Example of a space that is connected but not path connected?
Space which is connected but not path-connected
Groups in derived series are normal in the whole group I am considering a finitely generated, solvable group $G$ which has subexponential growth. Let $G=G_0\vartriangleright G_1\vartriangleright....\vartriangleright G_d\vartriangleright G_{d+1}=1$ denote the derived series of G.  It should be the case that $G_d$ is normal in $G$. Does anyone know why this is true? I don't know whether all of the assumptions above are necessary for the result. Adding Layer Files (.lyr, .lyrx) to QGIS At college we use ArcGIS Desktop 10, but that does not function on my Mac so I have QGIS there instead.  I want to do my exercises with QGIS, but in ArcGIS Desktop we use .lyr files with ArcMap and .lyrx files with ArcGIS Pro, and they are not supported by QGIS.  Does anyone know, how I can connect the *.lyr files to my *.shp files to use them on my Mac with QGIS? There was a post this morning asking about how many people disable JavaScript. Then I began to wonder what techniques might be used to determine if the user has it disabled.   Does anyone know of some short/simple ways to detect if JavaScript is disabled? My intention is to give a warning that the site is not able to function properly without the browser having JS enabled.   Eventually I would want to redirect them to content that is able to work in the absence of JS, but I need this detection as a placeholder to start. What do hollow/filled stars mean in chat? I was on chat in Stack Overflow and noticed that some of the message had grey stars with a black border while others were just black stars. What is the difference between the 2 star types? How distorted does the Andromeda Galaxy appear to us due to the speed of light? The Andromeda Galaxy appears to us at an angle to the galactic disk, i.e. we are not in the Andromeda Galaxy disc's plane, nor are we near the direction that the galaxy's pole points. Therefore, due to the geometry and distances involved, it would seem to me that we are seeing the 'far edge' a few thousand years later than we are seeing the 'near edge'. How far can a galaxy spin during that those few thousand years, and therefore how distorted are we seeing Andromeda? Can we infer how Andromeda or other large spiral galaxies seen at an angle would look if light were to travel instantly?  Might this phenomenon account for some of the unusual spin properties measured in galaxies, which is attributed to dark matter? Schengen Visa Refusal: Justification for the purpose and conditions of the intended stay was not reliable Schengen refusal formulae can be difficult to understand sometimes.  Sometimes an applicant receives a refusal with:       Justification for the purpose and conditions of the intended stay was not reliable.     often accompanied by:       Your intention to leave the territory of the Member States before the expiry of the visa applied for could not be ascertained.   What is meant by this refusal reason?  What are they trying to say? "Speed" of Gravity and Speed of Light Some threads here touching speed of gravity made me think about that. This lead to some questions.    The speed of gravity was not measured until today (at least there are no undebated papers to that effect). It seems common knowledge/belief among physicists that the speed of gravity is the same as the speed of light.    And this is my question: Is that speed of light = speed of gravity a result of GR or is that fed into the theory? Or is there some evidence from other sources than GR for this? Does the same speed imply some deep-lying relation between gravity and electromagnetism? For every $p\in [1,\infty)$, consider the set $\ell^p$ of real sequences $x=(x_n)=(x_1,x_2,\ldots)$ such that $\sum_{n=1}^\infty |x_n|^p&lt;\infty$. This is a Banach space with the norm $\Vert x\Vert_p=(\sum|x_n|^p)^{1/p}$.  I have the following problem:     Is it true that $\ell^p=\bigcup_{1\leq q&lt;p}\ell^q$ for $p&gt;1$?   I don't think it is true, but I'm having problems to show this. Clearly, the statement is true for some $p&gt;1$ iff it is true for every $p&gt;1$.  I'm trying to find a sequence $(a_n)$ such that $\sum |a_n|^s$ converges iff $s\geq 1$. I've tried many sequences (such as $(n^{1+1/n})$, involving $\log$, etc...), but none of them worked. PostgreSQL, SELECT from max id I made chili and it's too hot! If I cook it longer will the heat calm down? How to use LyX to create PDF file from the command line How to support different screen size in android Clocks for multiple timezones in GNOME Shell I looked everywhere but I couldn't find a way to display multiple clocks in GNOME 3. In classic GNOME and Unity, it is possible. Also, for some strange reason, additional timezones cannot be added to the clock using the time-date applet in classic GNOME. Any solutions? Converting LiDAR files from LAZ to LAS format I'm trying to convert LiDAR files from the LAZ format (the compressed version) into LAS (the uncompressed version) using  software.   However, I am not really sure how it works. I created a new output folder as I entered in the app interface, but it is totally empty.  I also had tried the following code in the command prompt window:   D:\LiDAR\Laszip\laszip.exe *.laz    and got a message saying 'no input specified'.  In my folder, there are about 100-ish.laz files as well as one imu.laz. Any suggestions? At the end of every day you will be required to write a review.   At the end of each day you will be required to write a review.   Which one of those sentences is better if this action will repeat itself every day for longer period of time, several weeks for example, maybe even months? Does anyone know a proof from the first principles that a nilpotent matrix has zero trace. No eigenvalues, no characteristic polynomials, just definition and basic facts about bases and matrices. The conditions $a^2b^2=b^2a^2$ and $a^3b^3=b^3a^3$ make the group $G$ abelian? I have seen many ways to make a USB an installer for about any Windows OS. But how can I (using grub or something like that) make it bootable to all editions on Windows XP and 7?   I have tried Googling it and researching, I've even tried to do it, But I dont understand much about GRUB or linux at all.  Please keep in mind that I am not very good with linux, so please use as many details as possible. I built a ZI model and it is producing predicted values that are from a very small range when compared to the observed values. Plus it does not produce any zeros. See the fitted vs. observed graph below.     My model structure is given below. My response is a count variable and the predictor is continuous water level measurements (scaled).   m.u.meanwl.gu &lt;- zeroinfl(GU ~ MeanWLScaled | MeanWLScaled, data = uluabat_wl_fg, dist = "negbin", link = "logit")   I need help to figure out what's wrong and fix it. Thanks in advance. This is solely a reference request. I have heard a few versions of the following theorem:     If the joint moment generating function $\mathbb{E}[e^{uX+vY}] = \mathbb{E}[e^{uX}]\mathbb{E}[e^{vY}]$ whenever the expectations are finite, then $X,Y$ are independent.   And there is a similar version for characteristic functions. Could anyone provide me a serious reference which proves one or both of these theorems?