text:
Proposal to add small-capitals formatting directive

I propose that a new formatting directive be added to access the font’s small capitals.

For example, <smcaps>some text</smcaps> would work, but I encourage discussion on any syntactic variant that appeals to you. The coolest thing is that since this is a simple matter of invoking the ᴄss font-variant: small-caps style spec, it is super-easy to implement. It would give better-looking pages for next to no effort.

If you wonder why this is needed, please see whatever the current word-of-the-day is at the Oxford English Dictionary at the time you read this. I will not link to the actual page, because it switches daily. But click through the ᴡᴏᴛᴅ link to see how real entries are supposed to look. You will see that the ᴏᴇᴅ uses small capitals for headwords, for authors in citations, and for the major volume in Roman numerals for multivolume works.

This is just one example; many, many reference works one would like to cite here use small capitals. It’s not just the ᴏᴇᴅ.

If you wonder why typographers consider small caps as integral a part of a font as italic, bold, or text figures, see Robert Bringhurst’s Elements of Typographic Style. I’m sure that ᴇʟ&ᴜ is using Georgia because it’s the most widely available font that supports text figures, as one of course wants to have. Like text figures, small capitals are an often-missed by critical component of good typography.

If you wonder why one cannot just use the Unicode small capitals, it’s because

• there are not very many of them;
• the Georgia font used here and in ᴇʟ&ᴜ proper does not even support them and so causes infelicitous fontsubbing;
• if you look at this posting from several different browsers and/or operating systems, you will get very different results
• some are only four or five yeras old in the spec, which means that even alterate serif fonts may not yet support the Unicode code points, as vendors are especially poor at this.

Let me show you how poorly Unicode small capitals are typically rendered by browsers. Consider this tr statement from the Perl language:

tr[aæbcdðeǝfgɠhiɨjklłmnoœɔȣprɹꝵstuʉɯvwyzʒγλπρψл]
[ᴀᴁʙᴄᴅᴆᴇⱻꜰɢʛʜɪᵻᴊᴋʟᴌᴍɴᴏɶᴐᴕᴘʀᴚꝶꜱᴛᴜᵾꟺᴠᴡʏᴢᴣᴦᴧᴨᴩᴪᴫ];

If you think that is bad, just imagine writing “ᴀ ᴁ ʙ ᴄ ᴅ ᴆ ᴇ ⱻ ꜰ ɢ ʛ ʜ ɪ ᵻ ᴊ ᴋ ʟ ᴌ ᴍ ɴ ᴏ ɶ ᴐ ᴕ ᴘ ʀ ᴚ ꝶ ꜱ ᴛ ᴜ ᵾ ꟺ ᴠ ᴡ ʏ ᴢ ᴣ ᴦ ᴧ ᴨ ᴩ ᴪ ᴫ” in the normal serif roman. It looks horrible. The ᴄss font-variant fixes all that.

However, even without using a modern serif font like Arno Pro (standard with Adobe ᴄs3) or Alfios (a very nice free font by George Douros), and just sticking with simple things like Georgia (preferred for text figures) or Times New Roman, if you used the ᴄss markup then the browser would use the right small caps without needing to mess around with funny Unicode, or worry about searches getting messed up. The browser even emulates small caps for fonts lacking them.

It would make our pages look better, and it would make our citations more accurate. It seems only fair and right that ᴇʟ&ᴜ be able to accurately cite standard reference works. Here is one example where I do so, but I used Unicode small caps only for Roman numeral volumes in the citations. I used simple bold where the ᴏᴇᴅ has small caps for its headwords, and I used the regular roman instead of small caps for the authors’ names in the citations.

It would look much better, and be more correct, to use actual small capitals when accurately citing references. You would hope that ᴇʟ&ᴜ would be able to accurately cite standard reputable reference works without all these lamentable compromises. And because of ᴄss, it would be very easy to implement and not risk harming clarity, portability, or searchability at all the way all alteratives do.

I have no particular attachment to the <smcaps>some text</smcaps> syntax; it’s just one idea. I realize that by making it ʜᴛᴍʟ-ish it would work only in the main text, not in commentary, but I was unable to think of something that would work in the markdown within comments that did not risk break backwards compatibility. Perhaps others can come up with a better syntax.

EDIT

Here’s a screen grab that shows how the ᴏᴇᴅ uses small caps in all three different ways:

It uses them for headwords, for authors’ names in citations, and for major volumes in roman numerals in citations. It’s the first that are especially useful, although the second is nice to have. The third doesn’t matter so much, although it’s nice to be able to make a complete citation.

They do all this through the ᴄss trick I mentioned earlier; it’s really easy to do.

• +1 I second this proposal. @Theta30: Each site is different; sites may adopt a UI of their choice/ set precedents in improvements.
– Kris
Feb 18, 2012 at 11:50
• @Theta30 Why would StackOverflow need small capitals? It doesn’t come up in programming, just in typesetting. It’s EL&U that needs them. EL&U already tries to look better with text figures and serifs. Sure, they might roll it out everywhere, but they don’t need to.
– tchrist Mod
Feb 18, 2012 at 12:52
• Can you do a screen capture to show the example you really want here? I really don't get the need for it unless you point out exactly what is wanted. Feb 18, 2012 at 15:00
• @Mitch Good idea, sure. Just a moment.
– tchrist Mod
Feb 18, 2012 at 15:30
• OED is no special case, it could be any of the many such: dictionaries, bibliographies, why even articles, blogs.
– Kris
Feb 19, 2012 at 14:54
• @Kris You are of course correct. The point is that small capitals are needed for proper citations. I just listed the ᴏᴇᴅ as one such source. They can also improve general readability.
– tchrist Mod
Feb 19, 2012 at 14:56
• I think at least some of the downvotes stem from the fact that much of your question is unreadable. Please, just stop with the Unicode nonsense. Unicode was never designed as a formatting tool. Feb 20, 2012 at 19:23
• @Marthaª If you expect people to revert to 1960’s ᴀꜱᴄɪɪ, then you need to change your input mechanism to go back to the Stone Age; you have no place complaining about things you let people enter. Second, the majority of the Web is now Unicode: why are you still in ᴀꜱᴄɪɪ-land? Third, if you won’t let us add formatting codes, then certainly we shall use each and every workaround for your deficit that is available to us, and Unicode is great for that. Stop using ancient broken systems, or add proper formatting codes. Doing neither is not the right answer. 😱 Sheesh! Let us quote things in full.
– tchrist Mod
Feb 20, 2012 at 19:34
• @tchrist: no need to get insulting. Like I said elsewhere, the fact that this computer is not as Unicode-compliant as one might wish is not within my control. The proper workaround for lack of small caps is to use all caps, not to insert a bunch of special characters that were never intended for the purpose. Feb 20, 2012 at 19:56
• @Marthaª You’re right about getting insulting, and I very sincerely apologize. As for old systems, you realize that the CSS font-variant small-caps approach would work on those systems? That’s because you still use ASCII within that. So it’s almost like you’re arguing that it should be done. I just want to be able to use the same font variants — bold, italic, and small-caps — as are found in whatever source I’m quoting from. What’s wrong with accuracy of citation?
– tchrist Mod
Feb 20, 2012 at 20:04
• @tchrist: I know that small caps are easily achieved with CSS, but that's neither here nor there: on StackOverflow, formatting is done with Markdown, not directly with CSS. Markdown is purposely simplified, and StackOverflow has further simplified it by removing some options. In some cases (underlining) I disagree with SO's choices; in other cases (small caps) I don't actually know whether they're supported by Markdown, but I don't much care either way, because there's an easy workaround: just use all caps. Feb 20, 2012 at 20:35
• Personally, I don't want to make small caps easier for people to use; I find the results really hard to read and they actively work against browser font settings -- so you're going to make me zoom the page so everything else will be too big, just to read your small caps? Small caps work great in print, but the web is apparently not ready for them yet and this would be about 97th on my list of formatting improvements for SE. Feb 21, 2012 at 16:12
• @MonicaCellio Why would small caps be any harder to read than lowercase? They are supposed to have the same x-height. Look in my screenshot: are those ‘harder to read’? If you have to zoom the page to read lowercase, then you are trying to read the page in too tiny a rendering — right? I agree that Unicode smallcaps can be hard to read due to browser fontsubbing to the wrong font, but this is precisely why I made the request, so that that doesn’t happen.
– tchrist Mod
Feb 21, 2012 at 16:47
• @tchrist: don't take the downvotes so personally, they just mean that they disagree with the proposal. I suspect (but don't know) that people don't see the utility of specifically small caps. If small caps were OK'd, what about all the other possibilities? I bet the SE developers have things higher on their development priority list than this. Feb 21, 2012 at 18:27
• Note that linguistic glossing is also done in small-caps. I tried glossing in one of my questions on linguistics.SE (see under the sub-heading with examples), and it looks like steaming pile of shite in all-caps. Jan 22, 2013 at 19:59

EDIT: Replaced incorrect samples at bottom with true ones showing the difference between faked small caps and real ones, and made all images clickable for enlargement.

