For reasons that are beyond me, the following MWE  \documentclass{scrreprt} \usepackage{classicthesis-ldpkg} \usepackage{bm} \usepackage{amsmath}  \begin{document}  \section{The values of $\beta$ for which $\omega_i \mid \bm{\omega} \mid^{-\beta}$ is defined at the origin}  \end{document}   fails to compile with the following error:  ! TeX capacity exceeded, sorry [input stack size=5000]. <to be read again>                    \HyPsd@@LetCommand l.9 ...a} \mid^{-\beta}$ is defined at the origin}   I've tried increasing the amount of memory available to pdfLatex but that doesn't solve the problem. I've also googled to no avail. Is there a workaround for this problem.


I know that $p$-norm of $x\in\Bbb{R}^n$ is defined as, for all $p\ge1$,$$\Vert{x}\Vert_p=\left(\sum_{i=1}^{n} \vert{x_i}\vert^p\right)^{1/p}.$$  The textbook refers to "Every norm is convex" for an example of convex functions.  I failed to prove $f(x)=\Vert{x}\Vert_p$ for all $p\ge1$, then tried to find the proof on the internet but I cannot find it.  Can someone let me understand why $p$-norm is convex for all $p\ge1$.


Let $g$ be a non-negative measurable function. Show $\int g(x)^p d\mu = \int_0^\infty p t^{p-1} m_g(t) dt$.

Let $g$ be a non-negative measurable function. For $1 \leq p < \infty$, show that   $$\int g(x)^p d\mu = \int_0^\infty p t^{p-1} m_g(t) dt$$   where $\mu$ is the Lebesgue measure and we are given   $$m_g(t) = \mu\{x | g(x) > t \}.$$   Attempt  The first thing I did is show that  $$\int g(x) d\mu = \int_0^\infty  m_g(t) dt$$ by creating a suitable simple function to approximate the right hand side and showing that it in fact equals the left hand side when we take the $\sup$ over all such simple functions. In attempting to show something similar for $g(x)^p$, note that for $t_i > t_{i+1}$ $$m_{g^p}(t_i^p) - m_{g^p}(t_{i+1}^p) = m_g(t_i) - m_g(t_{i+1})$$ since $$ t_{i+1} < g(x) \leq t_i \iff t_{i+1}^p < g(x)^p \leq t_i^p.$$  However, how do we achieve the $p t^{p-1}$ term on the right-hand side?


Apparition of quantized energy levels in quantum physics is usually explained in  analogy with sound waves in a box (like in music instruments): the wave has to satisfy the boundary conditions and only specific modes can exist in the cavity, hence specific energies and frequencies. That explains well the quantized energies of electrons in infinite wells or in atoms for exampples.  But photons in vacuum are also quantized, with energies proportional to nhnu. Does anyone have any intuitive explanation for that, not implying computations like field quantization?


Book where kids at a boarding school bid go contracts to do certain chores

I read a book in high school, it was about a foster kid who ran away too many times so he got sent to a boarding school in the mountains. In the boarding school kids could bid on contracts for what chores needed to be done, they were in gangs and before they made the system where certain groups would bid on contracts there had been much fighting and a few deaths.  The contracts were for different jobs at the boarding school. For example, some worked security, some cooked, and some also did medical stuff (I think) since they were gangs certain gangs would bid on whatever contracts.  There was also a girl that the protagonist liked, and she got beaten to death during a school dance (she was actually a robot) and the protagonist follows the robot to a secret door where the robot plugs itself in to try and be repaired.


Integrate $\int \frac{\sqrt x}{\sqrt {a^2-x^2}}dx$

I need to evaluate the integral $$\int \frac{\sqrt x}{\sqrt {a^2-x^2}}dx$$  I substituted $x=a\sin\theta$  Hence, the required integral is reduced to   $$\sqrt a \int \sqrt {\sin\theta}d\theta$$  However the integration of this function yields an elliptic function. Is there any way to integrate it so that it gives a more elementary function?


I have the following problem:  Let $R:=\mathbb{R}[X,Y]/(Y-X^2,Y+X)$ i) Show that $R\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$ ii) Conclude that $|\operatorname{Spec}R|=2$. How do these two ideals look like?  So for the first one I got the hint to eliminate one variable at a time and see what happens. Doing that I got: $1.) \mathbb{R}[X]/(-X^2,X)\cong \mathbb{R}[X]/(-X^2)\times\mathbb{R}[X]/(X)\cong\mathbb{R}[X](-X^2)\times \mathbb{R}$ $2.) \mathbb{R}[Y]/(Y,Y)=\mathbb{R}[Y]/(Y)\cong\mathbb{R}$ using the chinese remainder theorem in $1.)$. But since $\mathbb{R}[X]/(-X^2,X)\times\mathbb{R}[Y]/(Y)\ncong\mathbb{R}[X,Y]/(Y-X^2,Y+X)$ and the fact that there is still $\mathbb{R}[X]/(-X^2)$ left in the first equation, I don't see how this leads me to the desired isomorphism. For the second one I don't see how an isomorphism can lead me to the number of ideals, because I'm pretty sure $A\cong B$ doesn't imply $\operatorname{Spec}A \cong \operatorname{Spec}B$ for rings $A,B$ (I've seen it in a book). Can someone help me with this problem? Thanks in advance.


I've been trying to find an answer to this question for a long time.  What are the relationships/differences between Bias, Variance and Residuals?  I think I do understand Bias, Variance and Residuals as separate concepts. Correct me if I'm wrong -  Bias is the difference between the average expected results from different runs of the model and the true values from data.  Variance is the variability in the expected results (predictions) of a given data point between different runs of the model.  Residual is the difference between the expected results from a model and the true values from data. y - y^ Residual seems somewhat similar to Bias. But is that my misunderstanding? Please explain to me in plain words and also simple equations the relationships or differences between these three.


An example for two finitely generated and residually finite whose quotients are finite and Isomorphic, but themselves are not Isomorphic

I'm Trying to find an example for two non isomorphic,  finitely generated,    residually finite groups $G_1$ and $G_2$ such that there exists $N_1\unlhd G_1$,$N_2\unlhd G_2$ while $G_1/N_2 \cong G_2/N_2$ and $|[G_1:N_1]|=|[G_2:N_2]|<\infty$.  It's my understanding that residually finite is not the same as finitely presented. Thank's in advance to all responders.


the capability to use external hard drive on xbox 360 is unlimited?

Hello I read in these questions:       These  question explain than can only be used 16 GB (or 32 GB partitioned) in a external USB storage Device on an Xbox 360  Listen to co-workers that a new update for Xbox 360 allows you to use the full capacity of a hard drive, for example a 1 TB external hard drive, but I have not found anything on  the internet.  Is this true?


I am learning the normal (Or Gaussiance) distribution, I see a result for error function, that is:  $\frac{2}{\sqrt{\pi}}\int_{0}^{+\infty}e^{-t^2}dt=1$  I thought so much about it, who can give me an explanation for this result?


Earlier questions not tied to my account

I found around half a dozen posts from me, done back in 2012 ish, that are not tied into my current account. How can a link be established?  Reading them it's obvious they're written by me, and not another 'Tim', of which there were several over the years!


Science fiction story about political acumen

I vaguely remember reading a science fiction story in which the character was introduced as a unambitious government official (a bureaucrat). I believe in the story it mentions that while his superiors had come and gone, he always remained due to his unoffensive nature. Throughout the story the character manipulates his way to meet his ends (which I believe had something to do with aliens and their rights).  I believe it was written by Asimov, but it might have been Arthur C. Clarke or Robert A. Heinlein.


relative homology is the reduced homology of the quotient

I read in Hatcher page 124 that      relative homology can be expressed as reduced absolute   homology in the case of good pairs $(X,A)$, but in fact there is a way of doing this for arbitrary pairs.    His argument goes as follows: $\displaystyle \tilde{H_n}(X/A)= \tilde{H_n}(X ∪ CA) = H_n(X ∪ CA,CA) = H_n(X ∪ CA − \{p\},CA − \{p\}) = H_n(X,A)$  Where $p$ is the apex of $CA$ the cone on $A$.  So I understand that the relation  $\tilde{H_n}(X/A)=H_n(X,A)$ holds without any condition on the pair $(X,A)$ where $X$ is a topological space and $A$ is any non empty subset of $X$. Is my understanding correct ? thank you for your help!


Show that $\sum_{k=-m}^n {m+k\choose r}{n-k\choose s}={m+n+1\choose r+s+1}$

Show that $$\sum_{k=-m}^n {m+k\choose r}{n-k\choose s}={m+n+1\choose r+s+1}$$  I first tried this algebraically, which was unsuccessful. Then, I tried to apply the Vandermonde Identity, but the index starts at -m so I am unsure how to continue.


Where do the collections go in 2.8+ when you hit Ctrl-G to make a group?

When I press Ctrl-G, the manual says it creates a collection with the selected items.  The screenshot shows my experience: select some meshes, press Ctrl-G, and I get a dialog box at the lower left.... and no other obvious effect. I dug around in the raw blend file using python and found I appear to have been creating collections with these commands, but they don't appear in the outliner? How does one use the hotkey to create a  usable collection?


If I enter the UK on 1 January and depart six months later using my passport, what is the earliest date I can re-enter the UK for another six months?


Independence of generalised coordinates and momenta in Hamiltonian mechanics

I am told that in Hamiltonian mechanics, we put the generalised coordinates $q_i$ and generalised momenta $p_i$ on equal footing, and treat them as being independent from one another. But I'm struggling to see how this makes sense given that we define generalised momenta by:  \begin{equation*} p_i=\frac{\partial{L}}{\partial{\dot{q_i}}} \end{equation*}  where $L=L(q_i,\dot{q_i},t)$ is the Lagrangian as usual. Surely this means that $p_i=p_i(q_i,\dot{q_i},t)$? There is clearly dependence upon the generalised coordinates here, so how does this dependence disappear when we move from the Lagrangian formalism to the Hamiltonian formalism?


Suppose we want to calculate a velocity. We identify all the relevant dimensions on which the solution could depend and write out and solve the equation $$l/t= a^x \, b^y \, c^z$$ where $a$, $b$, and $c$ are those relevant dimensions, and $l$ stands for length and $t$ for time.  I am having trouble understanding why this works. My thought process has been as follows; We seem to be looking for some function from $\mathbb{R}^n \rightarrow \mathbb{R}$ where $n$ is the number of relevant units. I guess we can assume this function exists since for any set of values the relevant parameters take we should be able to predict the velocity. If the function has the form written above I would say that it has to be dimensionally consistent since if not the solution would be dependent on the definition of one or more units which is obviously not the case (does someone have a better explanation for this?). I don't understand why we can write this function in the form $a^x \, b^y \, c^z$. How do we know the function doesn't take a different form?


Wiping portable hard drive with DD in Linux

I’ve got 3 portable hard drives one is 160GB, the other two are 500GB. I want to write zeros to them using Linux and . I found this command:   dd if=/dev/zero of=/dev/sda bs=?   How for the block size, what is the ideal block size for my 3 portable hard drives? (Note: I placed the ? at the end of the command.)


How do I use potentially copyrighted images in my course material?

I teach at a school and I create PowerPoint presentations to use in my classroom.  I also need to upload the PowerPoints to my school website for my students to access.  Access is restricted and students must sign in with their school codes.  Can I use images I find on Google search?  Are all images copyrighted?  If they do not have an "ownership" stamp on them, are they ok to use in this manner?  Nothing is being sold and the presentations are taken down at the end of each year.


I have a tablet PC running windows 8.1 but I want to install Ubuntu. It has UEFI.   How to do it?


