Smooth homotopic maps and closed forms..
Integrals of Pullbacks
Installing python module within code Let's assume that one has some modern HP printer and/or scanner which is not supported by HPLIP package from official repository. Currently Ubuntu versions have :  trusty (14.04LTS): 3.14.3-0ubuntu3.4 xenial (16.04LTS): 3.16.3+repack0-1 bionic (18.04LTS): 3.17.10+repack0-5 focal (20.04LTS): 3.20.3+dfsg0-2 groovy (20.10): 3.20.5+dfsg0-3build1 hirsute (21.04): 3.21.2+dfsg1-2   What can one do if printer is supported in newer version of HPLIP (checked this in )? Pie chart labels I want to create a pie chart with labels (one blank an one with percentage for the teacher, the mwe is the teachers version) so that my students have to fill the percentage in by themselves.  So far I created a pie chart using the code given in the answer here    and then I used labels from the code given in the answer here    Now I have this    The node in the violett part is the one I created manually and the other ones are implemented in the code, but I don't know what to change so that the automatic generated ones look like the one I created manually  My MWE      \documentclass[11pt]{article}   \usepackage{tikz} \usetikzlibrary{arrows}  \usepackage{xcolor}  \usepackage[utf8]{inputenc}  \definecolor{rosso}{RGB}{220,57,18} \definecolor{giallo}{RGB}{255,153,0} \definecolor{blu}{RGB}{102,140,217} \definecolor{verde}{RGB}{16,150,24} \definecolor{viola}{RGB}{153,0,153}  \makeatletter  \tikzstyle{chart}=[     legend label/.style={font={\scriptsize},anchor=west,align=left},     legend box/.style={rectangle, draw, minimum size=5pt},     axis/.style={black,semithick,-&gt;},     axis label/.style={anchor=east,font={\tiny}}, ]  \tikzstyle{pie chart}=[     chart,     slice/.style={line cap=round, line join=round, very thick,draw=white},     pie title/.style={font={\bf}},     slice type/.style 2 args={         ##1/.style={fill=##2},         values of ##1/.style={}     } ]  \pgfdeclarelayer{background} \pgfdeclarelayer{foreground} \pgfsetlayers{background,main,foreground}   \newcommand{\pie}[3][]{     \begin{scope}[#1]     \pgfmathsetmacro{\curA}{90}     \pgfmathsetmacro{\r}{1}     \def\c{(0,0)}     \node[pie title] at (90:1.3) {#2};     \foreach \v/\s in{#3}{         \pgfmathsetmacro{\deltaA}{\v/100*360}         \pgfmathsetmacro{\nextA}{\curA + \deltaA}         \pgfmathsetmacro{\midA}{(\curA+\nextA)/2}          \path[slice,\s] \c             -- +(\curA:\r)             arc (\curA:\nextA:\r)             -- cycle;         \pgfmathsetmacro{\d}{max((\deltaA * -(.5/50) + 1) ,1)}           \begin{pgfonlayer}{foreground}         \draw[*-,thin] \c -- (\midA:\r) node[above,near end, pos=\d,pie values,values of \s]{$\v\%$};         \end{pgfonlayer}               \global\let\curA\nextA     }     \end{scope} }  \newcommand{\legend}[2][]{     \begin{scope}[#1]     \path         \foreach \n/\s in {#2}             {                   ++(0,-10pt) node[\s,legend box] {} +(5pt,0) node[legend label] {\n}             }     ;     \end{scope} }   \begin{document}   \begin{tikzpicture} [     pie chart,     slice type={comet}{blu},     slice type={legno}{rosso},     slice type={coltello}{giallo},     slice type={sedia}{viola},     slice type={caffe}{verde},     pie values/.style={font={\small}},     scale=2 ]  \pie{Sommerjobs in Österreich}{52/comet,12/legno,20/sedia,16/coltello}   \legend[shift={(-1cm,-1cm)}]{{Eisverkäufer}/comet, {Schwimmbad}/legno, {Zettelverteiler}/coltello} \legend[shift={(1cm,-1cm)}]{{Kellner}/sedia}     \draw [*-,thin] (0.6,-0.2)  -- (0.7,-0.2 + 0.5ex) -- (2,0.5ex) node[above, near end]{20\%};    \end{tikzpicture}   \end{document} How do I disable 'Activities' hot corner in GNOME shell? GNOME shell has the so-called feature "hot corner", that opens the dashboard  if the mouse touches the top-left corner of a monitor screen.  