In The Elements of Typographical Style, Robert Bringhurst writes:

Genuine small caps are not simply shrunken versions of the full caps. They differ from large caps in stroke weight, letterfit, and internal proportions as well as in height. Any good set of small caps is designed as such from the ground up. Thickening, shrinking, and squashing the full caps with digital modification routines will only produce a parody.

He then presents an example of the relationship of faces:

The small caps of 2.2 are obviously different from the uppercase in 2.1; they are also less aggressive on the eye than the almost garishly thick bold of 3.5, things one should reach for seldom. Bold works best as a titling face.

Here is another Bringhurst example where you can see how different true small caps are from the parody simulations of scaled-down full caps:

Modern OpenType fonts do allow one to access the true small caps included with that font, but Stack Exchange is not concerned with such niceties. If they were, they would also do something about the default line length, which is too many ens long for comfortable reading.

Since we are not granted access to the technology that would allow for small caps to be accessed in the correct way, we are forced to resort to what Bringhurst calls a parody.

Under the current limitations at Stack Exchange sites, the only available way to poorly simulate small capitals is to use

• These are SMALL CAPITAL letters.

to create

• These are SMALL CAPITAL letters.

However, the stroke weighting is far too light, and so bolding it can look better:

• These are SMALL CAPITAL letters.

That’s a bit too heavy in weight, but is better than the skeletal effect produced by simple resizing as in the first example.

From this answer is an example of OED etymology examples using small caps in the non-bold style:

pronounce

ME. pronunce, pronounce, a. OFr. pronuncier (1277 in Godef. Compl.), for earlier purnuncier (mod.Fr. prononcer) :– late L. prōnunciāre for orig. prōnuntiāre to proclaim, announce, rehearse, narrate, pronounce, f. prō, PRO1 + nunti-āre to announce: cf. ANNOUNCE, ENOUNCE.

announce

a. OFr. anonce-r, earlier anoncier, anuncier :– L. adnuntiā-re, f. ad to + nuntiāre to bear a message, f. nunti-us bringing news. See AN- pref. 6.

enounce

ad. Fr. énoncer, ad. L. ēnuntiā-re (see ENUNCIATE), after the analogy of ANNOUNCE.

renounce

ad. Fr. renoncer (OFr. also renuncer) :– L. renuntiāre (-ciāre) to announce, proclaim, also to disclaim, protest against, f. re- re- + nuntiāre to make known, report: cf. ANNOUNCE, DENOUNCE, etc.

As you see, those are spindly and misshapen. Here is what you get when you bold them to thicken the stoke weight:

pronounce

ME. pronunce, pronounce, a. OFr. pronuncier (1277 in Godef. Compl.), for earlier purnuncier (mod.Fr. prononcer) :– late L. prōnunciāre for orig. prōnuntiāre to proclaim, announce, rehearse, narrate, pronounce, f. prō, PRO1 + nunti-āre to announce: cf. ANNOUNCE, ENOUNCE.

announce

a. OFr. anonce-r, earlier anoncier, anuncier :– L. adnuntiā-re, f. ad to + nuntiāre to bear a message, f. nunti-us bringing news. See AN- pref. 6.

enounce

ad. Fr. énoncer, ad. L. ēnuntiā-re (see ENUNCIATE), after the analogy of ANNOUNCE.

renounce

ad. Fr. renoncer (OFr. also renuncer) :– L. renuntiāre (-ciāre) to announce, proclaim, also to disclaim, protest against, f. re- re- + nuntiāre to make known, report: cf. ANNOUNCE, DENOUNCE, etc.

The second simulation is better than the first, because the stroke is no longer far too thin to match the normal letters. However, it is now a bit too thick. Even worse, the proportions have become grotesque (in the non-technical sense) making clear why small caps must be designed from the start, not parodied with digital routines.

Fortunately, modern fonts have these. Here’s what it looks like when you use actual small caps using Richard Slimbach’s Minion Pro typeface, which gives the small caps a different letterfit — and also proportions, which you can see if you look at the real and fake P or A.

Click on the image to see it without resizing artifacts.

See how much easier to read those small caps are than the two kinds of emulation available to us? Especially in the original image, the small caps are the same weight as everything else and so do not jump out at you as messed up the way the existing emulations do. They just plain work as typography, and there is no substitute for them.

Here in a nutshell is the difference, using Minion Pro in Chrome:

That’s really quite terrible: no wonder Bringhurst calls these emulations parodies!

Notice how the stroke width of the emulated small caps is no longer a match for the regular characters of the same font, and the letterfit it simply atrocious. The Firefox emulation is somewhat less lame about letterfit here than the embarrassing joke that Chrome presented:

(Those aren’t directly comparable because although the face is the same, the point size of the actual font I used in Firefox is slightly larger than the earlier one in Chrome.)

As you see, the real small caps are more generous to the eye in several ways. There’s nothing to be done about stroke width and proportion, so even Firefox’s improved emulation is still a far cry from the real small caps in the font itself.

Unfortunately, Stack Exchange doesn’t care (enough?) to make the font’s actual small capitals available to us, even with the lame emulation, and so nasty parodies that Bringhurst speaks of are all we’re permitted to use.

Technical Notes

The actual small caps in the first example are using CSS with font-feature-settings: "smcp" 1 and therefore use the true small caps in the font instead of trying to fake it. The emulated ones in the second examples are using CSS with font-variant: small-caps which despite its name perversely enough only emulates them!

• I would cheerfully give up boldfacing and code to have small caps and underlining, which would allow me to emulate the typographic conventions which dominate contemporary linguistic texts. Dec 28, 2014 at 5:21
• @StoneyB So that people can see the sort of thing you’d get with real ones instead of fake ones, I’ve added versions that show what real small capitals look like using the font’s underlying small-cap features.
– tchrist Mod
Dec 30, 2014 at 14:42
• What do you use to get true small caps for your 'Actual' reproductions? AFAIK Word can't get at them - its small caps feature just emulates by shrinking the size. Dec 30, 2014 at 15:00
• @StoneyB Sigh. Time to go back to something else.
– tchrist Mod
Dec 30, 2014 at 15:03
• @StoneyB Broken images now replaced with correct ones. I finally got around to showing the real small caps from the font proper, without resorting to bad emulations. It makes a huge difference in readability. Thanks very much for bringing this to my attention.
– tchrist Mod
Feb 15, 2015 at 1:32
• I've given up with the  cheat. The line spacing goes wrong in quoted blocks. I'm not 100% sure if that happened before 'The great styling shift of March 5th' or not so italics will have to do. Mar 28, 2015 at 8:38
• @Frank Yes, it changed with the styling change.
– tchrist Mod
Mar 28, 2015 at 11:46

There is actually no absolute need for small caps in any type of writing that I know about. They are always an aesthetic choice, not a semantic one. In other words, there is nothing that can only be communicated via small caps, instead of via judicious use of all-caps plus some bold or italic.