Extract raster values to multipoint shapefile and write to new field using gdal/python

I have a raster with one band and I would like to query a set of overlying points (.shp) to determine how many points as well as which points points fall under a range of certain pixel values associated with the raster.  This is straightforward in ArcGIS but I want to use GDAL/OGR/Python to automate this process.   I can think of a few ways to potentially accomplish this: (1) Join the raster values to the points, add a new field with the raster values and then query the resulting new_points.shp file.  (2) Write an effective SQL statement that queries the points and the raster to write out a new file with only those points that correspond to the value range I'm interested in. Potentially using a VRT file (3) Convert the raster to a shapefile using gdal_polygonize (very time intensive!) and then use an SQL statement along the lines of SELECT COUNT(*) FROM points, new_poly WHERE ST_INTERSECTS(new_poly.geometry,points.geometry) -dialect SQLITE input.vrt again using a vrt table.   Number (2) seems like the best and most efficient option, but I am unfamiliar with querying both raster and vector data simultaneously. Is there a standard or accepted way to do this?  EDIT: Another option seems to be the gdallocationinfo utility, but it seems that you can only pass lat/long coordinates and not shapefiles.


Many times I have read statements like, "the age of the universe is 14 billion years" . For example this wikipedia page .   Now, my question is, which observers' are these time intervals? According to whom 14 billion years?


Why will my Minecraft on pc keep crashing?

My minecraft always crashes when I hit the play it loads but then it comes back with a crash report and I can't even see the minecraft home screen. How can I fix this? My parents think someone has hacked into my minecraft.  Crash Report  ---- Minecraft Crash Report ---- // Don't be sad, have a hug! <3              <<<< Whats this mean?  Time: 12/19/16 4:32 PM Description: Initializing game  org.lwjgl.LWJGLException: Pixel format not accelerated     at org.lwjgl.opengl.WindowsPeerInfo.nChoosePixelFormat(Native Method)     at org.lwjgl.opengl.WindowsPeerInfo.choosePixelFormat(WindowsPeerInfo.java:52)     at org.lwjgl.opengl.WindowsDisplay.createWindow(WindowsDisplay.java:247)     at org.lwjgl.opengl.Display.createWindow(Display.java:306)     at org.lwjgl.opengl.Display.create(Display.java:848)     at org.lwjgl.opengl.Display.create(Display.java:757)     at org.lwjgl.opengl.Display.create(Display.java:739)     at beq.ap(SourceFile:597)     at beq.an(SourceFile:433)     at beq.a(SourceFile:380)     at net.minecraft.client.main.Main.main(SourceFile:124)   A detailed walkthrough of the error, its code path and all known details is as follows: ---------------------------------------------------------------------------------------  -- Head -- Thread: Client thread Stacktrace:     at org.lwjgl.opengl.WindowsPeerInfo.nChoosePixelFormat(Native Method)     at org.lwjgl.opengl.WindowsPeerInfo.choosePixelFormat(WindowsPeerInfo.java:52)     at org.lwjgl.opengl.WindowsDisplay.createWindow(WindowsDisplay.java:247)     at org.lwjgl.opengl.Display.createWindow(Display.java:306)     at org.lwjgl.opengl.Display.create(Display.java:848)     at org.lwjgl.opengl.Display.create(Display.java:757)     at org.lwjgl.opengl.Display.create(Display.java:739)     at beq.ap(SourceFile:597)     at beq.an(SourceFile:433)  -- Initialization -- Details: Stacktrace:     at beq.a(SourceFile:380)     at net.minecraft.client.main.Main.main(SourceFile:124)  -- System Details -- Details:     Minecraft Version: 1.11     Operating System: Windows 7 (x86) version 6.1     Java Version: 1.8.0_25, Oracle Corporation     Java VM Version: Java HotSpot(TM) Client VM (mixed mode), Oracle Corporation     Memory: 75557872 bytes (72 MB) / 148910080 bytes (142 MB) up to 523501568 bytes (499 MB)     JVM Flags: 6 total; -XX:HeapDumpPath=MojangTricksIntelDriversForPerformance_javaw.exe_minecraft.exe.heapdump -Xmx512M -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn128M     IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0     Launched Version: 1.11     LWJGL: 2.9.4     OpenGL: ~~ERROR~~ RuntimeException: No OpenGL context found in the current thread.     GL Caps:      Using VBOs: Yes     Is Modded: Probably not. Jar signature remains and client brand is untouched.     Type: Client (map_client.txt)     Resource Packs:      Current Language: ~~ERROR~~ NullPointerException: null     Profiler Position: N/A (disabled)     CPU: <unknown>


Please anybody help me!  I am building kernel from source code downloaded from . I successfully built it and installed modules. Now i want that my kernel option should come at the boot time and i want to select it. After doing some search on google  i copyed bzImage in /boot folder. i copyed System.map file in /boot folder   Now i want to make a entry for kernel at boot time. I know that i have to make changes in "/etc/grub.d/" and "/etc/default/grub" after that i will have to run "update-grub" but problem is that how i will set fields.   set root='(hd0,msdos6)'  search --no-floppy --fs-uuid --set=root c291827c-6678-4067-ad09-01481681a9f9  echo 'Loading Linux 3.5.0-45-generic ...'  linux /boot/vmlinuz-3.5.0-45-generic root=UUID=c291827c-6678-4067-ad09-01481681a9f9 ro recovery nomodeset  echo 'Loading initial ramdisk ...'  initrd /boot/initrd.img-3.5.0-45-generic   These are some of the fields but i do not know how to get value of uuid, what to set in root (like hd0,msdos6), what is its meaning , how to get initial ramdisk image?  Please do not say that this question is similar to this or that question. I have searched it already at google and stack overflow but nothing solved my problem , all i got is 100s of tab opened in my browser.  My Requirements :-  How to get uuid for new kernel image? what is (hd0,msdos6)? how to get this value for new kernel image?   Plesae help me!


Is it more expensive to buy airplane tickets around Christmas?

Do airlines charge you more if you book a trip around Christmas for a trip that is happening in, say, august?  I am currently looking for tickets and the price seems to have gone up quite a bit in the last few days, thought that might be very subjective.  I can find lots of information for flights taking place around Christmas, but none about booking around Christmas.  Edit upon request: Is the very same flight more expensive when bought around Christmas as opposed to the beginning of January or December.  Edit regarding the duplicate question: I fail to see how that answers my question. I'm looking for something like Willeke mentioned in their comment      Just before Christmas it is rather likely that a lot of people buy tickets to give under the tree, so it is not unlikely that prices go up at the end of December.   Just maybe backed up with some data, ideally.


I feel like this is a lot easier than I'm making it, but for some reason I just can't wrap my head around it.  Let's say I'm sampling a voltage, for argument's sake. I want to know the average voltage over a period of time. If I know the number of samples - it's simply:  $$\frac{\sum_0^n s_n}{n}$$  But, what if I'm trying to do it live? It becomes:  $$\frac{1}{T}\int_0^T s(x) dx$$  But in that case, since $T$ is changing, the first sample will be weighted  most heavily, with weight decreasing over time.  Is there an easy way to get the average when I don't know how many samples I have ($n$ or $T$ in this case)? What if the number of samples is significantly large?


How black hole can have mass when it has no size

In physics we define mass as:  Mass is both a property of a physical body and a measure of its resistance to acceleration when a net force is applied.  In mathematics we define a point as:  A point is a primitive notion that models an exact location in the space, and has no length, width, or thickness.  And in physics we define black hole as when a certain amount of mass contracts to a point called singularity. So this seems weird that black a black hole has a mass but in a dimension less point. But definition of mass says it should have some physical body (means it have some dimensions).


Converting ArcMap to ArcGlobe code using ArcPy

I have a code that should read the mouse coordinates, but it only works in ArcMap, can I somehow translate it into code for ArcGlobe, otherwise it gives an error: CreateObject cannot open map document. def onMouseDownMap(self, x, y, button, shift):         mxd = arcpy.mapping.MapDocument("CURRENT")         df = mxd.activeDataFrame         sr = df.spatialReference         point = arcpy.Point(X=x, Y=y)         pointGeometry = arcpy.PointGeometry(point,sr).projecntAs(arcpy.SpatialReference(4326))         X=pointGeometry.firstPoint.X         Y=pointGeometry.firstPoint.Y         pythonaddins.MessageBox("Your mouse clicked at " + str(X) + " , " + str(Y),"My Coordinates:")


How to make a simmilarity matrix with relative abundance data?

I want to make a simmilarity matrix but I don´t know what simmilarity index should I use. I have relative abundance data (as ratios) of five species (the same five species in all the plots). The data looks something like this:     id sp1 sp2 sp3 sp4 sp5     One 0.1 0.9 0.0 0.0 0.0   Two 0.2 0.1 0.1 0.5 0.1     Should I use Bray-Curtis simmilarity index? Should I use Spearman rank correlation? What index do you recommend?


javascript - regular expression to validate date in mm/dd/yyyy format


I downloaded the _Sent dataview to my server. Now I need to join the _Sent data with the campaign names to filter. How can I get from the _Sent dataview to the campaign name?


Problem in package manager occoured while adding APT for a third party software

I was trying to add a repository in synaptic package manager and I end up with an error.  This is what it shows when I open synaptic package manager.  E: Malformed line 1 in source list /etc/apt/sources.list (type) E: The list of sources could not be read. Go to the repository dialog to correct the problem. E: _cache->open() failed, please report.  W: Ignoring file 'Macaulay2.list.save.3' in directory '/etc/apt/sources.list.d/' as it has an invalid filename extension W: Ignoring file 'Macaulay2.list.save.1' in directory '/etc/apt/sources.list.d/' as it has an invalid filename extension W: Ignoring file 'Macaulay2.list.save.4' in directory '/etc/apt/sources.list.d/' as it has an invalid filename extension W: Ignoring file 'Macaulay2.list.save.2' in directory '/etc/apt/sources.list.d/' as it has an invalid filename extension   Actually,  I was trying to install a software called Macaulay 2 following online instruction.


Distribution of $\sum_{j=1}^n\ln\left(\frac{X_{(j)}}{X_{(1)}}\right)$ when $X_i$'s are i.i.d Pareto variables

Let $X_1,X_2,\ldots,X_n$ be i.i.d variables having a Pareto distribution with density $$f(x)=\frac{a\theta^a}{x^{a+1}}1_{x>\theta}\,,$$ where $a,\theta>0$. What is the distribution of $\sum\limits_{j=1}^n \ln\left(\frac{X_{(j)}}{X_{(1)}}\right)$ ?   Suppose $\mathsf{Gamma}(p,\alpha)$ denotes the density $g(t)\propto e^{-\alpha t}t^{p-1}1_{t>0}$.  We have $$T=\sum_{j=1}^n\ln\left(\frac{X_{(j)}}{X_{(1)}}\right)=\sum_{j=1}^n\ln(X_{(j)})-n\ln(X_{(1)})=\sum_{j=1}^n \ln X_j-n\ln X_{(1)}$$  Now,   \begin{align}&\ln(X_j/\theta)\stackrel{\text{i.i.d}}{\sim}\mathsf{Exp}\text{ with mean }1/a\qquad,\,j=1,\ldots,n \\&\implies\sum_{j=1}^n\ln(X_j/\theta)=\sum_{j=1}^n\ln X_j-n\ln \theta\sim\mathsf{Gamma}(n,a) \end{align}  I could show that $X_{(1)}$ has another Pareto density, so that $$\ln\left(\frac{X_{(1)}}{\theta}\right)=\ln X_{(1)}-\ln \theta \sim \mathsf{Exp}\text{ with mean }1/(na)$$   Not sure if the last two facts help me get the exact distribution of $T$.    Edit:  Turns out this was rather simple had I simply rewritten $T$ as   $$T=\sum_{j=1}^n \ln\left(\frac{X_j}{X_{(1)}}\right)=\sum_{j=1}^n(\ln X_j-\ln X_{(1)})=\sum_{j=1}^n (Y_j-Y_{(1)})\,,$$  where $Y_j=\ln (X_j/\theta)$. Since $aY_j\sim\mathsf{Exp}(1)$, using  result I have $a T\sim \mathsf{Gamma}(n-1,1)$.   This is equivalent to $T\sim \mathsf{Gamma}(n-1,a)$ or $2aT\sim \chi^2_{2n-2}$.