I want this disabled I used to have a GNOME shell extension, yet the repository is not found anymore:  git clone git@github.com/Ahrak/gnome-shell-extension-disable-hot-corners.git fatal: repository 'git@github.com/Ahrak/gnome-shell-extension-disable-hot-corners.git' does not exist Blank screen after installing nvidia restricted driver Did I correctly derive this recurrence equation formula The div containing tags for a question doesn't reflow, causing layout issues for questions with long/many tags This appears to be a css bug which (I think) has recently been introduced. It's most visible when viewing questions on Stack Exchange sites using mobile devices (the full site with responsiveness, not the mobile site) but can easily be reproduced by resizing a browser window on a question where the combined width of the tags is large. A couple of example questions show this behaviour:  On Meta Stack Overflow:   On Meta Stack Exchange:     Using the Meta Stack Overflow question to demonstrate (as the total width of the tags is larger):  At 1100px, the tags just about fit into their containing div.     At 800px, the tags appear on top of related questions:     At 450px, the tags are now wider than the view (the last tag is completely off the screen), causing scroll bars to appear:      This doesn't happen to lists of questions - the tags flow onto multiple lines:     Reproduced on: { Firefox 81, Chrome 84, Edge 84 } on Windows 10, and Chrome 85 on Android 11. Why do games run slow on CPU Maybe my question sounds naive because I'm not a game developer but I dont see objective reasons for this. An average cpu is in times more powerful than an average gpu like a few graphics cards in one. The most repeated reasons in internet:  the GPU isn't as busy as the CPU  If the gpu renders the screen how it can not be busy The modern cpus are powerful enough. They are not busy most of time. For example my cpu's usage is 3%.  many GPU's are designed to process graphics commands in parallel, CPU single threads them  What bothers the games to run a few parallel processes even on one cpu core? In my opinion its not correct to tell that the gpu is better if games never use 100% of the cpu's capacity. To be specific they dont use even 50%.  To clarify my question based on responses in the comments:  Did you mean to ask &quot;Why do games render more slowly on the CPU?&quot;  Yes I mean why the cpu cant do the whole work for games when it is underloaded and especially if it does the largest part of work in any case.  You can not compare GPUs and CPUs directly, because they do different things.  What bothers them to do the same things?  The CPU isn't as well suited to performing rendering calculations  I dont understand what &quot;suited&quot; means. And why the cpu is not suitable for primitive tasks aka paint roller.  adding additional parallel processes doesn't improve performance  Then why do you produce multicore graphics cards and multicore central processing units? Just give various parts of one task to a few processes if one process is slow and 100% of the capacity is not used. What bothers to emulate the gpu? Its also unclear for me why when you play without a separate graphics module the games see only one cpu core when you play with the gpu they see and use all the cpu cores. May be some magic. How to debug EntityMalformedException? I've got fatal error EntityMalformedException: Missing bundle property on entity of type node. in entity_extract_ids() (line 7700 of .\includes\common.inc) when trying to access user/xyz.  I tried to retrieve info about the malformed node at line 7700, where the error message is built, thinks like :  if (!isset($entity-&gt;{$info['entity keys']['bundle']}) || $entity-&gt;{$info['entity keys']['bundle']} === '') {  dpm($info);// or dpm($entity);  throw new EntityMalformedException(t('Missing bundle property on entity of type @entity_type.', array('@entity_type' =&gt; $entity_type))); }   dpm($entity) returns an unexpected user object, and $info a huge qty of things.   Could somebody put me on the right way ?  I already read whatever I could find about Missing bundle property errors, but none helped solving.  