text:
## Linear Algebra and Its Applications, Exercise 3.4.23

Exercise 3.4.23. Given the step function $y$ with $y(x) = 1$ for $0 \le x \le \pi$ and $y(x) = 0$ for $\pi < x < 2\pi$, find the following Fourier coefficients:

$a_0 = \frac{(y, 1)}{(1, 1)} \qquad a_1 = \frac{(y, \cos x)}{(\cos x, \cos x)} \qquad b_1 = \frac{(y, \sin x)}{(\sin x, \sin x)}$

Answer: For $a_0$ the numerator is

$(y, 1) = \int_0^{2\pi} y(x) \cdot 1 \;\mathrm{d}x = \int_0^{\pi} 1 \;\mathrm{d}x + \int_{\pi}^{2\pi} 0 \;\mathrm{d}x = \pi$

and the denominator is

$(1, 1) = \int_0^{2\pi} 1^2 \;\mathrm{d}x = 2\pi$

so that $a_0 = \frac{\pi}{2\pi} = \frac{1}{2}$.

For $a_1$ the numerator is

$(y, \cos x) = \int_0^{2\pi} y(x) \cos x \;\mathrm{d}x = \int_0^{\pi} 1 \cdot \cos x \;\mathrm{d}x + \int_{\pi}^{2\pi} 0 \cdot \cos x \;\mathrm{d}x$

$= \int_0^{\pi} \cos x = \sin x \;\big|_0^{\pi} = 0 - 0 = 0$

so that $a_1 = 0$.

For $b_1$ the numerator is

$(y, \sin x) = \int_0^{2\pi} y(x) \sin x \;\mathrm{d}x = \int_0^{\pi} 1 \cdot \sin x \;\mathrm{d}x + \int_{\pi}^{2\pi} 0 \cdot \sin x \;\mathrm{d}x$

$= \int_0^{\pi} \sin x = (-\cos x) \;\big|_0^{\pi} = -(-1) - (-1) = 1 + 1 = 2$

and the denominator is

$(\sin x, \sin x) = \int_0^{2\pi} \sin^2 x \;\mathrm{d}x = \left[ \frac{1}{2}x - \frac{1}{4} \sin 2x \right] \;\big|_0^{2\pi}$

$= \left[ \frac{1}{2}\cdot(2\pi) - \frac{1}{4} \sin 2\pi \right] - \left[ \frac{1}{2} \cdot 0 - \frac{1}{4} \sin 2 \cdot 0 \right] = \pi - \frac{1}{4} \cdot 0 - 0 + \frac{1}{4} \cdot 0 = \pi$

so that $b_1 = \frac{2}{\pi}$.

So we have $a_0 = \frac{1}{2}$, $a_1 = 0$, and $b_1 = \frac{2}{\pi}$.

NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.

If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.

This entry was posted in linear algebra and tagged , . Bookmark the permalink.


text:
Unlimited royalty free music tracks, footage, graphics & courses! Unlimited asset downloads! From $16.50/m Advertisement # I Turn Knobs, Until It Sounds Good—Mixing With Tchad Blake Length:ShortLanguages: In this article I summarised what I know about Tchad Blake, how he mixes and the tools he uses. ## Background Tchad is one of my favourite characters from the pro-audio world. He is a producer, recording engineer, mixing engineer and musician. He collaborates with the Mix with The Masters educational company where he teaches one-week mixing and recording courses in the south of France. The courses cost around$10,000 for a one-week seminar.

Tchad's won multiple Grammy awards, such as:

• Sheryl Crow—The Globe Sessions, 1998
• Suzanne Vega—Beauty & Crime, 2007
• The Black Keys—Brothers, 2010

Tchad is famous for strange, eccentric sounds, tones, sound design textures and spaces. Much of the time he reaches these sounds through unorthodox tools and methods.

Be it metal pipes, screwdrivers, scissors or a coat hanger, he works with anything. Tchad likes to create binaural records for which he uses a dummy-head with artificial ears.

## General Mixing Philosophy

Instead of specialising in any sound or style, Tchad does his thing and mixes any music he feels like when taking on a new project.

Tchad lets the music dictate the direction when mixing. Emotions are the most important part of his job. With more than 30 years in the profession and counting he still tries to figure out things.

## Mixing the Mid-Range

Tchad doesn't use any special techniques. Most of the time he uses volume, panning, EQ and compressor. For stereo field he pans things to left and right, for example guitar to left and vocal to right. But not always hard panned, like in LCR, but rather what the song needs.

## Mixing Loudness

Before the computer era, he used only 1-2 dB compression on the master bus.

Nowadays he gets materials, which on people used a lot of Waves L3 limiter. And when they hear his mixes, they are disappointed. Louder sounds better, even for himself as well.

He uses McDSP ML4000, to stay in the loudness competition. Tchad likes how it sounds but his mastering engineer doesn't. He laughs at it because it shrinks the space he needs for the job. He puts on a limiter from the start of the mixing but he deletes it when sending to mastering.

It is a good tip to attach the louder version as well, so everybody can listen to it in both versions so there is no surprise.

## Sidechain Compression

He uses it very rarely. For example opening a gate. Essentially Tchad avoids it because he feels it to be complicated.

## Visual Tools—VU Metering, Peak Metering

Tchad uses them as general tools. They can be any type of, like VU or peak. When he is in a studio that has great tools, he uses them and checks the visuals. But he never makes a decision based only on them.

## Monitor Speakers

At home Tchad uses the Linn 328a. Linn is a British brand making hi-fi products. The pair were \$32,000 back in 2005. He recommends them highly even at this luxury price.

The best in them is that they provide the same frequency response and tone at every sound pressure level. The lows are going so low, which is unusual in this category.

During teaching, he uses the Neumann KH 310, the Barefoot MicroMain 27 and the Yamaha NS10.

## DAW Usage

Tchad uses Pro Tools exclusively for mixing, editing and production.

## Plugins

Sound Toys Devil Loc: Tchad uses this mainly on drums with sends

SansAmp PSA-1: he uses this on almost everything: drums, basses, vocal, guitar. This is Tchad's absolute favourite plugin. The style of it is a bit of lo-fi. You can use it for saturation and distortion. SansAmp plugin is part of the Pro Tools plugin suite

Tip: if you use Ableton you can try Saturator to get a taste of the possibilities. Its sound is different, but it contains several algorithms and characters to do the job

Tchad also uses these plugin brands:

• URS
• Audio Ease
• Eventide
• Massey
• Soundtoys
• OhmBoyz
• McDSP
• iZotope
• Prosonique
• SSL

### Plugins By Type

• EQ: URS API for every channel
• Compressor: SSL channel for kick and snare, Massey MT4-et for everything else
• Drum bus: C4 multi band compressor és SSL compressor (sometimes 2 SSL)
• Sends: Echoboy, Altiverb

### Master Channel Plugins

• Slate VTM
• Crange Song Phoenix
• EMI Chandler Curve Bender
• ML4000
• Ofxord Inflator

### Vocal Chain

• Soundtoys Decapitator
• Waves LA-3A
• Waves L1
• Waves RVox
• Bomb Factory Fairchild
• Waves 1176
• Oxford Compressor

### Group Plugins

• Guitar: SansAmp
• Snares: SansAmp
• Bass: SansAmp

Many times Tchad uses them only for coloration, like tape simulation, saturation, distortion and compressors.

With tape emulation he doesn't aim for authentic sound, but more or less just doing colouring. Sometimes he even uses it on the master track as well, trying out different kinds of saturations.

## Favorite Guitar Pedal

Most often, he uses Univibe.

He listens mostly to these artists:

• Dre
• Timbaland
• Eminem
• 50 cent
• Missey E
• Audioslave
• Queens of the Stoneage
• Goldfrapp
• Kings Of Leon

## Summary

• Buy the most expensive monitor speakers you can afford
• Learn the DAW and its plugins well, use them, and maybe you will find a favourite, like the case with SansAmp for him
• The workflow and flow experience are first class elements for the whole job. Try to focus your attention for long hours, but with frequent breaks
• Mixing is ideal for remote work. You don't need to go to a studio or office.

format: plain


text:
+0

# coordinates

+1
108
1

Write the equation of a circle whose diameter is 12 and whose center is at (-6,-3)

Apr 6, 2021

#1
+484
0

If the denominator of the circle is \$12\$, the radius is \$6\$.

If the center is at \$(-6,-3)\$, then the equation is \$(x-(-6))^2+(y-(-3))^2=r^2\$ for some radius r.

Putting these together, we get: \$(x-(-6))^2+(y-(-3))^2=6^2\$, so \$\boxed{(x+6)^2+(y+3)^2=36}\$

Putting it in non-standard form by expanding gives \$x^2+12x+6^2+y^2+6y+3^2=36\$, so \$x^2+12x+y^2+6y=-9\$. However, the actual equation for a circle is the standard one that was shown first, it is MUCH more common. But if you graph both equations, they give the same circle.

Apr 6, 2021


text:
[ / / / / / / / / / / / / / ] [ dir / fur / hk / kc / lewd / rzabczan / sonyeon / strek / v9k ]

# /cyber/ - Cyberpunk & Science Fiction

A board dedicated to all things cyberpunk (and all other futuristic science fiction) NSFW welcome
Winner of the 8th Attention-Hungry Games
/cats/ - ñaa~

Server upgrade almost done. Tweaking kernel and making micro-adjustments to improve site performance. If you find any problems, please report them to /sudo/. Thanks.
Name Email Select/drop/paste files here * = required field [▶ Show post options & limits]Confused? See the FAQ.
Flag Noneaspari syndicatecayman globalcyberdyne systemsdatadyneE.Y.EeurocorpFEMAhomeland securityilluminatikeycardlaughing manmajestic 12neurolabomnicorpono-sendaipyrojunkiessarif industriesshinohara heavy industriestoha heavy industries (東亜重工)umbrella corporationweyland-yutani (replaces files and can be used instead) Do not bump(you can also write sage in the email field)Spoiler images(this replaces the thumbnails of your images with question marks) (For file and post deletion.) Allowed file types:jpg, jpeg, gif, png, webm, mp4, swf, pdfMax filesize is 12 MB.Max image dimensions are 10000 x 10000. You may upload 5 per post.

"A future is not given to you. It is something you must take for yourself. "

File: 1437342761800-0.png (333.05 KB, 620x520, 31:26, toptechtransparent.png)

File: 1437342761802-1.jpg (69.93 KB, 620x465, 4:3, cyberdeck1.jpg)

File: 1437342761802-2.jpg (47.57 KB, 620x349, 620:349, cyberdeck2.jpg)

File: 1437342761802-3.png (15.99 KB, 462x466, 231:233, behold.png)

No.28346

Lets talk about mobile hacker gear.

No.28448

>>28346

>that fourth pic

Fucking schway.

No.28500

YouTube embed. Click thumbnail to play.

