OpenLLM-France/wikimedia huggingface dataset:
# Topology/Sequences

A sequence in a space $X$ is defined as a function from the set of natural numbers into that space, that is $f:\mathbb {N} \to X$. The members of the domain of the sequence are $f(1),f(2),\ldots$ and are denoted by $f(n)=a_{n}$. The sequence itself, or more specifically its domain are often denoted by $\left\langle a_{i}\right\rangle$.
The idea is that you have an infinite list of elements from the space; the first element of the sequence is $f(1)$, the next is $f(2)$, etc. For example, consider the sequence in $\mathbb {R}$ given by $f(n)=1/n$. This is simply the points $1,1/2,1/3,1/4,...$ Also, consider the constant sequence $f(n)=1$. You can think of this as the number 1, repeated over and over.

## Convergence

Let $X$ be a set and let ${\mathcal {T}}$ be a topology on $X$ Let $\left\langle x_{i}\right\rangle$ be a sequence in $X$ and let $x\in X$
We say that "$\left\langle x_{i}\right\rangle$ converges to $x$" if for any neighborhood $U$ of $x$, there exists $N\in \mathbb {N}$ such that $n\in \mathbb {N}$ and $n>N$ together imply $x_{n}\in U$
This is written as $\lim _{n\to \infty }x_{n}=x$

## Exercises

* Give a rigorous description of the following sequences of natural numbers: (i) $1,2,3,4,5\dots$ (ii) $2,-4,6,-8,10,\ldots$
* Let $X$ be a set and let ${\mathcal {T}}$ be a topology over $X$. Let $x\in X$ and let $U$ be a neighbourhood of $x$. Let $U_{1}\subset U$ and $x\in U_{1}$. Similarly construct neighbourhoods $U_{i}\subset U_{i-1}$ with $x\in U_{i}\forall i$. Let $\left\langle x_{i}\right\rangle$ be a sequence such that each $x_{i}\in U_{i}$. Prove that $\lim _{n\to \infty }x_{n}=x$
# Topology/Vector Bundles

A vector bundle is, broadly speaking, a family of vector spaces which is continuously indexed by a topological space. An important example is the tangent bundle of a manifold.
The formal definition is the following:
Definition (Vector bundle) A real vector bundle on a topological space $B$ is a space $E$ together with a continuous map $p:E\rightarrow B$ with the following properties:
(1) For each $b\in B$, $p^{-1}(b)$ is isomorphic to $\mathbf {R} ^{n}$
(2) $B$ is covered by open sets $U_{i}$ such that there exist homeomorphisms $h_{i}:p^{-1}(U_{i})\rightarrow U_{i}\times \mathbf {R} ^{n}$ and $h_{i}\circ h_{j}^{-1}U_{i}\cap U_{j}\times \mathbf {R} ^{n}\rightarrow U_{i}\cap U_{j}\times \mathbf {R} ^{n}$ is the identity on the first factor and a linear isomorphism on the second.
Replacing $\mathbf {R}$ with $\mathbf {C}$, we get the definition of a complex vector bundle.
We call $E$ the total space of the vector bundle and $B$, the base space.
One can define a smooth vector bundle as following:
$E$ and $B$ have to be smooth manifolds and every maps appearing in the previous definition have to be smooth.
As we have stated before, the tangent bundle of a smooth manifold is a smooth vector bundle.
# Topology/Singular Homology

First we define the standard simplices as the convex span of the standard basis vectors. We then take as a boundary map $d_{n}:\langle e_{1},\ldots ,e_{n}\rangle \mapsto \sum _{k=1}^{n}\langle e_{1},\ldots ,e_{k-1},e_{k+1},\ldots ,e_{n}\rangle$
Next we transport this structure to a topological space X: A simplex s in X is the image of a continous map from some standard simplex.
Now let $C_{n}(X)=\langle \sigma :\Delta _{n}\to X\rangle$ be the free groups on the simplices in X. The maps $d_{n}$ now induce a new chain map on the complex $C_{\bullet }$
Now using the definition of homology as in the previous section we define $H_{n}=\ker d_{n}/\operatorname {Im} d_{n+1}$ (Exercise: prove that this is well-defined.)
# Total Annihilation

This guide will cover important topics for Total Annihilation, a strategy game released on PC and Macintosh.

