OpenLLM-France/wikimedia huggingface dataset:
# Moving objects in retarded gravitational potentials of an expanding spherical shell/Preface

Brief historical review →

## Preface
### Summary

* Retarded gravitational potentials of a very large spherical shell with mass.
* Acceleration forces on objects with mass within such a shell.
* Concept of the Schwarzschild distance from the outer invisible surface of such a shell ("black shell") to the visible universe.
* Gravitational redshift due to the mass of the black shell.
* Evolution of the Schwarzschild distance due to the continuously increasing mass of the black shell.

### Abstract

The principles of retarded gravitational potentials are presented and explained. The application of retarded gravitational potentials to an expanding spherical shell of matter with a large mass (a "black shell") leads to acceleration forces on moving objects within such a huge shell.
The concept of a Schwarzschild distance from the inner surface of a hollow spherical cap to the outer Hubble sphere is introduced. This can be used to determine equivalent spherical masses acting on a sample mass and which can provide information about the evolution of the universe. The Schwarzschild limit is referred to as the inner surface of the hollow spherical cap, and therefore, to the outer limit of the visible universe.
The unexpected high values of the cosmological redshift that are observed at extremely far astronomical objects including the cosmic microwave background could be related to the strong asymmetrical effect of the gravitation of the outer black shell of the universe. Due to the integrative effect of the retarded gravitational potentials of a concave shaped spherical black shell the gravitational forces of masses within the Schwarzschild distance are so enormous that the light from any atoms can no longer reach us. Exactly at the boundary to our visible universe, the gravitational redshift is infinite, just like on the surface of a convex shaped spherical black hole.
The evolvement of the Schwarzschild distance due to the continuously increasing mass of the outer invisible shell of our universe has two inflection points around the very points in time and space, where the cosmic microwave background as well as the youngest galaxies can be observed today. The strongly increasing Schwarzschild distance between these two points in time goes hand in hand with the postulated massive transformation of dark matter to "dark energy". Therefore, the effect of retarded gravitational potentials could also contribute to the explanation of the accelerated expansion of the universe, which often is related to the effect of "dark energy".
It seems that the hypothesis of relevant dark matter that continuously moves beyond the event horizon of our visible universe could open the gates for further interesting investigations and findings.
A shorter version of this Wikibook is available on Research Gate.

### References

* ↑ Bautsch, Markus (2024). "Retarded gravitational potentials on the scale of the universe". doi:10.13140/RG.2.2.27349.23529. {{cite journal}}: Cite journal requires |journal= (help)
# Muggles' Guide to Harry Potter/Characters/Gabrielle Delacour
## Overview

Gabrielle Delacour is Fleur Delacour's sister.

## Role in the Books
### Goblet of Fire

We first see Gabrielle when she is one of the hostages for the Four Champions in the Second Task of the Triwizard Tournament. Each of the Champions is given one hour to rescue that which is most dear to them from the bottom of the lake. Gabrielle is what is most precious to Fleur. Fleur fails in her attempt to reach Gabrielle, and is so relieved when Harry surfaces with her that she runs over and kisses him, and also Ron who had some incidental role in her return.
Gabrielle is present in the audience for the Third Task, though she plays very little part. She does wave to Harry, who waves back at her.

### Half-Blood Prince

Gabrielle is mentioned in passing by Fleur as part of her planning for her wedding to Bill Weasley along with the fact that she never stops talking about Harry.

### Deathly Hallows

Gabrielle is one of the bridesmaids at the wedding of Fleur Delacour and Bill Weasley. She arrives two days before the ceremony, with Monsieur and Madame (Apolline) Delacour, and follows Fleur around, prattling away at her in French and trying to help out. She flirts with Harry by batting her eyelashes, much to Ginny's annoyance. She served as a bridesmaid alongside Ginny.

## Relationships with Other Characters

Gabrielle clearly has a strong connection to her sister.
Gabrielle also developed a crush on Harry after he saved her from the lake, given that she never stopped talking about him along with batting her eyelashes when the two met again for Bill and Fleur's wedding. However, the crush went nowhere.

