Main Page

(Difference between revisions)
Jump to: navigation, search
m
m (Undo revision 11704 by Philipp Kuehl (talk))
Line 1: Line 1:
−
{{Stub}}
+
__NOTOC__<nonumbers/>
−
#LyX 2.1 created this file. For more info see http://www.lyx.org/
+
{| style="float:right; margin-left:20px; max-width:20em; border:solid thin black; padding:.5ex;"
−
\lyxformat 474
+
|-
−
\begin_document
+
|<!-- The 10 --> Recent changes:
−
\begin_header
+
<DPL>
−
\textclass article
+
namespace=Main
−
\use_default_options true
+
nottitlematch=Main_Page|Sandbox|Links
−
\maintain_unincluded_children false
+
ordermethod=lastedit
−
\language english
+
order=descending
−
\language_package default
+
minoredits=exclude
−
\inputencoding auto
+
count=10
−
\fontencoding global
+
</DPL>
−
\font_roman default
+
|-
−
\font_sans default
+
|}
−
\font_typewriter default
+
== Welcome to the Manifold Atlas Project:<br>- a scientific Wiki and<br>- an on-line journal, the [http://www.boma.mpim-bonn.mpg.de Bulletin of the Manifold Atlas] ==
−
\font_math auto
+
The [[Manifold Atlas:About|Manifold Atlas]] has six chapters:
−
\font_default_family default
+
−
\use_non_tex_fonts false
+
−
\font_sc false
+
−
\font_osf false
+
−
\font_sf_scale 100
+
−
\font_tt_scale 100
+
−
\graphics default
+
−
\default_output_format default
+
−
\output_sync 0
+
−
\bibtex_command default
+
−
\index_command default
+
−
\paperfontsize default
+
−
\use_hyperref false
+
−
\papersize default
+
−
\use_geometry false
+
−
\use_package amsmath 1
+
−
\use_package amssymb 1
+
−
\use_package cancel 1
+
−
\use_package esint 1
+
−
\use_package mathdots 1
+
−
\use_package mathtools 1
+
−
\use_package mhchem 1
+
−
\use_package stackrel 1
+
−
\use_package stmaryrd 1
+
−
\use_package undertilde 1
+
−
\cite_engine basic
+
−
\cite_engine_type default
+
−
\biblio_style plain
+
−
\use_bibtopic false
+
−
\use_indices false
+
−
\paperorientation portrait
+
−
\suppress_date false
+
−
\justification true
+
−
\use_refstyle 1
+
−
\index Index
+
−
\shortcut idx
+
−
\color #008000
+
−
\end_index
+
−
\secnumdepth 3
+
−
\tocdepth 3
+
−
\paragraph_separation indent
+
−
\paragraph_indentation default
+
−
\quotes_language english
+
−
\papercolumns 1
+
−
\papersides 1
+
−
\paperpagestyle default
+
−
\tracking_changes false
+
−
\output_changes false
+
−
\html_math_output 0
+
−
\html_css_as_file 0
+
−
\html_be_strict false
+
−
\end_header
+
−
+
−
\begin_body
+
* '''[[:Category:Manifolds|Manifolds]]:''' with pages about '''constructions''' and '''examples''' of manifolds as well as their '''invariants''' and '''properties'''.
−
+
* '''[[:Category:Theory|Theory]]:''' with pages summarising useful '''general facts''' and '''theorems'''.
+
* '''[[:Category:Definitions|Definitions]]:''' with pages giving succinct and precise '''definitions''' of important concepts in the theory of manifolds.
+
* '''[[:Category:Problems|Problems]]:''' with pages listing '''persistent and deep open problems''', their status and their history.
+
* '''[[:Category:History|History]]:''' with pages about the '''history''' of the study of manifolds.
+
<!--* '''[[:Category:Questions|Questions]]:''' with pages containing '''questions''' and '''answers''' about any aspect of the study of manifolds.-->
+
* '''[[:Category:Exercises|Exercises]]:''' with pages containing exercises about the study of manifolds.
+
<!-- * '''[[:Category:Philosophy|Philosophy]]:''' with pages on the philosophy of mathematics as it relates to manifolds. -->
−
\begin_layout Standard
+
You will find the pages listed alphabetically by clicking each chapter.
−
The state determinted by two temperatures (refering
+
−
\begin_inset Formula $T_{0}$
+
−
\end_inset
+
−
+
−
as constant heat sink) :
+
[[Manifold Atlas:Page evolution|Atlas pages]] offer a workspace for collaboratively organising and creating knowledge about manifolds.
−
\begin_inset Formula
+
−
$$
+
−
\begin{cases}
+
−
C\frac{dT}{dt}+K\left(T-T_{0}\right)=K_{h}\left(T_{h}-T\right) & \,
+
−
C_{h}\frac{dT_{h}}{dt}=P_{h}-K_{h}\left(T_{h}-T\right) & \,
+