## Contents

* The Basics
* Units
* Structures
* Tactics and Strategy Guide
* Maps
* Patching
* Community
* Websites
* Mods and Addons to Total Annihilation
* List of Abbreviations
# Traditional Chinese Medicine/Ge Gen Huang Qin Huang Lian Tang

The formula Ge Gen Huang Qin Huang Lian Tang, designed to relieve the exterior, clear away heat from the interior, and stop diarrhea, consists of the following:
| No. | Pinyin | Simplified Chinese | Grams |
| 1 | Ge Gen | 葛根 | 15 |
| 2 | Zhi Gan Cao | 炙甘草 | 6 |
| 3 | Huang Qin | 黄芩 | 9 |
| 4 | Huang Lian | 黄连 | 9 |
back to :
* Stopping Dysentery By Clearing Away Heat
* Formula Design
* Prescriptions
# Traditional Chinese Medicine/Glossaries

TCM | Pulse | TCM Terms | Acupuncture | Formula Design | Single Herbs | Usage Of Herbs | Prescriptions | Usage Of Prescriptions | Sources | Materia Medica | Interactions |
Glossaries
* Chinese Medical Terms
* Single Herbs
* Prescriptions
* Source Of Materia Medica
* Herb To Herb Interactions
# Traditional Chinese Medicine/Gua Di San

Gua Di San consists of the following:
* Gua Di (Pedicellus Cucumeris), ao (simmered) until yellow : 1-2gm
* Chi Xiao Dou (Semen Phaseoli) : 1-2gm
# Traditional Chinese Medicine/Gua Lou Xie Bai Gui Zhi Tang

The formula Gua Lou Xie Bai Gui Zhi Tang, consists of the following:
| No. | Pinyin | Simplified Chinese | Grams |
| 1 | Gua Lou | 栝楼 | 12 |
| 2 | Xie Bai | 薤白 | 9 |
| 3 | Mi Jiu (rice wine) | 米酒 | 30 ml |
back to:
* Removing Obstruction By Activating Yang
* Formula Design
* Prescriptions
# Traditional Chinese Medicine/Ge Gen

Name Means:
* Ge-Coarse grass linen
* Gen-Root
English Name:
* kudzu root
* pueraria
Chinese Name:
Latin Name:
Taste & Temperature:
* Xin-Spicy
* Gan-Sweet
* Liang-Cool
Channels:
* Foot Tai Yin of Spleen
* Foot Yang Ming of Stomach
Actions & Indications:
* disperse Wind-Heat (Spicy & Cool)
* raise Yang Qi
* diarrhea
* release muscles & clear heat
* nourish fluids & alleviate thirst
* treat hypertension
* treat heart and brain diseases due to lack of blood circulation
Contraindication:
Caution:
* Yin deficiency
* Blood deficiency
* chronic skin infection
Dosage:

### References

* ↑ Haiying Liu, Nongxue Qiu, Huihuang Ding, Ruiqi Yao. “Polyphenols contents and antioxidant capacity of 68 Chinese herbals suitable for medical or food uses”, Food Research International, Volume 41, Issue 4, 2008, Pages 363-370.
* ↑ China Pharmacopoeia Committee. (2000). Pharmacopoeia of the People’s Republic of China (Vol. 1). Beijing: China Chemical Industry Press.
back to:
* Xin Liang Jie Biao
* TCM Materia Medica
# Traditional Chinese Medicine/Ge Gen Tang

The formula Ge Gen Tang, designed to relieve the exterior with pungent and warm herbs, consists of the following:
| No. | Pinyin | Simplified Chinese | Grams |
| 1 | Ge Gen | 葛根 | 9 |
| 2 | Ma Huang | 麻黄(草麻黄) | 6 |
| 3 | Gui Zhi | 桂枝 | 6 |
| 4 | Shao Yao | 芍药 | 6 |
| 5 | Sheng Jiang | 生姜 | 3 |
| 6 | Da Zao | 大枣 | 3 |
| 7 | Zhi Gan Cao | 炙甘草 | 3 |
back to:
* Formula Design
* Relieving The Exterior With Pungent And Warm Herbs
# Traditional Chinese Medicine/Gui Zhi

Cinnamon Twig
(Chinese: 桂枝)
Taste & Temperature:
* Xin-Spicy
* Gan-Sweet
* Wen-Warm
Channels:
* Hand Tai Yin of Lung (b/c Xin-Spicy?)
* Foot Tai Yang of Urinary Bladder
* Hand Shao Yin of Heart
Actions & Indications:
* harmonize Ying/Wei Qi
* warm channels, dispel Cold
* warm & activate Yang Qi in chest
* warm & activate Yang Qi in Blood Vessels
Contrainditations:
* warm frebile disorders
* Yin deficiency Heat
* Blood Heat with vomiting
Caution:
* pregnancy
* excessive menstruation
Dosage:
* 1-3 qian (3-9 grams)
* 9-15 qian (27-45 grams) ???
Used: Often
Friend: Ma Huang
back to
* TCM Materia Medica
* Xin Wen Jie Biao
# Traditional Chinese Medicine/Ge Gen Tang Jia Chuan Xiong Xin Yi Tang

