how to parenthetically modify something which I don't know what it is?
"Give him a box that everyone knows what it contains."
Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$ Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$. $AD,CF, BE$ are altitudes. Is there a simple way? Which props in Star Trek: Picard are reused from the original TNG show and films (if any)? What is a word/idiom for 'unable to decide'? Let's say I have an important decision to make and I can't decide between two competing things (like break up with a girl or not break up with her). What would be a word/idiom to express that? Before the seasonal flu vaccine was recommended for all healthy adults, people in developed countries might get vaccinated against on the order of 10 different pathogens and develop immunity for some more via natural exposure.  Now the same person is expected to take a seasonal flu vaccine for a new strain every year - won't this put them in an uncharted territory as far as effects on the immune systems are concerned within a couple of decades? Finding Command-Line Arguments of Programs I know that unix has man pages, but is there a place I can look to discover command-line arguments of programs? Going to command prompt and typing notepad /? doesn't give anything. Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$ I have a simple query:  select * from countries   with the following results:  country_name ------------ Albania Andorra Antigua .....   I would like to return the results in one row, so like this:  Albania, Andorra, Antigua, ...   Of course, I can write a PL/SQL function to do the job (I already did in Oracle 10g), but is there a nicer, preferably non-Oracle-specific solution (or may be a built-in function) for this task?  I would generally use it to avoid multiple rows in a sub-query, so if a person has more then one citizenship, I do not want her/him to be a duplicate in the list.  My question is based on the similar question on .  UPDATE: My function looks like this:  CREATE OR REPLACE FUNCTION APPEND_FIELD (sqlstr in varchar2, sep in varchar2 ) return varchar2 is ret varchar2(4000) := ''; TYPE cur_typ IS REF CURSOR; rec cur_typ; field varchar2(4000); begin      OPEN rec FOR sqlstr;      LOOP          FETCH rec INTO field;          EXIT WHEN rec%NOTFOUND;          ret := ret || field || sep;      END LOOP;      if length(ret) = 0 then           RETURN '';      else           RETURN substr(ret,1,length(ret)-length(sep));      end if; end; On-shell and off-shell transformations in Noether's theorem For any transformation of the fields,  $$\varphi\to\varphi'=\varphi+\delta\varphi$$ the change in the Lagrangian can be written as  $$\delta\mathcal L = \text{EoM} + \partial_\mu j^\mu\tag{1}$$where "EoM" represents the equations of motion (Euler-Lagrange equations) and all other terms can be written as a total derivative of some function $j^\mu$, which is a known function in terms of the Lagrangian.   I would like to distinguish the different realizations of transformations. Let's assume that the transformation (1) leaves the action invariant, $\delta S=0$.    $\delta\mathcal L=0$   EoM $=0$, "on-shell": Noether current is conserved, $\partial_\mu j^\mu=0$. EoM $=\partial_\mu b^\mu\neq0$, "off-shell": modified Noether current $J^\mu = j^\mu+b^\mu$ is conserved, $\partial_\mu J^\mu=0$.   $\delta\mathcal L =\partial_\mu a^\mu \neq 0$, "quasi-symmetry"   EoM $=0$, "on-shell": modified Noether current $J^\mu = j^\mu-a^\mu$ is conserved, $\partial_\mu J^\mu=0$.  EoM $=\partial_\mu b^\mu\neq0$, "off-shell": modified Noether current $J^\mu = j^\mu-a^\mu+b^\mu$ is conserved, $\partial_\mu J^\mu=0$.     Is this listing correct?      What roles do the terms "on/off-shell" and "(quasi) symmetry" play in Noether's theorem?   Related: , , , , . Suppose there are $2$ permutations given by $p$ and $q$. I need to check whether $p$ belongs to the group generated by $q$, and if so, it's representation in a power of $q$. In other words, I've been given $p$ and $q$, I need to check whether $\exists i \in \{ 0,...,|q|-1 \} \text{ such that } p = q^i$ I know that if $m = \gcd(i, |q|)$, then $|q^i| = \frac{|q|}{m}$. Now, say that such an $i$ exists. Then, $$ |p| = \frac{|q|}{\gcd(i, |q|)} \Rightarrow \gcd(i, |q|) = \frac{|q|}{|p|} $$ Thus, a necessary condition for such an $i$ to exist is: $|p|$ divides $|q|$ Say that this holds, and $\frac{|q|}{|p|} = r$, where r is an integer. Then we just have to solve $\gcd(i, |q|) = r$ for $ i \in \{ 0,...,|q|-1 \}$. Can this be done? If not manually, then by some efficient algorithm? (Note: Just looping over all values of $i$ is not efficient as $i$ may be very large) Edit: Another way I can think of solving this is by writing both $p$ and $q$ as product of disjoint cycles: $$ p = c_1c_2\ldots c_k \text{ and } q = d_1d_2\ldots d_l $$ And thus, as disjoint cycles commute: $$ p^i = c_1^ic_2^i\ldots c_k^i $$ How to proceed after this? If a person uses the wrong form of your or you're, would that be considered a spelling or grammatical error? I can really see it swinging both ways...  