TikZ seems to graph the cube root function with the code provided - on the positive x-axis. Why isn't TikZ plotting the whole graph?  \documentclass[10pt]{amsart} \usepackage{tikz} \usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings} \usepackage{tkz-euclide} \usetkzobj{all} \usepackage{pgfplots} \pgfplotsset{compat=1.11}   \begin{document}  \noindent \hspace*{\fill} \begin{tikzpicture} \begin{axis}[width=6in,axis equal image,clip=false,     axis lines=middle,     xmin=-10,xmax=10,     domain=-10:10, samples=201,     xlabel=$x$,ylabel=$y$,     ymin=-2.5,ymax=2.5,     restrict y to domain=-2.5:2.5,     enlargelimits={abs=1cm},     axis line style={latex-latex},     ticklabel style={font=\tiny,fill=white},     xtick={\empty},ytick={\empty},     xlabel style={at={(ticklabel* cs:1)},anchor=north west},     ylabel style={at={(ticklabel* cs:1)},anchor=south west} ] \addplot[samples=501,domain=-10:10,blue] {x^(1/3))} node[above,pos=0.9]{$\scriptstyle{y} = f(x)$}; \end{axis} \end{tikzpicture} \hspace{\fill}  \end{document}

When I found that a simple x^(1.0/3.0) does not yield a graph in PGFplots for negative values of x, I attempted to define my own function for CubeRoot using pgfmathdeclarefunction as below. But, am not able to get them to work.    These are based on , and .   This compiles as is, but has a problem if I set \DomainMin to a negative value. The CubeRootB function does not even compile, and I do not see what the problem with it is.  \documentclass{article} \usepackage{tikz}  \newcommand*{\DomainMin}{0.1} %\newcommand*{\DomainMin}{-2.0} % CubeRootA gives and error if DomainMin < 0  \tikzstyle{MyPlotStyle}=[domain=\DomainMin:2,samples=100,smooth]  \pgfmathdeclarefunction{gauss}{3}{% From links mentioned in the question     \pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}% }  \pgfmathdeclarefunction{CubeRootA}{1}{%     \pgfmathparse{%         ifthenelse(equal(#1,abs(#1)),%             (#1)^(1.0/3.0),%            #1 >= 0             -1.0*((abs(#1))^(1.0/3.0))% #1 is negative         )%     }% }  \pgfmathdeclarefunction{CubeRootB}{1}{%     \pgfmathparse{%         \pgfmathifthenelse             {\pgfmathequal{#1}{\pgfmathabs{#1}}}%             {exp(ln(#1)/3.0)}%            #1 >= 0             {-1.0*(exp(ln(abs(#1))/3.0))}% #1 is negative     }%      }  % Modified version of CubeRootB per Caramdir's suggestion \pgfmathdeclarefunction{CubeRootC}{1}{%         \pgfmathparse{%             ifthenelse(                 equal(#1,abs(#1)),%                 exp(ln(#1)/3.0),%            #1 >= 0                 -1.0*(exp(ln(abs(#1))/3.0))% #1 is negative             )         }%     }      \begin{document} \begin{tikzpicture} \draw [help lines] (-2,-2) grid [step=0.5] (2,2); \draw plot [MyPlotStyle] (\x,{gauss(\x,0,0.5)}); % \draw plot [MyPlotStyle] (\x,{    CubeRootA(\x)});% Error if DomainMin < 0 %\draw plot [MyPlotStyle] (\x,{1.0+CubeRootB(\x)});% Does not compile \draw plot [MyPlotStyle] (\x,{    CubeRootC(\x)});% Error if DomainMin < 0 \end{tikzpicture} \end{document}


I am working in QGIS (version 3.10). I know that in order to make certain distance analysis (in my case I want to do a heat map) a layer should have meters as units. Initially from the automatic SRC EPSG: 4326- WGS 84 I change my point layer' SRC to one set on metres (3857- WGS84/ Pseudo-Mercator). It does work in the sense the units do change to meters, however the points appear somewhere else. I tried to change the SRC of the project, start from scratch with the new SRC, different SRC combinations (using different SRCs for the project and/ or point layer) but just cannot get the units and the location both right.

I put 4 different layers into my ArcMap document, but only one of them will show up on the map! I should be seeing the other 3 layers as well. When I do a Zoom to layer, I can see one layer, but I cannot figure out how to make the other 3 show up at once on top of each other.  Before I opened ArcMap, I used ArcCatalog where I right-clicked 3/4 of the shapefiles and  clicked Properties → Coordinate system → Import and then clicked on my Trees layer, which has the coordinate system I want the other 3 to have. But when I opened ArcMap the 4 layers did not overlap, nor could I move them above or below each other.


It has an old SiS based graphics chip with 64mb memory, there were never 3D drivers for them. Ubuntu 10.10 doesn't even boot on it and my laptop, a Lenovo N200 with intel 9something graphics 128mb so I'm really worried. Broadband prices don;t come cheap in South Africa so the download has to be worth it. I can wait for the shipment but I've since orderd 10.10 and it hasn't come, so I don't know if I'm barred from using that service since I've been sent a disc every release.

For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?


I'm hooking up and old  HC-05 BT module and it powers even if vcc is disconnected, (if TX is high and is key is high), is it likely i fried something and it's broken?

I modified my Sega Master System to have a pause button on the actual controller. To process the signal, I soldered a quad NOR gate to the I/O and CPU circuits in the console. The idea is that the controller pause button sends a combined UP/DOWN signal, and the gate processes it and sends an NMI to the CPU, which is what the Pause button on the actual console does. This is the procedure recommended at the SMSPower forum, and I followed their diagrams.  Here's the thing: I installed the gate upside down, so that the packaging is resting on the circuit board, and the pins are sticking up in the air. I did this so it would be easier to solder the pins to the console, reasoning that the package is non-conductive anyway. When I tested it out, it didn't work correctly. As I was troubleshooting with my logic probe, I accidentally dislodged the Vcc connection, which I had soldered to a +5 Vcc solder point on the board. All of a sudden, it works correctly! I've checked the pin assignments over and over, and I'm positive that the Vcc pin isn't connected to anything; yet, the chip has power, and works as it is supposed to.  So, what is going on here? Was it a bad idea to install the chip package so that it touches the board? And why is the chip working when the Vcc pin is disconnected?  (edited to add requested information)  The gate is a CD4001AE Quad NOR; the datasheet is here:    The schematic is here, at the bottom of the page:


Last year I worked for X, a hat-trading company   or     Last year I worked for X, a hat trading company   For some reason I was inclined to go with the hyphenated version, which now seems wrong, but I'd like to be sure.

In the following two examples, is there any difference as to how amino acid should be hyphenated?   There are twenty amino acids. The amino acid content is 80%.   My intuition would be to hyphenate in the second example (where amino acid is a modifier) and not in the first, but I couldn't back it up.  Is there a general rule that would apply?


I was asked to prove p -> q |- ¬p or q by nature induction   $p \rightarrow q$         premise p                        assume q                        $\rightarrow e,1$ $¬ p \rightarrow ¬ q$ ¬p                       assume ¬p or q                   or-i, 3-5   is it correct?

Using only rules of natural deduction, I am trying to prove that $$p \implies q \vdash \lnot p \lor q$$ but am having a lot of difficulty. I was able to prove the other direction.   Could anyone show me or point me to the right direction?


I read a story when I was a child in the 70's that I cannot forget. It may have been from fiction written between 1950 - 1975. My older brother subscribed to several short fiction scifi magazines.  The story is of a young man who lived in a village. When villagers turned 16 their brains were measured as to what they could best hold.  At age 18, a specialized program was uploaded to their brains to make them the best possible specialist they could be, as needed by the society. One person would become the best keymaker, the best tailor, etc. Each persons identity in the social structure was based on optimizing the brain for their best possible application. The citizens were very proud of their occupations.  The young man was identified as imbecile and untrainable. He was sequestered to a prison. He read books and questioned his detainment - eventually breaking out. He goes on a journey to find out why he was imprisoned since he has demonstrated he is intelligent by learning so much while in prison. I will refrain from saying the ending...  Please help me identify this!

In the story I'm trying to recall, everybody on their thirteenth birthday (?) is assigned by some kind of brain analysis method a profession and given some kind of pill (?) that instantly (?) grants them the required knowledge and skills to start working immediately. Some professions are more sought after than others, especially in view of the olympic (?) games regularly held on a profession-by-profession basis.  The protagonist, however, is turned down from this system and dismissed with some general reason and has to work his way to adulthood the boring old way: studying from books. Eventually he rejects from his status as a "special" student and goes on the run, hiding from the teachers and envying the normal people.      Eventually, it turns out that the protagonist was actually smart enough that being spoonfed premade information was a waste. What he actually was assigned to was advancing the bundles of knowledge themselves, as well as being front line in the technological progress.  "Somebody has to write those textbooks! You can infuse knowledge about how to use today's technology, but you can't do that for tomorrow's - people that get assigned a profession become tied with their assigned technology and are only as relevant as that. If you want more, you must learn how things actually work, and there's no shortcut for that." (not an actual quote, but a specific passage as I remember it.)  The troubles the protagonists underwent were actually planned and necessary for him to acknowledge and accept his role in society.   This story was certainly longer than a couple pages, but it wasn't very long either. If it's a short story, it was probably written by Asimov, but I can't be sure. It rings me of Brave New World given the theme of government-issued population planning, but it certainly doesn't fit with anything else in the actual plot. Any idea?


I want to animate water splash.  All I want is to splash water from bottle to paper towel. Which method should I use ?    Thanks,

I am working on a project that requires the water to shoot out of the end of the pipe rather than what it is doing right. Now, I have played with some of the settings but am kinda afraid to mess with it too much since I am new to blender, and it does not play well when I mindlessly click.   Would I generate more fluid particles? Or would I change some property about the inflow animation? I added a cylinder object to the top of the pipe as well, I think that will help keep all the water inside of the pipe.   Thank you once again and have a great day!


