OpenLLM-France/wikimedia huggingface dataset:
# Canadian Criminal Law/Offences/Disobeying a Court Order
## Legislation

   127. (1) Every one who, without lawful excuse, disobeys a lawful order made by a court of justice or by a person or body of persons authorized by any Act to make or give the order, other than an order for the payment of money, is, unless a punishment or other mode of proceeding is expressly provided by law, guilty of
       (a) an indictable offence and liable to imprisonment for a term not exceeding two years; ...
   – CCC

## Prove of the Offence

* identity of accused
* date and time of incident
* jurisdiction (incl. region and province)
* the accused disobeyed a lawful order of the Court;
* the accused was without a lawful excuse;
* the accused intended to disobey the order of the Court; and
* what the order required the accused to do.
* ↑ R v Solar, 2012 SKQB 113 at 32
# Analytic Number Theory
## Table of Contents

* Useful summation formulas
* The Chebychev ψ and ϑ functions
* Arithmetic functions
* Characters and Dirichlet characters
* Dirichlet series
* Formulas for number-theoretic functions
* Partial fraction decomposition
* Tools from complex analysis

## Read More

* Discrete Mathematics Wikibook: Chapter on Analytic Number Theory.
# Analytic Number Theory/Characters and Dirichlet characters
## Definitions, basic properties

Definition 4.1
Let $G$ be a finite group. A character of G is a function $f:G\to \mathbb {C}$ such that
* $\forall \sigma ,\tau \in G:f(\sigma \tau )=f(\sigma )f(\tau )$ and
* $\exists \rho \in G:f(\rho )\neq 0$.
Lemma 4.2:
Let $G$ be a finite group and let $f:G\to \mathbb {C}$ be a character. Then
    $\forall \sigma \in G:|f(\sigma )|=1$.
In particular, $\forall \sigma \in G:f(\sigma )\neq 0$.
Proof:
Since $G$ is finite, each $\sigma \in G$ has finite order $n:=\mathrm {ord} (\sigma )$. Furthermore, let $\rho \in G$ such that $f(\rho )\neq 0$; then $f(\rho )=f(\sigma )f(\sigma ^{-1}\rho )$ and thus $f(\sigma )\neq 0$. Hence, we are allowed to cancel and
    $|f(\sigma )|=|f(\sigma ^{n+1})|=|f(\sigma )|^{n+1}\Rightarrow |f(\sigma )|=1$.$\Box$
Lemma 4.3:
Let $G$ be a finite group and let $f,g:G\to \mathbb {C}$ be characters. Then the function $h:G\to \mathbb {C} ,h(\tau ):=f(\tau )\cdot g(\tau )$ is also a character.
Proof:
    $h(\sigma \tau )=f(\sigma \tau )g(\sigma \tau )=f(\sigma )g(\sigma )f(\tau )g(\tau )=h(\sigma )h(\tau )\neq 0$,
since $\mathbb {C}$ is a field and thus free of zero divisors.$\Box$
Lemma 4.4:
Let $G$ be a finite group and let $f:G\to \mathbb {C}$ be a character. Then the function $g:G\to \mathbb {C} ,g(\tau ):={\frac {1}{f(\tau )}}$ is also a character.
Proof: Trivial, since $\forall \tau \in G:f(\tau )\neq 0$ as shown by the previous lemma.$\Box$
The previous three lemmas (or only the first, together with a few lemmas from elementary group theory) justify the following definition.
Definition 4.5
Let $G$ be a finite group. Then the group
    $\{f:G\to \mathbb {C} |f{\text{ is a character }}\}=\mathrm {Hom} (G,\mathbb {C} ^{\times })$
is called the character group of $G$.

