text:
# Is this number a prime?

Believe it or not, we do not yet have a code golf challenge for a simple primality test. While it may not be the most interesting challenge, particularly for "usual" languages, it can be nontrivial in many languages.

Rosetta code features lists by language of idiomatic approaches to primality testing, one using the Miller-Rabin test specifically and another using trial division. However, "most idiomatic" often does not coincide with "shortest." In an effort to make Programming Puzzles and Code Golf the go-to site for code golf, this challenge seeks to compile a catalog of the shortest approach in every language, similar to "Hello, World!" and Golf you a quine for great good!.

Furthermore, the capability of implementing a primality test is part of our definition of programming language, so this challenge will also serve as a directory of proven programming languages.

### Task

Write a full program that, given a strictly positive integer n as input, determines whether n is prime and prints a truthy or falsy value accordingly.

For the purpose of this challenge, an integer is prime if it has exactly two strictly positive divisors. Note that this excludes 1, who is its only strictly positive divisor.

Your algorithm must be deterministic (i.e., produce the correct output with probability 1) and should, in theory, work for arbitrarily large integers. In practice, you may assume that the input can be stored in your data type, as long as the program works for integers from 1 to 255.

### Input

• If your language is able to read from STDIN, accept command-line arguments or any other alternative form of user input, you can read the integer as its decimal representation, unary representation (using a character of your choice), byte array (big or little endian) or single byte (if this is your languages largest data type).

• If (and only if) your language is unable to accept any kind of user input, you may hardcode the input in your program.

In this case, the hardcoded integer must be easily exchangeable. In particular, it may appear only in a single place in the entire program.

For scoring purposes, submit the program that corresponds to the input 1.

### Output

Output has to be written to STDOUT or closest alternative.

If possible, output should consist solely of a truthy or falsy value (or a string representation thereof), optionally followed by a single newline.

The only exception to this rule is constant output of your language's interpreter that cannot be suppressed, such as a greeting, ANSI color codes or indentation.

### Additional rules

• This is not about finding the language with the shortest approach for prime testing, this is about finding the shortest approach in every language. Therefore, no answer will be marked as accepted.

• Submissions in most languages will be scored in bytes in an appropriate preexisting encoding, usually (but not necessarily) UTF-8.

The language Piet, for example, will be scored in codels, which is the natural choice for this language.

Some languages, like Folders, are a bit tricky to score. If in doubt, please ask on Meta.

• Unlike our usual rules, feel free to use a language (or language version) even if it's newer than this challenge. If anyone wants to abuse this by creating a language where the empty program performs a primality test, then congrats for paving the way for a very boring answer.

Note that there must be an interpreter so the submission can be tested. It is allowed (and even encouraged) to write this interpreter yourself for a previously unimplemented language.

• If your language of choice is a trivial variant of another (potentially more popular) language which already has an answer (think BASIC or SQL dialects, Unix shells or trivial Brainfuck derivatives like Headsecks or Unary), consider adding a note to the existing answer that the same or a very similar solution is also the shortest in the other language.

• Built-in functions for testing primality are allowed. This challenge is meant to catalog the shortest possible solution in each language, so if it's shorter to use a built-in in your language, go for it.

• Unless they have been overruled earlier, all standard rules apply, including the http://meta.codegolf.stackexchange.com/q/1061.

As a side note, please don't downvote boring (but valid) answers in languages where there is not much to golf; these are still useful to this question as it tries to compile a catalog as complete as possible. However, do primarily upvote answers in languages where the author actually had to put effort into golfing the code.

### Catalog

The Stack Snippet at the bottom of this post generates the catalog from the answers a) as a list of shortest solution per language and b) as an overall leaderboard.

To make sure that your answer shows up, please start your answer with a headline, using the following Markdown template:

## Language Name, N bytes

where N is the size of your submission. If you improve your score, you can keep old scores in the headline, by striking them through. For instance:

## Ruby, <s>104</s> <s>101</s> 96 bytes

If there you want to include multiple numbers in your header (e.g. because your score is the sum of two files or you want to list interpreter flag penalties separately), make sure that the actual score is the last number in the header:

## Perl, 43 + 2 (-p flag) = 45 bytes

You can also make the language name a link which will then show up in the snippet:

## [><>](http://esolangs.org/wiki/Fish), 121 bytes

 <link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b">

Shortest Solution by Language

Language	User	Score

Leaderboard

	Author	Language	Size

{{PLACE}}	{{NAME}}	{{LANGUAGE}}	{{SIZE}}	Link

{{LANGUAGE}}	{{NAME}}	{{SIZE}}	Link

• Can I take inputs as negative numbers, where abs(input) would be the number I am testing? – Stan Strum Sep 6 '17 at 3:40
• No, the input is a strictly positive integer. – Dennis Sep 6 '17 at 3:44
• @LyndonWhite This was intended as a catalog (like “Hello, World!”) of primality tests, so a unified submission format seemed preferable. It's one of two decisions about this challenge that I regret, the other being only allowing deterministic primality tests. – Dennis Dec 12 '17 at 12:51
• @Shaggy Seems like a question for meta. – Dennis Jun 25 '18 at 13:44
• Yeah, that's what I was thinking. I'll let you do the honours, seeing as it's your challenge. – Shaggy Jun 25 '18 at 13:45

# Perl 6, 20 bytes

say get~~$_%%one ^$_

Try it online!

There's also the built-in is-prime, but I thought it would be more interesting to do it without it. Surprisingly, this is only 4 bytes longer.

