OpenLLM-France/wikimedia huggingface dataset:
# Guide to Non-linear Dynamics in Accelerator Physics/Linear Motion

This chapter provides tools to describe linear motions

## Linear dynamics of a single particle

For the case of linear dynamics, the motion can be represented by a 2N x 2N matrix. This matrix maps phase space points into phase space points. Let us represent the initial phase space point by ${\vec {z}}_{0}$. The transformation can then be represented by
${\vec {z}}=M{\vec {z}}_{0}$.
The matrix $M$ will be symplectic. This means that
$M^{T}JM=J$
where
$J=\left({\begin{matrix}0&1&0&0&0&0\\-1&0&0&0&0&0\\0&0&0&1&0&0\\0&0&-1&0&0&0\\0&0&0&0&0&1\\0&0&0&0&-1&0\end{matrix}}\right)$.
Now, in quantum mechanics, we typically deal with Hermitian operators. These can be diagonalized by orthogonal matrices. With symplectic matrices, we can diagonalize the matrix, but here the transformation matrix will be symplectic. To do this, we find the eigenvectors of M. Let us label these as $v_{\pm 1,\pm 2,\pm 3}$ The positive and negative eigenmodes are related to each other by
$v_{-k}=iv_{k}^{*}$
We can define the normalization by defining an upper indexed vector
$v^{j}=-i{\rm {sgn}}(j)v_{j}^{*}$
Then we find the normalization condition
$v^{j}v_{k}=\delta _{jk}$
The matrix of eigenvectors
$U=(v_{1}\ v_{-1}v_{2}\ v_{-2}\ v_{3}\ v_{-3})$
is symplectic. The invariants are given in terms of the eigenvectors as
$G_{a}=-J(v_{a}v_{a}^{\dagger }+v_{a}^{*}v_{a}^{T})J$

## Linear Motion in terms of Lie operators

We may also describe the one turn map as an operator on x and p. Let us consider the rotation matrix ${\begin{pmatrix}x\\p\end{pmatrix}}={\begin{pmatrix}cos\mu &\sin \mu \\-\sin \mu &\cos \mu \end{pmatrix}}{\begin{pmatrix}x_{0}\\p_{0}\end{pmatrix}}$ We may represent this in terms of functions by the Lie operator $R=e^{{\frac {\mu }{2}}:x^{2}+p^{2}:}$ This operator acts on the functions x and p in the following way $Rx=\cos \mu x-\sin \mu p$ and $Rp=\sin \mu p+\cos \mu x$ The eigenfunctions of R are given by $h_{\pm }=x\mp ip$ with $Rh_{\pm }=e^{\pm i\mu }h_{\pm }$. $h_{\pm }$ are sometimes referred to as the resonance basis. In the non-linear problems, we will need to compute various operators built out the linear operator. Expanding in terms of the resonance basis will allow us to do these calculations.

## 2-D phase space

Here the one turn map is a 2 x 2 matrix with determinant 1. We can parametrize it by
$M_{x}=I\cos \mu +J_{x}\sin \mu$
where
$J_{x}=\left({\begin{matrix}\alpha &\beta \\-\gamma &-\alpha \end{matrix}}\right)$
# Guide to Photographic Gear/Table of Contents
## About

This Wikibook, titled "Guide to Photographic Gear", is aimed at being an in-depth guide to choosing photographic gear. We cover lenses and cameras, DSLRs and mirrorless, and everything in between. If you want to edit this book, sign your name in the "Editors" section below and take a look at the general structure of the book before you begin.

## Editors

If you want to be an editor, sign your name below by typing 4 tildes (~).
* WBK Lin (discuss • contribs) 05:35, 29 July 2020 (UTC)

## Table of Contents
### Introduction

* Introduction
* A Note on Brands
* Gear Acquisition Syndrome
* Choosing Cameras
* Choosing Lenses

### Canon

* Introduction to Canon
* Canon DSLR
* Canon Mirrorless
* Canon Point-and-Shoot
* Canon DSLR Lenses
* Canon Mirrorless Lenses
# Guide to Photographic Gear/Table of Contents/Choosing Cameras
## Choosing Cameras