dpm($entity) returns  uid (String, 2 characters ) 70 name (String, 9 characters ) John pass (String, 55 characters ) $S$DUwPuOuDPiDL4nRTYXqc7a5uOfMKey7pyhOFUEKka1XM... mail (String, 30 characters ) john@example.com theme (String, 0 characters ) signature (String, 0 characters ) signature_format (String, 13 characters ) filtered_html created (String, 10 characters ) 1396286331 access (String, 10 characters ) 1397146661 login (String, 10 characters ) 1396513460 status (String, 1 characters ) 1 timezone (NULL) language (String, 2 characters ) fr picture (NULL) init (String, 30 characters ) john@example.com data (Array, 5 elements) roles (Array, 1 element) og_user_node (Array, 0 elements) message_subscribe_email (Array, 1 element) field_bio (Array, 0 elements) field_name_first (Array, 1 element) field_name_last (Array, 1 element) field_facebook_url (Array, 0 elements) field_linkedin_url (Array, 0 elements) field_twitter_url (Array, 0 elements) user_trusted_contacts (Array, 1 element) group_group (Array, 1 element) group_access (Array, 1 element) metatags (Array, 0 elements) rdf_mapping (Array, 3 elements) realname (String, 13 characters ) John Doe content (Array, 13 elements) entity_view_prepared (Boolean) TRUE privatemsg_disabled (Boolean) FALSE Why are local variables not initialized in Java? Was there any reason why the designers of Java felt that local variables should not be given a default value? Seriously, if instance variables can be given a default value, then why can't we do the same for local variables?  And it also leads to problems as explained in :     Well this rule is most frustrating when trying to close a resource in a finally block. If I instantiate the resource inside a try, but try to close it within the finally, I get this error. If I move the instantiation outside the try, I get another error stating that a it must be within a try.      Very frustrating. Trying to identify a very old short story about aliens colonizing human bodies Don't remember the exact start to the story, but it went something like "walking along a path" or something, and when he hears what sounds like a shotgun blast behind him, he then feels something strike him in the butt. He passes out, and when he awakens, he discovers that the "shotgun blast" was actually a miniature spaceship that exploded and shot miniature aliens into his body. The aliens prove to be very beneficial because they clean up all the toxins and other poisons in his body. They can be transmitted through kissing or sexual activity.  Any help with the name of the story would be greatly appreciated.  Dan Is it possible to scale specific apps on Windows 10? Is it proper usage to replace a comma in a list with a semi-colon in this situation (see details)? While writing a proposal at work today I needed to mention a list of things and within that list were multi-part items. It seems like replacing the comma with a semi-colon in this situation would make the sentence easier to understand, but is it correct usage?  With standard punctuation this could get confusing:       Some of my favorite things to do are   camping, playing football and   baseball, watching Laurel and Hardy   Movies, and traveling.   Proposed alternative. Is this acceptable usage?       Some of my favorite things to do are   camping; playing football and   baseball; watching Laurel and Hardy   Movies; and traveling. Is ArcSDE no longer needed at ArcGIS 10.1? On the commutative property of multiplication (domain of integers, possibly reals) $ab = ba$  This is, inherently, true. Some texts drop it like an axiom without any justification. But I'm a bit curious where it stems from or basically why/how it works. If anyone could enlighten me a bit further, I'd be most grateful. Peano axioms? From set theory? Help.  What bugs me with this definition is it's real world "application":  Let's say I have a power output of 5 W ( $kg\cdot m^2 \cdot s^{-3}$) and I want 30% of that power output (to have some units and natural context).  Naturally, 30% is 30 1/100 (% is the unit). For simplicity, let's express that as:  $30$%$ = 30/100 = 3/10 = 3d$ where $d = 1/10$, a simpler unit (because %W would look... Wrong?).  