## Analysis

When reading the fourth, sixth and seventh books, Gabrielle appears to share similarities with Ginny Weasley:
* Both were the youngest sisters of the family.
* Both are also younger than Harry. Ginny is a year younger than him while Gabrielle is six years younger than Harry.
* Both of their first names start with 'G'.
* Both were selected as bridesmaids for Bill and Fleur's wedding.
* Both were saved by Harry from a perilous Water-filled location: Chamber of Secrets for Ginny, the Black Lake for Gabrielle.
* Both had a huge crush on Harry and were mentioned to have talked non-stop about him from their older siblings (Ron mentioned Ginny and Fleur mentioned Gabrielle).
* Both became relatives of Harry. Ginny married Harry while Gabrielle became a distant relative of Harry since Gabrielle's older sister, Fleur, married Bill, Ginny's oldest brother.
There were also differences:
* Gabrielle only had one older sister, while Ginny had six older brothers.
* Ginny has red hair while Gabrielle has blonde hair.
* Gabrielle is French while Ginny is British.
* Ginny first met Harry when he arrived at Platform 9 and 3/4 to start his first year at Hogwarts, while Gabrielle first met Harry when he was in his fourth year as a Triwizard Champion.

## Questions

Study questions are meant to be left for each student to answer; please don't answer them here.
# Nets, Webs and the Information Infrastructure
## Table of Contents

* Preface
* Introduction
* Enter the Net
* Viruses, Privacy and Security
* Net for us
* For Further Reading
* Notes
* Glossary
* Acknowledgment
* About the Author

## Information

This book is donated by UNDP Asia-Pacific Development Information Programme (UNDP-APDIP) to the community. The original publication by:
Author: Edwin S. Soriano © UNDP-APDIP, 2003, 49 pages
is located at http://www.apdip.net/publications/iespprimers/eprimer-nets.pdf
This wikibook is available under the terms of GNU Free Documentation License and Creative Commons Attribution License 2.5

## Notes

Numbers that are just placed in the middle of the sentence are citations, and should be linked to the Notes page. Do not delete these citation numbers! Use the {{nwiicite}} template to link them instead.
# Character Encodings/Code Tables/MS-DOS/Code page 30034

Code page 30034 is a code page intended for Cherokee.

