Unique Factorization Domain: Factorization
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
How do I disable the profiles button in Chrome? Since Chrome version 38, there's a pretty ugly button in the title bar of the Chrome window that allows you to switch profiles quickly.  Since I'm the only one that uses my computer, this is not really useful to me, and I'd rather reclaim the space for more open tabs.  I've looked in the settings but don't see a way to disable it.  How can I get rid of the button? How is Anti Aliasing Implemented in Ray Tracing? After reading a few articles online I can confidently say I am clueless on how Anti-Aliasing works when using Ray Tracing.  All I understand is that A Single Pixel/Ray is split into 4 sub-pixels and 4 rays rather than 1.  Could somebody please explain how this is done (preferably with code)? I'm trying to crack a cypher that I believe is Vigenère encrypted and I'm currently stuck.  I calculated the key length by finding repeated sequences in the cypher and calculating the the common factors.  Word    distance factors agzd    16       2,4,8,16        zna     92       2,4,23,46,92 zdc     54       2,3,6,9,18,27,54 csio    44       2,4,11,22,44 omy     46       2,23,46 zab     5        5   I assume the key-length is 4 as these are the once that are common factors, but from here on trying to map the correct caesar shiffre for each position I'm stuck.  Can somebody confirm that my key-length calculation has no errors which would explain why I can't solve the cypher.  Here is the cypher:  jD 2GSA 7HNA ZNA w.m. V7KXA 36HBM MKE5 /H SGP9 +R GKKJ 2I A4OTC KDBCUR. 19+R 8Y TKJ JG4 IGO6 6U4T OJ hH/BIK. 196 qFKT+9 BNJK ZD6+Q AGZD. kJ'R EaOP6 4NCR ZK 36 / AGZD6C/HOIE2D. x0ZNAC2S8IO8DI HB xX8D4D 0XK O66M 0Y MN62S 8TZABBD2Za8BI. lBJ HA+DF 6UU/ 2J /FOZDC6S8I OJ kDC8G OO 2BLCYZ O66M 0Y G 925F4 UL J2JHCTGH FHH3K What is integration by parts, really? Integration by parts comes up a lot - for instance, it appears in the definition of a weak derivative / distributional derivative, or as a tool that one can use to turn information about higher derivatives of a function into information about an integral of that function. Concrete examples of this latter category include: proving that $f \in C^2(S^1)$ implies that the Fourier series of $f$ converges absolutely and uniformly, and the Taylor series expansion with the integral formula for remainder.  However, I don't feel like I really understand what integration by parts is really doing. To me, it is just an algebraic trick that follows from the fundamental theorem of calculus and the product rule. Is there some more conceptual way to think about it?  How do you think about this useful idea? Converge or diverge? : $\sum_{n=1}^{\infty}\frac{\tan{n}}{2^{n}}$ Allow the creation of links in formatted code through markdown or the GUI As pointed out in  it is possible to create a link in formatted code. But, only by using explicit HTML. Since I think creating a link to documentation within a code block is a fairly common use case, it should be possible to do this using the GUI.   I should be able to highlight some code. Press the  code formatting button. Then highlight some code within that and press the link button and create a link.  Today this results in:  [parseInt][3]("01", 10);   it should result in:  ("01",10); "Goose"–"geese" vs. "moose"–"moose" Why is it that the plural of goose is geese but the plural of moose is moose? The same goes for mouse and house. Mouse becomes mice, yet house becomes houses. I have a shapefile with 3800 polygons representing the smallest administrative areas in Ireland. Many of these, in rural areas, have tiny populations, under 100 people. In urban areas, all would have adequate populations.  For each area I have a population figure, and various other attributes, all of which can be intelligently summed to give valid results for areas produced by combining the smaller areas.  I need to merge the areas to get say, 500 or 600 areas of reasonable population. I need to leave the larger (in population) areas alone, where possible. I would greatly prefer to do this automatically. This is necessary for model fitting purposes, primarily.  I've looked at a number of the dissolve questions here:   'Batch Dissolve Polygons based on Attributes in QGIS or FWTools' I think would require me to know which areas to merge, when this is what I need to calculate. 'Practical way of managing polygons and unions of them' and 'How do dissolve polygons from shapefile using open source tools?' have the same issue.   Any suggestions? What Android emulators are available? I will like to know some of the android emulators that work really well with Ubuntu 11.10 and above. I want to try 'whatsapp' on Ubuntu through an android emulator. Thanks in advance How can metagaming retries on poor skill checks be prevented? Non numbered chapter* header issue Real Time LaTeX? Possible Duplicate:          I'm looking for an application in which I can write pure LaTeX in one half of the screen and on the other half to see the compiled document in real time. This seems really like an obvious way to do LaTeX authoring but it doesn't look like any software is able to do it. LyX is not what I'm looking for. I want to edit the actual LaTeX and see it rendered in real time. Why isn't this already being done somewhere? Pgfplots with custom axis markers Assume you have a trigonometric function, say for simplicity sin(x). When plotting the function, how can one place the x-axis markers on 0, pi/2, pi, 3pi/2, 2pi, instead of the default numeric values that pgfplots uses? How to automatically generate a stacktrace when my program crashes Remove Indentation for a Single Paragraph Is there a way to remove the indentation at the beginning of a paragraph for a single paragraph.  I know I could do  \setlength{\parindent}{0cm} This is my paragraph.  Blah blah blah. \setlength{\parindent}{default}   Where default is whatever the default indentation is for the document class I am using (part of the problem is that I don't know what this default value is).  I feel as if there should be a better way to accomplish this than by the above method.  I am looking for a solution of the form:  \noindent This is my paragraph.  Blah blah blah.   Is there a way to do this, or will I have to resort to the former method?  If I have to resort to the former method, what is the default indentation value for the amsart document class? How handicapped am I in graduate admissions if I graduated from a lower tier university? Due to a combination of factors, I ended up going for my undergraduate studies to a relatively unknown university that was close to me geographically.  Let's say that I have a relatively standard background for someone trying to apply to top tier schools for graduate studies (some research experience, some low to medium quality publications, very strong grades, good recommendation letters). Then how much does the alma mater have an impact for someone like me? I obviously know that it is still possible to be accepted, but how much of a disadvantage am I looking at exactly? I am trying to find a story where a children's nursery turns into a jungle I read this short story(I believe it was under novella length, but I could be mistaken) a while back, and I am trying to identify the title for a friend.   Plot:      Parents(male and female) get a computer aided/holographic nursery for their children. The mother becomes increasingly agitated as the children withdraw more. The children are barely even featured in the story, and the ending concludes with lions possibly eating the parents.   Publishing date: Years ago.   Tech level: Seemingly functional AI, not much more. Can I move Xcode and Android Studio to SD card I'm planning to buy a 64GB SD card to supplement the storage on my MacBook Air 128GB (early 2015)  I wanted to know if I can move my Xcode and android studio to it as both have them take a significant part of the memory.  If this can happen, I wanted to know how can I move these two to the SD card. I'm fairly new to macOS and have no idea how to do this. During Thor's interrogation, Agent Coulson exits the room and Loki enters and informs him that his father Odin had passed away and that he cannot undo his banishment. Not only does he communicate with Thor, but he goes to the area where Mjölnir is embedded in the rock and attempts to lift it, with SHIELD scientists and agents completely oblivious to his presence. Loki shows a similar ability when he converses with 'The Other' and when he manipulates Erik Selvig. Is this a part of Loki's illusion powers or another one of his abilities that has not been addressed? How was he able to visit Earth without using the Bifrost? Comprehensive list of tools that simplify the generation of LaTeX tables