The formula Ge Gen Tang Jia Chuan Xiong Xin Yi Tang, designed to regulate the yingfen and weifen levels, to promote the dispersing function of the lung and to dredge obstruction, consists of the following:
| No. | Pinyin | Simplified Chinese | Grams |
| 1 | Ge Gen | 葛根 | 9 |
| 2 | Ma Huang | 麻黄(草麻黄) | 6 |
| 3 | Gui Zhi | 桂枝 | 6 |
| 4 | Sheng Jiang | 生姜 | 3 |
| 5 | Zhi Gan Cao | 炙甘草 | 6 |
| 6 | Bai Shao Yao | 白芍药 | 9 |
| 7 | Da Zao | 大枣 | 6 |
| 8 | Chuan Xiong | 川芎 | 9 |
| 9 | Xin Yi | 辛夷 | 9 |
back to :
* Relieving The Exterior With Pungent And Warm Herbs
* Formula Design
* Glossaries
* Prescriptions
# Traditional Chinese Medicine/Gui Zhi Jia Huang Qi Tang

The formula Gui Zhi Jia Huang Qi Tang, designed to address the syndrome of tawny sweat and disharmony between ying and wei (nutrient and defensive qi) and yang-qi resulting from the attack of dampness upon channels, consists of the following:
| No. | Pinyin | Simplified Chinese | Grams |
| 1 | Gui Zhi | 桂枝 | 6 |
| 2 | Shan Yao | 山药 | 6 |
| 3 | Sheng Jiang | 生姜 | 6 |
| 4 | Da Zao | 大枣 | 3 pieces |
| 5 | Zhi Gan Cao | 炙甘草 | 3 |
| 6 | Huang Qi | 黄芪 | 6 |
back to :
* Reinforcing The Defensive Qi By Consolidating Superficial Resistance
* Formula Design
* Prescriptions
# Traditional Chinese Medicine/Hao Qin Qing Dan Tang

Hao Qin Qing Dan Tang is composed of the following:
* Qing Hao (Herba Artemisiae Annuae) : 4.5-6g
* Huang Qin (Radix Scutellariae) : 4.5-9g
* Zhu Ru ( Caulis Bambusae in Taenia) : 9g
* Ban Xia (Rhizoma Pinelliae) : 4.5g
* Zhi Qiao (Fructus Aurantii) : 4.5g
* Chen Pi (Pericarpium Citri Reticulatae) : 4.5g
* Chi Fu Ling (Poria Rubra) : 9g
* Bi Yu San (Jasper Powder) : 9g
Note:
# Using Ratpoison/Basic Keystrokes

There are a few important keystrokes that are good to remember while using Ratpoison. When you have started your console window, why stop there? It is time to learn how to execute any program, and to switch between these in an effective manner.

## Switching and killing programs

Assuming that you have your console still running (if not, do Ctrl+t c), you can execute programs from within that window, just like any other window manager. Again, the difference is that there are no borders and that you cannot switch between these programs with your mouse. Type xclock if you are out of ideas about which program to start. Now, to change back to the console window you press Ctrl+t n. N of course means next, so you probably already guessed that Ctrl+t p moves to the previous window. Now, the difference between “next” and “previous” is non-existent if you are running only two programs, but as you run more and more programs simultaneously, it becomes ever more useful to be able to move “forward” and “backward” in some sense.
Now, how do you close a program? A number of programs have their own kill bindings (ex. Ctrl+x Ctrl+c for Emacs, Ctrl+w for Firefox and Xchat etc.) but ratpoison provides one command guaranteed to close and kill all running programs: the Ctrl+t k salute. The k stands for kill, and is implemented much the same way as clicking on the “close” button mainstream window managers provide.

## Handling many programs

Now, if you have got a multitude of programs running, it is tiresome to repetitively type Ctrl+n n enough times to get to the proper program when you need it. Ctrl+t number switches to a certain window. Keep in mind that this list is zero-indexed and sorted chronologically—the first program started is accessed via Ctrl+t 0, not 1.
Also, you can use Ctrl+t instead of Ctrl+t n to move to the next program. If you want to do a quick alt tab-like (that is, switch to last program accessed) command, Ctrl+t Ctrl+t will do that.
# Using POSper/User guide
## Using POSper
### Sales Workflow

Choose the sales window from the left hand menu options.