## Character set

The following table shows code page 30034. Each character is shown with its equivalent Unicode code point. Only the second half of the table (128–255) is shown, the first half (0–127) being the same as code page 437.
Code page 30034 :
| | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| 8x 128 | Ꭰ 13A0 | Ꭱ 13A1 | Ꭲ 13A2 | Ꭳ 13A3 | Ꭴ 13A4 | Ꭵ 13A5 | Ꭶ 13A6 | Ꭷ 13A7 | Ꭸ 13A8 | Ꭹ 13A9 | Ꭺ 13AA | Ꭻ 13AB | Ꭼ 13AC | Ꭽ 13AD | Ꭾ 13AE | Ꭿ 13AF |
| 9x 144 | Ꮀ 13B0 | Ꮁ 13B1 | Ꮂ 13B2 | Ꮃ 13B3 | Ꮄ 13B4 | Ꮅ 13B5 | Ꮆ 13B6 | Ꮇ 13B7 | Ꮈ 13B8 | Ꮉ 13B9 | Ꮊ 13BA | Ꮋ 13BB | Ꮌ 13BC | Ꮍ 13BD | Ꮎ 13BE | Ꮏ 13BF |
| Ax 160 | Ꮐ 13C0 | Ꮑ 13C1 | Ꮒ 13C2 | Ꮓ 13C3 | Ꮔ 13C4 | Ꮕ 13C5 | Ꮖ 13C6 | Ꮗ 13C7 | Ꮘ 13C8 | Ꮙ 13C9 | Ꮚ 13CA | Ꮛ 13CB | Ꮜ 13CC | Ꮝ 13CD | Ꮞ 13CE | Ꮟ 13CF |
| Bx 176 | ░ 2591 | ▒ 2592 | ▓ 2593 | │ 2502 | ┤ 2524 | Ꮠ 13D0 | Ꮡ 13D1 | Ꮢ 13D2 | Ꮣ 13D3 | ╣ 2563 | ║ 2551 | ╗ 2557 | ╝ 255D | Ꮤ 13D4 | Ꮥ 13D5 | ┐ 2510 |
| Cx 192 | └ 2514 | ┴ 2534 | ┬ 252C | ├ 251C | ─ 2500 | ┼ 253C | Ꮦ 13D6 | Ꮧ 13D7 | ╚ 255A | ╔ 2554 | ╩ 2569 | ╦ 2566 | ╠ 2560 | ═ 2550 | ╬ 256C | Ꮨ 13D8 |
| Dx 208 | Ꮩ 13D9 | Ꮪ 13DA | Ꮫ 13DB | Ꮬ 13DC | Ꮭ 13DD | ╒ 2552 | Ꮮ 13DE | Ꮯ 13DF | Ꮰ 13E0 | ┘ 2518 | ┌ 250C | █ 2588 | ▄ 2584 | ▌ 258C | ▐ 2590 | ▀ 2580 |
| Ex 224 | α 03B1 | Ꮲ 13E2 | Ꮳ 13E3 | Ꮴ 13E4 | Ꮵ 13E5 | Ꮶ 13E6 | Ꮷ 13E7 | Ꮸ 13E8 | Ꮹ 13E9 | Ꮺ 13EA | Ꮻ 13EB | Ꮼ 13EC | Ꮽ 13ED | Ꮾ 13EE | Ꮿ 13EF | Ᏸ 13F0 |
| Fx 240 | ≡ 2261 | Ᏺ 13F2 | Ᏻ 13F3 | Ᏼ 13F4 | Ꮱ 13E1 | Ᏹ 13F1 | ÷ 00F7 | ≈ 2248 | ° 00B0 | ∙ 2219 | · 00B7 | √ 221A | ⁿ 207F | ² 00B2 | ■ 25A0 | NBSP 00A0 |
Symbols and punctuation  Differences from code page 437
# Abstract Algebra/3x3 real matrices

The algebra M(3,R) of 3 x 3 real matrices, having nine dimensions, is well beyond visual scope. Nevertheless, study of nilpotents of second degree brings to light some shiny facets.

## Alternative basis

Let $p={\begin{pmatrix}0&1&0\\0&0&1\\0&0&0\end{pmatrix}}$. Using matrix multiplication, the reader will compute matrices p$^2$ and p$^3$. Next, consider
    $q={\begin{pmatrix}0&1&0\\0&0&-1\\0&0&0\end{pmatrix}}\quad r={\begin{pmatrix}0&0&0\\1&0&0\\0&1&0\end{pmatrix}}\quad s={\begin{pmatrix}0&0&0\\1&0&0\\0&-1&0\end{pmatrix}}$.
Exercises: 1) Show p p = − q q.
2) Show r r = − s s.
3) Show pr = qs.
4) Show p s = q r.
5) Show r p = s q.
6) Show s p = r q.
7) Show pr + ps + 2sp is twice the identity matrix.
8) Show that { pr, ps, rp, sp } is a linearly dependent subset of M(3,R).
9) Show that { p, q, r, s, pp, rr, pr, ps, rp } is a basis for M(3,R).