If Markdown has small-cap capabilities and it just hasn't been enabled for StackOverflow, then I would have no objections to enabling it, but this isn't something that I think the developers should spend a lot of time on.

What is absolutely worse than useless is using Unicode small-caps, because more often than not, the result is unreadable. Especially for acronyms/initialisms, just use all caps, for heaven's sake. (I would argue that it is actually incorrect to use small caps for acronyms*.)

* Small caps are a formatting choice like bold or italic: they do not affect whether a text is correctly spelled and punctuated. Capital letters, on the other hand, carry semantic weight: england is an incorrect spelling. Similarly, I believe that because ascii or oed would be incorrect spellings of these acronyms (or initialisms or abbreviations or whatever you want to call them), small-caps ᴀꜱᴄɪɪ and ᴏᴇᴅ are also incorrect spellings. Instead, you should write them as all-caps ASCII and OED, even if small caps are available as a formatting choice.

• @tchrist: I can't read what you intend to do. This is a work computer over which I have very little control, so it's not a question of declining to add anything; it's just that Windows XP is not always as Unicode-compliant as one would wish. Feb 20, 2012 at 19:51
• @tchrist: Oh, the software has support -- you can tell that from the way Marthaª's screenshot shows the codepoints -- but the fonts, not so much...
– SamB
Feb 21, 2012 at 2:10
• @tchrist, your tone in comments to Martha is coming across as quite insulting. Assuming that wasn't your intent, could you take a few deep breaths or something before posting? You obviously feel strongly about this, but there's no reason to get snippy at other people whose opinions are just as valid as yours. Feb 21, 2012 at 16:15
• One issue brought up in the original request that this answer doesn't address is citation: it's nice to be able to preserve the original formatting of quotes from sources like the OED and countless others. Dec 1, 2015 at 9:21
• @sumelic: if you absolutely can't use all caps, there's always the asdf workaround. Dec 1, 2015 at 16:28

If adding a small-caps option to EL&U is technologically feasible and straightforward, I would love to have the option to use them. As matters stand, when I quote definitions from old (and some new) dictionaries, I generally replace small-and-large-cap words with all-cap equivalents; but the closer my retyped versions are to the originals, the better I like it.

I came here through your comment on my question, and couldn't leave without my 5 cents:

Modern HTML tries to more and more separate structure/semantics from styling, and Markdown as a lighter way to write a subset of HTML even more so. It is for this reason that in HTML one should use x and x (emphasis and strong emphasis) instead of x and x (italic and bold) – not to mention ! –, and the Markdown codes *x* and **x** stand for the former and not the latter. Because of that I think allowing more styling-oriented markup in questions and answers on SE would be the wrong move.

From that separation perspective, the question would be: What kind of semantics would you like to lead to a styling in small caps? For example, on the Oxford English Dictionary website, small caps are used to style names. Since HTML does not have a <name> tag, the correct way to implement this would be to use a  with a class attribute

1929 F. M. McNeill Scots Kitchen

and then have an associated style sheet that contains

span.name { font-variant: small-caps; }

And it would be even better to also use something like  instead of  in the above example. However, to enable something like that on SE would necessitate to agree on a whole host of additional semantic classes.

Of course, SE could go beyond the small subset of HTML whitelisted in questions and answers and allow to use something like , but a) that would go against semantics & style separation, and b) I guess it would it make harder for them to filter out other kinds of HTML markup that might have malicious side effects. Also, we are not the designers of this website, just the guys who write all the text. ;-)

• Most of what you've written is quite correct. The exception is that font-variant:small-caps is broken, and so you must instead use font-feature-settings: "smcp" 1. Otherwise it just fakes it instead of using the font's real small caps. See my examples of the difference between the two. Mind you, the face in question actually has to HAVE small caps for this to work.
– tchrist Mod
May 5, 2015 at 4:35
• The HTML preference is interesting, but it doesn't seem to me to mesh very well with typographical conventions. I never knew that Stack Exchange uses  and  rather than italic and bold, and so they've been essentially the same thing in my use of the site. And in your own writing, it makes sense to say that the word semantics is emphasized, but the phrase Oxford English Dictionary, not so much. Yet they are marked with the same styling (unless you've used a <title> styling or something to mark the latter). May 5, 2015 at 7:58
• @tchrist, I didn't know that. Broken in specific browsers, or generally? And font-feature-setting is in the standard? Good to know. Yes, of couse the font needs to have proper small caps, which makes it even harder to ensure that the markup renders properly across browsers and platforms. Web typography has come a long way, but it isn't completely there yet. May 5, 2015 at 13:25
• @sumelic, I just checked (you can do that with "Inspect Element" in some browsers), and strangely emphasis in the answer is actually implemented using , but emphasis in a comment is implemented using . And you are right, emphasizing "Oxford English Dictionary" doesn't make sense, the idea is rather that titles are styled in italics, and I basically abused semantic markup to achieve a certain presentation. As I wrote, unless we have a bunch of additional semantic markup, the separation idea cannot be perfectly realized. May 5, 2015 at 13:26
• And you are right, typography with its roots in putting lead blocks together is concerned with getting the styling right, and the distinction between semantics and styling, while implicitly there, is not very well developed. I think this tension can be overcome within a specific individually administrated website, where the writer uses classed spans for semantics and then does the typography through the CSS. But on a huge site like SE, with its many different communities and user's backgrounds, I don't really see this happening. May 5, 2015 at 13:37


text:
# DexUnit¶

class astropy.units.function.DexUnit(physical_unit=None, function_unit=None)[source]

Logarithmic physical units expressed in magnitudes

Parameters
physical_unit

Unit that is encapsulated within the magnitude function unit. If not given, dimensionless.

function_unit

By default, this is dex, but this allows one to use an equivalent unit such as `0.5 dex.

Methods Summary

 to_string(self[, format]) Output the unit in the given format as a string.

Methods Documentation

to_string(self, format='generic')[source]

Output the unit in the given format as a string.

The physical unit is appended, within parentheses, to the function unit, as in “dB(mW)”, with both units set using the given format

Parameters
formatastropy.units.format.Base instance or str

The name of a format or a formatter object. If not provided, defaults to the generic format.

format: plain


text:
# Introduction¶

Currently we support two different formats

A target dataset in PLINK binary format must consist of three files: .bed, .bim, and a .fam file - where bed contains the compressed genotype data, bim contains the SNP information and fam contains the family information. Currently we only support a SNP major PLINK input (default output of the latest PLINK program).

The .bed and .bim file must have the same prefix.

If you want to use a .fam file with a different prefix from the .bed and .bim file, you can do

--target <bim bed prefix>,<fam file>

Warning

You MUST ensure the fam file contains the correct number of samples

Note

-9 will NOT be considered as missing for quantitative traits

If your binary file is separated into individual chromosomes, then you can place an # in place of the chromosome number. PRSice will automatically substitute # with 1-22

i.e. If your files are chr1.,chr2.,...,chr22., just use

--target chr#

Note

If an external fam file is provided, the substitution will not be performed on it. This is because all chromosome should have the same fam file. fam file from any of the chromosome should be ok

Todo

We will incorporate a new function in next version where we allow different number of autosomes to be specified. This should allow users to use PRSice on other organisms. However, due to complication in handling non-diploid chromosomes, we will only support diploid organisms (and exclude all sex chromosomes), i.e. Mouse

### BGEN¶

We also support BGEN v1.2. To specify a BGEN file, you simply add --type bgen or --ld-type bgen to your PRSice command

As BGEN does not store the phenotype information and sometime not even the sample ID, you must provide a phenotype file (--pheno-file) for PRSice to run. Or you can provide a sample file using

--target <bgen prefix>,<sample file>

Note

We will still require this sample file even if you are doing --no-regress as we do want the sample ID. we might loosen this requirement later on.