The first step to get into photography is to choose a camera type, a camera system, and then a camera. There are three main types of cameras in photography:
* Point-and-Shoot: no professional photographer really uses these. Point-and-Shoot cameras are very limited in terms of lenses and gear.
* Digital SLR: a DSLR (or Digital SLR, Digital Single Lens Reflex) camera is the most popular choice for photographers. It combines the variety of an SLR to the ease of a digital sensor. However, DSLRs are very bulky and complex, so it is a bit more vulnerable to breakage.
* SLR: an SLR (or Single Lens Reflex) camera is a DSLR without the digital sensor. Instead, it uses a roll of film. This is what photographers used to use. An SLR, however, needs to process the film before you can see the image, so it is always less convenient than other cameras.
* Mirrorless: more and more photographers are getting attracted to mirrorless cameras these days. Mirrorless cameras are much lighter and smaller than DSLRs, have no complicated mirror system inside, and have a great viewfinder system that allows you to "see" changes. However, mirrorless cameras autofocus systems do seem to be worse than DSLRs, and their color and dynamic range do seem to be worse as well. However, these changes can often be corrected in post-processing, and many brands seem to have no issue with this at all.
After you have chosen your type of camera, it is time to choose a system (a brand). Below is a chart for various types of cameras and manufacturers.
Camera Brands :
| DSLR | SLR | Point-and-Shoot | Mirrorless |
| Canon | Pentax | Canon | Fujifilm |
| Nikon | Hasselblad | Nikon | Sony |
| Pentax | Leica | Fujifilm | Panasonic |
| Leica | Fujifilm | Panasonic | Canon |
| Sigma | Sony | Olympus | Hasselblad |
| Olympus | Panasonic | Sigma | Leica |
| | | | Nikon |
| | | | Sigma |
After you have chosen a brand, go to each brand's section in this book to choose cameras (and then choose lenses).
# Guide to Photographic Gear/Table of Contents/A Note on Brands
## A Note on Brands

If you read our Table of Contents, then you may have seen a very long list of brands. First of all, let me say this to you: this book is not biased in any way towards any specific brand. We will list pros and cons for each brand, but they are not influenced by any outside sources. In the end, it is up to you to decide which brand you want to go for.
There are two types of brands in this book. One kind sells cameras and lenses, and the other is a third-party focused only at selling lenses. We will cover both of them in this book.
# Guide to Photographic Gear/Table of Contents/Canon DSLR
## Recommendations

Here are my recommendations for Canon DSLRs. Check below if you fit each condition, and look under each heading for the suggested camera.

### If you are...

A beginning photographer who wants to expand and budget is of concern, consider the Canon EOS Rebel T7i.
A beginning photographer who just wants to play around and budget is of concern, consider the Canon EOS Rebel T6i.
A beginning photographer who wants to expand and budget is not of concern, consider the Canon EOS Rebel T8i.
An intermediate photographer who wants to explore more options and budget is of concern, consider the Canon EOS 80D.
An intermediate photographer who wants to explore more options and budget is not of concern, consider the Canon EOS 90D.
An intermediate photographer who wants to be an advanced photographer and budget is not of concern, consider the Canon EOS 5D Mark II.
An advanced photographer who wants to get the best value for his money, consider the Canon EOS 5D Mark IV.
An advanced photographer who wants to have the best Canon DSLR but still has a concern of budget, consider the Canon EOS 7D Mark II.
An advanced photographer who wants to grow, explore more options, and get the most feature-packed camera, consider the Canon EOS-1D X Mark III.
# Guitar/Guitar Chords Song Library/Movie songs

The following is a list of notable easy to learn movie songs to be played on the guitar. Some of the items link to the different informal chords to specific songs which represent many different authors' own interpretations of the original songs. Most of the chords on the list are relatively easy to learn, and would be a great start for novice guitar players whom are interested in improving their playing abilities.
The technical difficulty and skill level required to play each of the songs is defined with a star rating system:
* - Easy Songs
* - Intermediate Songs
* - Difficult Songs
2010s Adele - Skyfall
2000s The 5,6,7,8's - Woo Hoo
Counting Crows - Accidentally in Love
Enya - May It Be
Gary Jules - Mad World
Smash Mouth - All Star
1990s Aerosmith - I Don't Want to Miss a Thing
Whitney Houston - I Will Always Love You
Celine Dion - My Heart Will Go On
Bryan Adams - (Everything I Do) I Do It For You
Elton John - Circle of Life
Elton John - Can You Feel the Love Tonight
Peabo Bryson & Regina Belle - A Whole New World
Randy Newman - You've Got A Friend In Me
1980s Survivor - Eye Of The Tiger
Berlin - Take My Breath Away
Huey Lewis and the News - The Power Of Love
Don Felder - Heavy Metal (Takin' A Ride)
1970s Monty Python - Always Look on the Bright Side of Life
North Star Camp Kids Chorus - Are You Ready for the Summer
1960s Ennio Morricone - The Good The Bad And The Ugly
1950s Doris Day - Que Sera, Sera (Whatever Will Be, Will Be)
1930s Judy Garland - Somewhere Over The Rainbow