There are two types of people: scientists and everyone else.  A scientist is somebody who studies theory and evidence to further their understanding of the world. The key word is evidence. The scientist does not just blindly follow a theory because it is written in some book, they follow it because they have studied the evidence for it. As such, their beliefs are based on that evidence, and one cannot call this scientists belief in science for a religious position.   Then there's everyone else. These people do not know the theory (at least not from a formal, rigorous standpoint), they certainly have never studied the evidence, or been academically trained in the field. Their familiarity with the science comes down to watching youtube videos by Vsauce, at most. They'll often talk about "climate change" and "the big bang" and "the god particle" or whatever else buzzword's going around, but they don't actually understand the rigorous definition of those words nor the proper evidence. They might have heard that evidence exists, but if you ask them on the spot what sort of evidence it is, how it was found, how the experiment can be repeated and tested, and all these standard methods of scientific inquiry, they won't have a clue.  So essentially we have a group of people that have been given a shallow introduction to a certain topic, and have been told that certain things are true, and then they just take that on faith.   How is that any different from religion? Is science, as it is believed in by most normal people (and not actual scientists), just the same as religion, and thus similarly irrational?    For example, do you believe that the Big Bang is true? Okay, if your answer is yes, describe to me a procedure which I can follow in order to obtain evidence to support your claim. Don't google the internet, it has to be coming from you only. You can't do it, can you? Hence, you are akin to a religious believer. You belief is not rational.


Why does water short out PCBs? (i.e. Why doesn't electricity follow the path of least resistance?)

If copper is more conductive than water (at any reasonable PH), submerging copper electronic circuits in should have no effect, as the electricity should continue to follow the path of least resistance (the highly conductive copper PCB paths, for example) rather than shorting into the mildly conductive water.  However, dumping water on electronics clearly shorts them out, even though copper is the superior conductor.    Why does this occur when the path of least resistance should be the copper rather than the water?


Null pointer exception with app shutting down

i know this question has been asked before but my code is still not working after applying the patches. when i touch the fetch button it crashes and shows the error   java.lang.NullPointerException: Attempt to invoke virtual method 'androidx.recyclerview.widget.RecyclerView$Adapter androidx.recyclerview.widget.RecyclerView.getAdapter()' on a null object reference     at com.example.csitcms.myrecyclerviewActivity$1.onChildAdded(myrecyclerviewActivity.java:35)'   The last line of the code shows the error below:  public class myrecyclerviewActivity extends AppCompatActivity {     RecyclerView recyclerView;      @Override     protected void onCreate(@Nullable Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.my_recycler_view);          DatabaseReference databaseReference= FirebaseDatabase.getInstance().getReference();         databaseReference.addChildEventListener(new ChildEventListener() {             @Override             public void onChildAdded(@NonNull DataSnapshot dataSnapshot, @Nullable String s) {                  String filename= dataSnapshot.getKey();                 String url= dataSnapshot.getValue(String.class);                  ((MyAdapter)recyclerView.getAdapter()).update(filename,url);             }


When libreoffice calc is install in simdock libreoffice calc can not open how can you write in the correct command. Thanks.


I coming back to C# programming after some years of HTML/ASP. I came across these lines and cannot find what it does. It is a method in a class:  private string PeekNext() {     if (pos < 0)         // pos < 0 indicates that there are no more tokens         return null;     if (pos < tokens.Length)     {         if (tokens[pos].Length == 0)         {             ++pos;             return PeekNext();         }         return tokens[pos];     }     string line = reader.ReadLine();     if (line == null)     {         // There is no more data to read         pos = -1;         return null;     }     // Split the line that was read on white space characters     tokens = line.Split(null);     pos = 0;     return PeekNext(); }   Is it calling itself until some of the other Returns happens?  What is happening here, never seen a method returning itself!? What is Returned, empty string or what...? Or maybe I just missed it before.  Maybe simple but puzzles me.


Since $i = \sqrt{-1}, i^2 = -1, i^3=-i, i^4 =1$ I understand to calculate, say,  $i^{999}$ I just have to $i^{999} = i^{4 \cdot 249 + 3} = (i^4)^{249} \cdot i^{3} = -i$ But I have a question here, why can't I do something like $i^{999} = (i^4)^{\frac{999}{4}} = 1$ clearly the answer is wrong, infact everytime I'll only end up with $1$. Can anyone point out which step exactly is invalid and with reasons like why is it wrong.   Which naturally extends the question to, how do you calculate $i$ to the power of any "rational" exponent. Like $i^{743/5}$ or something.  Thanks.


Suppose I want to know whether $\sqrt{7}\in\mathbb{Q}_5$, or more generally, whether $\sqrt{n}\in\mathbb{Q}_p$ for $n\in\mathbb{Z}$, $p$ an odd prime. What are the techniques for determining this? Am I supposed to "lift" it from $\mathbb{Z}/p\mathbb{Z}$ using Hensel's lemma? Could I see an example?


I want to make a power DC supply with voltage rating 0-200V. I want it to be a variable power supply with voltage from 1V to 200v. What should be my approach?


Embedding images explodes generated PDF size

I am using  $ pdflatex --version pdfTeX 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) kpathsea version 6.2.3   to compile a 30-page pdf output. Twelve of the pages look like this (the rest are only text):    All items are generated by this code:  \newcommand{\weapon}[8] { \begin{multicols}{2}   \noindent \textbf{#2} \\   Необходима сила: #3  \\   Обсег: #4  \\   Щети: #5  \\   Свойства: #6  \\   Маса: #7  \\   Стойност: #8  \\   \includegraphics[height=0.13\textheight]{../images/#1}~ \end{multicols} \vspace{0.01cm} }   This bring the file size to:  remote: warning: File build/elementaris-fantasy.pdf is 63.06 MB; this is larger than GitHub's recommended maximum file size of 50.00 MB   The images I am using are not scaled and some of them are quire large.  How can I reduce the size of the PDF file? The purpose of the PDF is to be printed on sheets of paper as reference for a game.


I have many tables in Ms Excel, and I need to export to a latex file to write an article. I don't want include a figure, I want to copy/import a table from Microsoft Excel.  Then I need an easy method to transform something like this:  Linha;Diâmetro, D;Espessurra, t;Área Transversal, At ; Poço - Manifold;10.75 pol;0.625 pol;19.880 pol²;0.013 m² Manifold - Costa;22 pol;0.5 pol;33.772 pol²;0.022 m²     In this:  \begin{table}[htbp]   \centering   \caption{Add caption}     \begin{tabular}{rcccc}     \hline     Linha & Diâmetro, D & Espessurra, t & \multicolumn{2}{c}{Área Transversal, At } \\     \hline     Poço - Manifold & 10.75 pol & 0.625 pol & 19.880 pol² & \textbf{0.013 m²} \\     Manifold - Costa & 22 pol & 0.5 pol & 33.772 pol² & \textbf{0.022 m²} \\     \hline     \end{tabular}%   \label{tab:addlabel}% \end{table}%


Im just learning sobovel space, I was wondering if the weak derivate holds similar things of the original derivate.  Let $U\subset \mathbb{R^n}$ is a open set, and $u\in W^{1,p}$   if $$Du=0 \ \ a.e$$  implies $u=\mathrm{const}?$


Unless they will agree to paint the house red, do not hire them.      I don't want to bother you for a ride to Boston, unless you'll be   driving there anyway.   I don't understand why both subordinate clauses are future. I thought that it was not possible to use "will" with "unless".   It sounds better to me to say:       I won't bother you for a ride to Boston, unless you drive / are driving    there anyway.   and     Unless they agree to paint the house red, do not hire them.   Why is the future tense used in the examples at the top? Is it because the two main clauses are present and do not relate to the future, so if it wasn't phrased like that, we might think these sentences take place in the present (which is not true)?


Is it possible to add keyframes and animate geometry without Shape Keys? Just like regular objects? Like moving vertices, edges and such?


Which databases use real multidimensional indices? Is oracle ever using several indices to get data from tables, or will it always take the one that seems to have the highest selectivity? How about other dbms?


Which is correct – "whoever" or "whomever" in this example?

I say that "whoever" is the correct grammatical choice in the following sentence:     Give the raise to the hardest-working employee, whoever/whomever that may be.   I say "whoever" is correct. The reason is that, when we isolate the "whoever/whomever" clause ("whomever that may be"), the phrase converts to "It may be he". "It may be he who is the hardest-working employee", not "It may be him who is the hardest-working employee". Thus, I believe "whoever" is the correct choice here. Am I right? And is my explanation in determining "whoever" on point?  This question is different because the "whoever" clause is at the end of the sentence.


Does the "elbow-handshake" have any relation to the phrase "rubbing elbows"?

This is probably answerable with a general reference (or a pair of such references), but I have not been able to find one.   Etymology Online does not cover the origin of "rubbing-elbows" as meaning to socialize or mingle in a crowd in either the section covering  or . Other top search hits just cover the meaning of the phrase in discussions of synonyms for socializing (hob-nob etc.), without going into the history and origins.  There is also the "elbow-handshake" (or less formally the "elbow-bump"), where literally rubbing elbows or forearms substitutes for a handshake greeting.  traces this to a leprosy outbreak circa 1970 (in Hawaii, among peoples whose primary language may or may not have been English), but is very light on references. I first recall hearing of this handshake from watching a documentary about one of the , where it was presented as a de-facto greeting replacement that crossed cultures, creeds and nations.  My questions are what is the origin and time period of the phrase "rubbing elbows"? And does the practice of greeting with elbows or arms instead of hand have a more definite origin? And if so, is there any evidence that it was adopted with any conscious awareness of a literal acting out of a the common idiom "rubbing elbows"?


How do I get a list of all files (and directories) in a given directory in Python?


How does Blizzard determine if I preordered a retail copy of Diablo 3: Reaper of Souls?

Procrastination caused me to only reserve my copy of Diablo 3: Reaper of Souls this morning at Best Buy. I'm not sure this will count as a preorder by which I can earn preorder loot. How does Blizzard determine what constitutes a Diablo 3: Reaper of Souls preorder?


I have multi visitor visa for six month in UK and I have traveled two times with each trip for two weeks and I want to travel for third time to stay only for two weeks. Is it possible?


Showing a surjective homomorphism maps Sylow $p$-groups to Sylow $p$-groups

If $f:G\to H$ is a surjective homomorphism of finite groups, then $f$ sends Sylow $p$-subgroups to Sylow $p$-subgroups.   Here's what I have. Suppose $\vert G \vert=p^km$ with $(p,m)=1$. Let $P\in \text{Syl}_p(G)$. Then $\vert P \vert =p^k$. By the 1st Isomorphism Theorem, $\vert H\vert =p^km/ \vert \ker (f)\vert=p^ln$ for some $l\le m$ and $n\bigg\vert m$, with $(p,n)=1$. How can I show $f(P)$ has order $p^l$? Is there a better approach to this?


Is there an expression in English for "being asked to act on your own suggestion"?  Here's an example of the scenario that I'm thinking about:     Wife: Husband, the living room light is broken. We need to buy a new one.   Husband: Sure, honey. When you go to the market today, could you buy a new light?


There are ten girls and four boys in Mr. Fat's Combinatorics class, Find the number of. . .

There are ten girls and four boys in Mr. Fat's combinatorics class. In how many ways can these students sit around a circular table such that no boys are next to each other? (Source : Titu Andreescu Combinatorics Textbook).  Here is my solution to this problem, however the number I got as an answer was extremely large and I felt I might have made a mistake so I need MSE to help verify and (probably) point out the error(s) in my solutions. Solution 1. Let us use the Subtraction Principle in this case. There are 10 + 4 persons to be sitted around a circle, there are at most 13! ways to carry out this task.  Now.  Let us find all such sitting arrangements in which it is compulsory for two boys to sit next to each other, in this case, we can regard the two boys as an entity,  say boys $B_1$ $B_2$ as  $X$ and boys $B_3$ $B_4$ as $Y$. Then in this case, the problem is this reduced to finding the number of possible cyclic permutations of the set P = {X, Y,  1, . . 10}, where 1, 2, 3, ... 10 denotes the girls.  The number of such cyclic permutations is at most 11!. But since we can permutate 2 boys from 4 boys in at most $_4P_2$/2 = 6 ways.  The number of such cyclic permutations is at most 11!$\cdot 6$ ways.   Hence,  by the Subtraction Principle, there are at most 13! - 6(11!) = 5987520000 ways to arrange 10 girls and 14 boys in a circle such that no two boys are sitted together.   Solution 2. In this case I used a direct approach by considering possible cases.  Case 1. A boy sits between every two girls. In this case we can select 7 out of 10 girl occupy the first 7 sits around the circle. The number of ways to permute 7 girls from 10 is at most $10P_7$/7 = 240 ways.   Since 6! Was is the number of ways to sit them around a circle,  these 7 girls can occupy this sit in at most 240(6!) ways. Now the remaining 4 boys can sit anywhere provided that no two persons occupy the same seat, their sitting arrangements can be done in at most 6! ways. Hence for this case, we have a total of 240(6!)(6!) ways possible sitting arrangements.   Case 2. A boy sits between every two girls, in this case,  we treat the two girls as a single entity like before, say X and Y.  And we can permute two girls from 10 in at most $\10P_2$/2 =45ways. These 5 entities can sit around the 5 available sits in at most 4! Ways.  This leaves us with a total of 45(4!) ways to execute the task. Now. The remaining 4 boys can sit on the remaining four sits around the circle in at most 3! ways.  This leaves us with a total of 45(4!)(3!) ways.  Obviously these are the only two cases we consider, hence for this solution, the answer is thus 240(6!)(6!) + 45(3!)(4!) = 12448080. But this answer doesn't correspond with my initial answer.  What's my mistake?


For Strings you have to use equals to compare them, because == only compares the references.  Does it give the expected result if I compare chars with == ?    I have seen similar questions on stackoverflow, E.g.      However, I haven't seen one that asks about using == on chars.


Tracking down an old book (pre-1970) about Intelligent Plant life

I'm looking for a short story that I read in the 1960's as a teenager. The plot was about planetary exploration. The hero finds intelligent plant life that has all of the answers to man's questions. The only exception is when Man is too stupid to comprehend and then the plant replies "You don't have the words". The twist is that the conversation is simply a web to entrap the questioner who's transformed into a soporific state and then consumed.


Create a bootable usb in a mac for a non-mac system

I'm trying to make a bootable USB stick on Mac OS X and get the Acer Aspire accept it. Windows 7 is gone completely on the Acer and Ubuntu 13.04 or 13.10 does not start at all. I tried to make a Mac-bootable USB stick, but I cannot.


How to get latest timestamped result from time series in a join table


I need to understand the Linux versioning system and distribution concepts. what are public, stable or final terms for versions?


I am supposed to prove that if two continuous functions $f:\mathbb R\rightarrow\mathbb R$ and $g:\mathbb R\rightarrow\mathbb R$ coincide on a dense subset $\\D$ of $\mathbb R$, then they coincide everywhere.  I know that since $\\f$ and $\\g$ are continuous at every point in $\mathbb R$, then the preimage of any open neighborhood of any real number $\\a$ must also be an open neighborhood of $\\f^{-1}(a)$.  But I'm lost on how to use that to get to the conclusion.  Do I have to use the concept of connected sets?


Very useful when you forget a sudo at the beginning of your command, !! acts like an alias of the previous command. Example : $ mv /very/long/path/for/a/protected/sensible/file/caution.h . (...) Permission denined $ sudo !! sudo mv /very/long/path/for(...) . [sudo] password :   How do we call that double !! trick ? Researches over internet are difficult because of that token. How does it work ? I suspect a link with the history command. Where it is defined ? Can I define some other myself ?  EDIT : Some interesting event designators !!:* It refers to the arguments of the previous command. Use case : cat /a/file/to/read/with/long/path nano !!:*  :p Just print the command without executing it, you have to put it at the end of the event designator. $ !-5:p sudo rm /etc/fstab -f  .


One of the basic premises of the Potterverse is that Muggles are much, much more common than wizards. This is what in part necessitates the need for the Wizarding world to hide itself away because, despite their superior powers, they would be overwhelmed by the far more massive Muggle population should conflict break out.  However, we also know that wizards and witches have been around a long time. In Prisoner of Azkaban, Hermione's letter mentions:      I bet he’s learning loads, I’m really jealous – the ancient Egyptian wizards were fascinating.   Given that in one of Ron's letters, the Pyramids were mentioned as magical locations, this means that while we don't have a definitive date of when wizardry entered the world, we can definitively say that wizards and witches have been around since at least  Most likely they have been around much longer than that.  I could not find any evidence that suggests that magical people reproduce any faster or slower than a Muggle. Furthermore, being born to magical parents almost always means the child will also be magical (Squibs are considered very rare). While I don't have statistical evidence, it seems that merely having only one magical parent is enough to make it likely that the child will have magical abilities - based on Severus Snape, Seamus Finnigan, and of course, Tom Marvolo Riddle. Finally, there are of course Muggle-Borns, which while they are certainly very rare as a percentage of the Muggle population, they seem quite common enough at Hogwarts.   Finally, it's fairly easy to make the argument that Wizards are more powerful than Muggles in ancient times, given the lack of Muggle technology. In the modern era, there are  that Muggle weapons have exceeded Wizarding power, though there is not total consensus on this. It would be hard to argue, however, that Muggles had superior power (via technology) than Wizards prior to the 20th century.   In summary:   Magical people have been around for at least 4500 years, probably longer. Magical people reproduce at roughly the same rate as Muggles. For most of history, magical people have had superior power to Muggles.   The question:  Given these reasons, why is is it that the Wizarding population does not dominate the human population via ?  In-universe answer only, please. I'm not looking for a "J.K. Rowling is bad at maths" kind of answer.


How do I execute a command in each subdirectory?

I'm using Puppet and I need to create symlinks between two folders. I have around 10 folders with the same structure and I always want to execute my link command in xx/yy/zz.  Something like this:  ln -s aa/bb/folder_to_link  folders_1_to_x/yy/link_name   I tried following  directions but had no success.  Is there an easy to write command that can accomplish this?


How can I install Adobe reader on Ubuntu 18.04.1?

I'm trying to install Acrobat reader on Ubuntu latest version. I followed the step by step instructions in , but when I try to execute the wine commands   wine AcroRdrDC1800920044_en_US.exe   I got the following error:   it looks like wine32 is missing, you should install it. as root, please execute "apt-get install wine32" it looks like wine32 is missing, you should install it. as root, please execute "apt-get install wine32" wine: Mauvais format EXE pour Z:\home\morad\Téléchargements\AcroRdrDC1800920044_en_US.exe.    Can anyone help me to fix this issue? Thanks in advance.


Does anyone have any experience with Ubuntu running on the Yoga 2 Pro in terms of the functionality of the touchscreen?


Failed to connect to lvmetad - Stuck on boot

I upgraded my PC to Ubuntu 17.10, and now that I've restarted my PC I get this message:  Failed to connect to lvmetad. Falling back to device scanning. /dev/mapper/ubuntu--vg--root: clean, 500699/15081472 files, 9150222/60315648 blocks   It gets stuck on this.   What's the problem and how can I fix it?


Using reverse proxy prevent login flooding

I have set $conf['reverse_proxy'] = TRUE; in settings.php, but the IP address logged in the flood table is 127.0.0.1, not the one passed through the X-Forwarded-For header. Nginx is configured to send the X-Forwarded-For header to Apache, but it seems Drupal isn't recognizing it.  This is pretty bad because a few failed logins can lockout for everyone.  How can I make Drupal use the IP passed within the X-Forwarded-For header?


Close voting and comments that challenge consistency

When I vote to close a question and leave an explanation, a common response is     Here are dozens of older questions that meet the same criteria. Why don't you close all of those?   Should I respond to comments like these? If so, how?


Note: we have $a>0,b>0,c>0$.  Solve $(1-a)^2+(1-b)^2+(1-c)^2 \ge \frac{c^2(1-a^2)(1-b^2)}{(ab+c)^2}+\frac{b^2(1-a^2)(1-c^2)}{(ac+b)^2}+\frac{a^2(1-c^2)(1-b^2)}{(bc+a)^2}$ where $a>0,b>0,c>0$. Elementary (high-school) methods are preferred.   I'm not an expert in inequalities. I only know GM-AM and it does not appear to be working. It is not clear to me how to take advantage of the symmetry here.


Modifying Wireless components of a network, to become Wired

I'm wanting to change the configuration of my home network. A partial schematic of the network is as follows:    when I say "partial" there are other things connected to the ADSL router which for simplicity, I've left out.  Please pay particular attention to the "Wireless Client"s at the bottom. I want to change their configuration such that the network looks like this:    So you can see, I want to make these clients wired clients, which will go into some box (marked ?????), and to have that box talk to the wireless network.  My question is firstly, is it possible? Assuming it is possible, what type of hardware does "?????" need to be? Or, do I need a couple of pieces of hardware?  I will pre-empt the question "why" by giving a little background. Currently, "Wireless Client #1" and "Wireless Client #2" are not computers, but are satellite tv receivers. Neither has wireless functionality, I currently (for each of them) have a wireless bridge dongle going into the RJ45 socket, thereby allowing them to talk out to the wlan and ultimately to the web. I'm looking at getting some more clients of this type, and I don't really want to buy a dongle for each. I'd sooner sit some kind of router/access point/bridge with the receivers under the tv, and have that router/access point/bridge communicate with the wireless network on the clients' behalf. But I'n not exactly sure what that box needs to be.   Lastly, the obvious option of plumbing into the adsl router amd bypassing the wireless network altogether, I'm put off this option purely because of the geography of the house. I'm not really ina position to lay cables right now.


I have an old computer that can't handle a boot stick install, so i have to create an actual, old fashioned boot CD.  However, the image size for Ubuntu 12.04 is 732MB, which is too large for a CD, which can hold only 700MB.  The maintainers of Ubuntu 12.04 say the image size will never go over 700MB, and indeed, the download size seemed to be 689MB.  Brasero says it won't burn the CD because the file is too big, what's going on?


In what sense does the Schrödinger equation obey the De Broglie relation?

I've seen various accounts how the Schrödinger equation satisfies the De Broglie relation. However, they all show this only for the simply case of a free particle. A general solution to Schrödinger's equation in some potential would be an infinite linear combination of eigen-states for which we can't define a specific wavelength. While dwelling around the subject I thought maybe we can assign a De Broglie wavelength to the individual eigen-states which form the general solution, but that route is also problematic (for instance the eigen-states of the harmonic oscillator also don't have a well defined wavelength).  The root of the problem, I think, is that the De Broglie relation is a global relation (we can't talk about 'infinitesimal wavelength') while the Schrödinger equation is, by virtue of being a differential equation, a local relation. So, I'm struggling to see how a local relation can encode a global property like wavelength.


