OpenLLM-France/wikimedia huggingface dataset:
# Swing Dancing/Connection

The basic connection in swing is far different than that the traditional ballroom position, both in the open and closed positions.
In both open and closed positions, be sure to keep a decent amount of "frame" or "tension". Some people will also refer to this as "giving weight". All this means is to be sure to give a small amount of pressure back to your partner - this will make it significantly easier to feel the moves and will help with momentum in turns.

## The Open Position

In the open position, the lead begins with their arms bent at roughly a 90-degree angle at waist height with their hands curved and thumbs up (pretend you're holding a soda can, then point your thumbs up and you basically have the right shape). The follow's arms are similar to a position of pushing a shopping cart - similarly bent at about 90-degrees at waist height with palms parallel to the ground and the fingers curved (as to fit into the lead's hands). These are exaggerated descriptions, you can relax into more natural hand positions, but be sure to keep your arms bent and around waist level.

## The Closed Position

This position is significantly closer to the traditional ballroom position. The lead puts their right hand on the follow's back approximately at the level of the follow's shoulder blade. Keeping this hand high will help significantly when you go to lead a move that requires you to drop the hand to the follow's waist. The left hand should be in a similar position as in the open position, approximately at the waist and bent. The follow should keep their left hand on the front of the lead's shoulder. Moving the hand to the lead's back will prevent you from feeling when the lead comes forward and can result in some awkward accidents and generally a weaker sense of lead. The right hand should be similar to the open position, approximately at waist height. A note about the left and right hands for the lead and follow, respectively - moving the hand up closer to shoulder height, in a more traditional ballroom style will prevent the lead from being able to effectively signal a turn out of the closed position. Plus, it's just more stylistically appropriate to keep the hand low.
# External Links

* Catullus 114 A Translation of Catullus 114
* Catullus 114 Another Translation of Catullus 114
# Text and Translation

Meter - Hendecasyllabic
| Line | Latin Text | English Translation |
| 1 | Cenabis bene, mi Fabulle, apud me | You will dine well, my Fabullus, at my house |
| 2 | paucis, si tibi di favent, diebus, | in a few days (if the gods favor you), |
| 3 | si tecum attuleris bonam atque magnam | and if you bring with you a nice big |
| 4 | cenam, non sine candida puella | dinner, not without a pretty girl |
| 5 | et vino et sale et omnibus cachinnis. | and wine and wit and laughs for everyone. |
| 6 | Haec si, inquam, attuleris, venuste noster, | I say: if you bring these, my charming one, |
| 7 | cenabis bene; nam tui Catulli | you will dine well—for the little purse |
| 8 | plenus sacculus est aranearum. | of your Catullus is full of cobwebs. |
| 9 | Sed contra accipies meros amores, | But in return you will receive pure friendship |
| 10 | seu quid suavius elegantiusve est: | (or something more elegant and more delightful): |
| 11 | nam unguentum dabo, quod meae puellae | for I will give you an oil, which onto my girl |
| 12 | donarunt Veneres Cupidinesque; | Venuses and Cupids have bestowed; |
| 13 | quod tu cum olfacies, deos rogabis | and when you smell it, you will ask the gods |
| 14 | totum ut te faciant, Fabulle, nasum. | to make you, Fabullus, nothing but nose. |

# Connotations of The Text

This poem is an dinner invitation to Catullus's friend, Fabullus.

### Line 3

* si - if...
This is the catch for Fabullus - he will dine well if he does all the things about to be listed. It is put at the beginning of the line for emphasis.

### Line 4

* candida - white; fair
Can mean white, but here means beautiful/of pale skin - pale skin was a sign of beauty in Roman times.

### Line 5

* sale - salt
This word means salt normally, but came to mean wit. This was because salt was used to add flavour the meat, and so in a literary terms the 'flavour' to words is wit.
* cachinnis - laughs
This word is probably derived from Greek since the letter ch was not a Latin sound. The harsh sound that comes from saying this word may reflect the sounds of the laughter described.

### Line 8

* plenus sacculus est aranearum - lit. - full the purse is of cobwebs'
The poem makes use of hyperbaton. This is the re-arranging of the word order to create emphasis and effect. Hyperbaton is particularly common in inflected languages, such as Latin and Ancient Greek where the word order does not matter. The joke here is still used today - cobwebs sprung up where nothing has been touched for a while - and Catullus is broke.

### Line 11

* unguentum - perfume; oil
The reference to the "oil" or perfume, may be a subtle compliment to Catullus's girl. Both Roman men and women would wear perfume to make themselves smell more attractive.