## See also

* Guitar/Guitar Chords Song Library
# Guitar/Guitar Chords Song Library

The following is a list of notable easy to learn guitar songs from the 1950s to the present. Some of the items link to the different informal chords to specific songs which represent many different authors' own interpretations of the original songs. Most of the chords on the list are relatively easy to learn, and would be a great start for novice guitar players who are interested in improving their playing abilities.
The technical difficulty and skill level required to play each of the songs is defined with a star rating system:
* - Easy Song
* - Intermediate Song
* - Difficult Song
| 2010s | 2000s | 1990s |
| Main article: Chords cheat sheet of 2010s songs |

## Additional Chords by Special Themes

| Holiday songs | Children's songs | Movie songs | TV Theme songs | Dance/Electronic songs |
# Guitar/Guitar Chords Song Library/Dance-Electronic songs

The following is a list of notable easy to learn Dance/Electronic songs (mostly Euro-House/Euro-Dance and House songs) to be played on the guitar. Some of the items link to the different informal chords to specific songs which represent many different authors' own interpretations of the original songs. Most of the chords on the list are relatively easy to learn, and would be a great start for novice guitar players whom are interested in improving their playing abilities.
The technical difficulty and skill level required to play each of the songs is defined with a star rating system:
* - Easy Songs
* - Intermediate Songs
* - Difficult Songs
| 2010s | 2000s | 1990s |
| Avicii - Levels David Guetta featuring Sia - Titanium Rihanna - We Found Love | The Black Eyed Peas - I Gotta Feeling Gigi D’Agostino – I'll Fly With You (L’Amour Toujours) David Guetta – Love Don't Let Me Go Kristine W – Save My Soul LMC vs. U2 – Take Me To The Clouds Above Modjo – Lady (Hear Me Tonight) Planet Funk – Chase The Sun Röyksopp – Remind Me Elvis Presley vs. JXL - A Little Less Conversation Kate Ryan - Voyage Voyage (remix to Desireless song) | Cornershop - Brimful Of Asha N-Trance – Set You Free 2 Brothers on the 4th Floor – Dreams (Will Come Alive) Pet Shop Boys - Go West Alice Deejay – Back In My Life Cabballero – Dancing With Tears In My Eyes Corona – Rhythm Of The Night DJ Jurgen – Better Off Alone Double You & Alexia – Dancing With An Angel Dr. Alban – Sing Hallelujah! Fatboy Slim – Praise You Haddaway - What Is Love? Onda del Futuro – Terra Playahitty – The Summer Is Magic Sash! – Stay |

## See also

* Guitar/Guitar Chords Song Library
# Guitar/Guitar chords cheat sheet of popular songs from the 1960s

The following is a list of notable easy to learn guitar songs from the 1960s. These are informal chords to songs which represent many different authors' own interpretations of the original songs. Most of the chords on the list are relatively easy to learn, and would be a great start for novice guitar players who are interested in improving their playing abilities.
The technical difficulty and skill level required to play each of the songs is defined with a star rating system:
* - Easy Song
* - Intermediate Song
* - Difficult Song
Ben E. King - Stand By Me
Betty Everett - The Shoop Shoop Song (It's in His Kiss)
Buffalo Springfield - For What It's Worth
Chubby Checker - Let's Twist Again
The Chiffons - One Fine Day
David Bowie - Space Oddity
Elvis Presley - Can't Help Falling In Love
Jimi Hendrix - Hey Joe
Joe Cocker - With a Little Help from My Friends
Johnny Cash - Ring Of Fire
Johnny Rivers - Secret Agent Man
Little Eva - The Locomotion
Louis Armstrong - What a Wonderful World
The Mamas & the Papas - California Dreamin'
The Monkees - Daydream Believer
The Monkees - I'm A Believer
Marmalade - Reflections of my Life
Petula Clark - Downtown
Ralph McTell - Streets Of London
Sam Cooke - Wonderful World
Scott McKenzie - San Francisco
Shocking Blue - Venus
Simon & Garfunkel - Mrs. Robinson
Simon & Garfunkel - The Sounds of Silence
Skeeter Davis - End of the World
Sonny & Cher - The Beat Goes On
Strawberry Alarm Clock - Incense and Peppermints
The Animals - Don't Let Me Be Misunderstood
The Animals - The House of the Rising Sun
The Beach Boys - Good Vibrations
The Beach Boys - I Get Around
The Beach Boys - Surfin' USA
The Beatles - All You Need Is Love
The Beatles - Eight Days A Week
The Beatles - Help!
The Beatles - Here Come the Sun
The Beatles - Let it Be
The Beatles - Love Me Do
The Beatles - While My Guitar Gently Weeps
The Beatles - Yellow Submarine
The Beatles - Yesterday
The Byrds - Turn! Turn! Turn!
The Crystals - Da Doo Ron Ron
The Moody Blues - Nights in White Satin
The Righteous Brothers - Unchained Melody
The Rolling Stones - Angie
The Rolling Stones – Everybody Needs Somebody to Love
The Rolling Stones - Wild Horses
The Rolling Stones - You Can't Always Get What You Want
The Shadows - Apache
The Shirelles - Will You Love Me Tomorrow
The Supremes - You Can't Hurry Love
The Surfaris - Wipe Out
The Temptations - My Girl
The Troggs - Love is all Around
The Turtles - You Showed Me
The Wallace Collection - Daydream
Van Morrison - Brown Eyed Girl