No.28512

File: 1437431215284-0.jpg (743.74 KB, 2448x3264, 3:4, 5 - Just opened.jpg)

File: 1437431215285-1.jpg (656.45 KB, 2676x2007, 4:3, 6 - ytVYu.jpg)

File: 1437431215285-2.jpg (614.38 KB, 2448x3264, 3:4, 7 - Windows 7.jpg)

File: 1437431215286-3.jpg (599.74 KB, 2448x3264, 3:4, 8 - Mac OS X 1082.jpg)

Not mine, but pretty schway.

What's the point of those "cyberdecks"? They look cool, but I don't get the purpose.

No.28513

>>28512

They just resemble Gibson's vision of the future. They dont have the purpose to be of practical use.

No.28514

>>28512

Inconspicuous

No.28516

>>28512

This is pretty schway. Seems like an ideal way to carry a gaming set up to a lan party.

No.28517

That 3rd pic sort of calls to me.

>tfw you'll never be able to punch deck like Case.

No.28518

>>28512

Why are they so schway?

maybe i have been reading too much Gibsons works.

No.28529

>>28517

you too can make one of these user. Its literally regular computer components in a gutted musical keyboard with a typing keyboard glued on and a strap attached. Make it nfc enabled and you can use it with a vr headset for maximum cyberpunk.

No.28543

>>28346

Source on pics #2 and #3?

No.28551

The goal here is to find a balance between utility and inconspicuousness. Here's my idea for the ultimate mobile wizard:

It's all in the backpack: a fanless low power PC, camelbak for hydration, some high density snacks; change of clothes; UPS attached to an umbrella with a solar sheet top (sit down to use for "shade" to not look like a madman). Ultimate schway if the umbrella can deploy/retract by lever, similar to a recliner couch. Backup power using an arbitrary number of AA batteries.

The PC - sound via bone conducting headphones; monitor via (doesn't exist yet but) VR/AR headset (probably Oculus Rift CV2); custom keyboard that fits inside front pockets, works like the Datahand; CLI only as AR overlay on a FLOSS OS.

The clothes - cargo pants and a techy t-shirt that "explains" the setup (a shirt promoting VR or whatever). If it could be pulled off, wear whatever looks least conspicuous.

Everything else - keep work online; do not own anything that you cannot carry on you; do not have a permanent place of residence; keep a taser; use only prepaid debit cards or bitcoin; and finally use something small or quick for long distances, like a skateboard, skate shoes, or just a taxi.

No.28559

No.28566

>>28551

>VR/AR

You could already probably pull off a cli-only headset that's inside a pair of sunglasses.

>use something small or quick for long distances

>skateboard or skate shoes

just buy a fucking bike, you can knock off 100 miles in a day with a good bike no problem, and you can go really fast too. The only problem is if it gets stolen, which shouldn't be much of a problem if you lock it properly.

No.28567

>>28566

for maxiumum schway you can lock your bike with a rfid implant detecting ignition switch.

No.28574

>>28512

looks like a great way to scratch your mobo.

No.28693

File: 1437521083942-0.jpg (75.13 KB, 622x440, 311:220, XroZ1.jpg)

File: 1437521083944-1.jpg (340.33 KB, 1920x1080, 16:9, d74919f1d2458b2575a077a1b6….jpg)

File: 1437521083945-2.jpg (341.23 KB, 1920x1080, 16:9, 948e0a1bdde003031633495872….jpg)

>>28559

Thanks, I'm seriously contemplating making this my winter project.

What would you put into deck for this incoming first generation of VR HMDs? According to Oculus, here are the minimum specs required to run things in vr without getting simsick: https://www.oculus.com/en-us/blog/powering-the-rift/

Intel's been making a big push for integrated graphics support for VR; AMD has been getting there in the same vein with their APUs as well. I'll probably go with an intel mini-itx board with something like an i5-4590 to keep the wattage low as well eight gigs of whatever memory sticks I have lying around. I wanna avoid any off-the-shelf case because that just wouldn't be schway. But for storage the case would probably have a couple ssd storage slots for easy swapping and 60-75% mechanical keyboard soldered on.

Discrete graphics seem to be the only viable solution in the immediate future. I fear any GPU that is more than six or seven inches in length would be just as cumbersome as the deck shown in the instructable. A mini GTX 970 is capable of playing games at 1080p, 60-70fps and that's without having it display an image to each eye; I'd love to have something that averaged at 90fps but that would end up being costly as shit. Speaking of which, I hear that AMD's R9 Nano will have great price-to-performance ratio thanks to its HBM, too; so I'm not sure what I could go with.

This is something that I'd want to use while on the go so it needs to be capable of running without wall power. The only way I can do this would be to probably find a picoPSU with 500w output and connect it to one or two 12v external rechargeable batteries. Do you users think that would work?

No.28696

>>28693

GPUS typically come with a very cumbersome case. You can try carefully shaving off some of the case to reduce it in size. Alternatively, consider getting 2 small gpus instead of one big one.

No.28715

File: 1437545844541-0.png (170.8 KB, 500x428, 125:107, Small-Form-Factor1_500.png)

File: 1437545844545-1.jpg (43.59 KB, 800x551, 800:551, nano.jpg)

>>28696

>GPUS typically come with a very cumbersome case.

Both mini GTX 970s and the upcoming R9 Nano brush over six inches in length; I'd end up installing either of them horizontally to save space. I don't think I'll have to swap out any of their heatsinks for the sake of reducing size.

>Alternatively, consider getting 2 small gpus instead of one big one.

Then I'd have to get a micro-ATX board which would only increase the size of the deck; having a single gpu to render each eye would be great but that just wouldn't be feasible in terms of portability.

I'm more worried about the power supply. Computer PSUs that are designed to take 12v DC power as input exist; they're typically used by people who are in the market for setting up a computer in their cars, boats or solar-powered shacks. You could easily give power to the components of a mini-itx board for as long as the battery lasts. The only problem with this is finding a way to monitor the state of the battery itself; 12v external batteries aren't very cumbersome, don't you think? I can't find much information on mini-itx machines running on these kinds of PSUs so I can't really say that it's worth it, but I can say that it is possible to make it portable while still keeping it somewhat lightweight.

No.28716

>>28715

>The only problem with this is finding a way to monitor the state of the battery itself

Not really. The real problem is supplying the required current, because a 12V battery is not anywhere near 12V, necessarily. Monitoring the batteries can be done the same as anything else with batteries.

But you're right, the PSU is the problem. There's a lot of information on mini-ITX machines and picoPSUs but very few have massive GPUs and high end power requirements. This project is largely in it's own class as far as power goes.

Most laptops use low-power processors and few of them have AC adapters over maybe 150W. Most picoPSUs are smaller than that.

No.28718

File: 1437551441780.jpg (494.69 KB, 1280x923, 1280:923, Acer_Aspire_8920_Gemstone_….JPG)

:^)

No.28723

File: 1437557870487.jpg (424.77 KB, 2560x1920, 4:3, jp6hK7u.jpg)

No.28724

i posted a badly drawn design some time ago in either /tech/ or /g/.

It had a wearable keyboard, a googleglass-like peripheral and the computer itself was in a backpack. Sadly i dont have the pic anymore

No.28726

File: 1437564131529.jpg (33.03 KB, 645x418, 645:418, Cicret-1.jpg)

No.28730

>>28726

cannot wait for cicret

No.28736

File: 1437585752141.jpg (99.79 KB, 1200x675, 16:9, post-1-0-01387700-14081442….jpg)

waiting for this thing to come out

and I might keep shilling for it as long it didn't

No.28745

>>28730

>implying the company is not just scamming everybody

No.28747

>>28726

>>28730

what if you have hairy arms?

No.28748

>>28747

>the future

>being some stoneage monkey

No.28749

No.28758

>>28747

like this anon pointed out >>28748 , its the future, replace your skin with enduretaniumum exoskeleton.

No.28812

File: 1437654313903.jpg (264.92 KB, 595x950, 119:190, 1413469450141-0.jpg)

I've been wanting to make a helmet like this.

Played around with a few designs and ideas.

The problem is finding something to use as the shell. I was thinking one of those disco lights, but I can't find one big enough anywhere.

No.28813

>>28812

Just make the shell yourself.

Alternatively create a 3d model and find someone to print it for you.

No.28814

File: 1437656606767.jpg (680.07 KB, 1198x1406, 599:703, proxy2.jpg)

>>28812

this thing looks like a planetarium device. Have fun spending some million dollars on it. You better make it by yourself.

No.28829

>>28812

all the tech aside, isn't it just a helmet on his face?

No.28832

File: 1437669506730.jpg (88.63 KB, 534x800, 267:400, 1133.jpg)

Fucking awesome potential for this, I want to see modded Thync receivers that can do more intense feelings.

http://www.thync.com/

(pic unrelated)

No.28833

>>28812

What would this thing even do.

No.28846

File: 1437679210873.jpg (61.48 KB, 400x300, 4:3, absolutely disgusting.jpg)

>>28512

>all that trouble just to run Windows or OSX

No.28847

>>28832

>$299 for a tDCS device >$20 for ten-piece electrode packs

lol no, it'll be doa; I bet most of the funding they received went into that shitty-looking app they're shipping with it because doing tdcs is as simple as two sponges coupled with a 9v battery.

No.28849

>>28832

It's amazing how fucking close that it is "theync."

They really need to choose a different domain name.

No.28860

>>28847

not to mention that its ugly as fuck

No.32153

File: 1441139793518.jpg (521.95 KB, 2816x2112, 4:3, 1437665532212.jpg)

No.32155

>>28736

What is that?

No.32156

>>32155

I think it is raspery pi. They turn into this a game console with lunix.

No.32158

>>28512

Nothing schway about running non-free software.

No.32163

File: 1441159906379.jpg (20.17 KB, 500x343, 500:343, 376856.jpg)

>>32158

>non-free

>software

I know what those words mean individually but when you say them in a sentence like that it just doesn't make any sense

No.32169

>>28512

>not using windows 10 with botnet disabled

No.32170

>>32163

No.32175

>>32170

But that's free software

I'm pretty sure free software isn't non-free software

Sorry if that puts a damper on your whole "have you heard the good news" shtick, I know you've probably been waiting all day to pull that out

No.32191

>>32175

Some drugs weren't meant to be taken but some children were born to die in the womb.

No.32192

>>32175

>not understanding opposites

did you pass the third grade? Because I have yet to see evidence of it.

No.32222

>>32169

>implying it actually disables

No.32225

File: 1441232481761.gif (2 MB, 248x215, 248:215, Pet-washing-machine.gif)

>>32222

No.32236

>>32192

>Literally arguing that opposites are not opposites

>And calling other people retarded for thinking opposites are opposites

No.32245

>>32222

If you look very carefully, I mean squint like jack sparrow having a fist in his asshole, you can see in your outgoing connections that nothing is going to microsoft.

No.32569

>>32245

Yes but how do you know that they aren't disguising it as other outgoing traffic. How do you know they aren't downloading when you aren't looking. Don't trust software you can't modify buddy.

