Trying to understand the difference between $\Delta t$ and $dt$
Difference between $\Delta$, $d$ and $\delta$
How do I display a decimal value to 2 decimal places? When displaying the value of a decimal currently with .ToString(), it's accurate to like 15 decimal places, and since I'm using it to represent dollars and cents, I only want the output to be 2 decimal places.   Do I use a variation of .ToString() for this? What are recommended, general strategies to start block-cipher design and/or analysis? I (and many others for that matter) have always been fascinated by the inner workings of the modern building block of cryptography: block ciphers.  Now, the ressources on the "black art" of design and analysis of these ciphers are sparse; especially for the entry level. Available information like  seems to be somewhat outdated (due to its age).  What's the general consensus of the “best” (read: recommended) strategy to start designing and/or analyzing modern cryptographical block ciphers?    Nota bene: Think of this as a general, wiki-alike question – for learning purposes only. (Besides that, this Q&amp;A would represent a place we can point people to when alike algorithm design questions arise.) My impression for how Poincare and Lorentz representations are linked in $3+1$ dimensions is:   Assuming positive mass for simplicity, irreducible representations of the Poincare group are indexed by their mass $M$ and spin $s$. Irreducible representations of the Lorentz group are indexed by two numbers $(s_1, s_2)$ and when restricted to the rotation subgroup contains spins from $|s_1 - s_2|$ up to $s_1 + s_2$ in integer steps. Particles transform in representations of the Poincare group, while fields transform in representations of the Lorentz group. They are related by defining $$|\mathbf{p}, \lambda \rangle = a^\dagger(\mathbf{p}, \lambda) |0 \rangle$$ where $\lambda$ is the helicity, and the field is defined in terms of the creation and annihilation operators in the usual way. The only requirement is that the Lorentz representation used for the field contains the spin $s$ used in the Poincare irrep. A relativistic wave equation is imposed to eliminate the unwanted degrees of freedom.   For example, a massive spin $1$ particle may be embedded in a vector field, which is in the $(1/2, 1/2)$ irrep of the Lorentz group. This vector field has one extra degree of freedom that is eliminated by the equation $\partial_\mu A^\mu = 0$.  Assuming this is right, I'm wondering why I've never heard of "alternative" embeddings. For instance, why can't one embed a spin $1$ particle inside the $(1, 0)$ irrep, which doesn't have any extra degrees of freedom at all, or inside the $(1, 1)$ irrep? For massive particles, I've only ever seen spin $0$ in $(0, 0)$, spin $1/2$ in $(1/2, 0) + (0, 1/2)$, and spin $1$ in $(1/2, 1/2)$. Are other embeddings very clunky, or not allowed, or are they actually used somewhere? Equation for a smooth staircase function I am looking for a smooth staircase equation $f(h,w,x)$ that is a function of the step height $h$, step width $w$ in the range $x$.   I cannot use the unit step or other similar functions since they are just one step. I have been experimenting with various sigmoid curves and while I can get a single smooth step I cannot get to realize the staircase shape. The closest staircase function I have found is given in  in equation (18) and depicted in Fig. 4 and it is a close example of what I want (i.e generate a staircase in the range $x$ for arbitrary step heights and widths) but it is not smooth at all.  Regarding smooth steps, a likely starting point I found is  but it gives a smooth function of just a single step. I have been unable to modify the equation to make it into a staircase. I would like to specify arbitrary step heights and widths and generate a smooth staircase in the range $x$ specified.    Edit (Extra info): The smooth function I mention above has the problem that the upper, horizontal line is not equal in length to the lower, horizontal line which is why I have been unable to adapt it into a staircase function   Edit 2 Including some pictures     Edit 2 Plot of $s$ with a steep slope showing a different width on the first horizontal line Let $Z_i,Z_2,\ldots$ be IID Random Variables with density $f$. Suppose that $P(Z_i&gt;0)=1$ and that $\lambda=\lim_{x \to 0+} f(x)&gt;0$. How can I show that $X_n=n \times \min\{Z_i\}$ has a limiting exponential distribution with mean$1/\lambda$?  I know that the CDF of the first order Statistic is for $t&gt;0$  $$F_{min \{ Z_i \}} (t)= 1- \left[ 1-F(t) \right]^{n}$$  Convergence in distribution requires that $F_n (t) \to F(t)$ for some distribution function $F$ but I cannot quite take the limit of the above, with $t$ replaced by $x/n$, as the distribution is not known. I guess I have to insert the second piece of information somewhere but I do not recognise where.  Could you please give me a hint or two?  Thank you. Can the software be downloaded on an Android device?  