## One-parameter subgroups of GL(3,R)

Consider the subspace $T_{p}=\{xI+yp+zpp:x,y,z\in R\}$. In fact, T$_p$ is a 3-dimensional subalgebra of M(3,R).
Since p is nilpotent of second degree, the exponential series for tp , t in R, has only three terms:
    $\exp(tp)=1+tp+{\frac {t^{2}}{2}}p^{2}.$ The parameter t traces out a parabola in the plane x = 1 of T$_p$.
The parabola is in fact a group isomorphic to (R, +) since $\exp(tp)\times \exp(sp)=\exp((s+t)p)$. In contrast to orthogonal subgroups of GL(3,R), this group is not compact.
Exercise : Show there are similar one-parameter subgroups in subspaces $T_{s},\ T_{q},\ T_{r}$ of M(3,R).
# Math for Non-Geeks: Exercises: Sequence

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## Questions: Sequences

Exercise
Which of the following statements are true?
* Every index $n$ can uniquely be matched to a sequence element $a_{n}$ .
* Every sequence element $a_{n}$ can uniquely be matched to an index $n$.
* A sequence being neither bounded from above nor from below does not exist.
* A sequence increasing and decreasing monotonically does not exist.
* A sequence increasing and decreasing strictly monotonically does not exist.
* A sequence increasing monotonically and being bounded from above does not exist.
Solution
* True.
* False. A constant sequence is a great counterexample. As all sequence elements $a_{n}$, $n\in \mathbb {N}$, have the same value, you can match this value to every index $n\in \mathbb {N}$ and not only one unique index.
* False. The sequence $\left(a_{n}\right)_{n\in \mathbb {N} }=1,\,-2,\,3,\,-4,\,5,\,-6,\,\ldots$ is neither bounded from above nor from below.
* False. Every constant sequence is monotonically increasing and decreasing. Only „strict monotonicity“ implies that the sequence elements need to be unequal.
* True.
* False. The sequence $(a_{n})_{n\in \mathbb {N} }$ with $a_{n}:=1-{\tfrac {1}{n}}$ for all $n\in \mathbb {N}$ is bounded from above, as $a_{n}<1$ holds for all $n\in \mathbb {N}$. Furthermore, it's monotonically increasing. For all $n\in \mathbb {N}$, we have ${\tfrac {1}{n+1}}<{\tfrac {1}{n}}$ and therefore $a_{n}=1-{\tfrac {1}{n}}<1-{\tfrac {1}{n+1}}=a_{n+1}$.

## Exercise: Find a sequence

Exercise
Find a sequence $(a_{n})_{n\in \mathbb {N} }$ fulfilling the following conditions:
* $a_{n}<a_{n+2}$ for all $n\in \mathbb {N}$
* $a_{n}>a_{n+1}$ for all odd $n$
Write down an explicit and a recursive formula for your sequence!
Solution
One possible sequence is
$(a_{n})_{n\in \mathbb {N} }=1,0,2,1,3,2,4,3,5,4,6,5,7,6,\ldots$
An explicit formula of this sequence is given by
$a_{n}={\begin{cases}{\frac {n+1}{2}}&{\text{for }}n{\text{ odd}}\\{\frac {n}{2}}-1&{\text{for }}n{\text{ even}}\\\end{cases}}$ A recursive formula of this sequence is given by $a_{1}:=1,a_{2}:=0$ and for all $n\geq 2$:
$a_{n}:=a_{n-2}+1$
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# Math for Non-Geeks/ Exercises: Sequences
## Questions: Sequences

Exercise
Which of the following statements are true?
* Every index $n$ can uniquely be matched to a sequence element $a_{n}$ .
* Every sequence element $a_{n}$ can uniquely be matched to an index $n$.
* A sequence being neither bounded from above nor from below does not exist.
* A sequence increasing and decreasing monotonically does not exist.
* A sequence increasing and decreasing strictly monotonically does not exist.
* A sequence increasing monotonically and being bounded from above does not exist.
Solution
* True.
* False. A constant sequence is a great counterexample. As all sequence elements $a_{n}$, $n\in \mathbb {N}$, have the same value, you can match this value to every index $n\in \mathbb {N}$ and not only one unique index.
* False. The sequence $\left(a_{n}\right)_{n\in \mathbb {N} }=1,\,-2,\,3,\,-4,\,5,\,-6,\,\ldots$ is neither bounded from above nor from below.
* False. Every constant sequence is monotonically increasing and decreasing. Only „strict monotonicity“ implies that the sequence elements need to be unequal.
* True.
* False. The sequence $(a_{n})_{n\in \mathbb {N} }$ with $a_{n}:=1-{\tfrac {1}{n}}$ for all $n\in \mathbb {N}$ is bounded from above, as $a_{n}<1$ holds for all $n\in \mathbb {N}$. Furthermore, it's monotonically increasing. For all $n\in \mathbb {N}$, we have ${\tfrac {1}{n+1}}<{\tfrac {1}{n}}$ and therefore $a_{n}=1-{\tfrac {1}{n}}<1-{\tfrac {1}{n+1}}=a_{n+1}$.