[[Manifold Atlas:Editorial Policy#Editorial criteria|Mature pages]] are [[Manifold Atlas: Editorial Policy|refereed]] by the [[Manifold Atlas:Editorial Board|editorial board]]: if approved they are published in the [http://www.boma.mpim-bonn.mpg.de BoMA].
−
\end{cases}
+
−
$$
+
−
+
−
\end_inset
+
== General information ==
−
+
For more information please follow these links: [[Manifold Atlas:About|About the Atlas]] and the [[Manifold Atlas:Editorial Board|Editorial Board]].
−
Matrix representation:
+
For information about how to contribute please follows these links: [[Manifold Atlas:Writing in the Atlas|Writing in the Atlas]] and [[Manifold Atlas:Community Portal|Community Portal]].
−
\begin_inset Formula
+
−
$$
+
−
$$
+
−
+
−
\end_inset
+
== Using the Manifold Atlas ==
−
+
The page [[Manifold Atlas:User orientation|User orientation]] gives information for registered users.
+
The page [[Manifold Atlas:Author orientation|Author orientation]] gives information about writing in the Atlas.
+
* [[Manifold Atlas:User orientation#Writing_on_discussion_pages|Join the discussion]] about a page.
+
* [[Manifold Atlas:Writing groups#Open-editing pages|Add to or edit ]] existing open-editing articles.
+
* [[Manifold Atlas:Create_a_new open-editing page|Create a new open-editing page]].
+
* [[Manifold Atlas:Create a new restricted-editing page|Create a new restricted-editing page]].
+
<!--
+
The '''[[Manifold Atlas:Community Portal|community portal]]''' is a general discussion forum.
−
\end_layout
+
You can either '''[[Manifold Atlas:Create_a_new page|create a new page]]''' and '''discuss''' or '''modify''' all articles by clicking on <b>'discussion'</b> or <b>'edit'</b> at the top of each page. Don't forget to [[Special:UserLogin|log in]]!
−
+
−
\begin_layout Standard
+
The [[Manifold Atlas:Community Portal|Community Portal]] is a general discussion forum.
−
Eigenvalues of
+
−
\begin_inset Formula $M$
+
−
\end_inset
+
−
+
−
:
+
Read the [[Manifold Atlas:Author information|author information]] for important information about writing articles in the Manifold Atlas.-->
−
\begin_inset Formula
+
−
$$\begin{array}{rcl}
+
−
\lambda & = & -\frac{CK_{h}+C_{h}K+C_{h}K_{h}\pm\sqrt{C^{2}K_{h}^{2}-2CC_{h}KK_{h}+2CC_{h}K_{h}^{2}+C_{h}^{2}K^{2}+2C_{h}^{2}KK_{h}+C_{h}^{2}K_{h}^{2}}}{2CC_{h}}
+
−
\lambda & = & -\frac{1}{2}\left[\frac{K_{h}}{C_{h}}+\frac{K}{C}+\frac{K_{h}}{C}\pm\sqrt{\frac{K_{h}^{2}}{C_{h}^{2}}-2\frac{KK_{h}}{CC_{h}}+2\frac{K_{h}^{2}}{CC_{h}}+\frac{K^{2}}{C^{2}}+2\frac{KK_{h}}{C^{2}}+\frac{K_{h}^{2}}{C^{2}}}\right]
+
== Registering for the Manifold Atlas==
+
* Please '''[[Manifold Atlas:Registration|register]]''' with a verified email address in order to write and discuss in the Manifold Atlas.
−
\, & \, & \mbox{denoting}\;\begin{cases}
+
* To sign up for email up-dates about changes at the Atlas visit the [[Manifold Atlas:The Atlas Observer|Atlas Observer]].
−
\gamma & =\frac{K}{C}
+
−
\gamma_{m} & =\frac{K_{h}}{C}
+
−
\gamma_{h} & =\frac{K_{h}}{C_{h}}
+
−
\end{cases}
+
−
\lambda & = & -\frac{1}{2}\left[\gamma_{h}+\gamma+\gamma_{m}\pm\sqrt{\gamma_{h}^{2}-2\gamma\gamma_{h}+2\gamma_{m}\gamma_{h}+\gamma^{2}+2\gamma\gamma_{m}+\gamma_{m}^{2}}\right]
+
−
+
−
\lambda & = & -\frac{1}{2}\left[\gamma+\gamma_{m}+\gamma_{h}\pm\sqrt{\left(\gamma+\gamma_{m}+\gamma_{h}\right)^{2}-4\gamma\gamma_{h}}\right]
+
−
+
−
\, & \, & \mbox{denotinng}\begin{cases}
+
−
\gamma+\gamma_{m}+\gamma_{h}=\gamma_{+} & \,
+
−
+
−
\gamma\gamma_{h}=\gamma_{*}^{2} & \,
+
−
\end{cases}
+
−
\, & \, & \gamma_{+}\gg\gamma_{*}
+
−
\lambda & = & -\frac{1}{2}\left[\gamma_{+}\pm\sqrt{\gamma_{+}^{2}-4\gamma_{*}^{2}}\right]
+
−
+
−
\lambda & \approx & -\frac{1}{2}\left[\gamma_{+}\pm\left(\gamma_{+}-2\frac{\gamma_{*}^{2}}{\gamma_{+}}\right)\right]
+
−
+
−
\, & \, & \begin{cases}
+
−
\lambda_{+} & =-\gamma_{+}
+
−
\lambda_{-} & =-\frac{\gamma_{*}^{2}}{\gamma_{+}}=-\frac{\gamma\gamma_{h}}{\gamma+\gamma_{m}+\gamma_{h}}=-\frac{\gamma\gamma_{h}}{\gamma+\gamma_{m}+\gamma_{h}}
+
−
\end{cases}
+
−
\end{array}$$
+
−
+
−
+
−
\end_inset
+
−
+
−
+
−
+
−
\end_layout
+
−
+
−
+
−
\end_body
+
−
\end_document
+
−
+
−
</wikitex>
+
−
== References ==
+
−
{{#RefList:}}
+
−
[[Category:]]
+