If yes, then what is the process? Can't unhide objects Travelling with two different passports Duplicate questions in feed, and questions incorrectly marked as unanswered I see duplicate questions in the feed (Why is the book still wanted if Aida has memorized it?) and the question is marked as "unanswered" even though it has an upvoted answer.  I would expect unique questions in the feed, as well as questions with answers to not be marked as unanswered.   App Version: 1.6.3.4 Device: iPhone 6 OS Version: Version 10.2 (Build 14C92) What is a word that means to say in a positive sense? For instance, when writers say that a person was sexually assaulted instead of saying raped.  Or people use let go instead of fired.  What is that called? How does a calculator calculate the sine, cosine, tangent using just a number? Sine $\theta$ = opposite/hypotenuse   Cosine $\theta$  = adjacent/hypotenuse   Tangent $\theta$  = opposite/adjacent      In order to calculate the sine or the cosine or the tangent I need to know $3$ sides of a right triangle. $2$ for each corresponding trigonometric function. How does a calculator calculate the sine, cosine, tangent of a number (that is actually an angle ?) without knowing any sides? As you can see, objects are falling down when I run the game. Ground is unable to stop those obstacles. Obstacles are rapidly traveling through y axis. I tried by freezing y axis. And, unchecked Use Gravity. I tried by checking Is Kinematic also. But, if I freeze y axis. Than, obstacles completely freeze through y. If there was no ground than the objects don't fall. Same thing happen when I unchecked Use Gravity. I want those obstacles to move if Player hit them. How to stop those obstacles from falling down?   Info : How do I prove that a graph is a topological manifold So...as what do we close too localized questions now? So we got  which works very well and is very nice and handy. But there is one question left, as what do we close ?  It actually helps , "too localized" was removed because it was misused most of the time:     5(A). "Too Localized" is no longer necessary since the specific   off-topic reasons now address its main use case. (new)      Too Localized was, by far, the most misused close reason in our   surveys, with both Community Managers and Moderators deeming over 50%   of randomly sampled TL closures to not have merited closure (including   on SO).      Today, TL is used helpfully on code dump questions on SO, but the new   OT reasons are where this is now correctly addressed. SO can use   "Large blocks of code with requests for debugging without meaningful   supporting info" as a specific OT reason.   But the new dialog leaves us with only four options:        Programming questions are off-topic on Meta Stack Overflow.   This question does not appear to seek input and discussion from the community. If you have encountered a problem on one of our sites, please describe it in detail.   Changes to the system or to the circumstances affecting the asker have rendered it obsolete. If you encounter a similar problem, please post a new question.   Other (add a comment explaining what is wrong)      Only the "other" reason does very well fit on "too localized" questions now, doe we close it with that? how to reset a lost admin password? Currently I'm running Linux-3.0 and I want to update it to Linux-3.3.1 the latest stable kernel release as mentioned at . Can I update to 3.3.1 in Ubuntu without any risk of crashes? I'm updating my kernel regularly as provided by the Update Manager..Currently I have Linux-3.0.0.17..Can I update?  NOTE:  The latest kernel version any user is supposed to use in Ubuntu is updated automatically via the Update Manager, so no action is normally required by user regarding kernel upgrades. What the question author is referring to is mainline kernel, see: Young Adult book about kids being bred for genetic purity in a world where races no longer exist I'm looking for a book I read in Junior High (probably) about a world where everyone was basically the same race.  One genetically pure male and female teenager of each race still exists.  They are transporting a genetically pure boy to meet his genetically pure female counterpart and accidentally introduce him to a genetically pure female of a different race.  And, of course, chaos ensues.  Any thoughts? What is the music on S3E16 when Todoroki was fighting group of ninjas? I think the single dashes (hyphens) should be placed between the numbers and units in this sentence:     ...in a cylinder of 3-inch radius and 24-inch length.   Is that correct and should hyphens be added to this second sentence?     ...making a trench nearly 15 feet wide and more than 30 feet long. What are sentences like "the longer X, the more Y" called and can they be used in formal written English? What is the type of sentence exemplified below called? Is it appropriate to use it in a scientific paper and formal written English in general?     1. The more pronounced the variation, the   more the waste.      2. The more you give, the more you get.      3. The longer I live, the more I realize the impact of attitude on life.