With BGEN, a number of other PRSice options become effective: - --hard: Normally, with BGEN format, we will calculate the PRS using the dosage information. But you can ask for hard-thresholding by using the --hard option. Then we will code the SNP as the genotype with probability larger than threshold specified by --hard-thres. If no such genotype is presented, the SNP will be coded as missing - --hard-thres: The genotype probability threshold. SNPs with no genotype having a probability larger than this threshold will be treated as missing

Note

Similar to PLINK files, you can use the # substitution for BGEN files that are separated into different chromosomes

## Phenotype files¶

PRSice also support an external phenotype file as in input using the --pheno-file This file should contain the FID and IID (or just IID if --ignore-fid is set) and the target phenotype.

You can specify the target phenotype name using --pheno-col. Multiple phenotype can be provided using a comma separated list. e.g.

  --pheno-col A,B,C

will cause PRSice to perform the analysis on phenotype A, B and C.

Note

When multiple phenotype is provided, PRSice will generate a set of results for each phenotype with the prefix of <Prefix>.<Pheno> where <Prefix> is the parameter provided to the --out option

# Target File Related Commands¶

• --binary-target

Indicate whether the target phenotype is binary or not. Either T or F should be provided where T represent a binary phenotype. For multiple phenotypes, the input should be separated by comma without space.

Default: T if --beta is set and F otherwise

• --geno

Filter SNPs based on gentype missingness. Must be a value between 0.0 and 1.0.

• --info Filter SNPs based on info score. Only used for imputed target. The INFO score is calculated as the MaCH imputation r-squared value. The pseudo code is represented as follow:

    m=Mean of expected genotype
v=variance of expected genotype
p=m/2
p_a = 2p(1-p)
INFO = v/p_a

• --keep

File containing the sample(s) to be extracted from the target file. First column should be FID and the second column should be IID. If --ignore-fid is set, first column should be IID Mutually exclusive from --remove

• --maf

Filter SNPs based on minor allele frequency (MAF)

Note

When perform MAF filtering on dosage data, we will calculate the MAF using the hard-coded genotype

• --nonfounders

By default, PRSice will exclude all non-founders from the analysis. When this flag is set, non-founders will be included in the regression model but will still be excluded from LD estimation.

• --pheno-col

Headers of phenotypes to be included from the phenotype file. When multiple phenotypes are provided, the phenotype name will be used as part of the file output prefix

• --pheno-file | -f

Phenotype file containing the phenotype(s). First column must be FID of the samples and the second column must be IID of the samples. When --ignore-fid is set, first column must be the IID of the samples. Must contain a header if --pheno-col is specified

• --prevalence | -k

Prevalence of all binary trait. If provided, PRSice will adjust the ascertainment bias of the R2.

Note

When multiple binary trait is found, prevalence information must be provided for all of them (Either adjust all binary traits, or don't adjust at all). For example, if there are 3 traits A, B and C, where A and C are binary traits with population prevalence of 0.1 and 0.2 respectively. The correct input should be --binary-target T,F,T --prevalence 0.1,0.2

• --remove

File containing the sample(s) to be removed from the target file. First column should be FID and the second column should be IID. If --ignore-fid is set, first column should be IID Mutually exclusive from --keep

• --target | -t

Target genotype file. Currently support both BGEN and binary PLINK format. For multiple chromosome input, simply substitute the chromosome number with #. PRSice will automatically replace # with 1-22. You can also specify a separate fam/sample file by --target <prefix>,<fam/sample file>

• --type

File type of the target file. Support bed (binary plink) and bgen format. Default: bed

# Dosage Related Commands¶

• --hard-thres

Hard threshold for the dosage data. SNPs with be coded as the genotype with probability higher than the threshold specified here. If no such genotype is presented, the SNP will be treated as missing.

Note

If dosage data is used as a LD reference, it will always be hard coded to calculate the LD

Default: 0.9

• --hard

When set, will use hard thresholding instead of dosage for PRS construction. Default is to use dosage.


text:
# probability question (“birthday paradox”)

$n$ people attend the same meeting, what is the chance that two people share the same birthday? Given the first $b$ birthdays, the probability the next person doesn't share a birthday with any that went before is $(365-b)/365$. The probability that none share the same birthday is the following: $\Pi_{0}^{n-1}\frac{365-b}{365}$. How many people would have to attend a meeting so that there is at least a $50$% chance that two people share a birthday?

So I set $\Pi_{0}^{n-1}\frac{365-b}{365}=.5$ and from there I manipulated some algebra to get $\frac{364!}{(364-n)!365^{n}}=.5\iff (364-n)!365^{n}=364!/.5=.....$

There has to be an easier way of simplifying this.

-
The problem actually asks you $\Pi_{0}^{n-1}\frac{365-b}{365} \geq .5$. You can basically simplify $(364-n)!$ remember that $1/.5=2$, then you get an equation which is hard to solev, but you can guess easily the solution by test and error.... –  N. S. Jan 26 '12 at 16:35
The only question is to determine how many times this was already asked on the site. –  Did Jan 26 '12 at 19:42

Paul Halmos asked this question in his "automathography", I Want to Be a Mathematician, and solved it as follows:

In other words, the problem amounts to this: find the smallest $n$ for which $$\prod_{k=0}^{n-1} \left(1-\frac{k}{365}\right) \lt \frac{1}{2}.$$

The indicated product is dominated by

$$\frac{1}{n} \sum_{k=0}^{n-1} \left(1-\frac{k}{365}\right)^n \lt \left(\frac{1}{n} \int_0^n \left(1-\frac{x}{365}\right)\mathrm dx\right)^n = \left(1- \frac{n}{730}\right)^n \lt e^{-n^2/730}.$$

The last term is less than $1/2$ if and only if $n \gt \sqrt{730 \log 2} \approx 22.6.$

Hence $n=23$.

-

$\displaystyle{p(n) = 1 - \left(\frac{364}{365}\right)^{C(n,2)} = 1 - \left(\frac{364}{365}\right)^{n(n-1)/2} }$

Sorry if my latex is not right.

The big trick with most prob questions is to ask what is the prob if it doesn't happen.

So you take 1 (total sample space) - P(not your birthday) = P(share your birthday)

Because P(A) = 1- not(P(A)).

so there are 364 days that are not your birthday, and the total number of days is 365. Thus 364/365 is the prob of not(P(A)).

Now the C(n,2) comes from the pairs (two people having the same birthday)

so your answer is $\left(\frac{364}{365}\right)^{n(n-1)/2} = .5$

solve for n, and from Maple 22.98452752.

-
if you assume that the event of a birthday is not independent, then think about 1*(1-1/365)...(1-364/365)...now you can aprox that with exp(x) aprox 1+x. So P(share birthday) = 1- P(not share birthday) which is aprox. 1- exp(-(n^2)/(2*365)) –  yiyi Jan 26 '12 at 17:05


text:
# Take all the CO2 in the atmosphere and put it into a layer on the surface of earth, how thick would the layer be?

I teach a Middle School (year 8) Geometry course and have a student attempting to answer this question. My assumptions:

1. earth's radius is $3959 \text{ mi}$
2. earth is a sphere
3. There is approximately $3 \cdot 10^{15}$ kg of CO2 in earth's atmosphere
4. The density of CO2 at 1atm is $\dfrac{1562 \text{ kg}}{\text{cubic meter}}$
5. Conversion between cu meters and cu ft are $1:35.3147$. And cu ft to cu mi is $5280^3:1$

So, first, with assumption (3 and 4) we can compute the volume of CO2 in the atmosphere to be $\approx 1.92 \cdot 10^{12} \text{ m}^3$ or about $369 \text{ cu mi}$ of CO2.

