I have taken a few quantum mechanics courses recently, which has involved quite a bit of work with quantum spin. The professors keep saying that spin is analogous to a classical body spinning on its axis. However they always make sure we clearly understand this isn't exactly what is happening, because quantum mechanics deals with point particles. Because they don't have extent, there is nothing 'poking out' from the centre of the particle that can spin around the axis.  However it seems to me that if particles in quantum mechanics have this property, it would suggest that they might not be point particles after all, and have some 'size'. No doubt this has been investigated quite thoroughly.  I was wondering then why intrinsic spin isn't considered evidence that particles aren't just points, and have 'size' or 'shape'?

I'm currently reading Alonso and Finn's Electromagnetism book.  It explains that the spin contributes to the magnetic moment and is somewhat comparable to a rotation of the particle around its own axis. It says that the spin of a particle is caused by a certain internal structure, which makes sense in the aforementioned analogy.  Right underneath the paragraph with the explanation of spin, it says "The electron has no known internal structure", but since it does have a spin, does that mean that we know the electron has an internal structure but we just don't know what it is?


If in a group there are only two conjugacy classes then group is isomorphic  to Z2 . This statement is true or not ?

Can you show me a reasonably simple (using only elementary group-theoretic tools) example of infinite group with just 2 conjugacy classes ?


I try save variable name like this:  #define TEST someVariable #define makeString(x) #x  int main(int argc, char *argv[]) {     char TEST[] = makeString(TEST);     printf("%s    %s\n", TEST, makeString(TEST));     return 0; }   Output is :  appden4ik@appDen4ik:/opt/preprocessor/Debug$ ./preprocessor  TEST    TEST'   I want next output:  someVariable      someVariable   Where I am wrong?

For example, how to avoid writing the 'func_name' twice?  #ifndef TEST_FUN #  define TEST_FUN func_name #  define TEST_FUN_NAME "func_name" #endif   I'd like to follow the  rule.  Version of C preprocessor:  $ cpp --version cpp (GCC) 4.1.2 20070626 (Red Hat 4.1.2-14)


As the subject indicates, does Android support any of the Extended File Systems ("ext", "ext2", "ext3" and "ext4") for removable storage cards (such as Micro SDXC storage cards)?  Android is a Linux-based operating system, so surely such filesystems would be supported?  My question relates to both Android 4.4-4.4.4 ("KitKat") and Android 5.0-5.1.1 ("Lollipop"), as I am just about to buy the Sony Xperia Z Ultra which runs the former, but has an upgrade available for "Lollipop"...  The reason I ask is because Extended File Systems have a number of distinct advantages over Microsoft filesystems, and I do not use Microsoft Windows-based operating systems at all (well, at work I do - but personal stuff can't be used with their computers...), so it's only logical to utilize Extended Filesystems where possible, for the technical advantages.

I know that on a rooted phone, it's reasonably normal to create a small ext4 partition for App2SD to use, but I'm not asking about that case:  I have a non-rooted HTC Desire running Froyo, and I'd like to format the whole of my SD card as ext4 instead of FAT.  I'm aware that this will mean that Windows PCs won't be able to use the card, but all my PCs run Linux so they should be fine.  Will the phone be able to access and use the card in this case?


How to convert "2013-10-21 12:00:00.004" to datetime object in Python? The problem is there is decimal number in seconds.

I am able to parse strings containing date/time with time.strptime  >>> import time >>> time.strptime('30/03/09 16:31:32', '%d/%m/%y %H:%M:%S') (2009, 3, 30, 16, 31, 32, 0, 89, -1)   How can I parse a time string that contains milliseconds?  >>> time.strptime('30/03/09 16:31:32.123', '%d/%m/%y %H:%M:%S') Traceback (most recent call last):   File "<stdin>", line 1, in <module>   File "/usr/lib/python2.5/_strptime.py", line 333, in strptime     data_string[found.end():]) ValueError: unconverted data remains: .123


Combinatorial argument for $$1+\sum\limits_{r=1}^{r=n} \ r\cdot r! = (n+1)!$$  The algebraic proof is easy as $r=(r+1)-1$.

The sum $\sum_{k=1}^nk(k!)$ can be easily calculated by noting $k(k!)=(k+1)!-k!$. Is there a way to calculate the sum nicely using a combinatorial argument. Is it possible to notice it is $(n+1)!-1$ combinatorially?


Given $n$ random points on a circumference, what is the probability of them lying in the same semicircumference?  Feedback on my solution and/or alternative solutions would be appreciated.  EDIT This is a duplicate of math.stackexchange.com/q/18369/27978

Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?