No.32586

Google glass a corpcuck, any other AR tech available? I know there's a how-to for making a RasPi into a wearable eye-projection computer.

No.32587

>>32586

Microsoft hololens

No.32589

File: 1441551676940.jpg (64.6 KB, 253x600, 253:600, that's illegal.jpg)

>>32587

But user, that's even more corptastic

No.32620

>>28833

>>28829

Looks to me it's a full computer he's wearing. The things over the back of his head look like drives of some sort, and I'm sure there are plenty of displays under the dome. I imagine it's got a camera(s) in it. Either he uses voice to operate, or there are controls in a pocket somewhere or something.

No.32646

>>32569

Nothing is stopping me from modifying windows files at all. I can edit them by take ownership, then text editor. What you're talking about is full tinfoil hat shit.

No.32692

>>32155

open pandora is my guess

No.32706

>>32646

Gee I wonder if I can edit the source code of the Windows Kernel. Oh that's right the source code is CLOSED SOURCE which means that I CAN NOT EVEN LOOK AT IT. Also you post makes little sense, I suggest you git gud at English before posting retarded shit.

No.32753

>>32245

post proof and I'll install Windows 10 on all of my computers.

No.32900

No.33488

If the goal wasn't to jack in to a VR gaming headset, and just have a deck-style computer for average use and ricing, what do you chummers think would be the best way to build it? Go with separate parts and build a desktop in a deck or go with something like a Banana Pi and have room to embed a screen, keyboard, and mouse pad?

Also, what are all the alternatives to the Raspberry Pi? I remember seeing a chart once but I can't find it.

No.33491

File: 1442510324577-0.jpg (46.67 KB, 600x409, 600:409, keyer.jpg)

File: 1442510324579-1.jpg (25.44 KB, 500x455, 100:91, glove.jpg)

I've been looking at the Pandora and it's successor the Pyra and I was wondering why their performance lags so far behind say, modern smartphones, which also contain shit like cameras and accelerometers?

And on a related note, wouldn't the best starting point for a cyberdeck be a tablet PC? I don't know how easy that would be to modify, but the specs of, say, the Jolla are pretty damn good and an open project like that shouldn't be too hard to work with.

Also, I came across this board which I think has potential.

https://www.olimex.com/Products/OLinuXino/open-source-hardware

Another issue is input. The obvious choice would be a physical qwerty keyboard, but these are fairly bulky and really require a flat surface to type on, which isn't ideal. Another option would be a touchscreen interface, which is very space efficient but not very schway these days. Voice input is cool but you will look like an idiot.

Some sort of chorded keyboard similar to pic related could be suitable, and would also allow fast one handed typing, although assuming one key is used per finger only 31 characters could be represented (no 00000). This could be easily integrated into a glove, and when typing with both hands up to 1023 characters would be possible, which could mean superfast typing in eastern languages.

My idea is to have a glove (fingerless, obviously) with sensors to detect movement of the fingers, which should be very simple. If it could detect both downwards and upwards movements, 242 characters could be typed with one hand which is more than enough for coding and leaves options for window management and other shortcuts. Something a bit more solid like the second pic could provide delicious clicky tactile feedback and make typing much faster and easier, since one would only have to make very small movements.

No.33897

File: 1442870986076.jpeg (232.54 KB, 960x1280, 3:4, cyberpunk.ru.jpeg)

Anyone recommending a high end PC as a cyberdeck misses the point. Something like a smartphone with a VR headset would be pretty damn close to the classic Gibson Ono-Sendai - a "toy" computer with a huge portion of its limited compute power dedicated to fancy outputs and network connectivity, with the real magic happening in the Matrix/Cloud. In the Matrix/Cloud you can build your own little fiefdom with one or more systems, be they physical hardware or (less secure) VMs/VPSes on somebody else's hardware.

Keep in mind the original system that inspired the concept of portable cyberdecks was an Apple IIc.

No.33898

>>33491

>I've been looking at the Pandora and it's successor the Pyra and I was wondering why their performance lags so far behind say, modern smartphones, which also contain shit like cameras and accelerometers?

It turns out that a megacorp's economies of scale and willingness to use proprietary tech give it a leg up on a bunch of amateur free software nuts in enhancing a system's performance/price ratio.

>And on a related note, wouldn't the best starting point for a cyberdeck be a tablet PC?

Sure, as long as you go with something hacker friendly (read: x86 or something with 100% upstream kernel support on Linux). Those cheap $50 tablets with locked bootloaders won't do you a bit of good. No.33968 >>33897 So set up a pi to basically be a mobile terminal for a server back home? Go somewhere with wifi and work like you're on your own computer. Hell, I did this with my smartphone for a while. Used an SSH app to do stuff on a ~club. Too bad my phone's a piece of shit, I woulda done more otherwise. Maybe when I get one that isn't terrible. No.33978 >>28726 Very usefull when you fapping at bathroom. No.33986 >>33968 Yeah, a ~6" phablet with USB OTG Host support docked into a keyboard+batterypack cyberdeck would be pretty schway if you can't do the goggles yet. VX Connectbot is the best of the Android SSH clients for using full sized USB keyboards if you go that route. No.34700 YouTube embed. Click thumbnail to play. I'm thinking that something like embed, but in 3D w/ head tracking could mean that the deck could be less keyboard-focused and more focused on more space for protection/ventilation/power. No.34787 >>34763 this is spam. someone with javascript enabled please report. No.35023 >>32163 Smelly dumb newfag scum. No.38207 No.38208 No.38233 >>32620 No no. Look at it. It's literally a helmet worn on the front of his face. You can find old kevlar helmets from milsurp shops online for like 100bucks. Figure out a way to rig a vr phone into it and you could make that pretty schway. No.38271 >>28718 >2012 No.41589 https://imgur.com/a/Y4iLt Raspberry Pi deck. You could make these pretty tiny if you combined it with a one-hand keyboard, Rift or a >9000 monocle for a display, and put most of the RAM on the cloud… No.41594 >>28829 >>28833 >>32620 >>38233 I don't think that's supposed to be an old kevlar helmet. It's covered in what are presumably sensors. No.41599 >>41589 >put most of the RAM on the cloud… u wot m8. That's now how RAM works. It's a cache for virtual memory. Tying it to the network would make it slow as balls. No.41626 >>41589 wait, is that a notebook keyboard? How do you connect it to rpi? No.45485 >>32153 Ah, I remember this guy. He made a 2nd version with directions on /diy/ No.45486 >>28718 I just realized that photo is recursive. No.45501 If you have the brouzouf you can work something easily off the ODroid UX4. Makes the Raspberry Pi look like an 87 Honda. No.45511 >>45501 I still want one of those chinese monocle displays. No.45514 File: fe665548e6e25f9⋯.gif (35.23 KB, 323x480, 323:480, phone.gif) >>28736 I had a phone like that back in 2000. >pic related No.45525 >>45514 Oh shit, I had that too. No.45555 File: 318dc220b967ba0⋯.jpg (49.37 KB, 462x400, 231:200, no5510_00.jpg) >>45525 I never grokked predictive text on candybar or clam phones. Still can't. Though I use swiftkey on my Android these days. ALWAYS went for full QWERTY phones. I had a 5510 too once. Hell, I had a Sharp Zaurus with custom rom for wardriving back in 2003-2004. THAT was cool. No.45556 File: 1c31bee1ba64a67⋯.jpg (48.91 KB, 400x425, 16:17, mutts nuts.jpg) >>45555 >pic related Dead tech now though. No.45576 File: 7cf13c07fab8503⋯.png (233.59 KB, 433x620, 433:620, dubbelsbevestigt.png) >>45555 Checked! No.45624 >>28567 >ignition pretty sure we're talking bicycle here. low cost, quiet, easier to stash, no license/tax. No.45625 Can we have some tech that is 2000+ and NOT a disaster waiting to happen? Then again that might be a troublesome category… No.46350 File: 99e40b5423ed6c8⋯.jpg (959.67 KB, 1202x1346, 601:673, 04937c8c-74c8-40e9-b9d4-cc….jpg) DIY Punk Cyber-headphones No.47650 zsfvf Fszv fSD faFa F No.47655 >>45625 >>46350 didn't listen No.47656 >>45556 Schway as fuck. Do those things really don't exist no more? No.47658 >>47655 He's listening … to the future! No.47662 >>28747 just shave or wax your arms then lol No.47706 >>32170 >>35023 You don't have to know much about technology to like/be cyberpunk. There was a poll on the r/Cyberpunk subreddit asking users how good they were with computers and the majority of fans were there for the aesthetic and mood of cyberpunk, not the in-depth technological aspect. Even William Gibson is actually pretty poor with computers, he writes his books on a typewriter. No.47707 >>47706 But in-universe his characters were all technically apt. Similarly, in-universe, we should be technically apt. Go learn. No.47732 >>47706 Oh, well if /r/Cyberpunk, the biggest shithole on the internet, says so … No.47734 Imagine turning the old powerglove into a portable computer, That'll look nice and I suppose it'll hold some function to it. Most likely already been done though. No.47735 >>47734 I don't think anyone has made it into an actual portable computer … yet. There have been several projects to turn it into different, much better, controllers. If you wanted to make it into a computer, I imagine a Pi-zero, or similar SBC for around$10 could be used. it wouldn't be very hard.

Where would you mount the screen? Maybe it should run up a cable to a pair of glasses and use a micro-display, like old Cyberpunk drawings.

No.47741

>>47735

Yeah that isn't a bad idea actually, When I find some time I'll give something of the sort a shot, Will create a thread if I succeed.

No.47749

>>47741

Create a thread with drawings, and update it as you make progress. This place could use someone actually doing something.


text:
# Compact group actions and automatic properness

I am currently re-reading a course on basic algebraic topology, and I am focussing on the parts that I feel I had very little understanding of. There is one exercise in the chapter devoted to groups acting on topological spaces (preceding the chapter on covering spaces) that I have spent several frustrating hours on, but I just can't crack.

I will state the question below, but PLEASE, DO NOT POST A SOLUTION OR A HINT. I am only interested in knowing wether the statement in question is true. I have looked on the internet for a reference about this fact, but didn't get anywhere. If you know a book that gives proves it, or a document online where this is discussed, I would like to get the reference, in case I continue to fail at giving a proof of this the next week.

I recall some terminology first: let $X,Y$ be two topological spaces, and $f:X\rightarrow Y$ a map that isn't supposed to be continuous. The author defines such a map to be $\mathrm{PROPER}$ whenever the following two properties are satisfied : $f$ is a closed map, and $\forall y\in Y, ~f^{-1}(\lbrace y\rbrace)$ is a compact subspace of $X$. It then follows that for all compact subsets $K$ of $Y,~f^{-1}(K)$ is a compact subset of $X$. Also, if $X$ is Hausdorff, and $Y$ is a locally compact Hausdorff, then properness is equivalent to this property.