A sentence with the incorrect use of the word is technically grammatically incorrect, but the root cause could be simple spelling error. If a person speaks a sentence with an incorrect use of the word in question, it seems grammatically correct. When you look at the reader's script, it is then determined to be a spelling error.  When shown in writing, should the error be marked as a spelling or grammatical error? In the film and book series, Year 4 (Goblet of Fire), how is it Mad-Eye Moody/Barty Crouch could see Harry through his Magical Eye even when he was under the Invisibility Cloak?  As the cloak is a True Invisibility cloak, immune to charms and spells, and according to legend invisible to even Death, how did Mad-Eye detect Harry Potter under the cloak? How Nagini and Mrs. Norris were able to sense Harry were through other senses, such as smell and warmth, but not visually.  I'm referring to the scene/chapter where Snape follows Harry at night. Harry hides under the Invisibility Cloak but his foot is stuck at the broken staircase. Eventually Mad-Eye arrives, sees Harry through his Magical Eye, and talks Snape away. How can I selectively disable paste blockers Is there any point of using "return !0" in javascript? ModernCV Remove horizontal line in sections I want to write my cv with moderncv-Classic style. Can you tell me, how I can remove the horizontal line in the left of each section? relative polar coordinates for TikZ elements in axis environment I would like to annotate a patch plot with lines whose start and end points are given in absolute polar and relative polar coordinates, respectively.  The patch plot, based on cartesian data, comes out as a circular shape centred around the origin (0,0) and shall be simulated here by a plain circle.  Lines should start at the circumference of the shape and point away from the shape under a given angle and have a well defined length. Therefore, the use of relative polar coordinates for the line's end point.  What seems to be straightforward with TikZ (left) fails inside the axis environment of pgfplots (right): neither the inclination angle nor the length of the line are correct if relative polar coordinates are used.    What is wrong with the rel. polar coordinates here?  The code:  \documentclass{standalone}  \usepackage{pgfplots} \pgfplotsset{compat=1.13}  \begin{document}  \begin{tikzpicture}   \draw(0,0) circle[radius=0.01];   \draw[blue] (0,0) circle[radius=1];   \draw[thick] (45:1) -- ++(45:0.5); \end{tikzpicture}  \begin{tikzpicture}   \begin{axis}[tiny,enlargelimits,   axis equal,   xmin=-2,xmax=2,   ymin=-1,ymax=1,   xtick={-2,-1,0,1,2},   ytick={-2,-1,0,1,2},   grid=major,   ]   \draw[blue] (0,0) circle[radius=1];   \draw[blue, dashdotted] (0,0) -- (45:2);   \draw[thick] (45:1) -- ++(45:0.5); %  \draw[thick] (45:1) -- (45:1.5); %absolute coordinates do work   \end{axis} \end{tikzpicture}  \end{document} What do you recommend as an optimal point and orientation for mounting a rear-view mirror? I'm open to handlebar-, glasses-, or helmet-mounted.  Some of the considerations, as I understand it, are:   Ease of mounting. View provided. Vibration. Likelihood of breaking. Robustness for repeated off and on (for glasses-mounted).   I've got a hybrid bike with flat handlebars.  I'd also welcome specific product recommendations and recommendations about other aspects to look for in a mirror. How does one know when to use a gerund or an infinitive? As a native speaker of English, the gerund version of this sentence sounds better:  infinitive:     When used together in chains,   extension methods are an unprecedented   tool to produce extremely concise   code.   gerund:     When used together in chains,   extension methods are an unprecedented   tool for producing extremely concise   code.   But how can I explain to someone learning English how to decide in situations like these whether to use the infinitive or the gerund? Dropping one of the columns when using one-hot encoding Highest power of a prime $p$ dividing $N!$ Motivation for Ramanujan's mysterious $\pi$ formula The following formula for $\pi$ was discovered by Ramanujan: $$\frac1{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^\infty \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}\!$$   Does anyone know how it works, or what the motivation for it is?