I read in a book that: let $f(K,R)$ is cryptographic transformation of $R$ using $K$, $K\{R\}$ means $R$ is encrypted using $K$ and $h\{R\}$ is the hash of $R$ and then the example follows.  I want to know what is difference between cryptographic transformation of $R$ and encryption of $R$ using the same key? Aren't they same thing?
What is the difference between encrypting something and hashing something?  in what situations would I want one or the other?
Assume that the matrices $A,\: B\in \mathbb{R}^{n\times n}$ satisfy  $$ A^k=0,\,\, \text{for some $\,k\in \mathbb{Z^+}$}\quad\text{and}\quad AB=BA. $$  Prove that $$\det(A+B)=\det B.$$ Screen goes white when posting a comment Since iOS 11.2 all the way through 12.2 beta 4, if you post or discard a comment on any post on any SE community, the screen will turn white. This has been ongoing continuously for a year now, and it affects both the SE app and the SO app.   You can go back to the previous screen and open the question again, and everything appears as normal. You can also rotate the screen to get the text to come back. Using the arrows to navigate between the question and answers updates the HUD, but the screen remains white unless one of the above is done to get the text back.        UPDATE: After posting anything (comment, answer), the screen goes all white except for the sidebar. Perhaps it is intentional, but I prefer last week’s behavior of going back to the content. Not major, since the sidebar icons still work. Nesting quotes in JavaScript/HTML Game resource timers - general implementation I'm interested in understanding how resource generation timers work on many of the mmorts type games out there. I can't wrap my head exactly around how the timers are synched with servers, especially with multiple users. If I need to provide more details, please let me know.  Thanks! How can I align a multiple-line footnote text right to the footnote mark? How can I have the following "footnote layout"?  Some Text Some Text Some Text Some Text² Some Text   2 FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT   FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT FOOTNOTETEXT   My problem is that the footnote text starting with the second line is too far left.  \documentclass{article} \usepackage{blindtext}  \begin{document}     \blindtext\footnote{\blindtext} \end{document} Do not allow giving minus one for new user questions I always see Stack Overflow users giving -1 to new users' questions. This is not how you welcome a new user to the community. A new user does not know the rules yet.    I suggest that if one wants to give -1 to a new user, you prevent that and ask the downvoter to write a comment instead. new user = 2 first questions    I see the credit rating on my question is now at -9?  My question, is she not well formed or formatted? If you don't agree with the content of a question do you down-rate it? If an Ubuntu user asks a question that might not be reasonable, will you also down-rate it?  No. You post an answer that will present your thinking and correct him? I think that is part of the problem. When you first go to a community like Facebook, and you don't know the faces, you don't feel like any of those people are your relations. Newbies exist here as well, especially in a professional community.    First, welcome the new user in more appropriate way. And most importantly, force them to see/read how to post a good question. Understand the meaning of `$_` Could you explain the following sentences from Bash manual about $_, especially the parts in bold,  maybe with some examples?      At shell startup, set to the absolute pathname used to   invoke the shell or shell script being executed as passed in the environment   or argument list.      Subsequently, expands to the last argument to the previous   command, after expansion.      Also set to the full pathname used to invoke each   command executed and placed in the environment exported to that command.     When checking mail, this parameter holds the name of the mail file. Java - Splitting a CSV file into an Array Mirror modifier mirrors on different axis/axes from the selected one(s) I have 2 objects a face and an ear. Mirror modifier works fine for the face. But when I use mirror modifier to duplicate the ear on X axis, it duplicates on Z axis. And when I use mirror modifier on Z axis it mirrors on X axis. How to correct the axis orientation? Read Value from URL in PHP In PHP 5, what is the difference between using self and $this?  When is each appropriate? Nearby objects won't move independently? I created a thick glass bottle and duplicated the interior faces to make a new object to create the liquid inside.   I went in the edit mode, selected the faces I wanted to copy and duplicated them with ShiftD. Then I pressed P to  separate the duplicated faces.   Now I try to make a duplicate of that liquid to make it flow out of the bottle, and I simply need the duplicate of one face of it. So I go to edit mode and do as I did to make the liquid from the bottle faces... but as soon as I'm back to the object mode and I want to move the duplicated faces, every thing moves with it...   