So, now we can find the thickness of the layer by solving the equation

\begin{align*} 369 &= \dfrac{4 \pi \cdot (3959 + x)^3}{3} - \dfrac{4 \pi (3959)^3}{3} \\ \end{align*}

Where $x$ is the thickness of the layer of CO2 on earth's surface in miles.

\begin{align*} 369 \cdot \dfrac{3}{4 \pi} &= (3959+x)^3 - (3959)^3 \\[.5pc] 369 \cdot \dfrac{3}{4 \pi}+3959^3 &= (3959+x)^3 \\[.5pc] \sqrt[3]{369 \cdot \dfrac{3}{4 \pi}+3959^3} &= 3959 + x \\[.5pc] 3959.0000018746 &\approx 3959 + x \\[.5pc] .00000018746 &\approx x \end{align*}

So, the layer of CO2 on earth's surface would be $\approx 1.87 \cdot 10^{-6} \text{ mi}$ or $.1187 \text{ in}$ in thickness. Which is less than half the thickness of an iPhone 6.

My Question: This result seems incredibly small. Where did I go wrong? Or, is this reasonable. I have no intuition and would be interested in a second opinion!

• Please note that we use SI units here. If you must refer to quaint old units, please use the SI units as your primary units, and put the archaic stuff in parentheses afterwards. (oh, and you've missed the unit on the Earth's radius) – EnergyNumbers Jun 14 '16 at 10:02
• userLTK is right... your density of CO2 should be the same as the density of air at sea level... which is 3 orders of magnitude smaller than your number. – farrenthorpe Jun 14 '16 at 13:59
• Another way to get a quick estimate, to check your answer, is to estimate the thickness of the Earth's atmosphere to some arbitrary level, say 100 mbars, The carbon dioxide fraction is currently about 404 ppm, so convert that to a fraction and multiply by the atmospheric thickness. Of course, CO2 is denser than air so you must make a density correction. You will find that the answer is massively more than you have calculated. Also, 'EnergyNumbers' is correct. The civilized world uses SI units! – Gordon Stanger Jun 14 '16 at 14:14
• @farrenthorpe I hadn't noticed that we took the density number from CO2 as a solid, but I guess that makes sense that a cubic meter wouldn't weigh 1562 kg as a gas! Thank you for pointing that out. Also, didn't realize that the SI units was a problem. Also, figured that this was the right place to ask the question and that someone might be interested in answer. But perhaps wrong spot? – Nick H Jun 15 '16 at 2:23
• I think it's appropriate to find the thickness of the CO as a solid. If it's a gas, how do you make it form a thin layer at the bottom of the atmosphere? – J Thomas Dec 30 '18 at 19:47

Ok, based on the comments above, this is where I am at...

1. earth's radius is $6371 \text{ km}$
2. earth is a sphere
3. There is approximately $3 \cdot 10^{15}$ kg of CO2 in earth's atmosphere
4. The density of CO2 at 1atm is $\dfrac{1.977 \text{ kg}}{\text{ m}^3}$

So, first, with assumption (3 and 4) we can compute the volume of CO2 in the atmosphere to be $\approx 1.52 \cdot 10^{15} \text{ m}^3$ or $1.52 \cdot 10^6 \text{ km}^3$.

So, now we can find the thickness of the layer by solving the equation

\begin{align*} 1.52 \cdot 10^6 &= \dfrac{4 \pi \cdot (6371 + x)^3}{3} - \dfrac{4 \pi (6371)^3}{3} \\ \end{align*}

Where $x$ is the thickness of the layer of CO2 on earth's surface in km.

\begin{align*} 1.52 \cdot 10^6 \text{ km}^3 &= \dfrac{4 \pi \cdot (6371 + x)^3}{3} - \dfrac{4 \pi (6371)^3}{3} \\[.5pc] \dfrac{3}{4\pi} \cdot 1.52 \cdot 10^6 \text{ km}^3 &= (6371+x)^3 - 6371^3 \\ \dfrac{1.14}{\pi} \cdot 10^6 \text{ km}^3&= (6371+x)^3 - 6371^3 \\ 3.63 \cdot 10^5 +6371^3 \text{ km}^3 &= (6371 + x)^3 \\ \sqrt[3]{3.63 \cdot 10^5 +6371^3 \text{ km}^3} &= 6371 + x \\ 6371.0029811 \text{ km} &\approx 6371 + x \\ .0029811 \text{ km} &\approx x \end{align*}

So, the layer of CO2 on earth's surface would be 2.98 meters thick...

• That's about right. However, since you used a value of $3\cdot10^{15}$ kg (one significant digit), you should round that final result to 3 meters. – David Hammen Jun 15 '16 at 13:00
• An alternative approach is that the volume of a thin spherical shell of radius $r$ and height $h$ is approximately $4\pi r^2 h$, valid for $h\lll r$. You can see this by expanding $\frac43 \pi (r+h)^3 - \frac 43 \pi r^3 = \frac 43 \pi (3r^2h + 3rh^2 + h^3) = 4\pi r^2h(1+h/r+\frac13 (h/r)^2) \approx 4\pi r^2h$ for small $h$. Approximation is something 8th grade students should start learning. The calculation is much simpler with this approximation: $(1.52\times10^{15}\,\text{m}^3)/(4\pi\,(6371\,\text{km})^2) \approx 2.98\,\text{m}$ – David Hammen Jun 15 '16 at 13:02
• Also note that the density value of 1.977 kg/m^3 is an empirical value that reflects the non-ideal nature of carbon dioxide. You'll get a slightly different value for the density of CO2 at standard temperature and pressure if you use the ideal gas law. I don't know if your students know about the ideal gas law. If they do, it might be a better learning experience to have them calculate that density value rather than taking it as a given. (They should arrive at 1.963 kg/m^3.) – David Hammen Jun 15 '16 at 13:11
• A couple of final comments: That value of $3\cdot 10^{15}$ kg is a bit outdated. Humanity has continued to pump CO2 into the atmosphere. The current value is about $3.16\cdot 10^{15}$ kg. Finally, as a teacher you should attach units to all of your calculations. Students regular make a mess of calculations because they get their units wrong. It is your job as a teacher to show them how to not make those mistakes. – David Hammen Jun 15 '16 at 13:17
• @DavidHammen yes, you are right about the units, Thanks for mentioning the gas law too. – Nick H Jun 16 '16 at 2:28

A rough estimate is the portion of CO2 in the atmosphere (408 ppm) times the mean height (5.6 km) which gives 2.3 m.


text:
## Tsukuba Journal of Mathematics

### On first order linear PDE systems all of whose solutions are harmonic functions

#### Abstract

We study the first order linear system $u_{\tilde{z}} + \bar{v}_{w} = 0, u_{\bar{w}} - \bar{v}_{z} = 0$ in a domain $\Omega \subset \mathbb{C}^{2}$ (first considered by G. Cimmino, [3]). We prove a Morera type theorem, emphasizing the analogy to the Cauchy-Riemann system, and a representation formula yielding a result on removable singularities of solutions to (2). We derive (by a Hilbert space technique outlined in [5]) compatibility relations among the free terms and boundary data in the boundary value problem $u_{\tilde{z}}+ \bar{v}_{w} = f, u_{\bar{w}} - \bar{v}_{z} = g$ in $\Omega$, and $u = \varphi,v = \psi$ on $\partial \Omega$. If $F = (u, v) : \Omega \to \mathbb{C}^{2}$ is a solution to (2) such that $\sup_{\varepsilon \gt O}$\int_{\partial \Omega_{\varepsilon}}|F(z, w)|^{p} d\sigma_{\varepsilon}(z, w} \lt \infty$for some$p \geq 2$, then we show that$F$admits non tangential limits at almost every$(\xi, \omega) \in \partial\Omega\$.

#### Article information

Source
Tsukuba J. Math., Volume 30, Number 1 (2006), 149-170.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496165034

Digital Object Identifier
doi:10.21099/tkbjm/1496165034

Mathematical Reviews number (MathSciNet)
MR2248289

Zentralblatt MATH identifier
1123.35011

#### Citation

Dragomir, Sorin; Lanconelli, Ermanno. On first order linear PDE systems all of whose solutions are harmonic functions. Tsukuba J. Math. 30 (2006), no. 1, 149--170. doi:10.21099/tkbjm/1496165034. https://projecteuclid.org/euclid.tkbjm/1496165034


text:
## Text and variables

Show off your games, demos and other (playable) creations.
BobTheBuilder
Prole
Posts: 4
Joined: Wed Jan 02, 2019 10:03 am

### Text and variables

Is there a way of setting a text (love.graphics.print("Hello)) to a variable? For example, when I click the "g" button, a variable will increase by 10 and will cause a text to change to 10.

