My logic textbook defines the notion of logic equivalence as:  A proposition $P$ is logically equivalent to a proposition $Q$ (written $P\Leftrightarrow Q$) when the biconditional $P\leftrightarrow Q$ is a tautology.   Using this definition one can easily show that given two propositions $P$ and $Q$ the conditional $P\rightarrow Q$ is equivalent to $\sim P\vee Q$, that is:  $$P\rightarrow Q\Leftrightarrow \sim P\vee Q.$$ But when I try to interpret this with words it seems not to correspond to what my intuition says an equivalence between proposition should mean.   For instance, consider the propositions  $P:\textrm{There is smoke}$  $Q:\textrm{There is fire}$  Then, according to the previous equivalence, the proposition:  $$P\rightarrow Q: \textrm{If there is smoke then there is fire}$$  is equivalent to:  $$\sim P\vee Q: \textrm{There is no smoke or there is fire}.$$  Why does this make sense?  Thanks.

I just started doing logic and everything is going fine. But we just got to Material Implication and I don't really understand it. From for example $q$, we can get $q \lor \lnot p$ by Disjunction, and from there, using Material Implication, we can get $p \to q$.   The thing I don't understand is how is this valid. Let's say    $p$ is "it's raining", and  $q$ is "the floor is wet",    and $p \to q$ holds. But just because the floor is wet, doesn't mean that it's raining. So how can we conclude that $p \to q$ just from $q$?  I'm sorry if it's confusing.


Light moves along straight lines... Got it.   So if the light from that faraway star is traveling in a straight line, and that beam is, considering the distaces involved, at best one or two photons "wide", why, when I move six feet or so to my left, can I still see the star? IOW, why aren't there "dark" areas between the beams of starlight, where the stars "disappear"?

It would seem that far-away stars are at such a distance that I should be able to take a step to the side and not have the star's photons hit my eye. How do stars release so many photons to fill in such great angular distances?


suppose that $u$ is differentiable function and verifies: $$\lim_{x\to +\infty}u(x)=1$$ do we have $\lim_{x\to +\infty}u'(x)=0$?  My idea: we inserve limits   $$\lim_{x\to +\infty}u'(x)=lim_{x\to +\infty}\lim_{h\to 0}\frac{u(x+h)-u(x)}{h}=\lim_{h\to 0}lim_{x\to +\infty}\frac{u(x+h)-u(x)}{h}=\lim_{h\to 0}\frac{1-1}{h}=0$$

I've been thinking about this problem: Let $f: (a, +\infty) \to \mathbb{R}$ be a differentiable function such that $\lim\limits_{x \to +\infty} f(x) = L < \infty$. Then must it be the case that $\lim\limits_{x\to +\infty}f'(x) = 0$?  It looks like it's true, but I haven't managed to work out a proof. I came up with this, but it's pretty sketchy:  $$ \begin{align} \lim_{x \to +\infty} f'(x) &= \lim_{x \to +\infty} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \\ &= \lim_{h \to 0} \lim_{x \to +\infty} \frac{f(x+h)-f(x)}{h} \\ &= \lim_{h \to 0} \frac1{h} \lim_{x \to +\infty}[f(x+h)-f(x)] \\ &= \lim_{h \to 0} \frac1{h}(L-L) \\ &= \lim_{h \to 0} \frac{0}{h} \\ &= 0 \end{align} $$  In particular, I don't think I can swap the order of the limits just like that. Is this correct, and if it isn't, how can we prove the statement? I know there is  already, but I think this is different in two aspects. First, that question assumes that $\lim\limits_{x \to +\infty}f'(x)$ exists, which I don't. Second, I also wanted to know if interchanging limits is a valid operation in this case.


About a week and a half ago, I updated/upgraded my 16.04 using sudo apt upgrade.  Since then, every time the laptop resumes from sleep, I get a strange border around all popup dialogs.  Any idea how to prevent it?  I tried updating/upgrading again but the problem continues.

NB: Nvidia has released an official fix; please see ,  and/or .  Upon waking up Ubuntu 16.04 from Suspend, the following graphical glitches appear around all windows, context menus, and similar:      This is currently known to affect the following NVIDIA cards running the proprietary drivers:  NVIDIA GeForce 610M, driver version 375.39, 340.102 NVIDIA GT 630M, driver version 375.39 NVIDIA GTX 650, driver version 375.39 NVIDIA GT 740M, driver version 378.13 NVIDIA GTX 745, unknown driver version NVIDIA GTX 850M, driver version 375.39, 378.13 NVIDIA GT 940M, driver version 375.39 NVIDIA GTX 950M, unknown driver version NVIDIA GTX 960M, driver version 378.13 NVIDIA GTX 970, driver version 375.39 NVIDIA GTX 970M, driver version 375.39 NVIDIA GTX 980 TI, unknown driver version NVIDIA GTX 1060, driver version 375.26, 375.39, 378.09 NVIDIA GTX 1070, driver version 378.09  The above above list has been sourced from reports from other users here on AU,  thread, and  thread. NB: This is be no means an exclusive list. It probably effects nearly all Nvidia cards.  Furthermore, this issue has been replicated on a clean install where the only change was a software update and the installation of the latest NVIDIA drivers.  What is going on, and how can it be resolved?


I have a table of data with input values and target values, and I was tasked to do something quite peculiar. I was tasked to run a sort of exponential regression and report back with the coefficients and the series of exponents. Let me explain:  Vanilla Linear Regression will minimize sum of squared error to create a linear combination in the format of $[a_1x_1 + a_2x_2...]$ where $a_i$ represents the series of coefficients and $x_i$ represents the different input features. This means that solving for the coefficients on linear regression is fairly easy given enough linearly independent data points.  I was given a dataset, and I was tasked to create an equation in the form of $[a_1x_1^{n_1} + a_2x_2^{n_2}...]$ where $a_i$ is the coefficients, $x_i$ is the input features, and $n_i$ signifies an exponential value.   I believe that since $a_i$ and $n_i$ need to be solved for, there are too many variables involved to go about this problem in a simple manner.   Is something like this even something like this even solvable? If so, how would you go about it statistically, and how would you go about it in python?  p.s. The task also says that all exponents, $n_i$, need to be between 0 and 1, so that might make it a bit easier.  p.s.s. I know that $[a_1x_1^{n_1} + a_2x_2^{n_2}...]$  is not linear unless all $n_i$ variables are either 0 or 1 but I wrote "linear regression" in the title because the two general formulas are similar.

I have developed different non-linear models, all of them follow the following formula: y=b0 + b1*(x1)^b2 + b3*(x2)^b4 where y is the dependent variable;x1 and x2 are independent variables;b0, b1, b2, b3, and b4 are the estimated regression coefficients. different values of b0, b1, b2, b3, and b4 have been estimated with different R-square and adjusted R-square. All estimated regression coefficients in all models are positive, the range of all estimated values are between 0.001-5 the difference only in the combinations of regression coefficient values in the models. by example : model 1 : y= 2.5 + 0.01*(x1)^2 + 0.2*(x2)^0.5 model 2 : y= 2.3 + 0.005*(x1)^3 + 0.25*(x2)^0.4 I estimated the regression coefficients based on the Gauss-newton method and by assuming different initial values for the regression coefficient for each run (model). how to select the best model based on anything except R-square? how to determine the goodness of fit for these models?


The answer is False.   Since $\mathbb{R}^2$ is not a subset of $\mathbb{R}^3$.  However, can someone explicitly define the difference between a subset and subspace? I am somewhat struggling with the technicality of the following definition  Subspace: a subspace, U of a vector space V, is a subset of V, $U \subset V$, such that U is a vector space in its own right, over the same field.  Vector space: A vector space over a field is a set $V$ of objects that is closed under binary operation ('addition') and scalar multiplication  Also, what would make $\mathbb{R}^2$ a subspace of $\mathbb{R}^3$ if anything?  Thanks!

The definition from my textbook is:     A subspace of a vector space is a set of vectors that satisfies   two requirements:       If $v$ and $w$ are vectors in the subspace and $c$ is any   scalar, then      (1) $v + w$ is in the subspace.      (2) $cv$ is in the subspace.   And my textbook says vector space $\mathbb{R}^2$ is not a subspace of $\mathbb{R}^3$ but let say $V=\begin{pmatrix}a\\b\end{pmatrix}$ and $W=\begin{pmatrix}c\\d\end{pmatrix}$, so $V$ and $W$ are all in $\mathbb{R}^2$, and clearly $V+W$ is in $\mathbb{R}^2$, $cV$ or $cW$ is in $\mathbb{R}^2$ too, so the first two requirements are met, why we say $\mathbb{R}^2$ is not a subspace of $\mathbb{R}^3$? It looks like we have to add $V$ and $W$ should be in $\mathbb{R}^3$ as well, but why we don't have this in the definition?


Is there a logfile of the messages that are printed onscreen underneath the splash screen in 16.04?  If so, where are they, or what is the name of the file?

I noticed that my /var/log/boot.log file has date 2016-04-22, last time I booted in 15.10. Where are Xenial boot.log files located?


I have an older server that's running 13.10, I want to update it to the LTS version.  Will a simple do-release-upgrade do the job, or do I need to tell it to update specifically to 14.04 instead of the current newest version?

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


From time to time, a popup like this popups up and installs some random app.     I scanned my PC with Avast, but it did not recognize any threat.  And how to remove it?

What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.


Let $z_1,z_2,z_3 \in \mathbb{C}$ with $z_i=1$ for $i=1,2,3$ and $z_{1}+z_{2}+z_3=0$. Show that $z_i$ are vertices for a equilateral triangle.  Tip: Think about the case $z_3=1$. What then follows the general case?  My attempt:  Since $z_3=1=1+0i$, it must be $z_1+z_2=-1$ with $z_1:=a_1+ib_1$ and $z_2:=a_2+ib_2$. Adding these equations leads to $(a_1+a_2)+i(b_1+b_2)=-1+0i$.  So $a_1+a_2=-1$ and $b_1+b_2=0$. Now I am stuck with my argumentation, there are just too many variables...  Any Ideas?

Suppose $a,b,c$ lie in the unit circle of the complex plane and satisfy $a+b+c = 0$. Then, $a,b,c$ form the vertices of an equilateral triangle. Try So, I want to show that $|b-a|=|c-a|=|b-c|$. We are given $|a| = |b| = |c| = 1$ and $a+b+c=0$. Since $|z| = z \overline{z} $, we have $$ (b-a)( \overline{b}-\overline{a} ) = (c-a)( \overline{c} - \overline{a} )$$ which simplifies to $$ |b| - b \overline{a} - a \overline{b} - |a| = |c| - c \overline{a} - a \overline{c} - |a| $$ Hence, $$ c \overline{a} + a \overline{c} - b \overline{a} - a \overline{b} = 0$$ $$ a( \overline{c} - \overline{b} ) + \overline{a} ( c-b) = 0 $$ Here I am stuck. Perhaps this is the wrong approach?


