What is the risk of installing a custom ROM whose build has been terminated by the developer(which may be a stable). I think no more future build updates will be available. I know there will be having higher chances of security risk. What are the other risks should I bother?   As there is no security updates further, how to can I use it securely?  ROM is the one which I have previously used, possibly having least bugs. Is it safe for continuing or switch to other ROM?   Device : rooted Redmi 1S, nougat 7.1.1

Are there any risks to manually flashing a stock or custom ROM?   Does it have the potential to brick the device? Will it void my warranty? Will I stop getting updates? Anything else I should be aware of?   (See also: )


All my pictures taken indoors show very low-light. I guess it should be giving more brightness when I chose f/5.6 aperture, 1/25 sec, ISO 200. And I doubt I might be doing something wrong or if its time to upgrade my camera.  Is there something I can do to improve the exposure in my pictures without using any flash, increasing ISO, reducing shutter speed? Adding a sample image:

I have a Canon 60D that I use for my primary hobby that is photography, but sometimes the pictures that I took are with the incorrect exposure like this:    So I want to know how I can choose the correct exposure for situations like night, intense light, poor light conditions...  PS: The image is intentionally unfocused because I was playing with styling my photos a bit, not that it's a problem.


I've noticed an odd behavior on a 2-server HA cluster and I was hoping someone could confirm my suspicion, or maybe offer some other explanation... Here is my setup:   A 2-server SQL 2012 SP1 installation SQL AlwaysOn HA has been enabled for a few databases CPUs are 2.4GHz, 4 cores RAM is 34 GB (it is an AWS instance, hence the odd number) Resource utilization is relatively low - each server has 14+ GB memory free, and SQL is not capped on how much memory to use Disk access time is fine - rarely going over 15ms/Read or Write Databases are not big - 1 GB, 1.5 GB, 7.5 GB SQL server process is using 16 GB Private Bytes, 15 GB Working Set   Overall, no resource issues are noted. Now for the odd part. SQL is not restarted (process has been running for almost 6 months) but it seems that every ~50 days, the Page Life Expectancy counter drops to (almost) 0. Up until that point it climbs steadily, no drops. Here is a perf graph:    When I look at the counter data (I don't have the exact number, just an hourly aggregation) it seems the PLE counter value reached about 4,295,000 sec (roughly 50 days) every time (at least every time I have data for).   My crazy theory is that the PLE number is held as milliseconds as an unsigned long int (which has a limit of 4,294,967,295) and at 49.71 days it resets, either by design, or because of a bug. This would explain the behavior of the two servers and the identical pattern they have. Or it could be something totally different and I am just not making any sense. :)  Has anyone seen anything like that, or can explain this behavior?  P.S. I saw  post, but my case seems slightly different.  P.P.S. This is a repost - I originally posted it , but was advised the audience here is more appropriate.  Thanks!


Is there a way to find the which directory or file is taking up the largest space on the Ubuntu Server?   I tried df -h  root@s-production:~# df -h Filesystem      Size  Used Avail Use% Mounted on udev            2.0G  4.0K  2.0G   1% /dev tmpfs           396M  364K  395M   1% /run /dev/vda1        40G  8.1G   30G  22% / none            4.0K     0  4.0K   0% /sys/fs/cgroup none            5.0M     0  5.0M   0% /run/lock none            2.0G     0  2.0G   0% /run/shm none            100M     0  100M   0% /run/user

I've run into a problem on one of my servers running 16.04: there is no disk space left.  I have no idea what is taking up the space. Is there a command to list the current directory sizes, so I can traverse and end up in the directory taking up all the space?


By ratio test,  $$ \sum^\infty_{n=1} \frac{n!}{n^n}$$  converges as the limit will become $e^{-1}$. If I add $e^n$ to it, the ratio test then fails:  $$ \sum^\infty_{n=1} \frac{e^n \cdot n!}{n^n}$$  How would I be able to show that this series is convergent/divergent?

Any suggestion/hint, not the whole solution, how to determine convergence/divergence of $$ \sum_{n=1}^{\infty}\dfrac{e^n \cdot n!}{n^n} $$ I'm currently stuck.


So I had gotten Minecraft about a  year ago and I paid for an account. We have another computer so my brother plays on it with my account. Now we both can play on it at the same time. Is there a way for us both to play together without an actual server you have to pay for?

I bought a Minecraft account for my little brother for Christmas, and I'd like to play with him on my server every now and then. If I log in while he's on, however, it kicks him off since we have the same username. Is there any way to change my username so that I can play with him, or anything I can do so that we can both play together using this account on my server?  I'm open to anything that could let us play, whether it be username changes, server property changes, etc.


I have a bash script that does a curl request for a URL. All curl headers and information is contained in a variable, here is a simplified example  STRING="'http://www.mydomain.com/url' -H 'mydomain.com'"   I originally had the script working by doing echo and xargs to pass it, but I've been reading that it might not be a good way to do things  I ran into issues when just trying curl $STRING, and adding double quotes to make it curl "$STRING" now gives a curl error stating "curl: (1) Protocol "'http" not supported or disabled in libcurl"  I'm guessing there is some simple thing I am overlooking here possibly relating to the quotes and spaces (I tried escaping single quotes earlier and that just added them literally in the string)  If I echo $STRING it displays it as written with all quotes and single quotes, and doing echo $STRING | xargs curl does what I want correctly, it does curl with my string as it's input

Or, an introductory guide to robust filename handling and other string passing in shell scripts.  I wrote a shell script which works well most of the time. But it chokes on some inputs (e.g. on some file names).  I encountered a problem such as the following:   I have a file name containing a space hello world, and it was treated as two separate files hello and world. I have an input line with two consecutive spaces and they shrank to one in the input. Leading and trailing whitespace disappears from input lines. Sometimes, when the input contains one of the characters \[*?, they are replaced by some text which is is actually the name of files. There is an apostrophe ' (or a double quote ") in the input and things got weird after that point. There is a backslash in the input (or: I am using Cygwin and some of my file names have Windows-style \ separators).   What is going on and how do I fix it?


I want to know example of a sequence of function $\{f_n\}$ where each $f_n$ is continuous and the pointwise limit $f$ is continuous, but $f_n$ is not uniformly convergent. clearly, I need to think for a $f_n$ where there exist an $x$ such that $f_n(x)$ is not monotone.

Please help me out with this problem:  Let $f_n(x) : [0,1] \to \mathbb R$ be a sequence of continuous functions convergent at every $x \in [0,1]$ to a continuous function $f: [0,1]  \to \mathbb R$ . Does $f_n$ converge uniformly to $f$?  My first solution: I read this example in  posted earlier and I think it works: Take a sequence $f_n:[0,1] \to \mathbb R$ such that $f_n$ increases linearly from $0$ to $1$ on the interval $\left[ 0,\frac{1}{n} \right]$, decreases linearly from $1$ to $0$ on the intreval $\left[ \frac{1}{n}, \frac{2}{n} \right]$, and is $0$ on $\left[ \frac{2}{n},1 \right]$. Then $f_{n} \to 0$ nonuniformly.  Is this answer true? Also, if anyone can give some examples of such function with detailed proof, I will very appreciative?


Framework: From RMT, eigenvalues have a semicircle distribution for symmetric matrices each with i.i.d normally distributed entries as the size of the matrix grows. The restrictions on i.i.d have recently been shown to not matter so we can proceed nevertheless. Example: If we take a covariance matrix of all stock tickets beginning in A comparing the average daily return over a period of time (or any process with no underlying relation), each we can assume lognormal distribution forming a, lets say 10000 by 10000 symmetric matrix. Thus we get a sequence of random covariance matrices. Each of the entries we assume to be i.i.d since the stocks have 'nothing' to do with each other (although a weaker results holds for non-i.i.d entries). Now this series of matrices forms a chain of covariance matrices tending towards the underlying covariance matrix of the entire history of the stocks (if we sampled correctly). Random Matrix Theory implications: We known from RMT that once we decompose these matrices into their eigenvalues, the eigenvalues tend to the semicircle distribution. Since this distribution is continuous, there's a spread in results i.e. there is some underlying variance to the eigenvalue decomposition of covariance matrices. Conclusion: Thus when we use covariance matrices shouldn't there be some sort of hypothesis test that's able to filter out this underlying distribution, similar to comparing normal distributions where we need to account for variance when comparing two mean values. This would be dependent on how i.i.d the random variables are, the size of the matrix, the number of samples taken, and the mean/variance of the random variables themselves. What would be weird about this hypothesis test is that we'd expects as $n$ gets larger so does the error bound, captured by the asymptotic relationship between the size and convergence to the semicircle distribution. TLDR: Is there some sort of hypothesis testing for PCA, or any eigenvalue method, that filters out the underlying tendency of random matrices to share similar eigen-distributions? Similar to how when you compare the mean of two normal distributions you need to perform a hypothesis test to account for the variance.

Framework: From RMT, eigenvalues have a semicircle distribution for symmetric matrices each with i.i.d normally distributed entries as the size of the matrix grows. The restrictions on i.i.d have recently been shown to not matter so we can proceed nevertheless. Example: If we take a covariance matrix of all stock tickers beginning in A comparing the average daily return over a period of time (or any process with no underlying relation), with each entry we can assume lognormal distribution forming a, lets say, 10000 by 10000 symmetric matrix. Over a duration of time we get a sequence of such matrices. Each of the entries we assume to be i.i.d since the stocks have 'nothing' to do with each other (although a weaker results holds for non-i.i.d entries). Now this series of matrices forms a chain of covariance matrices tending towards the underlying covariance matrix of the entire history of the stocks (if we sampled correctly). Random Matrix Theory implications: We known from RMT that once we decompose these matrices into their eigenvalues, the eigenvalues tend to the semicircle distribution. Since this distribution is continuous, there's a spread in results i.e. there is some underlying variance to the eigenvalue decomposition of covariance matrices. Conclusion: Thus when we use covariance matrices shouldn't there be some sort of hypothesis test that's able to filter out this underlying distribution, similar to comparing normal distributions where we need to account for variance when comparing two mean values. This would be dependent on how i.i.d the random variables are, the size of the matrix, the number of samples taken, and the mean/variance of the random variables themselves. What would be weird about this hypothesis test is that we'd expects as $n$ gets larger so does the error bound, captured by the asymptotic relationship between the size and convergence to the semicircle distribution. TLDR: Is there some sort of hypothesis testing for PCA, or any eigenvalue method, that filters out the underlying tendency of random matrices to share similar eigen-distributions? Similar to how when you compare the mean of two normal distributions you need to perform a hypothesis test to account for the variance. Edit - Solution: I found this paper  which seems quite promising although it'll take a few days for me to fully understand. It seems like this is an on-going area of research. Any further comments or recommendations are always appreciated.


I'm working with several Windows 10 machines and often installing new OS builds, and I only know how to customize the command prompt display by manually adjusting the font, colors, etc. in the properties dialog. Is there a way to copy the settings from a particular command prompt shortcut and automatically apply them to another shortcut, possibly on another machine?   I don't want the change to affect all command prompts on the machine, so the registry defaults are not an option. For example, I use different color backgrounds for different environments, so I can easily tell them apart. This needs to be applied to each command prompt shortcut separately, not to the global defaults.

Where are the default settings saved for the Command Prompt defaults?  Are they stored in the registry somewhere, or in a file?  I would love to make a .reg file to set my default preferences when logging into a machine for the first time.  I'm talking about the default application settings: QuickEdit mode, buffer size, text color, etc.


Again a confusing Issue: Here I copied the array into another variable and I expect not to change the original array when I change something in another one but both arrays change Why?    const groups = [[1, 2, 3, 4 ,5], [2,3]];  const sets = [...groups];    sets[1].push(9000); // I just push a number into sets NOT groups    console.log(sets);  console.log(groups);       This only happens if we have an array of arrays! What I'm missing and How to fix this?

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.


Is it true that the order of the group $U(n)$ for $n>2$ is always an even number? If yes, how to go about proving it? U(n) is the set of positive integers less than n and co-prime to n ,which is a group under multiplication modulo.

I'm struggling with this. I know it is going to use Lagrange's Theorem.  This is what I have so far.  Suppose $|U_n| = k.$  This implies $a^k = 1$ for all $a$ in $U_n$ and $|a|$ divides $k$.  Now, what can be said about the order of an element $a$? I haven't been able to conclude that it's even with what I have, therefore I continued so: $|\langle a\rangle|$ divides $k$ where $\langle a\rangle$ is the cyclic subgroup generated by $a.$  However, I haven't been able to conclude that $|\langle a\rangle|$ is even.   So I tried using this:  an element $a$ is in $U_n$ iff gcd$(a, n) = 1$.  Any hints?


As Blender is an open-source Program of coarse I can Edit its program files !  I want to make my own mesh (Car/Bus/) and I want it become a a regular mesh In add menu like a cube,sphere (Because I use it many times)  Why?  I do not want my mesh to be in file and every time i want to use i must imported.  How Can i Make it ? - Of coarse it will be made with Python - ( Are n't I right ? )  N.B : Plese in answer Be ware that i am new to blender python. bpy.  Refrence  Consider that this is my mesh:   And I Want Its Shortcut in This Menu Here:

I want to add things like basic tables/chairs/houses I have made over the past year to my ShiftA menu. Is it possible to do this?


so i just started learning this subject. i undestand the basics of it but can't seem to understand how to prove a curtain claim on it.  for example i received a question as homework that i would really appreaciate it if someone could help me with it, please explain it step by step:   $A \subset \mathbb R$ has an upper bound. $B = \{ -a \mid a \in A\}$   prove that $B$ has a lower bound and that $\inf B = -\sup A$.  please help.. thank you.

Let $A$ be a nonempty subset of real numbers which is bounded below. Let $-A$ be the set of of all numbers $-x$, where $x$ is in $A$. Prove that $\inf A = -\sup(-A)$   So far this is what I have  Let $\alpha=\inf(A)$, which allows us to say that $\alpha \leq x$ for all $x \in A$. Therefore, we know that $-\alpha \geq -x$ for all $x \in -A$. Therefore we know that $-\alpha$ is an upper bound of $-A$. $\ \ \ \ $  Now let $b$ be the upper bound of $-A$. There exists $b \geq-x \implies-b \leq x$ for all $x \in A$. Hence, \begin{align} -b & \leq \alpha\\ -\alpha & \leq b\\ -\alpha & = - \inf(A) = \sup (-A) \end{align}  By multiplying $-1$ on both sides, we get that $\inf(A) = -\sup (-A)$  Is my proof correct?


I've been trying stuff with angle sums, Sine law and Thales theorem, but either I'm making very bad mistakes or I'm just tired - either way I would love some outside input. Thank you.

$\triangle ABC$ is an isosceles triangle such that $AB=AC$ and $\angle  BAC$=$20^\circ$. And a point D is on $\overline{AC}$ so that AD=BC, , How to find $\angle{DBC}$?    I could not get how to use the condition $AD=BC$ , How do I use the condition to find $\angle{DBC}$?  EDIT 1: With MvG's observation, we can prove the following fact.     If we set on a point $O$ in $\triangle{ABC}$ such that $\triangle{OBC}$ is a regular triangle, then $O$ is the circumcenter of $\triangle{BCD}$.   First, we will show if we set a point $E$ on the segment $AC$ such that $OE=OB=OC=BC$, then $D=E$.  Becuase $\triangle{ABC}$ is a isosceles triangle, the point $O$ is on the bisecting line of $\angle{BAC}$. $\angle{OAE}=20^\circ/2=10^\circ$.   And because $OE=OC$, $\angle{OCE}=\angle{OEC}=20^\circ$, $\angle{EOA}=20^\circ-10^\circ=10^\circ=\angle{EAO}$.   Therefore $\triangle{AOE}$ is an isosceles triangle such that $EA=EO$. so $AD=BC=AE$, $D=E$.  Now we can see the point $O$ is a circumcenter of the $\triangle{DBC}$ because $OB=OC=OD.$  By using this fact, we can find $\angle{DBC}=70^\circ$,


What relationship does speed have with balance in the driving of a cycle? Is it related to the principle of a gyroscope?

Why does a bike/bicycle fall when its speed is very low or close to zero and is balanced when going with a high speed?


I need to order the results by how the values in IN() clause are set up, here is the example code.  SELECT nickname, age WHERE id IN(3, 1, 2) ORDER BY ?; <- this is where I need the results go back according to the IN() clause   This the result as of now, (using PHPmyadmin, not yet php coded).  nickname | age | true id of the row j        | 11  | 1 jj       | 22  | 2 jjj      | 33  | 3   The result that I need is:  nickname | age | true id of the row jjj      | 33  | 3 j        | 11  | 1 jj       | 22  | 2   Can I do this with using IN() clause? This is the only idea that I came up with so if you have any idea/s that I may try then please tell me.

I am wondering if there is away (possibly a better way) to order by the order of the values in an IN() clause.  The problem is that I have 2 queries, one that gets all of the IDs and the second that retrieves all the information. The first creates the order of the IDs which I want the second to order by. The IDs are put in an IN() clause in the correct order.  So it'd be something like (extremely simplified):  SELECT id FROM table1 WHERE ... ORDER BY display_order, name  SELECT name, description, ... WHERE id IN ([id's from first])   The issue is that the second query does not return the results in the same order that the IDs are put into the IN() clause.  One solution I have found is to put all of the IDs into a temp table with an auto incrementing field which is then joined into the second query.  Is there a better option?  Note: As the first query is run "by the user" and the second is run in a background process, there is no way to combine the 2 into 1 query using sub queries.  I am using MySQL, but I'm thinking it might be useful to have it noted what options there are for other DBs as well.


I don't know why I am having null despite comparing the code to the ones I've written before.  This is my Java code to insert data into table:    @FXML     private void rewards_Parameters(){         try{             String sql = "INSERT INTO SetUpReward VALUES(?,?,?,?,?,?)";             if(sql !=null){                 pst =con.prepareStatement(sql);                 pst.setString(2, txt_minGiftValue.getText());                 pst.setString(3, txt_maxGiftValue.getText());                 pst.setString(4, txt_RewardPoint.getText());                  pst.execute();             }         }catch(SQLException e){             JOptionPane.showMessageDialog(null, e);         }         }   My Init process...   /**  * FXML Controller class  *  * @author JIDO  */ public class IGisftCardController implements Initializable {     Connection con =null;     ResultSet rs = null;   PreparedStatement pst ;   Stacktrace:  Caused by:   java.lang.NullPointerException     at view_controller.IGisftCardController.loadReward(IGisftCardController.java:249)     at view_controller.IGisftCardController.initialize(IGisftCardController.java:168)     at javafx.fxml.FXMLLoader.loadImpl(FXMLLoader.java:2548)     ... 22 more Exception running application igiftcardfx.IGiftCardFX Java Result: 1

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?


As you see, I create the graphics in the same document. I would like that Figure one and Figure two are written in the same line and not one more upwards.  \documentclass[english,12pt,oneside, a4paper]{article}  \usepackage{graphicx}    \usepackage{tikz}  \begin{filecontents}{innovation.tex} \begin{tikzpicture}   [node distance=.8cm,   start chain=going below,]      \node[punktchain, join] (intro) {Buyer a};      \node[punktchain, join] (probf)      {Multiple  dddddddddddddddddddddddddd$e_i$ in R\&D};      \node[punktchain, join] (investeringer)      {Multiple  bids $(y_i,p_i)$};      \node[punktchain, join] (perfekt) {Buyer s};      \node[punktchain, join] (perfekt) {Supplier};         \end{tikzpicture}   \end{filecontents}    \begin{filecontents}{supply.tex} \begin{tikzpicture}   [node distance=.8cm,   start chain=going below,]      \node[punktchain, join] (intro) {Buyer announces $V(y)$};      \node[punktchain, join] (probf)      {Multiple };      \node[punktchain, join] (investeringer)      {Buye};      \node[punktchain, join] (perfekt) {Su      \node[punktchain, join] (perfekt) {Su};         \end{tikzpicture}   \end{filecontents}   \begin{figure}     \centering     \begin{minipage}{0.45\textwidth}         \centering         \input{innovation} % first figure itself         \caption{first figure}     \end{minipage}\hfill     \begin{minipage}{0.45\textwidth}         \centering         \input{supply} % second figure itself         \caption{second figure}     \end{minipage} \end{figure}   \begin{document}  \begin{figure}     \centering     \begin{minipage}{0.45\textwidth}         \centering         \input{innovation} % first figure itself         \caption{first figure}     \end{minipage}\hfill     \begin{minipage}{0.45\textwidth}         \centering         \input{supply} % second figure itself         \caption{second figure}     \end{minipage} \end{figure}  \end{document}

I want to place two (or more) figures with side by side. The figures are independent, so need separate captions, with no overall caption for the two. I know how to do this with minipages within a figure environment. But the captions don't line up without trail and error \vspace's before the individual captions. Is there a way to line up the captions automatically?


The reason is Alt-F1+Scroll and click is a lot of work for navigating the stuff I have open.  I’m using Ubuntu Desktop 18.04.

Just upgraded from Ubuntu 17.04 to Ubuntu 17.10.  Please help me to shift the side bar (aka Ubuntu Dock) to bottom.   I tried running the following command which used to work with older Ubuntu releases   gsettings set com.canonical.Unity.Launcher launcher-position Bottom   but it's not working.


compiling latest kernel, from kernel.org: (2018.07.23)     make clean arch/x86/Makefile:184: *** Compiler lacks asm-goto support..  Stop.   while: kernel linux-4.14.57   does not give such error.  this compiler is used:  gcc -v Using built-in specs. COLLECT_GCC=gcc COLLECT_LTO_WRAPPER=/usr/libexec/gcc/x86_64-redhat-linux/4.8.5/lto-wrapper Target: x86_64-redhat-linux Configured with: ../configure --prefix=/usr --mandir=/usr/share/man --infodir=/usr/share/info --with-bugurl=http://bugzilla.redhat.com/bugzilla --enable-bootstrap --enable-shared --enable-threads=posix --enable-checking=release --with-system-zlib --enable-__cxa_atexit --disable-libunwind-exceptions --enable-gnu-unique-object --enable-linker-build-id --with-linker-hash-style=gnu --enable-languages=c,c++,objc,obj-c++,java,fortran,ada,go,lto --enable-plugin --enable-initfini-array --disable-libgcj --with-isl=/builddir/build/BUILD/gcc-4.8.5-20150702/obj-x86_64-redhat-linux/isl-install --with-cloog=/builddir/build/BUILD/gcc-4.8.5-20150702/obj-x86_64-redhat-linux/cloog-install --enable-gnu-indirect-function --with-tune=generic --with-arch_32=x86-64 --build=x86_64-redhat-linux Thread model: posix gcc version 4.8.5 20150623 (Red Hat 4.8.5-28) (GCC)    Why do I have thos errors ?

I want to learn Linux Kernel and I've downloaded the latest kernel version. Now I want to configure Linux with make menuconfig and I'm receiving an error:     Arch/x86/Makefile:184  Compiler lacks asm-goto support...   Can somebody help me?


Would it be wrong to argue that if one considers a countable set $A$ and a real function $f:\mathbb{R}\to\mathbb{R}$, then the range of $f$ on $A$, that is the set $f(A)=\{f(a)\mid a\in A\}$, is countable?

One of my homework problems asks to prove that if $f:X\to Y$ is a function and $A$ is a countable subset of $X$, then $f(A)$ is countable.  I believe I have a valid proof by partitioning the set A into equivalency classes based in image under $f$. Then using that partition as domain for a choice function $C_f$ back to $A$. So now the function $f$ restricted to the domain (range $C_f$) $f|_{range(C_f)}$ maps to $f(A)$ 1-1 and onto. Therefore  $$|f(A)|=|range(C_f)|\leq |A|=\aleph_0$$ $\therefore f(A)$ is a countable set. $\quad \blacksquare$  My problem is that I used the axiom of countable choice $AC_\omega$ in my proof but that isn't a part of the course I am taking. Does anyone have a simpler proof or one that does not involve Choice?


I'm attempting to create a procedural shadernode to render a radial grid for the top / bottom of the saucer section of the Enterprise, and I'm running into difficulty. My initial instinct is to use the Bricks texture as the primary basis for my shader, as it has the correct combination of large interior spaces separated by solid lines, but I can't quite get it to render in a proper grid pattern on the top of a cylinder (as a test shape) - the most I've manged to achieve is radial lines on the top, by following  answer almost verbatim, but the latitudinal lines elude me. (Edit: Adding a screenshot of wat I've managed to do so far)  Is there some combination of rotating and scaling vectors that I should be looking at? It seems like it would be a relatively common use case... Edit: Somewhat answered by the question , although the math is a bit (a lot) beyond me - the answer seems to be to apply spherical projection to the vector used to project the brick shader. Have yet to make it work, but thank you :)

I'm playing around with nodes within cycles and I'd love to create a chevron like texture like the image below. Anyone an idea how to accomplish this?


$$\sum_{n=1}^\infty \cos (n \pi )$$   This question has been asked before   But I think the series diverges because it is not a single value. The results are alternating between and 1 and -1.

Does the series $\sum \limits _{n=0}^{\infty} \cos(n\pi)$ converge or diverge?   On substituting values I get alternate $1$ and $-1$.    So taking sum of infinite GP, I get $\dfrac 1 2$. So it looks like it converges.


I want to ask a question. Why $x^p - \alpha^p = (x - \alpha)^p$?

Definition charactersitic $p$: a field has characterstic $p$ is its prime field is isomorphic to $\mathbb{Z}/p\mathbb{Z}$.  Proposition: let $K$ be a field of characteristic $p$. Then for any $a, b \in K$ we have $(a + b)^p = a^p + b^p$.  Proof: (from my text) because $p \choose i$ is divisible by $p$ for $0 < 1 < p$ it is zero $\mod p$, so $p \choose i$  $a^{p - i}b^i$ is zero (this is the part I don't understand), so it follows from Newton's binomial law.  I understand that the prime field of $K$ is isomorphic to $\mathbb{Z}/p\mathbb{Z}$, so if $a, b$ are in the prime field, then $p \choose i$  $a^{p - i}b^i$ is zero, but that is not necessarily the case is it?


I have a remote Windows 2012R2 server that runs a lot of important stuff. I, stupidly, accidentally, did an ipconfig /release on that server from the other side of the continent. Now that server no longer has an IP address and I have no way of accessing it. There is nobody nearby with physical access.  I have full access to literally everything on that network, but I can not figure out any way to have it refresh its IP address or reboot. I have admin access to:   the DNS server the DHCP server the AD DC server the router guest Hyper-V machines that are still running on that server other random workstations on the domain the MAC address of the server in question   The only thing I don't have is a remote power switch to reset the damned server. I'm travelling for a month and I desperately need this server up, but I seem to have screwed myself so hard with this that there is no recovery. Does anyone have any ideas of any way to force this thing to renew its IP address or reboot?  This question has been marked as a duplicate, but it really is not. The other question is about steps to prevent situations like the one I am in to happen. But my question is, once I have lost contact with my remote machine, is there anything that can be done, given the considerable amount of information I have about the LAN of the remote machine? Is there for instance a generalization of a magic packet technology which can restart a machine, or something similar?   In other words: given that I am already stuck, is waiting my only option?  UPDATE: turns out that the ipconfig /release only released the IPv4 address, but it still had an IPv6 address. Once I found that from looking through the router logs, I was able to reboot it using that and the shutdown -r -m \\IPv6Address command.    EDITOR'S NOTE (Scott): Note that this solution (and the others suggested in the comments below) is irrelevant and not applicable to the question of which this one is allegedly a duplicate.

I use a remote desktop program (usually ) to connect to a Windows machine everyday. The remote computer has a fixed IP address, and if the computer is on and responsive, I can access it and even reboot the computer remotely if necessary.  Unfortunately, if the remote computer freezes (for example, if it gets a blue screen), as far as I know, I can't use a remote desktop solution to restart it. Similarly, if my computer is off, I can't use remote desktop to boot it.   I know that one solution is to ask somebody who is physically near the computer to press the reboot or power on button, but I am opening this thread because I am interested in solutions that do not require the physical presence of people to turn on or reboot a remote frozen computer.  Is this possible? If so, what are my options?


So I wanted to know where the source code is. I know how to get the .ISO file but how can I see or change the code? My goal is to make a Custom OS based on Ubuntu. How can I see the code of .ISO file and are there any documentation on Ubuntu source code?

I would like to know where to find the source code of Ubuntu. I'd like to see how far it is "open source".


When you look for "Arduino relay module"s, you usually see one form "SONGLE" that says on it:  10A 250 VAC    10A 125 VAC   10A 30  VDC    10A 28  VDC   My question:   Why do some Arduino relay modules can handle up to 250 VAC but not above 30 VDC?

I'm looking for a high current DC switch (able to switch something like 5V@30A) and I've encountered several DPDT that might do what I need, however they are only rated for AC applications (3A@250VAC or 6A@125VAC). Are these rating convertible to DC? or is that something that only the facturarer would know?


How do I solve for M modulo 2021 where M is the product of all numbers relatively prime to 2021 that are less than 2021. I know Wilson's Theorem but that's applicable for modulo p where p is prime. Should I use CRT by breaking 2021 into 43 and 47 but even that seems intractable to me. Any help is appreciated.

How can we compute the product of all invertibles in $\Bbb Z_n$?  In the special case $n=p$ where $p$ is a prime it is Wilson's theorem. By pairing inverses it reduces to computing the product of all $a$ such that $a^2\equiv 1\pmod{n}.\,$  How can we do that?


I am trying to get a handle on how stock trades actually go through practically. Let's assume a stock with only one buyer and one seller to make things easier to understand.  Scenario 1: Alice has an ASK price of $10.00 and Bob has a BID price of $9.00. Scenario 2: Alice has an ASK price of $9.50 and Bob has a BID price of $9.50. Scenario 3: Alice has an ASK price of $9.00 and Bob has a BID price of $10.00.  In scenario 1, the trade obviously doesn't happen, because they aren't compatible. The seller wants more than the buyer is willing to pay.  In scenario 2, the trade goes through because it's a match made in heaven.  In scenario 3, I am confused. I'd like to think the trade goes through, because why wouldn't it? But at what price does the trade happen? At the seller's price? Or the buyer's? Or does the stock get sold at the ASK price and bought at the BID price and the difference goes somewhere?  I wish to understand how scenario 3 works. And in general, I want to understand if I am thinking about this correctly. How do trades happen? How do buyers and sellers get matched with each other?

Let's assume a very simplified situation. There is only one seller asking for 10$ and there is only one buyer bidding 20$. At what price would the transaction go?   Some answers say it won't, because the ask price has to match the bid price. () Other answers say, that the time ordering is important. () Which answer is correct? What is the final price in the presented situation?


I have two numbers in scientific notation and I want to do some comparison between them in an if statement in bash. While doing so, I am getting error like bwlow: E.g:  bash-4.2$ a=10e-12 bash-4.2$ b=12e-12 bash-4.2$ if (( a > b )); then r=1; else r=0; fi bash: ((: 10e: value too great for base (error token is "10e")   The same problem doesn't arise if a and b are integers. I see problem with floating numbers to if I use the above statement. Is there a simple way by which I can do the comparison within if statement?

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.


Are there integers $a$ and $b$ such that $a^5b+3$ and $ab^5+3$ are both perfect cubes of integers? $a,b$ are distinct integers.  P.S.: I think trying to find some special cases would not be helpful.

Find the integer solutions: $$a·b^5+3=x^3,a^5·b+3=y^3$$ This is the first problem of today's USAJMO (has finished),I only find a trival result that $x\equiv y \pmod6$ and $abxy≠0 \pmod 3$.  Thanks in advance!


I am struggling to choose the correct tense for this question:  What were the names of the sons of Mahatma Gandhi?  OR  What are the names of the sons of Mahatma Ghandi?  His sons have passed away so I would naturally opt for 'were', but they are still his sons so 'are' seems more appropriate. Is this correct? Thank you.

Is it correct to say "What was your name?"? The reason I am asking this is, generally the name of the person will not change. One should say "What is your name?"


I am importing a large struct from Matlab to Python using the scipy.io. The data seems to be imported OK, but it is full of nested lists, which I am not able to simplify. Here's one of the simplest examples:  sc = sio.loadmat(matlabFile) sc['DieID']['w']   which results in the following output:  array([[array([[ 1309.09090909]]), array([[ 1309.09090909]]),     array([[1000]], dtype=uint16)]], dtype=object)   Could you please suggest how do I reduce this particular field to a simple list [1309.09090909, 1309.09090909, 1000]?  Thank you for your help!

Is there a simple way to flatten a list of iterables with a list comprehension, or failing that, what would you all consider to be the best way to flatten a shallow list like this, balancing performance and readability?  I tried to flatten such a list with a nested list comprehension, like this:  [image for image in menuitem for menuitem in list_of_menuitems]   But I get in trouble of the NameError variety there, because the name 'menuitem' is not defined.  After googling and looking around on Stack Overflow, I got the desired results with a reduce statement:  reduce(list.__add__, map(lambda x: list(x), list_of_menuitems))   But this method is fairly unreadable because I need that list(x) call there because x is a Django QuerySet object.  Conclusion:   Thanks to everyone who contributed to this question.  Here is a summary of what I learned.  I'm also making this a community wiki in case others want to add to or correct these observations.  My original reduce statement is redundant and is better written this way:  >>> reduce(list.__add__, (list(mi) for mi in list_of_menuitems))   This is the correct syntax for a nested list comprehension (Brilliant summary !):  >>> [image for mi in list_of_menuitems for image in mi]   But neither of these methods are as efficient as using itertools.chain:  >>> from itertools import chain >>> list(chain(*list_of_menuitems))   And as @cdleary notes, it's probably better style to avoid * operator magic by using chain.from_iterable like so:  >>> chain = itertools.chain.from_iterable([[1,2],[3],[5,89],[],[6]]) >>> print(list(chain)) >>> [1, 2, 3, 5, 89, 6]


If we will use crop lenses only on crop bodies, why do we call crop lenses for example "10mm" when they are effectively "16mm" (with a crop factor of 1.6 in this case)?  I am familiar with the history and the difference between a full-frame and a crop body. My question was about why we call these lenses different in focal lengths since they both yield the same field of view in degrees (the crop lens on a crop body, and the FF lens on a FF body). I know the lens doesn't actually turn into a longer focal length optically on a crop body, but since the result is the same, why not just label it that way?

So, I mount a 200mm lens on my Canon 450D. It effectively becomes a 320mm lens. Is this the equivalent of 320mm on a full frame camera? That is, from what I've figured out I get an equivalent field of view but nothing I've read is indicating that I get the magnification to go along with it.  So as my question says in the title, does my crop sensor camera really turn my lens into a longer one (in terms of magnification), or does it just look like it based on the reduced field of view I get?


This is the sample data that I've got     id program Community ID sdg     246 #NoWasteGiving2020 97 11   246 #NoWasteGiving2020 97 17   246 #NoWasteGiving2020 97 10     With the data on the table above, how do I get the data to just be shown in one row and the sdg shown in one row. so at the end of the day the data will look like this: 246   #NoWasteGiving2020  97  10,11,17  This is the query that I've wrote select Distinct a.id, a.title as program, b.community_id, c.goal_id as sdg from programs_program as a join associates_programcommunity as b on a.id = b.program_id join associates_communitygoal as c on b.community_id = c.community_id

Consider a database table holding names, with three rows:  Peter Paul Mary   Is there an easy way to turn this into a single string of Peter, Paul, Mary?


Should I use vector logo in SVG format in website? To make responsive logo in responsive website. Need suggestions, which format will be best?

I'm pretty new to photoshop and illustrator and trying to create a simple text-based logo to use on my web site, for example:   You get wildly different versions of that depending on what browser you use to render the text (which is why I obviously must create the image myself), but for example on Chrome you can already see a blurriness around the edges of the font.  The problem I'm having in Illustrator is that when I write in a certain font (e.g. "Arial Rounded MT Bold" at 24pt), the font looks beautiful and crisp against my background colour at 200% zoom, but I start to see blurring at 100% - then I'm not sure what it is about the 'save to web' process, but the image loses further clarity by the time it ends up on my website (as a 'type optimised' png).  I'd read somewhere that photoshop was better for saving images of text for web, but I see a similar blurriness there even in advance of exporting (and of course a 200% zoom in photoshop just pixelates the image).  So what I'm really lacking is a step-by-step for-dummies type guide of how to get crisp images of text onto a website.  At this point I'm not sure if perhaps I've just chosen a bad colour contrast, or fonts that don't scale well - although I'm also wondering if there's something significant in the fact the font looks beautiful in Illustrator at 200% or larger - perhaps that means I should be exporting the font from Illustrator at a larger size than required and then doing additional downsizing (somehow!) afterwards - although of course again I can't trust web browsers to do that for me.  EDIT: I should also have noted that the effect is much worse on my monitor versus my laptop (tempting to say I have a bad monitor but there's many websites where the monitor version looks fine too!)


I am struggling to solve this error that happens only when I am on night mode (I am using Theme.MaterialComponents.DayNight) and when rotating the screen... on day mode it works fine with no issues.     Attempt to read from field 'float android.content.res.Configuration.fontScale' on a null object reference   I have no idea where it is coming from, I am not using any custom fonts.

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?


When you've cut something with ctrl + r, but not every cut leaves the same ammount of room inbetween each of the cuts, how do you fix that? (see picture with half assed arrow drawings)    And    Why am I only offered one cut on the top instead of a full line (see picture and marked blue spots and red circle)     Scrolling doesn't fix it, as it only adds more cuts on the vertical face, instead of continuing a horizontal cut:

why does the loop-cut-and-slide operation ignore certain faces but happily cut others?the model is symmetrical so it is a bit strange to pick 3 faces that won't get cut. I tried applying it to see if it was just a graphics glitch causing the purple line to not display over everything, but it did end up cutting only what the line was selecting, instead of the whole mesh.    as requested,here's a paste of the blend:


After 3 hours of searching the web for this I gave up...  I have added a "banner image" field to the basic page. I want to use the image as a background. I wanted to capture the image path in a preprocess_field function but I tried every possible methods on the \Drupal\image\Plugin\Field\FieldType\ImageItem object and can't seem to find the way to get the path.  mytheme.theme:  function mytheme_preprocess_field(&$variables){   if($variables['field_name'] == 'field_banner_image'){     /** @var \Drupal\image\Plugin\Field\FieldType\ImageItem $field */     $field = $variables['element']['#items'][0];             $variables['banner_url'] = $field->getValue(); // not working, tried everything...   } }   Then in my field--field-banner-image.html.twig:

I want to render an image as a background image via an inline style in twig. I created a field called bg_image and attached it to the standard plain page.  After fiddling around for hours I was able to get the Image URL in node.html.twig  {{ file_url(node.field_bg_image.0.entity.uri.value) }}   but I could not get it to work inside field--field-bg_image.html.twig  Can I get the node from there anyhow, so I can then get the image?  How can I get the image URL to use as inline style? I thought maybe I can pass a variable from field--field-bg_image.html.twig to image.html.twig and then just render  {{ uri }}   instead of  <img{{ attributes.addClass(classes) }} />   but I could not get it to pass the variable there unless I use includes  {% include 'image.html.twig' with {'image': image, 'isFromField': isFromField} %}   (isFromField is true, when it comes from the field--field-bg_image.html.twig) But that didn't work either. The Image was never rendered that way.  Would be very glad if you can help - my php knowledge is very basic. Thanks


I have a problem, there is a website with a load of JS code. When I click on a certain element, some functions are called. How can I find out which functions (and in which files)?  For example, there's something like this  $( document ).ready(function() {    $("a").on('click', function() { $('c').css('opacity', '0.8'); });    $("ul#main li a").on('click', function() { $('c').toggle('.menu'); });    $("nav a").on('click', function() { callSomeFunctions(); }); });   And then I've got a menu like this

click

   How can I find out that those 3 lines above are executed?  Thanks!

I have a page where some event listeners are attached to input boxes and select boxes. Is there a way to find out which event listeners are observing a particular DOM node and for what event?  Events are attached using:    Event.observe; DOM's addEventListener; As element attribute element.onclick.


Please consider the following MWE:  \documentclass{article}  \PassOptionsToPackage{prologue,usenames,dvipsnames,svgnames,table}{xcolor} \usepackage{xcolor}  \usepackage{pgfplots}     \pgfplotsset{compat=newest}  \begin{document}  \textcolor{Blue!55!Green}{Text here}  \end{document}   Since the new year's MiKTeX update, the xcolor package must be loaded along with the prologue option in order to counteract interaction bugs with PSTricks, TiKZ, etc. (as noted ).  However, if xcolor+prologue is loaded BEFORE pgfplots, it generates the following GhostScript error: Error: /undefined in color, Operand Stack: XC@mapped.  If xcolor+prologue is loaded AFTER pgfplots, the following error arises during compilation (LaTeX=>PS=>PDF): ! Package xcolor Error: Undefined color 'Blue'.  Any ideas on how to solve this issue?

I use tikz (and tikzpicture) a fair bit, but files that used to compile fine before the latest slew of updates to pgf, and pstricks, no longer seem to do so (at least, on my MikTeX installation). The MWE (below) seems to compile correctly, but the DVI can't be rendered using yap, and dvi -> ps -> pdf fails (the dvi -> ps seems to be ok -- to the extent it isn't throwing errors), but ps2pdf fails miserably, with the following errors:   Error: /undefined in XC@.  Operand stack:    --nostringval--   --nostringval--   --nostringval--   --nostringval--   -  -nostringval--   --nostringval-- Execution stack: %interp_exit   .runexec2   --nostringval--   --nostringval--   --  nostringval--   2   %stopped_push   --nostringval--   --nostringval--   --  nostringval--   false   1   %stopped_push   2045   1   3   %oparray_pop    2044   1   3   %oparray_pop   2025   1   3   %oparray_pop   1884   1   3    %oparray_pop   --nostringval--   %errorexec_pop   .runexec2   --nostringval-  -   --nostringval--   --nostringval--   2   %stopped_push   --nostringval-- Dictionary stack:   --dict:979/1684(ro)(G)--   --dict:1/20(G)--   --dict:87/200(L)--   --    dict:182/300(L)--   --dict:58/200(L)--   Current allocation mode is local   Current file position is 99615   GPL Ghostscript 9.26: Unrecoverable error, exit code 1   Here is the MWE:  \documentclass[12pt,letterpaper,oneside]{article}  \usepackage{tikz}  \usetikzlibrary{decorations,shapes,arrows,matrix,positioning}  \begin{document}  \begin{center} \begin{tikzpicture}[x=0.175cm,y=0.175cm,scale=1]  % set up maximum and minimum x- and y-coordinates \def\xmin{0} \def\xmax{23.5} \def\ymin{0} \def\ymax{23.5}  % draw and label axes    \draw[->,thick] (\xmin,0) -- (\xmax,0) node[below=8pt,near end]  {\small{abundance ($N$)}};   \draw[->,thick] (0,\ymin) -- (0,\ymax) node[above=12pt,near   start,rotate=90] { \small{birth rate ($b$)}};  % draw vertical reference line at K/2=50   \draw[color=black, thick,  smooth] (0,20) -- (20,0)  node[below=6pt,midway,rotate=-45] {\small{slope~$=a$}};  % draw circle around point where function intersects x-axis \draw [red] (0,20)  ellipse (0.2cm and 0.2cm) node[right=3pt,black] {$b_0$};   \end{tikzpicture}  \end{center}   \end{document}


I am looking over Linear Algebra,and am stuck on this problem.   V is the space of real polynomials of degree 2 or less, and I want to find a dual basis to the basis $\{1,x,x^2\}$. I know the general technique, that each element of the dual basis $e_i'$evaluates to $0$ on the basis vectors $e_j$ for which $i \neq j$ and $1$ when $i=j$ but every time I try and do this on these basis vectors, I get stuck.   Any help appreciated.   Also, a more general question: what is the method for determining in general whether or not something is a dual basis? I know you have to show it to be linearly independent and spanning, and showing linear independence is generally quite easy, but how do I show spanning? If I have a dual basis I'm presuming it doesn't necessarily have to satisfy the above criterion (evaluating to 0 and 1 on different basis vectors), and this is just a way of finding one dual basis, so how would I test whether or not a given dual basis is spanning?   Thanks.

Let $V$ be the space of polynomials of degree at most $2$, with basis $\{1,x,x^2 \}$.Find the dual basis to $\{1,x,x^2\}$.   I know that the dual basis of $\{f_1,f_2,f_3\}$ is the basis $\{f_1^*,f_2^*,f_3^*\}$ where $f_i^*(a_1f_1,\ldots,a_3f_3)$ but I'm not sure how to actually compute the dual basis.


Im currently working on a project and I keep running into the error java.lang.RuntimeException: Error receiving broadcast Intent { act=android.net.wifi.WIFI_AP_STATE_CHANGED flg=0x4000010 (has extras) } in cn.ingenic.glasssync.utils.WifiAPUtils$1@428319e Reading the logs further I also see a null pointer exception where it says: Caused by: java.lang.NullPointerException: println needs a message 01-06 10:57:26.272 12372 12372 E AndroidRuntime:    at android.util.Log.println_native(Native Method) 01-06 10:57:26.272 12372 12372 E AndroidRuntime:    at android.util.Log.e(Log.java:249) 01-06 10:57:26.272 12372 12372 E AndroidRuntime:    at cn.ingenic.glasssync.utils.WifiAPUtils.getValidApSsid(WifiAPUtils.java:225) 01-06 10:57:26.272 12372 12372 E AndroidRuntime:    at cn.ingenic.glasssync.utils.WifiAPUtils$1.onReceive(WifiAPUtils.java:202) When I check line 225 in WifiAPUtils.java and replace it with a valid string I then get the error 01-11 00:00:50.590 29176 29217 E AndroidRuntime: FATAL EXCEPTION: Thread-2 01-11 00:00:50.590 29176 29217 E AndroidRuntime: Process: cn.ingenic.glasssync:remote, PID: 29176 01-11 00:00:50.590 29176 29217 E AndroidRuntime: java.lang.ExceptionInInitializerError 01-11 00:00:50.590 29176 29217 E AndroidRuntime:     at com.baidu.location.Jni.j(Unknown Source:0) 01-11 00:00:50.590 29176 29217 E AndroidRuntime:     at com.baidu.location.t$a.X(Unknown Source:8) 01-11 00:00:50.590 29176 29217 E AndroidRuntime:     at com.baidu.location.ae.run(Unknown Source:10) 01-11 00:00:50.590 29176 29217 E AndroidRuntime: Caused by: java.lang.IllegalStateException: no found the liblocSDK4d.so file, please correct settings Would anyone happen to know what could be the cause of this error here is the snippet of the code that could be potentially causing this error: private BroadcastReceiver mWifiStateBroadcastReceiver = new BroadcastReceiver() {                      @Override         public void onReceive(Context context, Intent intent) {         Log.i(TAG,"WifiAPUtils onReceive: "+intent.getAction());         if(WIFI_AP_STATE_CHANGED_ACTION.equals(intent.getAction())) {             int cstate = intent.getIntExtra(EXTRA_WIFI_AP_STATE, -1);             if(cstate == WIFI_AP_STATE_ENABLED) {             if(mHandler != null)                 mHandler.sendEmptyMessage(MESSAGE_AP_STATE_ENABLED);                /*notify glass to reconnect*/             String ssid = getValidApSsid(context);             String pw = getValidPassword(context);             int security = getValidSecurity(context);             SettingModule.getInstance(context).sendWifiApInfo(ssid, pw, security);              }if(cstate == WIFI_AP_STATE_DISABLED  || cstate == WIFI_AP_STATE_FAILED) {             if(mHandler != null)                 mHandler.sendEmptyMessage(MESSAGE_AP_STATE_FAILED);             }         }         }     };              public enum WifiCipherType {         WIFICIPHER_NOPASS, WIFICIPHER_WPA, WIFICIPHER_WEP, WIFICIPHER_INVALID, WIFICIPHER_WPA2     }          public String getValidApSsid(Context context) {         try {             Method method = mWifiManager.getClass().getMethod("getWifiApConfiguration");             WifiConfiguration configuration = (WifiConfiguration)method.invoke(mWifiManager);             return configuration.SSID;           } catch (Exception e) {                 Log.e(TAG,"testing" + e.getMessage());                 return null;                 }     }


Can the E Adhaar card or the Nationalized Bank Passbook be used as identify proof for traveling with Jet Airways within India?

Is post office ID card accepted as ID proof for flight to travel withinin India? What else other than PAN card, driving license is accepted as ID? Where do I need to show it?


I am new to Ubuntu and am currently working with Ubuntu 14.04 LTS. I installed VirtualBox to create another Ubuntu VM. Initially I had problems with maximizing my Ubuntu VMscreen. I resolved the issue by installing the drivers. I rebooted the system and tried again, but the issue persists. Please excuse my layman terms.

I've recently installed Ubuntu on Oracle's Virtualbox.  Now I want to install the guest additions.  I started up my Ubuntu guest OS, clicked "Devices" and chose "Install Guest Additions". Nothing happened, and I don't see the CD icon on my desktop.  How can I make this work?


Given 2 integers $a$ and $b$ whose gcd is 1 (coprime). Now the value of $ax + by$ can be any multiple of gcd$(a, b)$, which is 1 in this case. So literally  $ax + by$ can be any integer value. I have verified it for some small coprime numbers, but what is the mathematical reason behind this?

How can i prove that  if $\gcd(a,b)=1$ there exist $x>0$ and $y>0$ such that $ax-by=1$?


my NTFS drives have always mounted with write access now suddenly they don't. How do I get them to mount with write access?  I mount them simply by going to "other locations" and clicking the drive.  I'm on Ubuntu Budgie 18.04.

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


What I really want to know is can this be something they can fix in the future with an update? Will I be able to see Pokemon in the future on my phone even if it doesn't have a gyroscope or will I just have to get a new phone? And does anyone know when the next update will come?

When initiating a battle it starts off in AR mode, but then warns me saying my phone's orientation is not detected. I am then forced to turn off AR mode. Has anybody experienced this? If so, what are the solutions?    Per comments, I am unsure this is a permissions issue. I have everything turned on.


Yes, I am aware of observations of "massive objects", for example near the center of the galaxy. But is there any evidence that the object in question is a black hole, with all its commonly attributed properties? Or are black holes just an unconfirmed artifact of general relativity, i.e. something that is an abstract mathematical concept and not a real object?  I am not asking about means of detecting them, I am aware of those means. I'm interested if there's anything suggesting that the properties commonly attributed to black holes, considered a "fact", other than large mass, have anything to do with reality, or are completely abstract and deduced from math.

Yes, I am aware of observations of "massive objects", for example near the center of the galaxy. But is there any evidence that the object in question is a black hole, with all its commonly attributed properties? Or are black holes just an unconfirmed artifact of general relativity, i.e. something that is an abstract mathematical concept and not a real object?  EDIT: That is not an answer to my question. I did not ask about means of detecting them, I am aware of those means. I'm interested if there's anything suggesting that the properties commonly attributed to black holes, other than large mass, have anything to do with reality, or are completely abstract and deduced from math.


I've tried a few examples below when trying to examine what's going on when creating (instantiating?) Java's built in data structures Works:         LinkedList<Integer> test1 = new LinkedList<Integer>();          List<Integer> test3 = new LinkedList<Integer>();          Queue<Integer> test5 = new LinkedList<Integer>();          Set<Integer> test6 = new HashSet<Integer>();  Doesn't work:         LinkedList<Integer> test2 = new List<Integer>();          Queue<Integer> test4 = new List<Integer>();   From digging around, I see that  LinkedList is it's own class that implements List HashSet is it's own class that implements Set List and Queue is an interface  So is it correct to say that the way this works is that you need to do the following? [Interface]<type> name = new [Class]<type>()' Is this saying you are creating an object of the Class but are going to be using the methods of the Interface? Is there a reason why this is the case? Does this have something to  do with polymorphism? I recently asked a question and not sure if they are related.

I have seen this mentioned a few times and I am not clear on what it means. When and why would you do this?   I know what interfaces do, but the fact I am not clear on this makes me think I am missing out on using them correctly.   Is it just so if you were to do:  IInterface classRef = new ObjectWhatever()   You could use any class that implements IInterface? When would you need to do that? The only thing I can think of is if you have a method and you are unsure of what object will be passed except for it implementing IInterface. I cannot think how often you would need to do that.   Also, how could you write a method that takes in an object that implements an interface? Is that possible?


Can I make a shell script trash files instead of delete them?  In the past I used gvfs-trash but this doesn't appear to exist in Ubuntu 10.10.

I would like to know if there is a command I can issue in a terminal so I do not classically remove (rm) the file, but instead move it to trash (i.e. Nautilus Move to Trash behavior).  In case there is such a command, I would also be interested in knowing what it is.


Prove that there is a nonsingular $T \in M_n(R)$ such that $A = TBT^{−1}$ if and only if there is a nonsingular $S \in M_n$ such that both $A = SBS^{−1}$ and $\bar{A} = S\bar{B}S^{−1}$. (Here $M_n$ is the set of $n \times n$ complex matrices).  If direction: We can take $S = T$ i.e. imaginary part being zero. Then, $A = SBS^{-1}$ obviously. Moreover, $\bar{A} = \overline{SBS^{-1}} = \bar{S}\bar{B}\bar{S^{-1}} = S\bar{B}S^{-1}$. The only if direction: Let $S = H+iC$ and $\bar{S} = H-iC$ where $H,C \in M_n(R)$. Then, $A = SBS^{-1} = (H + iC)B(H+iC)^{-1}, \bar{A} = \bar{S}\bar{B}\bar{S^{-1}} = (H-iC)\bar{B}(H-iC)^{-1} = S\bar{B}S^{−1} =(H + iC)\bar{B}(H+iC)^{-1}$. I guess I should show that $S = \bar{S}$ i.e. $H+iC = H - iC$. Because if complex conjugate of $S$ is equal to $S$ then $S \in M_n(R)$ so, we will complete the proof.

Given a field $F$ and a subfield $K$ of $F$. Let $A$, $B$ be $n\times n$ matrices such that all the entries of $A$ and $B$ are in $K$. Is it true that if $A$ is similar to $B$ in $F^{n\times n}$ then they are similar in $K^{n\times n}$?   Any help ... thanks!


This is a all in one printer (printer, scanner). Tried to run hplip-3.19.1.run according to HP, but seems not working. How to troubleshoot?

Let's assume that one has some modern HP printer and/or scanner which is not supported by HPLIP package from official repository. Currently Ubuntu versions have :  trusty (14.04LTS): 3.14.3-0ubuntu3.4 xenial (16.04LTS): 3.16.3+repack0-1 bionic (18.04LTS): 3.17.10+repack0-5 focal (20.04LTS): 3.20.3+dfsg0-2 groovy (20.10): 3.20.5+dfsg0-3build1 hirsute (21.04): 3.21.2+dfsg1-2   What can one do if printer is supported in newer version of HPLIP (checked this in )?


I would like to call a jar file from a windows batch file. One requirement is to be able to pass all the batch file arguments as-is to the jar file invocation. For example,  Required Command line:  foo.bat --flag1=x --flag2=y --flag3=z   The batch file foo.bat should invoke foo.jar like follows:  java -jar foo.jar --flag1=x --flag2=y --flag3=z   How do I make the batch file do this?  I can do some batch variable magic with % to do this, but is there a simpler way to do this?

I'd like to find a Windows batch counterpart to Bash's $@ that holds a list of all arguments passed into a script.   Or I have to bother with shift?


I have run the JDK 1.8 installer from , and it all apparently installed correctly. But in the terminal, when I do:    javac -version   It still reports 1.6.0_65  What am I doing wrong?  I'm using Mavericks 10.9.4

Questions  Why do versions differ?   Should we trust Oracle's verification routine?    In some cases, the  is different from the version shown at the command line.   Example    That example, in detail  According to Oracle in the browser:    Java 7 Update 9   According to the Java Console:   Java Plug-in 10.9.2.05 Using JRE version 1.7.0_09-b05 Java HotSpot(TM) 64-Bit Server VM   According to the java command:   sh-3.2$ java -version java version "1.8.0-ea" Java(TM) SE Runtime Environment (build 1.8.0-ea-b58) Java HotSpot(TM) 64-Bit Server VM (build 25.0-b02, mixed mode)


I know how to get them (extended Euclidean algorithm using the mod and the number you want the inverse of if their gcd is 1, the inverse is the number you get * the one you have in the linear combination), but I don't understand what this means.  I know inverses are important for decryption for example. I just don't quite understand how it works. And why exactly is it that you can only have an inverse when gcd(a,m)=1 ? (a being any number, m being the mod your are using)

Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.  Can someone help me with this?


I have cooked chicken breasts today and they read 83c (safe is 73c) with a ThermoWorks Thermopop (best company in the industry). When I sliced them they had small pink strips on the inside. What does it mean? Was the chicken safe? Is it impossible for chicken to be both slightly pink and safe?

Last night I was grilling chicken thighs on a barbecue and I was told that if there was any pink inside them, they are not safe to eat. My question is twofold:  (a) Is this true?  (b) Is there a way to tell that doesn't involve cutting the thighs open to have a look at the colour?


I have a local Git repository and all I want to do is copy all of the files from a particular revision to a folder outside of the working directory. I was assuming that it would just be a single command.  I'm probably missing something obvious, but I can't for the life of me work it out.  Thanks, LJ

I've been wondering whether there is a good "git export" solution that creates a copy of a tree without the .git repository directory. There are at least three methods I know of:   git clone followed by removing the .git repository directory.  alludes to this functionality but starts with "Just read the desired tree into the index..." which I'm not entirely sure how to do.  is a third party script that essentially does a git clone into a temporary location followed by rsync --exclude='.git' into the final destination.   None of these solutions really strike me as being satisfactory. The closest one to svn export might be option 1, because both those require the target directory to be empty first. But option 2 seems even better, assuming I can figure out what it means to read a tree into the index.


How to add class on a textbox if its empty? I am using getmdl.io framework. What I want to do is when the textbox is empty I want to add a class which is (is-focused, is-invalid and is-dirty)
      <input class="mdl-textfield__input" type="text" id="fullname" name="fullname" autocomplete="off">      Full name
   and this is my javascript code when the submit button is click.  function validate () {     var f = _('fullname').value;     if (f == "") {         _('fn').className += " is-invalid";     } }

I have an element that already has a class: <div class="someclass">     <img ... id="image1" name="image1" /> </div>  Now, I want to create a JavaScript function that will add a class to the div (not replace, but add). How can I do that?


I am using Ubuntu 18.04 ..Using apt and synaptic when trying to install apt says that I have broken packages and synaptic wants to uninstall programs that I use in order to install wine what is a good way to install wine with out going through the headache of removing packages just to have it installed?   Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies: winehq-devel : Depends: wine-devel (= 4.2~bionic) E: Unable to correct problems, you have held broken packages.   the problem came because I needed to uninstall then reinstall wine for other purposes this is not a duplicate of  because I did not update Ubuntu. the problem its self came from having to reinstall wine not updating ubuntu

After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.


As I understand it, there were two things that could hypothetically destroy the One Ring: dragonfire and lava in a volcano. Unfortunately, the last dragon was killed before the events of Lord of the Rings, so that option wasn't available.  However, surely there were other volcanoes in Middle Earth, even if they may have been much further away than Mt. Doom. Moreover, there were also probably plenty of places where the dwarves had dug deep enough to hit lava, which could have served the purpose equally well. Neither of these options would have been without danger, but surely almost anything would be better than, you know, sending a pair of hobbits deep into the heart of the enemy's territory.  So why didn't the Fellowship just hike to some volcano on the far side of Harad, or get a dwarven guide to take them deep under some mountains, and cast the One Ring into the lava there?

Was there something more mystical about Mount Doom that meant another volcano wouldn't work and no matter how much energy was put into it, it would not be destroyed?  A comment mentioned that not even Ancalagon the Black, the greatest dragon, could not have done it; but how about a Balrog? What about another Maia or a Vala? Could a sufficiently advanced technology destroy it? Given that middle earth was becoming more industrialized wasn't it only a matter of time until a furnace or other artificial heat source that was hot enough was created?  If some catastrophe destroyed Middle Earth entirely would the ring be unmade, or would Eru have to do it himself?


When we paste a table from a note pad or word or any other source its not coming in a good table format in this Stack Overflow question editor/text box space. My question is how do you make an unscrambled table (good format table) here. What do you do to make this happen? For example I paste the following table from Notepad, but it looks non-understandable:  ID    LinkID  PC  TotalnoofoccurenceofID                  10R46   R*1005  8017    2 10R46   R*10335 5019    2 100R91  R*1005  8017    1 10R91   R*243   8870    1 10M95   R*4918  8305    3 10M95   R*9017  8305    3 10M95   R*9470  8221    3    I saw some people changed this into a good HTML-like table format.

It seems like a lot of people try to display tables in Stack Overflow questions, but don't do a very good job. Is there Markdown syntax that supports creating a proper table?


Let $\mathfrak{a}:=(f_1,\ldots,f_r)\subset k[x_1,\ldots,x_n],\mathfrak{b}:=(g_1,\ldots,g_s)\subset k[y_1,\ldots,y_m]$ be radical ideals. Then I wish to prove that $\mathfrak{c}:=(f_1,\ldots,f_r,g_1,\ldots,g_s)\subset k[x_1,\ldots,x_n,y_1,\ldots,y_m]$ is a radical ideal. If we set $x=(x_i)_i,\ y=(y_i)_i$ for simplicity, then otherwise stated, I wish to prove that $$\sqrt{k[x,y]\mathfrak{a}+[x,y]\mathfrak{b}}=k[x,y]\mathfrak{a}+[x,y]\mathfrak{b}=\mathfrak{c}$$ Trivially we have $\supseteq$. Suppose $f^t\in k[x,y]\mathfrak{a}+[x,y]\mathfrak{b}$ for some $t\in\mathbb{N}$, so let $f^t=f'(x,y)f''(x)+g'(x,y)g''(y),\ f',g'\in k[x,y],\ f''\in\mathfrak{a},\ g''\in\mathfrak{b}$. However, I can't figure out the next step from here.  Edit: $k$ is algebraically closed.

Let $X\in\mathbb{A}^n$ and $Y\in\mathbb{A}^m$ be affine varieties (irreducible algebraic sets). Then, if we denote by $i_X$ and $i_Y$ their ideals in their respective affine spaces, we define their product in $\mathbb{A}^{n+m}$ as the set $$ X\times Y = \{(x,y):x\in X\text{ and } y\in Y\} = \{(x,y):x\in Z(i_X)\text{ and }y\in Z(i_Y)\}. $$ Using the second characterization it's easy to show that in fact $X\times Y$ is closed in $\mathbb{A}^{n+m}$ and particularly that $X\times Y = Z(I_X+I_Y)$, where $I_X$ and $I_Y$ are the vanishing ideals of $X\times\mathbb{A}^m$ and $\mathbb{A}^n\times Y$ (these ideals clearly are in bijective correspondence with $i_X$ and $i_Y$, respectively).  Then, by the Nullstellensatz, we get $I(X\times Y) = \sqrt{I_X+I_Y}$. The problem is that the references I've seen claim that in fact $I(X\times Y) = I_X+I_Y$ (, example 2.3.9 in page 25, and Georges' answer in , specially the last display).   This would only be true if $I_X+I_Y$ is radical, which I haven't been able to show for this case and know isn't true in general (see ). Are my references wrong, or what am I missing?


I have a file sharing website . It's hosted on a dedicated server which have 16gb RAM and 2tb storage . Now I need more storage and RAM but my hosting service can't provide more than 2tb on single machine . Can I host this site on 2 server with another 2 Tb storage . Will I get 4tb storage for my site . I'm using apache as a server , MySQL for database and php for server side language .

I'm planning on releasing an iOS app that downloads video from my server. If hundreds of people on the launch day try to do this, then my website and the services that my server provides will clearly go down. How do you host a website on multiple servers? When someone tries to access my site, how is their request passed to an available server? How do Apple and Google do it? Thanks for your help.


I would like to launch a .exe when a specific USB device is connected (for instance a Akai LPK25 USB MIDI keyboard).  Is there a simple way to do this with Windows?

I know it has been discussed that it is not possible to start an application from an usb drive upon connection due to limitations of autorun (or autoplay??) in Win 7. But it is possible to create a scheduled task having an event type trigger. Surely there must be an event occurring when the drive -- or any USB device, for that matter -- is connected.    Does anybody have the slightest idea which Event ID should I use? Or at least what type of event? Where can I find the event in event viewer?


We all know that there is a limit to the lowest temperature which can be achieved i.e. $0K$. But I wanted to know if there is a limit to the highest temperature which can be attained. And if there is a limit, what is that temperature?

If temperature makes particles vibrate faster, and movement is limited by the speed of light, then I would assume that temperature must be limited as well. Why is there no limit?


I am having problem in triggering the 5V relay with the output GPIO pin of ESP8266 node MCU. I think the voltage provided by the output GPIO pin is not enough to trigger the relay. I'm thinking of turning of the a AC operating light using the relay. How to do please explain. Can we replace the relay with any transistor circuit to operate the same? Please explain elaborately with the schematics.

I'm currently working on a project where I turn off the ac appliances when the input signals of the relay get high. I'm using a 5V 10A relay and ESP8266 node MCU. But the problem is controller is unable to switch the relay. What should I do? Please help.


I need to show that $f:[0,1] \rightarrow \mathbb{R}$ is Riemann integrable on $[0,1]$ if for all $x \in [0,1]$, $\lim\limits_{t \rightarrow x} f(t)$ exists.  I need to show first $f$ is bounded. Using the compactness of $[0,1]$, I tried using a finite subcover of $[0,1]$ generated from the definition of the limit existing. Now to show that $U(P,f) - L(P,f) < \varepsilon$, I have no idea how to start that part of the proof. Any help is welcome, although help with an elementary approach is preferred since chapter 6 of baby Rudin is mostly what I can work with.

Suppose $f : [ 0, 1 ] → \mathbb{R}$ and $\lim\limits_{x \rightarrow c} f ( x )$ exists for all $c \in [ a , b ]$. Show that $f$ is Riemann integrable on $[ a , b ]$.  I can show this $f$ is bounded on $[a,b]$ since the limit exists at every point. But I'm not sure how to proceed. Any hints or help would be great.


I am reading the elements of integration by Robert Bartle.  In chapter 2 the definition of a $\sigma$ algebra is given like this.  A family $\sum$ of subsets of a set X is said to be a $\sigma$ algebra if   (i) $\phi$, X belongs to $\sum$.   (ii)If A belongs to $\sum$ then the compliment $X \backslash A$ belongs to $\sum$  (iii) If $(A_n)$ is a sequence of sets in $\sum$ then union $\cup^\infty_{n=1}A_n$ belongs to $\sum$  Then in chapter 9, the definition of an algebra is given like this.  A family $\sum$ of subsets of a set X is said to be an algebra if   (i) $\phi$, X belongs to $\sum$.  (ii) If E belongs to $\sum$ then its complement $X \backslash E$ also belongs to $\sum$.  (iii) If $E_1,...,E_n)$ belongs to $\sum$ then their union $\cup^n_{j=1} E_j$ also belongs to $\sum$.   What is the difference between these two definitions.  What is the difference between a $\sigma$ algebra and an algebra?

An algebra is a collection of subsets closed under finite unions and intersections. A sigma algebra is a collection closed under countable unions and intersections.   Whats the difference between finite and countable unions and intersections? Does "countable" mean it implies there can be infinitely many unions and intersections?    Secondly, I was reading a definition  For an algebra on a set: By De Morgan's law, $A \cap B = (A^c \cup B^c)^c$, thus an algebra is a collection of subsets closed under finite unions and intersections.  What law are they using here to get $A \cap B = (A^c \cup B^c)^c$? I thought de morgan's law was $(A\cap B)^c = A^c \cup B^c$?  Finally, what exactly do they mean by "closed under finite unions and intersections?


hyperref: Wrong DVI mode driver option `dvips',(hyperref) because pdfTeX or LuaTeX is running in PDF mode. \ProcessKeyvalOptions{Hyp}   How can i fix this error?   I m trying to compile a template of MMA journal. It is under this link

I'm having this Error when I try to compile my .tex file with xelatex:  ! Package hyperref Error: Wrong DVI mode driver option `dvips', (hyperref)                because XeTeX is running.  See the hyperref package documentation for explanation.   This is my LaTeX header  \documentclass[10pt, a4paper, dvips,]{moderncv}  \moderncvtheme[grey, roman]{classic}  \usepackage{ifxetex} \ifxetex % only for xelatex \usepackage{xltxtra} % this should load both fontspec & xunicode \usepackage{fontspec} \setromanfont{Helvetica Neue} \else % \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \fi % \ifxetex   Any ideas?  EDIT:  I removed the 'dvips', now I get:  ! Package hyperref Error: Wrong driver option `pdftex', (hyperref)                because pdfTeX in PDF mode is not detected.  See the hyperref package documentation for explanation.   Now my first latex line  \documentclass[10pt, a4paper]{moderncv}   Any clues ?


questions asks how to write 0 in unary and the answer given was (literally) as nothing (with no symbol). I'm wondering how you would write a decimal (0.1 for example) in unary. Since 1^(-n) = 1, I presume it's impossible, $$.x = x,$$ $$.xx = xx$$ and so on. Is there a way to write numbers with decimal places in unary?

In the decimal system: $...-3, -2, -1, 0, 1, 2, 3...$ In the binary system: $...-11, -10, -1, 0, 1, 10, 11...$ In the unary system: $-111, -11, -1, \text{ ??? }, 1, 11, 111...$   I was only able to find a related question but none with an answer so far:


I am passing different types of argument to the fun(), the code gets compiled, but still, the same function that prints "Class B" is getting executed. Shouldn't there happen overloading of functions? Why does this happen?  #include <iostream> using namespace std;  class A {     public:     void fun(int x)     {         cout<<"class A"<<endl;     }  };  class B: public A {     public:     void fun (char c)     {         cout<<"Class B"<<endl;     } };  int main() {     B obj;     obj.fun('c');     obj.fun(3); }

I have a function with the same name, but with different signature in a base and derived classes. When I am trying to use the base class's function in another class that inherits from the derived, I receive an error. See the following code:  class A {     public:     void foo(string s){}; };  class B : public A {     public:     int foo(int i){}; };  class C : public B {     public:     void bar()     {         string s;         foo(s);     } };   I receive the following error from the gcc compiler:  In member function `void C::bar()': no matching function for call to `C::foo(std::string&)' candidates are: int B::foo(int)   If I remove int foo(int i){}; from class B, or if I rename it from foo1, everything works fine.   What's the problem with this?


how can I put these two images beside each other, How can I do that?  code I tried  I am attaching figure it look like this.  \documentclass[tikz,border=3.14pt]{standalone} \usepackage{tikz-3dplot} \usetikzlibrary{arrows.meta}  %\usepackage{graphicx} %\usepackage{caption} %\usepackage{subcaption}  %\usepackage{xcolor}   \begin{document}  %\begin{figure}[!tbp] %    \begin{subfigure}[b] \tdplotsetmaincoords{60}{97} \begin{tikzpicture} [scale=2.0, line cap=round, line join=round, >=latex,tdplot_main_coords]  \draw[->] (0,0,0) -- (3,0,0)node[below]{$x$}; \draw[->] (0,0,0) -- (0,3,0)node[below]{$y$}; \draw[->] (0,0,0) -- (0,0,3.5)node[left]{$z$}; \draw[fill] (0,0,0) circle (0.5pt) node[above, left]{$o$};   \draw[thick] (2.5,1,0) -- (2.5,1.5,0) -- (1.5,1.7,0) -- (1.5,1.2,0) -- (2.5,1,0) -- (0,0.7,2)node[below]{$ $}; %cube lower square  \draw[thick] (0,1.2,1.7) -- (0,0.7,2) -- (0,1,2.8) -- (0,1.5,2.5) -- (0,1.2,1.7) node[below]{$ $}; %cube upper square  \draw[thick] (0,1.2,1.7) -- (2.5,1.5,0) node[below]{$ $}; \draw[thick] (0,1.5,2.5) -- (1.5,1.7,0) node[below]{$ $}; \draw[thick, dashed] (0,1,2.8) -- (1.5,1.2,0) node[below]{$ $};   \draw[fill] (0,1.18,2.3) circle (0.5pt) node[above, left]{$ $}; \draw[thick,->] (0,1.18,2.3) -- (0,1.18,3.6)node[below, left]{$\hat{k}$}; \draw[thick,->] (0,1.18,2.3) -- (0,2,3.6)node[below, right]{$\widehat{n_k}$};  \draw[thick] (0,1.18,3.2) .. controls (0,1.18,3.3) and (0,1.6,3.4) .. (0,1.74,3.2); %angle \draw[fill] (0,1.5,3.31) circle (0.05pt) node[above]{$ \gamma_k $};  %\draw (0,0) node[minimum size=2cm,draw] {square}; %\draw (0,-2) node[minimum size=2cm,draw,circle] {circle};    \end{tikzpicture} %\end{subfigure}   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %\hfill % \begin{subfigure}[b] \tdplotsetmaincoords{60}{97} \begin{tikzpicture} [scale=2.0, line cap=round, line join=round, >=latex,tdplot_main_coords]  \draw[->] (0,0,0) -- (3,0,0)node[below]{$x$}; \draw[->] (0,0,0) -- (0,3,0)node[below]{$y$}; \draw[->] (0,0,0) -- (0,0,3.5)node[left]{$z$}; \draw[fill] (0,0,0) circle (0.5pt) node[above, left]{$o$};   \draw[thick] (2.5,1,0) -- (2.5,1.5,0) -- (1.5,1.7,0) -- (1.5,1.2,0) -- (2.5,1,0) -- (0,0.7,2)node[below]{$ $}; %cube lower square  \draw[thick, rotate=90] (0,1.9,-1.2) ellipse (18pt and 30pt);% upper circle \draw[thick, rotate=90] (0,-1.1,-1.27) ellipse (18pt and 30pt);% lower circle  %\draw[thick] (0,1.2,1.7) -- (0,0.7,2) -- (0,1,2.8) -- (0,1.5,2.5) -- (0,1.2,1.7) node[below]{$ $}; %cube upper square \draw[thick] (0,0.7,2) .. controls (0,1,2) and (0,1,2) .. (0,1.2,1.7); \draw[thick] (0,0.7,2) .. controls (0,0.7,1.8) and (0,0.7,2.4) .. (0,1,2.8); \draw[thick] (0,1,2.8) .. controls (0,1.1,2.8) and (0,1.2,2.8) .. (0,1.5,2.5); \draw[thick] (0,1.5,2.5) .. controls (0,1.4,2.3) and (0,1.3,2.4) .. (0,1.2,1.7);     \draw[thick] (0,1.2,1.7) -- (2.5,1.5,0) node[below]{$ $}; \draw[thick] (0,1.5,2.5) -- (1.5,1.7,0) node[below]{$ $}; \draw[thick, dashed] (0,1,2.8) -- (1.5,1.2,0) node[below]{$ $};   \draw[fill] (0,1.18,2.3) circle (0.5pt) node[above, left]{$ $}; \draw[thick,->] (0,1.18,2.3) -- (0,1.18,3.6)node[below, left]{$\hat{k}$}; \draw[thick,->] (0,1.18,2.3) -- (0,2,3.6)node[below, right]{$\widehat{n_k}$};  \draw[thick] (0,1.18,3.2) .. controls (0,1.18,3.3) and (0,1.6,3.4) .. (0,1.74,3.2); %angle   % Points \draw[fill] (0,1.5,2.5) circle (0.05pt) node[above, right]{$ \Delta{S_k} $};  \draw[fill] (2.5,1.24,0) circle (0.05pt) node[below]{$ \Delta{y_k} $}; \draw[fill] (2,1.6,0) circle (0.05pt) node[below, right]{$ \Delta{x_k} $}; \draw[fill] (1.7,1.16,0) circle (0.05pt) node[below]{$ \Delta{A_k} $}; \draw[fill] (2.96,0.6,0) circle (0.05pt) node[below]{$ R $}; \draw[fill] (0,0.4,1.7) circle (0.05pt) node[below]{$ S $}; \draw[fill] (0,1,2.6) circle (0.05pt) node[below, left]{$ (x_k,y_k,z_k) $};      %\draw (0,0) node[minimum size=2cm,draw] {square}; %\draw (0,-2) node[minimum size=2cm,draw,circle] {circle};    \end{tikzpicture}   %\end{subfigure} %  \caption{fig 11}  %\end{figure} \end{document}

I have used the following code:      \begin{figure}[h]   \begin{tikzpicture}          \draw[->] (-0.5,0) -- (4,0) node[right] {$x$};         \draw[->] (0,-0.5) -- (0,4) node[above] {$y$};         \draw (0,0.5) -- (4,2);         \draw [dashed] (0,1.5) -- (4,4);   \end{tikzpicture}   \caption{No Interaction} \label{fig:M1}    \begin{tikzpicture}         \draw[->] (-0.5,0) -- (4,0) node[right] {$x$};         \draw[->] (0,-0.5) -- (0,4) node[above] {$y$};         \draw (0,0.5) -- (4,2.5);         \draw [dashed] (0,1.5) -- (4,3.5);   \end{tikzpicture}.  \caption{Interaction} \label{fig:M2}   \end{figure}     to insert two figures, however it places them one on top of the other and I would like them next to each other but labelled independently, is this possible?


I am a citizen of Pakistan and on my way to San Francisco I have 20 hour stay at Heathrow airport. Do I need a transit visa if I would want to stay at a hotel overnight in London heathrow?   I have a valid US visa and confirmed flight to San Francisco from London!

Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.