Snaker1
Prole
Posts: 9
Joined: Wed Dec 19, 2018 7:43 pm

### Re: Text and variables

Not sure if I understand your question but try:

Code: Select all

love.graphics.print("This is the variable g:"..tostring(g), 0, 0)
If you have a variable like g that is a number, you need to call the function tostring to convert it into a string.

To concatenate two strings together, you use the operator .. like:

Code: Select all

name = "Tom"
new_string = "Hello:"..name
Here is an example:

Code: Select all

function love.load()
g = 0
end
function love.mousepressed()
g = g + 1
end
function love.draw()
love.graphics.print("g is: "..tostring(g), 0, 0)
end
This will increase g every time the mouse is clicked.

Now you only need to include checks for the mouse position, so that g gets only increased when the mouse is in a certain area. I am sure you can do that!

I hope this helps!

I think you are in the wrong sub forum, by the way. ;P

zorg
Party member
Posts: 2554
Joined: Thu Dec 13, 2012 2:55 pm
Location: Absurdistan, Hungary
Contact:

### Re: Text and variables

Hi and welcome to the forums;

yes, just use a variable, and print that.

Code: Select all

local v = 10
function love.keypressed(k)
if k == 'g' then v = v + 10 end
end
function love.draw()
love.graphics.print(v,0,0)
end

If that's not what you meant, then clarify further.

Also i hate being ninja'd by others

Edit:
Snaker1 wrote:
Wed Jan 02, 2019 10:43 pm
If you have a variable ... that is a number, you need to call the function tostring to convert it into a string.
That's a bit incorrect, lua itself usually coerces numbers into strings, the string concat. operator (..) certainly does.
Me and my stuff True Neutral Aspirant. Why, yes, i do indeed enjoy sarcastically correcting others when they make the most blatant of spelling mistakes. No bullying or trolling the innocent tho.

Snaker1
Prole
Posts: 9
Joined: Wed Dec 19, 2018 7:43 pm

### Re: Text and variables

zorg wrote:
Wed Jan 02, 2019 10:45 pm
That's a bit incorrect, lua itself usually coerces numbers into strings, the string concat. operator (..) certainly does.
Yes, true but I tried to teach him about how to explicitly convert a string into a number because that is pretty important as well.

Good point though, that (..) can implicitly convert it. Should have mentioned that.

### Who is online

Users browsing this forum: No registered users and 23 guests


text:
The Annals of Probability

Good rough path sequences and applications to anticipating stochastic calculus

Abstract

We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is assumed. Under a simple condition on the stochastic process, we show that the unique solution of the above SDE understood in the rough path sense is actually a Stratonovich solution. We then show that this condition is satisfied by the Brownian motion. As application, we obtain rather flexible results such as support theorems, large deviation principles and Wong–Zakai approximations for SDEs driven by Brownian motion along anticipating vectorfields. In particular, this unifies many results on anticipative SDEs.

Article information

Source
Ann. Probab., Volume 35, Number 3 (2007), 1172-1193.

Dates
First available in Project Euclid: 10 May 2007

https://projecteuclid.org/euclid.aop/1178804326

Digital Object Identifier
doi:10.1214/009117906000000827

Mathematical Reviews number (MathSciNet)
MR2319719

Zentralblatt MATH identifier
1132.60053

Subjects
Primary: 60H99: None of the above, but in this section

Citation

Coutin, Laure; Friz, Peter; Victoir, Nicolas. Good rough path sequences and applications to anticipating stochastic calculus. Ann. Probab. 35 (2007), no. 3, 1172--1193. doi:10.1214/009117906000000827. https://projecteuclid.org/euclid.aop/1178804326

References

• Ahn, H. and Kohatsu-Higa, A. (1995). The Euler scheme for anticipating stochastic differential equations. Stochastics Stochastics Rep. 54 247--269.
• Caballero, M. E., Fernández, B. and Nualart, D. (1995). Smoothness of distributions for solutions of anticipating stochastic differential equations. Stochastics Stochastics Rep. 52 303--322.
• Caballero, M. E., Fernández, B. and Nualart, D. (1997). Composition of skeletons and support theorems. In Stochastic Differential and Difference Equations (I. Csiszár and Gy. Michaletzky, eds.) 21--33. Birkhäuser, Boston.
• Friz, P. (2005). Continuity of the Itô-map for Hölder rough paths with applications to the support theorem in Hölder norm. In Probability and Partial Differential Equations in Modern Applied Mathematics (E. C. Waymire and J. Duan, eds.) 117--135. Springer, New York.
• Friz, P., Lyons, T. and Stroock, D. (2006). Lévy's area under conditioning. Ann. Inst. H. Poincare Probab. Statist. 42 89--101.
• Friz, P. and Victoir, N. (2005). Approximations of the Brownian rough path with applications to stochastic analysis. Ann. Inst. H. Poincare Probab. Statist. 41 703--724.
• Friz, P. and Victoir, N. (2006). A note on the notion of geometric rough path. Probab. Theory Related Fields 136 395--416.
• Kohatsu-Higa, A. and León, J. A. (1997). Anticipating stochastic differential equations of Stratonovich type. Appl. Math. Optim. 36 263--289.
• Kohatsu-Higa, A., León, J. A. and Nualart, D. (1997). Stochastic differential equations with random coefficients. Bernoulli 3 233--245.
• Lejay, A. (2003). Introduction to rough paths. Séminaire de Probabilités XXXVII. Lecture Notes in Math. 1832 1--59. Springer, Berlin.
• Lejay, A. and Lyons, T. (2003). On the importance of the Lévy area for studying the limits functions of converging stochastic processes. Application to homogenization. Current Trends in Potential Theory 63--84.
• Lejay, A. and Victoir, N. (2006). On $(p,q)$-rough paths. J. Differential Equations 225 103--133.
• Lévy, P. (1948). Processus Stochastiques et Mouvement Brownien. Gauthier-Villars, Paris.
• Lyons, T. (1998). J. Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 215--310.
• Lyons, T. and Qian, Z. (2002). System Control and Rough Paths. Oxford Univ. Press.
• Ledoux, M., Qian, Z. and Zhang, T. (2002). Large deviations and support theorem for diffusion processes via rough paths. Stochastic Process. Appl. 102 265--283.
• Millet, A. and Nualart, D. (1992). Support theorems for a class of anticipating stochastic differential equations. Stochastics Stochastics Rep. 39 1--24.
• Millet, A., Nualart, D. and Sanz, M. (1992). Large deviations for a class of anticipating stochastic differential equations. Ann. Probab. 20 1902--1931.
• Nualart, D. (1995). The Malliavin Calculus and Related Topics. Springer, New York.
• Ocone, D. and Pardoux, E. (1989). A generalized Itô--Ventzell formula. Application to a class of anticipating stochastic differential equations. Ann. Inst. H. Poincaré Probab. Statist. 25 39--71.
• Reutenauer, C. (1993). Free Lie Algebras. Oxford Science Publications.
• Rovira, C. and Sanz-Solé, M. (1997). Anticipating stochastic differential equations: Regularity of the law. J. Funct. Anal. 143 157--179.
• Sanz-Solé, M. and Sarrà, M. (1999). Logarithmic estimates for the density of an anticipating stochastic differential equation. Stochastic Process. Appl. 79 301--321.
• Stroock, D. W. (1993). Probability Theory, an Analytic View. Cambridge Univ. Press.
• Stroock, D. and Varadhan, S. R. (1972). On the support of diffusion processes with applications to the strong maximum principle. Proc. Sixth Berkeley Sympos. Math. Statist. Probability III. Probability Theory 333--359. Univ. California Press, Berkeley.
• Young, L. C. (1936). An inequality of Hölder type, connected with Stieltjes integration. Acta Math. 67 251--282.


text:
# Thread: Volume of a pyramid

1. ## Volume of a pyramid

I have two different problems that are built around the volume of the following:

A three sided pyramid has sides of the following planes y= 0, y- x = 4, 2x + y + z = 4
The base sits at the plane z = -6

I have tried to draw a sketch but am still having trouble with this. I have the base being a platform at z = -6 and one side is along the y axis ( y = 0)

I believe my function should be 4 - 2x - y and that I am dealing with a double integral.