### Explanation:

get                # Get a line of input
~~              # Smartmatch it by setting $_ to input$_%%          # Is input divisible by
one       # Only one of
^$_ # The range 0 to input-1? say # And print Note that this works because n%%0 is boolified to False. # 05AB1E, 3 bytes fнQ find all factors and see if last one equals input. Try it online! • Built-ins are allowed, so just p is enough. – Grimy Mar 29 at 13:32 # Gol><>, 4 bytes ISPh Thanks to ASCII-only for letting me now I didn't need 2 bytes, since it was redundant. Try it online! • The ?1 is needed?????? – ASCII-only Feb 20 at 16:07 • @ASCII-only Thank you for pointing that out, I didn't even think of that. Fixing it now! – KrystosTheOverlord Feb 20 at 17:23 • At least in this particular implementation of Gol><>, P is implemented by the is_probably_prime function. Unfortunately, this challenge requires a deterministic primality test. – Dennis Feb 20 at 19:37 • @Dennis The is_probably_prime function is a wrapper for the sympy isprime function, which is deterministic up to $2^{64}$. If the sympy library is not available, then it does a non-deterministic check. – Jo King Mar 15 at 1:58 # dc, 17 22 bytes ?d*5+v[dz%rdz<M*]dsMxp Try it online! I've been on a bit of a dc kick lately and although there's already a dc solution here, this is 10 5 bytes shorter. It follows the I/O request of the original question, which does add two bytes for the explicit input and output (rather than the usual rules these days that allow implicit stack I/O), but okay. This outputs zero for composite numbers and non-zero for primes. How it works: this program builds a stack consisting of the modulo of the input with the current stack size (so the stack looks like, from bottom to top, i%2, i%3, i%4, ...), then when it decides it's gone far enough (stack size = input) it multiplies the stack as it unwinds the recursion. • This fails for 1 and 2. – Ørjan Johansen Mar 16 at 0:22 • Oof, you're right. Not sure how I missed that. It took me five bytes to fix (by precomposing with d*5+v, i.e., x -> int(sqrt(x^2+5)), i.e., 1->2, 2->3, n->n for n>2) – Sophia Lechner Mar 18 at 18:09 # Java, 108 bytes interface P{static void main(String[]a){long l=new Long(a[0]),i=1;for(;0<l%++i%l;);System.out.print(l==i);}} Try it online! Port of my Ink answer. Would beat all existing answers in C, C#, Python (2 and 3), and possibly other languages if ported. # Ungolfed interface PrimeChecker { // Unlike members of classes, members of interfaces are public by default. static void main(String[] args) { long input = new Long(args[0]), div = 1; for (; 0 < ( input % (++div) // Trial division, finish when div divides input % input /* If input is at least 2, this has no effect. But (1 % n) = 1 for any n > 1 so without this, the loop would never end when the input is 1 */ ); ) { /* The loop body is empty, we're just using it to set div */ } // div is now the lowest number greater than 1 that divides the input // (or 2, if the input is 1) // The input is prime iff that number is equal to the input System.out.println(input == div); } } • Note for those who, like me, didn't understand the existence of the last %l at first, it's to shortcut the loop when the input is 1. – Olivier Grégoire May 16 at 15:42 # Pyth, 8 bytes &>Q1!tPQ Alternative that doesn't support values less than 2: !tPQ • Context: The 4-byte version was the only one at the time that comment was posted. – CalculatorFeline Mar 20 '16 at 4:18 # Perl, 35 bytes Uses regular expressions...$_=1x$_;s/^(11+?)\g1+$//;print$_>1 That's 34 bytes of code, plus one byte for the -n switch needed to fetch a line from stdin. Outputs 1 if the number is prime, or nothing otherwise # K, 25 bytes 0:$~x!1+*/1+!(x:. 0:)-1
• How should this be run? I tried kona/k program <<< input, but that doesn't seem to work. – Dennis Sep 11 '15 at 19:00

# Stuck, 3 bytes

iv|

Prints 1 for primes and 0 for non-primes. (The definition of "truthy/falsy values" means I can't use iv, because Stuck prints False/True without knowing what those are.)

# Scala, 96 bytes

#!/usr/bin/env scala
print(((a:Int)=>if(a==2)true;else!2.to(a-1).exists(a%_==0))(args(0).toInt))

JVM and yet not last place :D

Does use some bash functionality but I'm using Scala so don't be too hard on me.

• It's possible in 50 bytes. :) – Emil Lundberg Sep 24 '15 at 12:07
• @EmilLundberg That code won't run. You need a main method or use the same trick I used. – Martijn Sep 24 '15 at 15:13
• Huh, you're right that it doesn't compile as scalac prime.scala. But it does run as scala prime.scala. – Emil Lundberg Sep 24 '15 at 15:47

# XPath 2.0, 45 40 bytes

$i>1 and empty((2 to$i -1)[$i mod .=0]) For readability, incl. non-mandatory spaces (45 bytes)$i > 1 and empty((2 to $i - 1)[$i mod . = 0])

In XPath, the only way to hand input like an integer to the processor is by passing it a parameter, in this case $i. This is hardly performant, and obvious improvement would be to use:$i > 1 and empty((2 to math:sqrt($i) cast as xs:integer)[$i mod . = 0])

But since "shortest in any given language" and not performance was the goal, I'll leave the original in.

### How it works

For people new to XPath, it works as follows:

1. Create a sequence up to the current number:

(2 to $i - 1) 2. Filter all that have a modulo zero (i.e., that divide properly) [$i mod . = 0]

3. Test if the resulting sequence is empty, if it non-empty, there is a divisor

empty(...)

4. Also test for special-case 1:

$i > 1 The query as a whole returns the string true (2, 5, 101, 5483) or false (1, 4, 5487). As a nice consequence, you can find all divisors (not prime divisors!) using an even shorter expression: (2 to$i - 1)[$i mod . = 0] will return (3, 5, 7, 15, 21, 35) for input 105. # XSLT 3.0, 209203 201 bytes <transform xmlns="http://www.w3.org/1999/XSL/Transform" xmlns:x="x" version="3.0"><function name="x:p" expand-text="1"><param name="i"/>{$i>1 and empty((2 to $i -1)[$i mod .=0])}</function></transform>

Update 1: removed spaces in $i > 1, . = 0 and$i - 1.
Update 2: changed expand-text="yes" in expand-text="1", which is a new XSLT 3.0 feature

In expanded form, with the usual prefixes:

<xsl:stylesheet
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:x="x"
version="3.0">

