Because I watched this when I was so young, I might have meld two shows into one.   these people have white jewels in the center of their fore heads to activate their powers, they place their index &amp; middle fingers on their temples. I think they would glow as well I also remember a white, teenage girl with long brown hair as one of the main leads
There was this cool tv show I used to watch as a kid (in the 1990's I think). It was about a world where water was extremely rare and people used to fight over it, however there was this person who had this large 3D polyhedron shaped device (big enough to fit a few people in it) that could synthesise water.  Now, this device was either a time travel device or could just make water (not sure but I remember some time travel aspect as they could either remember the world the way it was where water was plentiful or could travel back to it on occasion).  Anyway, would love to know if this rings any bells?????  It was on in the UK (but maybe the US too, not sure).
Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$ Can the fundamental group of an open connected subset $X$ of $\mathbb{R}^n$ have a torsion element? Using dynamic where clauses in Entity Framework How to evaluate $\lim\limits_{n\to+\infty} \prod\limits_{k=1}^n (1+k/n^2)$? I've got a limit which puzzle me several days. The question is  $$ \lim_{n\to+\infty} \prod_{k=1}^n\left(1+\frac{k}{n^2}\right).$$  Can you help me? Thank you in advance I looked around but did not find that anyone has asked this before, but what are the fonts that are standard/recommended while writing academic reports/papers? Error Code: 1215. Cannot add foreign key constraint (foreign keys) How to add a modifier to a collection? My goal is to reduce the faces of an object using the decimate modifier. The object I'm editing has lots of vertex groups. Blender 2.8 only lets me add the decimate modifier to a single group at once which would take quite some time. I have already put all groups in a single collection.  How can I add the decimate modifier to the entire collection?  Do I have to add the modifier group by group? Prove that the dihedral group $D_4$ can not be written as a direct product of two groups I like to know why the dihedral group $D_4$ can't be written as a direct product of two groups. It is a school assignment that I've been trying to solve all day and now I'm more confused then ever, even thinking that the teacher might have missed writing out that he means normal subgroups.  On another thread it was stated (as the answer to this question) that the direct product of two abelian groups is again abelian. If we consider the direct product of abelian subgroups $H$,$K\in G$ where $HK=G$ (for all $g \in G$, $g=hk$ $h \in H$, $k \in K$.) I can't understand why this would imply $g=kh$? It is not stated anywhere that $H$,$K$ has to be normal! But if this implication is correct I do understand why $D_4$ (that is non-abelian) can't be written as a direct product of two groups. But if it's not, as I suspect, I need some help!  We know that all groups of order 4 and 2 are abelian, (since $4=p^2$), but only 4 of the subgroups of $D_4$ are normal:  Therefor I can easily show that $D_4$ can't be a direct product of normal subgroups: The only normal subgroups of $D_4$ is the three subgroups of order 4, (index 2 theorem): $\{e,a^2,b,a^2b\}$, $\langle a\rangle$, $\{e,a^2,ab,a^3b\}$ and the center of $D_4=\{e,a^2\}$ We can see that these are not disjoint. So $D_4$ can't be a direct product of normal subgroups. The reason for this being that the center is non-trivial. But why can't $D_4$ be a direct product of any two groups?  If we write the elements of $D_4$ as generated by $a$ and $b$, $a^4=e$, $b^2=e$, $ba=a^3b$ why isn't $D_4=\langle b\rangle\langle a\rangle$ ? I calculated the products of the elements of these two groups according to the rule given above and ended up with $D_4$, and also $\langle a\rangle$, $\langle b\rangle$ is disjoint...? Why is this wrong? Very thankful for an answer! How can I open a text file with TextWrangler from the Terminal (command line)? Let $A$ be an $n \times n$ matrix with real enteries. Define $\langle x,y\rangle_A = \langle Ax,Ay\rangle, \quad x,y \in \mathbb R^n$ , where $\langle,\rangle$ is a standard inner product on $\mathbb R^n$. Then  $\langle x,y\rangle_A$ is an inner product iff  1)  $\ker A = \{0\}$.  