# Sources

* Oxford Latin Reader by Maurice Balme and James Morewood (1997)

# External Links

* Catullus 13 A Translation of Catullus 13
# The Poetry of Gaius Valerius Catullus/12
## Text & Translation

Meter - Hendecasyllabic
| Line | Latin Text | English Translation |
| 1 | Marrucine Asini, manu sinistra | Marrucinus Asinius, you do not use becomingly |
| 2 | non belle uteris: in ioco atque vino | your left hand: in jest and wine |
| 3 | tollis lintea neglegentiorum. | you carry away the napkins of the more careless. |
| 4 | Hoc salsum esse putas? Fugit te, inepte: | Do you think this is witty? You're crazy, foolish man: |
| 5 | quamvis sordida res et invenusta est. | it is a thing ever so mean and inelegant. |
| 6 | Non credis mihi? Crede Pollioni | You don't believe me? Believe Pollio |
| 7 | fratri, qui tua furta vel talento | your brother, who would have your thefts |
| 8 | mutari velit: est enim leporum | exchanged even for a talent: for he is |
| 9 | differtus puer ac facetiarum. | boy stuffed full of charms and wit. |
| 10 | Quare aut hendecasyllabos trecentos | Therefore either expect three hundred hendecasyllables |
| 11 | exspecta, aut mihi linteum remitte, | or send back my napkin to me, |
| 12 | quod me non movet aestimatione, | which does not move me by its value, |
| 13 | verum est mnemosynum mei sodalis. | but is a remembrance of my comrade. |
| 14 | Nam sudaria Saetaba ex Hiberis | For Saetabian napkins from Spain |
| 15 | miserunt mihi muneri Fabullus | Fabullus and Veranius sent to me |
| 16 | et Veranius: haec amem necesse est | as a gift: it is necessary that I love these things |
| 17 | ut Veraniolum meum et Fabullum. | just as I love my dear Veranius and Fabullus. |

## External Links

* Catullus 12 A Translation of Catullus 12
* Catullus 12 Another Translation of Catullus 12
# External Links

* Catullus 115 A Translation of Catullus 115
* Catullus 115 Another Translation of Catullus 115
# External Links

* Catullus 116 A Translation of Catullus 116
* Catullus 116 Another Translation of Catullus 116
# The Poetry of Gaius Valerius Catullus/113
## Text and Translation

Meters - Elegiac couplets
| Line | Latin Text | English Translation |
| 1 | Consule Pompeio primum duo, Cinna, solebant | In Pompey's first consulship, Cinna, |
| 2 | Maeciliam: facto consule nunc iterum | two men frequented Maecilia: now appointed consul again, |
| 3 | manserunt duo, sed creverunt milia in unum | the two have remained, but against each one a thousand have grown. |
| 4 | singula. Fecundum semen adulterio. | The seed of adultery is fertile. |

## Translation notes
### Line 1

* Consule Pomeio primum: the year of the first consulship of Gnaeus Pompeius Magnus, 70 B.C.
* Solebant: soleo, meaning "to be used to" or "to be wont", here used euphemistically

### Line 2

* Maeciliam: A well-known Roman name. Possibly a misspelling of Mucillam, a diminutive of Mucia, and therefore a possible reference to Mucia Tertia, the daughter of Quintus Mucius Scaevola and the third wife of Pompey; she was divorced by the latter on accusations of adultery.
* facto consule nunc iterum: the year of Pompey's second consulship, 55 B.C.

### Line 3

* cereverunt milia in unum/singula: a thousand (rivals) have sprung up against each man, the implication being that between the consulships, Maecilia's lovers have grown from two to two thousand.

### Line 4

* adulterio: dative of possession; est is omitted
# External Links

* Catullus 111 A Translation of Catullus 111
* Catullus 111 Another Translation of Catullus 111
# The Poetry of Gaius Valerius Catullus/112/112A
## Text & Translation

| Line | Latin Text | English Translation |
| 1 | Multus homo es, Naso, neque tecum multus homo est quin | You are a big man, Naso, but it's not a big man the one |
| 2 | te scindat: Naso, multus es et pathicus. | who splits you: Naso, you are big man and a catamite. |

## External Links

* Catullus 112 A Translation of Catullus 112
* Catullus 112 Another Translation of Catullus 112
# United Nations History/League Attacked

← League Formed | UN Formed →

## Overview

The League lacked its own armed force and so depended on the Great Powers to enforce its resolutions, keep to economic sanctions which the League ordered, or provide an army, when needed, for the League to use. However, they were often reluctant to do so. Benito Mussolini stated that "The League is very well when sparrows shout, but no good at all when eagles fall out."

