scholarly journals Approximation forte pour les variétés avec une action d’un groupe linéaire

2018 ◽  
Vol 154 (4) ◽  
pp. 773-819 ◽  
Author(s):  
Yang Cao
Keyword(s):  
Homogeneous Space ◽  
Algebraic Group ◽  
Number Field ◽  
Strong Approximation ◽  
Linear Algebraic Group ◽  
List Type ◽  
Type Number ◽  
Finite Set ◽  
Open Embedding

Let $G$ be a connected linear algebraic group over a number field $k$. Let $U{\hookrightarrow}X$ be a $G$-equivariant open embedding of a $G$-homogeneous space $U$ with connected stabilizers into a smooth $G$-variety $X$. We prove that $X$ satisfies strong approximation with Brauer–Manin condition off a set $S$ of places of $k$ under either of the following hypotheses:(i)$S$ is the set of archimedean places;(ii)$S$ is a non-empty finite set and $\bar{k}^{\times }=\bar{k}[X]^{\times }$.The proof builds upon the case $X=U$, which has been the object of several works.

scholarly journals Closures of locally divergent orbits of maximal tori and values of homogeneous forms

2020 ◽  
pp. 1-36
Author(s):  
GEORGE TOMANOV
Keyword(s):  
Algebraic Group ◽  
Number Field ◽  
Direct Product ◽  
Finite Union ◽  
The Other ◽  
Parabolic Subgroups ◽  
Maximal Tori ◽  
Closed Orbits ◽  
Finite Set ◽  
Split Torus

Abstract Let ${\mathbf {G}}$ be a semisimple algebraic group over a number field K, $\mathcal {S}$ a finite set of places of K, $K_{\mathcal {S}}$ the direct product of the completions $K_{v}, v \in \mathcal {S}$ , and ${\mathcal O}$ the ring of $\mathcal {S}$ -integers of K. Let $G = {\mathbf {G}}(K_{\mathcal {S}})$ , $\Gamma = {\mathbf {G}}({\mathcal O})$ and $\pi :G \rightarrow G/\Gamma $ the quotient map. We describe the closures of the locally divergent orbits ${T\pi (g)}$ where T is a maximal $K_{\mathcal {S}}$ -split torus in G. If $\# S = 2$ then the closure $\overline {T\pi (g)}$ is a finite union of T-orbits stratified in terms of parabolic subgroups of ${\mathbf {G}} \times {\mathbf {G}}$ and, consequently, $\overline {T\pi (g)}$ is homogeneous (i.e. $\overline {T\pi (g)}= H\pi (g)$ for a subgroup H of G) if and only if ${T\pi (g)}$ is closed. On the other hand, if $\# \mathcal {S}> 2$ and K is not a $\mathrm {CM}$ -field then $\overline {T\pi (g)}$ is homogeneous for ${\mathbf {G}} = \mathbf {SL}_{n}$ and, generally, non-homogeneous but squeezed between closed orbits of two reductive subgroups of equal semisimple K-ranks for ${\mathbf {G}} \neq \mathbf {SL}_{n}$ . As an application, we prove that $\overline {f({\mathcal O}^{n})} = K_{\mathcal {S}}$ for the class of non-rational locally K-decomposable homogeneous forms $f \in K_{\mathcal {S}}[x_1, \ldots , x_{n}]$ .

Maximal Subsets of a given Set having No Triple in Common with a Steiner Triple System on the set

1969 ◽  
Vol 12 (6) ◽  
pp. 777-778 ◽  
Author(s):  
N. Sauer ◽  
J. Schönheim
Keyword(s):  
Triple System ◽  
Steiner Triple System ◽  
List Type ◽  
Type Number ◽  
Recent Letter ◽  
Unordered Pair ◽  
Maximal Size ◽  
Finite Set ◽  
Image Position

Let E be a finite set containing n elements, n ≡ 1, 3 (mod 6), S = S(E) a Steiner triple system on E, i.e. each unordered pair of elements of E is a subset of exactly one triple in S. Let T be a subset of E such that none of the triples of elements of T is a member of S. Erdös has asked (in a recent letter to the authors) for the maximal size of such a set T. Denote max |T| for fixed n and S by f(n, S). We prove in this note the following result:(i)(ii)for every n ≡ 1, 3 (mod 6) there exists a Steiner triple system S0 such that equality holds in i.

scholarly journals ON THE DISTRIBUTION OF TORSION POINTS MODULO PRIMES

2012 ◽  
Vol 86 (2) ◽  
pp. 339-347 ◽  
Author(s):  
YEN-MEI J. CHEN ◽  
YEN-LIANG KUAN
Keyword(s):  
Positive Integer ◽  
Algebraic Group ◽  
Number Field ◽  
Divisor Function ◽  
Good Reduction ◽  
Torsion Points ◽  
Average Value ◽  
Finite Set ◽  
Dimension One

AbstractLet $\Bbb A$ be a commutative algebraic group defined over a number field K. For a prime ℘ in K where $\Bbb A$ has good reduction, let N℘,n be the number of n-torsion points of the reduction of $\Bbb A$ modulo ℘ where n is a positive integer. When $\Bbb A$ is of dimension one and n is relatively prime to a fixed finite set of primes depending on $\Bbb A_{/K}$, we determine the average values of N℘,n as the prime ℘ varies. This average value as a function of n always agrees with a divisor function.