COUNT(id): query cost: 463    COUNT(*): query cost: 91.47    Can someone help me to understand why COUNT(id) is more expensive than COUNT(*)?

I have the following query:  select column_name, count(column_name) from table group by column_name having count(column_name) > 1;   What would be the difference if I replaced all calls to count(column_name) to count(*)?  This question was inspired by .    To clarify the accepted answer (and maybe my question), replacing count(column_name) with count(*) would return an extra row in the result that contains a null and the count of null values in the column.


Type erasure is the process of removing generic information for backward compatibility on compiled class. Then, I can't know what type of class are the objects in a generic class, but in an inherited class, for example:  package generics.testing;  class Box<T> {     private T value;      public Box() {         System.out.println("GenericSuperClass: " + getClass().getGenericSuperclass());     }      public T getValue() {         return value;     }      public void setValue(T value) {         this.value = value;     } }  class IntegerBox extends Box<Integer> {}  public class GenericsTesting {     public static void main(String[] args) {         Box<String> box = new Box<>();         IntegerBox ibox = new IntegerBox();     } }   I get:  GenericSuperClass: class java.lang.Object GenericSuperClass: generics.testing.Box<java.lang.Integer>   My question is, why is that information generics.testing.Box<java.lang.Integer> preserved and where is stored?

I read about Java's type erasure .  When does type erasure occur? At compile time or runtime? When the class is loaded? When the class is instantiated?  A lot of sites (including the official tutorial mentioned above) say type erasure occurs at compile time. If the type information is completely removed at compile time, how does the JDK check type compatibility when a method using generics is invoked with no type information or wrong type information?  Consider the following example: Say class A has a method, empty(Box<? extends Number> b). We compile A.java and get the class file A.class.  public class A {     public static void empty(Box<? extends Number> b) {} }     public class Box<T> {}   Now we create another class B which invokes the method empty with a non-parameterized argument (raw type): empty(new Box()). If we compile B.java with A.class in the classpath, javac is smart enough to raise a warning. So A.class has some type information stored in it.  public class B {     public static void invoke() {         // java: unchecked method invocation:         //  method empty in class A is applied to given types         //  required: Box<? extends java.lang.Number>         //  found:    Box         // java: unchecked conversion         //  required: Box<? extends java.lang.Number>         //  found:    Box         A.empty(new Box());     } }   My guess would be that type erasure occurs when the class is loaded, but it is just a guess. So when does it happen?


Very recently, a paper has been published that says: I plan to incorporate X into my research in the future.  The aforementioned paper was published recently, so the follow up containing X is not published (nor do I know if the author is working on it right now). Would it be OK for me to then to do the research suggested in the paper? The idea to incorporate X into the research was an idea I developed independently, but it also happened to be in the "future work" of another paper, if that makes any difference.

I recently read a paper, which posed some interesting questions in a section named further research.   They concluded the section by writing, "we leave all these questions for our future research".   I am really interested in one of the questions, is it considered inappropriate to write a paper handling one of those questions? The pronoun "our" indicates that the author wish to dig in to this question himself. However the paper was published in 2012, and by browsing the authors personal webpage I get no sign of a paper like that in progress.  In case I wish to write a paper on that particular topic, should I notify the author who posed the question? (Say, by asking, is question X still open?)


Why do we use this formula to find the total resistance? Lets say we have three resistors in a parallel circuit  $$R_t = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}$$  Where does it come from?

I understand that for resistors in series we need to add R for each resistor to get the equivalent resistance, where R is resistance. I also understand the mathematical manipulations that show that for resistors in parallel we need to add the 1/R for each resistor to get the equivalent resistance. However I have a couple of questions that have to do with the physical interpretation of the mathematical manipulations involved.   First, I am trying to understand why in the case of parallel resistors we have to add 1/R's instead of adding R's as in the case of resistors in series i.e. could it be thought that the current in the wire is like a sort of water flow in the pipe that has two horizontal parallel pipes positioned one on top of the other and in between connected by a number of vertical pipes that have a tap each that could be adjusted to represent different resistances. Then at the top of each vertical pipe the water pressure P exists and at the bottom the pressure will be reduced by P*R.   For example, suppose we have three vertical pipes, so then the pressure at the bottom of each (after the tap) is P*R for the total of 3*P*R so why is the equivalent resistance not 3*R*P but 1/R = (1/R1 + 1/R2 + 1/R3) and how can I be able to visualize this relation?


I've noticed that many people say things like: "that's the dad of my babies"  "We're the love of each other's life"  And other people say: "That's my babies' dad"  "We're each other's love life"  So what's the difference between those two and when to use it? Feel free to give more examples :)  Thanks!

I gave a quick answer to part of  which had not been covered by previous answers, trying to clarify the reason you would say time of decoding but not decoding’s time. I said it was ’s usually indicates possession, but of course there were several counterexamples that would have occurred to me after a moment’s consideration, and these where helpfully supplied:   Britain’s climate two days’ time  a day’s work  the sun’s rays   I am still of a mind to say that possession of some sort is what allows the ’s. Even though the sun does not have title to its rays, they do belong to the sun. Now, at the risk of duplicating the original question and/or being pigheaded, I am curious as to why time of decoding but not decoding’s time is correct, if not for the reason I gave.


I want to drive  (RT314F06) from a 3.3v output gate of an GIO pin of a R-PI3.  --edit--  There is already  answer on SO, but it is incomplete in the way that it does not tell which discrete components to use. I my case this is important since I'm too novice to decide which components to choose myself.  --edit--  Given that I have also a 6v power-supply, what component should I use to upshift the 3.3v to 6v?  The relay requires 6V and has an internal resistance of 55 Ohm. So, if I am correct, the driver needs to be capable of driving about 100mA.  Can I use a converter like ? I think it can shift only to 6v and I can't find how much current it can drive.  Thanks for the advice.

I don't have a very good knowledge of electrical engineering yet but I'm working on it. I will like to know as simple as possible, how can i drive a latching relay that needs about 70-90mA if the raspberry pi can only deliver about 40mA. I need to find a relay that can handle home appliances but can be controlled by the raspberry pi.


I configured Activity Monitor like this on all of my machines. I also set up my non-techie friends' Macs this way as well:    It was the best "health snapshot" for the Mac I'd figured out, and not hard to set up. I'd advise friends & clients to always make sure they "see green" when they're having system speed or responsiveness issues.   And then, this was a great signal that either a RAM upgrade is called for, or some app is out of control.  But now, this option was removed in Mavericks. And it's extra annoying because Mavericks promises to use memory better on some laptops. And I was looking forward to seeing how the pie chart compares.  Does anyone know a way to (1) simply display this same chart, or even (2) set the Activity Monitor's dock icon to it?

I just purchased a new MacBook Pro with Mavericks installed and noticed that Activity Monitor doesn't have the "Show Memory Usage" dock icon option anymore.  I really liked this option since I used it to prevent disk swapping by closing applications when I had too many open.  What gives?


I'm trying to rig a face and I made seperate objects for eyelashes, as the character is going to be stylized. Eyelashes are made using basic mesh with added subdivision -> shrinkwrap -> solidify  how can I make the eyelash mesh precisely follow the eyelid?  Any help is much appreciated.

When trying to control the eyelid and eyelashes mesh (both are part of the same mesh although the eyelashes are not attached to the rest of the head). Moving the gaze bone up causes the eyelids to move at the appropriate speed, but the eyelashes move at a different speed and don't stay where they need to be.  Eyelid deform bones are circled in red. These bones are restricted to X rotation only.     After changing the gaze bone to make the character look up, eye lashes detach.   I have tried weight painting the eyelashes but it doesn't make a difference unless the weight is set to zero and then the eyelashes don't move at all.  Is there a way to fix this?  Link to the .blend file:


Here is the sample   Hit http://security.ubuntu.com raring-security/main Translation-en              Hit http://security.ubuntu.com raring-security/multiverse Translation-en        Hit http://security.ubuntu.com raring-security/restricted Translation-en        Hit http://security.ubuntu.com raring-security/universe Translation-en          Ign http://security.ubuntu.com raring-security/main Translation-en_US           Ign http://security.ubuntu.com raring-security/multiverse Translation-en_US Ign http://security.ubuntu.com raring-security/restricted Translation-en_US Ign http://security.ubuntu.com raring-security/universe Translation-en_US Ign http://pk.archive.ubuntu.com raring Release.gpg Ign http://pk.archive.ubuntu.com raring-updates Release.gpg Ign http://pk.archive.ubuntu.com raring-backports Release.gpg Ign http://pk.archive.ubuntu.com raring Release Ign http://pk.archive.ubuntu.com raring-updates Release Ign http://pk.archive.ubuntu.com raring-backports Release 100% [Waiting for headers]    Or if I stop this and try to install any software it gives the other error (I tried vlc and this time)   Package dependencies cannot be resolved This error could be caused by required additional software packages which are missing or not installable. Furthermore there could be a conflict between software packages which are not allowed to be installed at the same time. Details The following packages have unmet dependencies: vlc-plugin-notify: Depends: vlc-nox (= 2.0.8-0ubuntu0.13.04.1) but 2.0.8-0ubuntu0.13.04.1 is to be installed                    Depends: libc6 (>= 2.8) but 2.17-0ubuntu5 is to be installed                    Depends: libgdk-pixbuf2.0-0 (>= 2.22.0) but 2.28.0-0ubuntu1 is to be installed                    Depends: libglib2.0-0 (>= 2.12.0) but 2.36.0-1ubuntu2 is to be installed                    Depends: libgtk2.0-0 (>= 2.8.0) but 2.24.17-0ubuntu2 is to be installed vlc-plugin-pulse: Depends: vlc-nox (= 2.0.8-0ubuntu0.13.04.1) but 2.0.8-0ubuntu0.13.04.1 is to be installed                   Depends: libc6 (>= 2.8) but 2.17-0ubuntu5 is to be installed                   Depends: libpulse0 (>= 1:1.0) but 1:3.0-0ubuntu6 is to be installed   Please Help !