Revision as of 15:50, 29 June 2015

Recent changes:

Welcome to the Manifold Atlas Project:
- a scientific Wiki and
- an on-line journal, the Bulletin of the Manifold Atlas

The Manifold Atlas has six chapters:

  • Manifolds: with pages about constructions and examples of manifolds as well as their invariants and properties.
  • Theory: with pages summarising useful general facts and theorems.
  • Definitions: with pages giving succinct and precise definitions of important concepts in the theory of manifolds.
  • Problems: with pages listing persistent and deep open problems, their status and their history.
  • History: with pages about the history of the study of manifolds.
  • Exercises: with pages containing exercises about the study of manifolds.

You will find the pages listed alphabetically by clicking each chapter.

Atlas pages offer a workspace for collaboratively organising and creating knowledge about manifolds.

Mature pages are refereed by the editorial board: if approved they are published in the BoMA.

General information

For more information please follow these links: About the Atlas and the Editorial Board.

For information about how to contribute please follows these links: Writing in the Atlas and Community Portal.

Using the Manifold Atlas

The page User orientation gives information for registered users.

The page Author orientation gives information about writing in the Atlas.

Registering for the Manifold Atlas

  • Please register with a verified email address in order to write and discuss in the Manifold Atlas.
  • To sign up for email up-dates about changes at the Atlas visit the Atlas Observer.
Retrieved from "http://www.map.mpim-bonn.mpg.de/index.php?title=Main_Page&oldid=11705"
Personal tools
Namespaces
Variants
Actions
Navigation
Interaction
Toolbox