#### Using a Barcode Scanner

Simply scan the barcode. Each item scanned which has an entry in the stock table will add an entry to the sales ticket. When all of the items have been scanned, press the equals '=' sign on the screen and the payment options dialog will appear. The dialog has options for cash, cheque, ticket, card, and free. Choose the relevant option e.g. cash and type in the amount handed over by the customer. POSper will calculate the change. Press the printer button to print the receipt and open the till. Press OK to complete the transaction and return to the sales screen.

#### Using a Keyboard or the On Screen Keypad

This functions much as the barcode scanner does. Simply type in the barcode number and POSper will lookup the barcode item in the stock table. Then when return on the keyboard or the button with the barcode symbol on the screen is pressed, the item will be added to the sales ticket.

#### Using the Catalog

POSper maintains a catalog of current stock items, if icons have been added in the stock management screen they are displayed on the bottom right of the sales screen using images loaded into the database at the time of the stock update. If the images are not added to the stock items, the default icon is used.
To use these icons to make a sales transaction, select the category the stock item is in. Type in the number of items to be sold on the on screen keypad, press the multiply button '*' and only then choose the item itself from the catalog window. If only one item is to be sold, don't bother with the number or the multiply button, simply press the item's screen icon. The required number of items will be added to the sales ticket. When all of the items are added, complete the transaction as per the barcode scanner.

### Selling General items which don't have barcodes/stock entries

Previously add a "General Item" entry to the stock database with an icon and with £0.00 as the price. When selling such an item, choose the general item from the catalog to add the item to the sales ticket. Then select the "General Item" on the sales ticket and press the pencil button to change the price and number of units being sold.

## Reports

If you need reports that are not available in POSper you'll have to make your own. But don't worry. It's not hard.
# Using Plasma
## Table of Contents

* Introduction
* What is Plasma
** First impressions
* Navigating Plasma
* Customize Plasma
** History of Plasma
# Using Plasma/Printable version

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Using_Plasma

# Introduction
### Plasma: A Neo-Introduction

Plasma is an uncommon name for an uncommon concept which offers a user common services. What does that all mean? It will all be revealed but first let us introduce to you the common services that Plasma offers.

## Plasma is

* A place to put common files
* A place to put commonly needed information
* A way to organize tasks
* A way to control your work (or play!) area to your exact specifications
* A way to move from any type of work environment the very large to the very small, the option filled to the very constrained and still have control over the same data with much of the same power.
* A thing of Beauty

## Plasma's Role

Plasma is both the replacement for the Desktop metaphor in KDE5 as well as a framework for creating interfaces. We will be focusing on what Plasma does for users.
Plasma offers widgets, a place to put them, panels which can be hidden and themes. Many of the things that you are used to from other desktop software are now available as widgets so you can build a desktop as you see fit. By default it is setup as a traditional desktop so you will recognize many things right off.

# What is Plasma

Plasma is the graphical environment used by KDE.
# Using Ratpoison/Aliasing
## The command shell

Ratpoison has a built-in "run" dialog, a quick way to launch any program without having to start a console. Type C-t ! to get a little command box from which you can launch your program. This is most useful for launching graphical applications without tying up a console, as you won't be able to see any of the output of any purely command line programs.
From the same command prompt you can invoke the ratpoison command to tweak settings and do various actions. All these commands can be looked up in the mainpage, and they are all preceded by ratpoison -c.
For example, to set the "rudeness level" to five (will be explained soon) you type ratpoison -c rudeness 5.
All these commands can of course be executed from within a console window; C-t ! is simply a more convenient variant of a command shell.

### Aliasing

As mentioned before, ratpoison can be thought of as GNU Screen for window managing; like command line shells, it is possible to alias long commands to shorter versions.
This can be done through the extended command ability (which resembles C-t !), which is invoked via "C-t :". This opens a little box just like C-t ! does, but instead of executing shell commands, the input will be sent to ratpoison which will attempt to interpret this input as a ratpoison command; suppose one often runs Mozilla Firefox, but one grew weary of always opening a shell with C-t c and then typing in "mozilla-firefox &" (the ampersand is necessary so you can use the terminal for other things, otherwise the terminal will simply display any error or informative messages Firefox emits), or "C-t ! mozilla-firefox"?
One could decide to use a shorter name- input C-t :, and enter in "alias firefox exec mozilla-firefox", which would allow one to simply C-t: firefox, and Firefox would open up; one could even go C-t: "alias f exec mozilla-firefox" if they were rather lazy, and used no other programs beginning with the letter "f".
Aliasing is not limited to regular program names- if one drops the "exec", one could alias the command "quit" to "q": "C-t : alias q quit".
As a matter of fact, all the keyboard shortcuts one has learned for ratpoison, like C-t p, they all are actually aliases for longer commands! C-t q (which quits ratpoison) is actually an alias for C-t : quit. This is another area of borrowing from Emacs- Emacs similarly represents all keys on a keyboard and all combinations thereof, as aliases of Emacs functions.
(In these examples the command "exec" is necessary to have ratpoison evaluate the succeeding string as a shell command, and not another ratpoison command. Please see the official documentation on exec for more details; exec essentially does the same thing as C-t !).
# Using Plasma/What is Plasma

