PE and characterizing chip seals in the field. Moreover, the ground truth PE values were estimated using an image analysis algorithm implemented on side-view images of cores extracted in the field. The ground truth PE values were estimated using four approaches: the average elevation method, percent embedment of each aggregate method, the peak method, and the aggregate circumference method. The analysis showed that the correlations between the different PE estimation methods are relatively weak, indicating the various methods provide different information and may relate to different characteristics. The general regression models for PE values estimated using the average elevation method and the mean profile depth (MPD) acquired using laser texture scans and the average least dimension (ALD) yielded the highest R2 value of 0.50. The model showed a consistent decreasing trend between PE and MPD estimated using laser texture scans and side-view images. Moreover, the model matched the expected behavior that PE should reach 100% as MPD reaches 0. Finally, four models were recommended correlating PE estimated using the average elevation and each aggregate methods to the MPD (mm) estimated from laser texture scans and ALD (mm) estimated from side-view images.
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