## Required algebra

We need the following result from group theory:
Lemma 4.6
Let $G$ be a finite Abelian group, let $H\leq G$ be a subgroup of order $n\in \mathbb {N}$, and let $\tau \in G\setminus H$ such that $k\in \mathbb {N}$ is the smallest number such that $\tau ^{k}\in H$. Then the group
    $N:=\{\tau ^{n}\sigma |\sigma \in H\}$
is a subgroup of $G$ containing $H$ of order $k\cdot n$.
Proof:
Since $G$ is the disjoint union of the cosets of $H$, $N$ is the disjoint union $\bigcup _{j=0}^{n-1}\tau ^{j}H$, as $\rho H=H\Leftrightarrow \rho \in H$ and $\tau ^{l}H=\tau ^{m}H\Leftrightarrow \tau ^{l-m}\in H\Leftrightarrow k|(l-m)$. Hence, the cardinality of $N$ equals $k\cdot n$.
Furthermore, if $\tau ^{l}\sigma ,\tau ^{m}\rho \in N$, then $\tau ^{l}\sigma (\tau ^{m}\rho )^{-1}=\tau ^{l-m}\sigma \rho ^{-1}\in N$, and hence $N$ is a subgroup.$\Box$
# Analytic Number Theory/Dirichlet series

For the remainder of this book, we shall use Riemann's convention of denoting complex numbers:
$s=\sigma +it$

## Definition

Definition 5.1:
Let $f$ be an arithmetic function. Then the Dirichlet series associated to $f$ is the series
    $\sum _{n=1}^{\infty }{\frac {f(n)}{n^{s}}}$,
where $s$ ranges over the complex numbers.

## Convergence considerations

Theorem 5.2 (abscissa of absolute convergence):
Let $f$ be an arithmetic function such that the series of absolute values associated to the Dirichlet series associated to $f$
    $\sum _{n=1}^{\infty }\left|{\frac {f(n)}{n^{s}}}\right|$
neither diverges at all $s\in \mathbb {C}$ nor converges for all $s\in \mathbb {C}$. Then there exists $\sigma _{a}\in \mathbb {R}$, called the abscissa of absolute convergence, such that the Dirichlet series associated to $f$ converges absolutely for all $\sigma +it$, $\sigma >\sigma _{a}$ and it's associated series of absolute values diverges for all $\sigma +it$, $\sigma <\sigma _{a}$.
Proof:
Denote by $S$ the set of all real numbers $\sigma$ such that
    $\sum _{n=1}^{\infty }\left|{\frac {f(n)}{n^{s}}}\right|$
diverges. Due to the assumption, this set is neither empty nor equal to $\mathbb {C}$. Further, if $\sigma _{0}+it_{0}\notin S$, then for all $\sigma >\sigma _{0}$ and all $t$ $\sigma +it\notin S$, since
    $\left|{\frac {f(n)}{n^{s_{0}}}}\right|={\frac {|f(n)|}{n^{\sigma _{0}}}}\geq {\frac {|f(n)|}{n^{\sigma }}}=\left|{\frac {f(n)}{n^{s}}}\right|$
and due to the comparison test. It follows that $S$ has a supremum. Let $\sigma _{a}$ be that supremum. By definition, for $\sigma >\sigma _{a}$ we have convergence, and if we had convergence for $\sigma <\sigma _{a}$ we would have found a lower upper bound due to the above argument, contradicting the definition of $\sigma _{a}$.$\Box$
Theorem 5.3 (abscissa of conditional convergence):

## Formulas

Theorem 8.4 (Euler product):
Let $f$ be a strongly multiplicative function, and let $s\in \mathbb {C}$ such that the corresponding Dirichlet series converges absolutely. Then for that series we have the formula
    $\sum _{n=1}^{\infty }{\frac {f(n)}{n^{s}}}=\prod _{p{\text{ prime}}}{\frac {1}{1-{\frac {f(p)}{p^{s}}}}}$.
Proof:
This follows directly from theorem 2.11 and the fact that $f$ strongly multiplicative $\Rightarrow$ ${\frac {f(n)}{n^{s}}}$ strongly multiplicative.$\Box$
# Celestia/3D Models
## Introduction

In addition to its internally defined spherical objects, Celestia can use 3D models to display bodies with complicated shapes.