This may be a very basic question but I am not seeing how it works. Consider the standard example of an ice skate rotating about his/her center of mass and pulling in his/her arms. The torque is zero so we have conservation of angular momentum. This implies that $\omega$ increases to keep $I\omega$ constant, but then $K_{rot}=\frac{1}{2}I\omega^2$ doesn't stay constant, it increases. This implies that there is work done, but what force is doing this work?


I have a Model as follows:  class TankJournal(models.Model):     user = models.ForeignKey(User)     tank = models.ForeignKey(TankProfile)     ts = models.IntegerField(max_length=15)     title = models.CharField(max_length=50)     body = models.TextField()   I also have a model form for the above model as follows:  class JournalForm(ModelForm):     tank = forms.IntegerField(widget=forms.HiddenInput())       class Meta:         model = TankJournal         exclude = ('user','ts')   I want to know how to set the default value for that tank hidden field. Here is my function to show/save the form so far:  def addJournal(request, id=0):     if not request.user.is_authenticated():         return HttpResponseRedirect('/')      # checking if they own the tank     from django.contrib.auth.models import User     user = User.objects.get(pk=request.session['id'])      if request.method == 'POST':         form = JournalForm(request.POST)         if form.is_valid():             obj = form.save(commit=False)              # setting the user and ts             from time import time             obj.ts = int(time())             obj.user = user              obj.tank = TankProfile.objects.get(pk=form.cleaned_data['tank_id'])              # saving the test             obj.save()      else:         form = JournalForm()      try:         tank = TankProfile.objects.get(user=user, id=id)     except TankProfile.DoesNotExist:         return HttpResponseRedirect('/error/')


Evaluate using complex numbers: $\prod^{n}_{k=1}\cos\left(\frac{k\pi}{m}\right)$, where $m=2n+1$

Evaluate using complex numbers: $$\prod^{n}_{k=1}\cos\left(\frac{k\pi}{m}\right)$$ where $m=2n+1$.   $\bf{My\; Try::}$ Let $\displaystyle P = \prod^{n}_{k=1}\cos\left(\frac{k\pi}{m}\right).$ Now let $\displaystyle \cos \left(\frac{k\pi}{m}\right) = \frac{e^{\frac{ik}{m}}+e^{\frac{-ik}{m}}}{2}$ and Let $e^{\frac{i\pi}{m}} = \omega$  So we get $$P = \frac{1}{2^n}\left\{(\omega+\omega^{-1})(\omega^2+\omega^{-2})\cdots(\omega^n+\omega^{-n})\right\}$$  So $$P = \frac{(1+\omega^2)(1+\omega^4)\cdots(1+\omega^{2n})}{2^n\cdot \omega^{\frac{n(n+1)}{2}}}$$  Now How can i solve after that, Help required, Thanks


How many positive factorials are also perfect Squares. So for example $1!=1=1^2$. How many others exist other than 1?  Is there any way to prove this?


What are appropriate Circle of Confusion values for high-megapixel cameras?

Since the film days we have used 0.03 CoC for determining depth of field and similar calculations. In digital terms, does this best match with 6 or 12 or 24 or 36Mpixel full frame sensors? If this matches with 12Mpix (a guess), then could you suggest a useful value of CoC for 36Mpix please?


If null set is an element of a set then will it belongs to set or subset?

if $$A=\left\{\varnothing \right\}$$ we know that $A$ is a Singleton Set whose single element is a Null set. That is $A$  is a set containing another set which is Null set.  Now are these two statements True?  $1.$ $\varnothing \in A$  $2.$ $\varnothing \subset A$


The formal solution of the time-dependent Schrödinger equation

Consider the time-dependent  (or some equation in Schrödinger form) written down as $$ \tag 1 i \partial_{0} \Psi ~=~ \hat{ H}~ \Psi . $$ Usually, one likes to write that it has a formal solution of the form $$ \tag 2 \Psi (t) ~=~ \exp\left[-i \int \limits_{0}^{t} \hat{ H}(t^{\prime}) ~\mathrm dt^{\prime}\right]\Psi (0). $$ However, this form for the solution of $(1)$ is actually built by the method of successive approximations which actually returns a solution of the form $$ \tag 3 \Psi (t) ~=~ \hat{\mathrm T} \exp\left[-i \int \limits_{0}^{t} \hat{H}(t^{\prime})~\mathrm  dt^{\prime}\right]\Psi (0), \qquad t>0, $$ where $\hat{\mathrm T}$ is the time-ordering operator.  It seems that $(3)$ doesn't coincide with $(2)$, but formally $(2)$ seems to be perfectly fine: it satisfies $(1)$ and the initial conditions. So where is the mistake?


I am having trouble finding the surface area of the part of the paraboloid that lies in the first octant of $z=5-x^2-y^2$.  So, I realized that the first octant refers to when, $x,y,z \ge 0$. How do I proceed with this?


Yesterday I updated my Dell Latitude D650 laptop with the new LTS edition of Kubuntu, v.16.04.  I was previously running the 14.04 LTS release. After completing the update and restarting the computer, I was given a black terminal screen with the prompt Login:_ instead of the normal user-account login screen with picture icons for accounts.    I've tried logging in as my username, Administrator, Root, and anything else I can think of, and tried as many different plausible password combinations as i can and it always comes back with a invalid login message.    Please, somebody tell me there is a way to unlock my computer so I don't have to wipe it and start over? I was never prompted to change any login settings in the update process...


I'm really confused about Harry Potter's blood status

I'm confused because Harry Potter is a half-blood even though he was born from a Muggle-born and a pure-blood. Does a Muggle-born count as a Muggle when giving birth or what?


Pronunciation differences between "finite" and "infinite"

In my experience, "finite" is pronounced (IPA) ˈfaɪnaɪt while "infinite" is ˈɪnfɪnɪt.  In general, the prefix "in" negates an adjective, but does not change the pronunciation. Based on this, I would expect ˈɪnfaɪnaɪt.  Is there a reason for this "deviation from the norm"? Are there dialects/regions that actually say ˈɪnfaɪnaɪt (or ˈfɪnɪt, for that matter)?


Why is there a preflash from a built-in flash when using remote flash only?

When using Nikon D7000 with an off-camera SB600 (which cannot be used as commander) in TTL mode, the built-in flash must be opened to make it work (to serve as a commander), even if this built-in flash is set to off.  This built-in flash does not trigger when taking a photo, but does preflash. Why?  Searching for an explanation, I found that this is required to measure something. But what?   A shutter speed in aperture mode? In this case, the speed will be completely wrong, since during preflash, the scene will be lighter than when taking photo, since in this last case, the built-in flash will not trigger. Built-in flash intensity? But why do we need it, since the built-in flash will not be used while taking photo? Remote flash? Again, the measure will be wrong, for the same reason as in the first point.   What I'm missing?


Similarity in the solution for diffusion and Schrödinger equations

Both diffusion and Schrödinger equations are PDEs (first order in time and second order in space) with a different physical meaning. When solving a simple case of 1d diffusion with fixed boundary conditions we can solve the equation by using Fourier expansion and find that the space components of the density function is a sum over all possible modes, which is a very similar solution for a particle in a box. My questions is, first, is there some intuitive analogs between those two different cases? Second, is there any physical meaning (or any other intuition) for the "modes" in the diffusion solution?


Are all 23 chromosomes connected as one long strand of DNA?

This has perpetually confused me. Is our genome made up of two long strands, each strand made up of 23 continuous chromosomes that bind together, or are they 23 free floating separate pair of chromosomes? I think it's the latter because I just learn that genes on different chromosomes assort independently, which would be hard if the genome was a long string, but I'm still not sure.


I see in real world some time light pass through our ears and nose,i wanted to know how to make light pass through a mesh in blender cycles?


I am looking through the Deities & Demigods book for D&D 3.5 and it lists all the different powers and feats/salient abilities, but it does not touch on progressing your Divine Rank. Is this strictly up to the DM? Is there an XP chart for Divine Rank, or something? How does advancement as a god work? I am unable to locate any explanation.  In particular, I'm interested in how one attains Divine Rank 1 from Divine Rank 0.


If we know spin isn't actually rotation, why do we still speak of intrinsic angular momentum?

The spin of an electron was classically thought of a spinning ball of charge. We know that that is not the case in the quantum picture, as the electron is pointlike.  So why, then, do we still describe quantum spin as "intrinsic angular momentum?" Why isn't it just "intrinsic magnetic moment," or something else?


Is it possible to reject  $$H_0\!: \mu_1 = \mu_2 = \mu_3,$$  for example, with an F test in the context of an ANOVA table, but not reject any of the following: \begin{align} H_0\!: \mu_1 &= \mu_2  \\ H_0\!: \mu_3 &= \mu_2  \\ H_0\!: \mu_1 &= \mu_3 \end{align} for example, using a ?  It seems like one of those cases where at least one member of a set of twins or triplets is guilty, but it cannot be determined which one is guilty.  If so, like how?  If not, please prove it.


Spring JDBC throws an error which impacted my Spring related unit testing

I am working on Spring Boot Rest Controller and everything is working fine including its unit testing.  When I added the Spring-jdbc(4.3.5.RELEASE) in my maven configuration, all my unit test classes are failing due to a null pointer exception. And if I remove it all my spring related unit testing classes are working fine again.  I have been using Spring so many years but this is the first time I have encountered this issue.   What is the root cause? I am using Spring boot 1.4.2.  Code:  @Test public void verifyEmail() throws Exception {                mockServer.expect(requestTo("localhost:8080//api/v1/userEmails?email=test@test.com&catalogId=10051"))         .andExpect(method(HttpMethod.GET))         .andRespond(withSuccess("True", MediaType.APPLICATION_JSON));      String s = acquisitionService.verifyEmail("test@test.com","10051");      mockServer.verify();      assertEquals("Assert Status", s, "True");                 }   Error Stack trace:  java.lang.NullPointerException     at org.dmc.api.service.AcquisitionServiceImpl.getOrderConfirmData(AcquisitionServiceImpl.java:461)     at org.dmc.api.service.AcquisitionServiceTest.orderConfirmDataTest(AcquisitionServiceTest.java:547)     at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)     at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)     at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)     at java.lang.reflect.Method.invoke(Method.java:498)     at org.junit.runners.model.FrameworkMethod$1.runReflectiveCall(FrameworkMethod.java:50)     at org.junit.internal.runners.model.ReflectiveCallable.run(ReflectiveCallable.java:12)     at org.junit.runners.model.FrameworkMethod.invokeExplosively(FrameworkMethod.java:47)     at org.junit.internal.runners.statements.InvokeMethod.evaluate(InvokeMethod.java:17)     at org.junit.internal.runners.statements.RunBefores.evaluate(RunBefores.java:26)     at org.springframework.test.context.junit4.statements.RunBeforeTestMethodCallbacks.evaluate(RunBeforeTestMethodCallbacks.java:75)     at org.springframework.test.context.junit4.statements.RunAfterTestMethodCallbacks.evaluate(RunAfterTestMethodCallbacks.java:86)     at org.springframework.test.context.junit4.statements.SpringRepeat.evaluate(SpringRepeat.java:84)     at org.junit.runners.ParentRunner.runLeaf(ParentRunner.java:325)     at org.springframework.test.context.junit4.SpringJUnit4ClassRunner.runChild(SpringJUnit4ClassRunner.java:252)     at org.springframework.test.context.junit4.SpringJUnit4ClassRunner.runChild(SpringJUnit4ClassRunner.java:94)     at org.junit.runners.ParentRunner$3.run(ParentRunner.java:290)     at org.junit.runners.ParentRunner$1.schedule(ParentRunner.java:71)     at org.junit.runners.ParentRunner.runChildren(ParentRunner.java:288)     at org.junit.runners.ParentRunner.access$000(ParentRunner.java:58)     at org.junit.runners.ParentRunner$2.evaluate(ParentRunner.java:268)     at org.springframework.test.context.junit4.statements.RunBeforeTestClassCallbacks.evaluate(RunBeforeTestClassCallbacks.java:61)     at org.springframework.test.context.junit4.statements.RunAfterTestClassCallbacks.evaluate(RunAfterTestClassCallbacks.java:70)     at org.junit.runners.ParentRunner.run(ParentRunner.java:363)     at org.springframework.test.context.junit4.SpringJUnit4ClassRunner.run(SpringJUnit4ClassRunner.java:191)     at org.junit.runner.JUnitCore.run(JUnitCore.java:137)     at com.intellij.junit4.JUnit4IdeaTestRunner.startRunnerWithArgs(JUnit4IdeaTestRunner.java:68)     at com.intellij.rt.execution.junit.IdeaTestRunner$Repeater.startRunnerWithArgs(IdeaTestRunner.java:51)     at com.intellij.rt.execution.junit.JUnitStarter.prepareStreamsAndStart(JUnitStarter.java:242)     at com.intellij.rt.execution.junit.JUnitStarter.main(JUnitStarter.java:70)


How do I install AMD Radeon HD 7570M/Intel Hybrid drivers?