The question is: Find the range of parameter 'a' for which the variable line $y = 2x + a $ lies between the circles $(x-1)^2+(y-1)^2$=1 and $(x-8)^2+(y-1)^2=4$ without intersecting or touching other circle. Now, how I solved it was realising the line has a positive slope of $+2$ and thus if it's a tangent to circle #1 then it's intercept should be negative and so using the condition of tangency, $a^2= m^2(r_1)^2+(r_1)^2= 4+1 $ And thus, as $a$ can only be negative (otherwise a positive value of $a$ will make the line intersect the circle) Thus, making the lower bound of $a> √5$ Similarly for the bigger circle $a<{√20=√[(2^2)(2^2)+(2^2)] }$ Hence I find that the solution should be $(√5,√20)$ but the actual solution is$ (2√5-15,-√5-1)$

Find the range of parameter $a$ for which the variable line $y = 2x + a$ lies between the circles $(x-1)^2+(y-1)^2=1$ and $(x-8)^2+(y-1)^2=4$ without intersecting or touching either circle.  Now, how I solved it was realising the line has a positive slope of $+2$, and thus if it's a tangent to circle #1 then its intercept should be negative. And so, using the condition of tangency, $$a^2= m^2(r_1)^2+(r_1)^2= 4+1 $$ And thus, as $a$ can only be negative (otherwise a positive value of $a$ will make the line intersect the circle). Thus, making the lower bound of $a> - \sqrt 5$. Similarly for the bigger circle $a<-\sqrt{20}=-\sqrt{(2^2)(2^2)+(2^2)}$ Hence I find that the solution should be $(-\sqrt5,-\sqrt{20})$, but the actual solution is $\left(2\sqrt 5-15,-\sqrt 5-1\right)$.


So I'm trying to create a Gmail filter that shows me all of the important emails that are unread and not archived. I'm using the following filter: is:important AND is:unread and is:inbox However it appears that it is only showing unread emails that are on the first page of the email and it is missing some of the emails that I have that are clearly marked "important" and they are unread. In addition to that I have another filter that should just show me any email that is not important but unread, and I'm having a similar issue with that is:unread and is:inbox -is:important

I'm trying to find mails that have one address in the recipients but another not in it.  I'm trying things like from:address1@gmail.com and not from:address2@gmail.com and from:(address1@gmail.com and not address2@gmail.com)  None of them work, and I can't find a good help page about boolean operators either.  Anyone has any idea?


In formal (not colloquial) English, is an organisation such as a sports club singular, plural, or is it discretionary?  E.g. is it preferable to write "The X club WAS formed" or "The X club WERE formed", or doesn't it matter?

I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved?


Where does the Higgs field get the energy which it transfers when some particles interact with it? And how do these interactions give mass to other bodies?

I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost. Is there a way to explain how the Higgs field works, in a way that people like me might have a hope of understanding?


I was reading through Enderton's "Mathematical Introduction to Logic" and came across 2 examples, one a formula, one a relationship:   ∃x(Qx→∀x Qx) ∀y∃x Pxy $\nvDash$ ∃x∀yPxy    Enderton claims the first one is a validity. I fail to see how this is the case. How would I show this?  For the second one, I explicitly defined a predicate P: a 2 place predicate that says ($y*x = 1)$ so the statement would read as following: For all y, there exists such that ($y*x = 1)$ but the right side would read: there exists x such that for all y, ($y*x = 1)$. Now if you do it the converse way, ie ∃x∀yPxy  $\vDash$ ∀y∃x Pxy then this relationship is actually true. My question is, is the example I provided enough to show the relationship holds for (2)?  edit: Not an exact duplicate, since there is a second part of the question that is not answered in the linked thread.

Why is this true?  $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$


I am using Ubuntu 18.04. I have disabled the lock screen but enabled suspend mode after 10 minutes.  Each time my PC goes into suspend mode, the first thing that I see when I move the mouse is a protection screen:    Then I have to click the bottom arrow and move it to the top.  Is it possible to disable the protection screen? So that I am directly on my desktop after moving the mouse?

I need to remove the annoying new "locking" screen that shows a giant clock: I can't remove it with just moving the mouse (as with any other desktop environment), the animation is slow, and it isn't asking me for a password!  I managed to disable it, just to discover that now I can't lock my screen on purpose, so I can't go away from the computer.  Just to clarify, I want to:   After some time the screen could go black, but if I move the mouse or press any key then I can use it directly (like a normal screensaver). If I press super-L then it is locked, and I must type the password to unlock (like a normal lock screen).   I found several "solutions", but none seems to work:


In PCA we start with a dataset and we reduce its dimensions by giving it new features that are each a linear combination of the original features of the dataset, and only keeping the ones with maximum variance.  These new features of our reduced dataset are eigenvectors of the covariance matrix of our original dataset. For some reason, making the new features the eigenvectors of the original covariance matrix does two things:   These new features will have a much larger variance than any of the features in the original dataset had. I don’t see why… These new features will all have zero covariance with one another…I also don’t see why.    Update - I understand why they have zero covariance with one a other: it's because the covariance matrices is symmetric, meaning that its eigenvectors are perpendicular.   Covariance can be thought of as a dot product between two vectors, and if the vectors are perpendicular, the dot product is zero.  But...I'm still confused as to why we use THOSE directions.

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.   I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it.        I strongly believe in the following quote:     You do not really understand something unless you can explain it to your grandmother. -- Albert Einstein   Well, I can't explain these concepts to a layman or grandma.   Why PCA, eigenvectors & eigenvalues? What was the need for these concepts? How would you explain these to a layman?


I have been working with blender 2.79 and trying to render a two dimensional video with a transparent background. When I look up examples they all seem to use a tool called "film". I can't find this anywhere can someone help me. Am I missing a setting?

I would like to render an animation as a series of .png images with transparent backgrounds for use in a video. Is this possible?


In the Gini Coefficient's , it is defined as $G= 1 - \frac{\Sigma_{i=1}^n f(y_i)(S_{i-1}+S_i)}{S_n}$ for discrete variables, where $S_i= \Sigma_{j=1}^i f(y_i)y_i$ and $S_0=0$ ($y$ being the discrete variable that takes $n$ different values), and it says that $AUC= \frac{1}{2}(1+G).$. However, I don't quite understand how I can get the AUC from that.   Let's suppose that I have response variables $y_1,...,y_k \in \{0,1\}$ in some test set and probabilities $\hat{p_1},...,\hat{p_k}$ for these observations generated by a logistic regression. With that information, how can I obtain $G$ to subsequently calculate AUC?

I am interested in calculating area under the curve (AUC), or the c-statistic, by hand for a binary logistic regression model.  For example, in the validation dataset, I have the true value for the dependent variable, retention (1 = retained; 0 = not retained), as well as a predicted retention status for each observation generated by my regression analysis using a model that was built using the training set (this will range from 0 to 1).  My initial thoughts were to identify the "correct" number of model classifications and simply divide the number of "correct" observations by the number of total observations to calculate the c-statistic. By "correct", if the true retention status of an observation = 1 and the predicted retention status is > 0.5 then that is a "correct" classification. Additionally, if the true retention status of an observation = 0 and the predicted retention status is < 0.5 then that is also a "correct" classification. I assume a "tie" would occur when the predicted value = 0.5, but that phenomenon does not occur in my validation dataset. On the other hand, "incorrect" classifications would be if the true retention status of an observation = 1 and the predicted retention status is < 0.5 or if the true retention status for an outcome = 0 and the predicted retention status is > 0.5. I am aware of TP, FP, FN, TN, but not aware of how to calculate the c-statistic given this information.


When can we say two matrices have the same Jordan form?   Well, it's obvious that if they're similar then they have the same Jordan form, but can we look further?  What if they have the same eigenvalues? That's not enough either because $\begin{bmatrix}0 & 1\\0&0\end{bmatrix}$ and  $\begin{bmatrix}0 & 0\\0&0\end{bmatrix}$ have the same values but they are not similar and therefore don't have the same Jordan form.  I can't find an example where two matrices have the same characteristic equation and minimal polynomial yet they are not similar but I am unable to prove it.  Is it enough to have the same algebraic multiplicity and geometric multiplicity?  I am not looking for the minimal condition where two matrices have the same Jordan form

I have a qualifying exam coming up in a couple days and I am just trying to understand some pathological examples I have in my notes. I will list a similar problem which I know the solution to and then the question.  True or False:   let $A,B \in \mathbb{Q}^{n \times n }$  Suppose $xI-A$ and $xI-B$ are equivalent then $\det(xI-A) = \det(xI-B)$.     I wrote in my notes this is true because any two matrices are equivalent in $\mathbb{Q[x]}^{n \times n}$ if and only if they have the same invariant factors.  Since the characteristic polynomial is a product of the invariant factors it follows that $\det(xI-A) = \det(xI-B)$.        True or False:   let $A,B \in \mathbb{Q}^{n \times n }$. If $\det(xI-A) = \det(xI-B)$ (in $\mathbb{Q}[x]$) then $xI-A$ and $xI-B$ are equivalent  in $\mathbb{Q}[x]^{n \times n}$   I think this is false because of the fact that equality of determinants is not strong enough to guarantee all invariant factors are equal but I do not have an example.


I have a number of reaction equations, I would like to label them as (r.1),(r.2),... etc, using \align.  So we would have:     equation 1      (r.1)      equation 2      (r.2)      equation 3      (r.3)      equation 4      (r.4)   I would very much appreciate any help.

I want to introduce a set of chemical reactions (see code below) within a text containing some standard equations. Standard equations should be numbered continuously, but the chemical reactions should be numbered R1-Rn. How can i do that ?  \begin{align}   \ce{CH4} &+ \frac{3}{2}\ce{O2} \rightarrow \ce{CO} + 2\ce{H2O} \label{eqn:hom2}\\   \ce{CO}  &+ \frac{1}{2}\ce{O2} \rightarrow \ce{CO2} \label{eqn:hom3}  \end{align}


Show that the Fejer kernel $$F_N(x) = \sum_{-N}^{N} \left( 1 - \dfrac{|n|}{N}\right)e_n$$ where $e_n(x) = e^{2\pi i n x}$ is the trigonometric monomial, can be written as  $$F_N(x) = \frac{e^{\pi i (N-1)x}\sin (\pi N x)}{\sin (\pi x)}$$ on the interval $(0,1)$.  Until so far I have researched, found and proven that $$F_N(x) = \frac{1}{N} \left|\sum_{i=0}^{N-1}e_n \right|^2$$ which is a gread leap for me, but not really for the whole proof. I also found a hint saying that I should use the geometric sums $$\sum_{i=0}^{N-1}e_n = \frac{e_N - e_0}{e_1 - e_0}$$ However, I do not know how that helps me. Any hints on how I can proceed would be greatly appreciated!