Would someone be willing to sketch this? Or help me with what my limits for x and y are?

2. Originally Posted by Frostking
I have two different problems that are built around the volume of the following:

A three sided pyramid has sides of the following planes y= 0, y- x = 4, 2x + y + z = 4
The base sits at the plane z = -6

I have tried to draw a sketch but am still having trouble with this. I have the base being a platform at z = -6 and one side is along the y axis ( y = 0)

I believe my function should be 4 - 2x - y and that I am dealing with a double integral.

Would someone be willing to sketch this? Or help me with what my limits for x and y are?
Here's the sketch:

Now, to find the limits of integration:

If your dealing with a triple integral, we see that $-6\leqslant z\leqslant 4-2x-y$. Now, when $y=0$, $y-x=4\implies -x=4\implies x=-4$ and when $y=0,z=-6$, $2x+y+z=4\implies 2x-6=4\implies 2x=10\implies x=5$. Thus, $-4\leqslant x\leqslant 5$. Finally, we can conclude that $0\leqslant y\leqslant x+4$

So your triple integral would be $\int_{-4}^5\int_0^{x+4}\int_{-6}^{4-2x-y}\,dz\,dy\,dx$

The double integral would be $\int_{-4}^5\int_0^{x+4}\left(10-2x-y\right)\,dy\,dx$, which is a result from the triple integral.

Does this make sense?

3. ## Limits of integration

Your sketch and detailed explanation helped a lot. I am still struggling with how to envision these shapes. Geometry and spacial problems are tough for me. Thanks very much for your time and effort. I will study your post and try to come up with the limits on my own. Frostking


text:
# Glossary¶

Bit
The smallest unit of information in computing, abbreviation of the term Binary digIT.
Blob
Binary Large OBject, typically a large binary file stored in a database.
Bug
Defect in a computer program which stops it from working as intended, see also debug.
Class
In object-oriented programming a class is a template that can be used to create an object.
CPU
Central Processing Unit, part of the computer that executes machine instructions.
Debug
The activity of identifying and removing a bug (defect) from a computer program.
DNS
Domain Name Server a machine that translates URLs to IP addresses.
DRY
Don’t repeat yourself. Make use of a variables for frequently used values. Make use of functions for frequently used processing logic.
Function
A set of instructions for performing a procedure. Most commonly a function takes a set of arguments and returns a value.
HTTP
HyperText Transfer Protocol, commonly used for web browsing.
Hypervisor
A piece of software that allows you to run a virtual machine.
List
A common data structure representing an ordered collection of elements. Also known as an array.
Method
A method refers to a function that is part of a class.
Init
Abbreviation of the word “initialise”. Usually used to represent a one time event that that results in the creation of a new entity.
Integer
A whole number, i.e. a number that can be expressed without a fractional component.
I/O
Input/Output; often used in the context of reading and writing data to disk.
Object
In object-oriented programming an object is an instance of a class.
Object-oriented programming
Programming methodology centered around the concept of objects rather than actions and procedures.
Pipe
A pipe is a means to redirect the output from one command into another. The character used to represent a pipe is the vertical bar: |.
RAM
Random Access Memory, fast access volatile memory.
Recursion
A procedure whose implementation calls itself. Of practical use for problems where the solution depends on smaller instances of the same problem.
Scope
Determines which parts of a program has access to what. For example any part of a program can have access to a global variable. However, if a variable is contained within the scope of a function only code within that function can access the variable.
Shell
Program that allows the user to interact with the operating system’s services and programs, see also terminal.
Standard input stream

Stream of characters ingested by a program, often abbreviated as stdin. A common way to send data to a program is to pipe them from the standard output stream of another program. In the below we use the echo command to send the string foo bar baz to the standard input stream of the wc command.

\$ echo "foo bar baz" | wc
1       3      12

Standard error stream
Stream of characters, representing error output, emitted by a program. Commonly viewed in the shell when running a command. Often abbreviated as stderr.
Standard Library
A set of functionality that comes built-in with the core programming language.
Standard output stream
Stream of characters emitted by a program. Commonly viewed in the shell when running a command. The standard output stream can be redirected using a pipe. Often abbreviated as stdout.
State
All the information, to which a program has access, at a particular point in time.
String
A list of characters used to represent text.
TDD
See test-driven development
Terminal
Application for accessing a shell, see also shell.
Test-driven development

Methodology used in software development that makes use of rapid iterations of development cycles. The development cycle includes three steps:

1. Write a test
2. Write minimal code to make the test pass
3. Refactor the code if necessary
URL
Unique Resource Location
Virtual machine
An operating system running within a hypervisor rather than on the physical computer.
VM
See virtual machine.


text:
Ounaies, Hichem

Compute Distance To:
 Author ID: ounaies.hichem Published as: Ounaies, Hichem; Ounaies, H.
 Documents Indexed: 15 Publications since 1994 Co-Authors: 10 Co-Authors with 12 Joint Publications 273 Co-Co-Authors
all top 5

Co-Authors

 3 single-authored 4 Bahrouni, Anouar 3 Bahrouni, Sabri 3 Rădulescu, Vicenţiu D. 2 Benrhouma, Mohamed 1 Balabane, Mikhael 1 Bedoui, Nizar 1 Ben, Mabrouk Anouar 1 Chteoui, Riadh 1 Dolbeault, Jean 1 Tavares, Leandro S.
all top 5

Serials

 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Differential and Integral Equations 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Applied Mathematics Letters 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Partial Differential Equations 1 Topological Methods in Nonlinear Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Mediterranean Journal of Mathematics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Nonlinear Analysis. Theory, Methods & Applications
all top 5

Fields

 14 Partial differential equations (35-XX) 3 Functional analysis (46-XX) 1 Ordinary differential equations (34-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX)