## Usage in Celestia

A 3D model will be displayed when Celestia encounters the Mesh directive in one of its catalog files. For example,
If a Texture declaration is included in the entry for the same object, that texture image will replace all diffuse material texture images specified in the model file.

## Model Types

Celestia can display three different types of 3D model files.

### 3DS

Originally developed by the authors of 3D Studio Max, the .3DS binary file format is used by many different software packages. Model files usually can be created in this format by choosing it in the "Export" menu of your favorite 3D modeling program.

### CMS

CMS Model Files are unique to Celestia. They use a simple textual format. The CMS format is deprecated.

### CMOD

CMOD Model Files are unique to Celestia. They have both binary and textual forms. The format was designed for efficient use by OpenGL code. When drawing a CMOD model, Celestia's framerate is about 1.5-2x as fast as when drawing the equivalent 3DS model.
A 3DS to CMOD conversion program is available. CMOD export scripts are available for Anim8or and Blender.

## Modeling Programs

* Blender 3D - this is an open-source, free software that is extremely powerful. However, it is quite intimidating to use for beginners. Blender 3D: Noob to Pro is a Wikibook that has good guides to help you, if needed. Note: as of version 2.80, Blender no longer supports exporting 3DS models.
* Anim8or - free modelling software. This is only available for Windows, however.

## Limitations

* 3DS models have a limit of 65536 vertices and polygons, making extremely high-resolution models impossible. This limitation, however, does not exist for CMOD models.
* Models in Celestia do not (yet?) cast shadows on themselves or on other objects.
* Translucent model surfaces are not properly depth sorted. Some are drawn correctly, but some are not.
* DSC Nebula Meshes are not depth sorted at all. They always are drawn in the order that Celestia reads them.
# Celestia/Acknowledgements

Celestia was created by Chris Laurel.
The Celestia AUTHORS file lists the following people:
* Chris Laurel <claurel@gmail.com>
* Clint Weisbrod <cweisbrod@cogeco.ca>
* Fridger Schrempp <t00fri@mail.desy.de>
* Bob Ippolito <bob@redivi.com>
* Christophe Teyssier <chris@teyssier.org>
* Hank Ramsey <hramsey@users.sourceforge.net>
* Grant Hutchison <grant.celestia@xemaps.com>
* Pat Suwalski <pat@suwalski.net>
* Toti
* Da Woon Jung <dirkpitt2050@users.sf.net>
* Vincent Giangiulio <vince.gian@free.fr>
* Andrew Tribick
* Dmitry Brant
* Hleb Valoshka
* Levin Li
* Łukasz Buczyński
Other contributors to the Celestia software distribution are cited in the README file.
Authors who have generously contributed material from their previously written documentation to this wikibook include:
* Chris Laurel
* Selden Ball
Add yourself here if appropriate
People who have made original contributions to this wikibook include:
* Chris Laurel
* Selden Ball
* John Van Vliet
* LukeCEL
* SevenSpheres
add yourself here if appropriate
Many other people have also made valuable contributions to the Celestia community in various ways. Those that deserve special mention here are:
And if we've inadvertently left out anyone you think should be mentioned, please add them!
# Celestia/1.7.0 Changes

List of changes in Celestia 1.7.0 (work in progress).

## Rendering

* Blackbody star colors are default
* Fading orbits (can be toggled)
* On ringed planets, the side of the rings facing away from the star is in shadow
* LunarLambert makes objects brighter - apparently this is correct?
* Sprite nebulae fade at a distance
* Visibility of different object types (planets, moons, etc), as well as rings, can be toggled individually
* Stars and planets can be rendered out to a distance of 1 billion light-years (increased from 10 million light-years)

## Info display

* Dwarf planets and minor moons are shown in the right-click menu of their parent body (they aren't in 1.6.x)
* Temperatures are calculated for circumbinary planets

## Data

* Updates to most data files, models, and textures
* Default temperatures and bolometric corrections for main-sequence stars updated

## Audio

* Audio support has been added - thread

## New parameters
### STC files

* Temperature - in degrees Kelvin
* BoloCorrection - Bolometric correction
* Extinction - the number of magnitudes by which the star's light is extinguished