<xsl:function name="x:p" expand-text="yes">
<xsl:param name="i"/>{
$i > 1 and empty((2 to$i - 1)[$i mod . = 0]) }</xsl:function> </xsl:stylesheet> This method uses the XSLT 3.0 feature to have a function as entry point (earlier versions did not support this). It uses the same XPath expression explained in my other post. XSLT is notoriously verbose and starts with quite a few bytes declaring namespaces etc. The function must be called with a typed value that derives from xs:integer. Most processor will consider that the default type if given an integer literal. # SWI-Prolog, 51 bytes a(X):-X>1,\+ (Y is X-1,between(2,Y,I),0=:=X mod I). This uses predicate between/3 which is not an ISO-Prolog predicate. • You can save 6 bytes by shifting the range of I up by 1 (thus removing the necessity for Y) and using I-1 in the mod. TIO link – 0 ' Dec 20 '17 at 20:42 • You can save another 2 bytes by replacing a(X) with -X. – 0 ' Dec 23 '17 at 17:33 • A bit of competition: codegolf.stackexchange.com/questions/57617/… – 0 ' Dec 24 '17 at 6:30 # JavaScript, 57 Prime finding regex. alert(!/^1?$|^(11+?)\1+$/.test(Array(prompt()+1).join(1))) • That won't work. prompt() returns a string, not a number, so for input 3, you wind up with the string 31. The whole conversion isn't needed though. The questions allows reading the input in unary. – Dennis Sep 17 '15 at 19:40 • Yeah, I was thinking of a way to fix it. Guess I never got around to actually fixing it... – RK. Sep 17 '15 at 19:59 • Just adding + before the prompt() should work. – ETHproductions Dec 6 '15 at 18:49 # Python 3, 54 bytes A just for fun post that abuses the all function. y=int(input());print(all(y%p for p in range(2,y))|y>1) Explanation: Takes all the numbers from 2 to y and calculate the mod of y and that number and return false if any of those are 0. Edits: Add the 1 check (+4 bytes) Fix the check 1 logic (0 bytes) Remove the [] (Thanks FryAmTheEggman!) (-2 bytes) Remove the -1 from range (Thanks FryAmTheEggman!) (-2 bytes) • all can take a generator, so you don't need []. Also range(a,b) already returns [a, ..., b-1]. – FryAmTheEggman Sep 17 '15 at 19:50 • Cool, thanks for the tip :) – J Atkin Sep 17 '15 at 23:37 # Python 2, 45 bytes Not the smallest entry, but I took a slightly different approach to detecting the prime numbers. Maybe it inspires someone to create an even smaller version. I couldn't discover any more savings myself. i=a=n=input() while i>2:i-=1;a*=n%i print a>1 ## Scala, 50 bytes val i=readInt print(i>1&&(2 to i-1 forall(i%_>0))) In case output to STDERR is forbidden, 65 bytes: val i=scala.io.StdIn.readInt print(i>1&&(2 to i-1 forall(i%_>0))) # Desmos, 108104 94 bytes k=2 1\left\{\sum _{n=2}^k\operatorname{sign}\left(\operatorname{mod}\left(k,n\right)\right)+2=k,0\right\} To use, enter a new line. Then, call p\left(n\rgiht). The output will be bottom right on that line. Edit 1: Shaved {x-1} to x. Edit 2: Changed input format to a more STDIN-esque model. • I'm not sure how Desmos works or is scored, but \left\{2=\sum _{n=1}^x\left\{0=\operatorname{mod}\left(x,n\right),0\right\},0\right\} at... possibly 101 bytes? – lirtosiast Sep 29 '15 at 4:31 • 1. The link gives me timeouts. If I change the protocol to HTTP, it works. 2. The question doesn't allow submitting functions. The closest to user input I could find is putting k=1 in one field and \left\{\sum _{n=2}^k\operatorname{sign}\left(\operatorname{mod}\left(k,n\right)\right)+2=k,0\right\} in the next. – Dennis Sep 29 '15 at 6:58 # Simplex v.0.5, 23 bytes Can probably be golfed. It's really the square root declaration that hurts. *regrets removing p (prime checking) command from syntax and sighs* i*R1UEY{&%n?[j1=o#]R@M} i ~~ takes numeric input * ~~ copies and increments pointer R1UEY ~~ takes the square root and rounds it down { } ~~ repeats until zero cell met at end & ~~ read and store the value to the register % ~~ takes input mod current, move pointer left n ~~ logically negates current (0 -> 1, 1 -> 0) ?[ ] ~~ evaluates inside if the current cell j1= ~~ inserts a new cell to check for a 1 case o# ~~ outputs the result and terminates program R@ ~~ goes right, pulls the value from the register M ~~ decrement value # Groovy, 36 bytes I found a variation of this in a course on groovy that I'm taking: p={x->x==2||!(2..x-1).find{x%it==0}} Test code: println ((2..20).collect {"Is$it prime? ${p(it) ? 'Yes':'No'}"}) • p={x->!(2..<x).find{x%it==0}|x==2}, saves 2 bytes. – Gurupad Mamadapur Jan 17 '17 at 9:06 # PHP, 59 bytes Credit goes to Geobit's answer. I basically just changed it from java to PHP. function f($n){for($i=2;$i<$n;)$n=$n%$i++<1?:$n;echo$n>1;}
• function f($n){for($i=1;++$i<$n;)$n=$n%$i?$n:0;echo\$n>1;} is shorter. The language name is "Java" by the way, not "java". – Blackhole Nov 7 '15 at 10:59

# AppleScript, 158 Bytes

Note that the special case for 1 adds a full 20 bytes.

set x to(display dialog""default answer"")'s text returned's words as number
repeat with i from 2 to x/2
if x mod i=0 then return 0
end
if x=1 then return 0
1

If this program ever returns 0, it won't get to the final statement, which returns 1. Therefore, truthy is 1, falsey is 0.

• This might be golfed more. Might not need words. Might not need as number, because x+0 might make a number. Might not need spaces after numbers (from2, 0then, 1then). I can't check because I'm off my Mac. – kernigh Nov 17 '17 at 0:55

# Microscript II, 2 bytes

N;

Unlike the original Microscript, Microscript II provides a builtin for primality testing.

## DStack, 66 bytes

025SSd01kKCccscS0kT0cK1kAsd34SSd1ccd0sd1ddsScsdk0cD0cS0kTcdsKkdtcK

# Mathematica, 48 47 bytes

<<PrimalityProving`
Echo@ProvablePrimeQ@Input[]

Saved 1 byte thanks to Martin Büttner. Echo is a new function in Mathematica 10.3. In older versions, use Print.

# C, 59 bytes

main(_,i){scanf("%d",&_);for(i=_;_%--i;);putchar(!--i+48);}

If anything other than 1 counted as "falsey", then this would be 3 bytes smaller:

main(_,i){scanf("%d",&_);for(i=_;_%--i;);putchar(i+48);}

Please tell me if the second one is valid.

• 1. Your code gives a FP exception for input 1 on my system. 2. An integer n is falsy if the statement if(n){...} does not execute .... For C, this means that only 0 is falsy. – Dennis Nov 16 '15 at 3:33

# Mouse-2002, 22 bytes

?x:x.1-&FACT &SQR x.\!

Uses Wilson's theorem:

?x:                      ~ get an integer input; put it in x
x.1-                  ~ put x-1 on the stack
&FACT             ~ factorial it and push
&SQR        ~ square it and push
x.\!   ~ modulo (x-1)!^2 % x; print

The version that doesn't use a variable is eight bytes longer, but this is because Mouse's stack operations have four- and five-byte long names. :(

## Pyke, 2 bytes

_P

If the P function is given a negative number, it returns whether it's prime or not.

# Factor, 56 bytes

Literally ungolfable.

USING: math.primes conv io ;
readln string>number prime?
• I haven't used Factor recently, so I don't remember what must be done to print the t/f result of prime? – kernigh Nov 17 '17 at 1:04
• @kernigh print or maybe >string print? why are you asking – cat Nov 18 '17 at 18:24
• The task wants the result on STDOUT or something like it. This code leaves the result on the stack, and I can't remember if Factor would print the result, or if one must add more code to print the result. – kernigh Nov 20 '17 at 5:59

## Pyth, 2 bytes

P_

Try it here!