## Article X of the League of Nations (1919)

"The Members of the League undertake to respect and preserve as against external aggression the territorial integrity and existing political independence of all Members of the League. In case of any such aggression or in case of any threat or danger of such aggression the Council shall advise upon the means by which this obligation shall be fulfilled."
Because of these provisions, the United States Senate decided to not ratify the League's Charter.

## Anit-Moderni

The League was attacked as being a conspiracy to bring in the One World Government, the Anti-Christ (the supposed "King of the Jews", and set up world wide Judaism. It was also claimed to be Masonic and Nihilistic.

## Chaco War

The League failed to prevent the Chaco War between Bolivia and Paraguay in 1932 over the arid Gran Chaco region of South America. Although the region was sparsely populated, it gave control of the Paraguay River which would have given one of the two landlocked countries access to the Atlantic Ocean, and there was also speculation, later proved incorrect, that the Chaco would be a rich source of petroleum. Border skirmishes throughout the late 1920s culminated in an all-out war in 1932, when the Bolivian army, following the orders of President Daniel Salamanca Urey, attacked a Paraguayan garrison at Vanguardia. Paraguay appealed to the League of Nations, but the League did not take action when the Pan-American conference offered to mediate instead.
The war was a disaster for both sides, causing 100,000 casualties and bringing both countries to the brink of economic disaster. By the time a ceasefire was negotiated on 12 June 1935, Paraguay had seized control over most of the region. This was recognized in a 1938 truce by which Paraguay was awarded three-quarters of the Chaco Boreal.
# United Nations History/Gladwyn Jebb

← UN Formed | Trygve Lie →

## Gladwyn Jebb

Hubert Miles Gladwyn Jebb, 1st Baron Gladwyn, GCMG, GCVO, CB, known as Gladwyn Jebb (April 25, 1900 – October 24, 1996), was a prominent British civil servant, diplomat and politician as well as the first Acting Secretary-General of the United Nations.

## Diplomatic Service

Entering the Diplomatic Service, in 1924, Jebb's career included: served in Tehran [Iran], Rome [Italy], and the Foreign Office; Private Secretary to Parliamentary Under-Secretary of State, 1929-31; Private Secretary to Permanent Under-Secretary of State, 1937-40; appointed to Ministry of Economic Warfare with temporary rank of Assistant Under-Secretary, August 1940; Acting Counsellor in Foreign Office, 1941; Head of Reconstruction Department, 1942; Counsellor, 1943, in that capacity attended the Conferences of Quebec [Canada], Cairo [Egypt], Tehran, Dumbarton Oaks [United States], Yalta [Soviet Union], San Francisco and Potsdam [Germany]; Executive Secretary of Preparatory Commission of the United Nations (August 1945) with temp. rank of Minister; Acting Secretary-General of UN, February 1946; Deputy to Foreign Secretary on Conference of Foreign Ministers, March 1946; Assistant Under-Secretary of State and United Nations Adviser, 1946-47; UK representative on Brussels Treaty Permanent Commission with personal rank of Ambassador, April 1948; Deputy Under-Secretary, 1949-50; Permanent Representative of the UK to the United Nations, 1950-54; British Ambassador to France, 1954-60, retired; Deputy Leader of Liberal Party in House of Lords, and Liberal Spokesman on foreign affairs and defence, 1965-88; Member, European Parliament, 1973-76 (Vice President, Political Committee); contested (L) Suffolk, European Parliament, 1979.

## Association with Churchill

Gladwyn Jebb was at Munich with Chamberlain, at Yalta and Potsdam with Churchill. His contribution to the establishment of the United Nations and NATO was sufficient on its own to have made him a major figure of the twentieth century. He was Britain's representative at the UN during the Korean War, our ambassador in Paris during the Suez crisis and he played a crucial part in Britain's first attempt to join the Common Market, famously vetoed by de Gaulle.

## Establishing the UN

The first meetings of the United Nations were held in London, before its move to New York. The first session of the General Assembly was held in Central Hall Westminster on 10 January 1946. With British diplomat Gladwyn Jebb (later Lord Gladwyn) acting as Secretary-General the United Nations was duly inaugurated, and the first General Assembly President and Secretary-General elected. One week later the Security Council met for the first time, in Church House, Westminster, with the Soviet presence in Iran immediately on the agenda. In 1947 two dedicated divisions were set up within the Foreign Office to handle United Nations issues, covering political and economic aspects respectively.
# UMD Analysis Qualifying Exam/Aug12 Complex
## Problem 4

* Suppose $h(z)$ is holomorphic on a region containing the disk $\{|z|\leq R\}$ and that $|h(z)|<R$ if $|z|=R$. How many solutions does the equation $h(z)=z$ have in the disc $\{|z|\leq R\}$? Justify your answer.