My system is overheating frequently, and sometimes it shuts down, so I think I have to install the AMD/Intel Hybrid drivers to fix this problem... My laptop is  and I am running Xubuntu 16.04 amd64 (I made a zero installation today).  02:00.0 VGA compatible controller [0300]: Advanced Micro Devices, Inc. [AMD/ATI] Thames [Radeon HD 7550M/7570M/7650M] [1002:6841] (prog-if 00 [VGA controller])   This is what I have tried:   Installing drivers with sudo apt-get install fglrx fglrx-amdcccle fglrx-dev -- didn't work. Installing drivers with .deb packages from  -- didn't work. Following the instructions here and here -- didn't work.   Now I am trying to install the drivers manually, as described  and in  using  that I have downloaded from AMD Website.  When I try to run the .run file as root, this error message appears:  ERROR: Please install the required pre-requisites before proceeding with AMD Catalyst installation. Please check file usr/share/ati/fglrx-install.log for more details   I have checked the /usr/share/ati/fglrx-install.log and the content is:  NOTE: If your system has logged the missing packages required for installation, install them in the order as per the log file to resolve package-dependency issues.  fglrx installation requires that the system has kernel headers.  /lib/modules/4.4.0-22-generic/build/include/linux/version.h cannot be found on this system. Install kernel headers using the command apt-get install linux-headers-4.4.0-22-generic.   So I ran sudo apt-get install linux-headers-4.4.0-22-generic and:  Reading package lists... Done Building dependency tree        Reading state information... Done linux-headers-4.4.0-22-generic is already the newest version (4.4.0-22.39). 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.


I am looking for a derivation for the inverse of a 2x2 matrix. I am also wondering why the determinant is involved in the expression. I am familiar with high school maths and linear algebra. If there is an intuitive reason for expression i would also be interested in that.


Is there a tool that does the opposite of a dissolve?  I would like to break a shapefile into multiple files based on an attribute.


Using the pigeonhole principle prove that the decimal expansion of $1/k$ for any $k\in\Bbb N_{>0}$ becomes cyclic at some point

Prove if $k$ is any positive integer, the decimal expansion of $\frac{1}{k}$ eventually gets into a repeating cycle.   I'm stuck here , i've thought about applying the pigeonhole principle and induction here but to no avail...  My answer is asking for a proof through pigeonhole principle or induction.. the one linked does not show those..  Please don't close this.


If the best linear approximation (using least squares) of my data points is the line $y=mx+b$, how can I calculate the approximation error? If I compute standard deviation of differences between observations and predictions $e_i=real(x_i)-(mx_i+b)$, can I later say that a real (but not observed) value $y_r=real(x_0)$ belongs to the interval $[y_p-\sigma, y_p+\sigma]$ ($y_p=mx_0+b$) with probability ~68%, assuming normal distribution?  To clarify:  I made observations regarding a function $f(x)$ by evaluating it a some points $x_i$. I fit these observations to a line $l(x)=mx+b$. For $x_0$ that I did not observe, I'd like to know how big can $f(x_0)-l(x_0)$  be. Using the method above, is it correct to say that $f(x_0) \in [l(x_0)-\sigma, l(x_0)+\sigma]$ with prob. ~68%?


Running a jar file in another java program

How can i run a jar file inside another java program? I found this: Runtime.exec("java -jar " + filepath) but i keep getting an error that says its a non-static method that it is being run from a static context when it is not even in a static method. I've searched a lot and couldn't find an answer.


I want to stop receiving messages from a certain group chat I've been made a part of. I don't want to simply "hide alerts" from it, I don't want the messages to come in at all. Is there any way to do that? Deleting the conversation doesn't seem to help.


Limit of the Sequence: $a_{n+1}=a_n+\frac{1}{a_n}$ with $a_1=1$

$\lim_{x\to\infty} a_n$ defined as $a_{n+1}=a_n+\frac{1}{a_n}$ with $a_1=1$.  I've tried writing out the first few terms and this sum is increasing, but progressively less-so over time. I'm just not certain how to go about caclulating the limit here. I feel that it does have a finite limit, but I'm not certain of what it is.


I understand this is a repeat question, but I can't find a succinct answer (or as a newbie, I can't succinctly understand an answer). I have 2 sets of lists that I want to reference (separately) within a function: cols = ['snow','ice'] metrics ['feet','inches']  def avg(df):  df1 = df.groupby(cols[0], as_index=False)[metrics[0]].mean()     .sort_values(metrics[0]).drop_duplicates()     return df1  avg(df)  This runs properly. How can I add an additional metric index (and if not, why not and what's the best approach)? Like this: def avg(df):  df1 = df.groupby(cols[0], as_index=False)[metrics[0,1]].mean()     .sort_values(metrics[0]).drop_duplicates()     return df1  avg(df)  Thank you


Multiple operating systems on one computer

Can I have Ubuntu and Windows 7 on the same computer? If so, how do I do this? I want to be able to choose which operating system to boot up to when I turn on my computer.


Is that proved that breaking ECDSA as hard as solving ECDLP?

Is that proved that breaking ECDSA (Elliptic Curve Digital Signature Algorithm) as hard as solving ECDLP(Elliptic Curve Discrete Logarithm Problem)?


Command block shovel how to make it able to destroy course dirt

I was trying to make a wooden shovel to break course dirt and I already have enter a command called /give @p 1 0 {CanDestroy:[“”]}, but the course dirt won't break when I want to do it.   It just says "missingno" when I scroll over the shovel. How to solve this?


When saving data locally for a mobile game, how to protect it?

I am designing a mobile (iOS/Android) game and I try to save data (such as levels, coins, status) in local files.  In this way, I am concerning a case that someone can just copy these files and give them to a friend, so the friend can have achieve certain levels and all the coins held in the data files right away.  Instead of saving the data in a server, is there any way to prevent this happen?  I am thinking to encrypt the data with a key that is unique for a device. Is this a good idea or it might cause some other problem?


Is there a list of pre-installed command-line tools for macOS?

I'm currently in the process of developing some shell scripts but have run into a problem: whilst I am able to execute numerous commands on my Mac, when I try to run it on other people's computers I get Command not found errors indicating that they do not have the specific command line tools installed.  It is my belief that many of these tools come as a result of installing Xcode and other package managers like Homebrew. My question is: is there a list or another way of finding out if a specific command (tool) is pre-installed on a standard Mac computer (without Xcode installed) without having to manually test it on someone else's computer?  For example,  post hints that git is pre-installed which is only the case if you have installed Xcode, otherwise, git is unavailable.   P.S. For my specific case, I am wondering if hexdump is pre-installed or not (without Xcode)


unable to handle this popup used almost handler

HI. can you suggest me how to handle this popup as i have used almost every handler to handle it but still no result? please provide some solution. the highlight is shown which is to be handled. answer ASAP.


Is it possible to display the full, absolute URL of the home page in Drupal 7, like  www.example.com/The-best-example-possible ?  I'd like to display the full URL of the home page, not just the hostname.


$V$ is a vector space and for any positive integer $n$, there exists a linearly independent subset $S_n \subseteq V$ of size $n$.  Is $V$ infinite-dimensional and how do I go about proving this?


I make a small solar energy harvester. I'm searching for the type of diode with lowest drop voltage. Any suggestion for the type of diode for me ?  Thank you


Did any of Voldemort's dedicated followers know he wasn't pure-blood?

In the question  Anthony's  notes that:      Families like the Malfoys were more than willing to serve Lord Voldemort, whose father was a Muggle (not even a Muggle-born wizard).   In the books was there ever any indication that the Malfoys, or any of Voldemort's most loyal followers, were aware of his half-blood status?  I believe Voldemort went to great lengths to hide that information from others. I'm not even sure Snape was aware, though Dumbledore, Harry, Hermione, and Ron knew through their hunting of the Horcruxes.


Banner : Welcome back! If you found this question useful, don't forget to vote both the question and the answers up

Visited  today and was welcomed with a banner which read as:     Welcome back! If you found this question useful,   don't forget to vote both the question and the answers up   Snapshot:    I was wondering if similar kind of banners are shown to users when they visit  and all other Stack Exchange sites, after a considerable time gap.  Yes, it feels good to be welcomed !!!  So, if the answer is yes, what is the minimum time gap?


Is there a log file equivalent to manifest.txt

I am trying to revert everything installed while compiling dependencies. I looked inside  but couldn't find the location of the installed libraries. Which log can I look into to remove/revert everything installed from the sources?


How many levels are there for Steam Trading Card badges?

With the new Steam Trading Cards, I decided to craft the badge for CS:GO. I got this:    I then noticed that this is only a level 1 badge, and there was a level 2 badge to get. So I crafted it too:    Now it says there's a level 3 badge to get next. How many levels are there in total?


Integral of the reciprocal of a complex polynomial

For a polynomial P(z) of degree $n\geq2$, show that there exists some $R_{1}>0$ such that for $R>R_{1}$ it holds that: $$\int_{C_{R}}\frac{1}{P(z)}dz=0$$ where $C_{R}$ is a circle of radius R with the centre $0$.  I am already aware of the fact that $$\lim_{R\to \infty}\int_{C_{R}}\frac{1}{P(z)}dz=0$$ and how to go about proving it but I'm not sure how to evaluate the first integral written above without using any limit. Would I maybe use a similar approach as was used to show the latter integral?


Let $\alpha=\sqrt{2+\sqrt{3}}$.  Let $L=\mathbb{Q}(\alpha)$.      Determine $Gal(L/\mathbb{Q})$   Thanks for your help.