Plasma is the graphical environment used by KDE.
# Using Ratpoison

This is a book that is aimed to help the average user work with the simple yet powerful window manager Ratpoison. Please note that this book is very far from finished, but if you want to help, feel free to write some!

## Table of Contents

* Introduction
* Your first steps
** Basic Keystrokes
* Advanced Usage
** Aliasing
** Rebinding keys
** Splitting Windows
** The Config File
** Advanced Commands
** Pulling it all together: an example configuration file
* Tips and Tricks
* Where to Go from Here
* External Resources
# Using Plasma/Introduction
### Plasma: A Neo-Introduction

Plasma is an uncommon name for an uncommon concept which offers a user common services. What does that all mean? It will all be revealed but first let us introduce to you the common services that Plasma offers.

## Plasma is

* A place to put common files
* A place to put commonly needed information
* A way to organize tasks
* A way to control your work (or play!) area to your exact specifications
* A way to move from any type of work environment the very large to the very small, the option filled to the very constrained and still have control over the same data with much of the same power.
* A thing of Beauty

## Plasma's Role

Plasma is both the replacement for the Desktop metaphor in KDE5 as well as a framework for creating interfaces. We will be focusing on what Plasma does for users.
Plasma offers widgets, a place to put them, panels which can be hidden and themes. Many of the things that you are used to from other desktop software are now available as widgets so you can build a desktop as you see fit. By default it is setup as a traditional desktop so you will recognize many things right off.
# Using Ratpoison/Advanced Usage

This section deals with largely modifying keys and commands to do other things and to extend ratpoison's functionality.
# Using Ratpoison/Cover

Welcome to the WikiTextBook on<br.> Using Ratpoison
Go to Contents >>
The logotype of Ratpoison
# Wild ARMs 2/Characters/Brad Evans
### Brad Evans

Brad is one of the more complex characters on the whole in Wild ARMs 2. A military genius in a war ten years ago, he is now hunted as a criminal due to events beyond his control. What's more, he seems to have a connection to the sinister Odessa organization that is the main source of grief throughout the game. His truly noble intentions are not proved until he reveals himself after being presumed dead with an impressive show of firepower against Odessa's forces, saving the entire team in the process. Note that, although the Japanese version presents Brad as a homosexual, this aspect is mostly glossed over in the American version, either due to bad translation or an unwillingness on Sony's part to present something considered taboo in Western culture in a video game. Nevertheless, Brad's sexuality is not difficult to ascertain from common wisdom even in the English translation.
Gameplay-wise, Brad is a very solid character. With the highest HP, defense, and strength ratings in the game, he is an essential member of most teams throughout the game. However, later on, especially against the optional bosses, his usefulness wanes due to an inability to cause as much sheer damage as Ashley and Kanon. He also suffers from the second lowest speed in the game, and the lowest magic resistance. His accuracy also tends to be rather low.

#### Tools

* Kick Boots - Kick directly in front of you, opening rusted doors and chests and moving blocks.
* Bombs - Explode after a few seconds and destroy weakened walls and obstacles.
* Earthquake - A giant hammer creates a shockwave that destroys all destroyable objects in the room.

#### Force Powers

* Lock-On - Causes the chosen arm to hit for more damage with 100% accuracy. This is generally believed to be Brad's most useful skill due to his low accuracy.
* Combine - The equipped medium takes form and attacks as a guardian. Only usable when Tim is in the party.
* ARM X 2 - Able to use two ARMs in one round. Risky due to Brad's low accuracy.
* Boost - Hits with the selected arm for 300% damage with no chance to miss. Slightly less useful than Lock-On due to the amount of FP required to use.

#### ARMs

* Bazooka - Strong single target attack.
* Pineapple - Medium strength attack on a group of enemies.
* AM Cluster - Strong missile barrage on random enemies.
* Lawnmower - Strong attack on all enemies.
* Rail Gun - Incredibly powerful attack on one enemy.
* Mini Scud - Very strong attack on one enemy.
* Sky Eye - Very strong attack on a group of enemies.
* EZ Missile - Extremely damaging attack on all enemies.