I have looked at similar questions:      However neither one of them answer my problem.  I am running 12.04 AMD64 and have recently started getting an issue that when I update my repos from my connection at home through a terminal, using sudo apt-get update, it takes forever (literally after 2 hours it was at 28%), however when I run from a different location it takes less than 5 minutes to complete.  I have attempted changing which mirror I use but that does not solve the issue. I have also cut down what is in my sources list but this also makes no difference. There are no faults on my ADSL line as I have already contacted my ISP to check this. It also makes no difference if I use a WiFi or network cable connection.  What could be my issue?    A speed test (www.speedtest.net) comes out at about 0.9 Mbps down and 0.42 Mbps up (which is a shade under the advertised line speed), I reside in South Africa and use the UCT LEG server. But I have also tried the other mirrors available in SA....none of them make a difference.


Does Gödel's Second Incompleteness Theorem imply that no Theoretical Physics model of reality can be proved to be consistent using the laws of physics?  I work partially in Quantum Information Theory research which recently has had a resurgence of Quantum Foundations research themes. One of the themes of this field asks whether Quantum Mechanics, or more specifically, Quantum Information Theory is a fundamental theory of reality.   QIT is a particularly mathematical theory of reality, with highly mathematically phrased axioms:    States are vectors in Hilbert Space,  Evolutions are described by unitary operators and  Von-Neumann's Projection postulate.    We can contrast these to other physical theory axioms, such as the rather physically based axioms of Relativity: equivalent reference frames and the frame independence of the speed of light.  Does Gödel's 2nd Incompleteness Theory imply that we cannot prove the consistency of our physical reality (at least as seen through the lens of QIT) using theory derived from QIT's axioms, or that if we do require consistency of QIT theory/experimental reality that we cannot ever prove that it's founding axioms are consistent?  How do we deal with this apparent paradox or anomaly? Surely it has implications for work into Quantum Foundations/the study of physics as a fundamental model of reality?

prevents a universal axiomatic system for math. Is there any reason to believe that it also prevents a  for physics?    Edit:  I haven't before seen a formulation of Gödel that included time. The formulation I've seen is that any axiomatic systems capable of doing arithmetic can express statements that will be either 1) impossible to prove true or false or 2) possible to prove both true and false.  This leads to the question: Are theories of (nearly) everything, axiomatic systems capable of doing arithmetic? (Given they are able to describe a digital computer, I think it's safe to say they are.) If so, it follows that such a theory will be able to describe something that the theory will be either unable to analyse or will result in an ambiguous result. (Might this be what forces things like the Heisenberg uncertainty principle?)


Can a ball be decomposed into a finite number of point sets and reassembled into two balls identical to the original?  What is the true nature of this paradox ? I don't really understand this ?

The discovery of  was of course a great thing in mathematics but raises the issue of the relation between mathematics and reality. Empirically there are good reasons for faith in mathematical proofs: well derived mathematical theories and formulas, used in an accurate manner in science, really bring observable results. I don't know any scientific failures where mathematical results was blamed.  Naturally constructive proofs are preferable but there shouldn't be any problem with : the mathematical-logical machinery should guaranty the expected success. With or without the use of the law of the excluded middle!  So how to explain the non-intuitive theorem of Banach-Tarski? Which are the "weak pillars" or combinations of them? Personally I can't see the axiom of choice as a problem, since it only is a condition of what's to be called a set. Is the theorem perhaps a sign of lack of continuity in reality?     I really would like a big list of suggestions what "axioms" could be   changed to avoid the "possibility" of the the theorem.     I have been re-considering. Suppose that a new discrete theory about space and time was developed and was found to be consistent with observations. How long would it take before a corresponding theory was developed from a pure geometrical perspective? Compare with the corresponding theories of Heisenberg and Schrödinger!  What was explained in one way in the discrete theory maybe was described in a totally differnt way in the continuous theory? And who knows, maybe similar constructions as in the paradoxes of Banach-Tarski and Sierpinski-Mazurkiewicz, would be used to explain the expansion of what is now called dark energy? And even "worse", to explain the result of high energy proton- proton collisions?  It strikes me that the relative terms of consistency as is used in mathematics is all what is needed for the mathematical material to be used in scientific theories. Physicists do sometimes use mathematics in extraordinary ways and get good results.  But that does not make it less interesting to ponder the pillars of the "paradoxes".  Also, thanks for reopen and for great answers!


I found disk brakes online, . I am just wondering if they would fit on my bike. I have a Nishiki Pueblo

I have a Gary Fisher bike (wahoo I believe). I think it's considered the entry level Fisher mountain bike.  Could I put on disc brakes as opposed to using the standard  brakes on this bike?  Standard brakes are the rim brakes.   Thanks Carlos


Let a function defined on the real line be differentiable at the real number $1$. As the integer tends to infinity, what does the expression $f (1+1/n^2)+f(1+2/n^2)+⋅⋅⋅f(1+n/n^2)- nf(1)$ tend to? My answer is $0$, since each term gets multiplied by $0$. I got this by distributing the $nf(1)$ between the other $n$ terms. And, since the the function is differentiable at $1$, it is a bounded quantity which multiplied by $0$ each time. Is my answer correct?

If $f:\mathbb{R}\to\mathbb{R}$ be a differentiable at $x=c$ then how can I show that $$\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$$ I had no clue which result should I use to prove this. Please give some hints.   Thanks!


I have a two-step optimization problem now, which is \begin{equation} \max_{\boldsymbol{x}\in\mathcal{X}}\min_{\boldsymbol{y}\in\mathcal{Y}}f(\boldsymbol{x},\boldsymbol{y}) \;. \end{equation} I am curious under which conditions I can switch the order of $\min$ and $\max$ to \begin{equation} \min_{\boldsymbol{y}\in\mathcal{Y}}\max_{\boldsymbol{x}\in\mathcal{X}}f(\boldsymbol{x},\boldsymbol{y}) \;. \end{equation} Could anybody please refer me to some literature about this topic?  Thanks!

Let $X \subset \mathbb{R}^n$ and $Y \subset \mathbb{R}^m$ be compact sets.  Consider a continuous function $f : X \times Y \rightarrow \mathbb{R}$.  Say under which condition we have  $$ \min_{x \in X}  \max_{y \in Y} f(x,y) = \max_{y \in Y} \min_{x \in X} f(x,y). $$  From  we have that $\max_{y \in Y} \min_{x \in X} f(x,y) \leq \min_{x \in X}  \max_{y \in Y} f(x,y)$. So here we are looking for conditions on $f$ such that we have the equality.


I am using Ubuntu 12.04, TexLive 2012 from backports, TexLive full installation.  However, when I try to compile via latexmk, I get an error message that biber is missing.  How to get biber working on 12.04 - but please only with packages from the repository, not with manual installation.

I am getting really confused now. I installed Tex Live 2012 on my Xubuntu 12.04 with a backport and I installed TexMaker.  I could user PdfLatex right away and it generated everything I needed except my bibliography. I read that Tex Live 2012 comes with biblatex so I just changed the bibtex command in TexMaker from "bibtex" to "biblatex". However, that does not exist. So I did  sudo apt-get remove biblatex sudo apt-get install biblatex   The package is installed but I don't find the binary. Using bibtex the whole thing crashes. Which does not surprise me since I want to userbiber:  \usepackage[backend=biber]{biblatex}   Btw does biber come with biblatex? So far I couldn't get any clear explanation what biber and biblatex are to each other.  EDIT: I had to remove texlive completely and install it with the install script form . Apparently the newest version of biber does not work with the older version of biblatex I had.


I have laptop with 8 GB RAM and 1TB HDD. I have swapfile which is 2 GB (Ubuntu 18.04 uses a swapfile instead of a separate swap partition by default) and I want to increase it to use hibernation.  I want to increase it from 2 GB to 16 GB. Here is a screenshot of GParted:    I tried to increase it with fallocate -l 16G but it did not work.  Also there is the image from free -m:

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


I have the following code:   public class ClassExample {      void DoSomthing<T>(string name, T value)     {         SendToDatabase(name, value);     }      public class ParameterType     {         public readonly string Name;         public readonly Type DisplayType;         public readonly string Value;          public ParameterType(string name, Type type, string value)         {             if (string.IsNullOrEmpty(name))                 throw new ArgumentNullException("name");             if (type == null)                 throw new ArgumentNullException("type");              this.Name = name;             this.DisplayType = type;             this.Value = value;         }     }      public void GetTypes()     {         List<ParameterType> l = report.GetParameterTypes();          foreach (ParameterType p in l)         {             DoSomthing<p.DisplayType>(p.Name, (p.DisplayType)p.Value);         }      } }   Now, I know I cannot perform DoSomething() is there any other way to use this function?

What's the best way to call a generic method when the type parameter isn't known at compile time, but instead is obtained dynamically at runtime?  Consider the following sample code - inside the Example() method, what's the most concise way to invoke GenericMethod<T>() using the Type stored in the myType variable?  public class Sample {     public void Example(string typeName)     {         Type myType = FindType(typeName);          // What goes here to call GenericMethod<T>()?         GenericMethod<myType>(); // This doesn't work          // What changes to call StaticMethod<T>()?         Sample.StaticMethod<myType>(); // This also doesn't work     }      public void GenericMethod<T>()     {         // ...     }      public static void StaticMethod<T>()     {         //...     } }


I am finding it difficult to understand the four states of two entangled qubits, $$\left|00\right>$$ $$\left|01\right> + \left|10\right>$$ $$\left|01\right> - \left|10\right>$$ $$\left|11\right>$$   states that two qubits have these four states, and calls the $\left|01\right> + \left|10\right>$ the $\left|T_0\right>$ state, and $\left|01\right> - \left|10\right>$ the singlet state, $\left|S\right>$. However, what does the difference between the minus and plus signify? I understand that in both states the qubits have the property of being opposite to one another, but that's it.  It would be greatly appreciated if someone could help me understand this difference!    Before I mark an answer as correct, the main understanding I now have, is that, although when squared having an identical probability, the states differ when transformations are applied to it? Is this basically like this image, taken from ?     Note; I think my question differs from . The OP of that post already understands the presence and meaning of the minus sign, but rather asks why the minus sign is associated with $S=0$, which is a different question. Yet this question has been marked as duplicate, without any argument why it is still the same. I would like to see an argument against.

I'm working on some exercise regarding the spin coupling of two electrons. There we have the wavefunctions corresponding to the S values as  $$\begin{align} S = 1: &\begin{array}{c}\uparrow\uparrow \\ \dfrac{1}{\sqrt 2}(\uparrow\downarrow+\downarrow \uparrow) \\ \downarrow\downarrow\end{array} \\[5mm] S = 0: &\ \frac{1}{\sqrt{2}} (\uparrow\downarrow-\downarrow\uparrow) \end{align}$$  I understand that the three wavefunctions for $S=1$ are symmetric and the one for $S=0$ is antisymmetric. My question is, why is the combination with the minus sign is the one for $S=0$?  My thinking is that in a $\uparrow \downarrow$ or $\downarrow\uparrow$ combination the $S_z$ components would already add up to $0$ so that the minus sign would not change anything in the fact that $S=0$.   Or is it that $\downarrow\uparrow$ or $\uparrow\downarrow$ each represent a state with $S=1$ and $S_z = 0$ so that subtracting the one from the other gives $S=1-1=0$?


starting from September android 7.1 and below users are going to have issues with the internet so is there anyway to renew those certificates so i can use my phone properly?

In January 2021 all devices with Android prior to 7.1.1 will not be able to connect to HTTPS servers using Let's Encrypt certificate () Is there any workaround that's system-wide (i.e. all apps, not just a single app, like using Firefox) for the SSL certificate expiration on Jan 11th 2021? Assume that one has root access to their device, and that upgrading to a newer device is not an option.


I tried to to modify an existing script to work..the start option works fine. The "stop" option works ( it does kill the process successfully but gave some strange errors. Please see the output at the bottom. Can anyone please help?   #!/bin/sh   # ckconfig: 35 99 1   ### BEGIN INIT INFO   # Provides: kibana # Required-Start: $syslog $network $named $remote_fs $time networker # Required-Stop: $syslog # Should-Start: $ALL # Should-Stop: $ALL # Default-Start: 3 5 # Default-Stop: 0 6 # Description: Start the kibana application ### END INIT INFO  SCRIPT_NAME="$0"   SERVICE_NAME="kibana"    usage()   {       echo "USAGE: kibana start|stop" 1>&2       exit 1   }   start() {         export kibana_exec="nohup /data/kibana-main/bin/kibana > /data/logs/kibana/kibana.log 2>&1 "         export kibana_parms="&"         if [ ! -f $kibana_exec ]; then                 echo "kibana ERROR"                 RETVAL=1                 return 1         fi         /bin/su - Delk_admin_dev -c "$kibana_exec $kibana_parms 2>&1"         RETVAL=$?         return $RETVAL }  stop() {         export PIDFILE="`(ps -eaf | grep kibana | awk '{print $2}')`"         export pid=$PIDFILE         if [ ! -f $kibana_exec ]; then                 echo "kibana ERROR"                 RETVAL=1                 return 1         fi         /bin/su - Delk_admin_dev -c "kill -15 $pid"         RETVAL=$?         return $RETVAL }   case "$1" in         start)                 start                 ;;         stop)                 stop                 ;;         *)                 /bin/echo $"Usage: kibana {start|stop}"                 ;; esac  exit $?     [Delk_admin_dev@pvmdlr001 ~]$ ./newbash stop ./newbash: line 39: [: too many arguments Password: -bash: line 1: 8197: command not found

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


I am very new at all of this stuff and this one thing bugs me very much...  If an astronaut is orbiting earth, it should be experiencing Time a bit faster than those on earth, correct?  Well then because of the speed he is traveling, he will also experience Time a little slower than those on earth.  Correct me if I’m wrong but those should pretty much cancel out, but that sounds completely wrong to me.   If you could answer this question and fix any of my poor logic/ reasoning, that would be awesome :)

Today the NASA International Space Station started the 100000 orbit after 17 years in the space. I just wonder if there were a team of astronauts which were in the Lab for all the duration of last 17 years, how much older they would be due to the combination of Einstein's especial theory of relativity and general theory of relativity?   Here is the link to NASA's youtube video.


I'm not a DBA, just a 'regular' user.   I've got a script that I run weekly against both our development and production server which 'upserts' values into a table not directly owned by me.   Last week I started receiving ORA-01031 errors whenever I attempted to run this script on the development server but not on the production server.   As far as I know, there have been no system level changes.  On further investigation this seemed to only impact me. Other users were able to run the scripts without issue on either system.   Addtionally this occurs to any update/insert I attempt regardless of table.  Our DBA dropped and recreated my account, which didn't seem to impact anything. What other items should we be checking?

When I try to execute a view that includes tables from different schemas an ORA-001031 Insufficient privileges is thrown.  These tables have execute permission for the schema where the view was created.  If I execute the view's SQL Statement it works.  What am I missing?


Why did this happen? and now that Nerull is dead in 4e, and the Raven Queen rules over the death itself, who rules over the death?

As  outlines, the Raven Queen was a mortal until she killed Nerull and took his stuff. Why is her portfolio different from his, then? She's got Winter and Fate (Nerull didn't), but doesn't have Nerull's signature Death schtick; instead she safeguards the sanctity and finality of death. What gives?


Evaluation of $\displaystyle \int_{0}^{2}\frac{\arctan(x)}{x^2+x+2}dx$   $\bf{My\; Try::}$ Let $\displaystyle I = \int_{0}^{2}\frac{\arctan(x)}{x^2+x+2}dx = \int_{0}^{2}\frac{\arctan(x)}{\left(x+\frac{1}{2}\right)^2+\left(\frac{\sqrt{7}}{2}\right)^2}dx$  Now Put $\displaystyle a=\frac{1}{2}$ and $\displaystyle b=\frac{\sqrt{7}}{2}\;,$ So Integral $\displaystyle I = \int_{0}^{2}\frac{\arctan x}{(x+a)^2+b^2}dx$  Now Put $x+a=b\tan \theta\;,$ Then $dx = b\sec^2 \theta d\theta$  So Integral $\displaystyle I = \frac{1}{b}\int\arctan(b\tan \theta-a)d\theta$  Now How can I solve after that, Help me  Thanks

I am tring to evaluate $$I=\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$$ The first thing I did was to notice that $$\frac{1}{x^2+2x+2}=\frac{1}{(x+1)^2+1}=\frac{d}{dx}\arctan(x+1)$$ So I integrated by parts in order to get $$I=\arctan 2\arctan 3-\int_0^2\frac{\arctan(x+1)}{1+x^2}dx$$ I let $x=u+1$ but when I do that I get $$I=\arctan 2\arctan 3+\int_{-1}^1\frac{\arctan(u)}{1+(1+u)^2}du    =\arctan 2\arctan 3$$ Now this is not close to the approximation given by wolfram. What have I done wrong and how to solve this?


The electron drift speed is estimated to be very low.How could there is current almost the instant a circuit is closed??   By the discussions it is known that The information about beginning of the flow of current is transmitted through the propagation of electromagnetic waves(electric impulse)and not with the drift velocity of the electrons. But I want any one to explain how this process takes place.CURIE:)

My question is basically what exactly is electricity? I've simply been told before that it's a flow of electrons, but this seems too basic and doesn't show that electricity is instant.  What I mean is turning a switch has no delay between that and a light coming on. Is it really instantaneous? Or is it just so fast that we don't notice it?


Consider a current-carrying ring as shown, having no resistance. Now, we can say that the fields around this would be constant. Thus, we must expect this system not to radiate energy. Considering it in another manner, the charges present inside are moving on a curved path with drift velocity. Their motion is thus accelerated and so we must expect them to radiate energy. With both ideas contradicting each other, which one is correct?

If a charge travels in a circle it must accelerate, thereby producing EM.  However, a wire in a circular loop is analogous to many charges moving in a circle. So, why don't circular currents produce EM? (I have not found any evidence that circular currents can produce EM).  A similar question is: . However, my question asks about circular wires and direct current. Thanks.


I've seen several seatposts on the market with suspension built into them such as the Thudbuster, Redshift, and Kinect and was wondering if anyone is using one for mountain biking?  Is it worth the money and does it improve the ride quality?  Let me know your thoughts. Thanks!

I'm planning a ride from Birmingham to London on the Grand Union Canal (UK), which will be quite bumpy for most of the 145 mile distance.  I have a front suspension bike and can't afford a new full suspension bike.  Do suspension seat posts actually work?  If so, I'll get one of them.  Can anyone recommend a good model?


In the context of Krull dimension, given any commutative ring $R$ and $\mathfrak{p}\subset R$ a prime ideal, we have (almost by definition) $$ \mathrm{ht}\:\mathfrak{p}+\mathrm{coht}\:\mathfrak{p} \leq \dim R $$ In the special circumstance of the coordinate ring of an (irreducible) affine variety, i.e. $R$ being a finitely generated $K$-algebra which is an integral domain we have the equality $$ \mathrm{ht}\:\mathfrak{p}+\mathrm{coht}\:\mathfrak{p} = \dim R\quad (*) $$     I was curious on when (which type of rings) this equality $(*)$ happens? By the way, does this equality/inequality have a name?   First of all seems like we better assume $\dim R<\infty$ for preventing things to go haywire.  Then if $\mathfrak{p}_0\subsetneq\cdots\subsetneq \mathfrak{p}_m=\mathfrak{p}$ is a chain the length of which is $\mathrm{ht} \: \mathfrak{p}$ and $\mathfrak{p}\subsetneq\cdots\subsetneq \mathfrak{p}_n=\mathfrak{m}$ a chain the length of which is $\mathrm{coht}\: \mathfrak{p}$, then defining $n$ as the length of the two chains combined: $$n\leq  \mathrm{ht}\:\mathfrak{m}\leq \dim R.$$ So we have two inequalities we need to satisfy. The second inequality can be satisfied by assuming $R$ is equicodimensional, i.e. $\operatorname{ht}\mathfrak{m}=\dim R$ for any maximal ideal $\mathfrak m$.  The first one is trickier. It is happening because it is possible to have another maximal chain of primes inside $\mathfrak{m}$ which doesn't pass through $\mathfrak{p}$ and its length is bigger than $n$. I know of one way to make this imposible (which may not be the most general condition):  Fact: If $R$ is a equicodimensional Cohen-Macaulay ring then every maximal chain of prime ideals is of the same length $\dim R$.  So what I have come up with is if $R$ is a equicodimensional CM-ring then the equality (*) holds (right?).      How much further can one go in stating the most general condition for the onset of equality $(*)$? Is it even useful to go further?

Let $A$ be an integral domain of finite Krull dimension. Let $\mathfrak{p}$ be a prime ideal. Is it true that $$\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$$   where $\dim$ refers to the Krull dimension of a ring?    Hartshorne states it as Theorem 1.8A in Chapter I (for the case $A$ a finitely-generated $k$-algebra which is an integral domain) and cites Matsumura and Atiyah–Macdonald, but I haven't been able to find anything which looks relevant in either. (Disclaimer: I know nothing about dimension theory, and very little commutative algebra.) If it is true (under additional assumptions, if need be), where can I find a complete proof?  It is obvious that $$\operatorname{height} \mathfrak{p} + \dim A/\mathfrak{p} \le \dim A$$ by a lifting argument, but the reverse inequality is eluding me.  Localisation doesn't seem to be the answer, since localisation can change the dimension...


Someone please explain why singular to plural to singular is correct. In my opinion, this makes no sense.  Edit for clarification of what I'm asking: My point is that double linking verbs are not OK as they lack an object in between (and cannot share a subject or object in such cases). One of my sources for this is here:   And here: , which is partially relevant. Except that we're taking it to a whole new level by changing plurality of a word!  Also:   Same idea goes for sentences like "All there is is a cat" (which, again, I find ungrammatical) or "A cat is is all there" (flipped around version, or the predicate adjective form of the predicate nominative using the same singular form instead of going from plural to singular or singular to plural which is an even more extreme case of incorrectness I believe).  BUT, people still say things like this: "all there is are socks." So why not say, "all there are is a sock?" Same idea in terms of grammar? Or is that wrong? Why can a predicate nominative not be flipped to a predicate adjective form? Quite confused here.

This is a phrase I've heard many people use, and it sounds wrong to me; e.g.:     The thing about that is, is that she might take it the wrong way.   It seems to treat "The thing [...] is"—the entire phrase—as the subject of the sentence. Of course, even if that were allowed, the comma placement would still be questionable.  I'm curious to know:   Is there a name for this wording? Is it specific to a certain dialect? Is its etymology known?


Find a post that needs editing. Edit the post and save your edits. Realize you forgot to describe the changes in the edit comments box.  It just says something like "replaced xxx characters in body" or "edited tags", etc. Go back to edit and describe your actual changes better and save. The edit history is not updated with the revised comment!

It often occurs to me to add an edit summary to a question-edit immediately after submitting the edit, especially if the changes aren't obvious (formatting etc.). So I:   Click "edit" again. Fill in the summary Click on "Save Edits".   The 'edit' (no actual change has been made to the title/body/tags)  is accepted, but the summary doesn't show up, i.e. it is silently rejected.   I don't think it should work this way because the summary has been added by the original editor within the original edit's edit-window. In fact if I remember correctly, it to used to work as expected earlier; so perhaps this is a recent change.


There is an application that reads files content of a certain folder and visualizes results in parallel . In case of parallel file access on HDD it works really good, but when I am doing the same things on DVD Rom it works awfull long. When I am wrap the file IO in a lock granting that it only single file read possible) I suisfied with DVD performance, but lacking performance on HDD.  Currently thinking of a mechanism of recognition of a storage performance by given folder path, and then, having some metric I would like to load balance parallel file reading.  How can I get such a metrics? (or if there is a way to get just slow devices like DVD, USB2?)  Is there better solution rather the one I am thinking of?

In C# how do you detect is a specific drive is a Hard Drive, Network Drive, CDRom, or floppy?


A similar, but more severe, issue was reported back in 2010 and marked as completed: . A milder issue currently exists.  When a user is ignored and their small avatar is displayed in the "people in room" avatar grid, extra whitespace appears immediately below the row the avatar is in.  Normal spacing:    First row:    Second row:    Third row:    Changing the width of the browser window has no effect.   Chrome 41, Windows 7.

When I ignore a user, the avatar list looks weird.    The blank line beneath the row with the avatar of the ignoree is quite annoying.    I use Google Chrome on OS X.  There was a  tagged  but it still looks weird.


My laptop is INSPIRON 1545 with the following configurations   2GB ram 250GB hard disk Intel® Core™2 Duo CPU T6400 @ 2.00GHz × 2    I installed ubuntu 16.04 last month but it was quite laggy on my laptop. I really want to use use it. i am currently using solus which is good but is there a way to use ubuntu on my laptop without it lagging?

What are your tips for improving overall system performance on ubuntu? Inspired by this  I realized that some default settings may be rather conservative on Ubuntu and that it's possible to tweak it with little or no risk if you wish to make it faster.  This is not meant to be application specific (e.g. make firefox load pages faster), but system wide.  Preferably 1 tip per answer, with enough detail for people to implement it.  A couple of mine would be:   Install  (via Software Center or sudo apt-get install preload); Change  value - "which controls the degree to which the kernel prefers to swap when it tries to free memory";   What are yours?  PS: Since this is not intended to have a unique answer but rather, several useful tips, I'm making this community wiki out-of-the-box.


Let $H \triangleleft G$ such that $[G:H]=n$. Show that $g^n \in H$ for all $g \in G$.   So I've been trying this for a while and got to nowhere. So I tried to solve it by arriving to a contradiction. So take $g \in G$ such that $g^n \notin H$. Then if  $G=\bigcup_{i=0}^{n-1}Hg^i$,  I was able to arrive to a contradiction. However I wasn't able to prove that $Hg^j \cap Hg^k = \emptyset$ for every $0 \leq k,j \leq n-1$ as to be able to write $G$ as that disjoint union of coclases.  Am I on the right track? Is that true? Any hint if not?  Edit:     The idea is not to use the quotient group. It's an exercise of a chapter of Rotman's Introduction to Theory of Groups which is previous to the introduction to the quotient group.

I need some help in relation to this exercise    "Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$."  I'm not allowed to use quotient groups in the proof, because the exercise is in the chapter before.   I tried by induction on $n$. The case $n=1,n=2$ are obvious, but even  the case $n=3$ is giving me trouble so I give up studying the general case of the inductive step.  My other approach was studying left or right coset of $G$. But I only proved that if $g \in aH$ then $g^2 \notin aH$ if $a \notin H$, and I can't find a way to demonstrate that $g^n \in H$. (my starting idea was to prove that every power of $g$ is in a different coset but then I realize that in this way I don't handle several case, for example $g$ has period strictly lesser than $n$ and in conclusion it doesn't prove the exercise)  Maybe I'm missing something about indexes, and this is why I asked here for some help,  (I can't use quotient groups because they are introduced later than this exercise, forgot to add this info in the beginning) Thanks in advance :)


How can I compute $$\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}\quad?$$    My attempt: Looking at the limits of the integration I see that we should induce some $\tan^{-1}(x)$ so if we put $\infty$ we would get something like $\frac{\pi}{2}$ . But I am not sure how to proceed . Partial fractions don't yield good integral.

Let $a$ be a non-zero real number. Is it true that the value of $$\int\limits_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$$  is independent on $a$?


I have a feature class with x/y values populated on the native projection of the feature class (state plane).  In the same feature class I also have Lat/Long fields that I need to populate (WGS 84 in decimal degree).  The problem I have is the calculate geometry function doesn't allow me to choose a different projection other than State Plane when I try to auto populate the Lat/Long values.  Does anyone have any python code or ideas that might help with this request?


This is my first time in this website. I'm a student in master 2 ans I'm following a course about elliptic curves. And I'm didn't really understand how to calculer the order of a function at a point P for a curve C. (see the picture for the example)    My questions are : 1) How to see Y and X like functions on K(C) ? 2) How to calculate ord(Y) on (0,0)  Thanks a lot for the help !

I cannot understand the definition of the order function in "Joseph H. Silverman, The Arithmetic of Elliptic Curves", which is as follows:  $$\text{ord}_p: \bar K[C]_p \to \{ 0,1,\dots \} \cup \{ \infty \}$$  where $C$ is a curve and $$\text{ord}_p(f) = \sup \{ d \in \mathbb N : f \in M^{d} _p \} , \\ M_p = \{ g \in \bar K [C] : g(p) = 0 \} .$$  How can we compute the order of a function at a point, with the above definition? Give an example.


Each plane with grass has transparency on it so that if I just rendered one grass plane it would not be a problem but when i duplicate them then they return to black

Using v2.73, cycles and a very simple scene: an array of cubes, no big deal.   If I set the shader's material to transparent, the cubes in the foreground do become transparent but those far away in the back do not disappear completely and this strange dark things appear (visible in rendered mode and in final renders)    I've played with the clipping distance on the viewport and camera, but I can't figure out how to make those ghosts go away...


My understanding is that BFGS and L-BFGS solve the same type of optimization problems as GD and it's variants.   Why is GD the go to algorithm for training neural networks?

I have made two solvers to implement neural networks, one is based on stochastic gradient descent (SGD) while the other is based on the BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm.   I have read a lot of material and find it is common to use SGD rather BFGS, but I have found that BFGS performs better than SGD.   Can anyone can tell me why people prefer SGD to BFGS?


Suppose R be the ring of real valued continuous functions defined over [0,1].And if M is a maximal ideal of R.Then prove that M will be of following form. M={f in R| f(x)=0} for a fixed x in R  Obviously the ideal given by M(x)={f in R|f(x)=0} is an maximal ideal for a fixed choice of x in [0,1].  But starting from a random Maximal ideal how can I get to that form? Thanks in Advance

Let $S$ be the ring of all continuous functions from $[0,1]$ to $\mathbb R$. How to prove that all maximal ideals of $S$ have the form $M_{x_0}=\{f\in S \mid f(x_0)=0\}$?   Thanks in advance.


What controls this?  I've signed up for many g-mail accounts before without a phone number and for some reason I am being prompted for one.  I tried clearing cookies.  I am trying to sign up for a throwaway google account so I can download some chrome extensions.  I do not want my computer\browser to be bound to me via a phone number for privacy concerns.  Please do not advice me to use a friend's phone number.  This is not scaleable.  I create many throwaways for different accounts.  I am going to download my extensions and forget about it.  It's also not fair for google to assume that everyone has a phone (I could be a bum using McDonalds wifi) or friends.

When I want to register an account with Gmail now, it says "Google will send a text message containing a verification code to your mobile phone."  I don't want to give Google my mobile phone number!!  How do I get around this?


How can I pass jQuery selector from one function to another?  Does it work like passing variables from one function to another?  i.e:    function hasSelector(){   var items = $('#item1, #item2, #item3');   return items; }  function useSelector(){   //var items = $('#item1, #item2, #item3');   //items.on('click'...);      hasSelector().on('click', function(){     alert(items);   )}; }      Edit: Thanks to some clarifications in comments I've decided to change hasSelector() into object (I had to pass parameter aswell which i forgot to mention here. Nonetheless I've still used a function.)    var hasSelector = {   items : function(){     return $('#item1, #item2, #item3');   } }  function useSelector(){    hasSelector.items().on('click', function(){     alert(hasSelector.items(this));   }); }  useSelector();
Item 1

Item 2

Item 3
 //returning [obj Obj] since I'm calling on all 3 items at once.

