Own math symbols I'm not professionalist on latex and I need help.  I don't know how to create two sybols:      Could you help me?
How to look up a symbol or identify a letter from a math alphabet or other character? I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?
This problem is from Romanian G.M. and although it is very short, it is also (I think) very hard. Let $x, y, z$ real non-negative numbers such that $x+y+z=3$. Prove that   $$27 \leq (x^2+2)(y^2+2)(z^2+2) \leq 44 $$  I didn't succeed in any of the inequalities, I only managed to find the equality cases ($x=y=z=1$ for the first one and one of them $3$ and the others $0$). Any hint/idea/solution is welcome. On the  it is mentioned that it is not a Cayley graph.    How it this proved? Honestly I don't even know how to start this. The only criteria I can think of is that all vertices must have the same degree. Also the degree being odd should imply that one generator of the group has order 2. But then how do I proceed?  Edit: As already mentioned in the comments, the link did not answer my question. Modal vs Non-Modal vs Auxiliary modal vs Conjugated Verb Modal vs Non-Modal vs Auxiliary modal vs Conjugated Verb   How are these kinds of verb related to each other? Specially Non-Modals and Conjugated Verb. Is the "Auxiliary modal" just another name for "Auxiliary verb"? R: Trouble using SMOTE package "invalid 'labels'" Rails Previous Sunday in Relation to Any DateTime Get the subdomain from a URL Getting the subdomain from a URL sounds easy at first.  http://www.domain.example   Scan for the first period then return whatever came after the "http://" ...  Then you remember  http://super.duper.domain.example   Oh. So then you think, okay, find the last period, go back a word and get everything before!   Then you remember  http://super.duper.domain.co.uk   And you're back to square one. Anyone have any great ideas besides storing a list of all TLDs? Robot arm move a box What does **Ens** stand for? Earlier someone was asking about the category "Ens" described in Categories for the Working Mathematician. My question is more basic: What does Ens stand for?  Most of the categories have names that are self explanatory, and maybe this one does too.  But for the life of me I can't think of it, and a Google search was no help. extended stars-and-bars problem(where the upper limit of the variable is bounded) The problem of counting the solutions $(a_1,a_2,\ldots,a_n)$ with integer $a_i\geq0$ for $i\in\{1,2,\ldots,n\}$ such that $$a_1+a_2+a_3+....a_n=N$$ can be solved with a stars-and-bars argument. What is the solution if one adds the constraint that $a_i\leq r_i$ for certain integers $r_1,\ldots,r_n$?  e.g. for $n=3$, $N=6$ and $(r_1,r_2,r_3)=(3,3,2)$, the tuple $(a_1,a_2,a_3)=(2,3,1)$ is a solution, but $(2,1,3)$ is not a solution because $a_3=3&gt;2=r_3$. Making yogurt at home is a fairly straight-forward process.  Heat milk to 180F (82C), cool that milk to at least 110F (43C), add live cultures, usually in the form of yogurt with said cultures, incubate, then chill.   There are several variables in the process, some of which are: The fat content of the milk (I typically use whole), how long to hold the milk during the initial heat step, how long it takes to cool the milk, the temperature of the incubation step, and the length of time for incubation, to name a few.  While length of time for incubation, and temperature at this stage, clearly contribute to sourness, I am trying to nail down the variable that contributes to a creamy texture.  I'm not referring to breaking or clumping, as described in .  My yogurt comes out smooth.    My initial hypothesis is that holding the milk for a length of time at the initial 180F(82C) (rather than immediately removing from heat and/or chilling) has an impact on final texture. Any thoughts or experience that might inform my hypothesis? Converting the beta coefficient from matrix to scalar notation in OLS regression Solve for $x$ in $6x^2-25x+12+\frac{25}{x}+\frac{6}{x^2}=0$ How can I test the quality of a RNG? On electronics.stackexchange we had  about constructing a True Random Number Generator. Since the method relies on noise, which isn't deterministic, the only way to test the quality of the RNG seems to be empirical. Not being a statistician I suggested to test a long bit sequence for normality, but I have no idea what outcome is acceptable and what isn't. For instance counting single bits I guess we have a thumbs-up for a 499500/500500 distribution, but when is the ratio too much skewed to be acceptable? Same for 2-bit and longer sequences. Of course, if testing for normality is a Bad Idea™, I'd like to hear it, including better alternatives.    edit Diehard was mentioned a few times, but I'm not sure this answers my question. The normality test should give a normal distribution, with better bell curve approximations for longer sequences. Diehard seems also to have tests which either should result in normal or exponential distributions. But my question remains: how do I judge the results? Just by looking at the curve and discern a bell curve in it? To get back at my first example, a 499500/500500 distribution is definitely OK, and a 950000/50000 distribution definitely is a no-no, so where does the switch-over happen? How can I convert a complex number into an exponent form I am trying to figure out how can I disable/hide the App Name in MacOS X Lion dock. I've also attached an image so you can see what I mean.    Someone has any idea about how can I hide that? Redirect based on country Let's say I have a site that has multiple versions for different countries, e.g.:  www.example.com/us www.example.com/uk www.example.com/ca   and I want to use IP geolocation to redirect users who go to www.example.com to the appropriate country version of the site.  What is the best way to do that without confusing crawlers such as Googlebot or running into other SEO type trouble? Clear named (and lored) item from players inventory 1.13 In 1.12, the command:  clear @p paper 0 1 {display:{Name:"[Winning Ticket] Musical Minecarts",Lore:[" Take this ticket to the reward "," collections at the entrance of the ", " Games area to claim your prize! "]}}   would remove a piece of paper with that specific name and lore from the player's inventory. I assumed the 1.13 conversion would be:   execute at @p as @p run clear @s paper{display:{Name:"[Winning Ticket] Musical Minecarts",Lore:[" Take this ticket to the reward "," collections at the entrance of the ", " Games area to claim your prize! "]}} 1   but this doesn't work. As well as this, the command:  give @p minecraft:paper{display:{Name:"[Winning Ticket] Musical Minecarts",Lore:[" Take this ticket to the reward "," collections at the entrance of the ", " Games area to claim your prize! "]}} 1   only gives the item, without the custom display name, despite the lore being correct. What is the correct syntax for these two commands? Maybe the concept, why it's used, and an example. I need help!  I need to prove that for any $2 \le n,k$ positive integers $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$  Thanks! What are "Commited Memory", "Cached", "Paged", "Not-paged pool" & How They are Different with "In-Use Memory"