I'm trying to read a proof for the existence of an $(\epsilon , \delta)$ approximation to the identity that is a trigonometric polynomial. For this, the Fejér Kernel is defined as $$F_N = \sum_{n = -N}^{N} (1 - \frac{|n|}{N})e_n$$  The author of the text also asserts that the following identity holds: $$F_N = \frac{1}{N} |\sum_{n = 0}^{N-1} e_n|^2$$   However, no proof is provided for this identity (since I suspect it should be easy to prove). I can't come up with my own proof for this nor could I find it by googling.   Is there any identity involving the characters $e_n$ that I should be using?  Thanks in advance


I can't create Windows software through Eclipse. Using "Run" does run the app as it should, but I would like to start it without Eclipse, preferably as an independent Windows app, using a mere double-click. Although  suggests several approaches, they all require additional knowledge that I do not posses.  I have tried using Launch4J but it also requires additional knowledge. I am astounded that it is so difficult to create a simple Windows-Java-app.  EDIT I am using this pom.xml:  <project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">  <modelVersion>4.0.0</modelVersion> <groupId>foo</groupId> <artifactId>bar</artifactId> <version>1.0.0</version> <name>baz</name> <description></description>  <dependencies> </dependencies>  <build>     <plugins>         <plugin>             <groupId>com.zenjava</groupId>             <artifactId>javafx-maven-plugin</artifactId>             <version>8.8.3</version>             <configuration>                 <mainClass>application.Main</mainClass>                 <updateExistingJar>true</updateExistingJar>                 <skipCopyingDependencies>true</skipCopyingDependencies>                 <useLibFolderContentForManifestClasspath>true</useLibFolderContentForManifestClasspath>             </configuration>             <executions>                 <execution>                     <phase>package</phase>                     <goals>                         <goal>build-jar</goal>                     </goals>                 </execution>             </executions>         </plugin>         <plugin>             <groupId>org.apache.maven.plugins</groupId>             <artifactId>maven-compiler-plugin</artifactId>             <version>3.5.1</version>             <configuration>                 <source>1.8</source>                 <target>1.8</target>             </configuration>         </plugin>     </plugins> </build> </project>   But Eclipse gives this error message:  Failed to execute goal com.zenjava:javafx-maven-plugin:8.8.3:build-jar   the goal being  clean compile package -e   Maven is installed, trying to run it with minimal appendancies.

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


If I have a light that is flickering at a frequency low enough to be perceived by the human eye, is there any type of material that exists that will smooth out the appearance of flickering? Similar to how a capacitor smooths the output of a rectifier?


I am trying to prove old test exercises and this one is resisting me.  I know you can believe that I meant $a^ 2 + b ^ 2$ is divisible by 4, but no, in the test it says that 4 is divisible by $a ^ 2+ b^2$.  Suppose that $ a,b \in \mathbb{Z}$  If 4 is divisible by $ a^2 + b^2$, then $a$ and $b$ are not odd.  I started like this:  Suppose that a and b are even, then $a = 2m$ and $b = 2n$ for some $m,n \in \mathbb{Z} $.   Thus  $$ a^2 = (2m)^2 \ \mbox{and}\ \  b^2= (2n)^2$$ $$ a ^2 + b^2= (2m)^2 + (2n)^2$$ $$ a^2 + b^2 = (4 m^2 + 4n^2) = 2(2m^2+2n^2) $$  Now $$2m ^ 2 + 2n^2\in \mathbb{Z} = k$$ Then  $$ a^2+b^2= 2k$$  Is this a correct proof?/ Any better ways to prove this.  Sorry for the lousy English. Thanks.

Prove by Contradiction     Suppose $a, b \in Z$. If $4|(a^2 + b^2)$, then $a$ and $b$ are not both odd.   So the contradiction: Assume $4|(a^2 + b^2)$, where $a$ and $b$ are both odd.  Then $a=2k+1$, $b=2l +1$  And then I substitute it into the equation and the result is something like this? $4|4(k^2 + k +l^2 + l) + 2$  What do I do next to prove this?


I am trying to calculate the following limit, without using the L'Hopital rule or series expansions:  lim (1+sin(1/n))^(n), n->infinity   I now that it is the same as:  lim (1+sin(n))^(1/n), n->0   But that's about all I know...  Any help?

How can you calculate  $$\lim_{x\rightarrow \infty}\left(1+\sin\frac{1}{x}\right)^x?$$  In general, what would be the strategy to solving a limit problem with a power?


Using the desktop google photos sync app, JPG files sync with resolutions like 2992x2000, and  NEF files like 3008x2000.  But with DNG files, only 1024x683?  Tried to download the file to see if it's a preview, but it doesn't seem so. Any idea why this happens only with DNG files, and how to resolve this issue?  Thanks in advance!

Through my NAS at home I store and backup all my photos on Google Drive. These photos also show up on Google Photos. I use Lightroom and convert all photos to DNG when copying to my NAS.  When I look at the photos in Google Photos the image is rather small. Clicking the (i) info button tells me the image has a resolution of 1024x680, file size 9.8 MB and a MP of 0.7. This is probably just a preview or thumbnail of some sort, but how do I view the image in larger resolutions in Google Photos?


I am trying to update Z values of the vertices of the polygon shape. The script bellow works for polygons without multiparts and donuts. If I run this script for polygon shape that contains multiparts and donuts, I get error. How can I make it work?  My script:  import arcpy  fc = r"C:\Scratch\fcTest.shp"  # Get Spatial Reference of dataset desc = arcpy.Describe(fc) sr = desc.spatialReference  with arcpy.da.UpdateCursor(fc, ["SHAPE@"]) as cursor:     for row in cursor:          # Get Geometry         geom = row[0]          # Create an empty array object         arr = arcpy.Array()          # Read points, if Z is found to be zero reset it to 1         for part in geom:             for pnt in part:                 if not pnt:                     arr.add(None)                     continue                  if pnt.Z == 0:                     pnt.Z = 1.0                   # Add updated point to Array                 arr.add(pnt)          # Construct new polygon geometry from array whilst setting spatial reference and indicating it has Z         newpoly = arcpy.Polygon(arr,sr,True)          #Update row         cursor.updateRow([newpoly])   Error:   Traceback (most recent call last):  File "C:\Scratch\fcTest.py", line 21, in <module>     if pnt.Z == 0:   AttributeError: 'NoneType' object has no attribute 'Z'    >>>

I am trying to update Z values of polygon features with point features. The code is (found on GIS Stack Exchange) working good if no 'interor ring' or 'multipart' features are present in the polygon features. The polygon is large data set with several 'interor rings' or 'multiparts'. I have no idea how to solve it. I have understood that 'NoneType' AttributeError refers to 'multipart' or 'inner rings' issue.  My code is :  import os import arcpy  arcpy.env.workspace = r"D:\acrpy\VV_test\scripts\map1" point_fc = r"D:\acrpy\VV_test\scripts\map1\VRTX_ZM_KAD_test.shp" polygon_fc = r"\acrpy\VV_test\scripts\map1\ZM_KAD__test.shp" my_field = "SHAPE@" my_field_pnt = "SHAPE@XYZ"   with arcpy.da.UpdateCursor(polygon_fc, my_field) as myUpdtCur:     for row in myUpdtCur:         geom = row[0]         arr_pol = arcpy.Array()         for part in geom:                         arr_part = arcpy.Array()             pnt_count = 0             for pnt in part:                 with arcpy.da.SearchCursor(point_fc, my_field_pnt) as mySrcCur:                     for srcPnt in mySrcCur:                         if int(pnt.X) == int(srcPnt[0][0]) and int(pnt.Y) == int(srcPnt[0][1]):                             updZpnt=srcPnt[0][2]                 del mySrcCur                 pnt_count += 1                                 print pnt_count                 myXYZPoint = arcpy.Point(pnt.X, pnt.Y, updZpnt)                 arr_part.add(myXYZPoint)             arr_pol.add(arr_part)         polygon = arcpy.Polygon(arr_pol,None, True)          row[0] = polygon         myUpdtCur.updateRow(row) del myUpdtCur    got the error: 76 77 78 79 80 81 82  Traceback (most recent call last): File "D:\acrpy\VV_test\scripts_OK\GIS_stackexcahnge\test_update Z values from point vertices to polygon vertices .py", line 21, in <module> if int(pnt.X) == int(srcPnt[0][0]) and int(pnt.Y) == int(srcPnt[0][1]): AttributeError: 'NoneType' object has no attribute 'X' >>>


I am new to UX just graduated and I was asked to do a design challenge about service accessibility.  They provided assets, personas and a use case scenario. The main problem is to find ways to the user reschedule medical appointments via a mobile app.   However, they asked me to do a workflow which is not a term that I am familiar with…just wondering if I should ping them back asking if they meant user flow?

I'm looking to clarify the differences/overlaps between the three and, if the terminology isn't accurate establish the correct terminology


I read a data sheet of a li-ion battery to use it in my project. In the data sheet, it is mentioned that c5mah= 2200mah. I couldn't understand what that means. Please help me with understanding that.

What exactly does mAh rating means? I know that it means the milliamperes supplied by the battery in one hour but i need a more conceptual and practical definition/example.   How does mAh rating tell the current supplied to the load? How does it vary with the load specification.   Also, suppose a mobile phone's battery has 3000mAh, if i supply it with 1000mA, then does it mean that the battery will be fully charged in 3 hours?   And will a 3000 mAh battery deliver a current of 3000mA for 1 hour to a load? Will this rating degrade in a practical scenario. Please explain.


I am developing an R package that uses third party functions available in the Bioconductor package "methyilumi"  In the code for my R package at the very beginning I import methylumi with library(methylumi).  During the development (I use roxygen2 and devtools) everything works fine. However, when I install the package and run my functions, I get the error: could not find function "methylumIDAT".  Of course everything is solved if I import the package manually, but how can I make so that methylumi is available whenever I load my own package?

I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "<Regex for 'doesn't contain hede'>" input   Desired output:  hoho hihi haha


What's wrong about $\sqrt{10} = \sqrt{9 + 1} = \sqrt{9} + \sqrt{1} = 3 + 1 = 4$?  I know that it's logically wrong because $4 \times 4 = 16$, but the syntax to me seems to be healthy as long as I can see, well, of course, because I'm novice and I can't see much, but I think this silly question could have a very detailed and deep answer about what's wrong and what's right in math and how to reason while solving. Thank you.

You learn in algebra that  $$\sqrt{ab}=\sqrt{a} \sqrt{b}$$ and that  $$\sqrt{\frac ab}=\frac {\sqrt a}{\sqrt b}$$ You also learn to never make the fatal mistake of thinking $$\sqrt{a+b}=\sqrt{a}+\sqrt{b}$$  However, I am wondering if there is a rule for $\sqrt{a+b}$. I would think it would be pretty complex, if it exists at all.  $$\sqrt{a+b}=\text{?}$$


There are many parameters when buying a bike, but the important one is the bike size. I want to know how to get the specs for the bike. Any good websites that help you in this regard?

I am just shopping for used bikes right now online.  I want to try and save myself a trip to visit the bikes by determining which bikes will fit me.    Does anyone have an approximate height-bike size conversion chart or inseam-bike size conversion chart?  I know that this will not 100% accurate as  observes.  I was just hoping to get an approximation.


My teacher told me that this was because frictional force resists relative motion between the engine and the car. However, in this case it seems to allow relative motion between the ground and the car.

When a car's engine injects fuel into the cylinder chambers, the reaction creates a force that generates rotational momentum to the shaft and over the transmission, it translates that power to the wheels, right?  But, something's bothering me, how does the car actually move, is it dependent on the force of friction? Wheels have a contact with the road in one exact point and when the drive gets to rotate them, a force is exerted on the road in the direction of movement and there is friction that is counteracting it.  Is the key to get a car properly moving to have the drive force equal or less than the force of friction to keep that point locked to the ground and use the rolling of the wheel for translational displacement ie. moving forward? If it's bigger than the force of friction, that would cause the wheels to spin in place?  Am I completely off or am I getting something right? If there's a knowledgeable person on this topic, I'd greatly appreciate some insight, perhaps even a bigger response with some basic vehicle physics.


There is no massless elementary particle that carries a nonzero electric charge. It seems necessary that an elementary particle must have nonzero mass in order to carry a nonzero electric charge. Can we deduce this theoretically from quantum field theory or exclude the possibility of electrically charged massless elementary particles?

Are there any massless (zero invariant mass) particles carrying electric charge?  If not, why not? Do we expect to see any or are they a theoretical impossibility?


I am new to JMeter and I want to learn JMeter step by step. Would you suggest me the easiest ways that how can I start a performance testing using JMeter??  Thanks,  Matvey H

I have just been assigned the tasks of doing some research and doing some JMeter tests of my own to get familiar with performance testing. As I have never used this tool before, I would just like to know where I can find good JMeter tutorials for beginners?


I get a error for an unexpanded parameter pack while expanding it.  This code is for testing purposes.  Later i want to call a differrent function with the head, tail and element. I need the element to call another template function and want to maintain the other argument to later call a different template function.  Current output of clang (version: 8.0.0)  test.cpp  #include <iostream>  template <int... Tail> class for_each_type {     public:     template <int element, int... Head>     int each() {         for_each_type<Tail..., element> _for;          _for.each<Head...>();         return element;     }      template <int element>     int each() {         return element;     } };  int main() {     for_each_type<> _for;      std::cout << _for.each<1, 1, 2, 2>() << std::endl; }   I expect the code to output 6, but the actual output is a error message.  To run start the compiler i just run clang++ test.cpp  The current error message is:  C:\Users\HP\Documents\GitHub\CPP-Game-Engine\src>clang++ test.cpp test.cpp:10:23: error: expected ';' after expression         _for.each<Head...>();                       ^                       ; test.cpp:10:9: error: expression contains unexpanded parameter pack 'Head'         _for.each<Head...>();         ^         ~~~~ test.cpp:10:23: error: expected expression         _for.each<Head...>();                       ^ 3 errors generated.

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


I just installed Minecraft Demo on my Windows 10.  So, after all that download:     Whenever I click the button that says "play demo" the window closes and reopens with the same error message. What's going on?  Merci d'avance!

Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved.


As shown in the picture I just want to make those 3 ends more round like a half circle maybe, but when I try to do that with Effect → Stylize → Round Corners it deforms/warps the whole object?   Why does it do this and how can I fix this or is there maybe another way to make the corners round (I know you can click on the round corner button thingy but that doesn't make them round enough)

I have the following figure in which I need to make a fillet to each its corners:   Is there some tool to avoid doing this manually? I tried the Effect > Stylize > Round Corners tool but it apply the roundness also to the circles. I'm using the CS6 version of Adobe Illustrator.


What is the intuition behind 'Infinitesimal generator matrix?What why we need it?Why it is called generator matrix?what it generates?

Let $\lambda \mu > 0$ and let $X$ be a Markov chain on $\{1,2\}$ with generators  $$ Q = \begin{pmatrix} -\mu & \mu \\ \lambda & -\lambda \end{pmatrix}$$  Write down the forward equations and solve them fro the transition probabilities, $p_{i,j}(t), i,j = 1, 2$.  The answers say:  "We have that   $$p_{11}' = -\mu p_{11} + \lambda p_{12}, \, \, \, p_{22}' = -\lambda p_{22} + \mu p_{21}$$  where $p_{12} = 1 - p_{11}$ and $p_{21} = 1 - p_{22}$. Solve these subject to $p_{ij}(t) = \delta_{ij}$, the Kronecker delta, to obtain that the matrix $P_t = \{p_{ij}(t)\}$."  The bits I don't understand are these  1) How do they get those equations in the first place? For example, why have they added $\lambda p_{12}$ when the coefficient for $p_{12} = \mu$?  2) How do you solve these equations? What do you do with that Kronecker delta to solve them?


In the file I am working on, some lengthy section titles are split up into two lines in the table of contents, with just one word dangling on the second line. Therefore, I would like to redefine the title of the section that appears in the table of contents, while keeping the original section title the same, such that everything fits neatly on one line in the table of contents. Is this possible and if so, how do I do it?

I am writing a book and one of my chapters has a very long title. As it can't be displayed correctly on the top of even pages, I provide a "short title name" via the   \chapter[short title]{long title}   command. But then, "short title" appears in the table of contents instead of the original/true/long one.  How can I have the "short title" in the header of even pages, and the "long title" in the ToC and in the "Title header"?  For reference, here is the code I use:  \documentclass[11pt,a4paper]{book} \begin{document} \tableofcontents  \chapter[Short title]{Very vey very very very very very very long title     i can't display in the header} Lorem ipsum dolor sit amet, consectetur adipiscing elit. \end{document}


I'm currently using Ubuntu 13.04 on my ASUS F201E laptop. I'm trying to install  I want to install Linux Mint 13 "Maya" - MATE (32-bit) because it's meant to be more compatible with my hardware.  I've already created a bootable USB (sudo dd if=./linuxmint-13-mate-dvd-32bit.iso of=/dev/sdb) with the new OS on it no problem, and am now trying to reboot and install this new OS on my laptop.  My USB is recognized in the BIOS, (lets me open "EasyFlash" Utilities) however it's not recognized in the boot preference order - at the moment it only shows Ubuntu (but in the past has recognized a USB here too... The only boot option that shows is my normal Ubuntu).  I've played around with other BIOS settings, nothing seems to work. My fast boot is disabled, my launch CSM is disabled. There is an Add New Boot option, and when I open it, I'm asked for a pathway and I don't know how to write a pathway to my USB. My SATA mode selection is IDE (I changed this, can always change it back if need be.) Serial ATA port 0.

I have a unique problem with an older Toshiba satellite laptop that happens to be a LegacyFree laptop meaning you can't access the bios via the normal F2, Del, Esc, etc.  I can only select a boot option in the beginning such as HDD, Removeable, CD, Floppy, etc.  The problem I ran into is the bootable USB I created is appearing as a bootable HDD not as a removable device and thus it is booting from the HDD in the computer because I can't change the HDD device priority.  Is there anyway when making the bootable USB to make it appear as a USB instead of HDD?  I've been using unetbootin and LinuxLive to create these bootable USBs.  NOTE: I am aware you can access LegacyFree Bios is through a program called Tsetup or HwSetup through windowsXP problem is that The laptop doesn't have any OS currently installed.


I'm trying to use a dynamic range of columns fetched from another query, specifically I want the results of this query:   SELECT COLUMN_NAME as DYNAMIC_COLUMN FROM information_schema.columns  WHERE table_name='TheTableName' AND column_name like 'TheColumnName%'   As columns for the SELECT statement of this query:  SELECT TheColumnResults FROM AnotherTable   My (wrong) approach is something like this:  SELECT( SELECT COLUMN_NAME as DYNAMIC_COLUMN FROM information_schema.columns  WHERE table_name='TheTableName' AND column_name like 'TheColumnName%' ) AS TheColumnResults SELECT TheColumnResults FROM AnotherTable   I just need a guidance on how to approach this or even if it's possible to set a dynamic range of columns at the SELECT statement.  Other (failed) approach I've used:  SELECT * FROM DATABASE.AnotherTable INNER JOIN information_schema.columns  WHERE Exists (SELECT COLUMN_NAME AS DYNAMIC_COLUMN FROM information_schema.columns  WHERE table_name='TheTableName' AND column_name like 'TheColumnName%' AND TABLE_SCHEMA = 'DATABASE')

I want to write a select statement that with some fixed columns and dynamic columns. here Dynamic Columns names are the rows in another table.  I have tried this but getting error. Please tell me where my error is  set @sql=(Select subject from tbl_subjects where C_Id=22); SELECT      ta.rollno,     ta.StdNm,     tc.C_Name,     @sql FROM     tbl_cmarks tm,     tbl_admission ta,     tbl_classes tc WHERE     tm.Cid = tc.C_Id         AND ta.rollno = tm.rollno         AND tm.Cid = 22 and tm.Examid=9    Mysql showing:     Error Code: 1242. Subquery returns more than 1 row   Could any one tell me how to do this in mysql?


What do you call a number which is the same written backwards? Example 16061.

The number I am thinking of is 80808. This is a palindrome. However, it is more than a palindrome, because it can be flipped or mirrored and will still read the same way.  Is there a word for this?


I tried counting subsets with r+1 elements from the set {1,2,....n, n+1} which gives RHS. However I could not come up with an answer corresponding to LHS. $$\binom{r}{r}+\binom{r+1}{r}+...+\binom{n}{r}=\binom{n+1}{r+1} $$

After reading , the most popular answer use the identity $$\sum_{t=0}^n \binom{t}{k} = \binom{n+1}{k+1}.$$  What's the name of this identity? Is it the identity of the  modified.  How can we prove it? I tried by induction, but without success. Can we also prove it algebraically?  Thanks for your help.    EDIT 01 : This identity is known as the  because, on Pascal's triangle, when the addends represented in the summation and the sum itself are highlighted, a hockey-stick shape is revealed.


Why does a 4mm lens have a wider angle of view than an 8mm lens ?

I read on the :     Focal-length determines the angle-of-view seen through a lens for a   given sensor-size. With a full-frame sensor a lens gives the same   angle-of-view as it would on a 35mm film camera. With a smaller   sensor, the angle-of-view becomes smaller. The crop-factor, also   called FLM, is the ratio representing the difference in equivalent   focal-lengths. So a 150mm on a full-frame DSLR such as the Nikon D700   gives the same angle-of-view as a 100mm on a D7000 since its FLM is   1.5X.      Short focal-lengths show a greater angle-of-view compared to longer   ones. [...]   In layman's terms, what is angle-of-view? Is it the same as focal length? If not, how is it different? How is it used? Why do I need to know about it?


I have simple php mysql data running page. with bootstrap.  How can i display an error when connection is lost?  How about popping up and modal as connection is lost & also trying to get connection & as connection gets back the modal disappears.   I have following modal:

              <button type="button" class="close" data-dismiss="modal"> x </button>
ERROR

You have lost connection
 Trying again...

How to detect the Internet connection is offline in JavaScript?


In other words, if $X$ is a set, then how do we call $Y=\{\{x\}:x\in X\}$?  $\{X\}$ is already named the trivial partition, so that cannot be it. Complete partition and total partition did not yield enough search results. Does it maybe not have a name?  A related question: does $Y$ exist for every $X$?


Is it possible to set up a multiseat environment with one graphic card and two Xorg instances? That is, one machine with a monitor/keyboard/mouse for the first Xorg instance and a second monitor/keyboard/mouse for another Xorg instance.  I am using Debian 8 with Intel HD4000 graphics. Every tutorial I have read describes multiseat environments with at least two graphic cards for multiple Xorg instances. I also could use Xephyr, but since this solution lacks performance I would rather prefer to use two Xorg instances.  At the end of the day I would like to have two distinct environments, not influencing each other. So the use of something like “screen1 LeftOf screen0” is not the right choice.

I am considering trying to setup a  system. It seems like this would be pretty straight forward if I had two graphics cards or if I didn't need hardware based OpenGL acceleration. Is it possible to setup a multi seat system with only a single dual-headed graphics card?


Is it possible to set the default display brightness so you don't have to re-adjust it everytime you reboot? My laptop display is killing my eyes at the login screen already because it starts at 100% brightness every time.

The brightness of my laptop is reset to max on every restart. I tried the solution provided at  but had no luck.   This command   cat /sys/class/backlight/acpi_video0/max_brightness   Returns   cat: /sys/class/backlight/acpi_video0/max_brightness: No such file or directory   Then I found that I don't have a folder named acpi_video0, but a folder called intel_backlight:    Every time I increase or decrease the brightness using the brightness control keys, the values in brightness and actual_brightness get updated.  Is there any method I could follow to set the brightness to a fixed value on every boot and vary it as and when I need it using the brightness control keys?


Just wondering if the [g] sound is sometimes used to link a word ending in [ŋ] and a word beginning with a vowel sound. For example, can "hang out" be pronounced as /hang-gout/?  If you know any helpful source about this inquiry, can you share it with me?  Thanks a bunch!

I'm getting into English recently and I'm a little confused by the way people pronounce a word that starts in a vowel right after a word ending in -ing.  For example:      You have to bring it up now?   I don't know if I should pronounce it as:   bring /ŋit/ brin' /nit/ bring /git/   Another example would be "I'm coming out".  Likewise, what about the ending -ang? For example:      We can just hang out and have a good time.    And to round it all up, what about a combination of the two? For example,      He got sick of hanging around waiting for you and went home.   I've been asking myself these questions for weeks.


This laptop has 3 years of use. After Windows 7 boots it starts having this freezing "waves" that last for a few seconds to a few minutes. I can use it again for a few seconds or minutes and then it happens again.  During the freezes the mouse still moves, but no clicks or keys are effective. Almost anything I try to do seem to trigger the freeze, like trying to connect wifi, trying to enter the Task Manager, trying to install Google Chrome.  In safe mode with network the problem is still present. I noticed it happening even in the BIOS utility (transitions from menus freezing for 2sec). I already restored de OS to the factory state with a full restore (formatting HDD) and it still happens. Thus, I don't think it's SW related.  I know the fan can still spin because I can hear it and there is hot air flowing through the vent. After the boot it's always making noise. After the first freeze it goes silent and no noticeable air flowing.  It never really freezes in a hard way and never turn off or restart. The HD Led never goes off, it's always on or blinking fast, like there is a lot of HD operations going on.  SMART stats:

A machine is described as being "really slow" or "freezing". How can I troubleshoot/resolve this issue? What should be the first steps to take?


I started reading the book Brownian motion by Mörters and Peres where I don't quite understand the following example. For completeness I've provided the definitions for brownian motion and finite dimensional distributions used in the book.  Definition $1.1$$ . \quad$ A real-valued stochastic process $\{B(t): t \geqslant 0\}$ is called a (linear) Brownian motion with start in $x \in \mathbb{R}$ if the following holds: $\bullet\hspace{0,2cm} B(0)=x,$ $\bullet\hspace{0,2cm}$the process has independent increments, i.e. for all times  $0 \leqslant t_{1} \leqslant t_{2} \leqslant \ldots \leqslant t_{n}$ the increments $B\left(t_{n}\right)-B\left(t_{n-1}\right), B\left(t_{n-1}\right)-B\left(t_{n-2}\right), \ldots, B\left(t_{2}\right)-B\left(t_{1}\right)$ are independent random variables, $\bullet\hspace{0,2cm}$ for all $t \geqslant 0$ and $h>0,$ the increments $B(t+h)-B(t)$ are normally distributed with expectation zero and variance $h$ $\bullet\hspace{0,2cm}$ almost surely, the function $t \mapsto B(t)$ is continuous. We say that $\{B(t): t \geqslant 0\}$ is a standard Brownian motion if $x=0$. By the finite-dimensional distributions of a stochastic process $\{B(t): t \geqslant 0\}$ we mean the laws of all the finite dimensional random vectors $$ \left(B\left(t_{1}\right), B\left(t_{2}\right), \ldots, B\left(t_{n}\right)\right), \text { for all } 0 \leqslant t_{1} \leqslant t_{2} \leqslant \ldots \leqslant t_{n} $$ To describe these joint laws it suffices to describe the joint law of $B(0)$ and the increments $$ \left(B\left(t_{1}\right)-B(0), B\left(t_{2}\right)-B\left(t_{1}\right), \ldots, B\left(t_{n}\right)-B\left(t_{n-1}\right)\right), \text { for all } 0 \leqslant t_{1} \leqslant t_{2} \leqslant \ldots \leqslant t_{n} $$    Example 1.2 Suppose that $\{B(t): t \geqslant 0\}$ is a Brownian motion and $U$ is an independent random variable, which is uniformly distributed on [0,1] . Then the process $\{\tilde{B}(t): t \geqslant 0\}$ defined by $$ \tilde{B}(t)=\left\{\begin{array}{ll} B(t) & \text { if } t \neq U \\ 0 & \text { if } t=U \end{array}\right. $$ has the same finite-dimensional distributions as a Brownian motion, but is discontinuous if $B(U) \neq 0,$ i.e. with probability one, and hence this process is not a Brownian motion.  Now my questions are  Why does $\tilde{B}(t)$ have the same finite-dimensional distributions as a Brownian motion ? Why is $B(U)\neq 1$ with probability one ?

In the book on Brownian Motion by Yuval Peres, he makes the following claim:     Suppose that $\{ B(t); \ t \geq 0 \}$ is a Brownian Motion and $U$ is an independent random variable, uniformly distributed on $[0, 1]$. Then the process $\{ \tilde{B} (t); \ t \geq 0 \}$ defined as,   $$\tilde{B}(t) = \begin{cases} B(t)  & \mbox{ if $t \neq U$} \\ 0  & \mbox{ if $t = U$} \end{cases}$$      has the same finite-dimensional distributions as a Brownian motion, but is discontinuous if $B(U) \neq 0$, i.e. with probability one, and hence this process is not a Brownian motion.   I'm having difficulty in proving that the finite dimensional joint distribution ( basically the joint distribution of $( \ \tilde{B}(t_1), \ \tilde{B}(t_2), \tilde{B}(t_3), \dots \tilde{B}(t_n) \ )$ ) is the same as the finite dimensional distribution of $B(t)$. Can you please give me some clues.


I would like to add a dagger symbol to one of my section headings that is actually a footnote, so that I can write a comment in the footer. Does anyone know how to change the footnote number to a dagger and then fix it to the section. Does anyone know how to do that?

How can I make LaTeX use symbols (*, †, ‡, and so on) instead of numbers to mark footnotes?  (The numbers are confusing because I use superscripted numbers for citations.)


please look at below output  [     {         "id": "8",         "title": "windows",         "subtitle": "win"     },     {         "id": "8",         "title": "windows",         "subtitle": "win"     } ]   I only want to display  [     {         "id": "8",         "title": "windows",         "subtitle": "win"     } ]   how can i do this? I have tried array_unique() but it is not giving me proper results.  Thanks in advance! please help me.

How can I remove duplicate values from a multi-dimensional array in PHP?  Example array:  Array (     [0] => Array     (         [0] => abc         [1] => def     )      [1] => Array     (         [0] => ghi         [1] => jkl     )      [2] => Array     (         [0] => mno         [1] => pql     )      [3] => Array     (         [0] => abc         [1] => def     )      [4] => Array     (         [0] => ghi         [1] => jkl     )      [5] => Array     (         [0] => mno         [1] => pql     )  )


I want to show that $\int\limits_{-\infty}^\infty e^{-\pi x^2}dx = 1$.  By definition $$\int\limits_{-\infty}^\infty e^{-\pi x^2}dx = \lim\limits_{t\to\infty}\int\limits_{-t}^t e^{-\pi x^2}dx$$ and since the integrand $e^{-\pi x^2}$ is an even function $$\int\limits_{-\infty}^\infty e^{-\pi x^2}dx = \lim\limits_{t\to\infty}\int\limits_{-t}^t e^{-\pi x^2}dx = 2\lim\limits_{t\to\infty}\int\limits_0^t e^{-\pi x^2}dx$$ i.e. we can equivalently show that $\lim\limits_{t\to\infty}\int\limits_0^t e^{-\pi x^2}dx=\frac{1}{2}$.  Since the antiderivative of $e^{-x^2}$ is given by the  we can't straightforwardly evaluate the integral, so I tried to use the power series expansion, hoping to be able to see that the resulting series will converge to $\frac{1}{2}$:  $$|\int\limits_0^t e^{-\pi x^2}dx-\frac{1}{2}| = |\int\limits_0^t\sum\limits_{n=0}^\infty\frac{\pi^n\cdot x^{2n}}{n!}dx - \frac{1}{2}| = |\sum\limits_{n=0}^\infty\frac{\pi^n\cdot t^{2n+1}}{n!\cdot(n+1)}-\frac{1}{2}|$$  However, I'm in a doubt that it converges and a quick check in Wolfram Mathematica shows indeed that with $t\to\infty$ the resulting series will diverge.  What am I doing wrong? Can anybody help me with a proof for this problem? Any help will be really appreciated.

How to prove  $$\int_{0}^{\infty} \mathrm{e}^{-x^2}\, dx = \frac{\sqrt \pi}{2}$$


I'm pretty new to LaTeX, so take it easy on me. 🤣  I'm trying to include a (single) French phrase in a (short, simple) document — and I want to get it right, more as a learning exercise, than because it really matters that much in this context.  Some googling (and tons of tex.se posts) have basically led me to the following combination of tool, environment, and packages: 1. , rendering a 2.  article, using 3.  and 4.  to get beautiful French and a blockquote:    Unfortunately, as shown above, while the \foreignquote{french}{La propriété, c'est le vol!} works as intended, it seems to leave the punctuation settings screwed up for the rest of the document:   Colons and semicolons, after that first \foreignquote (slash the implied \foreignlanguage), continue to be ‘french-spaced’ throughout the document; I'm very puzzled by the documentation on autopunct, but that, also, seems to be behaving strangely — despite my american setting, the periods remain stubbornly outside of the quote-marks.     Here's a MWE:  \documentclass[man]{apa}  \usepackage{polyglossia} \setdefaultlanguage{english} \setotherlanguage{french}  \usepackage[autostyle,autopunct,csdisplay,french=guillemets]{csquotes} \MakeAutoQuote{“}{”} \MakeAutoQuote*{‘}{’} \MakeForeignQuote{french}{«}{»}  % ...  \begin{document} \EnableQuotes \ldots\ and to the passion of his writings. He proceeds to cast doubt on many popularization of Proudhon's work, including the famous «La propriété, c'est le vol!»: \blockquote{It is only by reading Proudhon carefully — and fully — that it is possible to understand what he meant by “property” and why he regarded it as “theft”. A false impression of Proudhon's views on this, as well as on the other matters, is derived from such dicta.}  Throughout the work, Schapiro counter-asserts many other viewpoints that he feels are over-represented in both contemporary and later analyses: that Proudhon was a revolutionary (at least in the traditional, violent sense); that Proudhon was of, or for, the masses, as represented by the working-class; even that Proudhon was against statist violence \ldots \end{document}

I'm using polyglossia and lualatex to compile my source, and I am switching languages back and forth inside my document. It looks like polyglossia (or myself), is not doing what it is supposed to do:  \documentclass[12pt]{book} \usepackage{polyglossia} \setdefaultlanguage{english} \setotherlanguage{french} \begin{document} \textsc{url:} www. \\ \begin{french} \textsc{url:} www. \\ \end{french} \textsc{url:} www. \\ \end{document}   First line prints "url: www." in English: OK. Second line prints "url : www." in French: OK. Third line prints "url : www." in English: not OK (there should not be a space before the colon).  Am I doing something wrong ? Thank you.


In my formula I have several terms with the categorical variable color and color's interaction with other variables. Color can be either white or red. When looking at the summary of my model, color is replaced by colorwhite with no mention of colorred. Can someone explain the mechanics behind R only showing one level of my categorical variable in the summary?   example:  >summary(lm(foo~bar+color+color:bar)) coefficients bar colorwhite colorwhite:bar

I have a linear regression with two explanatory variables. One of them is a two level categorical variable. When I perform the fit, R tells me that the intercept is highly non significant. When I force the intercept to be zero in the regression, it tells me that the coefficient for the 0-level of the categorical variable is highly non significant. What should I do?


I've read the answers provided but I'm still confused that if an aerofoil is designed so that air flows faster over the upper surface for the purpose of providing lower pressure and hence lift why in inverted flight with the shortest airflow uppermost does the aerofoil not provide negative lift?

I've read many times, including here on  that the commonly known explanation of flight is wrong, and that airplanes can fly because the shape of their wings deflects air down. This makes sense, but as far as I can tell it doesn't explain upside down flight or symmetric wings.  The images I've seen show an inclined wing, which forces the air to go downwards. But how can planes fly upside down then?


Last night, I had a Swarm of Bats sharing a space with one of my PCs, and two of the others used spells against it: Fire Bolt and Poison Spray.  The question came up asking if it would affect the PC sharing the space with the swarm.  At the time, I ruled no, since they're not area affects, and I default to permissive during play so I can spend the time researching rules after.  However, I can't find any sources on what happens in this situation.  It seems to make sense that at least Poison Spray would affect the swarmed PC, but I can't find any sources one way or another.  Is there anything definitive anywhere?  If not, it seems like, RAW, it wouldn't, since, again, not area effects.

My players have walked into a Spider Lair and fought their first group of Spiderlings, or effectively a Swarm of Spiders from the MM.  I didn't realize until after the encounter that they have a reach of 0 for their attack and that they can move through and stay on a space taken up by another creature (which occurred to me is the only way it can actually make its attack.)  The party's going to fight more next session. What happens when a swarm is in a character's space attacking them, and someone casts a single-target spell against that swarm such as Hellish Rebuke or Fire Bolt? Since the swarm is invading that character's space (we assume because they are swarming around them or over them), is the character also potentially affected by the spell?


I am trying make a Victorian style dress for my model and I need a little help. I am trying to make shiny patterns using the nodes.I can't find any videos on this anywhere.

I have a skyscraper building but I only want the glass in the texture to be glossy.  How would I accomplish this?    Ok, I have done a test and here are the results.  Here is the original:   here is an adjusted image


I have a few questions about Ordered Logistic Regression Model (OLR). In general, how do I know if this is my model is good, and how do I enhance it?  Using this example from , if these are the outputs I am looking at:  ## R OUTPUTS ## Call: ## polr(formula = apply ~ pared + public + gpa, data = dat, Hess = TRUE)  ## Coefficients: ##          Value Std. Error t value ## pared   1.0477      0.266   3.942 ## public -0.0588      0.298  -0.197 ## gpa     0.6159      0.261   2.363 ##  ## Intercepts: ##                             Value  Std. Error t value ## unlikely|somewhat likely     2.204  0.780      2.827  ## somewhat likely|very likely  4.299  0.804      5.345  ##  ## Residual Deviance: 717.02  ## AIC: 727.02   ## R INPUT exp(cbind(OR = coef(m), ci))  ## R OUTPUT ##            OR  2.5 % 97.5 % ## pared  2.8511 1.6958  4.817 ## public 0.9429 0.5209  1.681 ## gpa    1.8514 1.1136  3.098   What can I do to enhance/improve my OLR model in R?  What output values should I be focusing on?  Does improving my OLR model mean looking at my P values and coefficients and removing the ones that are not statistically significant?   I am stuck as I don't really know what to do after I run the model.  Thank you.

I've fitted my model and am trying to understand whether it's any good. I've calculated the recommended metrics to assess it ($R^2$/ AUC / accuracy / prediction error / etc) but do not know how to interpret them. In short, how do I tell if my model is any good based on the metric? Is an $R^2$ of 0.6 (for example) sufficient to let me proceed to draw inferences or base scientific/business decisions?     This question is intentionally broad, to cover a wide variety of situations that members frequently encounter; such questions could be closed as duplicates of this one. Edits to broaden the scope beyond the metrics mentioned here are welcome, as are additional answers - particularly those that offer insight about other classes of metrics.


Univalent means not invective. My only thought on this is maybe to use reflection principle? Can someone drop me some hints?

Is the following statement true?  Suppose, $ f:D\to \mathbb C $ is an analytic function where $ D $ is the unit disc of radius $ 1 $ around $0 $. Suppose, $ f $ is analytic on the boundary of $ D $ as well. Then prove that, if $ f $ is one-one on the boundary of $ D $, then $ f $ is one-one on $ D $.  P.S. I think I got a solution. But I was wondering if this problem has a trivial solution.  Here is my solution, since nobody has posted a solution yet:-  Suppose, $ \gamma $ is the boundary of $ D $(assuming $ \gamma(t)=e^{2\pi it} $). Then $ f\circ \gamma $ is a simple continuously differentiable curve. So by Jordan curve theorem, $ f\circ \gamma $ divides $ \mathbb C $ into 2 path connected regions $ A_1, A_2 $ such that if $ a\in A_1 $, then $\int_{f\circ \gamma} \frac {1}{z-a} dz=2\pi i$ and if $ a\in A_2 $, then $\int_{f\circ \gamma} \frac {1}{z-a} dz=0$. So, $ f(z)=a $ for some $ a\in A_1,z\in D $ implies $ \int_{\gamma} \frac {f'(z)}{f(z)-a} dz=2\pi i $. So $ f(z)=a $ has only one solution in $ D $. Similarly if $ a\in A_2 $, then $\int_{\gamma} \frac {f'(z)}{f(z)-a}=0 $, so $ f(z)=a $ has no solution in $ D $. If $ f(z)=a $ for some $ z\in D, a\in f\circ \gamma $, then by open mapping theorem, $ f(z)=a' $ for some $ z\in D, a'\in A_2 $, which is not possible. So $ f $ is one-one in $ D $.


I wanted to make a number guesser game, and I wrote this code:  from random import randint as rand  number=rand(-1,1001) tries=0 def numguess():     guess=int(input("The chosen number is between 0 to 1000.\nEnter your guess : "))     tries=tries+1     numguess()  while True:     if number==guess:         print ("You won. My number was effectively" ,number,". \n It took you ",tries, "to guess the number.")         break       elif number<guess:         print ("The number I chose is lower than your guess")         numguess()      else:         print ("The number I chose is higher than your guess")         numguess()   When I run it, it asks me for input then raises a UnboundLocalError. Is there something I am doing wrong? I tried searching but I don't understand. Thank you.

What exactly are the Python scoping rules?  If I have some code:  code1 class Foo:    code2    def spam.....       code3       for code4..:        code5        x()   Where is x found?  Some possible choices include the list below:   In the enclosing source file In the class namespace In the function definition In the for loop index variable Inside the for loop   Also there is the context during execution, when the function spam is passed somewhere else. And maybe  pass a bit differently?  There must be a simple reference or algorithm somewhere.  It's a confusing world for intermediate Python programmers.


Moderator elections are here. I voted.  However, I find the voting page very biased. It's based on a feed, so if there's 30 people, I won't time nor the memory to read everyone's full description of why I should vote for them.   I doubt most users take the time to read each and every single candidates message.   A small synopsis/message that is written by the user and a different design would DEFINITELY make a huge difference in the way these elections took place and how effective they ultimately are.    Suggestion:    Required Meta Description of why we should vote for a moderator. 140 characters.   Different Design Tile view design where the candidates go across the screen (10 at a time for example) completely randomly (based on the refresh) and NOT based on the time they applied for the election.  Expand Details: "Click to Read More" sign or 3 sentences of the candidates "message" to their potential constituency/voters.   Hide the # of votes until the user voted. This is so biased. Heard Mentalty: feeling more secure voting for someone who has 50+ votes than with someone who has 30 even if they are much stronger than the other candidate. Pure herd mentality.    This would keep the election less biased and surely more effective giving us better moderators on stack exchange!

I believe that showing the post score for nomination posts during primaries is a bad idea.  When I loaded the primaries page during the election, the first thing I saw was a post voted -1. This immediately colored my impression of the post. Reading his post didn't indeed make me wish he was a moderator, but at the same point I couldn't bring myself to click on the down arrow. He wasn't an awesome candidate, but he wasn't a -2 score candidate either. Actually, I kinda wanted to sympathy upvote instead.  I want to judge by myself whether a candidate is worth or not my +1. For some of those people I don't have an opinion already, and I want to form one on my own. I don't want game theory to kick in, I don't want to be tricked into sympathy upvotes.  Having those numbers in large print as the first thing I see about them honestly prevents me from doing so. I'd rather have their avatar there.     Some people on chat do not agree with me;  I imagine they'll post explaining why I want to be aware of their opinion while forming my own.      Regardless of the discussion here, if you do prefer to hide the scores as you vote, here's the jQuery oneliner that does just that:  $(".vote-count-post").hide()


I have a text file filename for which I want to substitute a certain numerical string in row row_numby another one that starts with leading zeros. That row is:  "uuid": "34ba55d4-42fd-448e-862a-f1515"   And I would like to substitute the last four digits so that the desired end result is:  "uuid": "34ba55d4-42fd-448e-862a-f0155"   The command I am using is:  gawk  'NR=='$row_num'{gsub(/'1515'/,'0155')};1' filename > tmp && mv tmp filename   The problem is that linux interprets 0155 as an octal number due to the leading zero and returns:  "uuid": "34ba55d4-42fd-448e-862a-f109"   Resolving the interpretation by adding 10# to 0155 does not resolve my issue because then it is evaluated and the zero is avoided, yielding:  "uuid": "34ba55d4-42fd-448e-862a-f155"   How can I make the substitution so that I obtain the desired output?   I would like the solution to be general so that it also works in the case where the first element is nonzero, for which my provided solution does work.

Here is my script (to find the files that contain a specified pattern):  find . -type f \     -exec awk -v vawk="$1" '/'"$vawk"'/ {c++} c>0 { print ARGV[1]; exit 0 } END { if (! c) {exit 1}}' \{\} \;   I would like to use my script with an argument §:  MyScript.sh pattern   My problem is that I don't manage to put the $1 variable in awk.  When I try to debug my script  bash -x MyScript.sh pattern   Here is the output :  + find . -type f -exec awk -v vawk=pattern '// {c++} c>0 {print ARGV[1] ; exit 0 } END { if (! c) {exit 1}}' '{}' ';'   The $vawk variable seems to be empty.  Any idea?


I have a 5TB external NTFS drive thats nearly full. It was exhibiting an odd behavior: I would copy a file to it, the total space free would adjust accordingly, but the file was nowhere to be found.   So I ran check disk on it (from the Windows 7 UI, not the command line) on it and the check disk seemed to get stuck (The file number that it was working on did not change for over 36 hours), so I cancelled the check.  Now, the drive is unreadable. It is recognized in device manager, and in diskmgmt.msc it is shown as an unallocated drive, and it prompts to me allow disk management to initialize it with MBR or GPT.  So, at least the drive isn't broken. How can I recover the data?

What steps can I take to try to recover lost or inaccessible data from any storage device?  Answers:   This applies to any computer storage device, e.g. internal/external hard drives, USB sticks, flash memory. The most important thing is to STOP using it, any type of I/O can ruin your chances of a recovery.     We have separate questions covering common problems with USB flash drives in greater detail:


While I was reviewing I see below warning,   Your last flag was declined - please review it before flagging this post!   But when I see flagged post history I am not able to find out which was exactly declined, my last flag was before 2 days, and it is being displayed as helpful.  My declined flag is of 21 February.  Please help to understand this.

I went to flag something, and in the flag dialog I got the message  "Your last flag was declined - please review it before flagging this post!"    That's all well and good, but when I went to review my flags, the statement is not accurate.  My last 5 flags were all marked 'helpful'.  The 6th down the list is marked 'declined', but that wasn't my last flag.  The message should probably be modified to correspond to the actual condition that triggers it.  Perhaps it should say     One of your flags was recently declined - please review it before flagging this post!   I'm going to guess that this message is triggered if, of all the flags of mine that have been handled by a moderator, the one that was most recently handled was declined. This isn't necessarily the last flag that I raised (the one I raised most recently), as moderators might handle them in a different order than I raised them, and it's not necessarily the flag at the top of the list.  Thus, calling it my "last" flag seems like it could cause confusion.  Yes, I realize this is extremely minor.


I'm running a 3.5 campaign for a large group (8 players, I must be crazy), none of which have every played before, and several of which are quite young (ages 13-17).  I've got some ideas for changing up the set up to make it flow faster (mentioning who is "on deck," etc.), but I was wondering if there were any good rule changes / adjustments for 3.5 that would speed up combat and just generally make the game flow faster.

I'm looking for ways to speed up the combat in my D&D 3.5 game. It seems that turns - both player and non-player - simply take too long. I have thought about giving everyone a 30 second timer, but I'm afraid that might inhibit their ability to come up with strategy and tactics.


Is there any sensitive equation solver which will not show the result as approximately $0$ for this equation:  $$\cos x=e^{-\Large\frac{3}{10^{45}}}$$  or how can I calculate it?

Is there any sensitive equation solver which will not show the result as approximately 0 for this equation:  $cosx=e^{-\frac{x}{10^{45}}}$   being x is variable, or how can I calculate it?


I tried to upload my django project (apache2 + Ubuntu Server). This is my config file: <VirtualHost *:80>      ServerAdmin webmaster@localhost     DocumentRoot /var/www/html       ErrorLog /var/log/apache2/error.log     CustomLog /var/log/apache2/access.log combined          <Directory /home/my_user/project_name/project_name/>         <Files wsgi.py>             Require all granted         </Files>     </Directory>      WSGIDaemonProcess django_proj python-path=/home/my_user/project_name python-home=/home/my_user/project_name/venv     WSGIProcessGroup django_proj     WSGIScriptAlias / /home/my_user/project_name/project_name/wsgi.py  </VirtualHost>  but found this error when I type sudo cat /var/log/apache2/error.log: [core:error] [pid 20884:tid 140074095675136]  (13)Permission denied: [client some number] AH00035: access to /favicon.ico denied (filesystem path '/home/my_user/project_name/project_name/wsgi.py')  because search permissions are missing on a component of the path,  referer: http://my-ip-address/  and on my browser I get this error:  Forbidden You don't have permission to access this resource.  I much appreciate your help. I searched a lot, but I didn't find a solution.

hi i try to deploy my django project 2.2v on ubuntu apache server when i run cat /var/log/apache2/error.log i get this error:  [time] [wsgi:error] [pid 13224:tid 2323232] (13)Permission denied: [remote some number:number] mod_wsgi (pid=13323, process='django_app', application='django_project|'): Call to fopen() failed for '/root/project_name/project_name/wsgi.py'.  my wsgi.py import os  from django.core.wsgi import get_wsgi_application  os.environ.setdefault('DJANGO_SETTINGS_MODULE', 'project_name.settings')  application = get_wsgi_application()  This is my /etc/apache2/sites-available/django_proj.conf : <VirtualHost *:80>     Alias /static /root/project_name/static     <Directory /root/project_name/static>         Require all granted     </Directory>      Alias /meida /root/project_name/meida     <Directory /root/project_name/meida>         Require all granted     </Directory>      <Directory /root/project_name/zettapc>         <Files wsgi.py>             Require all granted         </Files>     </Directory>      WSGIScriptAlias / /root/project_name/project_name/wsgi.py     WSGIDaemonProcess django_app python-path=/root/project_name python-home=/root/project_name/venv/     WSGIProcessGroup django_app   </VirtualHost>  and output of on my browser is :  Internal Server Error  is there something i've missed please


This may sound like an odd question, but this is what I have the most trouble understanding on Stack Overflow (and other Stack Exchange sites). What is the correct way to upvote? Should I upvote every question I find interesting or should I do it sparingly. Could some of the more experienced users give a short list of their mental checkboxes they go through before upvoting?

I've been wondering about this ever since I signed up on SO. With answers, it's easy to determine what to upvote. Is it helpful, is it informative, is it correct?  None of that really applies to a question though. So which criteria are we supposed to use for upvoting questions? (And for that matter, which purpose does it serve? Upvoted answers are listed first, so here the effect is obvious. What difference does it make whether a question gets upvoted?)


I have dozens of vector layers that I want to join together in QGIS.    They have identical fields.    How do I do this?

I've imported several shapefiles which where exported from a Mapinfo .tab. Several  .tab-files are imported resulting in 20+ layers. Afterwards I want to export it to GeoJSON; but I'm reluctant to select each layer and export it manually. Is there a way to merge all the layers into one using QGIS?


If you place a map of the world on a sphere, it will look like the image is continuous. Basically the left end of the image is sort of a continuation of the right end. You won't be able to see any cuts.  I'm trying to create a clouds texture to add to my planet such that it will seem it has clouds. I managed to create the clouds in GIMP, however, I can't figure out how to make sure the left end of my image is a smooth continuation of the right end. For example if you were to map the below image to your sphere (I removed transparency to make it clearer), there would be a very obvious transition from the right end of the image back to the left end on your sphere. How would I create a texture such that I get rid of that?   Sorry for my lack of terminology.

Related:       I'd like to generate tileable Perlin noise.  I'm working from  PerlinNoise*() functions, which are like this:  // alpha is the "division factor" (how much to damp subsequent octaves with (usually 2)) // beta is the factor that multiplies your "jump" into the noise (usually 2) // n is the number of "octaves" to add in double PerlinNoise2D(double x,double y,double alpha,double beta,int n) {    int i;    double val,sum = 0;    double p[2],scale = 1;     p[0] = x;    p[1] = y;    for (i=0;i<n;i++) {       val = noise2(p);       sum += val / scale;       scale *= alpha;       p[0] *= beta;       p[1] *= beta;    }    return(sum); }   Using code like:  real val = PerlinNoise2D( x,y, 2, 2, 12 ) ; // test  return val*val*skyColor + 2*val*(1-val)*gray + (1-val)*(1-val)*cloudColor ;   Gives sky like    Which isn't tileable.  The pixel values are 0->256 (width and height), and pixel (0,0) uses (x,y)=(0,0) and pixel (256,256) uses (x,y)=(1,1)  How can I make it tileable?


