The present invention relates to multinozzle spraying apparatus for spraying insecticides and the like. A plurality of spray nozzles having differing spray characteristics are provided attached to a multiport turret member. The turret member is rotatably secured to a hollow spindle having a hose connection on the rearward end and a seating surface on the forward end thereof for continuously engaging a seating surface formed in the turret member during the rotation of the turret member. The seating surface of the hollow spindle includes a flow port therein, and ports are provided in the seating surface of the turret member each communicated with a separate spray nozzle and positioned with respect to the spindle flow port so that rotation of the turret member brings the ports therein into selective registration with the spindle flow port. Means for indicating the pressure of fluid passing through the apparatus to a selected spray nozzle are provided as well as means for adding selected quantities of dye or other separate ingredient to the fluid.

On transverse foliations . Equivalence of differentiable mappings and analytic mappings . Quelques applications du théorème de densité de Chebotarev

— (On the Bertrandias–Payan module in a p-extension – Capitulation kernel) For a number field K and a prime number p we denote by BPK the compositum of the cyclic p-extensions of K which are embeddable into a cyclic p-extension of arbitrary large degree. The extension BPK/K is p-ramified and is a finite extension of the compositum K̃ of the Zpextensions of K. The group BPK := Gal(BPK/K̃) is called the Bertrandias–Payan module. We study the transfer map jL/K : BPK −→ BPL (as a capitulation morphism of ideal classes) in a p-extension L/K. In the cyclic case of degree p, we prove that jL/K is injective except if L/K is kummerian, p-ramified, non globally cyclotomic but locally cyclotomic at p (Theorem 3.1). We give an explicit formula (Theorem 5.2) for | BP L | . | BPK |−1 and we show how its entirety depends on the torsion group TL of the Galois group of the maximal abelian p-ramified pro-pextension of L, by using a suitable p-adic logarithm. Ce texte, bien que personnel, résulte d’un travail en lien étroit avec Jean–François Jaulent (Bordeaux) et Thong Nguyen Quang Do (Besançon). L’originalité de la démarche étant que trois techniques sont proposées (une par auteur) pour aborder le même sujet tout en développant des conséquences et applications différentes. Ceci nous a semblé nécessaire dans la mesure où toutes ces techniques sont issues de la théorie du corps de classes, mais ont été Classification mathématique par sujets (2010). — 11R04,11R11, 11R16. Mots clefs. — Class field theory, p-ramification, Bertrandias–Payan module, capitulation of ideal classes, transfer map, Kummer theory. 26 Sur le module de Bertrandias–Payan dans une p-extension – Noyau de capitulation formalisées différemment (tant au plan des notions que des notations) selon les grands axes naturels du corps de classes (classes d’idéaux et d’idèles, corps de classes global p-adique et logarithmique, cohomologie galoisienne et théorie d’Iwasawa). Ainsi le lecteur est-il invité à comparer ces méthodologies qui ont a priori le même potentiel de résultats, mais avec des avantages et inconvénients différents selon le but recherché (allant du plus concret et numérique au plus abstrait et conceptuel), cette multiplicité étant souvent à l’origine de difficultés éditoriales d’antériorité (voir un historique au § 1.2). Remerciements : je remercie mes deux partenaires pour les nombreux échanges constructifs que nous avons eus. 1. Généralités sur le module de Bertrandias–Payan 1.1. Le schéma de la p-ramification abélienne. — En raison de la commodité que confère un livre, on se réfèrera le plus souvent à [Gr1] (2003) et notamment à l’édition Springer 2005, corrigée et augmentée, bien que de nombreuses références soient chaque fois concernées et seraient à citer (elles le sont dans le livre). Soit K un corps de nombres et soit p un nombre premier. On considère le schéma ci-après ([Gr1], § III.2, (c), Fig. 2.2), au sens ordinaire de la notion de classes d’idéaux, dans lequel K̃ est le composé des Zp-extensions de K, HK le p-corps de classes de Hilbert de K, Hpr K la pro-p-extension abélienne p-ramifiée (i.e., non ramifiée en dehors de p) maximale de K. Pour un corps k quelconque de caractéristique 6= p, on désigne par μk le groupe des racines p-ièmes de l’unité de k. On désigne par UK := ⊕ v|p Uv le Zp-module des unités locales p-principales 1 pour K, où chaque Uv est le groupe des unités v-principales du complété Kv de K en v | p, par WK = torZp ( UK ) = ⊕ v|p μKv , et par EK l’adhérence dans UK de l’image diagonale du groupe des unités globales (p-principales) EK de K. On suppose p > 2. On pose WK = WK/iK(μK) ⊆ torZp ( UK/EK ) ⊆ TK := torZp(Gal(H pr K /K)) (inclusions valables sous la conjecture de Leopoldt pour p dans K), où iK est l’injection diagonale :

/pdf/sur-le-module-de-bertrandias-payan-dans-une-p-extension-3e3qwyongc.pdf

Sur le module de Bertrandias–Payan dans une $p$-extension – Noyau de capitulation

For an odd prime p and a number field F containing a primitive p-th root of unity, we describe the Kummer radical A_F of the first layers of all the Z_p-extensions of F in terms of universal norms of p-units along the cyclotomic tower of F . We also study "twisted" radicals related to AF .

On universal norms and the first layers of Z_p-extensions of a number field

For an odd prime $$p$$
 and a number field $$F$$
 containing a primitive $$p$$
 -th root of unity, we describe the Kummer radical $${\mathcal {A}}_F$$
 of the first layers of all the $$\mathbb {Z}_p$$
 -extensions of $$F$$
 in terms of universal norms of $$p$$
 -units along the cyclotomic tower of $$F$$
 . We also study “twisted” radicals related to $${\mathcal {A}}_F$$
 .

On universal norms and the first layers of $\mathbb {Z}_p$-extensions of a number field

We use $\ell$-adic class field theory to take a new view on cyclotomic norms and Leopoldt or Gross generalized conjectures. By the way we recall and complete some classical results. We illustrate the logarithmic approach by various numerical examples and counter-examples obtained with PARI.

On cyclotomic norms and the conjectures of Leopoldt and Gross-Kuz'min

For a number fieldF that contains ζl a l
 th
 root of unity (l is a prime number), we determine thex such thatF
 
$$(\sqrt[\ell ]{x})$$

 can be embedded in a ℤl-extension. We approach the corresponding Kummer radical with the notion of being locally everywhere embedded in a ℤl-extension. An idelic description of Galois group is appropriate especially as we utilize the l-adic group of idele of [15]. The illustration concerns l=3 and biquadratic field ℚ
 
$$(\zeta _3 ,\sqrt d )$$

 . We detail the step of the calculus and fournish numerical tables.

Etage initial d'une ℤ-extension

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Hervé Thomas

Author Tools

Chat about Author

Papers

Etage initial d'une ℤ-extension