Let $X$ be a topological space, and $G$ a topological group. Suppose there is a continuous left group action $\rho: G\times X\rightarrow X,~(g,x)\mapsto g\cdot x$. Let $\theta:G\times X\rightarrow X\times X, ~(g,x)\mapsto (x,g\cdot x)$. The author defines the group action to be $\mathrm{proper}$ if $\theta$ is a proper map.

Here is the question: "Show the action of a compact Hausdorff group $G$ on a Hausdorff space $X$ is always proper".

As I said, I have struggled with this for days (since friday). IS THAT STATEMENT TRUE? There are no further hypothesis, $X$ is not supposed to be locally compact, and the action is completely arbitrary (continuous of course, but not supposed free, or other things).

-
I think it is a very unusual, and hence confusing, idea not to include "continuous" in the definition of "proper". Anyway, Theo certainly makes this continuity assumption in the fine text (mentioned in his answer) that he wrote for MathOverflow. – Georges Elencwajg May 23 '11 at 10:19

@Olivier: I think it's rather straightforward and no trickery is required. I'm reluctant to say anything more, since you don't want any hints... However, you can try to show first that the projection map $G \times X \to X$ and the action map $\rho$ are proper (since $G$ is compact). Their "combination" $\theta$ is then quite easily seen to be proper, as $X$ is Hausdorff. – t.b. May 23 '11 at 15:08


text:
# Liquidity measures for Commodities Futures

I would like to find a way to measure Liquidity for Commodities Futures. I found the following 4 papers/definitions:

The first 3 only refer to Stocks.

Are the above measures applicable both to Stocks and to Commodities?

Can they be applied to Future Contracts?

Would they be equally valid on daily basis vs a monthly or yearly basis?

• What is your goal in measuring liquidity? Mar 11 '21 at 23:26
• ADV (average daily volume) and OI (open interest) are the usual ones... but what are you trying to measure here? Mar 12 '21 at 0:23
• @user42108 My goal in measuring liquidity is to understand how liquid a future contract is compared to the others. Mar 12 '21 at 7:42
• @demully I'm trying to measure liquidity of future commodity contracts. Mar 12 '21 at 7:43
• "My goal in measuring liquidity is to understand how liquid a future contract is compared to the others" - different liquidity measures will give you different answers to that question, which is why I asked. In addition, commodity futures are likely to be different and probably more complicated than stocks when it comes to liquidity measurement as they are often traded via calendars or cross-market spreads (e.g. crack, crush...) which are an important source of liquidity. Mar 12 '21 at 14:06

Therefore, you can define the liquidity using the average daily volume in a recent time window as suggested by this answer adding some additional constraints/penalty, such as a minimum number of days with at least $$N$$ trades.


text: 1.3. And of course the real numbers in the interval (0,1) can be mapped to all other real numbers, so there are as many infinitely uncountable real numbers in (0,1) as in the whole set of real numbers. (b) If {Uα} is any collection (ﬁnite, inﬁnite, countable, or uncountable) of open sets, then ∪αUα is an open set. Proof: By Theorem 5, we know A r B = A ∩ (R r B), and the intersection of two open sets is open by Theorem 42. Integers $$\mathbb{Z}$$ When the need to distinguish between some values and others from a reference position appears is when negative numbers come into play. Each time, the collection of points was either finite or countable and the most important property of a point, in a sense, was its location in some coordinate or number system. I can tell that two sets have the same number of elements by trying to pair the elements up. Remove the middle third of this set, resulting in [0, 1/3] U [2/3, 1]. The set of all natural numbers in E1- the real line with Euclidean distance. So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc. Solved Examples. It isn’t open because every neighborhood of a rational number contains irrational numbers, and its complement isn’t open because every neighborhood of an irrational number contains rational numbers. Is 0 a whole number? Note that a similar argument applies to any set of finitely many numbers. So three is a whole number. It is the \smallest" closed set containing Gas a subset, in the sense that (i) Gis itself a closed set containing G, and (ii) every closed set containing Gas a subset also contains Gas a subset | every other closed set containing Gis \at least as large" as G. Whole numbers are the set of all the natural numbers including zero. Show that the set Q of rational numbers is neither open nor closed. Natural numbers are only closed under addition and multiplication, ie, the addition or multiplication of two natural numbers always results in another natural number. So suppose S is a set of natural numbers closed under addition. Real numbers in the interval (0,1) are uncountable, because they cannot be mapped one to one to either natural numbers or rational numbers. The intersection of ﬂnitely many open sets is open and the union of ﬂnitely many closed sets is closed. For instance take the two whole numbers 2 and 5. First of all,let us start be defining the term "closed" A set of numbers is said to be closed for an operation, if upon performing that operation between the numbers you get a member of that set. \begin{align} \quad d(x, y) = \left\{\begin{matrix} 0 & \mathrm{if} \: x = y\\ 1 & \mathrm{if} \: x \neq y \end{matrix}\right. A lower bound for the set (3, 6) could be any number that is less than 3, or the number 3 itself. Note. Show that the set N of natural numbers is a closed set in R. Show that A = {1/n : n E N} is not a closed set, but that A U {0) is a closed set. Open and Closed Sets In the previous chapters we dealt with collections of points: sequences and series. True or false? Now let’s look at a few examples of finite sets with operations that may not be familiar to us: e) The set {1 ,2,3,4 } is not closed under the operation of addition because 2 + 3 = 5, and 5 is not an element of the set {1,2,3,4}. The sum of any two natural numbers is also a natural number (for example, 4 + 2000 = 2004), and the product of any two natural numbers is a natural number (4 × 2000 = 8000). 6. True, because you can't multiply your way out of the set of integers. But then the set {1, 2, 3} is compact. I am trying to understand why ℕ the set of natural numbers is considered a Closed Set. The square root of a natural number is not guaranteed to be a natural number. One, both, or neither of the numbers at the endpoints of the interval may be included with the set of numbers in the interval. A more interesting example of a subset of $\mathbb{R}$ which is neither open nor closed is the set of irrational numbers. - Correct me if I am wrong but a limit point of a set is a point not in the set but every open neighborhood of the point has non-empty intersection with the set. In other words, a number u is a lower bound of a set S of numbers if for all x ε S, x u. If A is uncountable and B is any set, ... Start with the closed interval [0,1]. 100, 227, 198, 4321 are all whole numbers. In some cases, you may be able to find a counterexample that will prove the set is not closed under one of these operations. As to being Closed. So you've subtracted your way out of the set of whole numbers. De nition. 5. Solution: Yes. – 11 is not a natural number, so it is not in the set of natural numbers! The Integers . An inﬁnite intersection of open sets can be closed. The Attempt at a Solution I believe I understand why it is not an Open Set: Given that it includes 0 as a boundary point, it cannot be an open set. Now, let's think about negative five. This is not true for subtraction and division, though. So yes, 0 (zero) is not only a whole number but the first whole number. The sequence { n } of natural numbers converges to infinity, and so does every subsequence. The set of rational numbers Q ˆR is neither open nor closed. The empty set and the entire space are closed. Example. The two numbers that the continuous set of numbers are between are the endpoints of the line segment. For e.g Consider the set of whole numbers. Every open interval on the real line can be expressed as a countable union of disjoint open intervals (called component intervals ) unique except as to the order of the intervals. Any open interval is an open set. Lower bound of a set of numbers. The union of a finite number of closed sets is closed and the intersection of any number of closed sets is closed. The open sets satisfy: (a) If {U1,U2,...,Un} is a ﬁnite collection of open sets, then ∩n k=1Uk is an open set. Relevant definition A Set S in R m is closed iff its complement, S c = R m - S is open. The natural numbers are well-ordered: which means every set of natural numbers has a least element. The union of two closed sets is closed. 7. A number (any number) that is less than or equal to every number in the set. The union of open sets is an open set. Let k be the smallest element of S. By deﬁnition, no prime ideal con-taines 1, so V(1) = ;:Also, since 0 is in every ideal, V(0) = spec(R). Both R and the empty set are open. For the second equality, we have B r A = B ∩ (R r A), and the intersection of two closed sets is closed by Corollary 1. \end{align} Intervals: Representations of open and closed intervals on the real number line. Example 1: Are 100, 227, 198, 4321 whole numbers? De nition 1.23. For any two ideals Iand J, the product IJ is the ideal generated by products xywhere x2Iand y2J. For each of the following sets, make a conjecture about whether or not it is closed under addition and whether or not it is closed under multiplication. Example 5.17. A closed cell in Euclidean space The union in E of the open intervals (n, n+1) for all positive integers n. The interval (0,1) in E1- the real line with Euclidean distance A complement of an open set (relative to the space that the topology is defined on) is called a closed set. 2. 5. (a) The set of all odd natural numbers (b) The set of all even integers As another example, the set of rationals is not open because an open ball around a rational number contains irrationals; and it is not closed because there are sequences of rational numbers that converge to irrational numbers (such as the various infinite series that converge to ). … The set of natural numbers, also known as “counting numbers,” includes all whole numbers starting at 1 and then increasing. So, three is a whole number. A set may be both open and closed (a clopen set). If A is open and B is closed, prove that A r B is open and B r A is closed. An open subset of R is a subset E of R such that for every xin Ethere exists >0 such that B (x) is contained in E. For example, the open interval (2;5) is an open set. the intersection of all closed sets that contain G. According to (C3), Gis a closed set. 4. But infinity is not part of the natural numbers. Proof. ˜ 6. The entire set of natural numbers is closed under addition (but not subtraction). So, three is a whole number, it's an integer, and it's a rational number. So, it's a member of that set. The set of natural numbers N = {1,2,3,4, ... since it’s a union of open sets, so B = A∩U is relatively open in A. But if you're a whole number, you're also an integer, and you're also a rational number. If you subtract 2 - 5 you get a negative number -3, and no negative numbers are whole numbers. Def. 4/5/17 Relating the definitions of interior point vs. open set, and accumulation point vs. closed set. A set is closed in a metric space is every convergent Cauchy sequence in the set converges to a point in the set. The union of any number of open sets, or infinitely many open sets, is open. Consider the sets {a,b,c,d} and {1,2,3,Calvin}. 5. Topology of the Real Numbers 2 Theorem 3-2. Topology 5.1. The intersection of a finite number of open sets is open. The set of natural numbers N is not compact. 3.1. Yes. This poses few diﬃculties with ﬁnite sets, but inﬁnite sets require some care. The set of integers is closed under multiplication. The cardinality of a set is roughly the number of elements in a set. This provides a more straightforward proof that the entire set of real numbers is uncountable. A continuous set of numbers which includes all the numbers between two given numbers is often called an interval. Note that S1 \S2 \S3 \¢¢¢\Sn = (((S1 \S2)\S3)¢¢¢\Sn) for any family of sets fSig, i 2 N, and any natural number n. Thus, for an intersection of ﬂnitely many open sets we can take Closed sets Closed sets are complements of open sets. So three, and maybe I'll do it in the color of the category. The image below illustrates open and closed intervals on a number line. Points: sequences and series if you 're also a rational number all natural converges. ( a clopen set ) align } for instance take the two whole starting... 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Numbers ( but not the odd numbers ), Gis a closed set so does every subsequence many! C, d } and { 1,2,3, Calvin } at 1 and increasing... 'Ll do it in the previous chapters we dealt with collections of points: and! C = R m is closed in a metric space is every convergent Cauchy sequence in the set interval 0,1! So does every subsequence so it is not only a whole number but the whole. Includes all whole numbers G. According to ( C3 ), the multiples of,... Defined on ) is not guaranteed to be a natural number has a least.. - S is a whole is the set of natural numbers open or closed but the first whole number but the first whole number, 're! 'Re a whole number but the first whole number of ﬂnitely many closed sets contain! Two numbers that the set of integers C3 ), Gis a set! The even numbers ( but not the odd numbers ), Gis a closed set R is. Numbers including zero J, the product IJ is the ideal generated by xywhere! Set of rational numbers Q ˆR is neither open nor closed number, you 're also integer... Applies to any set of numbers are well-ordered: which means every set of whole numbers 2 5... In [ 0, 1/3 ] U [ 2/3, 1 ] 've... Set S in R m - S is a whole number, it 's integer! Previous chapters we dealt with collections of points: sequences and series the endpoints of the segment! It in the set of all the numbers between two given numbers considered... Of S. 5 a finite number of closed sets that contain G. According to ( ). The square root of a natural number is not a natural number, so it is not is the set of natural numbers open or closed subtraction! The elements is the set of natural numbers open or closed both open and the union of ﬂnitely many open sets, inﬁnite... C, d } and { 1,2,3, Calvin } way out of the line segment,.! Example 1: are 100 is the set of natural numbers open or closed 227, 198, 4321 whole numbers accumulation point vs. set! 1: are 100, 227, 198, 4321 are all whole numbers at! Is called a closed set equal to every number in the set of natural numbers including zero smallest. } for instance take the two numbers that is the set of natural numbers open or closed continuous set of natural numbers N not... Is defined on ) is not only a whole number, you 're also a rational..