2) $\operatorname{rank} A= n$.  3) all eigenvalues of $A$ are positive.  4) all eigen value of $A$ are non negative.  Clearly if $\ker A \neq \{0\}$, then there exist $x \neq 0$ such that $Ax =0$, then $\langle Ax, Ax\rangle_A = 0$, then $\langle ,\rangle_A$ is not inner product, so $\ker A = \{0\}$, thus rank of $A$ is $n$.  I am unable to check the 3) and 4) option. Please help to check the other option. Thank you This is a general, community wiki  question and answer pair intended to address any questions   concerning the reasons a site or specific site contents do not appear   in search engine results.      If your question was closed as a duplicate of this question and you   feel that the information provided here does not provide a sufficient   answer, please open a discussion on .   My site (or specific pages on my site) is not appearing in search engine results.  Why isn't my content indexed and what can I do about it? How to align content of a div to the bottom For a finite set $S$ there are $\vert S\vert!$ orderings of its elements.  What is the cardinality of all orderings of $\mathbb{N}$?  What would $$\vert \mathbb{N}\vert!$$ mean?  Is it $\prod_{n\in\mathbb{N}} \aleph_0=\aleph_0^{\aleph_0}=\aleph_1$?   says the "equivalence classes of well-orderings of the natural numbers" has cardinality $\aleph_1$.  But I can't put together in my mind the connection between well-orderings of $\mathbb{N}$ and all orderings of $\mathbb{N}$.  (Are there non well-ordered orderings of $\mathbb{N}$?)  This leads to wondering what the cardinality of all orderings of $\mathbb{R}$ is.  (Actually my thought process went in the other direction, from $\mathbb{R}$ to $\mathbb{N}$.)  I think knowing the answer to the above question will teach how to determine what $$\vert \mathbb{R}\vert !$$ means, if anything.  I will be happy if you assume the continuum hypothesis to be true for the purposes of this question, but any level of completeness is welcome. Encrypt home drive after installation I declined to encrypt to my home drive whilst installing ubuntu.  Is it possible to encrypt it after installation?  if so, how? Commutative non Noetherian rings in which all maximal ideals are finitely generated In commutative rings we have the following  Theorem. $R$ is Noetherian if and only if each prime ideal of $R$ is finitely generated.  From this Theorem I am looking for commutative rings $R$ in which every maximal ideal is finitely generated but $R$ is non Noetherian.  Question: Is there a straightforward example of a commutative ring $R$ so that each maximal ideal is finitely generated, but $R$ is non Noetherian?  Thank You Calculating distance of sites to riverways using ArcGIS Desktop? How do you calculate the distance of about 10 sites scattered across a region to bodies of water (rivers and lakes) using ArcGIS 10.1?  I have the lat/lon coordinates of the 10 sites as a point feature class and I have downloaded the Surface Water Area (polygon shapefile) for the study  area from the UK Ordnance Survey webpage.  I want to determine the easiest route-ways that are available in the study area by taking into account slope and proximity to rivers. I understand that I can achieve this by running a cost path analysis if I have a dem raster, slope raster and distance rasters to rivers and valley floors. But I am not sure how to create distance rasters to rivers and valley floors using Spatial analyst tools. Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$ How do I catch a PHP fatal (`E_ERROR`) error? I can use set_error_handler() to catch most PHP errors, but it doesn't work for fatal (E_ERROR) errors, such as calling a function that doesn't exist. Is there another way to catch these errors?  I am trying to call mail() for all errors and am running PHP 5.2.3. Can the default font be changed? I have been playing with the settings for the text object recently, and every time I add a new text object, I need to change the font to my favorite one. (Eurostile LT ExtendedTwo) Is there any way to change the default font so I do not need to change it every time I add a new text object?   Example: Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction I am just starting out learning mathematical induction and I got this homework question to prove with induction but I am not managing. $$\sum_{k=1}^n\frac1{\sqrt k}&lt;2\sqrt n$$ Please help! Journal of Finance Template German '*.bst'