## See also

* Guitar/Guitar Chords Song Library
# Guitar/Guitar chords cheat sheet of popular songs from the 1970s

The following is a list of notable easy to learn guitar songs from the 1970s. These are informal chords to songs which represent many different authors' own interpretations of the original songs. Most of the chords on the list are relatively easy to learn, and would be a great start for novice guitar players who are interested in improving their playing abilities.
The technical difficulty and skill level required to play each of the songs is defined with a star rating system:
* - Easy Song
* - Intermediate Song
* - Difficult Song
10cc - I'm Not in Love
America - A Horse With No Name
America - Sister Golden Hair
Bachman-Turner Overdrive - You Ain't Seen Nothing Yet
Black Sabbath - Paranoid
Blue Öyster Cult - (Don't Fear) The Reaper
Bob Marley & The Wailers - No Woman, No Cry
Bob Dylan - Knocking on Heaven’s Door
Bob Seger - We've Got Tonight
Boney M - Sunny
Boney M - Rasputin
Boston - Peace of Mind
Boston - Rock and Roll Band
The Buggles - Video Killed the Radio Star
Cat Stevens - Father And Son
Cat Stevens - Wild World
CCR - I Heard It Through the Grapevine
Cheap Trick - I Want You to Want Me
Don Mclean - American Pie
Don Mclean - Vincent
Elton John - Your Song
Eric Carmen - All by Myself
Eric Clapton - Layla
Eric Clapton - Wonderful Tonight
Iggy Pop - The Passenger
King Harvest - Dancing in the Moonlight
Gerry Rafferty - Baker Street
John Lennon - Imagine
Johnny Nash - I Can See Clearly Now
Led Zeppelin - Stairway to Heaven
Lou Reed - Walk on the Wild Side
Lynyrd Skynyrd - Free Bird
Lynyrd Skynyrd - Sweet Home Alabama
Peter Frampton - Baby, I Love Your Way
Pink Floyd - Comfortably Numb
Pink Floyd - Wish You Were Here
Queen - Crazy Little Thing Called Love
Queen - Fat Bottomed Girls
Rare Bird - Sympathy
Roberta Flack - Killing Me Softly with His Song
Scorpions - Always Somewhere
Smokie - Living Next Door to Alice
Sniff ‘N’ The Tears - Driver's Seat
Steve Harley & Cockney Rebel - Make Me Smile
Steve Miller Band - Jungle Love
Steve Miller Band - Rock'n Me
Supertramp - Breakfast in America
Talking Heads - Psycho Killer
The Undertones - Teenage Kicks
The Doors - Riders on the storm
The Eagles - Hotel California
The Four Seasons - December, 1963 (Oh, What a Night)
The Steve Miller Band - Fly Like an Eagle
The Who - Baba O'Riley
The Who - Behind Blue Eyes
The Who - The Seeker
The Who - Won't Get Fooled Again
Van Halen - You Really Got Me