text:
• Corpus ID: 235266008

# Existence results for a generalized fractional boundary value problem in $b$-metric space

@inproceedings{Haddouchi2021ExistenceRF,
title={Existence results for a generalized fractional boundary value problem in \$b\$-metric space},
year={2021}
}
This paper is concerned with a class of nonlinear boundary value problem involving fractional derivative in the φ-Riemann-Liouville sense. Some Properties of the Green’s function for this problem are mentioned. By means of the Banach contraction principle in b-metric space and the technique of the γ–ψ Geraghty contractive maps, existence and uniqueness results are obtained. Two examples are given to support the theoretical results.

## References

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Further results on existence of positive solutions of generalized fractional boundary value problems
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This paper studies two classes of boundary value problems within the generalized Caputo fractional operators. By applying the fixed point result of α - ϕ -Geraghty contractive type mappings, we
On the existence of positive solutions for generalized fractional boundary value problems
• Mathematics
• 2019
The existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the
A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces
• Mathematics
• 2020
In this paper, we investigate the existence of positive solutions for the new class of boundary value problems via ψ -Hilfer fractional differential equations. For our purpose, we use the α − ψ
Positive solutions of nonlocal fractional boundary value problem involving Riemann–Stieltjes integral condition
In this paper, we investigate the existence of positive solutions for a nonlocal fractional boundary value problem involving Caputo fractional derivative and nonlocal Riemann-Stieltjes integral
THEORY AND ANALYSIS OF ψ-FRACTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS
• Mathematics, Philosophy
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Fractional Differential Equations with Mixed Boundary Conditions
In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order $$\alpha \in (2,3)$$α∈(2,3), involving a general form
Applications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernel
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Using some fixed point theorems for contractive mappings, including α - γ -Geraghty type contraction, α -type F -contraction, and some other contractions in F $\mathcal{F}$ -metric space, this
Solution of fractional differential equations in quasi-b-metric and b-metric-like spaces
• H. Afshari
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In this article, using by α-admissible and αqsp$\alpha _{qs^{p}}$-admissible mappings, solutions of some fractional differential equations are investigated in quasi-b-metric and b-metric-like spaces.


text:
# Considering Units When manipulating system of Equations?

I few days ago I solved a problem on a website called brilliant.org, I can not seem to find the problem there anymore but I still remember it:

Q: You go to a candy store to buy m&ms and twizzlers, 1 pack of m&ms is 1 dollar, and one pack of twizzlers is 0.5 dollars. If you buy a total of 10 packs worth 6 dollars in total, how many packs of m&ms did you buy?

The solution is simple, you form a system of linear equations where x is the number of m&ms and y is the number of twizzlers.

$x + y = 10$

$x + \frac{y}{2} = 6$

Solving by subtracting the second equation from the first we eventually get x = 2, so we bought two packs if m&ms. However, from my physics classes I have learnt that you can not add or subtract two number having different units. I have tried multiple times to make the units match but with no success. For example, in the first equation x stands for the number of packets of m&ms and in the second x packets are being multiplied by 1 dollar per packet , so when we do x - x, we are subtracting dollars from packets? Also when we do 10 - 6, isn't it also packets - dollars? For this reason, subtracting the equations doesn't seem to make sense to me, so why are we still able to do so?

• When you write the equation, it is the numbers whose relation is represented. In order words, they are just plain numbers, no units – Shailesh Aug 30 '15 at 18:05
• so if these equations do not have units when do they have? Because if I remember correctly back when I took physics all the equations we dealt with had units, even if they where not visible we were implicitly meant to assume they were there or the equations would not make sense – fYre Aug 30 '15 at 18:12
• "If you buy a total of 10 packs" ... you've just added apples and oranges right off the bat, or more precisely, Twizzlers and M&Ms. – John Joy Aug 30 '15 at 18:20

## 3 Answers

In the first equation, $x+y=10$, the unit is "packs": $x$ packs plus $y$ packs equals $10$ packs. However, you can divide each side by "packs" and you end up with the unit "packs/packs," which we would call the "empty unit", i.e. no unit. The second equation has the unit "dollars," but again we divide both sides by "dollars" and end up with pure numbers without units.

So the equations involve pure numbers: no units are involved.

Pure numbers, without units, also happen in physics, so it is not true that "all the equations ... had units." Many physics quantities are pure, such as coefficient of friction, mechanical advantage, and efficiency. So are sines, cosines, and tangents of angles. (There may be a dispute over the proper units for angles--radians or degrees--but everyone agrees that the trigonometric function values themselves have no units.) One physics equation that involves no unit is "the coefficient of static friction of rubber on dry concrete is ten times that of ice on ice."

• I'm not exactly sure why the unit for x in first equation is packs and not packs of m&ms? – fYre Aug 30 '15 at 18:40
• @fYre $$x_{packs} = \text{M&M}_{packs}$$ The units tell you what we are measuring, packs, the variable name serves to differentiate the packs of M&Ms from the packs of Twizzlers. You could replace $x$ and $y$ with $\text{M&M}$ and $\text{Twizzler}$ if you wanted and the effect would be the same. – Zenohm Aug 30 '15 at 19:02

You can write your equations as \begin{align} x \text{ packets} + y \text{ packets} = 10 \text{ packets} \\ x \text{ packets} \cdot 1 \text{ dollars/packet} + y \text{ packets} \cdot 0.5 \text{ dollars/packet} = 6 \text{ dollars} \end{align} When you do so, you realize that $x$ and $y$ are unitless numbers, as you can see by dividing the top equation by the unit "packets").

Hence it's valid to apply operations like adding, subtracting, etc., to them.

When you subtract or add the equations, you have to change them to make sure that you can do so. The implications of this are that you can generally ignore the units or add them in afterwards.

I'll show you what I mean.

$$x_{packets} + y_{packets} = 10_{packets}$$ $$(1)x_{packets} + (0.5)y_{packets} = 6_{packets}$$

If you were to state the units on the second equation, they'd be something like 'packet dollars', or cost for the given number of packets at the given price. The idea here is similar to a kilowatt-hour, it isn't just the kilowatts or the hours, it is the product between the two.

When you are subtracting the equations, you have to change at least one of them so that a variable cancels out, mostly through multiplication.

Example,

$$(-1)(x_{packets} + y_{packets} = 10_{packets})$$ $$(1)x_{packets} + (0.5)y_{packets} = 6_{packets}$$

Now you can distribute in the negative dollar, add the equations together and solve for $y$.

So the equations become

$$(-1)x_{packets} + (-1)y_{packets} = -10_{packets}$$ $$(1)x_{packets} + (0.5)y_{packets} = 6_{packets}$$

Add them together

$$(-0.5)y_{packets} = -4_{packets}$$

Divide

$$y_{packets} = \frac{-4_{packets}}{-0.5} = 8_{packets}$$

And there's your answer.

All this shows is that you don't really have to worry about the units in equations like this, what you're looking for is a point where all the numbers line up and both equations become true.

And as John Hughes and Rory Daulton said, the units can just be cancelled out from the beginning.

Just don't worry about them.


text:
Clipping support in XeTeX

In pdflatex I'm used to clip graphics using something like this:

``````\includegraphics[trim=14mm 0mm 14mm 0mm,clip,width=1.2cm]{image.jpg}
``````

When I attempt this in XeLaTeX, no clipping occurs and I get a warning:

Package xetex.def Warning: No clipping support in XeTeX yet

It is obvious, that I could clip the image with a separate tool outside TeX, but for several reasons I would like to do this automatically from inside TeX (e.g. when migrating large old documents to XeTeX without messing around with the files)

Two questions:

1. Is there any workaround I should be aware of to do the clipping automatically during the TeX run? E.g. by replacing `\includegraphics` by something else (TikZ?)
2. Does anyone know if someone is working on clipping from inside XeTeX? Maybe there is a beta I could try?
-

The `graphics/x` output driver for XeLaTeX doesn't include clipping support yet. However, it is possible to clip using PGF/TikZ which brings his own driver (i.e. low level code) to do clipping. I have brought this issue up on `comp.text.tex`: Clipping support with XeLaTeX?. Also in the meantime Joseph Wright and I produced a clipping driver for XeTeX: Patch to add clipping support to XeTeX.