## Exercise: Find a sequence

Exercise
Find a sequence $(a_{n})_{n\in \mathbb {N} }$ fulfilling the following conditions:
* $a_{n}<a_{n+2}$ for all $n\in \mathbb {N}$
* $a_{n}>a_{n+1}$ for all odd $n$
Write down an explicit and a recursive formula for your sequence!
Solution
One possible sequence is
$(a_{n})_{n\in \mathbb {N} }=1,0,2,1,3,2,4,3,5,4,6,5,7,6,\ldots$
An explicit formula of this sequence is given by
$a_{n}={\begin{cases}{\frac {n+1}{2}}&{\text{for }}n{\text{ odd}}\\{\frac {n}{2}}-1&{\text{for }}n{\text{ even}}\\\end{cases}}$ A recursive formula of this sequence is given by $a_{1}:=1,a_{2}:=0$ and for all $n\geq 2$:
$a_{n}:=a_{n-2}+1$
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# Chess Opening Theory/1. e4/1...e5/2. Nc3/2...Bb4/3. d4
## Hrómadka Attack

This agressive move aims to counter the Zhuravlev with an more agressive variation than the normal 3. Bc4 or 3. Nd5, the most common moves, black's most natural point in the Zhuravlev is to take the knight on c3, however after d4, black can take the knight but they dont need to, the knight is pinned and cant go anywhere, the only plausible reason to take the knight is because of the doubled pawns, even If white gets the doubled pawns, white has a great position with optimal center control

## Possible Moves

3... d6 - Best move according to Stockfish 16, this is a position that even though white can ruin black's castle, you can't really start an attack on the black's king after 4. dxe5 dxe5 5. Qxd8+ Kxd8 and white has a +0.2 advantage but nothing much, white can also play Nf3 but black still doesn't have a great reason to play Bxc3+, computers recomend Nd7, and then white can play moves like Bc4, Bd3, Bd2 or a3, which now gives black a great reason to play Bxc3+ since after a3, the bishop Will be attacked
3... Qh4 - This dumb-looking move is actually the second best Stockfish 16 line, similar to the Stenitz Variation of the Scotch Game, black attack the e4 pawn, g3 is obviously a blunder because of Qxe4+ winning the Rook after Qe2, Qxh1, the best move is incredibly Be3! sacrificing the e4 pawn for development, many beginner to intermidiate level player, might get confused with Be3, that's why you can also play Bd2, and defend the pawn, Qxe4+??? is a catasthrophic blunder since white can simply take because the knight isn't pinned anymore
3... Bxc3?! (Exchange Line)- This is a natural move but considered a inacuracy in fact, this is so natural that it is played 42% of the time according to the lichess player database, played over 200.000 times, white gets a +0.9 position after bxc3, black doesn't have enough compenstation for the loss of the bishop pair, white's control in the center completely destroys black's advantage, and is simply not a favourable move
# Gujarati/Vocabulary