Citations contained in zbMATH Open

13 Publications have been cited 123 times in 78 Documents Cited by Year
Infinitely many solutions for a class of sublinear Schrödinger equations with indefinite potentials. Zbl 1326.35329
Bahrouni, Anouar; Ounaies, Hichem; Rădulescu, Vicenţiu D.
2015
Nodal solutions for a sublinear elliptic equation. Zbl 1087.35033
Balabane, Mikhaël; Dolbeault, Jean; Ounaies, Hichem
2003
Bound state solutions of sublinear Schrödinger equations with lack of compactness. Zbl 1429.35079
Bahrouni, Anouar; Ounaies, Hichem; Rădulescu, Vicenţiu D.
2019
Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems. Zbl 1436.35090
Bahrouni, Sabri; Ounaies, Hichem
2020
Perturbation method for a class of nonlinear Dirac equations. Zbl 0974.35101
Ounaies, H.
2000
Basic results of fractional Orlicz-Sobolev space and applications to non-local problems. Zbl 1448.35242
Bahrouni, Sabri; Ounaies, Hichem; Tavares, Leandro S.
2020
Compactly supported solutions of Schrödinger equations with small perturbation. Zbl 06892654
Bahrouni, Anouar; Ounaies, Hichem; Rădulescu, Vicenţiu D.
2018
Existence and uniqueness of positive solution for nonhomogeneous sublinear elliptic equations. Zbl 1177.35068
Benrhouma, Mohamed; Ounaies, Hichem
2009
Existence of solutions for a perturbation sublinear elliptic equation in $$\mathbb R^N$$. Zbl 1202.35097
Benrhouma, Mohamed; Ounaies, Hichem
2010
Study of an elliptic equation with a singular potential. Zbl 1023.35038
Ounaies, Hichem
2003
Infinitely many solutions for a class of sublinear Schrödinger-Maxwell equations in $$\mathbb {R}^N$$ with indefinite weight functions. Zbl 1313.35078
Bahrouni, Anouar; Ounaies, Hichem
2014
Existence and properties of radial solutions of a sub-linear elliptic equation. Zbl 1340.35037
Chteoui, Riadh; Ben, Mabrouk Anouar; Ounaies, Hichem
2015
Strauss and Lions type theorems for the fractional Sobolev spaces with variable exponent and applications to nonlocal Kirchhoff-Choquard problem. Zbl 1459.35147
Bahrouni, Sabri; Ounaies, Hichem
2021
Strauss and Lions type theorems for the fractional Sobolev spaces with variable exponent and applications to nonlocal Kirchhoff-Choquard problem. Zbl 1459.35147
Bahrouni, Sabri; Ounaies, Hichem
2021
Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems. Zbl 1436.35090
Bahrouni, Sabri; Ounaies, Hichem
2020
Basic results of fractional Orlicz-Sobolev space and applications to non-local problems. Zbl 1448.35242
Bahrouni, Sabri; Ounaies, Hichem; Tavares, Leandro S.
2020
Bound state solutions of sublinear Schrödinger equations with lack of compactness. Zbl 1429.35079
Bahrouni, Anouar; Ounaies, Hichem; Rădulescu, Vicenţiu D.
2019
Compactly supported solutions of Schrödinger equations with small perturbation. Zbl 06892654
Bahrouni, Anouar; Ounaies, Hichem; Rădulescu, Vicenţiu D.
2018
Infinitely many solutions for a class of sublinear Schrödinger equations with indefinite potentials. Zbl 1326.35329
Bahrouni, Anouar; Ounaies, Hichem; Rădulescu, Vicenţiu D.
2015
Existence and properties of radial solutions of a sub-linear elliptic equation. Zbl 1340.35037
Chteoui, Riadh; Ben, Mabrouk Anouar; Ounaies, Hichem
2015
Infinitely many solutions for a class of sublinear Schrödinger-Maxwell equations in $$\mathbb {R}^N$$ with indefinite weight functions. Zbl 1313.35078
Bahrouni, Anouar; Ounaies, Hichem
2014
Existence of solutions for a perturbation sublinear elliptic equation in $$\mathbb R^N$$. Zbl 1202.35097
Benrhouma, Mohamed; Ounaies, Hichem
2010
Existence and uniqueness of positive solution for nonhomogeneous sublinear elliptic equations. Zbl 1177.35068
Benrhouma, Mohamed; Ounaies, Hichem
2009
Nodal solutions for a sublinear elliptic equation. Zbl 1087.35033
Balabane, Mikhaël; Dolbeault, Jean; Ounaies, Hichem
2003
Study of an elliptic equation with a singular potential. Zbl 1023.35038
Ounaies, Hichem
2003
Perturbation method for a class of nonlinear Dirac equations. Zbl 0974.35101
Ounaies, H.
2000
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Cited by 121 Authors

 8 Rădulescu, Vicenţiu D. 7 Bahrouni, Anouar 7 Ounaies, Hichem 5 Bahrouni, Sabri 5 Dolbeault, Jean 3 Alberico, Angela 3 Ben Mabrouk, Anouar 3 Benrhouma, Mohamed 3 Chen, Sitong 3 Cianchi, Andrea 3 Esteban, Maria J. 3 Guan, Wen 3 Pick, Luboš 3 Salort, Ariel Martin 3 Slavíková, Lenka 3 Wang, Dabin 2 Chteoui, Riadh 2 Comech, Andrew 2 García-Huidobro, Marta 2 Hao, Xin’an 2 Loss, Michael 2 Manasevich, Raul F. 2 Nodari, Simona Rota 2 Tang, Xianhua 2 Winkert, Patrick 1 Abounouh, Mostafa 1 Afrouzi, Ghasem Alizadeh 1 Ahmad, Bashir 1 Al Moatassime, Hassan 1 Aljohani, Abdulrahman F. 1 Al-saedi, Ahmed Eid Salem 1 An, Tianqing 1 Bal, Kaushik 1 Baraket, Sami 1 Bazarbacha, Imen 1 Bedoui, Nizar 1 Ben Mohamed, Mohamed Lakdar 1 Biswas, Reshmi 1 Borrelli, William 1 Boussaid, Nabile 1 Bu, Weichun 1 Cardoso, Jose Anderson 1 Carlone, Raffaele 1 Cattani, Carlo 1 Cerda, Patricio 1 Chadli, Lalla Saadia 1 Chen, Jianhua 1 Cheng, Bitao 1 Chetouane, Rima 1 Choi, Q-Heung 1 Choi, Woocheol 1 Chrifi, Abderrazak 1 Colorado, Eduardo 1 Cortázar, Carmen 1 Cui, Na 1 Cui, Yujun 1 Da Silva, Edcarlos Domingos 1 de Albuquerque, José Carlos 1 Deng, Yihua 1 Di Menza, Laurent 1 Dudnikova, Tat’yana V. 1 El Houari, Hassan 1 Han, Zhiqing 1 Hong, Younghun 1 Huang, Xianjiu 1 Isernia, Teresa 1 Ji, Chao 1 Jung, Tacksun 1 Kowalczyk, Michał 1 Laptev, Ari 1 Le Treust, Loïc 1 Lewin, Mathieu 1 Li, Guidong 1 Li, Wenlong 1 Li, Zhenping 1 Lian, Wei 1 Liu, Lishan 1 Ma, Luping 1 Mai, Ali 1 Maione, Alberto 1 Mirzapour, Maryam 1 Mohanta, Kaushik 1 Molina, Sandra Monica 1 Moussa, Hassan 1 Mugnai, Dimitri 1 Mustafa, Octavian G. 1 Ning, Cui 1 O’Regan, Donal 1 Pereira, Denilson S. 1 Qin, Dongdong 1 Ren, Ming 1 Roy, Prosenjit 1 Secchi, Simone 1 Seok, Jinmyoung 1 Séré, Eric 1 Shen, Jihong 1 Shen, Liejun 1 Sk, Firoj 1 Stuart, David M. A. 1 Sun, Hongrui ...and 21 more Authors
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Cited in 45 Serials

 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Boundary Value Problems 4 Advances in Nonlinear Analysis 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 The Journal of Geometric Analysis 3 Annales Henri Poincaré 2 Applied Mathematics and Computation 2 Journal of Differential Equations 2 Asymptotic Analysis 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Electronic Journal of Differential Equations (EJDE) 2 Discrete and Continuous Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Advanced Nonlinear Studies 2 AIMS Mathematics 1 Applicable Analysis 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 Manuscripta Mathematica 1 Quaestiones Mathematicae 1 Acta Applicandae Mathematicae 1 Acta Mathematicae Applicatae Sinica. English Series 1 Revista Matemática Iberoamericana 1 Applied Mathematics Letters 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Topological Methods in Nonlinear Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 The Journal of Fourier Analysis and Applications 1 Mathematical Problems in Engineering 1 Journal of Inequalities and Applications 1 Communications in Contemporary Mathematics 1 Lobachevskii Journal of Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Complex Variables and Elliptic Equations 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Journal of Applied Analysis and Computation 1 Open Mathematics 1 Advances in Operator Theory 1 Electronic Research Archive
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Cited in 16 Fields

 73 Partial differential equations (35-XX) 10 Functional analysis (46-XX) 9 Quantum theory (81-XX) 5 Ordinary differential equations (34-XX) 5 Operator theory (47-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Fluid mechanics (76-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral equations (45-XX) 2 Numerical analysis (65-XX) 1 Real functions (26-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX)