My brother argues that "infinity is a quantity,an infinite number". I argued back saying infinity is a concept, a quality rather than an actual quantity. My brother was saying that $\frac{5}{\infty} \to 0$, but I argued that infinity on its own cannot be placed in a math expression in this manner, rather it is usually a part of an operator like a limit because $x \to \infty$ means $x$ increases and increases continuously forever not to an "infinite quantity. Who is right?  Can infinity, under any circumstance, be considered a quantity, or is infinity just a property, a concept?  Edit: The possible duplicate does not answer the question as to whether infinity can be called a quantity, mathematically.

It is states that ,Infinity is the notation used to denote greatest number.  And $\infty + \infty = \ infinity$ When my brother and i has discussed about it we have the following argument.   I say "infinity is not a real number".but my brother arguree with me And my proof is like the one which follows   $$\infty + \infty = \ infinity$$ And  $$\infty + 1= \ infinity$$ Since infinity not equal to zero,if infinity is a real number,then by 'cancellation law' $$\infty + \infty = \infty +1$$.  Therefore $$\infty=1$$ but it is not true .hence it is not a real number. Is it right proof?  2.As the discussion goes on my brother ask "why we say $\infty + \infty = \ infinity$" He give a proof like this  If infinity is a greatest number then $\infty + \infty $ is again a greatest number so we called it as infinity"  But my stand is "if p is a greatest number then p+p = 2p .therefore ,2p is the greatest number.then how you call p as a greatest number.  Again he say  to consider a statement " if $\infty$ is a greatest number then $\infty + \infty = \ infinity$"  Since infinity is undefined the statement is true.I accept it but I won't know whether it is exactly true.  I want to know 3. What is infinity? At last I was very confused about infinity .please someone explain the three question that I ask.Very thanks in Advance


I'm trying to print the date when I change the value on a cell (status column). But spreadsheets update the date to today's date. I wish it could save the date from when the status was changed. The code to print the date: function TIMESTAMP() {    var today = new Date();   var date = Utilities.formatDate(today, 'GMT-3', 'dd/MM/yyyy');   return date;  }  In the spreadsheet, the column D is where I set the status and columns H to J print the date from when the status was changed.  The code for column H is the following: =ARRAYFORMULA(IF(ROW(H:H)=1;"Logística";IF(ISBLANK(D:D);;IF((D:D>=3)*(D:D<6);TIMESTAMP();IF(D:D<1;"Aguardando Pagamento";IF(D:D=2;"Aguardando Etiqueta";IF(D:D=6;"Cancelado";"Aguardando Faturamento")))))))  The codes for columns I and J are similar to H. So, how to print the date from when the status in column D was changed and keep spreadsheet from updating to today's date?

I have a column A4:A (heading = Date), and other columns after it B4:O.  I want column A to fill in today's date automatically when I fill in any other columns (some of these B4:O maybe empty, but most will be filled) in that row. But I only want that to happen the first time I edit any other columns within that row.  What I've tried:  A7: =IF(B7 > 0,TODAY(),)


Why is there a need sometimes for an external crystal, even though the MCU  have an internal oscillator?  To give you an example, the  used in Arduino Uno has an internal 8Mhz internal oscillator, but also has settings for higher clocks. And additionally can be configured to use external oscillators as well. Why?  Similarly, there was a personal project where a , having 50Mhz CPU, was used with an external 8Mhz crystal for an audio codec.   Many of my assumptions maybe wrong, that is because of an unclear understanding of the need for something external, if there is a default choice.  Some assumptions     Stability Accuracy Cost   Please elaborate the exact purpose.

I always use the internal oscillator that pics have as I have never found the need to run anything at higher frequency than 8 MHz (which is the fastest the pics I use tend to be able to go). Are there any reasons, beyond going above 8 MHz, that mean I should use an external oscillator? It just seems like one more thing to go wrong to me but I'd be interested to hear what others do.


In Linux world one can just add shebang to the jar file and create an executable, it's widely  though whether this is a good practice or not. My question would be - is there something similar I can add to make the jar executable both on Windows and *nix platforms?

If I have a Java source file (*.java) or a class file (*.class), how can I convert it to a .exe file?  I also need an installer for my program.


I have been unable to identify the command for this specific volume variable, V. The closest commands I identified were \vee and \wedge but they do not possess the curvature found in this format. Any help would be appreciated!

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?


The command is used to flash a recovery. Do you have to use odin like tools to flash it or you can just use adb?  Thank you

If an android device is rooted, and you have an image for it. Can you flash it with the "fastboot flash" command of the adb? If not, why? If yes, then what are all the "odin" tools for?  Thank you.


I know that on click is used for dynamically generated elements ... so my AJAX returns data and the link to be clicked on ... but for some reason , nothing happens .. below is my code  // jquery for the click event     $(".back_to_followers").on('click', function(event){        event.preventDefault();       alert('clicked');       $('.user_media_result').empty();       $('.user_media_result').hide();       $('.list_of_followers').show();     });   and the link brought by AJAX  <a class="back_to_followers" style="color:blue; font-size:20px;" href="#"> Back to list of followers </a>

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I've seen this since... mm... yesterday? Well, in the sidebar over the amount of views I'm supposed to see something like this:    But instead I see this:      This happens on Chromium Version 31.0.1650.63 Debian jessie/sid (238485).  .module.question-stats doesn't have tagged element

This is on Stack Overflow. On Meta I'm able to see what the tags are on the right side of the screen. In fact, I think yesterday or some point earlier today I saw tags on the right side of the screen (I can't screenshot or remember correctly).  It's right above the asked and active heading.  I know this is minor but what happened to it? It might be useful for browsing instead of having to look at the bottom of the question post.    Found an image on Google and it shows the tags on the right side of the screen:


Sometimes I erroneously copy & enter file name into terminal, for example, instead of youtube-dl <some-link> I trying to execute <some-link> Just for now I wrote the script f like case "$1"     ...     '*youtu.be*': youtube-dl "$1" ;;     '*.html': links "$1" ;;     ...     else xdg-open "$1" ;; esac  Is there any ability in the bash to replace <input> by <command> <input> depending on <input>?

When run a command, if the command is not present, then some information regarding the failure of the command is displayed.  I am trying to take the information about that failed command as input to my script, which has to run automatically whenever the command fails.  Whenever the command fails the $? value would be 127. I have to catch this failed event and run my commands there.


I'm trying to write a function that calculates and displays cryptocurrency values with subtracted fees (-0.10000000 in the example for simplicity).  But I can't get it to display correct values for large numbers (and as this is about currency, correct values are somewhat important)...  Please see this fiddle  to see the problem.  my first idea was  $('#result').text(amount ? (amount + fees).toFixed(8) > 0 ? (amount + fees).toFixed(8) : 0 : 0)   but that yields the following results:  10000000.55555555 // 10000000.45555555  (correct) 100000000.55555555 // 100000000.45555556 (off by .00000001) 1000000000.55555555 // this time the INPUT div shows 1000000000.55555558 10000000000.55555555 // input shows 10000000000.55555534, result shows 10000000000.45555496   so there's obviously something wrong there... so then i thought "ok, i know javascript is strange with floats and i've always heard it's better to convert to int, calculate, then convert back to float".  so i tried   $('#result').text(amount ? (amount + fees).toFixed(8) > 0 ? (((amount + fees) * 100000000) / 100000000) : 0 : 0)   with following results:  10000000.55555555 // 10000000.45555555 (correct) 100000000.55555555 // 100000000.45555556 (same as above, so there's a pattern here) 1000000000.55555555 // 1000000000.55555558 / 1000000000.4555556 (yup, same values as above) 10000000000.55555555 // 10000000000.55555534 / 10000000000.455555 (now it's getting weird) ... 100000000000000.55555555 // shows 100000000000000.56250000 as input and 100000000000000.47 as result...   So I am obviously doing something wrong.. How can i make the function calculate the result CORRECTLY (with 8 decimals) and what am I doing wrong in my two attempts?  thank you very much :)  edit  yeah.. i know (as i wrote in my question) that float math is broken. but my question is how i can correctly convert/etc the numbers to get the correct result, and what is wrong about the way i tried to do it

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


I've been trying to get a value from txt1(jtextfield) which is an id in my database. But it keep saying java.lang.NullPointerException. Here is the code:  public void harga() {     try {         stat = con.createStatement();         String query = "SELECT harga from obat WHERE ID = '"+ Integer.valueOf(txt1.getText())+"'";         stat.executeQuery(query);         ResultSet rs = stat.getResultSet();         while (rs.next()) {             int harga = rs.getInt("harga");             //String nama = rs.getString("nama");             System.out.println(harga);         }      } catch (SQLException e) {         e.printStackTrace();     } }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Desired effect:    Just to clarify - this is LATEX code, asking for a replication with CONTEXT code. Did you understand that? Please leave comments if you didn't get that.  MWE (LaTeX):  \documentclass{memoir} \usepackage{tcolorbox}  \newtcolorbox{mybox}[2][]{   enhanced,   attach boxed title to top center={yshift=-\tcboxedtitleheight/2},   colframe=black,   colback=white,   fonttitle=\huge\scshape,   colbacktitle=white,   coltitle=black,   boxed title style={     boxrule=0pt,     colframe=white,     },   title=#2,   #1}  \begin{document} \pagestyle{empty}  \begin{mybox}{Goals} \\ \end{mybox}  \end{document}

I am planning to move to Context, however, the fact that I'll miss some of LaTeX packages (especially tcolorbox) feels sad. That's why I asked such a question.


I am doing an animation project and i used workbench to quickly render out the animation (i rendered to PNG sequence). However when i try to final render still images for testing all i get is the workbench version of the render. I've tried cycles and Eevee with no luck. When i set viewport from shaded to rendered using Cycles or Eevee i get proper rendered viewport as normal. Old files work as expected as well so i don't think blender is broken :). so its something i did when using workbench? If i copy and paste all geometry lights and camera to a new empty scene. all is well. Its so weird. Thoughts? Thanks in advance! Tony

Blender is rendering an older version of my project, not the most recent one. I have made it using the Blender Render but it does not want to render in cycles either. A black and grey screen is rendered as if everything is transparent. Checked general camera, lighting and compute devises in case I messed something up but I can't find anything. All my textures and objects look normal, does anybody know what is wrong or what to check?  Ok added link:


$a_n$ and $b_n$ are two bounden sequences  Prove  $$\liminf(a_n) + \liminf(b_n)\le \liminf(a_n +b_n)$$  Should I use  $$\inf(a+b) = \inf(a) + \inf(b)$$ and i could not come up with how to proceed from this. Or should i use a different approach?

I am stuck with the following problem.     Prove that $$\limsup_{n \to \infty} (a_n+b_n) \le \limsup_{n \to \infty} a_n + \limsup_{n \to \infty} b_n$$   I was thinking of using the triangle inequality saying $$|a_n + b_n| \le |a_n| + |b_n|$$ but the problem is not about absolute values of the sequence.  Intuitively it's clear that this is true because $a_n$ and $b_n$ can "reduce each others magnitude" if they have opposite signs, but I cannot express that algebraically...  Can someone help me out ?


Can anyone tell me the name of a science fiction short story where a spaceship is sent out on an exploration mission from Earth. And then after a few years, the progress of technology is such that humanity spreads to local space and picks up the forgotten original spacecraft as a relic? With the lone pilot waking up to a world far advanced It's an older one, definitely pre-2000. I remember reading it in a short anthology of sci-fi stories I found on the shelves of a used book store as a kid, so I can't remember a specific title or author. Please it's driving me crazy! The overall message of the story was to illustrate how the progression of technology can outpace previous efforts, suggesting it's better to wait until technology is more advanced, and asking the question how long should we really wait.

I'm a huge fan of SF from the golden age of SF, so this could be a fairly old book.  It was a story about a "generation" starship or sublight starship.  I believe most of the story was about their journey and some of the problems and difficulties.  I believe that something strange is observed along the way which later turns out to be them being passed by an FTL starship which was developed, on their long voyage, after they left Earth.  When they arrived at their destination they were amazed and, I believe, disheartened to be greeted by people from Earth.


There has been news in public about Mercury that passes in front of Sun which happens very rarely every 100 years, . So people on Earth can see it through special kind of telescope, of course, mercury looks like a dot on a sheet of paper comparing to the Sun. Thus, it makes me ask: Why doesn't the Sun gravitate Mercury so that in following years, Mercury goes inside the Sun? Mercury is the smallest planet in our solar system and the Sun has the maximum gravity in our solar system. So, I do not understand why Sun not 'eating' Mercury (take Mercury inside it). How? By the gravity of Sun and weakness of Mercury in terms of size and mass. It is such a very strange phenomenon in our solar system so that a small planet like Mercury takes millions of rotation around the sun and Sun's gravity doesn't affect the rotation of Mercury in a way that it makes it closer and closer so that it goes inside the Sun at the end.

The force of gravity is constantly being applied to an orbiting object.  And therefore the object is constantly accelerating.  Why doesn't gravity eventually "win" over the object's momentum, like a force such as friction eventually slows down a car that runs out of gas?  I understand (I think) how relativity explains it, but how does Newtonian mechanics explain it?


I am looking for some good software to simulate quantum computing, visually if possible.  I know about quirk ()  and IBM Q Experience ()  I just saw this question (  ) and the asker uses something that looks really neat :   Does someone knows what this is? And does someone knos other good software like these?  Thank you!!

Is there any way to emulate a quantum computer in my normal computer, so that I will be able to test and try quantum programming languages (such as )? I mean something that I can really test my hypothesis and gets the most accurate results.  Update: I'm not really looking for simulating a quantum computer, but I'm not sure if its possible to efficiently emulate one on a normal non-quantum based PC.


I'm an electrical engineering student and was doing a brief research regarding the round transformations of the AES-128 and came across the Wikipedia article describing the generation of the substitution box () from the mathematical point of view. In the corresponding article it was explained that a given element of the extension field GF(2^8) is initially inverted with respect to x^8+x^4+x^3+x+1. Subsequently, the result (inverse element) is undergoing an affine transformation. The transformation itself is actually comprehensible. However, I do not understand the corresponding C-implementation at all. My naive approach to understand the below shown implementation was to think of the matrix multiplication as a linear combination of the columns of this matrix weighted with the bits of the inverse element. Since the columns of this matrix seem to be cyclicly shifted this could somehow explain the execution of ROTL8 in the affine transformation. In the end, the addition with 0x63 is actually quite clear. #define ROTL8(x,shift) ((uint8_t) ((x) << (shift)) | ((x) >> (8 - (shift))))  void initialize_aes_sbox(uint8_t sbox[256]) {     uint8_t p = 1, q = 1;          /* loop invariant: p * q == 1 in the Galois field */     do {         /* multiply p by 3 */         p = p ^ (p << 1) ^ (p & 0x80 ? 0x11B : 0);          /* divide q by 3 (equals multiplication by 0xf6) */         q ^= q << 1;         q ^= q << 2;         q ^= q << 4;         q ^= q & 0x80 ? 0x09 : 0;          /* compute the affine transformation */         uint8_t xformed = q ^ ROTL8(q, 1) ^ ROTL8(q, 2) ^ ROTL8(q, 3) ^ ROTL8(q, 4);          sbox[p] = xformed ^ 0x63;     } while (p != 1);      /* 0 is a special case since it has no inverse */     sbox[0] = 0x63; }  Would it be possible to explain how the matrix multiplication in the affine transformation can be interpreted as the addition (XOR) of the rotated terms (ROTL8) of the inverse element? Best regards Ratbald

in Rijndael SubBytes() step all bytes of input block are substituted based on a lookup table S-Box. S-Box is initialized by taking all elements of $GF(2^8)$, calculating their multiplicative inverse and then calculating their affine transform. Here is C code which does that as found on wikipedia page. #include <stdint.h>  #define ROTL8(x,shift) ((uint8_t) ((x) << (shift)) | ((x) >> (8 - (shift))))  void initialize_aes_sbox(uint8_t sbox[256]) {     uint8_t p = 1, q = 1;          /* loop invariant: p * q == 1 in the Galois field */     do {         /* multiply p by 3 */         p = p ^ (p << 1) ^ (p & 0x80 ? 0x1B : 0);          /* divide q by 3 (equals multiplication by 0xf6) */         q ^= q << 1;         q ^= q << 2;         q ^= q << 4;         q ^= q & 0x80 ? 0x09 : 0;          /* compute the affine transformation */         uint8_t xformed = q ^ ROTL8(q, 1) ^ ROTL8(q, 2) ^ ROTL8(q, 3) ^ ROTL8(q, 4);          sbox[p] = xformed ^ 0x63;     } while (p != 1);      /* 0 is a special case since it has no inverse */     sbox[0] = 0x63; }  I cant wrap my head around how multiplicative inverse is being calculated here. I assume p here acts as input while q is its inverse. Hence $p*q = 1$. I want to understand how exactly this works because I am trying to implement a function that initializes Rijndael inverse S-Box, where first the inverse affine transform is calculated and then the multiplicative inverse.


We are building a kiosk system.  I have disabled everything but the swipe from the left.  By swiping from the left side of the screen they gain access to the start bar.  Is there a way to disable this in windows 10 standard.  Everything I have seen out there is detailing how to disable it on a laptop using their driver.  Our screen uses the default windows drivers which does not allow me to play with those settings.  Any help on this matter would be greatly appreciated.

Is it possible to disable 'left swipe / gesture' or 'App Switching' in tablet mode on a Surface 3? I am Left Handed and whenever I use the 'Pen' in One note, my palm rests on the left hand edge and opens up the App Switch view constantly. I have disabled tablet mode, disabled the keyboard, disabled Task View, had to move the task bar to the right so I don't hit the start button with my left hand, got 'Left Handed' set up in Device Settings for the pen, disabled Arrange Windows under Multi Tasking - any other left handers got this issue and fixed it? This is only an issue for me in tablet mode when using the pen in One note. Many thanks


Consider the sequence $x_n = \frac{\ln(n)}{\sqrt{n}}$. It seems that the sequence tends to $0$ because $\sqrt{n}> \ln(n)$ for all $n$. I need to prove this by definition or otherwise. Can anyone give me some hints helping me proving this?  Thanks is advance.

How can I prove that $\log^k(n) = O(n^\epsilon)$? (for any $\epsilon > 0 $ and for any integer and positive $k$).  I tried to do it by - definition , and to prove that exists $c,n_0 > 0$ so that for any $n > n_0 $ exists: $c \cdot n^\epsilon > \log^k(n) $, but I don't have idea how to continue for this point.    I will be happy to listen ideas :).


I have use jQuery Drill Down Menu From .  but this plugin is only work with given jQuery Version 1.4. If i am integrate with my project where jQuery 1.8.3, it produce following error into console.  Uncaught Error: Syntax error, unrecognized expression: [object Object][rel="2"]    Any solution?  I don't want to add another jQuery Version just for this menu effect, it increase page sige.

My company has purchased a product that renders an ASP.NET control on the page. This control uses jQuery 1.2.3 and adds a script tag to the page to reference it. The developers of the control will not support use of the control if it modified in any way (including modification to reference a different version of jQuery).  I'm about to start development of my own control and would like to use the features and speed improvements of jQuery 1.3. Both of these controls will need to exist on the same page.  How can I allow the purchased control to use jQuery 1.2.3 and new custom development to use jQuery 1.3? Also out of curiosity, what if we were to use an additional control that needed to reference yet another version of jQuery?


I have currently set up a Docker Swarm that has containers with node.js servers running in it. I am going to try different setups with different amount of node.js containers and see how long it takes to upload json data to servers. My purpose is to a cluster that can handle some stress.  I want to test million concurrent requests and see how server performs. I have currently tried tool called ab (Apache Benchmark) but it was not possible to create million connections with it. I also tried tool called siege but got following:  [fatal] unable to allocate memory for 1000000 simulated browser: Resource temporarily unavailable   What would you recommend me to use with this? Also is there something special I need to take into account in design side?

This is a  about capacity planning for web sites. Related:      What are some recommended tools and methods of capacity planning for web sites and web-applications? Please feel free to describe different tools and techniques for different web-servers, frameworks, etc., as well as best-practices that apply to web servers in general.


How to find a function from reals to reals such that the image of every open interval is the whole of R?  Is there one which maps rationals to rationals?

I wonder  whether there is a function $f\colon\Bbb R\to\Bbb R$ with the folowing characteristic?   for every two real numbers $\alpha,\beta,\alpha\lt\beta$,  $$\{f(x):x\in(\alpha,\beta)\}=\Bbb R$$   I can't  say such a function does not exist, neither can I construct a example  Thanks a lot!


Recently i started to do some home-made canning. The procedure I use is   Use a pressure cooker to build the jars (cristal ones) for about 10 minutes at 120C. Cook my vegetables (normally tomatoes, garlic, capsicum, eggplant, zuchini) the whole mix surely has a ph over 4.6 which is where the Clostridium botulinum lives. Put the cooked vegatables in the cristal jars (which will still be hot), close them, and put them back into the pressure cooker. Cook the closed jars for 20-25 minutes at 120C   My understanding is that botulism is a very serious disease, the most concerning part is that it does not alter the taste, color or texture of the food.  Currently I consume my canned food within 1 week.  The question is, given that I use 120C degrees when cooking, can I be reasonably safe? Is there a significant risk?   Follow up question: I would like to not only store my cooked vegetables, but also cook them with tofu or chicken and then preserve them using the same procedure, however I have not done so as I know tofu has quite a high PH. Would it be safe to use vegetables + tofu/chicken in the preserves?

Well, unfortunately the present my mom got me last Christmas turned out to be a pressure cooker and not a pressure canner.   I've read that it is unsafe to can low acid foods using a pressure cooker.    But is it safe to can high acid foods in a pressure cooker? I'd like to do this because it uses a lot less water and a lot less energy than boiling water canning.  Does a pressure cooker actually cook to a lower temperature than a pressure canner? (My pressure cooker just has two settings (high and low) and I don't know what the PSI is on them.


If the anode releases electrons and the cathode gains electrons, in the diagram below does the electron current flow from left to right? Or is it the flow of positive charges from left to right?

Using conventional notation in the diagram below, I understand that the circuit is not complete because the diode is in reverse bias. But knowing that the electrons actually flow from the negative to the positive terminal(direction of the arrows), wouldn't the electrons take a path from the negative terminal of the battery, go through the lamp and stop at the diode(the red path in the picture). If they would, then why doesn't the lamp light up with the first electrons that are able to flow through it before the voltage in the wire is built up and the current stops.


If $(G,*)$ is a group, prove that the identity and the inverse elements are unique.  What I did for the first one is:   Suppose $\exists e,g\in G$ such that $\forall a\in G a*e=e*a=a$ and also that $\forall a\in G a*g=g*a=a$, then $g=g*e=e$, hence $g=e$. The first equallity happens because $e$ is an identity, and the second happens because $g$ is an identity.   Is this right? I checked some notes of another class and their proof is much more longer and complicated (although I understand every step), what am I doing wrong?  For the second one, can I use that if $a$ is the inverse of $b$, then $b$ is the inverse of $a$? I feel that I shouldn't, but I'm not sure why.

I was given a group and I have to prove   a) If $f\cdot g = f$ or $g\cdot f = f$ then $g = 1$.  Is it right to do it using just Identity axiom of group:  $f \cdot g = f = f \cdot1 \Longrightarrow g = 1 ?$  Thanks.


Prove that $\mathcal{P}(A) \sim \{0,1\}^A$   We might can find a bijection function, however I am trying to prove it in other way. I want to F, G 1-1 functions and prove that those functions are inverse each other, once I did it, we know from a another proved claim that function is inverse if and only if function is bijection.  I define $F:\mathcal{P}(A) \to {0,1}^A$ by the following rule, for all $X\in \mathcal{P}(A)$, we have function $F(X): A \to \{0,1\}$ and for all $a\in A$ we define function $F(X)(a)=0$ its easy to prove that this function is 1-1.  Now I have to define $G:\{0,1\}^A \to \mathcal{P}(A)$ by the rule: for all $f\in \{0,1\}$, $G(f)=?$  My question is how can we define $G(f)$ to be 1-1 function? Moreover, any suggestions on this strategy will be highly appreciated.

I got this question in homework:     Let $\{0,1\}^A$ the set of all functions from A (not necessarily a finite set)       to $\{0,1\}$. Find a correspondence (function) between $\{0,1\}^A$ and       $\mathcal P(A)$ (The power set of $A$).       Prove that this correspondence is one-to-one and onto.   I don't know where to start, so I need a hint. What does it mean to find a correspondence? I'm not really supposed to define a function, right?  I guess once I have the correspondence defined somehow, the proof will be easier.  Any ideas? Thanks!


What seems implicit in  on youtube, is the claim that every directed multigraph (with loops) can be identified with a finite category and vice versa, if we consider the paths of the directed multigraph rather than just the edges (= 1-edge paths).  Is this true?  If it is true, why is there not more cross-fertilization between category theory and graph theory?       EDIT: The proposed identification:  The nodes are the objects of the finite category.  The identity morphisms are implicit (i.e. do not need to be depicted), but if they are to be depicted, then they are just a loop starting and ending at the corresponding vertex.  As stewbasic pointed out in the commented below, we need to stipulate that each edge in a path can only be traversed once. Each path should have a well-defined source and sink, so that the domain and codomain of our corresponding morphism are well-defined. We do not want to include arbitrary cycles.  Anyway, the morphisms are the paths of the directed multigraph, or the edges of the corresponding transitive closure of said multigraph (we want to interpret the arrows such that the associative rule holds, i.e. the composition of any two morphisms is again a morphism).      My guess would be that finite categories are uninteresting to the typical category theorist, not to mention 1-categories in general, and directed multigraphs are probably too pathological for the average graph theorist to care about.  Note that for this identification to work, we have to assume that the identity morphisms are implicit in the directed multigraph, but that really isn't a problem, since when composed with any other morphism they "disappear", at least in the sense that neglecting to draw the loops corresponding to the identity morphisms on the directed multigraph would not affect whether the transitive closure represents the corresponding finite category or not.      I assumed that nLab would have something to say about this, but no such luck:   From this page there is a clear correspondence between the transitive closure of a directed multigraph (or considering the paths of the multigraph instead of the edges) and posets, since we can define the nodes to be reflexive, antisymmetry follows from the multigraph being directed (from the nLab page it follows that symmetry for the relation implied by the multigraph holds if it is undirected), and transitivity follows from taking the transitive closure/considering paths instead of edges.  So if the above correspondence is correct, then in some sense finite categories, directed multigraphs, and posets all "coincide", essentially since they all describe the same type of relation.  I know that every monoid can be represented by a category with one object and the morphisms are just the elements of the monoid (the invertible elements being the isomorphisms).  EDIT: I think this question might be a duplicate, so I am voting to close this question. The original question did not come up in the suggestions or similar questions while writing this one, so thanks must go to Musa Al-hassy for finding and pointing out the similarity:

Given a graph G, and the set of paths in G called PathG.  Is there a monoid structure on PathG? Will concatenation be the multiplication formula? even if it's not defined for some paths?  What about the identity?


Sometimes I want to test the concepts of calculus in practice, but the most popular books like Thomas/Maurice is   a  little approach to me.Does someone know a book that works with calculus in practice (more than Pearson's books, contextualized problems...)

I read single variable calculus this semester, and the course is using Thomas Calculus as the textbook. But this book is just too huge, a single chapter contains 100 exercise questions! Now I'm looking for a concise and complete textbook. I'm not interested in routine, computational exercises, but rather some challenging problem sets.  I have quite a strong basic knowledge of calculus from high school, but I still have difficulties in solving a few questions from past exam papers. So I'm looking for more challenging exercises. In fact, I'm looking forward to solving Putnam level questions.  Please suggest some textbooks with these features. Thanks in advance.


As a particular example,  was closed as  back in 2009, when Stack Exchange didn't exist, and Stack Overflow was a site exclusively for programmers. Now that Stack Exchange exists, there are parts of the network (like Japanese.SE, where intra-"word" bolding is used and tokens like word_word_word aren't) that have requirements that I'm sure Jeff never anticipated when he gave  to that question.   Would it be acceptable for me to raise that issue again as either a  or  on MSO?

So there's a feature request (I'm not the OP) which has recently been tagged status-declined.  I was/am highly in favor of the request.  Now I'm depressed.  I will probably drown my sorrows tonight in a case of dark English ale (nothing like the old world).  This particular feature-request had 72 upvotes on it and the reason given for declining was not all that great (IMHO).  How long do we wait (realistically) before asking for a highly-popular feature request which was declined to be reconsidered?  (ok, to save you some forensic time the feature in question is , but this is really just in general)


I ran a specification with an outcome in $ terms, and a coefficient on a dummy variable was statistically significant. However, when I ran the exact same model with the outcome in log-dollar terms, the coefficient is not significant. Is this possible, or must there be a mistake?

I'm doing a Logistic Regression on company level using the total assets to control for company size. Due to the skewedness of the data, I do a log-transformation of the asset data. While I get no significance for the log-transformed variable, the not transformed variable is highly significant (p < 0.01). What could be a possible explanation of such a result? Does it mean that the relationship is not diminishing for extremely high and low values or does it show an outlier problem and should not be used for interpretation of the data.


A JavaScript code:    var age = 27; var obj = {   name: 'Jona',   city: 'Lisbon' };  function change(a, b) {   a = 30;   b.city = 'San Francisco'; } change(age, obj); console.log('age:', age); console.log('obj.city:', obj.city);     The result in console is 27, San Francisco respectively. I am confused with that why the value of age is 27 instead of 30. In my opinion, the value of variable age will be changed to 30 after calling function change. Can someone answer it?

The primitive types (number, string, etc.) are passed by value, but objects are unknown, because they can be both passed-by-value (in case we consider that a variable holding an object is in fact a reference to the object) and passed-by-reference (when we consider that the variable to the object holds the object itself).  Although it doesn't really matter at the end, I want to know what is the correct way to present the arguments passing conventions. Is there an excerpt from JavaScript specification, which defines what should be the semantics regarding this?


I wanted to install Ubuntu 17.10 alongside Windows 10. But it all got messed up while I was installing Ubuntu 17.10!  The problem is UEFI mode. I don't know UEFI. I still want to dual boot between Windows 10 and Ubuntu 17.10, So what can I do now?  Note: My laptop is Asuspro core i7 2.4 ghz processors, 8GB ddr3 ram, and entering the BIOS I didn't find so called UEFI!   I tried from Windows 10 Control Panel > Recovery but didn't find UEFI Firmware settings. How can I find it to configure?

I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this?


There is a guide here  that I would like to back up. All the links that go to * I also need to back up, and on a few of those pages there is pagination that links to still more pages under the same directory. How can I backup this page and all of it's sub pages?

No matter what browser I've tried (even Chrome), when saving a web page as local files, it's never quite exact. Lots of JavaScript & such seems to trip it up. I'm looking for some way to get a 100% perfect local copy of a web page. In other words, all CSS/images/JavaScripts should pull down as well AND the HTML references to said content should be changed to point to a local folder. Is there a way to do this? I'm primarily on a Mac but I have access to Linux.


What is the difference between:  int *array; array = (int*) calloc(5, sizeof(int));   and  int *array; array = calloc(5, sizeof(int));   I don't get it. Both samples work. At the university the professor explained why you need the (int*) before the calloc, but I didn't get it.  In the course was a code sample like this:  struct data{    int number;    char *name; }; typedef struct data student;  int main(){     student **list;     list = (student*) calloc(10, sizeof(student*));      //Create structures dynamic in list     ....      return 0; }   I hope someone can explain it to me. Thank you.

In , someone suggested in a  that I should not cast the result of malloc. i.e., I should do this: int *sieve = malloc(sizeof(int) * length);  rather than: int *sieve = (int *) malloc(sizeof(int) * length);  Why would this be the case?


What should happen if you type one of the following URLs into your browser?          ...because this is what you get:

Should Stack Exchanges sites with top-level domains have *.stackexchange.com redirects? For example:   stackoverflow.stackexchange.com serverfault.stackexchange.com superuser.stackexchange.com askubuntu.stackexchange.com seasonedadvice.stackexchange.com   (And also the meta.*.stackexchange.com versions of those too.)  It just seems like if someone hears about this Stack Exchange site Example that might help, they might try typing example.stackexchange.com instead of example.com.


I need to create simple buildings. Just pieces comprised of basic shapes, but I really do not want to UV unwrap and apply textures individually. What's the best way to go about this? I'm decent at modeling, but definitely will not have time to unwrap individually. I'm hoping to just use seamless textures. I was thinking SketchUp might be okay, but I believe the features I'm looking for are only in the paid version.

I just recently got into the nodes system, my knowledge on the subject is limited. I can't seem to find out how to tile textures using my current node setup, because it doesn't tile the them on its own. I know that I could be using a Vector Mapping node, but the way I'm modeling this requires that I texture each part of the building individually. If I use a Vector Mapping node, I'll have to manually adjust each individual part myself. The nodes I'm currently using  The problem that I'm having is that if I use the same nodes for a mesh with different dimensions they get stretched.  I want to avoid the need of using Vector Mapping nodes and just give it the ability to tile the texture so that it goes over a mesh of any size without stretching.


I am new to Ubuntu so please don't Tag "has been answered before" and tag some answer that only veterans understand. I have Ubuntu for several days now when I decided to install steam (didn't work at all but that's not my problem). I then decided to upgrade or update my NVidia driver (for gtx750ti if that matters). Ubuntu then asked me to setup some MOK Password (whatever that is, I didn't find a pleasant explanation) in order to do something with the driver at the next boot. So I did. Then I restarted the PC, was asked for the password, typed it in 2 times correctly (I am 100% sure) with this blue window telling me it was wrong. On the third try I tried to type it in on my German keyboard as if it was an American (just in case) and naturally that didn't work. So then I continued the normal boot, where I was asked Ubuntu Actions for Ubuntu (or so) Windows boot (or so) System setup  Ah yes, I have Ubuntu install Dualboot with windows (please forgive me if I am using some wrong terminology). So I selected Ubuntu and saw the normal Ubuntu logo (which was wierd because it was always stretched before for a few seconds). Then I got a black screen with a blinking underline cursor in the top left corner. And nothing happened. I turned my system off again by holding the power button. A second before it actually went off, i saw some letters and digits where the cursor was before. I tried that a few times and even tried recovery mode of 18.10 and 18.13 (or 18.10.3). I didn't want to do anything that I don't understand because I was afraid I could lose windows as well. So when I see Ubuntu Actions for Ubuntu (or so) Windows boot (or so) System setup Is that the boot already or is the boot where I am stuck? Also I have read something about GRUB online but I have no idea if that could help me or what it is or how I access it.

I just updated my laptop from Ubuntu 14.10 to Ubuntu 15.04.  Now on a restart it fails to make it to the login prompt.  The system looks to be in a cycle of failure and I see the message repeatedly  [ OK ] Started Light Display Manager. [ OK ] Started ACPI event daemon.        Starting ACPI event daemon...        Starting Network Manager Script Dispatcher Service.... [ OK ] Started Network Manager Script Dispatcher Service.   The contents of /var/log/Xorg.0.log show a segfault.  Sorry I can't copy the backtrace now, but the chain goes  /usr/bin/X /usr/bin/X /lib/x86_64-linux-gnu/libc.so.6 /lib/x86_64-linux-gnu/libc.so.6 /lib/x86_64-linux-gnu/libc.so.6 /usr/lib/x86_64-linux-gnu/xorg/extra-modules/nvidia_drv.so /usr/lib/x86_64-linux-gnu/xorg/extra-modules/nvidia_drv.so /usr/bin/X /usr/bin/X /lib/x86_64-linux-gnu/libc.so.6 /usr/bin/X Segmentation fault at address 0x41   I'm on a Dell Precision m3800.  Since the nVidia driver is implicated in the stack trace, I'll start with swapping that out.  Any suggestions for my next steps to try to fix this?  thanks, Dennis


Something like this. I would like to get only the second level menu items, not their parent items.  Home   Sub Menu Item 1 Sub Menu Item 2   About   Sub Menu Item 3 Sub Menu Item 4   For example, from this list I'd like an output of something like.

Sub Menu Item 1

Sub Menu Item 2

Sub Menu Item 3

Sub Menu Item 4

   I have been at this for weeks now, no answer I found on this site or any other has helped.

I have a menu defined in WP Admin that looks like this:    I want to be able to display all the child links on the sidebar whenever I am at a parent page. For example, if the user is on my "About Us" page, I want a list of the 4 links highlighted in green to appear on the sidebar.  I looked at the documentation for  and it doesn't appear to have any built-in way to specify a particular node of a given menu to use as the starting point when generating the links.  I created a solution for  which relied on the relationships created by the page parent, but I am looking for one which uses the menu system specifically.  Any help would be appreciated.


On two identical rectangles I use a swatch as fill color. The swatch is C=100, M=0, Y=0, K=0. On one rectangle I've set the Tint for the swatch to 10%, on the Other I've set the opacity to 10%. The result is not the same color on a white background. I'm not sure why this is.  I do understand one makes the rectangle transparent and the other does not, but on a white background I had not expected the difference because the Tint itself would also be calculated based on 0% being whit.

I have a problem. I'm working with an object at 50% opacity. When it's over the artboard itself the color looks great, but when I put a white object behind it I get this weird color that doesn't look accurate.  This happens with every object and only in CMYK. I'm pretty sure this never happened to me before so maybe I changed something in the settings or I don't know.  Does anyone have any idea?


Let $A$ be a countable subset of $\mathbb{R}^2$. How to show that $\mathbb{R}^2 - A$ is path-connected?  My effort:   Let $A = \{ a_1, a_2, a_3, \ldots \}$, where $a_n = (\alpha_n, \beta_n) \in \mathbb{R}^2$ for each $n \in \mathbb{N}$.   Let $x_1 = (\xi_1, \eta_1)$ and $x_2 = (\xi_2, \eta_2)$ be any two given points in $\mathbb{R}^2 - A$.   How to find (explicitly) a continuous function  $f \colon [0,1] \to \mathbb{R}^2 - A$ such that $f(0) = x_1$ and $f(1) = x_2$?   Or, how to find (explicitly) a polygonal path (i.e. a path consisting of a finite number of line segments ) from $x_1$ to $x_2$ none of whose edges intersects $A$?

Here's a question that I share:  Show that if $D$ is a countable subset of $\mathbb R^2$ (provided with its usual topology) then $X=\mathbb R^2 \backslash D $ is arcwise connected.


After reading former SE co-founder Jeff Atwood's blog post  I came to this problem. If I post a wonderful description about the features of a 1967 Chevrolet Camaro, do we want users to find this post easily with different search terms? For example, is it desirable to find this answer with   What is the first Chevrolet muscle car? What was the pace car in the 1967 Daytona 500? Did the Camaro ever have window vents? What was the black car in Better Off Dead? What was the Chevy II Nova frame based on?   These five questions may have the same answer, but certainly the site works better if there are 5 different ways to find a description of a 1967 camaro. Are more questions better? Shouldn't we reward users who improve the validity and usefulness of an answer rather than down-vote them?  Instead it appears SE policy stifles search engine effectiveness by reducing reputation when a presumed answer is already posted under a different question. Currently we treat search-engine augmenting questions as such:   OP presents a question. An arbitrary user with 3K+ reputation guesses what the answer is then searches SE for it. Using their judgement, they vote to close the OP question as duplicate and link the answered question (related or not) to it. The OP begins receiving downvotes for the duplicate question and is denied reputation which answers and views would have brought.   The end result is that users who broaden the search terms which can arrive at a good answer are stigmatized and in fact punished with loss of reputation because a duplicate answer was confused with a duplicate question.  There is a logic to connecting certain questions which ask the same thing, but there is no logic to associating several uniquely asked questions together only because they happen to arrive at the same answer. This also hurts the site.  Someone tell me I am missing something, this is my experience.  HOW MANY DIFFERENT questions are ideal for any single answer?

What should I do when I see a question that is a duplicate of another one?   Should I answer it? Should I downvote it? Should I comment? Should I edit the question to indicate it's a duplicate? If I can, should I (vote to) close the question? What happens when I vote to close as duplicate? Or: Why did a comment with my name on it just appear? Should I flag it for moderator attention? What about similar or related questions?


Basically I need to convert centimetres to inches which I am trying to do by diving the area in centimetres by 2.54.   But I just cannot get this to work.   echo "please enter width and then height"  read width read height  area=$(($width * $height)) inchesarea=$((area / 2.54))  echo $area echo $inchesarea   Should I be using bc for this?

Using echo "20+5" literally produces the text "20+5".  What command can I use to get the numeric sum, 25 in this case?  Also, what's the easiest way to do it just using bash for floating point? For example, echo $((3224/3807.0)) prints 0 :(.  I am looking for answers using either the basic command shell ('command line') itself or through using languages that are available from the command line.


The invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space ${\displaystyle \mathbb {R} ^{n}}$. As a consequence, it follows that if $U$ and $V$ are homeomorphic subsets of $\mathbb {R} ^{n}$ and $U$ open then $V$ is open. I would like to show that the last statement holds also for manifolds. (this was suggested by Lee Mosher(thank you!) in one of my posts). Let $X$ be a manifold and let $U$ and $V$ be homeomorphic subsets of $X$. To show that if $U$ is open in $X$ then $V$ is open in $X$. My attempt is as follows: Let $h:V \to U$ be a homeomorphism and pick $y \in V$, then $x=h(y)$ for some $x \in U$. Take coordinate charts, $(W_y,\psi)$ around y and $(W_x,\phi)$ around x. Then, $W_y \cap V \tilde{\rightarrow} h(W_y \cap V ) $ and $h(W_y \cap V )$ is open in $U$ and so it is open in $X$. So there is a chart $(W'_x,\phi')$ around x with $W'_x \subset h(W_y \cap V ) $ and $W'_x$ homeomorphic to a ball $B_x$ in $\mathbb {R} ^{n}$. Hence, it follows that, $$B_x \tilde{\rightarrow} W'_x \hookrightarrow h(W_y \cap V ) \tilde{\rightarrow} W_y \cap V \tilde{\rightarrow} \psi(W_y \cap V) $$ Let's denote by $Z_y$ the image of $B_x$ under the above composition. Then, $Z_y (\subset \mathbb {R} ^{n})$ is homeomorphic to $B_x$. Hence, by the invariance of domain in $\mathbb {R} ^{n}$ it follows that $Z_y$ is an open subset of $\mathbb {R} ^{n}$. So one can choose a ball $B_y$ around $\psi(y)$ contained in $Z_y$. Then, $\psi^{-1}(B_y)$ contains $y$, it is open in $W_y$ and so it is open in X. Finally, $\psi^{-1}(B_y)$ is contained in $V$ and so $V$ is open. Hope this is correct! I would like also to see other solutions to this question

This is corollary $2B.4$ in Hatcher's Algebraic Topology , state as following :   If $M$ is a compact $n-$ manifold and $N$ is a connected $n-$ manifold then an embedding $h : M \to N$ must be surjective , hence a homeomorphism .  The first , $h(M)$ must be close since $h(M)$ is compact and $N$ is Hausdorff . But I don't know why $h(M)$ is open just from invariance of domain theorem ? If we have $h(M)$ is also open then by connectedness we have $h(M)=N$ hence a homeomorphism .   To be more specific , I'm trying to prove that any continuous map $f : S^{n} \to \mathbb{R^{n}}$ can not be injective ( don't use Borsuk-Ulam theorem ) .


At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to translate?  This question assumes that the body is in empty space and unattached.

If a sphere has a torque vector coming out of it at point A, would the sphere rotate about its center or the axis of the torque vector?


I use the program Tiled to create tile maps, which export to the TMX format. However, I can't find a way to load them into my LWJGL game. I don't want anything that renders them automatically, I want to render them myself. I just need a way to read the data required for me to know where and what to draw in my game. Are there any libraries or code I can use to accomplish this?


I'm learning C programming now (I'm new to it), and I'm trying various things as well to understand how things work. So, I'm well aware that the following code isn't proper code; but I still tried it out to understand how it would be compiled:  #include <stdio.h> #include <stdlib.h>  int {     printf("I think C will give me %d %d %d %d %d.", 20);     return 0; }   And I'm getting this in the command line:   I think C will give me 20 8 108 108 2. Process returned 0 (0x0)   execution time : 0.234 s Press any key to continue.   Where from the numbers 8, 108, 108 and 2? How were they generated?  I'm just trying to understand how it works. Thanks.

I've just encountered a weird problem, I'm trying to printf an integer variable, but I forgot to specify the variable name, i.e.  printf("%d");   instead of  printf("%d", integerName);   Surprisingly the program compiles, there is output and it is not random. In fact, it happens to be the very integer I wanted to print in the first place, which happens to be m-1.  The errorneous printf statement will consistently output m-1 for as long as the program keeps running... In other words, it's behaving exactly as if the statement reads  printf("%d", m-1);   Anybody knows the reason behind this behaviour? I'm using g++ without any command line options.  #include <iostream> #define maxN 100 #define ON 1 #define OFF 0  using namespace std;  void clearArray(int* array, int n); int fillArray(int* array, int m, int n);  int main() {     int n = -1, i, m;     int array[maxN];     int found;      scanf("%d", &n);      while(n!=0)     {         found=0;         m = 1;         while(found!=1)         {             if(m != 2 && m != 3 && m != 4 && m != 6 && m != 12)             {                 clearArray(array, n);                 if(fillArray(array, m, n) == 0)                 {                     found = 1;                 }             }             m++;         }          printf("%d\n");          scanf("%d", &n);     }      return 0; }  void clearArray(int* array, int n) {     for(int i = 1; i <= n; i++)         array[i] = ON; }  int fillArray(int* array, int m, int n) {     int i = 1, j, offCounter = 0, incrementCounter;      while(offCounter != n)     {         if(*(array+i)==ON)          {             *(array+i) = OFF;             offCounter++;                }         else          {             j = 0;             while((*array+i+j)==OFF)             {                 j++;             }             *(array+i+j) = OFF;             offCounter++;                    }         if(*(array+13) == OFF && offCounter != n) return 1;         if(offCounter ==n) break;          incrementCounter = 0;                while(incrementCounter != m)         {             i++;             if(i > n) i = 1;             if(*(array+i) == ON) incrementCounter++;          }            }      return 0; }


When a Debian Developer uploads a package to sid (not a new package, just a version update to an existing one), how long does it take for that package to be merged into Ubuntu's repositories? Does it depend on the Ubuntu repository it is destined for (e.g. core/universe)? Does it depend on whether there have been Ubuntu-specific changes in the past? From what I have read, it seems that there is a cron job on the Ubuntu package servers which regularly pulls packages from Debian, but I haven't been able to find any information about how frequently it runs. (I have also seen that there is a Debian Import Freeze window when this is commented out - how would I know when this is?)

Why are packages in the official Ubuntu repositories older than the latest (upstream) versions from Debian Sid, PPAs, the authors, etc.?


The android, Bishop, in the Aliens movie hibernates with the rest of the Sulaco crew for the 17 day voyage. Does he need to sleep?  Unlike the Alien movie where Ash hibernated because was merely pretending to be human, Bishop does not need to pretend. The Weyland-Yutani representative, Carter Burke, implied it is company policy to include an android among the crew.     BURKE: "It's just common practice. We always have a synthetic on board."   Why did Bishop sleep?

In Aliens, it appears that Bishop awakes from being frozen. But why should he have been frozen in the first place? I can understand Ash being frozen, this was necessary to allay fears that he was actually an android. There was no need for such subterfuge in Aliens, since it is readily understood (with no issues) that Bishop was an android (until Ripley found out).


Let $\gamma_1, \gamma_2 : [0,1]\to\mathbb{C}$ closed paths and $w\in\mathbb{C}$ a point, so that $$\vert\gamma_2(t)-\gamma_1(t)\vert < \vert\gamma_1(t)-w\vert$$ on $[0,1]$. Prove that $$n(\gamma_1,w)=n(\gamma_2,w)$$   Hint: Use the path $\gamma(t)=\frac{\gamma_2(t)-a}{\gamma_1(t)-a}+a$.   I found some help with homotopy but we actually didn't learned something about this topic. We only get the definition of winding numbers $$n(\Gamma, z_0)=\frac{1}{2\pi i}\int_{\Gamma}\frac{d\zeta}{\zeta-z_0}$$  My first idea was, that I use this definition with $\gamma_2$ and solve the integral to get the line integral for $\gamma_1$. Unfortunately I don't know how to use the inequality given in the task. Any hints? Thank you very much!

Let $ w \in \Bbb C $, and let $ \gamma, \delta : [0,1] \rightarrow \Bbb C $ be closed curves such that for all $ t \in [0,1], |\gamma(t) - \delta(t)| < |\gamma(t) - w| $. By computing the winding number $n_\sigma(0)$ about the origin for the closed curve $\sigma(t) = (\delta(t) - w)/(\gamma(t) - w) $, show that $n_\gamma(w) = n_\delta(w)$.  This seems intuitively clear to me. (Informally, the inequality tells us that $\delta$ and $\gamma$ can never be on "opposite sides" of $w$, and hence their winding numbers must be equal. Making this rigorous isn't enough, however, since I need to use the winding number of $\sigma$ about 0.  I can also show that $n_\sigma(0) = n_\gamma(w) - n_\delta(w)$ (fairly elementarily), so it remains to show that $n_\sigma(0) = 0$. This is the bit that I'm stuck on.  Can someone give me a (small) hint (not a major hint)? If I still can't get anywhere, then I'll probably ask for a larger hint!  There is also a second part to this question - dependent on whether I'm able to do the first part with a hint, I may well update this question to include the second part.  (This is an example sheet question - completely non-examinable.)  Thanks! :)


Is there a way of inserting Ordnance Survey grid reference in a print composer? I know that a grid can be created but I don't wish to insert a grid, I just to need to include the eastings and northings as a text string in the title block.

I am using QGIS v3.12 and projection EPSG:27700 - British National Grid.  I am trying to add a label to my map layout which will give the grid reference of the centre of the map as a UK 8 digit grid reference ( e.g. "AB123456" ).  So far I have managed to get the x and y coordinates using the expression:   Grid reference at map centre: [%round(x (map_get (item_variables('Map1'), 'map_extent_center')),0)%] , [%round(y (map_get (item_variables('Map1'), 'map_extent_center')),0)%]   Is there any function available in QGIS that can translate these coordinates into the required format?   Sorry my coding skills are not that great!


I happend to change my whole /usr/ dir files to -rwxr-xr-x with command "sudo chmod 775 -R /usr/" now I firguire out that some special binary files like "su" "chkpaswd"and "sudo" should have the privilege of setuid ,and I have use chmod to return them back to fix same authority problem. But still have some mistory trouble like I cant use dolphin to mount the dev automaticly or use kwrite to rewrite some files by input passwd.It just says u dont have right to operate:Not authorized to perform operation and now ,I cant just open the appimage because of Cannot mount AppImage, please check your FUSE setup. You might still be able to extract the contents of this AppImage if you run it with the --appimage-extract option. See  for more information open dir error: No such file or directory I use debian 10 base os ubuntu 20.04 ,and this pic is what i have in /usr/. I did this dangerous operation because I want to use CAE on oridinary user. So ,can some handsome guys to told me are there any special files like "sudo" in dir /usr/ that I dont know? Thanks!!QwQ

I accidently ran  sudo chmod 755 -R /   instead of  sudo chmod 755 -R ./   I stopped it after few seconds, but now there is some problems such as  sudo: must be setuid root   How can I revert permissions back?


Let $L:\mathcal{C} \to  \mathcal{D}$ and $R:\mathcal{D} \to  \mathcal{C}$ to adjoint functors, therefore for each $X \in \mathcal{C}, Y \in \mathcal{D}$ we have natural bijections $$Hom_{\mathcal{D}}(L(X), Y) \cong Hom_{\mathcal{C}}(X, R(Y)) $$  My question is how to see that these induce natural transformation $\eta: id_{\mathcal{C}} \to RL$ (resp. $\epsilon: id_{\mathcal{D}} \to LR$)?  Here I don't see how to use the fact that $R$ and $L$ are adjoint to see that for arbitrary morphism $f: X \to X'$ in $\mathcal{C}$ following diagram commutates (therefore "natural transformation"):  $$ \require{AMScd} \begin{CD} X  @>{\eta_X}  >> RL(X)   \\ @VVfV  @VVRL(f)V   \\ X' @>{\eta_{X'}}>> RL(X')  \end{CD} $$

I am reading Homological Algebra by J.J. Rotman and am unable to do this problem.  Given an adjoint pair $(F,G)$ where $F : \mathcal{C} \to \mathcal{D} $ and $G : \mathcal{D} \to \mathcal{C} $ are two covariant functors, we can obtain a natural transformation $ \eta : \mathbb{1_{\mathcal{C}}} \to GF $.  I understand the definition of $\eta$ but am unable to prove that the transformation is natural. Couls someone please help me prove that for $f \in Hom (C,C')$, $GF(f)\eta_C=\eta_{C'}f$ ? Thanks !


Using the Nano text editor, I'm trying to save and exit a file.  I already have the file named.  I click Ctrl+X to exit. And then I click Y because I want to save the file. It asks for file to write, I pressed Enter to use the default name because its already named.  The problem is I get this message.   [Error writing /filename: Permission denied]   What am I doing wrong?

Sometimes, a graphical text editor like gedit or kate cannot be used (because you're in a virtual console for example). Luckily, there are text editors for the terminal. An easy one is nano, but I cannot understand how to work with it.  If I start nano by running nano, the bottom text is supposed to help me but all I see are things like ^G Get Help    ^O WriteOut.   How can I open text files for editing? How can I save the file? How can I quit the editor without saving the changes? How to edit? I heard that you've to enter some commands to begin editing in vi, is this true for nano too? Sometimes, if I manage to open a file, the text is unreadable due to its colors. How can I disable these colors? (see the image below) In the some files, lines are truncated because those do not fit in the screen. How can I prevent that from happening? (see the image below)


private List<Manufacturer> productManufacturer = new LinkedList<Manufacturer>();  I am not able to understand why <> this symbol is here and Manufacturer inside it to define a LinkedList in Java.

Can someone explained, as detailed as possible, the differences between the following types?  List List<Object> List<?>   Let me make this more specific. When would I want to use  // 1  public void CanYouGiveMeAnAnswer(List l) { }  // 2 public void CanYouGiveMeAnAnswer(List<Object> l) { }  // 3 public void CanYouGiveMeAnAnswer(List<?> l) { }


I'm studying generic where constraint and I bumped into this and get stuck. I've tried replicating the code by my own classes but I get "Inconsistent inaccessibility".  //this is the reference study class public class MainView<T> : System.Windows.Window where T : INotifyPropertyChanged, new(){}  //my own interface ITest{}  class B : ITest {     public B()     {      } }  public class MyClass<T> : B where T : ITest, new() {  }   I couldn't figure this out. What is there in the reference study class? How can I do the same signature with my own defined classes and interface?

Whats wrong with the following c# code? Compiler reports this error:  Inconsistent accessibility: parameter type 'ClassLibrary1.Interface1' is less accessible than method 'ClassLibrary1.Class1.Class1(ClassLibrary1.Interface1)'  with the following code:  interface Interface1<T> {     bool IsDataValid();     /* Other interfaces */ }  public class Class1<T> {     public Interface1<T> interface1;      public Class1(Interface1<T> interface1)     {         this.interface1 = interface1;     }  }   I've since designed my code differently using inheritence to but if anyone could tell me what the above is wrong I'd greatly appreciate it.


Pretty simple, for $a,b \in \mathbb R$, show that $|a-b|<\frac{|b|}{2}$ implies $\frac{|b|}{2}<|a|$.  I can see this graphically on the number line, but I can't seem to show it algebraically. I'm think it involves the triangle inequalities:  $$|x+y|\le|x|+|y|$$ $$|x-y|\ge||x|-|y||.$$

Edit: I was trying to find a general form of the question but I will just put the real question.  My textbook says |a-b|<|b|/2 implies |a|>|b|/2. I don't see how and the text doesn't provide a proof.


Both packages duplicity and python-gi are no longer available in the repositories. I'm using Ubuntu 16.04 LTS. Can anyone suggest a solution? Thank you in advance.  ~$ sudo apt-get install duplicity python-gi Reading package lists... Done Building dependency tree        Reading state information... Done Package python-gi is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  Package duplicity is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'duplicity' has no installation candidate E: Package 'python-gi' has no installation candidate

What does the above Error mean? What is an installation candidate?  I was trying to do  sudo apt-get install munin-memcached     and I get this message:  Reading package lists... Done Building dependency tree        Reading state information... Done Package munin-memcached is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package munin-memcached has no installation candidate   I googled for the problem and someone said to do a apt-get upgrade but it still did not solve my problem.


i used the following code so to persist the directory change after the program exits but the drawback is that it opens a new sub shell , so each tim a run it a new subshell is opened   import os, subprocess newpath="/usr/local/www/nginx" oschdir(newpath) subprocess.call(['bash'])   is there a wayout , i want to do this in FreeBSD 10.1,python3 , irrespective of the shell .  Is there a way out.

cd is the shell command to change the working directory. How do I change the current working directory in Python?


The other day I was in my car and though I'm a little unsure about what candy bar wrapper I used but I believe I moved my screen using a candy bar wrapper.  I keep thinking it was a York Peppermint Patty wrapper, but I could be wrong about that, either that or a Laura Bar wrapper.  I'm told an iPhone has a Capacitance Touch Screen which is different from earlier models of touch screen which relied on clicking or something else, but it's clearly not the same thing.  Using the old screens you could use a paper clip or whatever to interact with the phone, but with an iPhone it's the tip of your finger, and apparently a few other materials.   In particular I'm interested in being able to tap with it.

I know that tapping on the screen with an object doesn't cause any reaction in the user interface (e.g. it doesn't cause a click of a button shown from an application). To what is the iPod's screen sensitive, and what can I use to replace my fingers?  The problem I am trying to resolve is that, using my finger to play a game, I don't see part of the screen, and my finger hits something that causes the game to end (you know, those little bombs that are launched in the play field when you are trying to slice fruits).


My girlfriend and I am in the same college, but different major. She is a law school master student.  She just graduated from the master program and wanted to transfer to juris doctor in the same college.  I am wondering if it is appropriate for me to write the dean of law school a letter in support of her application.  Also, I am not sure what to write in the letter if appropriate. I would imagine saying that I would love to be able to continue studying with my girlfriend in the same college and things like that. Would you have any suggestions?  Thank you in advance!

When browsing their web sites, I noticed that apart from those listed academic requirements by different universities, they all require at least two reference letters from applicants, but they did not officially state that who should write those recommendation letters.Although I have collected several recommendation letters from my former teachers, I found it was quite hard to reach my former teachers whom I had not contacted for many years.It almost took me two months from the day I sent out my first email to the day I got enough recommendation letters from my former teachers. It has been puzzling me why the recommendation letters should be written by school lecturers or professors.The people who know you best are business partners, your close friends, family members like your parents, siblings, why they are not qualified to write the recommendation letters for me?


Is zenmap available for Ubuntu 20.04.1 LTS with nmap 7.80? I've already try the instruction at the following link:  but packages are not available.

I've just changed my primary computer from a laptop running XFCE and 19.10 to a desktop running Gnome 3 and 20.04 overall I'm very impressed.  One of the tools I tend to use all the time is Zenmap but I can't locate it in either the software catalogue or via running apt in a terminal window, so I assume it's been removed.   So   What's the rationale for this? Are their issues with Zenmap I should be aware of? Is there a simpler way of installing then the way outlined on Nmap's site (i.e.  ) Is there an alternative application that will let me port scan my LAN (IP address / open TCP port is a must-have, description of service and UDP ports are a nice to have since I'm generally just checking if a known port can be seen)


I have this Xml file  and I want to read same specific colums, there are currency online rates and  want to read only the 3 of them, how can I do that with php? I try this but with no results  <?php $file = "feed.xml"; $xml = simplexml_load_file($file);  foreach($xml -> item as $item){     echo $item[0]; } ?>

I'm currently using  but it sometimes falls over when the RSS or Atom feed isn't well formed. Are there any other options for parsing RSS and Atom feeds with PHP?


Trying to modify the view of a directroy, I prefer this view:    But I hate the right part where we see the info on each app.  Is it possible to modify it to be on default like this (without the information part on the right):

When I open a finder window I have this large side bar on the right hand site that provides some outline file info, size, modified date etc.  How can remove this sidebar?   My mac is running OSX 10.14.x (latest updates installed.)


My question is about the distinction between certain kinds of phase transitions. I understand what the difference between first and second order ones are. What is the difference between non equilibrium and equilibrium phase transitions?

I have come across the term Non-equilibrium phase transition. And unfortunately I can't find any examples of such a phenomenon. What examples of nonequilibrium phase transitions are known? Are there some analogies with "Ising-like" models, which clarify the main peculiarity of such transitions?  How to distinguish such a transition from equilibrium phase transitions?


I remember reading this one in an old sci-fi magazine from the 1970s or early 80s. I'm sort of fuzzy on the details, but this is how it went, as best I can recall:     A lone astronaut is on board a small space station at the edge of our solar system.  He might be in orbit around one of the gas or ice giant planets. His purpose is to be there when an alien species arrives to deliver some sort of biological substance that has some beneficial effect for mankind.   The previous astronaut with this duty cracked up, something the current guy refuses to do. Late in the story, he realizes that the substance delivered by the aliens has a sinister side effect, and the aliens are actually slowly conquering man as a result.   Unfortunately, the nature of his duty has somehow warped him in the same way as his predecessor.  He tries to write down what he's learned, but it's all alien scribbles that no one would understand. In a final act of defiance, the astronaut somehow crashes his station or ship into the alien one.  I think the atmosphere of a gas giant or frozen moon something begins pouring into the station.  The man is going to die, but he believes the aliens will be blamed as an aggressor, and thus save mankind.  Something like that.

Short story read in the 60's or 70's, an astronaut has to enter an alien ship and collect the tears/sweat? of an alien to use as a wonder drug for humans. The alien has some sort of presence which affects the mental state of any human near it.


Prove $\lim_{x \to c}{x^2}=c^2$ where $c$ is a real number with the $(\epsilon, \delta)$ definition. I know that you need to assume a value for $\delta$. However, I don't understand how that one assumption, which only represents one case, implies that the limit is always true. Please explain as you prove the limit.

Prove that $\lim_{x\to 2}x^2=4$ using $\epsilon-\delta$ definition.   By the mean of $\epsilon-\delta$ definition, $|x-2|\le \delta,|x+2|\le \delta+4$  then $|x-2||x+2|\le \delta(\delta+4),|x^2-4|\le \delta^2+4\delta$.  Assign $\epsilon=\delta^2+4\delta,|x^2-4|\le\epsilon$.  Q.E.D.  Is this method correct? If yes, why I always see people do this by putting $\delta = \min(1,\epsilon/5)$...?  Thanks.


I can find no String.Reverse() in .net that actually returns a string. (Any reason why there is none?) What would the most efficient code (least temp objects created etc) for reversing a string in .net be?

I've just had to write a string reverse function in C# 2.0 (i.e. LINQ not available) and came up with this:  public string Reverse(string text) {     char[] cArray = text.ToCharArray();     string reverse = String.Empty;     for (int i = cArray.Length - 1; i > -1; i--)     {         reverse += cArray[i];     }     return reverse; }   Personally I'm not crazy about the function and am convinced that there's a better way to do it. Is there?


Are there other ways to say Take your time?  I know:   Whenever you can It's not (terribly) urgent No rush   Any other ideas?

My manager asked me to finish the project as early as possible   Here there is no fixed deadline available but the manager wants me to finish the project soon. Consider the case where there is a deadline but I can take as much time as I want before the deadline to finish the project. In this case, is it appropriate for a person to say, "You can finish the project as late as possible (meaning, you have time to do), but do it before the deadline expires"?  I am looking for an exact opposite phrase for as early as possible. If it is not there, is there a phrase which can capture what I have mentioned in the above mentioned paragraph?


I know $\mathcal C([0, 1])$ has all maximal ideals of the form $M_p=\{f\in \mathcal C([0, 1]) : f(p) =0,\  p\in [0, 1] \}$. My question is little bit different.  If I replace $[0, 1]$ by $(0, 1)$  then how can I show that this ring has infinitely many prime ideals not of the form $M_p$ ?

Are there any prime ideals in the ring $C[0,1]$ of continuous functions $[0,1]\rightarrow \mathbb{R}$, which are not maximal? Perhaps, I duplicate smb's question, but this is an interesting problem! Could you give me any hint or give a link to some literature?


I am trying to return an integer if particular string is true. (For this I do not want to use an array).     public String calcNextDay()   {      if (day == "Sunday"){       return 0; // If day is Sunday return 0      }else if (day == "Monday"){       return 1; // If Day is Monday return 1      }else if (day == "Tuesday"){        return 2; // If day is tuesday return 2      }else if(day == "Wednesday"){        return 3; // If day is Wednesday return 3      }else if(day == "Thursday"){         return 4;// If day is Thursday return 4      }else if (day == "Friday"){          return 5;// If day is Friday return 5      }else if(day == "Saturday"){         return 6;// if day is Saturday return 6           }           }   I have also tried this, but am getting an error with the return dayValue stating it can not be converted to String (even though I do not want to turn it to a string)     public String calcNextDay()   {      int dayValue = 0;      if (day == "Sunday"){      dayValue = 0; // If day is Sunday return 0      }else if (day == "Monday"){      dayValue =1; // If Day is Monday return 1      }      return dayValue;      }   What am I doing wrong?   Based on the comments I changed some code to   Public String calcNextDay()   {      int dayValue = 0;      if (day.equals("Sunday")){         dayValue = 0;      }else if (day.equals("Monday")){         dayValue = 1;      }else if (day.equals("Tuesday")){         dayValue = 2;       }return dayValue;           }   error: incompatible types: int cannot be converted to String                     }return dayValue;  Thank you, I got passed that problem and then I get to the error Day.java:178: error: non-static variable dayValue cannot be referenced from a static context          System.out.println("Your day is stored as " + testday.setDay() + dayValue);                                                                           ^ 1 error  My main() is a static, but my dayValue is not

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I'm trying to append a value to a specific list inside a list. To me, the obvious way to do it looked something like this: groups = [[]]*5  for (idx,_) in enumerate(groups):     groups[idx].append(idx)  print(groups)  however, this code results in this [[0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4]]. When I run this I get what I was expecting from the previous code block: groups = [[]]*5  for (idx,_) in enumerate(groups):     groups[idx] = groups[idx] + [idx]  print(groups)  [[0], [1], [2], [3], [4]] so why does appending to an indexed list append to all lists in the parent list?

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


What's the difference between Explicitly implement the interface and Implement the interface.   When you derive a class from an interface, intellisense suggest you to do both.  But, what's the difference?

What are the differences in implementing interfaces implicitly and explicitly in C#?  When should you use implicit and when should you use explicit?  Are there any pros and/or cons to one or the other?    Microsoft's official guidelines (from first edition ) states that using explicit implementations are not recommended, since it gives the code unexpected behaviour.  I think this guideline is very valid in a pre-IoC-time, when you don't pass things around as interfaces.  Could anyone touch on that aspect as well?


I found these two sentences and I want an explanation for them to illustrate why they go like:         A number of boys were absent.      Although the subject is singular, but the sentence is considered as plural?         three eggs is plenty       And in this example, the writer used is instead of are.

Should I use is or are in this sentence?     100 apples are/is considered as a large number of apples.


Is there a built-in Python function such that with  vals=[1,2,3,4,5]   then foo(vals,2) gives   [[1,2],[3,4],[5]]    I am looking for the behaviour that Wolfram Language gives with   Partition[Range@5, UpTo@2]    {{1, 2}, {3, 4}, {5}}

I have a list of arbitrary length, and I need to split it up into equal size chunks and operate on it. There are some obvious ways to do this, like keeping a counter and two lists, and when the second list fills up, add it to the first list and empty the second list for the next round of data, but this is potentially extremely expensive.  I was wondering if anyone had a good solution to this for lists of any length, e.g. using generators.  I was looking for something useful in itertools but I couldn't find anything obviously useful. Might've missed it, though.  Related question:


I was asked for the probability of having at least one card from each type (hearts/spades/etc.) in a 5 cards hand chosen randomly from a 52 cards normal deck. my solution was $\frac{{{13}\choose{1}}^4{{48}\choose{1}}}{{52}\choose{5}}$ as in, choose one card from each type and then one from the 48 cards left, then divide it all by all the possible hands. my solution is wrong, and I don't understand why, can someone please point out where have I gone wrong?

If each suit is represented then we will have two cards from one suit and one card each from the remaining suits. So I am counting the ways this can happen like so -  ${52 \choose 1}$ ways of selecting the first card.  ${12 \choose 1}$ ways of selecting a card from the same suit as the first.  ${13 \choose 1}$ ways of selecting a card for each of the 3 remaining suits.  So I have -  $${52 \choose 1}{12 \choose 1}{13 \choose 1}{13 \choose 1}{13 \choose 1}$$  Then I have the sample space as $52 P 5$ as we are counting with regard to order on the numerator so we need to do the same for the denominator.  So I have $$\frac{{52 \choose 1}{12 \choose 1}{13 \choose 1}{13 \choose 1}{13 \choose 1}}{52P5}$$  Does that look correct?


After recently installing 12.04 through Wubi, Windows 7 is now not booting, not even in safe mode. There is one folder on the C drive that I need a copy of which I forgot to backup before installing Ubuntu, how do I access this through Ubuntu?

I'm new to Ubuntu, so can any of you give me a guide of how I can access my windows 7 files from my Ubuntu 12. I installed it using Wubi. Looked around everywhere but failed.


Here is my code  var destObj= Object.assign({}, sourceObj);     destObj.fields.forEach(item => {         if (item.fieldType == 'MULTI_SELECT_LOV') {             let newValues = [];             item.selectedValue.forEach(val => {                 newValues.push(val.dataName);             });             item.selectedValue = newValues;         }     })   after completion of code execution the both 'sourceObj' and 'destObj' are equal.  My intention is do not effect changes which are made on 'destObj' should not reflect in 'sourceObj'.

What is the most efficient way to clone a JavaScript object? I've seen obj = eval(uneval(o)); being used, but . I've done things like obj = JSON.parse(JSON.stringify(o)); but question the efficiency.  I've also seen recursive copying functions with various flaws.  I'm surprised no canonical solution exists.


Today I installed Ubuntu alongside windows 8 (option was first, without making partition). Everything was Ok but when the system restart there was no option to choose Ubuntu. By default it always start with my existing OS 8. Please Help me.  Thnx Lalit Kumar

I am using ubuntu 12.04. Can I install windows 7 and use it as a dual boot system. When I tried this earlier windows doesn't detect ubuntu.Is there any solution for this.


We were given the following question in our circuit theory class:      Find the relation between \$R,L,C\$ such that the net reactance across   terminals \$A\$ and \$B\$ is \$R\$.          – Schematic created using   I followed the generic method (equivalent parallel reactance):  $$\frac{1}{R}=\frac{1}{R+j\omega L} + \frac{1}{R+\frac{1}{j\omega C}}$$ to get the required relation (after eliminating \$\omega\$).  Upto that is okay. But I'm confused about something:  Suppose the system is inside a black box, with only terminals \$A\$ and \$B\$ outside. In that case how can we possibly distinguish between a black box containing this circuit vs. a black box which contains only a resistance \$R\$?

Two black boxes display the same impedance at all frequencies.  The first contains a single 1 Ohm resistor.  Each end is connected to a wire, so that two wires protrude from the box.  The second box looks identical from the outside, but inside there are 4 components.  A 1 F capacitor is in parallel with a 1 Ohm resistor, and a 1 H inductor is in parallel with the other 1 Ohm resistor.  The RC combo is in series with the RL combo, as shown in the figure   The boxes are painted black, unbreakable, impervious to x-rays, and magnetically shielded.     Demonstrate that the impedance of each box is 1 Ohm at all frequencies.     What measurement would allow one to determine which box contains the single resistor?


I am a new user of precise pangolin and learning to use the terminal. I just wonder whether there is any easy command/combination of commands to open an application (LibreOffice Writer, for example) via terminal, just like we use sudo apt-get install <<packagename>> to install an application.

How do I run a program in the background of a shell, with the ability to close the shell while leaving the program running? Lets say my UI is having problems or for some reason, I need to boot up a program from the terminal window, say, nm-applet:  nm-applet   When it's started, it occupies the foreground of the terminal window.  Is there any simple way to run the program in the background without needing to leave the terminal open or have it occupy the whole terminal?  On that note, I did find a way to run programs from the terminal and have it allow for other inputs, by appending an ampersand (&) to the command as such:  nm-applet &   But this isn't much use as any processes started in the terminal are killed once the terminal is closed.


I recently installed ubuntu-server on a VM and later on increased the virtual hard disk size from 10Gb to 70Gb. Here is the result of lsblk. user@ubuntuserver:/$ lsblk NAME                      MAJ:MIN RM  SIZE RO TYPE MOUNTPOINT fd0                         2:0    1    4K  0 disk  loop0                       7:0    0 30.3M  1 loop /snap/snapd/9279 loop1                       7:1    0   55M  1 loop /snap/core18/1880 loop2                       7:2    0 70.6M  1 loop /snap/lxd/16922 loop3                       7:3    0 55.3M  1 loop /snap/core18/1885 loop4                       7:4    0 29.9M  1 loop /snap/snapd/8542 loop5                       7:5    0 71.3M  1 loop /snap/lxd/16099 sda                         8:0    0   70G  0 disk  ├─sda1                      8:1    0    1M  0 part  ├─sda2                      8:2    0    1G  0 part /boot └─sda3                      8:3    0    9G  0 part    └─ubuntu--vg-ubuntu--lv 253:0    0    9G  0 lvm  / sr0                        11:0    1 1024M  0 rom   sr1                        11:1    1 1024M  0 rom    As you can see 70Gb are available on sda but only 9Gb are assigned to sda3 partition where the ubuntu-server resides. I am wondering how I can allocate the rest of the available space of sda to sda3 through the terminal (as I have no access to the Esxi server that actually manages the VMs). Note that ubuntu-server does not have a GUI, I can only connect to it through ssh to a root user, hence it has to be done using commands.

I recently installed an Ubuntu-server (20.04) on VM initially giving it only 10Gb RAM. Soon enough, I noticed that the program I need to install (Gluu-server) requires at least 40Gb. Hence, I proceeded to power off the VM and extend the memory to 70Gb. Running lsblk indeed shows that sda partition is 70Gb.  But sda3 on which the actual OS is installed has only 9Gb of free space. user@ubuntuserver:/$ lsblk NAME                      MAJ:MIN RM  SIZE RO TYPE MOUNTPOINT fd0                         2:0    1    4K  0 disk  loop0                       7:0    0 30.3M  1 loop /snap/snapd/9279 loop1                       7:1    0   55M  1 loop /snap/core18/1880 loop2                       7:2    0 70.6M  1 loop /snap/lxd/16922 loop3                       7:3    0 55.3M  1 loop /snap/core18/1885 loop4                       7:4    0 29.9M  1 loop /snap/snapd/8542 loop5                       7:5    0 71.3M  1 loop /snap/lxd/16099 sda                         8:0    0   70G  0 disk  ├─sda1                      8:1    0    1M  0 part  ├─sda2                      8:2    0    1G  0 part /boot └─sda3                      8:3    0    9G  0 part    └─ubuntu--vg-ubuntu--lv 253:0    0    9G  0 lvm  / sr0                        11:0    1 1024M  0 rom   sr1                        11:1    1 1024M  0 rom    I tried to install gluu server and I get this message: root@localhost:/install/community-edition-setup# ./setup.py Detected OS ubuntu 20 Warning: Available free disk space was determined to be 2.9 GB. This is less than the required disk space of 40 GB.  I am kinda confused. Why is the "available free disk space determined to be only 2.9 GB"? Is this a partitioning issue and how can I fix that?


I am complete rookie to Javascript, jQuery and JSON. For the most part the JSON data is displaying correctly. I have a list of JSON array comments that is rendered in HTML. I would like to include a different background color for list items. I realize that Mustache is a logicless template but can this be achieved. Below are the codes. Any advise will be very much appreciated. Thanks in advance!  HTML:

       JSON data:          {     "comments": [     {      "name": "John Smith",      "comment": "Would like background in light gray",      "timestamp": "18-11-2013"      },      {      "name": "Jane Doe",      "comment": "Would like background to be dark gray",      "timestamp": "26-11-1991"      },      {      "name": "Amy Lang",      "comment": "Would like background in light gray",      "timestamp": "30-5-1991"      },     {      "name": "Jessica Rabbit",      "comment": "Would like background to be dark gray",      "timestamp": "23-5-1988"      }      ] }

I have a list, and each item is linked, is there a way I can alternate the background colors for each item?

Link 1

Link 2

Link 3

Link 4

Link 5


I am learning a java language.I have a question , how enum is type safe in java.  public enum Direction {EAST,WEST,NORTH,SOUTH;}   How enum Direction is type safe? Please help me.


Is there any way to emulate the display of a pre element via CSS?  For example, can I keep the whitespace intact in this div by using a CSS rule?  <div class="preformatted">    Please procure the following items:      - Soup     - Jam     - Hyphens      - Cantaloupe </div>

Is it possible to to change a <span> tag (or <div>) to preformat its contents like a <pre> tag would using only CSS?


I'm new to Blender.  I'm running the latest (2.74).  I have made a complex scene, with a camera following a Curve Path.  I would simply like to stop the camera from moving, from time to time, to allow the viewer to take a good look at whatever the camera is pointing at, then continue along the path.  I have searched and searched and tried a few tutorials, but nothing works for me.  I'm missing a simple procedure, I know!  I've read about doing animation all with keyframes instead of following a path, which seem to make it easier to have control, but I don't want to re-invent my complex path.  I have tried messing the inserting keyframes manually into the timeline and then editing them in the Dope Sheet but failed miserably.

Im making a animation in blender that requires the camera to change speeds while moving along a path. I'm using the Curve/Path for the path. I need the camera to move at a certain speed going between 2 places, and then slow down while moving around something its focusing on.


Suppose I have an n-dimensional dataset and its points are roughly in the shape of an n-dimensional horseshoe or something along those lines. Using euclidian distance might be a bad idea, since points on the tip of the horseshoe would the appear close, although this wouldnt make any sense given the shape of the data.  It should be possible to find something like a (lower dimensional) topology and a meaningful metric on it, that uses the intrinsic topology of the data.  A couple of years ago, I had a longer discussion about that sort of thing, but i can't remember what it was called...

I am trying to understand the differences between the linear dimensionality reduction methods (e.g., PCA) and the nonlinear ones (e.g., Isomap).  I cannot quite understand what the (non)linearity implies in this context. I read from  that     By comparison, if PCA (a linear dimensionality reduction algorithm) is   used to reduce this same dataset into two dimensions, the resulting   values are not so well organized. This demonstrates that the   high-dimensional vectors (each representing a letter 'A') that sample   this manifold vary in a non-linear manner.   What does     the high-dimensional vectors (each representing a letter 'A') that   sample this manifold vary in a non-linear manner.   mean? Or more broadly, how do I understand the (non)linearity in this context?


I work with QGis 2.18.1 in Austria and need the city boundaries of Podgorica which is located in Montenegro.   Do you know where I can get or download it for free?

Does anyone know any sources for free European city boundary data?


I am trying to prepare an Ubuntu workstation for a colleague, which for storage has both a smaller SSD and also a larger HDD.  I would like to use the SSD for the root partition, and the HDD for the /home partition, and I would also like to ensure that the user's data is encrypted.  I am aware that Ubuntu 18.04 unfortunately does not support only homedir encryption, but drive encryption instead.  In the installer/disk partitioner, I selected the option for encryption, and set an encryption password, and then set up the desired partitions on the SSD and HDD (the computer is single boot, Ubuntu only).  After the installation completed, and I rebooted, I was not prompted for the encryption password, but Ubuntu loaded straight to the user login screen. I am not convinced that the installer has actually set up encryption in this slightly atypical setup.  Is it possible to encrypt the home partition/drive now, after the OS installation, or alternatively, could anyone guide me through exactly what I need to do in the disk partitioner?

Disappointed to see that the 18.04 installer no longer offers the option to encrypt the home directory. According to  bug report referenced in the installer, the recommended method for encryption these days is full-disk with LUKS, or fscrypt for directories. Full-disk encryption seems a bit overkill for my needs, and all the bugs and caveats mentioned on the  don't make it a very attractive option. All I really want is to protect my home directory from someone accessing my documents, photos, etc. if my laptop were to get stolen, making fscrypt the option for me.  The  has some examples on how to set it up, but I can't find any documentation aimed at encrypting the home directory on Ubuntu. The old ecryptfs tool is still available, but after setting it up Ubuntu would sometimes freeze at the login screen.  So my question is: How do I setup fscrypt to encrypt my /home directory and decrypt when I log in? I also liked how ecryptfs allowed decrypting the folder manually (eg. from disk images).  (A similar question was posted  and was unfortunately closed for being an "off-topic" bug report. To clarify, this is not a bug report. The fact that the encrypt home directory option was removed from the installer was intentional. All I'm asking here is how to setup fscrypt.)


Using Chrome on Windows. When I enter the following text in the editor, the markdown preview stops working, frozen, until the page is reloaded:  [tag:.]  It also happens if I precede [ and/or : with a \. Sometimes I don't need the closing ], but I cannot put my finger on the reason for that.  Additionally, if the above is entered into the editor and then posted, and then that post is edited, the markdown preview does not appear at all.

In the formatted preview for Questions & Answers, typing a tag link with an invalid tag name "crashes" the preview. As soon as you type the following the preview stops updating and an error can be observed in the Javascript console.   [tag:+]   Observed in Safari 7 and Chrome 31.   seems related to the business rule of not allowing certain characters in tags, but it sounds like a different bug.