Pyth now has implicit input!

format: plain


text:
infnorm - Maple Help

numapprox

 infnorm
 compute the L-infinity norm of a function

 Calling Sequence infnorm(f, x=a..b, 'xmax') infnorm(f, a..b, 'xmax')

Parameters

 f - procedure or expression representing the function x - variable name appearing in f, if f is an expression a, b - numerical values specifying the interval [a, b] xmax - (optional) name which will be assigned the point of maximum

Description

 • This procedure computes the ${L}_{\mathrm{\infty }}$ (minimax) norm of a given real function f(x) on the interval [a, b]. Specifically, it computes an estimate for the value

$\mathrm{max}\left(\left|f\left(x\right)\right|,x\in \left[a,b\right]\right)$

 • If the second argument is a range $a..b$ then the first argument is understood to be a Maple operator. If the second argument is an equation $x=a..b$ then the first argument is understood to be an expression in the variable x.
 • If the third argument 'xmax' is present then it must be a name. Upon return, its value will be an estimate for the value of x where the maximum of $\left|f\left(x\right)\right|$ is attained.
 • Various levels of user information will be displayed during the computation if infolevel[infnorm] is assigned values between 1 and 4.
 • The command with(numapprox,infnorm) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{numapprox}\right):$
 > $\mathrm{infnorm}\left(\mathrm{sin},0..2,'\mathrm{xmax}'\right)$
 ${1.0}$ (1)
 > $\mathrm{xmax}$
 ${1.570796332}$ (2)
 > $\mathrm{infnorm}\left(\frac{1}{\mathrm{\Gamma }\left(x\right)},x=1..2\right)$
 ${1.129173885}$ (3)
 > $r\left[2,3\right]≔\mathrm{minimax}\left(\frac{\mathrm{tan}\left(x\right)}{x},x=0..\frac{\mathrm{\pi }}{4},\left[2,3\right]\right)$
 ${{r}}_{{2}{,}{3}}{≔}\frac{{1.130422926}{+}\left({-}{0.07842798254}{-}{0.07066118710}{}{x}\right){}{x}}{{1.130423032}{+}\left({-}{0.07843711579}{+}\left({-}{0.4473405792}{+}{0.02547897687}{}{x}\right){}{x}\right){}{x}}$ (4)
 > $\mathrm{infnorm}\left(\frac{\mathrm{tan}\left(x\right)}{x}-r\left[2,3\right],x=0..\frac{\mathrm{\pi }}{4},'\mathrm{xmax}'\right)$
 ${9.388658362}{×}{{10}}^{{-8}}$ (5)
 > $\mathrm{xmax}$
 ${0.608882102369394}$ (6)


text:
v9.0 (2011)

### Description

Returns or sets the definition path as a String. The definition path is where the shader was defined, so for parser-based definitions, this means that the file that was parsed (eg., \Application\Shaders\cgfx\check3d.cgfx), whereas the plug-in based definition paths refer to the plug-in file where the definition was implemented (eg., \Application\Plugins\MyShader.dll), and the spdl-based definition paths point to the SPDL files (eg., \Application\Shaders\spdl\sitoon\sitoon_paint.spdl).