In the meantime the simplest way to get clipping is to use my `adjustbox` package which uses its own driver internally, including for XeLaTeX.

``````\usepackage{adjustbox}
% ...

`xetex.def` has some restrictions. The maintainers (Ross Moore and Jonathan Kew) seems not very familar with `\special`s of `xdvipdfmx`. I'm quite sure that `xdvipdfmx` can support clipping, since `dvipdfmx` (by Jin-Hwan Cho) supports clipping. –  Leo Liu Aug 5 '11 at 10:35
@Martin: Well, the `pgf`'s system layer for XeTeX also has some restrictions. Pity. –  Leo Liu Aug 5 '11 at 11:12


text:
# Figure-It-Out Function! - Part 6: The Second Reciprocal

Algebra Level 4

A function $$f(x)$$ is such that $$f(1) = 2$$, $$f(2)=1$$, and $$f(x)=\dfrac{1}{f(x-1)+f(x+1)}$$ for $$x \ge 2$$. Find

$\large (f(2014)f(2015))^{(f(2012)f(2013))^{...^{...^{(f(2)f(3))^{f(1)}}}}}$

×


text:
slide_index() is similar to slide(), but allows a secondary .i-ndex vector to be provided.

This is often useful in business calculations, when you want to compute a rolling computation looking "3 months back", which is approximately but not equivalent to, 3 * 30 days. slide_index() allows for these irregular window sizes.

slide_index(.x, .i, .f, ..., .before = 0L, .after = 0L, .complete = FALSE)

slide_index_vec(
.x,
.i,
.f,
...,
.before = 0L,
.after = 0L,
.complete = FALSE,
.ptype = NULL
)

slide_index_dbl(.x, .i, .f, ..., .before = 0L, .after = 0L, .complete = FALSE)

slide_index_int(.x, .i, .f, ..., .before = 0L, .after = 0L, .complete = FALSE)

slide_index_lgl(.x, .i, .f, ..., .before = 0L, .after = 0L, .complete = FALSE)

slide_index_chr(.x, .i, .f, ..., .before = 0L, .after = 0L, .complete = FALSE)

slide_index_dfr(
.x,
.i,
.f,
...,
.before = 0L,
.after = 0L,
.complete = FALSE,
.names_to = rlang::zap(),
.name_repair = c("unique", "universal", "check_unique")
)

slide_index_dfc(
.x,
.i,
.f,
...,
.before = 0L,
.after = 0L,
.complete = FALSE,
.size = NULL,
.name_repair = c("unique", "universal", "check_unique", "minimal")
)

## Arguments

.x [vector] The vector to iterate over and apply .f to. [vector] The index vector that determines the window sizes. It is fairly common to supply a date vector as the index, but not required. There are 3 restrictions on the index: The size of the index must match the size of .x, they will not be recycled to their common size. The index must be an increasing vector, but duplicate values are allowed. The index cannot have missing values. [function / formula] If a function, it is used as is. If a formula, e.g. ~ .x + 2, it is converted to a function. There are three ways to refer to the arguments: For a single argument function, use . For a two argument function, use .x and .y For more arguments, use ..1, ..2, ..3 etc This syntax allows you to create very compact anonymous functions. Additional arguments passed on to the mapped function. [vector(1) / function / Inf] If a vector of size 1, these represent the number of values before or after the current element of .i to include in the sliding window. Negative values are allowed, which allows you to "look forward" from the current element if used as the .before value, or "look backwards" if used as .after. Boundaries are computed from these elements as .i - .before and .i + .after. Any object that can be added or subtracted from .i with + and - can be used. For example, a lubridate period, such as lubridate::weeks(). If Inf, this selects all elements before or after the current element. If a function, or a one-sided formula which can be coerced to a function, it is applied to .i to compute the boundaries. Note that this function will only be applied to the unique values of .i, so it should not rely on the original length of .i in any way. This is useful for applying a complex arithmetic operation that can't be expressed with a single - or + operation. One example would be to use lubridate::add_with_rollback() to avoid invalid dates at the end of the month. The ranges that result from applying .before and .after have the same 3 restrictions as .i itself. [logical(1)] Should the function be evaluated on complete windows only? If FALSE, the default, then partial computations will be allowed. [vector(0) / NULL] A prototype corresponding to the type of the output. If NULL, the default, the output type is determined by computing the common type across the results of the calls to .f. If supplied, the result of each call to .f will be cast to that type, and the final output will have that type. If getOption("vctrs.no_guessing") is TRUE, the .ptype must be supplied. This is a way to make production code demand fixed types. This controls what to do with input names supplied in .... By default, input names are zapped. If a string, specifies a column where the input names will be copied. These names are often useful to identify rows with their original input. If a column name is supplied and ... is not named, an integer column is used instead. If NULL, the input names are used as row names. One of "unique", "universal", or "check_unique". See vec_as_names() for the meaning of these options. With vec_rbind(), the repair function is applied to all inputs separately. This is because vec_rbind() needs to align their columns before binding the rows, and thus needs all inputs to have unique names. On the other hand, vec_cbind() applies the repair function after all inputs have been concatenated together in a final data frame. Hence vec_cbind() allows the more permissive minimal names repair. If, NULL, the default, will determine the number of rows in vec_cbind() output by using the standard recycling rules. Alternatively, specify the desired number of rows, and any inputs of length 1 will be recycled appropriately.

## Value

A vector fulfilling the following invariants:

### slide_index()

• vec_size(slide_index(.x)) == vec_size(.x)

• vec_ptype(slide_index(.x)) == list()

### slide_index_vec() and slide_index_*() variants

• vec_size(slide_index_vec(.x)) == vec_size(.x)

• vec_size(slide_index_vec(.x)[[1]]) == 1L

• vec_ptype(slide_index_vec(.x, .ptype = ptype)) == ptype

## See also

slide(), hop_index(), slide_index2()

## Examples

library(lubridate)

x <- 1:5

# In some cases, sliding over x with a strict window size of 2
# will fit your use case.
slide(x, ~.x, .before = 1)
#> [[1]]
#> [1] 1
#>
#> [[2]]
#> [1] 1 2
#>
#> [[3]]
#> [1] 2 3
#>
#> [[4]]
#> [1] 3 4
#>
#> [[5]]
#> [1] 4 5
#>
# However, if this i is a date vector paired with x, when computing
# rolling calculations you might want to iterate over x while
# respecting the fact that i is an irregular sequence.
i <- as.Date("2019-08-15") + c(0:1, 4, 6, 7)

# For example, a "2 day" window should not pair "2019-08-19" and
# "2019-08-21" together, even though they are next to each other in x.
# slide_index() computes the lookback value from the current date in .i,
# meaning that if you are currently on "2019-08-21" and look back 1 day,
# it will correctly not include "2019-08-19".
slide_index(i, i, ~.x, .before = 1)
#> [[1]]
#> [1] "2019-08-15"
#>
#> [[2]]
#> [1] "2019-08-15" "2019-08-16"
#>
#> [[3]]
#> [1] "2019-08-19"
#>
#> [[4]]
#> [1] "2019-08-21"
#>
#> [[5]]
#> [1] "2019-08-21" "2019-08-22"
#>
# We could have equivalently used a lubridate period object for this as well,
# since i - lubridate::days(1) is allowed
slide_index(i, i, ~.x, .before = lubridate::days(1))
#> [[1]]
#> [1] "2019-08-15"
#>
#> [[2]]
#> [1] "2019-08-15" "2019-08-16"
#>
#> [[3]]
#> [1] "2019-08-19"
#>
#> [[4]]
#> [1] "2019-08-21"
#>
#> [[5]]
#> [1] "2019-08-21" "2019-08-22"
#>
# ---------------------------------------------------------------------------
# Functions for .before and .after

# In some cases, it might not be appropriate to compute
# .i - .before or .i + .after, either because there isn't a - or +
# method defined, or because there is an alternative way to perform the
# arithmetic. For example, subtracting 1 month with - months(1) (using
# lubridate) can sometimes land you on an invalid date that doesn't exist.
i <- as.Date(c("2019-01-31", "2019-02-28", "2019-03-31"))

# 2019-03-31 - months(1) = 2019-02-31, which doesn't exist
i - months(1)
#> [1] "2018-12-31" "2019-01-28" NA
# These NAs create problems with slide_index(), which doesn't allow
# missing values in the computed endpoints
try(slide_index(i, i, identity, .before = months(1)))
#> Error : Endpoints generated by .before cannot be NA.
#> ℹ They are NA at locations: 3.
# In these cases, it is more appropriate to use %m-%,
# which will snap to the end of the month, at least giving you something
# to work with.
i %m-% months(1)
#> [1] "2018-12-31" "2019-01-28" "2019-02-28"
# To use this as your .before or .after, supply an anonymous function of
# 1 argument that performs the computation
slide_index(i, i, identity, .before = ~.x %m-% months(1))
#> [[1]]
#> [1] "2019-01-31"
#>
#> [[2]]
#> [1] "2019-01-31" "2019-02-28"
#>
#> [[3]]
#> [1] "2019-02-28" "2019-03-31"
#>
# Notice that in the .after case, 2019-02-28 %m+% months(1) doesn't
# capture the end of March, so it isn't included in the 2nd result
slide_index(i, i, identity, .after = ~.x %m+% months(1))
#> [[1]]
#> [1] "2019-01-31" "2019-02-28"
#>
#> [[2]]
#> [1] "2019-02-28"
#>
#> [[3]]
#> [1] "2019-03-31"
#>
# ---------------------------------------------------------------------------

# When .i has repeated values, they are always grouped together.
i <- c(2017, 2017, 2018, 2019, 2020, 2020)
slide_index(i, i, ~.x)
#> [[1]]
#> [1] 2017 2017
#>
#> [[2]]
#> [1] 2017 2017
#>
#> [[3]]
#> [1] 2018
#>
#> [[4]]
#> [1] 2019
#>
#> [[5]]
#> [1] 2020 2020
#>
#> [[6]]
#> [1] 2020 2020
#> slide_index(i, i, ~.x, .after = 1)
#> [[1]]
#> [1] 2017 2017 2018
#>
#> [[2]]
#> [1] 2017 2017 2018
#>
#> [[3]]
#> [1] 2018 2019
#>
#> [[4]]
#> [1] 2019 2020 2020
#>
#> [[5]]
#> [1] 2020 2020
#>
#> [[6]]
#> [1] 2020 2020
#>
# ---------------------------------------------------------------------------
# Rolling regressions

# Rolling regressions are easy with slide_index() because:
# - Data frame .x values are iterated over rowwise
# - The index is respected by using .i
set.seed(123)

df <- data.frame(
y = rnorm(100),
x = rnorm(100),
i = as.Date("2019-08-15") + c(0, 2, 4, 6:102) # <- irregular
)

# 20 day rolling regression. Current day + 19 days back.
# Additionally, set .complete = TRUE to not compute partial results.
regr <- slide_index(df, df$i, ~lm(y ~ x, .x), .before = 19, .complete = TRUE) regr[16:18] #> [[1]] #> NULL #> #> [[2]] #> #> Call: #> lm(formula = y ~ x, data = .x) #> #> Coefficients: #> (Intercept) x #> 0.3257 0.2067 #> #> #> [[3]] #> #> Call: #> lm(formula = y ~ x, data = .x) #> #> Coefficients: #> (Intercept) x #> 0.2574 0.2632 #> #> # The first 16 slots are NULL because there is no possible way to # look back 19 days from the 16th index position and construct a full # window. But on the 17th index position, ""2019-09-03", if we look # back 19 days we get to ""2019-08-15", which is the same value as # i[1] so a full window can be constructed. df$i[16] - 19 >= df$i[1] # FALSE #> [1] FALSEdf$i[17] - 19 >= df$i[1] # TRUE #> [1] TRUE # --------------------------------------------------------------------------- # Accessing the current index value # A very simplistic version of purrr::map2() fake_map2 <- function(.x, .y, .f, ...) { Map(.f, .x, .y, ...) } # Occasionally you need to access the index value that you are currently on. # This is generally not possible with a single call to slide_index(), but # can be easily accomplished by following up a slide_index() call with a # purrr::map2(). In this example, we want to use the distance from the # current index value (in days) as a multiplier on x. Values further # away from the current date get a higher multiplier. set.seed(123) # 25 random days past 2000-01-01 i <- sort(as.Date("2000-01-01") + sample(100, 25)) df <- data.frame(i = i, x = rnorm(25)) weight_by_distance <- function(df, i) { df$weight = abs(as.integer(df$i - i)) df$x_weighted = df$x * df$weight
df
}

# Use slide_index() to just generate the rolling data.
# Here we take the current date + 5 days before + 5 days after.
dfs <- slide_index(df, df$i, ~.x, .before = 5, .after = 5) # Follow up with a map2() with i as the second input. # This allows you to track the current i value and weight accordingly. result <- fake_map2(dfs, df$i, weight_by_distance)

head(result)
#> [[1]]
#>            i          x weight x_weighted
#> 1 2000-01-08 -0.2179749      0   0.000000
#> 2 2000-01-10 -1.0260044      2  -2.052009
#>
#> [[2]]
#>            i          x weight x_weighted
#> 1 2000-01-08 -0.2179749      2 -0.4359498
#> 2 2000-01-10 -1.0260044      0  0.0000000
#> 3 2000-01-15 -0.7288912      5 -3.6444561
#>
#> [[3]]
#>            i          x weight x_weighted
#> 1 2000-01-10 -1.0260044      5 -5.1300222
#> 2 2000-01-15 -0.7288912      0  0.0000000
#> 3 2000-01-16 -0.6250393      1 -0.6250393
#>
#> [[4]]
#>            i          x weight x_weighted
#> 1 2000-01-15 -0.7288912      1 -0.7288912
#> 2 2000-01-16 -0.6250393      0  0.0000000
#>
#> [[5]]
#>            i         x weight x_weighted
#> 1 2000-01-26 -1.686693      0   0.000000
#> 2 2000-01-27  0.837787      1   0.837787
#>
#> [[6]]
#>            i          x weight x_weighted
#> 1 2000-01-26 -1.6866933      1 -1.6866933
#> 2 2000-01-27  0.8377870      0  0.0000000
#> 3 2000-02-01  0.1533731      5  0.7668656
#>


text:
My Math Forum probability question ?????

 Probability and Statistics Basic Probability and Statistics Math Forum

 May 24th, 2011, 06:23 AM #1 Senior Member   Joined: Mar 2011 Posts: 105 Thanks: 0 probability question ????? A restaurant found out 55% customers have coffees with their meal... If there are 12 people, what is the probablity to have exactly 7 people have coffee with their meal... A. 0.015 B. 0.222 C. 0.4242 D. 0.512... I don't know how to do it. But with this multiple choice: I chose D. Because I follow 55%.... So, if there are 12 people.... with 55% have coffees with their meal....... It would be 6.6 So it's between 6 and 7..... But it's closer to 7 than 6 ( it's 6.6) So it should be greater than 0.5 and I chose D Can somebody tell me how to solve it, please?
 May 24th, 2011, 07:53 AM #2 Senior Member   Joined: Sep 2009 Posts: 106 Thanks: 0 Re: probability question ????? I understand it like this, the prob is 0% because. if you have 12 ppl & 55% have cofee, then 6,6 ppl have coffee. But question says 7 people must have coffee. This can not happen.