#### Spectral classes

* Y - for Y-class brown dwarfs
* WO - for Wolf–Rayet stars of the oxygen sequence

### SSC files

* Mass - in Earth units
* New albedo parameters. Described in this issue, although the actual implementation isn't exactly the same as what was suggested.
** BondAlbedo - Bond albedo
** GeomAlbedo - Geometric albedo; replaces Albedo
** Reflectivity - the visible average global reflectivity
* TempDiscrepancy - this is added to the calculated equilibrium temperature
* Temperature - in degrees Kelvin; overrides TempDiscrepancy
* TailColor - for comets

### Units

For many parameters, units can be specified in angle brackets, like this: Radius<rE> 1.1

#### Length

For e.g. Distance, Radius, SemiMajorAxis
* <m> - meters
* <km> - kilometers
* <rE> - Earth radii
* <rJ> - Jupiter radii
* <rS> - solar radii
* <AU> - astronomical units
* <ly> - light-years
* <pc> - parsecs
* <kpc> - kiloparsecs
* <Mpc> - megaparsecs

#### Time

For e.g. Period
* 
 - seconds
* <min> - minutes
* <h> - hours
* <d> - days
* <y> - years

#### Angle

For e.g. RA, Dec, ArgOfPericenter
* <mas> - milliarcseconds
* <arcsec> - arcseconds
* <arcmin> - arcminutes
* <deg> - degrees
* <hRA> - hours of Right Ascension
* <rad> - radians

#### Mass

For Mass
* <kg> - kilograms
* <mE> - Earth masses
* <mJ> - Jupiter masses
Solar mass units weren't added, despite my suggestion to do so.

### Locations

New location types can be found here.

## Scripting

See CEL/CELX Scripting Documentation on celestia.mobi for new CEL/CELX commands.

## Notes

* ↑ SevenSpheres
# Celestia/3D Models/CMS File
## CMS File Reference

The CMS model format is deprecated. This means that its usage is discouraged and that it is likely to go away in a future version of Celestia.

### What's a CMS file?

"Celestia? Model? Simple?" files define simple shapes by deforming a sphere. Although deprecated, they are still used for a few generic objects such as asteroids, minor moons and the like.
They lie in the "models" directory of the Celestia root, or in an add-on's root subdirectory (itself in Celestia's "extra" directory).
They are plain text files, and can thus be modified with your favourite text editor.
The pound sign begins a comment: whatever lies after this sign up to the next carriage return is ignored by Celestia.

### "SphereDisplacementMesh" { ... }

All of the cms stuff is within this block. The parameters appearing within the accolades are:

#### "Size [ x y z ]"

When a model is placed in a circular orbit around a parent body without rotation settings (so it is tide-locked) and with a mean longitude of 0,
* x is the radial axis (running from the parent body to the model and through it: near-far)
* y is the polar axis (running perpendicular to the orbital plane: north-south)
* z is the orbital axis (running parallel to the orbit: forward-backward)
It defaults to [1.0 1.0 1.0].

#### "NoiseOffset [ a b c ]"

This is some kind of implementation of Perlin noise, and NoiseOffset (probably) moves the origin of the noise.
It defaults to [10 10 10].

#### "FeatureHeight f"

This controls the height of the bumps. Small numbers like 0.2 define a body that is roughly spherical with low hills, while larger numbers like 1.0 define a body with large hills.
It defaults to 0.0.

#### "Octaves i"

This defines the bumpiness of the model. Small values like 1 define a body with a fairly regular distortion, whereas large values like 9 define a very bumpy body. A value of zero gives a spherical body.
It defaults to 1.

#### "Slices i"

The Slices parameter controls the number of longitude lines. Together with Rings, this defines how much detail there is in the mesh. The default value of 20 defines a blocky mesh, while 200 defines a much smoother mesh that can take several seconds to render when displayed for the first time.
Setting Slices to a low value and Rings to a high value gives a mesh that is shaped like a peeled orange.