### C# Syntax

 ```// get accessor String rtn = ShaderDef.DefinitionPath; // set accessor ShaderDef.DefinitionPath = String;```


text:
Scrambled objects for least-squares regression
Odalric-Ambrym Maillard and Rémi Munos
In: NIPS 2010, december 2010, Vancouver.

## Abstract

We consider least-squares regression using a randomly generated subspace $\G_P\subset\F$ of finite dimension $P$, where $\F$ is a function space of infinite dimension, e.g.~$L_2([0,1]^d)$. $\G_P$ is defined as the span of $P$ random features that are linear combinations of the basis functions of $\F$ weighted by random Gaussian i.i.d.~coefficients. In particular, we consider multi-resolution random combinations at all scales of a given mother function, such as a hat function or a wavelet. In this latter case, the resulting Gaussian objects are called {\em scrambled wavelets} and we show that they enable to approximate functions in Sobolev spaces $H^{s}([0,1]^d)$. As a result, given $N$ data, the least-squares estimate $\hat g$ built from $P$ scrambled wavelets has excess risk $||f^* - \hat g||_\P^2 = O(||f^*||^2_{H^{s}([0,1]^d)}(\log N)/P + P(\log N )/N)$ for target functions $f^*\in H^{s}([0,1]^d)$ of smoothness order $s>d/2$. An interesting aspect of the resulting bounds is that they do not depend on the distribution $\P$ from which the data are generated, which is important in a statistical regression setting considered here. Randomization enables to adapt to any possible distribution. We conclude by describing an efficient numerical implementation using lazy expansions with numerical complexity $\tilde O(2^d N^{3/2}\log N + N^2)$, where $d$ is the dimension of the input space.


text:
# Laser Cutting Burn Marks And How to Get Rid of Them

There are tons of advice on how to clean laser cutting burn marks. Most of them are useless but the ones that work require quite a lot of elbow grease. Wouldn’t it be nice to not produce those marks in the first place?

I decided to get to the bottom of this question. And eventually, I did. Of course that path wasn’t very straight-forward… Nothing ever is.

This is one of the more hands-on projects of Damogran Labs. It has been carried out on a machine used at KlarArt – where it still works perfectly.

## The Physics

Laser cutter works by focusing a powerful beam of (invisible) light on a tiny surface area. The resulting energy density is so high that the material upon which the beam is focused promptly evaporates.

It doesn’t disappear, though – it goes up in smoke, cools down and sticks to the surface we need clean, thus creating the much-hated laser cutting burn marks.

It is vital that the smoke doesn’t get in the way of the laser beam. If it is not removed properly, it can become thick enough to block the light. It will ruin your work not by only staining it but it won’t cut through at all.

## The Original Machinery

So key to success is to remove that smoke as soon as possible. Laser cutters have two separate systems for that purpose: smoke extraction and air assist (or however they are officially called).

Smoke extraction is driven by a fan with high flow and low pressure. It draws air from above, down though the cutting table and out of the machine. Although the fan is high flow, the velocities aren’t nearly as high enough to keep smoke from getting in the way of the laser and/or settling down and staining your work.

For that reason another system is introduced – air assist. This is a high-pressure, low-flow air, routed directly in front of the lens. It creates a high-velocity flow exactly on the cutting spot and blows the smoke away the instant it is created.

Here is where the problem with cheaper machines lies. The pump used to provide air-assist-air is usually too small, of the wrong type, or both. In case of KlarArt‘s machine an aquarium air compressor was used.

That is a cheap, low-power reciprocating pump. The air is supplied in pulses where pressure peaks from each pulse dissipate in flexible tubing and also in compressible air itself. It provided just enough air for laser to cut through but that’s all. A lot of cleaning was required – to be more precise, sanding – because nothing could clean that burn marks.

## Modifications

### The Ideal Compressor

I guessed the ideal air-assist pump would be some kind of low-pressure air compressor, providing 100-ish liters per minute at pressure between 1 and 2 bar. But guess what, one does not simply find such a machine.

• The common workshop compressor has too much pressure. With it comes high power consumption, high temperatures, noise, etc.
• Airbrush compressors have too little flow. Also they probably won’t last long enough.
• Aquarium pumps are too low-power and don’t provide continuous stream of air.
• Special compressors are either insanely expensive, are insanely hard to find or don’t even exist.

### The Workaround Compressor

A workshop compressor is practically the only available choice. It is not a bad choice after all – you can get one in almost every hardware store for little money. Alas, all of them are too powerful for this application.

Luckily, they come with a convenient pressure regulator in case the nominal 6 bar is too much. Still, a piston compressor will always compress the air up to nominal pressure and then most of the energy will be lost on the regulator. So I decided to reduce nominal pressure by adjusting the pressure switch.

#### The Pressure Switch

Before doing anything please keep in mind that compressed-air, when misused, is effectively a bomb. Take it very seriously, monitor the pressure and be always ready to cut the power.

This is a switch that engages compressor motor when pressure inside pressure vessel falls below a factory-preset value. It can be changed, though. If you open the box there is a screw that compresses a torsion spring. If you unscrew it so that tension on the spring is released it will disengage the motor at a lower pressure.

By releasing the spring in pressure switch it will keep the pressure between 3 and 4 bar. The regulator will even out the hysteresis. Here are a few estimates on temperatures and power consumption.

#### Power And Temperature (A Quick Check)

According to $w = \frac{n}{n-1}p_1 v_1 ( ( \frac{p_2}{p_1} )^{\frac{n-1}{n}} – 1 )$, specific power for compression to 6 bar would be 187 kJ per kilogram of compressed air. Reducing this pressure to 4 bar yields 136 kJ/kg and reducing to 3 bar gives 103 kJ/kg. We just cut down our electricity costs between 30% and 45%. Also, the highest temperature went from $T_2 = T_2 (\frac{p_2}{p_1})^\frac{n-1}{n}$ = 187 °C at 6 bar to 136 °C at 4 and 128 °C at 3 bar.

Here I assume an ambient temperature of 25 °C and n, polytropic coefficient of 1.4. In reality it could be anywhere between 1.2 and 1.45. The numbers change accordingly but trend remains the same.

That’s good news. The compressor will work at lower power, which means longer lifespan, and lower temperatures, which also mean longer lifespan. I estimate that if original compressor is dimensioned for 5000 working hours, due to reduced power and temperature it should have no problems with 10 000 hours or more.

### Air Preparation

The compressor will take moist ambient air, and compress it. Along the piping between compressor and machine that moisture will condense and eventually it will reach your workpiece, ruining it.

The ideal way would be to dry air before compressor intake but such dryers are huge and expensive. Since the only requirement for air assist is that it doesn’t contain water, we could as well simply separate droplets just before they enter the machine. A simple cyclone separator would do the trick.

Then, the separator would trick us all. Specifically, in hot summer days there would be so much moisture that this little transparent cup would fill up completely in less than 20 minutes, disabling the whole separation business.

Therefore, I bought a new separator. Almost the same – instead of that little manual water-release valve at the bottom there is a mechanism that releases it automatically after the cup fills up.