### Solution 4

We know $|h(z)|=|h(z)-z+z|<R$ on $|z|=R$. Similarly, since $|h(z)-z|\geq 0$ then $|h(z)-z|+|z|\geq R$ on $|z|=R$. This gives $|h(z)-z+z|<R\leq |h(z)-z|+|z|$ on $z=R$.
So by Rouché's theorem, since both functions are holomorphic (i.e. have no poles), then $h(z)-z$ has the same number of zeros as $z$ on the domain $|z|<R$. Since $z$ has only one zero (namely 0), then there is only one solution to $h(z)=z$ inside the open disc $|z|<R$.
Observe that $h(z)\neq z$ for any $|z|=R$, since that would imply $|h(z)|=R$ for some $z$ on the boundary, contradicting the hypothesis.
Thus, there is only one solution to $h(z)=z$ inside the open disc $|z|\leq R$.
# UMD Analysis Qualifying Exam/Aug05 Real
## Problem 1

* Let $f$ be a bounded measurable function on $R$ for which there is a constant $C$ such that
* $\forall \epsilon >0,m(x\in R:|f|>\epsilon )<C/{\sqrt {\epsilon }}$
* Show that $f\in L^{1}(R)$.

## Solution 1

We will consider two different regions: {x:|f(x)|>1} and {x:|f(x)|<=1}, then show that the integrals of f over these regions are both finite. Since f is bounded by M, we can use the assumption that m(x:|f(x)|>1) < C/1, and the first integral is this bounded by MC.
For the second integral, consider the set E$_n$={x:|f(x)|<1/n}. By assumption, m(E$_n$)<C*n$^{1/2}$. For n>m, E$_n$ clearly contains E$_m$, so we can take the sets S$_n$=E$_{n+1}$\E$_n$, which is then {x:1/(n+1)<|f(x)|<=1/n}. Using the set containment, we can also produce a bound on m(S$_n$). The measure of S$_n$ can be larger than C*(n+1)$^{1/2}$-C*n$^{1/2}$ (up to C*(n+1)$^{1/2}$), but this extra mass can only be acquired at the expense of m(E$_n$), and would thus reduce the integral of |f|. Since we are interested in maximizing this integral and proving that this maximum is finite, a bound of C*(n+1)$^{1/2}$-C*n$^{1/2}$ is justified (ie this is the worst case, with each subsequent E$_n$ of maximum possible size as 1/n goes to zero).
This gives the integral an upper bound of the sum as n goes from 1 to infinity of (C*(n+1)$^{1/2}$-C*n$^{1/2}$)/n (by m(S$_n$)*(upper bound of |f| on S$_n$)). By comparing consecutive terms, we get the sum of C*n$^{1/2}$*(1/(n-1) - 1/n), for n = 2 to infinity, with a finite term at n=1. After computing the subtraction, each term becomes C*n$^{1/2}$/(n*(n-1)), which is of order C/n$^{3/2}$. Hence the sum converges, and gives us an upper bound for the integral.
Note: the argument for the size of S$_n$ is correct, but can definitely be expressed better.
# Waves/Group Velocity

Waves : 1 Dimensional Waves 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 Examples - Problems - Solutions - Terminology

### Group Velocity

We now ask the following question: How fast do wave packets move? Surprisingly, we often find that wave packets move at a speed very different from the phase speed, $c=\omega /k$, of the wave composing the wave packet.
We shall find that the speed of motion of wave packets, referred to as the group velocity, is given by
    $u=\ 0.1{\mbox{m}}^{-1}$. The phase speed of deep ocean waves is $c=(g/k)^{1/2}$. However, since $c\equiv \omega /k$, we find the frequency of deep ocean waves to be $\omega =(gk)^{1/2}$. The group velocity is therefore $u\equiv d\omega /dk=(g/k)^{1/2}/2=c/2$. For the specified central wavenumber, we find that $u\approx (9.8{\mbox{ m}}{\mbox{ s}}^{-2}/0.1{\mbox{ m}}^{-1})^{1/2}/2\approx 5{\mbox{ m}}{\mbox{ s}}^{-1}$. By contrast, the phase speed of deep ocean waves with this wavelength is $c\approx 10{\mbox{ m}}{\mbox{ s}}^{-1}$.
Dispersive waves are waves in which the phase speed varies with wavenumber. It is easy to show that dispersive waves have unequal phase and group velocities, while these velocities are equal for non-dispersive waves.