#### "Rings i"

The Rings parameters controls the number of latitude lines. Together with Slices, this defines how much detail there is in the mesh. It also defaults to 20.
Setting Slices to a high value and Rings to a low value gives a mesh that is shaped like a pile of doughnuts of varying thicknesses stacked on each other.
# Celestia/About this guide
## About This Guide

This Guide to Celestia is intended to be a comprehensive source of information for students, educators, and other users of Celestia. It will include instructions for obtaining, installing, using, customizing, and troubleshooting the Celestia software, as well as explanations of concepts and techniques from astronomy and computer graphics as needed to fully explore and understand Celestia and its universe. It is intended to address the needs of novice, casual, and advanced users.
The Guide to Celestia is just beginning development and is very far from complete. You can help by adding useful content. Members of the Celestia community are encouraged to be bold in editing this WikiBook to provide the additions and corrections needed to make it useful for themselves and others. Please share your knowledge here.
Go to Introductory Text
# Celestia/Bookmarks
## Introduction

A Cel: URL is a bookmark that saves the time, location, rendering options and other settings of a specific Celestia event or place. These URLs can be exported and published as regular HTML, so that any Celestia user can share a Celestia scene with any other.
The Windows version of Celestia includes a Bookmark menu. Those bookmarks are not the same as Cel: URLs.
To record a Cel: URL to your computer's "clipboard", type a Ctrl-C, or the usual "copy selected region" keyboard shortcut. On a Windows system, you can type a Ctrl-Insert.
To paste a Cel: URL into a document, type a Ctrl-V, or the usual "paste clipboard".

## Potential incompatibility warning

Unfortunately URLs recorded by one version of Celestia often are not compatible with other versions. The origin of Celestia's coordinate system changed in V1.5. As a result, URLs recorded by previous versions of Celestia place the viewpoint hundreds of AU from the intended viewpoint. Similarly, the rotation of the Earth was greatly improved in Celestia v1.6. As a result, URLs recorded by V1.5 for viewpoints on the Earth's surface will place the viewpoint tens of kilometers from the intended viewpoint. Also, although URLs recorded by previous versions of Celestia can be read by V1.6, the URLs generated by V1.6 cannot be used by previous versions of Celestia.

## Fix for Linux if clicking on a Cel: URL does not work

Depending on the specifics of your installation, Celestia might not have been registered to handle the Cel: URLs. If that is the case, you can remedy as follows (this should work on any system compliant with the XDG specifications).
* Enter xdg-mime default celestia.desktop x-scheme-handler/cel in a terminal. (This registers Celestia as the program that handles cel: links.)
* Edit celestia.desktop, replacing the line Exec=celestia-gnome with Exec=celestia-gnome %u, so that the system knows that it has to pass the URL argument to Celestia, when launching it. The desktop file is usually found in /usr/share/applications/ and if you don't want to edit files with root, you can instead copy it to $HOME/.local/share/applications/ and edit it there (or more generally copy it from $XDG_DATA_DIRS/applications to $XDG_DATA_HOME/applications/). Optionally, you can also add MimeType=x-scheme-handler/cel; to the desktop file. (See the XDG desktop entry spec.)
# Celestia/Bugs and Feature Requests
## Bugs

If you think you've found something wrong in Celestia, please report it using Issues on GitHub. Please review the known bugs to make sure your report is not a duplication. When reporting a problem, be sure to include a description of your system, especially the operating system, graphics card and OpenGL driver you're using.