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


I want to make simple subtract operation on float so that I don't get a final decimal but I got same result with float  Better than my bad english : code !      private double test(final double reloadingTime) {     double timeRestant = reloadingTime - 0.1;     System.out.println(timeRestant);     return timeRestant; }   main :       double test = test(2f);     test = test(test);     test = test(test);     test = test(test);     test = test(test);     test = test(test);   console :  1.9 1.7999999999999998 1.6999999999999997 1.5999999999999996 1.4999999999999996 1.3999999999999995   So two questions: Why? And how can I can get the true result?

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


I do not have a computer, just a printer. I have a .docx file saved on my Samasung Galaxy Tab 2, and need to print it ASAP. How do I do it?

I'm pretty sure the answer is "no" since printer manufacturers haven't yet started making drivers for Android (or iPhone).   I guess I'm just curious if anyone has heard anything about this and if/when it will become a reality.  (or perhaps if it already is, and I'm just oblivious to it?)


Please help check that $\int_0^{\pi/2}\frac{1}{\sqrt{1-k^2sin^2\theta}}d\theta$ is equivalent to $-\log\sqrt{1-k^2}$ for $k\to1$.  I really have no clue how to do this. Could anyone kindly help or provide some hint? Thanks so much!

The complete elliptic integral of the first kind is defined as $$K(k) = \int_0^{\pi/2} \frac{d x}{\sqrt{1 - k^2 \sin^2 x}}.$$ I would like to derive (at least the first term of) the asymptotic expansion for $k = 1 -\epsilon$. This is certainly not trivial due to lack of uniform convergence which implies that I can't use the Taylor expansion of the integrand. What is the best way to proceed?


I am inexperienced in publishing papers in scientific journals. I was going over recently published paper of mine and found that I accidentally reported mean with standard deviation when I meant to report mean with standard error. The correct standard error is shown in a figure in the paper but I am wondering if I should contact the editor to make the correction.

During my studies I've read a number of published articles where spelling mistakes have somehow squeaked through the review process. For example, I have found a paper with a section entitled Turbulance Model when the title should be Turbulence Model. I would love to be able to submit an errata if I knew it was going to be a one or two line email, but I don't know of anyone else who does this. Will editors be annoyed with little corrections like this? Surely there isn't a need to bother the corresponding Author with such a matter, is there?  To be clear, I am only thinking of cases like the example I've given; a clear spelling mistake or a missing word. I wouldn't start arguing with an author/editor over wording issues or other gray areas.


I wrote a shell script and run it with terminal. The script calls other programs and so has some child process.  How can I see TOTAL memory and CPU used for that script after running it ?  more generally : how can I see CPU and memory usage for a program after running it?

I'm trying to measure the memory of a process that I call via the command line (i.e., I want to find out much CPU/RAM the process takes). Is there any command that I can add to the command calling the process that will achieve this?


I've been finding all over the place that the common way to bind Enums to DropDowns is through helper methods, which seems a bit overbearing for such a seemingly simple task.  What is the best way to bind Enums to DropDownLists in ASP.Net MVC 4?

I'm trying to use the Html.DropDownList extension method but can't figure out how to use it with an enumeration.  Let's say I have an enumeration like this:  public enum ItemTypes {     Movie = 1,     Game = 2,     Book = 3 }   How do I go about creating a dropdown with these values using the Html.DropDownList extension method?  Or is my best bet to simply create a for loop and create the Html elements manually?


I had installed QGIS with it in ubuntu :  sudo apt-get install qgis python-qgis qgis-plugin-grass   refer to this guide :   then i try to import QGIS module that usually work in Windows QGIS Desktop application such as :  from qgis.core import * from osgeo import *   but then, i try to :  import processing   and it said:  No module named processing   Ok i see since this is run as external application, so i try to do something like this:  import sys sys.path.append('/usr/share/qgis/python/plugins') import processing   but what i've got is:  QPixmap: Must construct a QApplication before a QPaintDevice Aborted (core dumped)   Then i my python console was exited automatically  So my question is, how to import processing in ubuntu python console that had been QGIS installed?   I really need this module..

Inspired by , but for QGIS 3 (and therefore Python 3), I would like to use the QGIS processing algorithms in a standalone Python script without a GUI, with a standard installation of Ubuntu Linux. A simple import processing is insufficient: import processing processing.run(    "qgis:rasterlayerstatistics",    {        'INPUT': .'/somefile.tif',        'BAND': 1,        'OUTPUT_HTML_FILE': './result.html'    } )  Results in: Traceback (most recent call last):   File "<stdin>", line 1, in <module> ModuleNotFoundError: No module named 'processing'  How do you get access to the QGIS processing module to use the QGIS processing algorithms in a standalone Python script (not the QGIS interpreter)?


I'm new to Ubuntu. I got a disk from a friend which contains release 11.04 but package manager does not work. How do I solve this?  Here is the error message:  E: Encountered a section with no Package: header E: Problem with MergeList /var/lib/apt/lists/us.archive.ubuntu.com_ubuntu_dists_natty_main_binary-i386_Packages E: The package lists or status file could not be parsed or opened. E: _cache->open() failed, please report.

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


I have a sidebar below a topbar but when I try to make the sidebar's height 100% it disappears but when i put a px value to the height, it appears. I tried to do calc(100%-180px), 180px is the height of my topbar, but that also dosen't work.  HTML

suggestions

a little description

   home   ask   submit

   CSS  #topbar { background-color:white; border-bottom:solid 1px black; position:relative; height:180px; width:100%; }  #sidebar{ background-color:gray; width:300px; height:100%; }

I am working on a web application where I want the content to fill the height of the entire screen.  The page has a header, which contains a logo, and account information. This could be an arbitrary height. I want the content div to fill the rest of the page to the bottom.  I have a header div and a content div. At the moment I am using a table for the layout like so:  CSS and HTML    #page {     height: 100%; width: 100% }  #tdcontent {     height: 100%; }  #content {     overflow: auto; /* or overflow: hidden; */ }

...

...

     The entire height of the page is filled, and no scrolling is required.  For anything inside the content div, setting top: 0; will put it right underneath the header. Sometimes the content will be a real table, with its height set to 100%. Putting header inside content will not allow this to work.  Is there a way to achieve the same effect without using the table?  Update:  Elements inside the content div will have heights set to percentages as well. So something at 100% inside the div will fill it to the bottom. As will two elements at 50%.  Update 2:  For instance, if the header takes up 20% of the screen's height, a table specified at 50% inside #content would take up 40% of the screen space. So far, wrapping the entire thing in a table is the only thing that works.


I am trying to access the CSV file's data using the Java and Apache commons CSV library.  I am stucked in a problem.  The problem is: "To Display the data of particular row if "Name" Header is equal to the "rahul". when I run the code nothing is printed out there."  The data in exportdata.csv file is :   Name,Food,Phone rahul,Rice,9876416884  ram,Egg,8437123456 rohit,Burger,9814125755 amit,chicken,8568934464   And my code is :  public class csvexample {   public void readfile()  {     FileResource fr=new FileResource();     CSVParser parser=fr.getCSVParser();     for(CSVRecord record : parser)     {          String str=record.get("Name");         System.out.println(str);          if(str=="rahul")         {         System.out.print(record.get("Name") + "    ");         System.out.print(record.get("Phone") + "    ");         System.out.println(record.get("Food"));         }               } }   I think that the error is in the line if(str=="rahul") , I have checked that the program is not treating the str and "rahul" same when str="rahul" in First iteration of for loop.

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


I don't know whether the following statement is true or not: $x^{q^n}-x$ is a product of all monic irreducible polynomial in $\mathbb{F}_q[x]$ of degree dividing $n$ Note that we are not assuming $q$ is prime (so it's some power of some prime). I already know that if $q$ is a prime then the statement is true. But I don't know if this general version is also true. Could you explain this to me? Thanks in advance.

In the finite field of $q$ elements, the product of all monic irreducible polynomials with degree dividing $n$ is known to be $X^{q^n}-X$. Why is this?  I understand that $q^n=\sum_{d\mid n}dm_d(q)$, where $m_d(q)$ is the number of irreducible monic polynomials with degree $d$, and that each element of the field satisfies $X^{q}-X$.  How does the conclusion follow from this? I tried substituting the exponent to $X^{\sum_{d\mid n}dm_d(q)}-X$ but this doesn't seem to do much good.


My situation is this:  I will enter US on ESTA / VWP. With a New Zealand passport. Three weeks later, I will fly to Canada. I may be in Canada for 4 or more months (they give me up to 6 by default)  After that, three scenarios are possible:  I will go elsewhere (South America), but need to pass through the US to do that. I will fly from Canada to my home country (New Zealand). I will spend some more time (a few weeks perhaps) in the USA, and fly to New Zealand.  Over the years I've seen mixed information about whether or not time in Canada simply counts towards the 90 days US gives on the VWP, and therefore if total time in US + Canada is over 90 days, it could make it hard to re-enter the US without first leaving North America entirely; Or, they will simply start a new 90 days VWP upon re-entering the USA from Canada; Or, whether the US will consider the 90+ days in US + Canada and overstay (aka. a violation) of the VWP? The cause of my confusion I've seen it written on a US Customs web site back at that time (this was around 2011) passing through the US on the way to Canada would mean you can't stay more than 90 days in Canada (assuming just one day was spent in the US), and I then asked the US Consul in NZ to confirm I'd understood it correctly, and she said I had. She told me outright that if I plan to pass through the US on the way to Canada, I can not stay more than 90 days in the two countries, otherwise I've over stayed my VWP in the US and will need a visa if I wish to return to the US in the following 5 years. She advised I would need to get a Visa if I wanted to pass through the US to spend 90+ days in Canada. I also see this comment on travelwiki.org:  Visa Waiver Program requirements Travel under the Visa Waiver Program is limited to transit, tourism, or business purposes only; neither study, employment, nor journalism is permitted under the VWP. The 90-day limit cannot be extended nor will travel to Canada, Mexico, or the Caribbean reset the 90-day limit. Take care if transiting through the US on a trip exceeding 90 days to Canada and/or Mexico. Source:   Also,  to a similar question seems to imply the same thing, that it will be a problem. Yet,  to a similar questions, say the opposite. That there will be no issue. I completely agree that a short time spent in Canada (or Mexico) won't reset the 90 days.  But does going over 90 days due to staying an extended time in Canada make me an overstayer on the US VWP? And, what would happen if I was, for example, in Canada for 4 months and then wanted to spend some time in the US before heading back to New Zealand? Will they give me another 90 days of VWP?

I'm a Finnish citizen and, first, I will spend 10 days in the US, visiting my sister. I'll fly to Canada for my exchange studies and be there for 3.5 months (I have an ETa).   I have a flight back to the US to spend Christmas and New Year with my sister and her family.  My flight home to Finland in on 3rd January and my trip began on 18 August.   Am I able to reenter the US after exchange studies in Canada, or do I have to book new flights directly from there to Finland?