Regarding the Weyl spinor and its transformation properties

I am trying to prove the Lorentz invariance of the (left-handed) Weyl Lagrangian: $$\mathcal L=i\psi^\dagger\bar\sigma^\mu\partial_\mu\psi$$  A Lorentz transformation is realized as $\psi\to M\psi$, where $M=\exp[-\frac{i}{2}\omega_{\mu\nu}S^{\mu\nu}]$, and $S$ are the generators of the representation, i.e., $S^{0i}=-\frac{i}{2}\sigma^i$ and $S^{ij}=\frac{1}{2}\epsilon^{ijk}\sigma^k$. Therefore, the Lagrangian transforms as $$\mathcal L=i\psi^\dagger\bar\sigma^\mu\partial_\mu\psi\to i\psi^\dagger M^\dagger\bar\sigma^\mu M\partial_\mu \psi$$ so that if it actually is invariant, we must have $M^\dagger\bar\sigma^\mu M=\bar\sigma^\mu$ (and, in particular, $M^\dagger M=\mathbb I$). I think this is a nice relation, which expresses the invariance of the symbol $\bar\sigma^\mu$.  Now the thing is, I think this relation is not true. Take, for example, a boost in the $z$-direction with rapidity $\omega$. This means $$M=\exp[-i\omega S^{03}]=\exp\left[\frac{\omega}{2}\begin{pmatrix}-1& 0\\0&1\end{pmatrix}\right]=\begin{pmatrix}e^{-\omega/2}&0\\0&e^{\omega/2}\end{pmatrix}$$  In this case, it is easly seen that $M^\dagger M\neq\mathbb I$. My question is: what went wrong in my argument?


How do I sort an array with letters and numbers combined in bash?

I have an array with h4 h5 h1 h2 h3 in it and I would like to sort it according to the numbers, but don't know how. What is the best way to do this?  edit1: I would also like to sort an array via the numbers containing different letters, for example s4 h5 q1 h2 g3.


My purpose is to have an OS like unmanage vps/server for web hosting out there. For Learning in my own space before jumping to online!  I have a notebook Dell Vostro 3460 with i5 3230M. I have Window 7 Ultimate 32bit currently running. I want to know: What Ubuntu should I install for my purpose (Desktop or Server)? Should I use 32bit or 64bit? Which version is suitable for newbie start learning like me (12.04.3 LTS or 13.10)?  Thanks in advanced! Please, easy on me as I'm just starting out!


Objects disappear when adding boolean modifier

I am following an example from a book using Boolean modifier to cut hole in an object. I have two 3D objects overlapping and when I apply "difference" operation, the first object disappears. It's only one edge of the first object that's causing this problem- when I move the second object to other edges it works.  I am very new to Blender, is there anyway I can attach my Blender file for all to see? Thank you


The following is exercise 8 (section 2.6) in Algebra by Hungerford:     Let $p$ be an odd prime. Prove that there are at most two nonabelian groups of order $p^3$. (One has generators $a,b$ satisying $|a| = p^2; |b|=p;b^{-1}ab = a^{1+p}$ and the other has generators $a,b,c$ satisfying $|a|=|b| = |c|= p;c = a^{-1}b^{-1}ab;ca=ac;cb=bc$)   I realize that there are many links online classifying groups of order $p^3$. However, most of the solutions I have seen have required several pages of work.  Since this is just an exercise, I suspect there is a shorter solution. I have come up with the following:  We know that $Z(G) = p$ because $G$ is a $p$-group and if $|Z(G)| = p^2$ or $p^3$, then $G/Z(G)$ would be cyclic. Thus, $G$ would be abelian, contrary to hypothesis. So, let $c$ be a generator for $Z(G)$. Consider the quotient group $G/Z(G)$ which has order $p^2$. Hence, $G/Z(G) \cong \mathbb{Z}_p \times \mathbb{Z}_p$. Let $\overline{a},\overline{b}$ be generators for $G/Z(G)$ (the overlines denote passage to the quotient). Now, this means that every element in $G$ can be written as $a^ib^jc^k$ for $i,j,k \in \mathbb{Z}$. Since $c \in Z(G)$ we cannot have that $a,b$ commute (this is important later).   Notice that $\overline{a},\overline{b}$ both have order $p$ in $G/Z(G)$. Thus, $a^p,b^p \in Z(G)$. We consider cases of $a^p$ and $b^p$.  Case 1: both $a^p = b^p = 1$  Then, since $G/Z(G)$ is abelian, the commutator subgroup, $G'$, is contained in $Z(G)$ so that $|G'| = 1 $ or $p$. But, $|G'| = 1$ implies $G$ is abelian, contrary to hypothesis. So, $|G'| = p$ and consequently $G' = Z(G)$. Thus, since $a,b$ do not commute, $a^{-1}b^{-1}ab$ is nontrivial and $Z(G) = \langle a^{-1}b^{-1}ab\rangle$ (this is by the previous exercise where we showed that the commutator subgroup is generated by elements of this form). Thus, by possibly switching generators for $Z(G)$ this group satisfies the second pair of generators and relations in the question.  Case 2: $a^p \neq 1$ and $b^p = 1$ (or vice versa)  In this case $a^p$ is a nontrivial element in $Z(G)$ and since $Z(G)$ is cyclic of order $p$, $c = a^p$ and so $|a| = p^2$. This gives rise to the first pair of generators and relations.  It is here where I am stuck. These should be the only two, but I have not found a reason why we cannot have $a^p \neq 1$ and $b^p \neq 1$. How can I guarantee that this case does not occur (or gives one of the two cases above)? I assume this has something to do with the oddness of $p$, as I have not used this anywhere in the argument. Moreoever, any other suggestions or corrections on the current work would be greatly appreciated.   Thank You


If $M(\epsilon)$ is the $\sigma$-algebra generated by $\epsilon$, then $M(\epsilon)$ is the union of the $\sigma$-algebras generated by $F$ as $F$ ranges over all countable subsets of $\epsilon$  Proof: Let $M = \bigcup_{F\subset \epsilon}M(F)$, we need to show that $M = M(\epsilon)$. First, we will show that $M\subset M(\epsilon)$, observe that for each countable subset of $F$ of $\epsilon$ that $M(F)\subset M(\epsilon)$. Since, $F\subset \epsilon \subset M(\epsilon) \Rightarrow M(\epsilon)$ is a $\sigma$-algebra containing $F$ therefore $M(F)\subset M(\epsilon)$.  Now we need to show $M\subset \epsilon$ but this is where I am sort of lost, any suggestions is greatly appreciated. I know this is similar to another question that was asked but I didn't really like the notation and I wish to follow through with what I have set up already


Show continuous $f_1 : ~ ]a, b[ \to \mathbb{R}$ is uniform continuous $\Leftrightarrow$ continuous $f_2:~ [a, b] \to \mathbb{R}$ exists with...

Let $f_1 :~ ]a, b[ \to \mathbb{R}$ be continuous. Show that $f$ is uniformly continuous if and only if there is a continuous function $f_2: ~ [a, b] \to \mathbb{R}$ with $f_1(x) = f_2(x)$ for all $x \in ~]a, b[$. Having difficulties with proving the "$\Rightarrow$" implication.


Why doesn't Mertens's second theorem prove the Prime Number Theorem?

Mertens's second theorem states that $$\sum_{p \le x} \frac 1p = \log \log x+O(1).$$ Defining $p_x=p_{\lfloor x \rfloor}$ for all real $x \ge 1$, we can replace the sum by the integral $$\int_1^x \frac 1{p_t} \; dt=\log \log x+O(1)$$ and thus $\frac 1{p_x}$ is on the order of $\frac d{dx} \log \log x=\frac 1{x \log x}$, which simplifies to the prime number theorem. This is clearly not a valid proof, but why not? I suspect that it's in the step from the integral to the expression for $\frac 1{p_x}$, but I don't see why that isn't valid.


Let G be a group such that $(xy)^2 = (yx)^2$ for all x, y ∈ G. Show that $xy^2 = y^2x$ for all x, y ∈ G.

I'm not quite sure if I did this right but I had another solution that made no sense to me:   This is the solution I do not understand. I did not solve it this way.  $=>(xy)^{-1}(xy)^2(yx)^{-1} = (xy)^{-1}(yx)^2(yx)^{-1}$  $=>(xy)(yx)^{-1} = (xy)^{-1}(yx)$  then somehow we have   $=> xy^2 = x((x^{-1}y)x)^2$  $=> xy^2 = x(x(yx^{-1}))^2$  $=> xy^2 = (xyx)^{-1}(xyx^{-1})x$  $=> xy^2 = y^2x$  I'm positive that the solution above is wrong I just need confirmation.   This is my solution:  Since G is a group then for all x,y ∈ G there exists $x^{-1}$ , $y^{-1}$ ∈ G.  $(xy)^2 = (yx)^2$  $y^{-1}x^{-1}xyxy = y^{-1}x^{-1}yxyx$  $xy = y^{-1}x^{-1}yxyx$  $y = x^{-1}y^{-1}x^{-1}yxyx$  Take the left hand side of $xy^2 = y^2x$ and substitute $y = x^{-1}y^{-1}x^{-1}yxyx$  $xy^2 = x(x^{-1}y^{-1}x^{-1}yxyx)^2$  $xy^2 = x(x^{-1}y^{-1}x^{-1}yxyx)(x^{-1}y^{-1}x^{-1}yxyx)$  $xy^2 = xx^{-1}y^{-1}x^{-1}yxyxx^{-1}y^{-1}x^{-1}yxyx$  $xy^2 = y^{-1}x^{-1}yyxyx$  $xy^2 = y^{-1}x^{-1}y^2xyx$  $xyxy^2 = y^2xyx$  $y^{-1}x^{-1}xyxy^2 = y^2xyxx^{-1}y^{-1}$  $xy^2 = y^2x$.


limit of integral $n\int_{0}^{1} x^n f(x) \text{d}x$ as $n\rightarrow \infty$

I am trying to solve the following problem at the level of a senior undergrad analysis level. So, the problem is as follows: We are given a function $f$ which is continuous on the interval $\left [ 0,1 \right ]$, and the question is to find the limit: $$\lim_{n\rightarrow \infty}\int_{0}^{1}x^{n}f(x)dx\;.$$ The second part of the problem is to deduce the following limit: $$\lim_{n\rightarrow \infty}n\int_{0}^{1}x^{n}f(x)dx\;.$$  For the first part: I just did the following: For every $0\leq x< 1$: $x\leq M$, where $0< M< 1$. Then: $$\int_{0}^{1}x^{n}f(x)dx\leq M^{n}\int_{0}^{1}f(x)dx\;.$$ Then: $$\lim_{n\rightarrow \infty }\int_{0}^{1}x^{n}f(x)dx\leq \lim_{n\rightarrow \infty }M^{n}\int_{0}^{1}f(x)dx= 0.\int_{0}^{1}f(x)dx=0\;,$$ so $$\lim_{n\rightarrow \infty }\int_{0}^{1}x^{n}f(x)dx=\lim_{n\rightarrow \infty }f(1)\int_{0}^{1}1dx=f(1)\;.$$ Does that make sense? If not, please show me the correct one.  As for the second part, I have no idea what to do. Any help?


I am trying to attach my Vf page which is rendered as pdf to the Files section. But the error " Too many nested getContent calls." is being thrown. The code is as follows: VF Page (Only starting) <apex:page action="{!attachOfferPDF}"        standardController="Quote__c"        extensions="QuotePDFController"        readOnly="true"              applyHtmlTag="false"             sidebar="false"             showHeader="false"             cache="true"             renderAs="pdf">  Apex Controller: public with sharing class QuotePDFController { public PageReference rtn; public static string recursion = 'false' ; public string parId; public quote__c quotesRecords {get;set;} public Quote_header__mdt quotesHeaders {get;set;}  public QuotePDFController(ApexPages.StandardController standardController){     quotesRecords = new Quote__c();     parId = standardController.getId();         system.debug('parid '+parId);     quotesRecords = [select Id,Name, (SELECT Id,    Product_Name__c,DifficultyLevel__c,Product__r.Name,Level_Course__c,Onetime_Fee__c,OS__c,Vlab_Configuration__c,PerHourCost__c,PerChallengeEvaluationFee__c FROM Quote_Line_Items__r) FROM Quote__c where Id = 'a071y0000015mwEAAQ' limit 1];           } public void attachOfferPDF() {               if ( recursion == 'false'){         recursion = 'true';         system.debug(recursion);         PageReference pdfPage = Page.QuoteGeneration;         Blob pdfBlob = pdfPage.getContentAsPDF();         Attachment a = new Attachment(parentId = 'a071y0000015mwEAAQ', name='Rahul' + '.pdf', body = pdfBlob);         insert a;         system.debug('id is '+a.id);     }} }  Not able to figure why this error is being thrown.


how to protect the directory using password in LINUX (Need to add or modify files after encrypted )?