So 30% of power is then $5 W \cdot 3d$, and we can force it to "make sense" if we associate d with W or basically scale the unit of power by d (which is intuitively understood as being 10 times smaller then the output of 1 W) $dW$. And we want to scale these 5 units of $dW$ three times.  $5 dW \cdot 3$  But the commutative property says it is the same as scaling 3 units of $dW$ 5 times or:  $3 dW \cdot 5$  And the result is the same. This is the bit that hurts my head, the fact it is the same. I try to interpret the same as, for example 50 J of work, it's either applying 50 N over 1 m of distance or 1 N over 50 m of distance.    Down here is additional stuff I think I have (you don't have to read it if you know how to answer immediately). I don't claim it's correct, if anyone parses this information, feel free to correct me.  $m\sum\limits_{i=1}^{n}{1} = n\sum\limits_{i=1}^{m}{1}$  This is how I've been trying to break it down, as it is repeated addition. It is repeated $n$ times and multiplied by $m$, and reverse on the right side. There is $x = m - n$, so when I multiply $n$ $m$ times, each repeated addition of $n$ lacks exactly $x$ to $m$.  $mn = nm$  $x = m-n$  $m(m-x) = (m-x)m$  $m^2 - mx = m^2 - mx$  $ true $  And yes, sadly, I realise that I am using the very property I'm trying to prove ($xm$ shifted as $mx$ on the right-hand side.)  And it even calls in the distributive property of multiplication over addition which I derive (for myself, informally) from the very nature of multiplication and the way we "process" numbers:  For example, number $55$ times $2$  $55 = 5 \cdot 10^1 + 5 \cdot 10^0 = 5 \cdot 10 + 5 \cdot 1$  $(5 \cdot 10 + 5 \cdot 1) \cdot 2$  This is the basis of our positional notation which appends digits of varying orders of magnitude or units together in a way it makes "sense". Each one is b times bigger than the one to the right. Basic stuff. It is why I expressed 10 and 1 explicitly, those are what I consider units in this case.  Now, from the definition of multiplication, which is at its heart just repeated addition, it is truly the same if you add together $2$ $50$ times and then again $5$ times or "all at once" (figuratively, we are always doing the former mentally) $2$ $55$ times.  That added together gives 110, which is true.  To me, the distributive property (in case of integer multiplication) is a repercussion of the very definition of multiplication which is repeated addition (evading strict concepts). I am not certain whether this is a good way to look at it. Invoking JavaScript code in an iframe from the parent page Basically, I have an iframe embedded in a page and the iframe has some  routines I need to invoke from the parent page.  Now the opposite is quite simple as you only need to call parent.functionName(), but unfortunately, I need exactly the opposite of that.  Please note that my problem is not changing the source  of the iframe, but invoking a function defined in the iframe. "Always on Top" Windows with Java In Java, is there a way to have a window that is "Always on top" regardless if the user switches focus to another application?  I've searched the web, and all of the solutions lean to some sort of JNI interface with native bindings.  Truly this can't be the only way to do it?.. or is it? I am just looking for some clarification on this exercise:  Let $A = \{a,b,c,d\}$. Give an example of a relation $R$ on $A^2$ which is reflexive, symmetric, and not transitive.  I understand that if I was only dealing with $A$ and and not $A^2$ I could give an answer similar to:  $R = \{(a,a),(a,b),(a,d),(b,a),(b,b),(c,c),(d,a),(d,d)\}$  Here $R$ is reflexive, symmetric, and not transitive.  What is confusing me is the fact that we have $A^2$. I am not sure what I am missing here. I am looking through my book to see if I can figure this out, but if someone could help shed some light on this it would be appreciated.  Thanks,  Tony Why did Voldemort stop employing Occlumency against Harry in Deathly Hallows? I did setup an easy scene with an area light behind a window. In the glass (simple plane) which is in front the area light is visible - how can I turn this off so that the background is shining throgh?