* Gujarati
* Alphabet
* Grammar
* Gender
* Plural
* Conjugation
* Present
* Perfect
* Imperfect
* Future
* Pronouns
* Vocabulary
* Numbers
* Family relations
નમસકાર Namaskaar or નમસતે Namaste
    Hello
કેમ છો ? Kem chho?
    How are you?
મારું નામ હરશલ છે. Maarũ naam Harshal chhe.
    My name is Harshal.
આવજો ! Aavjo!
    See you later/goodbye
તમારું નામ શું છે ? Tamaarũ naam shũ chhe?
    What is your name?
તમે ક્યાં રહો છો ? Tame kyãã raho chho?
    Where do you live?
તમે ઘરે ક્યારે આવશો ? Tame ghare kyaare aavsho?
    When will you come home?
તમે શું કરો છો ? Tame shũ karo chho?
    What are you doing?
How are your exams going?
# Old English/Participles

There were two participles in Old English: The present and past. The present participle was approximately equivalent to the Modern English "-ing" form of a verb (as in "The singing person") and the past participle was the form used in an adjective or in a passive verbal construction to show what had happened to someone, like in Modern English "I was killed" or "The song was sung."

## Present participle

In the case of class 1 and 3 weak verbs, all strong verbs, and most or all irregular verbs, the suffix "-ende" was added to the stem of the verb to form the present participle, for example: "singan" - "singende" (in such strong verbs as had a long diphthong in the stem, and the "n" but not the "a" of the infinitive suffix, only "-nde" was added to the stem, for example "sēon" - "sēonde"). In class 2 weak verbs, the suffix "-ende" was added to the stem plus the "i" (or "iġ") of the infinitive suffix, for example: "macian" - "maciȝende". The present participle could be used as an adjective to show that someone was doing something, or usually did something; and as an adjective, it was declined like other adjectives, for example "se singenda mann" - "the singing man". It was also only rarely used to show a continuous or currently happening action, for example, "Iċ eom singende þone sang" - "I am singing the song". Note that when used like this it was not declined as an adjective.

## Past participle

The past participle was formed using a dental suffix for class 1 and 3 weak verbs ("-ed", "-t", or "-d", depending on the verb), and "-od" for class 2 weak verbs. Strong verbs took the suffix "-en" and the appropriate stem vowel change for their strong verb class, for example "singan" - "sungen". As earlier mentioned, the participle of a strong verb could be used as an adjective as in Modern English, to show that something had happened to a person (and when used like that, it was declined), or as part of the passive verb construction "ƿesan/ƿeorðan (past participle)" or the active perfect tense "habban (participle)" (note that for non-transitive verbs, it was sometimes "ƿesan (past participle" instead of "habban (past participle)". When used in the perfect construction, it could either be declined or not. If you wanted to decline it, use appropriate number form of the strong accusative adjectival form of the past participle, for example, you could say both "Iċ hæbbe þone mann ȝeslæġen" (I have the man slain) and "Iċ hæbbe þone mann ȝeslæġenne".

## "-able" adjectives

Both the past and present participles could have the adjectival suffix "-līċ" added to them, with the resulting word having a meaning like "(verb)-able", as in "ġeseƿenlīċ" - "visible".
# First Aid

This book covers in depth all topics required for a standard first aid course, and also includes a section on advanced topics. The basics covered include:
First aid is genologicaly defined as the first treatment given to an injured/infected person before taking him or her to a medical facility.
* Primary assessment and cardiopulmonary resuscitation or CPR
* Legal aspects of first aid. Including negligence and consent
* Circulatory emergencies. Such as bleeding, heart attack and stroke
* Respiratory emergencies. Such as asthma and anaphylactic shock
* Internal injuries. Such as broken bones, chest injuries, and internal bleeding
* Other injuries. Such as Burns, seizures, snake bites, and other medical conditions.
In the chapter on advanced topics, you'll find information about oxygen administration and airway management, automated external defibrillator or AED operation, wilderness techniques, additional assessments, and triage.
The intended audience is taking a first aid course from a certified instructor, and can read at a high school level. Please be advised that there are some images of the injuries and conditions discussed.
This is a wiki, so you can edit this book; and if you find a mistake, then please be bold and fix it. If you want to leave comments, please do so on the talk page for that module. If you want to help out even more, take a look through What needs to be done? for tasks that still need to be done, or start with whatever tasks you stumble across.