## Requests for New Features

If you think of features which would be useful to Celestia users, please add them to the Requests on GitHub, not here. Please check already made requests before reporting a new.
Old lists of suggested new features and Wish List items are included in this WikiBook, but they're very unlikely to be implemented if they aren't on the GitHub list. If you are interested in any of the features listed on those pages, you must take the responsibility of making sure they're requested on GitHub.
# Chemical Information Sources/SIRCh/Cheminformatics

* What is Cheminformatics?
** Introductory Resources
** Cheminformatics/Chemoinformatics Glossary and taxonomy at Cambridge Healthtech Institute (CHI)
* Academic Programs
* Professional Societies and Groups
* Companies and Independent Institutions
* Publications and Conferences
* Data Standards and Standards Groups
* Molecular Visualization Tools and Sites
* Other Guides to Cheminformatics Resources
** ChemDB.com
** PharmTao's Cheminformatics Portal
** Cheminformatics.org
** Cambridge Healthtech Institute
** High-Throughput-Screening Research
# Chemical Information Sources/SIRCh/Chemical Name and Formula Searches
##### Chemical Name Searching

* STN User Documentation (FIZ Karlsruhe)
* STN User Documentation and Training (CAS)
* Nomenclature Changes for CA index Names ] (Name changes that began to occur in December 2006)
* ChemIDplus Advanced (National Library of Medicine)
* ChemSketch (Advanced Chemistry Development) Freeware chemistry drawing program with a chemical name generator.
* R&D Chemicals – Rare Chemicals Database
* RxList-the Internet Drug Index: Index searchable by keyword, drug name, or imprint codes.
* ENZYME – Enzyme Nomenclature Database (swissprot)
* Chemical Register Chemical supplier list of commodity and specialty chemicals by name or CAS registry number

##### Abbreviations of Chemical Compounds

* Abbreviations, acronyms, trivial and trade names (Chemistry, Biology, Pharmacy Information Center)
* Abbreviations of Chemical Compounds (Free University, Berlin)
* Amino Acids at Free University, Berlin
* Origin of the Single-Letter Code for the Amino Acids (Dr. Margaret Oakley Dayhoff)
* Acronyms Database (Indiana University Chemistry Library)

##### Chemical Nomenclature

* Chemical Nomenclature Lite A Guide to Naming and Indexing Chemical Compounds (Charles H. Davis)
* Recommendations on Biochemical & Organic Nomenclature, Symbols & Terminology etc. (IUBMB)
* Recommendations on Organic & Biochemical Nomenclature, Symbols & Terminology etc. (IUPAC)
* IUPAC Nomenclature of Organic Chemistry Recommendations 1979 and 1993 (Advanced Chemistry Development)
** Guide to Name Construction (ACD)
* ACD/Chemsketch (freeware with functionality for naming organic structures of fewer than 50 atoms and 3 rings)
* Chemical Nomenclature Aids in the Indiana University Chemistry Library
* Molecules with Silly or Unusual Names
# Chemical Information Sources/SIRCh/Chemical Patent Searches/Markush Structure

Example of a Markush Chemical Patent Claim
Newsgroups: misc.int-property,sci.chem From: srctran@world.std.com (Gregory Aharonian) Subject: PATNEWS: A humongous, hierarchical, chemical Markush group Date: Thu, 2 Mar 1995 06:45:27 GMT
(check out its sprawling multi-page OG entry).
patents. Second, this lengthy first claim being a Markush group, results in zillions (2.94777 zillion to be exact) of combinations, for which I assume the examiner and applicant did quantum chemical GAUSSIAN evaluations for each one :-)
groups I have ever seen. Usually the chemical Markush groups state something like "this is made of A B and C, where A is any benzene derivative...", a two level hierarchy. This patent, however, is a three and four level hierarchy "this is made of A B C, where A is R1, and R1 is benzene or R121". It has a reductionist elegance in its hierarchical style.
patent arena, if you use a similar hierarchy to claim some object schema and all applications that are derivable from the claimed object class structure (which I still claim at least one company is trying to do :-)
Greg Aharonian Internet Patent News Service (for subscription info, send 'help' to patents@world.std.com ) (for prior art search services info, send 'prior' to patents@world.std.com ) (for WWW patent searching, try http://sunsite.unc.edu/patents/intropat.html )
5387671 Hexa- and heptapeptide anaphylatoxin-receptor ligands Abbott Laboratories
or a pharmaceutically acceptable salt thereof wherein the groups A through Q have the values:
wherein
all of the foregoing with the provisos that