Solar Corona Investigation by the Coronal Line Photometer at Lomnický Peak

1994 ◽  
Vol 144 ◽  
pp. 431-434
Author(s):  
M. Minarovjech ◽  
M. Rybanský
Keyword(s):  
Solar Corona ◽  
Time Resolution ◽  
Active Regions ◽  
High Time ◽  
High Time Resolution ◽  
List Type ◽  
Type Number ◽  
Coronal Line ◽  
Global Cycle

AbstractThis paper deals with a possibility to use the ground-based method of observation in order to solve basic problems connected with the solar corona research. Namely:1.heating of the solar corona2.course of the global cycle in the corona3.rotation of the solar corona and development of active regions.There is stressed a possibility of high-time resolution of the coronal line photometer at Lomnický Peak coronal station, and use of the latter to obtain crucial observations.

The LDE-Type Flare Occurrence (1969-1993)

1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Sunspot Cycle ◽  
List Type ◽  
Type Number ◽  
Solar Cycles ◽  
Type Iv ◽  
Long Duration ◽  
Cycle Maximum ◽  
Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

Discussion following the presentation by F. Deubner

1977 ◽  
Vol 36 ◽  
pp. 69-74
Keyword(s):  
List Type ◽  
The Sun ◽  
Type Number ◽  
Harmonic Motion ◽  
Locally Excited ◽  
Long Period ◽  
Coherent Wave ◽  
Short Period ◽  
Global Modes

The discussion was separated into 3 different topics according to the separation made by the reviewer between the different periods of waves observed in the sun :1) global modes (long period oscillations) with predominantly radial harmonic motion.2) modes with large coherent - wave systems but not necessarily global excitation (300 s oscillation).3) locally excited - short period waves.

Prominences and Solar Activity

1979 ◽  
Vol 44 ◽  
pp. 357-372
Author(s):  
Z. Švestka
Keyword(s):  
Solar Activity ◽  
Solar Cycle ◽  
List Type ◽  
Type Number ◽  
Flare Loops ◽  
Filament Activation

The following subjects were discussed:(1)Filament activation(2)Post-flare loops.(3)Surges and sprays.(4)Coronal transients.(5)Disk vs. limb observations.(6)Solar cycle variations of prominence occurrence.(7)Active prominences patrol service.Of all these items, (1) and (2) were discussed in most detail and we also pay most attention to them in this report. Items (3) and (4) did not bring anything new when compared with the earlier invited presentations given by RUST and ZIRIN and therefore, we omit them.

A New System For Optomanual Semiautomatic Quantitative Image Analysis

1977 ◽  
Vol 35 ◽  
pp. 210-211
Author(s):  
H.P. Rohr
Keyword(s):  
Image Analysis ◽  
Volume Density ◽  
List Type ◽  
Distribution Analysis ◽  
Type Number ◽  
Point Counting ◽  
Human Eye ◽  
Quantitative Image ◽  
Point Density ◽  
Electronic Counting

Today, in image analysis the broadest possible rationalization and economization have become desirable. Basically, there are two approaches for image analysis: The image analysis through the so-called scanning methods which are usually performed without the human eye and the systems of optical semiautomatic analysis completely relying on the human eye.The new MOP AM 01 opto-manual system (fig.) represents one of the very promising approaches in this field. The instrument consists of an electronic counting and storing unit, which incorporates a microprocessor and a keyboard for choice of measuring parameters, well designed for easy use.Using the MOP AM 01 there are three possibilities of image analysis:the manual point counting,the opto-manual point counting andthe measurement of absolute areas and/or length (size distribution analysis included).To determine a point density for the calculation of the corresponding volume density the intercepts lying within the structure are scanned with the light pen.

Hydration Chamber for Jeolco 200 Kv Microscope

1970 ◽  
Vol 28 ◽  
pp. 542-543
Author(s):  
V. R. Matricardi ◽  
G. G. Hausner ◽  
D. F. Parsons
Keyword(s):  
Electron Microscope ◽  
Water Vapor ◽  
Vapor Pressure ◽  
Pressure Gradient ◽  
Room Temperature ◽  
List Type ◽  
Type Number ◽  
Equilibrium Vapor Pressure

In order to observe room temperature hydrated specimens in an electron microscope, the following conditions should be satisfied: The specimen should be surrounded by water vapor as close as possible to the equilibrium vapor pressure corresponding to the temperature of the specimen.The specimen grid should be inserted, focused and photo graphed in the shortest possible time in order to minimize dehydration.The full area of the specimen grid should be visible in order to minimize the number of changes of specimen required.There should be no pressure gradient across the grid so that specimens can be straddled across holes.Leakage of water vapor to the column should be minimized.

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