 May 24th, 2011, 07:54 AM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: probability question ????? You need to use the formula for binomial probability: $P(x)=\binom{12}{7}(0.55)^7(1-0.55)^5\approx0.222$
May 24th, 2011, 03:43 PM   #4
Senior Member

Joined: Mar 2011

Posts: 105
Thanks: 0

Re: probability question ?????

Quote:
 Originally Posted by peaceofmind I understand it like this, the prob is 0% because. if you have 12 ppl & 55% have cofee, then 6,6 ppl have coffee. But question says 7 people must have coffee. This can not happen.
you understand it, Why it can't happen?

I know it's 6,6...but question say 7 people in 12 people..... So that's why we have to find the probability to get 7 people!!!

May 24th, 2011, 03:45 PM   #5
Senior Member

Joined: Mar 2011

Posts: 105
Thanks: 0

Re: probability question ?????

Quote:
 Originally Posted by MarkFL You need to use the formula for binomial probability: $P(x)=\binom{12}{7}(0.55)^7(1-0.55)^5\approx0.222$

THank you, Mr. MarkFL, again.....

My teacher didn't teach me this lesson.... But he put it on my Final Exam.......and didn't omit it..
I thought it was about simple lessons.
I failed that one question!!!!

Thank you, Mr. MarkFL

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text:
Conjecture for prime pairs of difference two

1. Jun 2, 2009

Loren Booda

Can it be proven that the number of prime pairs with a difference of two (that is, primes separated by only one even number) approaches infinity?

2. Jun 2, 2009

CRGreathouse

This is the of-yet-unproved Twin Prime Conjecture.

3. Jun 3, 2009

Dragonfall

Do you mean that infinitely many primes separated by the same even number? Or do you mean infinitely many primes separated by a multiple of the same even number? The latter is true.

4. Jun 3, 2009

CRGreathouse

I know Elliott-Halberstam implies that (via Goldston-Pintz-Yıldırım), but is it known unconditionally? As far as I know, $g_n>\sqrt{\log p_n}$ for all n sufficiently large has not been disproven.

Oh wait, I just reread what you wrote. The latter is trivially true, since all prime gaps but the first are divisible by 2.

5. Jun 4, 2009

Loren Booda

The number of pairs of primes with a difference of two.

6. Jun 4, 2009

Dragonfall

That would be the said "Twin Primes Conjecture".

7. Jun 4, 2009

HallsofIvy

But you wouldn't say "approaches" infinity in either case. Either the number of twin primes is infinite or it is a specific integer.


text:
# how to implement a DAC in VHDL

Status
Not open for further replies.

#### OhJ

##### Newbie level 3
hello,

can someone please help me with the basic explanation (1, 2, 3) / functionlity of how a DAC can be implemented in VHDL. Ive read so much info on the internet, im now confused. j Im wondering why things are being done differently.

My question is with regards to using a look-up table.
1) what determines the boundaries of the lookup table.
2) how do I calculate the steps based on the lookup table,
etc..

pls assist
regards
OhJ

#### K-J

hello,

can someone please help me with the basic explanation (1, 2, 3) / functionlity of how a DAC can be implemented in VHDL. Ive read so much info on the internet, im now confused.
You haven't given anyone here what you've read and what you're confused about, so all we can do is add to what you've read and maybe to your confusion...or maybe not.

First, a DAC cannot be implemented in VHDL. VHDL defines digital logic, 1 and 0, that's it. The voltage that 1 and 0 represent depends on the target device, but typically the I/O supply voltage is 3.3V and the parts can drive nearly rail to rail which means you can implent something that generates 0V and 3.3V directly. But now consider a digital signal that toggles very fast (say 100 MHz), half the time it is a 1 (3.3V), half the time it is 0 (0V). Put a multimeter on it and you'll read 3.3 / 2 = 1.65V. Look at the signal on a scope and you'll see that things are indeed toggling though. Now put a resistor in series with the output signal followed by a capacitor to ground. Make the RC time constant large enough such that the bandwidth of this filter is say 1 MHz. Now look at the node where the RC connect on the scope and you'll see a pretty stable 1.65V.

Now change the VHDL so that once every 4 clock cycles you output a 1, the other times 0. You'll now measure 3.3 / 4 = 0.82V at the RC.

Assuming you're understanding now that the ratio of ones to zeros basically defines the steady state voltage then you understand how to implement a DAC with VHDL plus an RC filter.

There are other points to consider when implementing a DAC, but since you asked no specific question with your post, I'll just leave it at this for now.

Im wondering why things are being done differently.
What's wrong with different? Not to mention 'different' from what?

My question is with regards to using a look-up table.
1) what determines the boundaries of the lookup table.
2) how do I calculate the steps based on the lookup table,
etc..
What lookup table? The above mentioned description for how to create a DAC requires no lookup table. The digital output is a pulse width modulated signal which can be implemented with at most two counters and nothing else.

Consider adding more specifics to whatever questions you actually have.

Kevin Jennings

graphene

### graphene

points: 2

#### gongdori

##### Full Member level 2
As Kevin said, FPGA cannot output somewhere between logic 1 and logic 0. Thus, you cannot implement a DAC with only FPGA.
But, you can also implement DAC with multiple output pins of FPGA and resistor network. You will get more information about it if you search R-2R ladder network.

#### OhJ

##### Newbie level 3
hello sirs,

I asked my question after reading several stuffs on the internet about DAC in VHDL, sine wave in VHDL, etc., for example: below:
http://www.doulos.com/knowhow/vhdl_designers_guide/models/analogtodigital_converter_model/
http://www.scribd.com/doc/60291432/...erter-circuitry-and-VHDL-code-for-the-DAC0808,

etc., I forgot the others. So I myself was now wondering what the basic concept of a DAC in VHDL is.

Thanks for your updates. Im working with a Nexys2 board and their DAC PMOD, which they say can convert digital to analog signals:
http://digilentinc.com/Products/Detail.cfm?NavPath=2,401,501&Prod=PMOD-DA1

so maybe I should be looking for how to control the PMOD instead?

On the other hand, what kind of input am I supposed to have for a DAC? suppose I am trying to control a DAC chip with VHDL. For ex: Somebody told me that I could have an 8bit digital input, for ex: "FF" or whatever which is fed into my system and this could be converted into an analog signal. I wasnt too comfortable with the explanation as I wondered how such could be done with pen and paper at least.

My idea is a system, suppose after synthesis, etc, and then I program my board with the .bit file, and then I can give inputs to the design using external sources: switches, whatever. Is this idea correct? I dont think so, but please help me clarify.

About the lookup table I mentioned earlier, I dont know how I got to the link, but the idea there was that there were some values hardcoded in a case statement, used as the DAC's inputs. My dilema here was how the beginning and ending values are determined, how the intervals are calculated and the relationships between them, etc. Ill look for the link and post it.

regards
OhJ

#### gongdori

##### Full Member level 2
The first link shows how to "model" DAC in VHDL. You cannot implement it on real circuit, but simulate it.
The second link shows how to build a interface module in VHDL to a specific DAC. In this case, you need to have a board with the FPGA and the specific silicon.
I hope it helps...

#### Kepsz

##### Member level 1
Pmod DA1 is outdated, if i know right, currently only DA2 is able to buy. (at least in Hungary only DA2 avaible)

Pmod DA2 is waits for 12 bit vector in the input ( in 16 bit form where 16 - 13 bits are control bits), so u can set the output voltage between gnd and V+ (3.3V?) in 4095 steps. This communication is a simply serial communication, wich can works up to 30MHz ( frequency is limited by DA2's capabilties ).

The DAC's very simple, if it's got the input, it will sets the output immideatly and keeps it while new data arrives.

This code below is the actualised version of Digilent's bit outdated example code for pmod DA2, using ieee.numeric_std instead of arith and others...:

Code:
library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use ieee.numeric_std.all;

entity DAC is
Port (
CLK, RST, START					: in std_logic;
D1, D2, CLK_OUT, nSYNC,DONE	: out std_logic;
DATA1, DATA2    					: in std_logic_vector(11 downto 0));
end DAC;

architecture Behavioral of DAC is
type states is (Idle,ShiftOut,SyncData);
signal current_state 		: states;
signal next_state    		: states;
signal temp1, temp2			: std_logic_vector(15 downto 0);
signal clk_div, shiftCounter, enShiftCounter, enParalelLoad       : std_logic;

begin

clkdiv: process(clk, rst)
variable clk_counter : integer range 0 to 5;  --for 120MHz system clock. 120/5 = 24MHz serial clock.
begin
if (rising_edge(clk)) then
if (rst = '1') then
clk_div <= '0';
clk_out <= '0';
clk_counter := 0;
else
if (clk_counter = 5) then
clk_div <= '1';
clk_out <= '1';
clk_counter := 0;
else
clk_div <= '0';
clk_out <= '0';
clk_counter := clk_counter + 1;
end if;
end if;
end if;
end process;

counter : process(clk_div, shiftcounter, enParalelLoad, enShiftCounter, DATA1, DATA2)
variable count : integer range 0 to 15;
begin
if (rising_edge(clk_div)) then
shiftCounter <= '0';
temp1 <= "0000" & DATA1;
temp2 <= "0000" & DATA2;
elsif (enShiftCounter = '1') then
temp1 <= temp1(14 downto 0)&temp1(15);
temp2 <= temp2(14 downto 0)&temp2(15);
count := count + 1;
if (count = 15) then
shiftcounter <= '1';
end if;
end if;
end if;
end process;

D1 <= temp1(15);
D2 <= temp2(15);

SYNC_PROC: process (clk_div, rst)
begin
if (rising_edge(clk_div)) then
if (rst = '1') then
current_state <= Idle;
else
current_state <= next_state;
end if;
end if;
end process;

OUTPUT_DECODE: process (CLK, current_state)
begin
if (rising_edge(CLK)) then
if (current_state = Idle) then
enShiftCounter <='0';
DONE <='1';
nSYNC <='1';
elsif (current_state = ShiftOut) then
enShiftCounter <='1';
DONE <='0';
nSYNC <='0';
else
enShiftCounter <='0';
DONE <='0';
nSYNC <='1';
end if;
end if;
end process;

NEXT_STATE_DECODE: process (CLK, current_state, START, shiftCounter)
begin
if (rising_edge(CLK)) then
next_state <= current_state;
case (current_state) is
when Idle =>
if (START = '1') then
next_state <= ShiftOut;
end if;
when ShiftOut =>
if (shiftCounter = '1') then
next_state <= SyncData;
end if;
when SyncData =>
if (START = '0') then
next_state <= Idle;
end if;
when others =>
next_state <= Idle;
end case;
end if;
end process;
end Behavioral;
This code is fully works, just edit the clkdiv process for your board's base clock.


text:
Accelerating the pace of engineering and science

# nLinearCoeffs

Number of nonzero linear coefficients

## Syntax

ncoeffs = nLinearCoeffs(obj)
ncoeffs = nLinearCoeffs(obj,delta)

## Description

ncoeffs = nLinearCoeffs(obj) returns the number of nonzero linear coefficients in the linear discriminant model obj.

ncoeffs = nLinearCoeffs(obj,delta) returns the number of nonzero linear coefficients for threshold parameter delta.

## Input Arguments

 obj Discriminant analysis classifier, produced using fitcdiscr. delta Scalar or vector value of the Delta parameter. See Gamma and Delta.

## Output Arguments

 ncoeffs Nonnegative integer, the number of nonzero coefficients in the discriminant analysis model obj. If you call nLinearCoeffs with a delta argument, ncoeffs is the number of nonzero linear coefficients for threshold parameter delta. If delta is a vector, ncoeffs is a vector with the same number of elements. If obj is a quadratic discriminant model, ncoeffs is the number of predictors in obj.

## Definitions

### Gamma and Delta

Regularization is the process of finding a small set of predictors that yield an effective predictive model. For linear discriminant analysis, there are two parameters, γ and δ, that control regularization as follows. cvshrink helps you select appropriate values of the parameters.

Let Σ represent the covariance matrix of the data X, and let $\stackrel{^}{X}$ be the centered data (the data X minus the mean by class). Define

$D=\text{diag}\left({\stackrel{^}{X}}^{T}*\stackrel{^}{X}\right).$

The regularized covariance matrix $\stackrel{˜}{\Sigma }$ is

$\stackrel{˜}{\Sigma }=\left(1-\gamma \right)\Sigma +\gamma D.$

Whenever γ ≥ MinGamma, $\stackrel{˜}{\Sigma }$ is nonsingular.

Let μk be the mean vector for those elements of X in class k, and let μ0 be the global mean vector (the mean of the rows of X). Let C be the correlation matrix of the data X, and let $\stackrel{˜}{C}$ be the regularized correlation matrix:

$\stackrel{˜}{C}=\left(1-\gamma \right)C+\gamma I,$

where I is the identity matrix.

The linear term in the regularized discriminant analysis classifier for a data point x is

${\left(x-{\mu }_{0}\right)}^{T}{\stackrel{˜}{\Sigma }}^{-1}\left({\mu }_{k}-{\mu }_{0}\right)=\left[{\left(x-{\mu }_{0}\right)}^{T}{D}^{-1/2}\right]\left[{\stackrel{˜}{C}}^{-1}{D}^{-1/2}\left({\mu }_{k}-{\mu }_{0}\right)\right].$

The parameter δ enters into this equation as a threshold on the final term in square brackets. Each component of the vector $\left[{\stackrel{˜}{C}}^{-1}{D}^{-1/2}\left({\mu }_{k}-{\mu }_{0}\right)\right]$ is set to zero if it is smaller in magnitude than the threshold δ. Therefore, for class k, if component j is thresholded to zero, component j of x does not enter into the evaluation of the posterior probability.

The DeltaPredictor property is a vector related to this threshold. When δ ≥ DeltaPredictor(i), all classes k have

$|{\stackrel{˜}{C}}^{-1}{D}^{-1/2}\left({\mu }_{k}-{\mu }_{0}\right)|\le \delta .$

Therefore, when δ ≥ DeltaPredictor(i), the regularized classifier does not use predictor i.

## Examples

expand all

### Find the Number of Nonzero Coefficients in a Discriminant Analysis Classifier

Find the number of nonzero coefficients in a discriminant analysis classifier for various Delta values.

Create a discriminant analysis classifier from the fishseriris data.