The goal is to isolate the decimal value (with simply turning the integer into a string and splitting it).  To that affect I have:  var x = 1001.1; var roundedDown = Math.floor(x); // Produces 1001 var decimal = x - roundedDown;   The expected value of decimal should be 0.1 (1001.1 - 1001). But instead I get 0.0999999 recurring.  I have tried with Math.trunc as well but get the same results.  Would anyone know why this is?

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


i have below code in playground   let a:Double = 5.2 let b:Double = 5.3 print(b-a)   if data type is double the result is 0.0999999999999996 but if data type is float then result is 0.1.please explain why ?


My laptop has two hard drives in it. And I want to install Ubuntu. Here's the thing, I want my SSD to be the hard drive that boots my system and allows it to run. I want the OS and system things there for the speed. Then, I want any downloads, documents, etc. To be on my separate HDD. Does anyone know how I could do this. Yes this is similar to my other question but that one was about how Ubuntu handles separate drives and this one is about how I could install Ubuntu with two.

I'm going to move from HDD to SSD (60GB) + HDD (250GB) setup. Basicly I want the system to be fast. Root partition will be on SSD but I'm not sure what to do with /home. All data like /pictures /documents will be linked to HDD that will be in a removable caddy adapter in my thinkpad. From time to time I might need to remove it and plug in a CD-ROM. This way I guess some part of /home partition will have to be on SSD to make the system bootable.   Does anyone has some tips? It's also important that the Eclipse and Browsers (Opera,Firefox) will run fast. Is it also enough to just copy the partition to SSD to I will have to make a clean install?


I am not well acquainted enough to judge this well. This plot was obtained from normplot in Matlab. There is a good linear fit although the tails are concerning. Does my data follow a normal distribution, judging from this?

I am working with a small dataset (21 observations) and have the following normal QQ plot in R:     Seeing that the plot does not support normality, what could I infer about the underlying distribution? It seems to me that a distribution more skewed to the right would be a better fit, is that right? Also, what other conclusions can we draw from the data?


I don't know what I did wrong.  Exception in thread "main" java.lang.NullPointerException     at helloWorld.HelloWorld.main(HelloWorld.java:30)   Feel free to tell me a much better way of doing this. The error seems like to be something I did wrong with the scanner during  "String feels1 = scan2.nextLine();" on line 13. I think  there might be a way easier way of writing this but I'm just testing.  public static void main(String[] args) {     Scanner scan = new Scanner(System.in);     System.out.println("Hello");     System.out.println("Who am I speaking with?");     String name = scan.nextLine();     System.out.println("Hello " + name + "!");      String feels = null;      do{         System.out.println(name + ", how are you doing today?");         System.out.println("[Good] [Bad] [Ok]");         Scanner scan2 = new Scanner(System.in);         String feels1 = scan2.nextLine();         if (!feels1.equalsIgnoreCase("good") || !feels1.equalsIgnoreCase("bad")                 || !feels1.equalsIgnoreCase("ok")){             break;         } else {             System.out.println("I don't understand you.");         }        } while ( !feels.equalsIgnoreCase("good") ||!feels.equalsIgnoreCase("bad")||             !feels.equalsIgnoreCase("ok") );               // The error lies here.             if ( !feels.equalsIgnoreCase("good") ){                 System.out.println("Im glad you're feeling good!");              }else if (!feels.equalsIgnoreCase("bad")){                 System.out.println("I hope you feel better!");              }else{                 System.out.println("I'm sure you'll feel better soon enough.");      }                 }   Edited:    public static void main(String[] args) {                 Scanner scan = new Scanner(System.in);                 System.out.println("Hello");                 System.out.println("Who am I speaking with?");                 String name = scan.nextLine();                 System.out.println("Hello " + name + "!");              do{                     Scanner scan2 = new Scanner(System.in);                     String feels = scan2.nextLine();                     System.out.println(name + ", how are you doing today?");                     System.out.println("[Good] [Bad] [Ok]");                     if (!feels.equalsIgnoreCase("good") || !feels.equalsIgnoreCase("bad")                                     || !feels.equalsIgnoreCase("ok")){                             break;                     } else {                             System.out.println("I don't understand you.");                     }                   } while ( !feels.equalsIgnoreCase("good") ||!feels.equalsIgnoreCase("bad")||                             !feels.equalsIgnoreCase("ok") );                             if ( !feels.equalsIgnoreCase("good") ){                                     System.out.println("Im glad you're feeling good!");                              }else if (!feels.equalsIgnoreCase("bad")){                                     System.out.println("I hope you feel better!");                              }else{                                     System.out.println("I'm sure you'll feel better soon enough.");              }                                    }

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?


I tried to install arm-none-eabi-gdb as a part of gcc-arm-embedded. I added PPA:  sudo add-apt-repository ppa:team-gcc-arm-embedded/ppa   and executed:   sudo apt install gcc-arm-embedded    It responded with:  Err:8 http://ppa.launchpad.net/team-gcc-arm-embedded/ppa/ubuntu focal Release   404  Not Found [IP: 91.189.95.83 80]   As far as I understand - gcc-arm-embedded doesn't have a version for Ubuntu 20. So I've changed release version for this PPA in Software & Updates to bionic so that I can avoid error 404.  Even though ubuntu 20 has libisl22, now I have unmet dependencies when I try to install gcc-arm-embedded:  The following packages have unmet dependencies:  gcc-arm-embedded : Depends: libisl15 (>= 0.15) but it is not installable E: Unable to correct problems, you have held broken packages.   I was unable to find a way to install requested version of libisl, as apt offers only two versions - libisl22 and libisl-dev and both are not accepted by installer.  I need advice on how to install arm-none-eabi-gdb. Thank you!

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.


I just switched jobs. My new job does not have a 401K so I have rolled over my 401K to a traditional IRA.  Here's the question: I haven't invested it yet. It just barely got there so it is all cash. I want the money in the market, but I also know that dollar cost averaging could mitigate some of the risks... especially since things could get hairy pretty quickly.   Should I dollar cost average and gradually get back into the market?

We'll likely be moving ~$100,000 (two Roth IRAs, about 80k/20k split) from a mix of Nationwide funds to a combination of Vanguard whole-market stock and bond index funds (details below). All else being equal, I'd prefer to move all of the money at once to 1) have enough money to buy Admiral rather than Investor shares 2) simplify the process.  That said, I'd prefer not to take on unnecessary risk, and would dollar cost average the transfer if it would have financial/risk benefits. Would dollar cost averaging make sense in this situation, or would a lump sum transfer work since the money is already in the market? (I'm not sure how similar/different my current and planned investments are, or how important this is).  Current Investments:   NWHJX Nationwide Bailard International Equities Fund Class A 11.90% NBDAX Nationwide Bond Fund Class A   14.80% NWHVX Nationwide Geneva MidCap Growth Fund Class A   12.50% NMFAX Nationwide Growth Fund Class A 38.00% NWGPX Nationwide HighMark Small Cap Core Fund Class A    11.60% NWJCX Nationwide Ziegler NYSE Arca Tech 100 Index Fund Class A   11.20%   Planned Investments (percentages still in the works):   VFIAX    Vanguard 500 Index Fd Admiral Shs   35.00% VTSAX    Vanguard Total Stock Market Index Fd Admiral Shs    35.00% VTIAX    Vanguard Total International Stock Index Fd Admiral 10.00% VBTLX    Vanguard Total Bond Market Index Fund Admiral Shares    20.00%


I can't find the problem. Hope someone can help me. (Translated using Google translate).

I getting an error report of:   Error report - SQL Error: ORA-02270: no matching unique or primary key for this column-list 02270. 00000 -  "no matching unique or primary key for this column-list" *Cause:    A REFERENCES clause in a CREATE/ALTER TABLE statement            gives a column-list for which there is no matching unique or primary            key constraint in the referenced table. *Action:   Find the correct column names using the ALL_CONS_COLUMNS            catalog view    Can I know why?  parent table      CREATE TABLE STUDENTINFO     (       Student_ID VARCHAR2 (10) PRIMARY KEY,       Full_Name VARCHAR2 (50) NOT NULL,       Contact_Number NUMBER (15)NOT NULL,       Address VARCHAR2 (50) NOT NULL,       Nationality VARCHAR2 (15) NOT NULL,       IC_PassportNo VARCHAR2 (15) NOT NULL,       Programme VARCHAR (75) NOT NULL,       Email_Address VARCHAR2 (50) NOT NULL REFERENCES                    USERNAMEPASSWORD(Username),       Parents_Number NUMBER (15)NOT NULL,       Fingerprint_Template clob     );   child table      create table bit_2015_sep_cit4114_fyp_G_     (        Student_ID VARCHAR2 (10) PRIMARY KEY REFERENCES STUDENTINFO(Student_ID),       Full_Name VARCHAR2 (50) NOT NULL REFERENCES STUDENTINFO(Full_Name),       Nationality VARCHAR2 (15) NOT NULL REFERENCES STUDENTINFO(Nationality),       Fingerprint_Template CLOB NOT NULL REFERENCES        STUDENTINFO(Fingerprint_Template),      "23/10/2015" VARCHAR2 (15) not null,     );   I keep nationality and fingerprint as duplicate because it will be time consuming in verifying based on all information stored in studentinfo, therefore by breaking into individual class will be easier and faster. like for the table STUDENTINFO consist 1 million record, in table bit_2015_sep_cit4114_fyp_G_ will only have 40 records. I keep the nationality column because I have 1 more column in my table structure which is visa renewal which calculated based on the value of nationality in the table.


I am completely new to blender and I was practicing how to make clothing out of a base mesh. I am using a technique where you duplicate a portion of the base mesh and expand out on it, but the vertices are not exactly how I want them. How can I adjust the mesh so the arm, neck and body holes are circular? Thank you!

I know that SZ0 makes vertices straightened on the z-axis, but I'm wondering if there's a way to make vertices into a complete circle on the z-axis with a hotkey?


My friend and I want to play GTA 5 together online, but I have an Xbox one and she has an Xbox 360. Can I join or invite them to my game so we can play together?

Grand Theft Auto Online exists on five different platforms: XBox 360, PS3, XBox One, PS4, and PC. Do any of these play on the same servers, allowing people on differing platforms to play together?


I am trying to redirect to external url. I use the below code.  <script> window.location.href= "www.radar.com"; </script>   But it redirect the url to this http://localhost/webtask/www.radar.com. But I want to  redirect to www.radar.com. I am unable to find the issue.Please help....

How can I redirect the user from one page to another using jQuery or pure JavaScript?