I'm trying to use ajax function to my theme. I think i can't just put the javascript code in my functions.php, i have to register it properly and enqueue it.  So i store the javascript file with .js extension and enqueue it from my themes js directory. Now ajax_url is only available globally in admin section not in front end.  To get the url we have to use <?php echo admin_url('admin-ajax.php'); ?> for front end .  How can i use it in the file as it is a js file? Php can not be interpreted.  Is there any other way to define the ajax_url in my js file for front end.  OR should i include it in the header.php with no option?

This AJAX function gets called on a click:  $.ajax({             url: 'site/ajax.php',             data: {id: $('section#single article input:last-of-type').attr('value'), cote: 'like'}         }).done(function(html) {}   It passes the ID of the post (which is contained in a hidden input) for function get_post_meta() that is located in ajax.php. This is what AJAX.php looks like:  $cote = get_post_meta($_GET['id'], 'cote', true); if($_GET['cote'] == 'like') {     $newCote = $cote++;     update_post_meta($_GET['id'], 'cote', $newCote); } else {     $newCote = $cote--;     update_post_meta($_GET['id'], 'cote', $newCote); }   It is suppose to update the custom post's "cote" field, but the problem is that function get_post_meta() is undefined in ajax.php. This is the error message:  Fatal error: Call to undefined function get_post_meta() in /home2/electro/public_html/beta... on line 2


I´m stuck with the section $c)$ of the following Hartshorne´s exercise  I have just proved $a)$ and $b)$. I wonder if you can help me. Thank you for your time

I´m studying Cech cohomology through Hartshorne´s algebraic geometry and EGA, and I´m stuck in two exercises, I wonder if you can help me. The first one is the exercise III.4.4, we want to prove that $$\varinjlim_{\mathfrak{U}}\check{H}^{1}(\mathfrak{U},\mathcal{F})=H^{1}(X,\mathcal{F})$$ where $\mathfrak{U}$ is a covering of $X$. (I attach a photo of the exercise)   I have just proved $a)$ and $b)$.  I´m also stuck with the last exercise of this section: Let $X$ be a topological spaces, $\mathcal{F}$ a sheaf of abelian groups, and $\mathfrak{U}=(U_{i})$ an open cover. Assume for any finite intersection $V=U_{i_{0}}\cap\cdots\cap U_{i_{p}}$ of open sets of the covering, and for any $k>0$, that $H^{k}(V,\mathcal{F}_{\mid V})=0$. Then prove that for all $p\geq 0$, the natural maps  $$\check{H}^{p}(\mathfrak{U},\mathcal{F})\rightarrow H^{p}(X,\mathcal{F})$$ of the last exercise (III. 4.4) are isomorphisms.  Thank you for your time.


What are some good resources for getting started with LaTeX? Also, what's the difference between LaTeX and TeX?  Thanks!

Which book (free or otherwise) was the most useful to you when you started learning LaTeX?  I am frequently asked this question by friends who want to learn LaTeX, and I recommend the book which got me started, , but I feel that there might be better options around.  Also see .


Trying to use Eclipse's auto-update to go from the Kepler release to the new Luna (using Ubuntu 14.04). Got everything set, started Eclipse in admin mode, and selected Help>Check for updates.   It appeared to be working, until it failed with this message:   An error occurred while uninstalling session context was:(profile=epp.package.standard, phase=org.eclipse.equinox.internal.p2.engine.phases.Uninstall, operand=[R]org.eclipse.platform_root 4.3.2.v20140221-1852 --> null, action=org.eclipse.equinox.internal.p2.touchpoint.natives.actions.CleanupzipAction). Backup of file /opt/eclipse/.eclipseproduct failed. File that was copied to backup could not be deleted: /opt/eclipse/.eclipseproduct   Kind of seems like some sort of permissions problem, but I have no idea how to fix it.

With Luna running, I select the Help:Check for Updates option and am shown a list of updates, which are all checked except the one for Luna 4.4.1.   I hit "Select All" and try to update. It fails with this message:   An error occurred while uninstalling session context was:(profile=epp.package.standard, phase=org.eclipse.equinox.internal.p2.engine.phases.Uninstall, operand=[R]org.eclipse.platform_root 4.4.0.v20140606-1558 --> null, action=org.eclipse.equinox.internal.p2.touchpoint.natives.actions.CleanupzipAction). Backup of file /opt/eclipse-luna/notice.html failed. File that was copied to backup could not be deleted: /opt/eclipse-luna/notice.html


I'm trying to call this function which should return the age of 57 but is returning 58 if I run it today October 18, 2016.      DateTime myDate3test = Convert.ToDateTime("1958-10-17 13:45:59.473");     Console.WriteLine(CalculateAge(myDate3test)); //this should return 57 if run today October 18, 2016 since the person is not yet 58       public static string CalculateAge(DateTime dtDateOfBirth)     {         int age = 0;         DateTime dtNow = DateTime.Now;         string measurement = string.Empty;          if (DateTime.Compare(dtNow, dtDateOfBirth) == 1)         {             TimeSpan tsAge = dtNow.Subtract(dtDateOfBirth);             DateTime dtAge = new DateTime(tsAge.Ticks);                var vNowDate = Convert.ToInt32(dtNow.ToString("yyyyMMdd"));             var vBirthdate = Convert.ToInt32(dtDateOfBirth.ToString("yyyyMMdd"));             double diff = (vNowDate - vBirthdate) / 10000;             age = Convert.ToInt32(Math.Truncate(diff));              measurement = " year";              if (age == 0) // patient is not 1 year old yet             {                 age = dtAge.Month - 1;                 measurement = " month";                  if (age == 0) // patient is not 1 month old yet                 {                     age = dtAge.Day - 1;                     measurement = " day";                 }             }             if (age > 1)             {                 measurement += "s";             }         }         else         {             // Future date!!!             measurement = " Unable to calculate age";             age = -1;         }          return age.ToString() + measurement;     }   Any help is appreciated.

Given a DateTime representing a person's birthday, how do I calculate their age in years?


The title is confusing, I know. Here's the scenario: I sacrifice two creatures with Whisper, Blood Liturgist, can I then, in response to the creatures becoming sacrifice targets, sacrifice one of those same creatures using Hell's Caretaker and have both abilities still resolve correctly? I would think I would be able to because Whisper's ability is already on the stack when I activate Hell's Caretaker, but I'm not positive.

Say I have a Zombie token, , and  on the battlefield. Can I sacrifice the Zombie token to activate both the Altar's and Seer's abilities?  Similarly, if I have one card in hand, and  and  on the battlefield can I discard the one card to both of their abilities?  If I have a  with 3 charge counters can I activate both of its abilities by tapping it to add a counter, and tapping it to remove 3 counters and destroy a permanent without untapping it in between?


A friend signed me up for a Google Apps account when it was free for a personal blog I planned to create. I no longer will be creating or maintaining a personal blog. I now want to use my free Google Apps account for a business domain that I own, AND I want to control the domain instead of bothering my buddy when I need help.  How do I transfer that account that was setup for me TO me, so I can take ownership of that free account and manage it myself for another domain. He is very busy now and I don’t want to keep bothering him. Like others who have asked, I want to maintain the free account too.

I have a Google Apps for your domain account for my domain which we will call DomainA  I have since replaced that domain with DomainB which is set up in the Google Apps account as an alias.   Since I want to let DomainA expire at some point in the future, I would like to change my primary domain to DomainB in my Google Apps account with DomainA as an alias.   How can I do this?


I have a nasty issue with my thesis. I want to accommodate space before paragraph with \setlength{\parindent}{<insert number and unit>}. When I do this without a title, I get through just fine, but when I include the title, things start go wrong. Here is the MWE:  \documentclass[12pt]{article}  \usepackage{mathtools} \usepackage{amssymb} \usepackage[T1]{fontenc} \usepackage[UTF8]{inputenc} \usepackage[slovene]{babel} \usepackage{fancyhdr} \usepackage{caption} \usepackage{parskip} \usepackage{tabu} \usepackage{graphicx} \usepackage{hyperref} \usepackage{enumitem} \usepackage{url} \usepackage{float}  \usepackage{blindtext}  \setlength{\parindent}{1cm}  \makeatletter \setlength{\@fptop}{0pt} \setlength{\@fpbot}{0pt plus 1fil} \makeatother  \pagestyle{fancy} \lhead{blah} \rhead{\leftmark} \cfoot{\thepage}  \begin{document}     \begin{titlepage}         \clearpage         \thispagestyle{empty}         \title{Blah blah}         \author{blah}         \date{12. april 2017}         \maketitle         \tableofcontents         \thispagestyle{empty}     \end{titlepage}      \section{blah 2}     I have a paragraph. Now, why won't this paragraph move. I don't know, I hope you do. Now let's see.      Oh dear, still the same problem. I want the first paragraph to have the same space too! What can I do? \end{document}   Now, for many people, this may seem just right, but not for me. I want a space before the first pargraph as well. I'm guessing that the \parindent function itself is built so that it doesn't have an effect on the first paragraph (my guess is pretty solid as I read multiple PhD theses in such format). But my aesthetic sense disagrees. Can anyone accommodate the \parindent definition so it will suit my needs (I don't know how to do it myself). Please help me, I want my thesis to look as good as possible.

I am trying to write a text where the first line of each paragraph has an indent(tab). But for some reason, in a chapter or a section or subsection, except the first paragraph, the rest of the paragraphs have an indent(tab). Is there any way to add an indent to the first paragraph in a chapter or section or subsection?


I have always seen the formulas of rotation having cross product of $\vec{r}$ and some linear quantity. For e.g. $\vec{\tau} = \vec{r}$ x $\vec{F}$, $\vec{L} = \vec{r}$ x $\vec{p}$ etc. But we have never been told the source of these formulas. I never understood where they came from and what is their derivation. Is the direction of rotational quantities just a reference and accordingly, in consideration with magnitudes we have derived a cross product?  I have been pondering upon this question for half a year but I had no success.

If I'm not wrong, torque is perpendicular to both the radius and force i. e. It is along the axis of rotation. Questions that arise are- why do we consider the length between the axis/point of rotation while calculating torque? More importantly why is torque a cross product?