### Controls

The laser cutter has an outlet at the back for connecting that puny little aquarium pump. There’s a relay that switches on just before the laser starts cutting. Connecting the whole compressor to that relay wouldn’t make sense. There would be too much delay before and after and the power of compressor would probably kill it anyway. It’s best to let compressor do its job of providing pressure separated from laser.

So I replaced a pump with a solenoid valve. It acts like a pump but doesn’t use a lot of power.

## The Whole Setup

Behold below, a photo of the back of the laser cutter:

1. Smoke extraction pipe: intake from outside
2. Smoke extraction: outlet pipe (to outside)
3. Power outlet for air assist: now connected to solenoid valve (5.)
4. Compressed air supply
5. Solenoid valve
6. Air filter / cyclone separator; mind the black float and the red drain tube below
7. Air assist: laser cutter intake
8. Outlet air pressure manometer
9. Pressure regulator knob

The above image in a few words: a machine thinks it is operating an air pump but is in fact opening and closing a valve. There is always enough compressed air available because there’s a compressor in the other room. Also the air is full of moisture but this is taken care of just before it’s too late.

### Fine Tuning

Now there’s just one more thing to set. We don’t want laser cutting burn marks on our work but we also don’t want to spend a fortune on power bills. A pressure regulator needs to be adjusted.

It’s hard to say to what value exactly. It depends on piping length, nozzle shape, laser power, material, other settings, and so on. It’s best to start with a random value and then increasing or decreasing the pressure right during the cutting process.

Start cutting and turn the knob until you’ve found the lowest pressure that still produces clean cuts.

Voilá! Laser cutting burn marks are gone!

### Pressure Regulator Position

I realize that if piping between compressor and laser cutter is long enough, there can be a significant pressure drop between the two ends. A lot of energy could be saved if regulator was right at the laser cutter inlet (but before the separator).

Keep in mind, if you want to use the regulator from compressor, it won’t work. Those aren’t made for pressures below 1 bar and will either let too much air through or shut off completely. You’ll have to find something more sophisticated.

### Fixing the Parts

Bear in mind that you’ll have to fix the parts more firmly than before. The high-velocity jet can exert a significant amount of force on your parts. If not the base material then any small parts you’ll cut out will fly away gladly. Or at least they will be displaced by the stream and ruined by the laser working in the surroundings.

Support tags could come in handy. Or nesting with a little more space between parts.

### Air Assist Nozzle

Basic nozzles are just simple cones with linear profile. A more streamlined shape would, in theory, produce less turbulent flow with a more powerful jet, thus requiring less flow/pressure for the same effect.

I have found more sophisticated nozzles. Since the machine I dealt with works perfectly, there was no need for further optimization. Maybe in the future…

(Edit: I did investigate this a little bit further in this blog post)

### Compressor Maintenance

Your compressor will probably be working overtime. Despite it will not be as thermally and mechanically stressed as designed, you should still take care of it.

Change the oil regularly and don’t forget to release condensate from pressure vessel on a weekly basis or even more often.

Also, before you clean the pressure vessel, check that it will not dissolve the paint. Of course, I didn’t do that. I cleaned the insides with a nitro solvent which dissolved everything inside, including paint. From that moment on the air from that compressor contained not only moisture but also disgusting grey goo which wouldn’t go away. Eventually we had to retire it and buy a whole new compressor.

## Comparison of Laser Cutting Burn Marks

This is a dragonfly, downloaded from filecnc.com. Burn marks, which are basically everywhere, would usually be sanded away but look quite cool on organic shapes like this. So they were left intact.

On the other hand, a Tie Fighter Interceptor from Thingyverse simply can’t take burn marks. Here’s what was cut with the new setup: no cleaning was done whatsoever.

## Conclusion

Normally I would just wish you luck but here I must say it again:

You can easily get electrocuted or blown to bits.

And good luck!


text:
# Activity: Liberal Studies AssigumentLiberal Studies Assignment: As part of this course , you are required t0 parlicipate in Iiberal studies

###### Question:

Activity: Liberal Studies Assigument Liberal Studies Assignment: As part of this course , you are required t0 parlicipate in Iiberal studies assignmenL You will be required l0 provide written assignments that highlight your understanding of & recent discovery related t0 genelics or cell biology in some way You are required t0 find reputable science news article from the intemet t0 write about Examples of excellent science news websiles are listed below. wwv sciencedaily com Www nylimes cOmpages/science news sciencemag org (no Win| wwnw nallre comnews Keep in mind Ihal Ihese are news sites and do not count as "primary literalure other words_ these are nol articles Ihat scientists use l0 communicale Iheir results But these news articles often reference Or Iink to Ihe original paper in question Here are Ihe requirements for (his assignment Find news article from one of Ihese sites Ihat Iist above 2 Write aboul 75% ol a page description of thoir finding (12 font double-spaced inch margins 3. The chosen article must be tied t0 genetics or cell biology research. You must include the Original reference information (tille , Journal , date Is sufliciert) al the boltom of your assignment The article must have been published within the past 12 months Al least one of Ihese new sites allows you l0 sort based 0n date Please make sure Ihat your assignment is in YOur own words The Onginality Check" component ol Tumnilin will bo aclive Therefore , please make sure that you upload your document as word processing file (Word or Pages) and nol as photo

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text:
Lessons:2Length:17 minutes
• Overview
• Transcript

# 1.2 Fix JavaScript Code Style With StandardJS

In this lesson, I’ll show you how we can run Standard both globally and locally within a project. We’ll take a look at how we can add some basic configuration using the package.json file, and I’ll show you how to ignore entire files, or specific rules within files. You’ll also learn how Standard can correct simple formatting errors in your code, to make it easy to write in the Standard style.

Code Snippet

This example configuration for Standard in package.json identifies a file to ignore and lets Standard know about a global variable.

"standard": {
"ignore": [
"app/non-standard.js"
],
"globals": [
"libraryGlobal"
]
}


text:
[NTG-context] writetolist causes mystery blank

Hi all,

I'm having a but of a problem using writetolist. In principle, I want to insert something into the table of contents, but I don't want to disturb the flow of the text. Unfortunately, the following code seems to generate a blank at the top of the page:

\showframe
\showmakeup

\starttext
\writetolist[section]{}{}%
\framed{This box has been pushed down}
\stoptext

I've also tried using a section command where the output has been set to empty:

\showframe
\showmakeup

before=,
after=,
command=\mydonothing]

\def\mydonothing#1#2{}

\starttext
\section{}%
\framed{This box has been pushed down}
\stoptext

but that also gets me a blank. Incidentally, the same thing happens with writebetweenlist, (except that this seems to sometimes push content onto a new page for some reason).

Any ideas?

--
Michael Murphy
___________________________________________________________________________________


text:
# Two pipes are submerged in sea water, arranged as shown in figure. Pipe A with length LA = 1.5m and one open end..

Q: Two pipes are submerged in sea water, arranged as shown in figure. Pipe A with length LA = 1.5m and one open end, contains a small sound source that sets up the standing wave with the second lowest resonant frequency of that pipe. Sound from pipe A sets up resonance in pipe B, which has both ends open. The resonance is at the second lowest resonant frequency of pipe B. The length of the pipe B is:

(a) 1 m

(b) 1.5 m

(c) 2 m

(d) 3 m

Ans: (c)

Sol: $\large 3 \frac{v}{4 L_A} = 2 \frac{v}{2 L_B}$

$\large 3 \frac{1}{4 L_A} = \frac{1}{ L_B}$

$\large L_B = \frac{4 L_A}{3}$

$\large L_B = \frac{4 \times 1.5}{3} = 2 m$


text:
Groupe d’études et de recherche en analyse des décisions

# Optimization of noisy blackboxes with adaptive precision

## Stéphane Alarie, Charles Audet, Pierre-Yves Bouchet et Sébastien Le Digabel

In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors. Sometimes, the source of these errors is identified and controllable, in the sense that it is possible to reduce the standard deviation of the stochastic noise it generates. A common strategy to deal with such a situation is to monotonically diminish this standard deviation, to asymptotically make it converge to zero and ensure convergence of algorithms because the noise is dismantled. This work presents MPMADS, an algorithm which follows this approach. However, in practice a reduction of the standard deviation increases the computation time, and makes the optimization process long. Therefore, a second algorithm called DPMADS is introduced to explore another strategy, which does not force the standard deviation to monotonically diminish. Although these strategies are proved to be theoretically equivalents, tests on analytical problems and an industrial blackbox are presented to illustrate practical differences.

, 29 pages


text:
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

i usually run long simulations in R on a remote server. i’ve read an article on linux journal about emailing yourself after something happens…i forgot. since my jobs are long, and i usually have to run multiple jobs sequentially, it’d be nice to look at my results immediately when they’re gone. good thing *nix based systems have the mail (or mailx) command:

echo "" | mail -s "Job Done" [email protected]

found the stuff here.

in R, i execute:

system('echo "" | mail -s "Job Done" [email protected]')

of course, these are empty emails. u can use “<” or cat with pipe to get results emailed to you.

cool!


text:
# A direct proof of the paracompactness of $\mathbb{Q}$

I know $\mathbb{Q}$ is metric, and thus paracompact. But is there a way to show that every covering has a locally finite refinement?

-
Can you do it for $\mathbb R$? The same refinement should work for the rationals. – Olivier Bégassat Jul 19 '12 at 20:06
@OlivierBégassat I can divide the real line in closed intervals, as big as I wish, extract a finite sub-covering. Refine it so that the covering of an interval don't cover "too many other intervals" and this should suffice. Is it correct? The refinement is possible thanks to the characteristics of the real line, I think (i.e. choping every open set at epsilon-distance from the interval he is covering). And paracompactness hold for every type of subspace... – Temitope.A Jul 19 '12 at 20:19

Here is a direct proof that $\Bbb Q$ is paracompact.

Let $\mathscr{U}$ be an open cover of $\Bbb Q$; without loss of generality assume that the elements of $\mathscr{U}$ are open intervals. For $A\subseteq\Bbb Q$ let $\operatorname{st}(A,\mathscr{U})=\bigcup\{U\in\mathscr{U}:U\cap A\ne\varnothing\}$; write $\operatorname{st}(x,\mathscr{U})$ for $\operatorname{st}(\{x\},\mathscr{U})$. For $x\in\Bbb Q$ let $\operatorname{st}^1(x,\mathscr{U})=\operatorname{st}(x,\mathscr{U})$, and for $n\in\Bbb Z^+$ let $\operatorname{st}^{n+1}(x,\mathscr{U})=\operatorname{st}\big(\operatorname{st}^n(x,\mathscr{U}),\mathscr{U}\big)$. Finally, for $x\in\Bbb Q$ let $I(x)=\bigcup\{\operatorname{st}^n(x,\mathscr{U}):n\in\Bbb Z^+\}$. Clearly $I(x)$ is open and order-convex, and $y\in I(x)$ iff $x\in I(y)$, so $\mathscr{I}=\{I(x):x\in\Bbb Q\}$ is a partition of $\Bbb Q$ into clopen, order-convex sets.

Fix $x_0\in\Bbb Q$, let $L=(\leftarrow,x_0]\cap I(x_0)$, and let $R=[x_0,\to)\cap I(x_0)$. If $\operatorname{st}(x_0,\mathscr{U})\nsupseteq R$, there must be an $x_1\in R\cap\operatorname{st}^2(x_0,\mathscr{U})\setminus\operatorname{st}(x_0,\mathscr{U})$. Given $x_n\in R\cap\operatorname{st}^{n+1}(x_0,\mathscr{U})\setminus\operatorname{st}^n(x_0,\mathscr{U})$, if $\operatorname{st}^{n+1}(x_0,\mathscr{U})\nsupseteq R$, there is an $x_{n+1}\in R\cap\operatorname{st}^{n+2}(x_0,\mathscr{U})\setminus\operatorname{st}^{n+1}(x_0,\mathscr{U})$. There are now two cases.

1. There is some $m_R\in\Bbb N$ such that $\operatorname{st}^{m_R+1}(x_0,\mathscr{U})\supseteq R$. Then for $n=0,\dots,m_R$ there are $U_n\in\mathscr{U}$ such that $x_n\in U_n$, and moreover $U_n\cap U_{n+1}\ne\varnothing$ if $n\ne m_R$; clearly $\{U_0,\dots,U_{m_R}\}$ covers $[x_0,x_{m_R}]$. If there is some $U_{m_R+1}\in\mathscr{U}$ such that $x_{m_R}\in U_{m_R+1}\supseteq R\cap[x_{m_R},\to)$, then $\{U_0,\dots,U_{m_R+1}\}$ is a finite and hence locally finite open cover of $R$ refining $\mathscr{U}$.

Otherwise there must be a strictly increasing sequence $\langle z_n:n\in\Bbb N\rangle$ in $R\cap[x_{m_R},\to)$ and sets $V_n\in\mathscr{U}$ for $n\in\Bbb N$ such that $x_{m_R},z_n\in V_n$, $z_{n+1}\notin V_n$, and $R\cap[x_{m_R},\to)\subseteq\bigcup_{n\in\Bbb N}V_n$. Moreover, we may assume that $z_0>x_{m_R}$. Let $W_0=V_0\cap(x_{m_R},z_1)$, and for $n\in\Bbb Z^+$ let $W_n=V_n\cap(z_{n-1},z_{n+1})$. $\mathscr{W}=\{W_n:n\in\Bbb N\}$ refines $\mathscr{U}$ and covers $R\cap[x_{m_R},\to)$, and each member of $\mathscr{W}$ meets at most two other members of $\mathscr{W}$, so $\mathscr{W}\cup\{U_0,\dots,U_{m_R}\}$ is a locally finite open cover of $R$ refining $\mathscr{U}$.

2. We end up with a sequence $\langle x_n:n\in\Bbb N\rangle$. Then for $n\in\Bbb N$ there are $U_n\in\mathscr{U}$ such that $x_n\in U_n$ and $U_n\cap U_{n+1}\ne\varnothing$. The choice of the points $x_n$ ensures that $U_m\cap U_n\ne\varnothing$ iff $|n-m|\le 1$, so $\{U_n:n\in\Bbb N\}$ is a locally finite open cover of $R$ refining $\mathscr{U}$.

Thus, in all cases we can find a locally finite open refinement $\mathscr{R}_R$ of $\mathscr{U}$ covering $R$. In similar fashion we can find a locally finite open refinement $\mathscr{R}_L$ of $\mathscr{U}$ covering $L$, and $\mathscr{R}=\mathscr{R}_L\cup\mathscr{R}_R$ is then a locally finite open refinement of $\mathscr{U}$ whose union is precisely $I(x_0)$.

Since we can do this for each $I\in\mathscr{I}$, $\mathscr{U}$ has a locally finite open refinement covering $\Bbb Q$, and $\Bbb Q$ is paracompact.

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# Sayre equation

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
$S_{h} \approx S_{h'} S_{h-h'}$
where the signs S are positive if the phase is 0 and negative if it is π and the $\approx$ symbol indicates a certain degree of probability that the relationship is true, which becomes higher the stronger the reflections are.


text:
# Boyle, M. (2012): Essentially Rational Animals

@incollection{boyle2012,
author = {Boyle, Matthew},
title = {Essentially Rational Animals},
booktitle = {Rethinking Epistemology},
shorttitle = {Essentially Rational Animals},
editor = {Abel, Günter and Conant, James},
publisher = {Walter De Gruyter},
pages = {395-427},
year = {2012},
file = {~/Library/Mobile Documents/iCloud~com~sonnysoftware~bot/Documents/be-library/boyle2012(old-copy)_Essentially_Rational_Animals.pdf.pdf; boyle2012_Essentially_Rational_Animals.pdf.pdf},
doi = {},
url = {},
langid = {},
abstract = {},
keywords = {concepts; perception; animals; rationality; conceptualism; reason},
}

## Notes

### The Classical View

The Classical View:
the view of definition “found in Aristotle and in that strain of medieval Aristotelianism of which Thomas Aquinas is the greatest expositor” (399) according to which the predicates appearing in the definition attach to the kind being defined (rather than individual members of the kind) (403, 404, 408)

Three “key ideas” of the Classical View:

first, the idea that “rational animal” belongs to the specification of the essence of humankind; secondly, the idea that, more specifically, this phrase characterizes our form; and finally, the idea that “rational” designates a characteristic that differentiates the genus “animal.” (399)

The “crucial implication” of the Classical View:

rationality is not a particular power rational animals are equipped with, but their distinctive manner of having powers. … I will argue that it [i.e. Classical View] enables us to avoid the following choice, which many authors take to be mandatory: either offer an account of cognition and action that applies uniformly to both rational and nonrational animals, or else deny that nonrational animals can literally be said to cognize and act. Furthermore, I will suggest that appreciating this idea puts us in a position to answer the common charge that conceiving of our minds as essentially rational involves a hyper-intellectualized or hyperidealized view of how our minds operate. (399-400)

### Differentia as Transformative of Genus

Boyle argues that the specific difference that sets one species from another “transforms” what it is to be a member of the genus of which both are species. He bases this primarily on this passage from Aristotle’s Metaphysics

By genus I mean that one identical thing which is predicated of both and is differentiated in no merely accidental way… For not only must the common nature attach to the different things, e.g. not only must both be animals, but this very animality must also be different for each… For I give the name of ‘difference in the genus’ to an otherness which makes the genus itself other. (Metaphysics X. 8, 1057b38–1058a7., quoted in [@boyle2012, 409])

### Rationality as Form

“rational” specifies the sort of frame that undergirds any concrete description of what it is to be a human being. For /it does not specify a particular characteristic that we exhibit but our distinctive manner of having characteristics/. This, I believe, is the significance of saying that “rational” characterizes the form of human being. [@boyle2012, 410]

The key claim here is that rationality “does not specify a particular characteristic that we exhibit but our distinctive manner of having characteristics.”

## Against the Transformative Conception (as Interpretation of Kant)

The argument is pretty straightforward. According to the Classical View (CV) being a rational animal means that acts of sensibility are not, in rational beings, essentially the same as they are in non-rational beings. Acts of sensibility are had in a rational way rather than in a non-rational way. I take this to be a straightforward commitment of Boyle’s view.

Could Kant endorse CV? In my view, no. This is because of the way Kant understands sensible acts as the outcome of our receptivity as opposed to our spontaneity. On Kant’s view any act of a substance is due to an exercise of its causal powers. So in one sense nothing merely “happens” to a substance—any property it has (anything that “inheres” in the substance) depends on an act of that very substance.

But Kant wants to distinguish between things that “happen” to a substance and things the substance “does” in a way which conforms to a distinction between passivity and activity. His explanation of the passive/active distinction thus hinges on his basic dichotomy between receptive powers of a substance and spontaneous powers of substance.

A receptive power is one whose actualization is ultimately grounded in something whose existence and nature is itself independent of that power. The clear example here is that of a sense modality. An actualization of one’s visual capacity is ultimately due to something whose existence and nature is entirely independent of that capacity or its exercise (and so on for all the other possible sense modalities).

A spontaneous power is one whose actualization is ultimately grounded in something whose existence and nature is not independent of the power so exercised. For example, what makes the mental transition from holding true the premises of an argument to holding true their conclusion a case of inference is that the rational agent recognize the support relation between premises and conclusion. Hence the nature of the ground of the inferential act itself appeals to the rational capacity of which it is an instance. TODO: Fix this!

If that distinction is correct then we need only one further premise to reject Boyle’s position. This is the premise that all and only rational acts are spontaneous. If that is right, and given the above distinction, then it would be contradictory to claim that acts of sensibility are rational, or have the form of rationality, since this would be to claim that they are both receptive and spontaneous, which is a contradiction.

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 Mosc. Math. J., 2014, Volume 14, Number 4, Pages 807–823 (Mi mmj545)

Weighted Radon transforms and first order differential systems on the plane

R. G. Novikov

CNRS (UMR 7641), Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France

Abstract: We consider weighted Radon transforms on the plane, where weights are given as finite Fourier series in angle variable. By means of additive Riemann–Hilbert problem techniques, we reduce inversion of these transforms to solving first order differential systems on $\mathbb R^2=\mathbb C$ with a decay condition at infinity. As a corollary, we obtain new injectivity and inversion results for weighted Radon transforms on the plane.

Key words and phrases: weighted Radon transforms, inversion methods, first order differential systems.

DOI: https://doi.org/10.17323/1609-4514-2014-14-4-807-823

Full text: http://www.mathjournals.org/.../2014-014-004-007.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 44A12, 53C65, 65R10
Received: August 3, 2012; in revised form July 5, 2014
Language:

Citation: R. G. Novikov, “Weighted Radon transforms and first order differential systems on the plane”, Mosc. Math. J., 14:4 (2014), 807–823

Citation in format AMSBIB
\Bibitem{Nov14} \by R.~G.~Novikov \paper Weighted Radon transforms and first order differential systems on the plane \jour Mosc. Math.~J. \yr 2014 \vol 14 \issue 4 \pages 807--823 \mathnet{http://mi.mathnet.ru/mmj545} \crossref{https://doi.org/10.17323/1609-4514-2014-14-4-807-823} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3292050} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000349324800007}

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This publication is cited in the following articles:
1. J. Ilmavirta, “Coherent quantum tomography”, SIAM J. Math. Anal., 48:5 (2016), 3039–3064
2. F. Monard, “Inversion of the attenuated geodesic X-ray transform over functions and vector fields on simple surfaces”, SIAM J. Math. Anal., 48:2 (2016), 1155–1177
3. F. O. Goncharov, “An iterative inversion of weighted Radon transforms along hyperplanes”, Inverse Probl., 33:12 (2017), 124005
4. F. O. Goncharov, R. G. Novikov, “An example of non-uniqueness for Radon transforms with continuous positive rotation invariant weights”, J. Geom. Anal., 28:4 (2018), 3807–3828
5. F. O. Goncharov, R. G. Novikov, “An example of non-uniqueness for the weighted Radon transforms along hyperplanes in multidimensions”, Inverse Probl., 34:5 (2018), 054001


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Article

# Intermediate Low Spin States in a Few-electron Quantum Dot in the $\nu\le 1$ Regime

• ##### S. Tarucha
Physical Review B (Impact Factor: 3.66). 12/2005; DOI: 10.1103/PhysRevB.74.033306
Source: arXiv

ABSTRACT We study the effects of electron-electron interactions in a circular few-electron vertical quantum dot in such a strong magnetic field that the filling factor $\nu\le 1$. We measure excitation spectra and find ground state transitions beyond the maximum density droplet ($\nu=1$) region. We compare the observed spectra with those calculated by exact diagonalization to identify the ground state quantum numbers, and find that intermediate low-spin states occur between adjacent spin-polarized magic number states. Comment: 4 pages, 4 figures

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