I use Kubuntu and recently upgraded to Raring directly from Precise. Until Precise, I always installed the OS using the alternate CD and not the desktop CD, because I could later on mount the image and use it as an offline package repo. For instance if I remove a package installed by the default installer and later I want to install it again, I can just install it from the ISO without needing to download it again. However, since Quantal the alternate CD no longer exists, so I am not sure how to set up the installed image as a local repo. I mean, doing find . -name "*.deb" inside the ISO tree after loopmounting it only shows a few packages like libc6 gcc and such and not the full set of packages that are actually installed -- I presume they are included in pre-installed form inside casper/filesystem.squashfs. Given this situation, is it or is it not possible to use the Raring install images as offline repos? If yes, how? Thank you! Edit: Quite a few people marked this as a dup of:  but the steps outlined there (that thread is from 2010) do not work with the Raring image. IIUC they would work only with the alternate images and they are not available any more. So anyway I tried those instructions and did:  $ mount | grep loop /mnt/sda8/samjnaa/ai/ubuntu/raring/kubuntu-13.04-desktop-amd64.iso on /mnt/loop0 type iso9660 (ro) $ sudo apt-cdrom -d /mnt/loop0/ add Using CD-ROM mount point /mnt/loop0/ Unmounting CD-ROM Waiting for disc... Please insert a Disc in the drive and press enter Mounting CD-ROM... E: Failed to mount the cdrom.

I have all images of Debian, Ubuntu and Ubuntustudio as .iso. How can I use them as repository to install my desired packages with sudo apt-get install package-name?  I easily mount the .iso file with Archive Mounter, but when adding CD-ROM in Software Sources it says Please Insert CD-ROM.   How should I do this without burning them to disk?


Let the roots be, $a,b$ and $c$  We have $$a+b+c=0\tag1$$ $$ab +bc +ca=-\frac68\tag2$$ $$abc = -\frac18\tag3$$

Can someone give me a hint on how can I solve the equation $$x^3 - x - 1 =0?$$  Thank you!


I wrote this statement in the main method  the Exception will be in the (GuaranteeYears) so i put it in the try block.  First in the main I make a Store object and pass number 4 in parameter, in the Store class I will have a array called arrProduct that will have the length 4:  boolean flag1 = true; while (flag1) {     try {         System.out.println("Ente GuaranteeYears");         int GuaranteeYears=read.nextInt();          StrongDevice s = new StrongDevice(code,type,price,Model,Capacity,GuaranteeYears); //the object          flag1 = false;         x.addProduct(s);      }   and this is my add method  public boolean addProduct(Product p) {     if(arrProduct.length==NumOfProduct)         return false;      arrProduct[NumOfProduct]=p;     NumOfProduct++;     return true; }   My question is: when I make the object and add it to the array it gives me NullPointerException - why that happened?

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?


So I have this one torus which I copied to get another torus. I did this by clicking shift+D. But now, Blender treats the tori as if they were one entity. If I select one, the other is automatically selected. I'm assuming this happened because I didn't separate them immediately by clicking P. How can I disconnect them now?

I added two torus objects, and when I click one of them, it also selects the other. They both share the same node thing. I want to delete one of them, but it keeps on deleting the other with it. I can't even undo placing the second torus without removing the other.


Since upgrading to Catalina (2016 Macbook Pro) a few weeks ago, every now and then I find there are "invisible rectangles" on on the screen where I can’t move my mouse. They're always [edit months later: not 100% always, actually] anchored to the top left, and could be on the primary or secondary monitor. They're varying widths and heights that don’t seem to correspond to any specific application windows. They don’t go away if you quit or hide applications. The usual width is anywhere from about 100 to 400px, and the height is anywhere from 200px to the full height of the screen. Theses things do disappear on their own sometimes, but disconnecting the external monitor doesn’t get rid of them — it just moves them the laptop screen, but usually with different proportions. They're always gone after a restart. I can’t seem to connect these to any specific app; like I said, they persist even if I quit all apps including utils that just run in the menu bar. Here’s a screen recording of me trying to move the mouse to the upper left corner, via regular moving and dragging a selection area:  I've tried looking in Activity Monitor when this is happening, but even with all the regular apps quit, there are still tons of system processes going on so it's hard to spot anything unusual. This look/sound like anything any of you have seen before?

In the bottom right corner of my Macbook Pro (running MacOS 10.15.3 Catalina with a second screen connected as main), sometimes, there is a region (invisible) where I just can't move the cursor to. I need to restart the MacBook Pro to let me access the region with my mouse cursor. The cursor just won't pass this region, just as if the screen has ended there. I have added a screenshot below and drawn the region. I read about applications that might behave weird and cause such an issue, but the problem persists even when all apps are closed. What could this be? Are there any known issues? Or yet better, known solutions? ... Update 1:  I have appended a screenshot of my arrangement and drawn a yellow box of the area which is not accessible.  Update 2:  The cursor is blocked from reaching the region in the third screenshot (I cannot reach the Files folder for example).  Update 3:  Today (2020/05/25, using Mac OS 10.15.4), the problem re-occured, but the non-accessible area has changed to the top-left, with the available height only being as much as the system menu and a width of 90%. (For example, I have a window in full height/width and I can no longer move the mouse cursor to the 'minimize' or 'close' window buttons).  Update 4:  2020/10/30, (using macOS 10.15.7) I returned my 15" MacBook Pro, because I thought the problem only appears on them. I encountered the same problem on a 13" MacBook with completely different apps installed. I suspect more and more that it's a very rare (race) condition / scaling bug in the OSX core that handles multiple display screens. The problem also happens on macOS 11.1 Big Sur.      Note: In the , someone has posted a video screenshot of what happens.


I have two random variables $X_{1}, X{2}$ following $U(0,1)$. I need to compute $E(X_{1}|X_{1} > X_{2})$. I am thinking that since the random variables are independent, so $X_{1}|X_{1} > X_{2}$ should just be $X_{1}$ and its expectation should be $\frac{1}{2}$. I don't have answer of this problem. I just want to check whether my approach is correct.

I am unable to compute conditional probability(x|x>y) in the above question. Also, I am unable to determine the region of integration for calculation of the above expectation.


In the elements of statistical learning book the lasso is written like this:  $\hat{\beta}^{lasso}=\operatorname{argmin}\left \{ \frac{1}{2}\sum_{i=1}^{N}(y_i-\beta_0-\sum_{j=1}^{p}x_{ij}\beta_j)^2 +\lambda \sum_{j=1}^{p}|\beta_j| \right \}$  Note that before the sum 1/2 is used. In some cases I see it as 1/(2N). Like e.g. this equation:  $\hat{\beta}^{lasso}=\operatorname{argmin}\left \{ \frac{1}{2N}\sum_{i=1}^{N}(y_i-\sum_{j=1}^{p}x_{ij}\beta_j)^2 +\lambda \sum_{j=1}^{p}|\beta_j| \right \}$  I don't understand what this would represent if I divide with the number of observations? I would very much appreciate any clarification.

This question might be dumb, but I noticed that there are two different formulations of the Lasso regression. We know that the Lasso problem is to minimize the objective consisting of the square loss plus the $L$-1 penalty term, expressed as follows, $$ \min_\beta \|y - X \beta\|_2^2 + \lambda \|\beta\|_1 \; $$  But often time I saw the Lasso estimator can be written as $$ \hat{\beta}_n(\lambda) = \displaystyle\arg \min_{\beta} \{\frac {1}{2n} \|y - X \beta\|_2^2 + \lambda \|\beta\|_1 \} $$  My question is, are the equivalent? Where does the term $\frac {1}{2n}$ come in? The connections between the two formulations is not obvious to me.   [Update] I guess anther question I should ask is,  Why is there the second formulation? What's the advantage, theoretically or computationally, of formulating the problem that way?


How can one prove the Killing form given by $B(X,Y)=Tr(ad(X) \circ ad(Y))$, where $X,Y \in \mathfrak{g}$ and $Tr$ is the trace, is $ad$-invariant. I mean, it verifies: $B(ad(X)(Y),Z)+B(Y,ad(X)(Z))=0$, with $ad$ the adjoint representation of Lie algebras and $ad(X)(Y)=[X,Y]$, Applying two times the Jacobi identity to $[Z,[X,[Y,W]]]$, I got: $ad(Z) \circ ad(X) \circ ad(Y)=ad(ad(Z)X) \circ ad(Y)+ad(X) \circ ad(ad(Z)Y)+ad(X) \circ ad(Y) \circ ad(Z)$ Then I tried to apply the trace, but I do not achieve what I want. Some ideas? Is there an easier way to do it?

Let $G$ be a matrix Lie group. Its Lie algebra $\mathfrak{g}$ comes equipped with a symmetric (2,0) tensor known as its Killing from, denoted $K$ and defined by  $$ K(X,Y) = -\text{Tr}(\text{ad}_X \circ \text{ad}_Y)$$  where $\text{ad}_X \in \text{GL}(\mathfrak{g})$ defined by $\text{ad}_X(Y)= [X,Y]$. Show that $K$ is Ad-invariant, in the sense that  $$  K(\text{Ad}_A(X), \text{Ad}_A(Y)) = K(X,Y) \quad \forall X,Y \in \mathfrak{g}, A \in G $$.  Here $\text{Ad}_A(X) = AXA^{-1} \in \mathfrak{g}$.   I suppose that it suffices to prove it on a basis, but it isn't a big deal to let $X$ and $Y$ be arbitrary. Choosing a basis $E_j$ for $\mathfrak{g}$, I write $$ [E_j,E_k] = {c_{jk}}^l E_l $$ $$ X = a^kE_k, Y = b^kE_k $$ and  $$ AE_kA^{-1} = {d_k}^lE_l. $$ Then $$ [X,[Y,E_m]] = [a^kE_k,[b^lE_l,E_m]] = a^kb^l {c_{kn}}^j {c_{lm}}^n E_j$$ and so the trace of this operator is $a^kb^l{c_{kn}}^j{c_{lj}}^n$. The left hand side is $$  [AXA^{-1},[AYA^{-1},E_m]] = [a^k{d_k}^lE_l,[b^n {d_n}^j E_j,E_m]]= a^kb^n{d_k}^l{d_n}^j {c_{jm}}^r {c_{lr}}^k E_k$$ so the trace of this operator is $$ a^kb^n{d_n}^j{d_k}^l{c_{jk}}^r{c_{lr}}^k $$  assuming the indices are correct. Now these two have to be the same somehow. Using that $\text{Ad}_A{[X,Y]}=[\text{Ad}_A{X}, \text{Ad}_A{Y}]$ may be promising, but I haven't found anything useful with it. A hint would be appreciated.


Suppose my opponent is playing Slivers, and has a  and a  on the field. On my side, I have a 1/1 Goblin token. My opponent declares both Slivers as attacking, and I block the Muscle Sliver with my Goblin. After combat, I Overload an , killing the Muscle Sliver. Since it took 1 damage and the +1/+1 from the  is removed, would the Metallic Sliver die?

I use  in a deck full of flying creatures. It is a 3/3 flyer with +1/+1 for each other flying creature in play. During a game, I had seven other flying creatures, making it a 10/10. My opponent cast a spell (and I'm sorry I don't recall the spell) that did 6 damage to all my creatures.  He contends that this kills Radiant Archangel as well because the static bonus of +1/+1 for all the flying creatures in play goes away once they are dead and the damage sticks around until the end of turn. Thus, after the spell resolves, the other flying creatures are gone so Radiant Archangel is only a 3/3, and it has 6 damage so it's dead.  I contend that when the damage was dealt, it was a 10/10 and survived the attack, and that the 6 damage can come out of the +1/+1 bonuses that the other flying creatures provided and that it lost once they were gone.  Does anybody have any official rulings on this?