Is there an existing authorative definition of the cryptographic term 'pepper'
Definition of "pepper" in hash functions
Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$ For the finite-dimensional case, we have a canonical isomorphism between $\mathbf{V}$, a vector space with the usual addition and scalar multiplication, and $(\mathbf{V}^*)^*$, the "dual of the dual of $\mathbf{V}$." This canonical isomorphism means that the isomorphism is always the same, independent of additional choices.   We can define a map $I : \mathbf{V} \to (\mathbf{V}^*)^*$ by $$x \mapsto I(x) \in (\mathbf{V}^*)^* \ \text{ where } \ I(x)(f) = f(x) \ \text{for any } \  f \in \mathbf{V}^*$$  My Question: what can go wrong in the infinite-dimensional case? The notes I am studying remark that if $\mathbf{V}$ is finite-dimensional, then $I$ is an isomorphism, but in the infinite-dimensional case we can go wrong? How? Custom question lists April status update Previous posts:                           After a long hiatus, a new Custom Question Lists update is out with a fresh new design.  What's shipped?  If you are participating in the Custom Question List alpha (by ), you'll see some brand new UI components when viewing question lists:  New tab bar and editor    Based on your feedback, we decided to rethink the whole UI, removing some confusing and redundant components, and bringing back some much loved pieces.  The new design is closer to "the existing question lists with advanced options" than "a radically new experience".  Huge shoutouts to our new designer, , for making this new design possible and to  for picking up development while I was on sabbatical!  Some important notes for existing testers:   The summary is back in its rightful place next to the tab bar.  If bounty or unanswered filters applied, the summary provides a clearer explanation of what you're looking at, inspired by /unanswered. The "Filter" and "Sort" popovers are gone. Sort was too similar to the existing tabs, and Filter was a form in a popover. (how were you supposed to submit or cancel?)  Now there's a dedicated UI for filtering. The complex "Create" and "Edit" modals are gone.  Now you just configure your list with the same UI as if you were filtering and click "Save filter" when you're ready to save. You can preview your changes before updating a filter.  Editing a saved filter and clicking apply shows you your new options while remembering what filter you were looking at.  You can then click "Save filter" to either update your existing filter or create a new one. We handle responsive better.  The tab bar has been set up so it compresses more naturally on narrower browsers and mobile devices.   New sidebar widget    A new right-sidebar widget has been added, similar to Watched Tags, to give you more direct access to your saved lists.  This is where indicators will live in Phase 3 (which I swear we are actually going to ship).  Please give it a try.  If you have any questions, bugs, or feedback, you can reply to this post directly or add a new question with the  tag.  A wider alpha  Since we're nearing launch, we're expanding the alpha out to the whole network.  So feel free to try this out on any site you frequent, to help suss out any site-specific issues.  What's next?  As always, Phase 3 of this project is adding indicators for new content, now in the right sidebar widget.  There's increasing interest in this feature from Enterprise, so I do really expect this to ship and get out of Alpha sooner rather than later and this time, I mean it. Probability Problem with $n$ keys A woman has $n$ keys, one of which will open a door. a)If she tries the keys at random, discarding those that do not work, what is the probability that she will open the door on her $k^{\mathrm{th}}$ try?  Attempt: On her first try, she will have the correct key with probability $\frac1n$. If this does not work, she will throw it away and on her second attempt, she will have the correct key with probability $\frac1{(n-1)}$. So on her $k^{\mathrm{th}}$ try, the probability is $\frac1{(n-(k-1))}$ This does not agree with my solutions.   b)The same as above but this time she does not discard the keys if they do not work.  Attempt: We want the probability on her $k^{\mathrm{th}}$ try. So we want to consider the probability that she must fail on her $k-1$ attempts. Since she keeps all her keys, the correct one is chosen with probability $\frac1n$ for each trial. So the desired probability is $(1-\frac{1}{n})^{k-1} (\frac1n)^k$. Again, does not agree with solutions.  I can't really see any mistake in my logic. Can anyone offer any advice? Many thanks Sequences in $C(X)$ converging uniformly implies uniform boundedness and equicontinuity Let $X$ be a metric space and let $\{ f_n \}_{n \geq 1}$ be a sequence in $C(X)$. Show that if $\{ f_n \}_{n \geq 1}$ converges uniformly on $X$ then $\{ f_n \}_{n \geq 1}$ is both uniformly bounded and equicontinuous.  Could I get a hint? Custom Login form question In my website have two types people login one is designer another is reader, i want people come to login my website by role. Mean designer go to design login form to login. Reader go to reader login form to login. my question is:   how to show two login forms in same page? how to check the role when the visiter login at the same time in login form? is it any module i can use or i need do something customize the user module and how    customize?   Plz help! Why can't I use the Delete key to delete in Photoshop CS6? The previous version of Photoshop I used was CS4 and whenever I selected a portion of an image with the magic wand and hit Delete, it simply deleted that portion of the image (rendering it transparent). Easy!  In CS6, this is not the case. Now when I select a portion of an image and hit Delete, it brings up the Fill dialogue.  For example I have this picture (it's a Vauxhall Corsa). I want to use the Magic Wand to render anything that isn't part of the car transparent, so I start by highlighting some clouds with the Magic Wand like so:     Click on images to see larger versions  Now when I hit Delete, instead of that area of the picture being deleted as I would expect based on my experience with CS4, I get this dialogue:    My questions are:   Can this dialogue be used to achieve the functionality I want? If so, how? If not, how do I delete the background in CS6? Simple homework question about normally distributed variables The question states:      Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is   normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$.   What is the mean and the variance of the random variable $Y$, where   $Y=X_1+...+X_n$.   How do I do this? How can I publish my game (*.aab file) on google play? Pulling a CSV file from website into QGIS with ability to automatically refresh? Why teach linear algebra before abstract algebra? Is there a reason why most undergraduate curriculums put linear algebra before abstract algebra?  I'm asking this because personally it seems to be much easier to understand the architecture behind linear algebra as supposed to simply solving problems after a course in abstract algebra. Graph nodes coordinates evaluation I've seen multiple servers where you can connect from any (recent) major version. (Example, 1.9, 1.8 OR 1.7) And they all seem to be able to do it. Alas, a simple google search did not fix the problem. Any ideas? Thanks guys.  (PS: The Minecraft server is running on the latest Spigot for 1.10 as of 6/27/16) How do I create an .exe for a Java program? Is there a single word for “one who explains his point of view very clearly”? UI annoyances in the suggested edit review on Stack Overflow I'm writing a php program that pulls from a database source. Some of the varchars have quotes that are displaying as black diamonds with a question mark in them (�, , I assume from Microsoft Word text).  How can I use php to strip these characters out? Antonym of "phobia" If a phobia is to have an irrational fear of something, what is the word for having an irrational affinity for something?  For example a numerologist may fear the number 13, but be attracted to (or even have a love for) the number 8. (Some would say this is irrational.) Show all of my question/answers to me even if they are deleted I made something like this:    I did this with the Ellipse Tool and the Line Tool.  Now the circle is accurate, but the lines inside are very inaccurate. Is there another tool that does the same thing but with a lot more accuracy? In my D&amp;D 5e campaign one of the PCs who's a wood elf started dating a dark elf, and as a result she got pregnant and she is about to give birth. One of the other players had their PC die and he is considering playing as the child of the couple.  My question is, which race is the child going to be?