### Derivation of Group Velocity Formula

We now derive equation (1.36). It is easiest to do this for the simplest wave packets, namely those constructed out of the superposition of just two sine waves. We will proceed by adding two waves with full space and time dependence:
    $A=\sin(k_{1}x-\omega _{1}t)+\sin(k_{2}x-\omega _{2}t)$ (2.37)
After algebraic and trigonometric manipulations familiar from earlier sections, we find
    $A=2\sin(k_{0}x-\omega _{0}t)\cos(\Delta kx-\Delta \omega t),$ (2.38)
where as before we have $k_{0}=(k_{1}+k_{2})/2$, $\omega _{0}=(\omega _{1}+\omega _{2})/2$, $\Delta k=(k_{2}-k_{1})/2$, and $\Delta \omega =(\omega _{2}-\omega _{1})/2$. Again think of this as a sine wave of frequency $\omega _{0}$ and wavenumber $k_{0}$ modulated by a cosine function. In this case the modulation pattern moves with a speed so as to keep the argument of the cosine function constant:
    $\Delta kx-\Delta \omega t=const.$ (2.39)
Differentiating this with respect to $t$ while holding $\Delta k$ and $\Delta \omega$ constant yields
    $u\equiv {\frac {dx}{dt}}={\frac {\Delta \omega }{\Delta k}}.$ (2.40)
In the limit in which the deltas become very small, this reduces to the derivative
    $u={\frac {d\omega }{dk}},$ (2.41)
which is the desired result.
Waves : 1 Dimensional Waves 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 Examples - Problems - Solutions - Terminology
# Waves/Interferometers

Waves : 1 Dimensional Waves 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 Examples - Problems - Solutions - Terminology

### Interferometers

An interferometer is a device which splits a beam of light into two sub-beams, shifts the phase of one sub-beam with respect to the other, and then superimposes the sub-beams so that they interfere constructively or destructively, depending on the magnitude of the phase shift between them. In this section we study the Michelson interferometer and interferometric effects in thin films.

#### The Michelson Interferometer

The American physicist Albert Michelson invented the optical interferometer illustrated in figure 1.13. The incoming beam is split into two beams by the half-silvered mirror. Each sub-beam reflects off of another mirror which returns it to the half-silvered mirror, where the two sub-beams recombine as shown. One of the reflecting mirrors is movable by a sensitive micrometer device, allowing the path length of the corresponding sub-beam, and hence the phase relationship between the two sub-beams, to be altered. As figure 1.13 shows, the difference in path length between the two sub-beams is $2x$ because the horizontal sub-beam traverses the path twice. Thus, constructive interference occurs when this path difference is an integral number of wavelengths, i. e.,
    $2x=m\lambda ,~~m=0,\pm 1,\pm 2,\ldots \quad {\mbox{(Michelson interferometer)}}$ (2.22)
where $\lambda$ is the wavelength of the light and $m$ is an integer. Note that $m$ is the number of wavelengths that fits evenly into the distance $2x$.
Waves : 1 Dimensional Waves 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 Examples - Problems - Solutions - Terminology
# Waves/Light

Waves : 1 Dimensional Waves 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 Examples - Problems - Solutions - Terminology

#### Light

Light moves in a vacuum at a speed of $c_{vac}=3\times 10^{8}{\mbox{ m}}{\mbox{ s}}^{-1}$. In transparent materials it moves at a speed less than $c_{vac}$ by a factor $n$ which is called the refractive index of the material:
    $c=c_{vac}/n.$
Often the refractive index takes the form
    $n^{2}\approx 1+{\frac {A}{1-(k/k_{R})^{2}}},$
where $k$ is the wavenumber and $k_{R}$ and $A$ are constants characteristic of the material. The angular frequency of light in a transparent medium is thus
    $\omega =kc={\frac {kc_{vac}}{n}}\approx {\frac {kc_{vac}}{\sqrt {1+A}}}(1+{\frac {1}{2}}{\frac {A}{1+A}}{\frac {k^{2}}{k_{R}^{2}}})$
so the frequency increases slightly with increasing k. Typically, when k is near k$_R$, the material becomes opaque.
Ultimately, this is due to resonance between the light and the atoms of the materials.
Waves : 1 Dimensional Waves 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 Examples - Problems - Solutions - Terminology