Is there any possibilities to protect the directory using the PIN number in Linux. But we need to add or modify files inside the encrypted directory.


How does ssh prompt for a password when all input and output is redirected?

I don’t actually need to run the command below, and I am aware of ssh keys if I did want to log in without typing a password. I would just like to know how ssh seems to circumvent my file redirection.  Running the following command, ssh prompts me for a password:  ssh nobody@192.168.1.151 > /dev/null 2> /dev/null < /dev/null   How does this work? stdin, stdout, and stderr are all redirected, but ssh still manages to print a prompt on my screen and read what I type. I tried adding the ssh arguments -t -t and -T (not both at once), to enable or disable pseudo-tty allocation, but it made no difference.  I also tried closing all input and output this way, although I don’t know if I typed it correctly. Still, ssh prompts for a password:  (exec 0<&- 1<&- 2<&- 0>&- 1>&- 2>&-; ssh nobody@192.168.1.151)


How much missing data is too much? Multiple Imputation (MICE) & R

Currently I am working on a large data set with well over 200 variables (238 to be exact) and 290 observations for each variable (in theory). This data set is missing quite a lot of values, with variables ranging from 0-100% 'missingness'. I will eventually be performing logistical regression on this data, so of my 238 columns I will at most only be using ten or so.  However as almost all of my columns are missing some data, I am turning to multiple imputation to fill in the blanks (using the MICE package).  My question is; given that I have a large amount of variation in the missing data, at what percentage missing should I start to exclude variables from the mice() function?   Can mice function well with variables that are missing 50% of their values? What about 60%, 70%, 80%, 90%?


How To echo constant Variable in php with variable name

I started learning php and Recently I've faced a problem with a constant variable in my code. recently I've created the Ninja class in the editor and set a stealth constant to the string "MAXIMUM", then I try to echo it to the page using the scope resolution operator (::).  <html>  <head>  <title> Scope it Out! </title>  </head>  <body>  <p>   <?php   class Person {    }   class Ninja extends Person {     // Add your code here...     const stealth = "Maximum";   }   // ...and here!   if(Ninja::stealth){      echo stealth;     }    ?>    </p>   </body>   </html>   Now question is "How can echo the const Variable in php???"


Ubuntu 15: after installing and configuring java, echo $JAVA_Home is working, Java -version is not working

I have installed the oracle Java 8 and configure it.  cmd-> echo $JAVA_HOME /usr/lib/jvm/oracle_jdk8 cmd-> echo $PATH /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games my oraclejdk.sh file:  cmd->java -version The program 'java' can be found in the following packages:  * default-jre  * gcj-4.9-jre-headless  * openjdk-7-jre-headless  * gcj-4.8-jre-headless  * openjdk-6-jre-headless  * openjdk-8-jre-headless Try: sudo apt-get install <selected package>   my oraclejdk.sh It's got empty accidentally now. I logged out couple of times, but still getting above results. I had export commands in it which I don't remember now.  Can you please help me in getting Java running on Ubuntu.  Note Duplicate: My question is not related to that mentioned answers. I have a configuration issue, where half echo $JAVA_HOME is showing that Java is installed, but Java -version can't locate the installed Java.


How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?

How do I prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$? for $x, y$ positive?  This should be easy, but I'm not seeing how.  A hint would be appreciated.


QGIS calculates main soil type of polygons from another polygon layer

I've been working with qgis for a while but somehow I never fiured this out, so I thought it's time to ask.  I have 2 shapefiles.   a polygon layer from nearby fields (SHAPE1 (the red outlines)) a polygon layer, with different polygons than SHAPE1, that has soiltypes as an attribute (sand, clay etc.) (SOIL (the funky disco colors, each color represents a different soil type)   What I want to find out is what the main soiltype for each polygon in SHAPE1 is. (preferably by adding a field to SHAPE1 with the attribute from SOIL)  Is this possible?


Supersymmetry calculations using computer algebra

Already the early papers on supergravity were written using computer algebra software to do some calculations. What modern packages do people normally use for doing such calculations? Of course Mathematica and presumable a lot of other programs can be made to do such calculations, I am wondering if there are special packages or tutorials how to do such calculations in them.


How to transfer a text message from phone to sim card?

I'm using huawei nova 3i,and right now when I transfer my sim card to other phone, my text messages are not there. But when I put it back to my phone, it's there. What should I do to transfer it from my phone to my sim?


Can I enroll in Apple's Developer Program from Kuwait?

How can I enroll in Apple's Developer Program from Kuwait?  I am from Kuwait. I have Apple IDs associated with the USA and associated with my country of origin. When I try to enroll with my Kuwait based account, I keep getting an error saying:     Sorry, you can’t enroll at this time.


Possible Duplicate:          I am on the lookout for good .NET CLR memory profiling tools.  My key requirement is that it will play well with IIS and standalone CLR Apps. Ideally I would see what objects are allocated, where they are allocated and what size they are?  Does anyone have any good experiences with a particular tool that you would be happy to recommend?


How do the beacons atop each mountain light up?

In the RotK movie, Gandalf and Merry light up the beacons of Gondor. These beacons have been built atop each peak of the White Mountains. Mysteriously, when one beacon is lit another also becomes lit as if by magic. What's the underlying technology here? How do these beacons work?


I can't destroy or place blocks in minecraft

I'm playing minecraft single player and every time I try to destroy or place blocks in every world and game mode it always comes up with the chat control instead.I tried restarting it and creating new worlds but nothing seems to be working. What should I do?


Showing raster map pixel's information(pixel value) when clicked on the map in OpenLayers?

Here is my raster map code and I want see pixel information like pixel value from it when I click on the map: const UnTiled = new ol.layer.Image({     opacity:0.9,     source: new ol.source.ImageWMS({         ratio: 1,         url: 'http://localhost:8080/geoserver/shomal/wms',         params: {                  'VERSION': '1.1.1',                 "STYLES": '',               "LAYERS": 'shomal:geotiff_coverage',               "exceptions": 'application/vnd.ogc.se_inimage',         }       })            });map.addLayer(UnTiled);


How to find latest file and delete old files in a group of files in zsh scripting?

I am facing problem in zsh scripting. I have group of files in a directory such as:  001_20160223.txt  /delete 001_20161102.txt  /delete 001_20161209.txt  /keep 005_20160502.txt  /delete  005_20161105.txt  /delete 005_20161206.txt  /keep 009_20160502.txt  /delete 009_20161105.txt  /delete 009_20161205.txt  /keep   Now, we have to sort files having same starting number for eg. 001 and then we have find latest file based on the date written in file name and delete old files. The same way we have to perform for other files also. So the final output in directory would be following:  001_20161209.txt  /keep 005_20161206.txt  /keep 009_20161205.txt  /keep   This is what I have tried so far:  files=($(find . -name "???_*.txt")) | if ((#files > 1)); then rm -- ${files[1,-2]}; fi   but it is deleting all files except the last one. I want to create a separate group of files having same starting name and then to delete it.


Can you help me for my algebra homework? Let n be square free positive integer. Prove that Zn has no nonzero nilpotent element.


How did they post process before Photoshop?

So, yes, I'm intrigued as to how they post process pictures before Photoshop (or computers, for that matter) came about. Or is post processing a by-product of the computer revolution?  My understanding of film photography (all from the film equivalent of a point-and-shoot we had when I was a kid) is that light burns into film then film gets developed. And, well, unlike bits, your end-product is tangible and "permanent", for lack of better term.  I'm woefully ignorant about film processing but I guess this is where the post-processing takes place? How do they tweak color temperatures? Remove red eyes? Retouch skin blemishes? Do they use special dyes/inks to achieve better colors/contrast?


What is the fastest, most efficient way to get alerts for Stack Overflow feeds?

I have tried using Google Reader, FeedDemon and different Chrome extensions to follow Stack Overflow's tag feeds (e.g. newest question RSS feeds for a given tag), but nothing seems to give me alerts quickly enough. Even if I set the refresh time to as little as one minute, there is considerable delay. Any suggestions/recommendations for a faster tool or way of getting updates?


Is resources reduction one of the important reasons that questions/answers are deleted?

Today I clicked a link to a question on SO and got,   That took me to another page, .  I am accustomed to things like GitHub.  All things can change, but all things have a history.  If you push your credentials into GitHub, you can hide that mistake, but you can't delete it.  I was surprised that a link I have, i.e. a direct path to something that was not hidden from me and that I did not randomly run across, brought me to a 404 - Removed!  Searching on the words "removed" and "deleted", I found things about pet vacuums, private lists with lifetimes and privileged access.  In fact, there are several places that lifetimes seem to be implicit in the automation associated with "deleted" content.  There is also information on features related to "deleted" content and time limitations.  Since the documentation uses the words "removed" and "deleted", and the site behaves as though the content I am trying to access has been removed/deleted, I am trying to understand why content would actually be removed/deleted.  I understand that there can be economic and physical reasons for restricting resources.  Do these reasons play an important factor when choosing to delete questions or answers (really, any content)?    I also understand why things get hidden.  I don't want to stop anything from being hidden.  I don't want to change why things are hidden.  I don't want to unhide anything that has been hidden.  I believe it is in my interest that the things being hidden are hidden.  I am interested in finding a way to be more liberal in allowing any person to access a hidden thing if the person knows the path to the hidden thing.  When I say, I am interested in finding a way...  I mean, I am trying to determine if there is an important system requirement that would prevent a feature change that allowed any person to access a hidden thing if the person knows the path to the hidden thing.  I think that an important aspect of my thinking is hinged on the bit, if the person knows the path to the hidden thing.  Everything I have read so far implies the idea behind hiding is to remove disruptive content from people's view.  For a few people, e.g. the ones that took the time to create a bookmark, the hidden thing is not a disruptive.  Nothing said so far has persuaded me that, for the general case privilege should be required to access hidden content accessed from a link.  Requiring privilege for people that don't already have the link, that still makes sense to me.


How do I prove that the limit as x approaches 0 of (sin(x)/x) = 1 using the definition of a limit?

If I let r be a positive number, I have to show that there exists a positive number, u, such that |x| < u implies that |(sin(x))/x - 1| < r. Now I've gone about this two different ways, but hit dead ends both times.  My first approach was to use the triangle inequality and the fact that -1 <= sin(x) <= 1. |(sin(x))/x - 1| <= |(sin(x))/x| + 1 = |sin(x)|/|x| + 1 <= 1/|x| + 1. I knew that if I could show that 1/|x| + 1 < r, that would mean |(sin(x))/x - 1| < r. However, the issue is that if 1/|x| + 1 < r, than 1 < r. But I need prove it with r being any positive number.  My second approach was to split it into left-hand and right-hand limits and use the squeeze theorem. I knew that if I show that each limit was 1, then the entire limit was 1. I decided to start with the left-hand limit. For x<0, 1/x <= sin(x)/x <= -1/x. However, since the limit as x approaches 0 from the left of 1/x = -oo and the limit as x approaches 0 from the left of -1/x is oo, the squeeze theorem really can't be applied.  What is it that I'm doing wrong?