I'm trying to understand the rationale behind definition of function. Why is function defined as a relation which relates input to only 1 output?  What would happen if we allow function to relate input to multiple output? Something like y^2 + x^2 = 4

I know that it is defined such that there is no more than one y-value output for any given x-value input, but I"m wondering WHY it is defined that way? Why can't we apply everything we know about functions to equations that have more than one y-value output for any given x-value input?   In short, what is the benefit or reason to define a function this way?  At the same time, a little historical context would also be appreciated (i.e., when the concept originated and why).  Thanks,  Moshe


We have a custom module for which we need to run on a daily basis. I am not sure  it is working, as I am unable to store the time correctly.   Does the following code allow me to create a variable, and use it to store the last time cron ran?  function mymodule_cron() {   if (variable_get('mymodule_last_run', 0) <= strtotime('-1 day')) {     // Omissis.     variable_set('mymodule_last_run', time());   } }  function mymodule_info($options) {   $variable['mymodule_last_run'] = array(     'title' => t('Last Run', array(), $options),     'type' => 'datetime',     'default' => t(time(), array(), $options),   ); }

What's the proper way to execute a function every 3 months? Watchdog variables don't seem to be available after a certain time. I could create another table to insert the execute function date to compare, but it doesn't seem to be the best approach.  The functionality of such functions are:   Send an eMail Tag an inactive user


What is this type of encode: Káº¿t ná»‘i nÃ´ng nghiá»‡p Viá»‡t  It should be "Kết nối nông nghiệp Việt" but the view can't render utf-8, i don't know why. Please take a look at the picture below.  Database config:     ORM::configure(array(     'connection_string' => 'mysql:host='.$db_hostname.';dbname='.$db_name.'',     'username' => ''.$db_username.'',     'password' => ''.$db_password.'' ));     //ORM::configure('driver_options', array(PDO::MYSQL_ATTR_INIT_COMMAND => 'SET NAMES utf8')); #i tried uncomment this line but it's still not working     //ORM::configure('error_mode', PDO::ERRMODE_WARNING);     //ORM::configure('return_result_sets', true);     //ORM::configure('logging', true);

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I am customizing my toc, but cannot figure out what the value of \thecontentslabel is for chapters that are marked not to be numbered...  In general where are these commands described? I don't know where the manual is. Tried KOMA-Script but didn't find anything.

I am having some issues with the hyperref package. I would like to create a Introduction chapter without a number so I use \chapter*{Introduction} and \addcontentsline{toc}{chapter}{Introduction} because I want it in the table of contents (see example).  But then the link in my PDF viewer gets it wrong and also the automatically created header is no longer correct (see picture). The table of contents shows the right page number (p.1) but the link is also wrong.   What is my mistake here?  \documentclass{scrbook}  \usepackage{hyperref} \usepackage{blindtext} \usepackage{glossaries}   \makeglossaries  \newacronym{eg}{e.g.}{% for example }   \begin{document}   \frontmatter  % abstract before the table of contents \chapter*{Abstract} \addcontentsline{toc}{chapter}{Abstract} \blindtext  \tableofcontents  % chapter with acronyms \cleardoublepage \phantomsection  \printglossary[type=\acronymtype] \addcontentsline{toc}{chapter}{Glossary}  \cleardoublepage \mainmatter   \phantomsection % \chapter{Introduction} % with this everything is correct but I don't want the number \chapter*{Introduction} \addcontentsline{toc}{chapter}{Introduction}  \blindtext  \pagebreak  \blindtext  % first chapter \chapter{Chapter1}  \gls{eg} \blindtext  \pagebreak  \blindtext   \end{document}


As a continuation to this  of mine I am having a problem with spaces in the toc. See attachment:    As you can see after subsection 2.3.9 the title and the enumeration of toc gets stuck together. How can I fix this? In the linked question the space between the number and the title is a little bit bigger.   The font I am using is Kerkis.

I'm using the simple ordinary \tableofcontents command to produce a table of contents, and I find that the resulting spacing between the section number and the section title is too small:    Can someone tell me how to fix this, please. My documentclass is memoir, if that matters.


I have no idea where to begin with proving the following  $$ \prod\limits_{i=1}^\infty \cos\left(\dfrac{t}{2^i}\right) = \dfrac{\sin( t)}{t}$$ I couldn't do it by expanding the cosine and no trigonometric identities appeared helpful.   Maybe someone has encountered that before? Hints welcome!

This limit seemed quite unusual to me as there aren't any intermediate forms or series expansions which are generally used in limits. Stuck on this for a while now .Here's how it goes :    $$ \lim \limits_{n \to \infty} \left[\cos\left(x \over 2\right)\cos\left(x \over 4\right)       \cos\left(x \over 8\right)\ \cdots\ \cos\left(x \over 2^{n}\right)\right] $$


Got very interested recently in a  video I saw running thru my feed:    Well, I got very intrigued about the physics of it and wanted to know your opinion about my guesses and how to proceed regarding them. I think that basically this mad motion is due to the fact that there's some ratio between the length of these pendulums. I spent a little time thinking and before solving the movement equations thought that maybe I couldn't use the approximation for small angles for that and MAYBE the initial motion would be related to a trasient term (indicating time interval which the system is oscillating for angles greater then 5 degrees) and then go to these repetitive patterns, for smaller angles in which the system is pretty much conservative). I thought about solving this numerically in Mathematica, plotting multiple pendulums with different lengths.

Recently I've seen various videos showing the . All of the videos which I have found have a pattern which repeats every $60\mathrm{s}$.   I am trying to work out the relationship between the period of the overall pattern and the difference in length between each of the pendulums.  From the small-angle approximation for the period of a simple pendulum, for each pendulum with period $T$ we have:  $$T\approx2\pi\sqrt{\frac{L}{g}},$$  Where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity.   If we take (say) $n$ pendulums, with lengths $L,L+d,\dots,L+(n-1)d$, then the pattern repeats at a period $t$ when all of $\frac{t}{L}\in\mathbb{Z}^{*}$, $\frac{t}{L+d}\in\mathbb{Z}^{*}$, $\dots$, $\frac{t}{L+(n-1)d}\in\mathbb{Z}^{*}$. where $\mathbb{Z}^{*}=\mathbb{N}\cup\{0\}$.   However, I'm not sure how to develop a direct relationship between $t$, $d$ and $L$.


In Iron Man 3, after escaping in the boat with Rhodes, we see Stark recharging his suit from a battery. My understanding was that the suit is powered by the arc reactor in his chest. Why does he then use the battery for recharging? Had the arc reactor stopped working? Or is my understanding of the arc reactor wrong?

In Iron Man 3, it shows Tony Stark having trouble charging his MK42 armour. At one point he even had a car battery connected to it. Why couldn't he use the arc reactor in his chest to charge his armour?


code 1: String s = Character.toString(button[0]); bt[0].setText(s);//bt[]: JButton array;, button[] = char array code 2: String s = Character.toString(button[0]); bt[0] = new JButton(s);   Suppose, I already initialize bt's by new JButton[num]; code 1 leads to null pointer exception, but code 2 run well. I think bt's already has a pointer value of null. then, i can modify them without restriction. but it isn't. I think code 2 initialize 2 times. but, it hasn't to be.

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


Let $f$ be twice continuously differentiable on $[a,b]$. Assume that $f(a)=f'(a)=f(b)=f'(b)=0$. $M=\max_{[a,b]}|f''|$. Show that $|f(x)|\leq M/16(b-a)^2$, for any $x\in [a,b]$.  At first glance, we can use Taylor formula on $[a,(a+b)/2]$, but gives the coefficient $1/8$ instead of $1/16$.   $$f(x)=f(a)+f'(a)(x-a)+\int_a^x \int_a^t f''(s)ds dt$$ implies $$|f(x)|\leq M \int_a^x \int_a^t ds dt=\frac{(b-a)^2}{8}.$$  Can we prove $1/16$ as the problem states?

Let $f:\left[a, b\right]\to\mathbb{R}$ be twice differentiable.  Suppose $f(a)=f(b)=f_{+}'(a)=f_{-}'(b)=0$ and $|f''(x)|\le M$.   Show that $|f(x)|\le \frac{M(b-a)^2}{16}$.  My try:  From taylor expansion we have $f(x)=\frac{f''(\xi _1)}{2}(x-a)^2$ and $f(x)=\frac{f''(\xi _2)}{2}(x-b)^2$.  Then $|f(x)|\le\frac{M}{2}(x-a)^2$ and $|f(x)|\le\frac{M}{2}(x-b)^2$  So $|f(x)|\le\min{(\frac{M}{2}(x-a)^2,\frac{M}{2}(x-b)^2)}\le\frac{M}{8}(b-a)^2$  But this conclusion is weaker than the aim.  And I thought through using $$f(c)=\frac{f''(\xi )}{2}(c-a)(c-b)$$ I can say$$|f(x)|\le\frac{M}{8}(b-a)^2$$ which only uses the condition that $f(a)=f(b)=0$ and is still weaker.  Any hints? Thank you in advance!


Assume that the candidate is a graduate of a good state school, e.g. North Carolina or Ohio State. Then I want to explore this candidate's probable viability in getting into "second tier" graduate schools, say 15-30th in a given field using the following academic combinations. The best combination would be something like a 3.9 GPA and a graduate exam (GRE or LSAT) score of 175 or better (out of 180). Assuming research and activities were competitive (and are held constant between candidates), would these candidates be able to do better than second tier (say top 15)? A second best combination might be something like a 3.5 GPA and a 175 exam score or a 3.9 GPA and a 165 exam score. How would this candidate "stack up" for a second tier grad school? Are the two sets equivalent or is one combination decidedly more competitive than the other? Third best would be something like 3.5 GPA and a 165 exam score. Would "second tier" grad school be a reach for such a person? If you changed "good state school" to "HYPSM" and kept exam scores and GPA constant, would that change matters? Explanation: Unlike the other question, this one is not about getting students in from the "bottom." This question is about how the TOP three (or so) categories sort themselves out.

When applying to a PhD program in the US, how does the admissions process work? If an applicant is weak in a particular area, is it possible to offset that by being strong in a different area?  Note that this question originated from this . Please feel free to edit the question to improve it.


Let $D$ be a principal ideal domain and $a$ and $b$ be nonzero elements of $D$. Prove that there exist elements $s$ and $t$ in $D$ such that $\gcd(a, b) = as + bt$.   I would like to use some properties of $\text{PID}$s to prove this but I am only thinking of well-ordering principle that is used to prove for integers, which I don't think I can use since $D$ is not necessarily the set of integers, right? Any ideas?

Just got a question about ideals of $F[x]$ being principal with $F$ being a field.  The proof basically starts assuming $g(x) \in N \subset F[x]$ where $N$ is an ideal and $g(x)$ is a minimal degree element. The rest is just deducing the what the division algorithm says.  But my question is that shouldn't we let $g(x)$ be arbitrary? Why are we choosing the minimal element?