```load fisheriris
obj = fitcdiscr(meas,species);```

Find the number of nonzero coefficients in obj.

`ncoeffs = nLinearCoeffs(obj)`
```ncoeffs =

4```

Find the number of nonzero coefficients for delta = 1, 2, 4, and 8.

```delta = [1 2 4 8];
ncoeffs = nLinearCoeffs(obj,delta)```
```ncoeffs =

4
4
3
0```

The DeltaPredictor property gives the values of delta where the number of nonzero coefficients changes.

`ncoeffs2 = nLinearCoeffs(obj,obj.DeltaPredictor)`
```ncoeffs2 =

4
3
1
2```


text:
# Dot Product Calculator

To use dot product calculator, choose the vector dimensions, enter the measurements of both vectors, and click Calculate

First vector (a)

i
j
k

Second vector (b)

i
j
k

Is This Tool Helpful?

## Dot Product Calcualtor

The dot product calculator finds the scalar product of 2-dimensional and 3-dimensional vectors. Users can find the step-by-step process in the result section by clicking on “show more”.

## What is dot product?

The dot product of two vectors is also known as its scalar product. This is because the result of this product is always a scalar quantity. It uses the sine function.

The dot product is helpful in finding the projection of one vector on the other. The dot product abides by the commutative and distributive properties. It is written as A.B and read as A dot B.

## Dot product formula:

Mathematically dot product is written as:

A.B = |A||B| Cosθ

|A| and |B| are the magnitudes of the vectors where theta is the angle between the vectors.

Another formula is:

A.B = (a1b1) + (a2b2) + (a3b3) + … + (anbn)

## How to find the dot product of two vectors?

Unlike the cross product, the dot product only has magnitude and no direction. The steps to calculate dot product by hand are:

1. Find the magnitude of the vector A.
2. Similarly, find the magnitude of the vector B.
3. Calculate the sin of angle using the trigonometry calculator or table.
4. Put the values in the formula and solve.

The second method is easy, simply multiply the first entry vector A with the first entry of vector B, the second entry of vector A with the second henry of vector B, and so on. Lastly, add all the values.

Example:

What is the value of the dot product for these two vectors?

A = 4 i + 6 j + 5 k
B = 3 i + 2 j + 7 k

Solution:

Step 1: Identify the entries.

a1 = 4, a2 = 6, a3 = 5
b1 = 3, b2 = 2, b3 = 7

Step 2: Put in the formula.

A.B = (a1b1) + (a2b2) + (a3b3) + … + (anbn)
A.B = (4)(3) + (6)(2) + (5)(7)

Step 3: Solve.

A.B = (4)(3) + (6)(2) + (5)(7)
A.B = 12 + 12 + 35
A.B = 59


text:
# What is the intuition behind using Monte Carlo to solve a differential equation

Conceptually, I understand how a numerical method like Monte Carlo is used to solve a definite integral. Because integral of a function is the area bounded by the curve, the ratio of random points that land inside the curve to the total number of points is the value of the integral.

Conceptually, can someone explain for a non math person, how we can solve a PDE/ODE using Monte Carlo?


text:
# Second Position of the Arms

Arms stretch to the sides of the body either just below shoulder height (Russian) or sloping downward and slightly rounded (Cecchetti)."

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text:
MathSciNet bibliographic data MR2361790 32S40 (32C38 34M35) Morando, Giovanni An existence theorem for tempered solutions of \$\scr D\$$\scr D$-modules on complex curves. Publ. Res. Inst. Math. Sci. 43 (2007), no. 3, 625–659. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


text:
# Revision history [back]

Can you try

export PYTHONNOUSERSITE=yes
sage

This should prevent Sage from picking up stuff in .local/lib. If that fixes your problem we can add it to the next release.