## See also

* Guitar/Guitar Chords Song Library
# Guitar/Guitar Tabs Song Library

Almost as soon as you start playing guitar, you will learn a handful of songs or riffs. But often after a while, you can't think anything new or interesting to play. Learning songs can be tough, but thinking of songs to learn can be even tougher. This page aims to simplify things, by providing a list of songs, and perhaps a tip or two for learning.
* Easy songs are songs that are played mostly with open chords, or involve uncomplicated riffs higher up on the neck. Easy song, difficult solos are those that have very challenging solos.
* Intermediate songs are songs that a beginner would find challenging, but an experienced guitarist should be able to pick up quickly. Generally the songs involve faster chord changes or difficult riffs.
* Difficult songs are songs that experienced players have a little trouble with. Beginners would likely be unable to play these songs because they have not yet developed their skill and coordination with their hands, but they do make excellent goals.
* Impossible songs are songs that make expert players scratch their head. They are extremely complicated, take lots of practice to play and require a high level of playing ability. These are the songs that make people say "Maybe one day I'll be able to play that."
Songs are organized alphabetically by band name or artist last name, then song title. Include non-standard tunings and any other important information. Please only list popular musicians (but not necessarily popular songs!), and please only list specific songs. Do not be tempted to include "Everything by Band X/Artist Y", because certainly not every single song they have recorded requires the same level of skill.

## Easy Songs

The White Stripes - Seven Nation Army
# Guitar/Guitar Chords Song Library/Holiday songs

The following is a list of notable easy to learn Holiday songs to be played on the guitar. Some of the items link to the different informal chords to specific songs which represent many different authors' own interpretations of the original songs. Most of the chords on the list are relatively easy to learn, and would be a great start for novice guitar players whom are interested in improving their playing abilities.
The technical difficulty and skill level required to play each of the songs is defined with a star rating system:
* - Easy Songs
* - Intermediate Songs
* - Difficult Songs

## Christmas

| Feliz Navidad Frosty the snow man John Lennon – Happy Xmas (War is Over) Frank Sinatra & Bing Crosby – Have yourself a Merry little Christmas Perry Como – It's beginning to look like Christmas Jingle bells Bing Crosby – Jinge bell rock Wham! – Last Christmas Martina McBride – Let it snow The Eagles – Please come home for Christmas | Rockin' around the Christmas Tree Rudolph the red-nosed reindeer Santa Claus is coming to town Silent Night Sleighride The Chipmunk song We wish you a merry Christmas White Christmas Winter wonderland |

## Birthday

* Happy Birthday To You
* The Beatles - Birthday

## Halloween

* Monstermash
* I Put a Spell on You
* Witch Doctor
* Ghostbusters (Capo 3)

## See also

* Guitar/Guitar Chords Song Library
# Guitar/Guitar Chords Song Library/TV Theme songs

The following is a list of notable easy to learn TV Theme songs to be played on the guitar. Some of the items link to the different informal chords to specific songs which represent many different authors' own interpretations of the original songs. Most of the chords on the list are relatively easy to learn, and would be a great start for novice guitar players whom are interested in improving their playing abilities.
The technical difficulty and skill level required to play each of the songs is defined with a star rating system:
* - Easy Songs
* - Intermediate Songs
* - Difficult Songs
2000s The Friendly Indians - I Know You Know (Psych theme)
Barenaked Ladies - The History of Everything (The Big Bang Theory theme)
1990s The Rembrandts - I'll Be There For You (Friends theme)
Jimi Jamison - I'm Always Here (Baywatch theme)
Vonda Shepard - Searchin' My Soul (Ally McBeal theme)
Beverly Hills, 90210 theme]
1980s Gary Portnoy - Where Everybody Knows Your Name (Cheers theme)
Jesse Frederick - Everywhere You Look (Full House theme)
Joey Scarbury - Believe It or Not (The Greatest American Hero theme)
Jan Hammer - Crockett's Theme (Miami Vice theme)
1970s The Mash - Suicide Is Painless (M*A*S*H theme)

## See also

* Guitar/Guitar Chords Song Library
# How To Tie A Tie/General Tips

* Check for symmetry. Adjust the knot so that you achieve optimal bilateral symmetry. Re-tie or upgrade to the Windsor if necessary. A slightly leaning knot can be wriggled with so it looks OK, but a seriously cockeyed knot will have the tie falling down your lapel and just look terrible. There are exceptions to this rule. Some knots are meant to be asymmetrical (often worn in Italy, for example).
* Keep it tight. A properly tied tie will, unfortunately for the wearer, need to be pulled extremely tight against the neck. A tie too loose may convey unprofessionalism.
* The Vicious V. According to the film, Outside Providence, a properly tied tie must possess the Vicious V. This is the sharp V formed by the scruching of the tie where it exits the knot.
* For the tall. Tall people will find that the knot sometimes will end up way "up" on the tie where it is narrow resulting in a small unflattering knot. You may want to look for specially made ties for tall people that will solve this problem.
* Be sure to dimple. Where the wider end of the tie exits the bottom of the knot there should be a clean symmetrical dimple.
* Untie your tie. Untie your tie after you are through wearing it, also untie it the same way you tied it. Your tie will last longer.