I played around and tried things, and while doing so I realized that if I dupe the liquid object in object mode using ShiftD and press 0 to place it where the original is, they move together if I duplicate it and place it somewhere else so that they are separated.   Also if I pick one of the two separated objects and make it intersect with the other one, release my left mouse button to place it there, and then try to move it again, they both move together, but not at the same speed.  I really don't understand what is going on and I'm sure it's really badly explained, so what I'll do is make a screen capture of my Outliner and record the behavior of the objects and upload those to help you understand. Making overview with linked detailed maps in QGIS? i want to create 4-5 detailed maps, and then an overview map that has rectangles that markes the locations of the detailed maps. Best case would be if the rectangles were links to the detailed map.   I have managed to make the overview and the rectangles, and think I know how to make the detailed maps one by one. The rectangles are drawn manually on the overview map. All layers that I plan on using are in the same QGIS project.  The final product that I hope to create would be the overview map on the first page, followed by the detailed maps. The overview would have links to the detailed maps, click on the rectangles to open the right detailed map.  Is there a way to link the detailed maps to the overview in QGIS 2.8 print composer?  I'm still not sure if I'm doing something wrong, when I try to create the overview. I want it to show the extents of all of my detailed maps.   Is this possible? Occasionally, you can see little tufts of leaves blowing in spots on the map      Do these mean anything? Is it ethical to use a recommendation letter from a deceased professor? She was a really nice professor and she wrote me a good recommendation letter that resulted in a lot of good results with applications. Recently, this professor died from brain cancer, which was a fast and shocking death for me.  Tomorrow is the deadline for a grant. What should I do? Is it professional to use letters from the deceased? How to parse a time into a Date object from user input in JavaScript? I am working on a form widget for users to enter a time of day into a text input (for a calendar application). Using JavaScript (we are using jQuery FWIW), I want to find the best way to parse the text that the user enters into a JavaScript Date() object so I can easily perform comparisons and other things on it.  I tried the parse() method and it is a little too picky for my needs. I would expect it to be able to successfully parse the following example input times (in addition to other logically similar time formats) as the same Date() object:   1:00 pm 1:00 p.m. 1:00 p 1:00pm 1:00p.m. 1:00p 1 pm 1 p.m. 1 p 1pm 1p.m. 1p 13:00 13   I am thinking that I might use regular expressions to split up the input and extract the information I want to use to create my Date() object. What is the best way to do this? How can I publish my thesis? I have a written thesis, as my Final year project. I have submitted in university.   but now i want to make it professionally mine.   I want to publish it some where but i don't have such kind of experience before. I am total Rookie in this field.  Any Expert Opinion?  Note: Thesis in About "Handwriting Recognition " Let $M$ be an A-module and $f \in \text{End}(M)$ an idempotent endomorphism. Show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$. I don't know how to approach this exercise, using only properties of modules and direct sums, without projections. Can you help me? Thanks in advance. What is the pressure at the center of the Earth? (Or a neutron star) The  has microgravity and is thought to be solid and almost 6000 degrees hot. What is the pressure like there? The confusing thing, for the common man I suppose, is that there's no gravity there, but lots of matter around it which does gravitate towards the center. How does that add up? Is the center just a gas cloud or is it highly compressed?  And I could add the aside question about what it is like in the microgravity center of a  or a black hole, but I don't expect anyone to know about that. The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain Let $\alpha = \frac{1+\sqrt{-19}}{2}$. Let $A = \mathbb Z[\alpha]$. Let's assume that we know that its invertibles are $\{1,-1\}$. During an exercise we proved that:     Lemma: If $(D,g)$ is a Euclidean domain such that its invertibles are $\{1,-1\}$, and $x$ is an element of minimal degree among the elements that are not invertible, then $D/(x)$ is isomorphic to $\mathbb Z/2\mathbb Z$ or $\mathbb Z/3\mathbb Z$.   Now the exercise asks:     Prove that $A$ is not a Euclidean Domain.   Everything hints to an argument by contradiction: let $(A, d)$ be a ED and $x$ an element of minimal degree among the non invertibles we'd like to show that $A/(x)$ is not isomorphic to $\mathbb Z/2\mathbb Z$ or $\mathbb Z/3\mathbb Z$.  How do we do that? My problem is that, since I don't know what this degree function looks like, I don't know how to choose this $x$!  I know that the elements of $A/(x)$ are of the form $a+(x)$, with $a$ of degree less than $x$ or zero. By minimality of $x$ this means that $a\in \{0, 1, -1\}$. Now I'm lost: how do we derive a contradiction from this?