Working through a book, I have stumbled upon a question I don't know how to solve:     Prove    $$2\cos(5B) + 2\cos(4B) + 2\cos(3B) + 2\cos(2B) + 2\cos(B) + 1 =  \dfrac{\sin\left(\frac{11B}2\right)}{{\sin\left(\frac B2\right)}}$$   (this is a smaller problem I have reduced the larger problem down from)  I don't know how to simply the cosine functions into a sine functions, as using the identity $\cos A + \cos B = 2\cos\left(\dfrac{A+B}2\right)\cos\left(\dfrac{A-B}2\right)$ simply gives me a result with even more cosine functions. I can't think of other identities that are helpful.

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series:  $$\sum_{k=0}^{n-1}\cos (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \cos \biggl( \frac{ 2 a + (n-1)\cdot d}{2}\biggr)$$  There is a slight difference in case of $\sin$, which is: $$\sum_{k=0}^{n-1}\sin (a+k \cdot d) =\frac{\sin(n \times \frac{d}{2})}{\sin ( \frac{d}{2} )} \times \sin\biggl( \frac{2  a + (n-1)\cdot d}{2}\biggr)$$   How do we prove the above two identities?


I'm creating a game and I need a fill command to have a 50-50 chance of opening one of two gates (Ex. This will be activated when a button is pressed to start game).  The obvious choice would to use the @r selector, but I don't know how to apply this to a command block command.  I'm running 1.10.2 and this is only a two player game. (For me and a friend)

I want to make a mini game in Minecraft were I need a random command generator for 9 commands. I need a random command to give the player a random item. I can't do the command block in the dispenser any more because it will just drop out instead of being placed. What different ways are there for generating randomness in commands, and which one would be best for my use? This question is similar to the one about , but I am specifically attempting to get randomness when using commands - the redstone solutions do not apply here.


I know 17.10 is the latest. I'm on 14.04. I want to go to 16.04 not 17.10. All tutorials I see online tell how to update to newest version.  Update 1: That answer is about servers. I'm talking about Ubuntu versions. That answer clearly tells u to make sure ur on the latest versionof ubuntu, whih I am not.

I like to keep all my servers running only the most stable versions of any operating system, so obviously I only run the LTS versions of Ubuntu.  I currently have a few servers running Ubuntu server 12.04 LTS. I'd like to upgrade them to 14.04. Is it safe to jump versions like that, and how can this be done?


Imagine an electron in the  hourglass-shaped $2p_x$-. It has two lobes. The probability of it being in the centre of the orbital is zero. This is the point that connects the two lobes of the orbital.  Now if I make an observation I find the electron in the right lobe of the orbital. I make another observation and still it's in the right lobe.  Now when I make the third observation the electron is in the left lobe. How did it go into the left lobe without passing through the centre of the orbital. The probability of it being at the centre is zero!

I saw on perhaps COSMOS, and have heard mention from other professors, that electrons sort of "teleport" or something, in their orbital and the quantum level. So looking at the orbitals for a lone hydrogen atom...  (source: ) ...some of those orbitals have 2 or more "blobs" that are separated from each other by some gap; there's some discontinuity. Take for example that (3,2,2) orbital in that image, where there are two blobs and a gap in between. How does the electron jump from place to another? How do you describe what's happening here?


Let $n$ be a natural number. we need to proove that: $$\forall{1\leq k\leq\tfrac{n}2}, \text{we have } {n \choose k-1} < {n \choose k} $$ I tried to do the following with induction: We set $n$ as a constant and doing induction on $k$: if $ k=1 $: ${n \choose 1} > {n \choose 0}$ and it can be shown by writing the exlpicit ration of the ${i\choose j} sign $ . Assuming that for every $k$ as it was set, the equation above is right, we will try to proove with induction that for $k+1$ we get: $$\forall{1\leq k+1\leq\tfrac{n}{2}}, \text{we have}{n\choose k} < {n \choose k+1}$$ But at this point, I am stuck, because I can't see how can I apply the induction assumption. I also tried to use pascal identity but I can't see how it fits in.

So I'm trying to do a proof for this problem:  If $\displaystyle{k \le \left\lfloor \frac{n}{2} \right\rfloor}$ then $$\displaystyle{\binom{n}{k-1} < \binom{n}{k}}$$  I can do it algebraically but my professor asked for a combinatorial proof.  How would one does it?


What would happen, if I were to trap the Sun in an almost perfectly reflective spherical mirror? I'm assuming this would accelerate the life of the sun and reduce the timescale required to turn it into a dwarf. How could I roughly estimate this timescale speed-up, if one occurs?   I'm assuming, of course, that the mirror is large enough to fit the sun in any of its giant phases.

I have looked for similar questions here on stack exchange. The closest example to this that I found is . That question assumed less than perfect absorption of material lining the inside of the sphere, and the effect of thermally re-radiating it inside the sphere.  A lot of the answers focused on that much of the thermal radiation would not be reflected back to the star, and is likely to be reabsorbed by the sphere at another location. On the other hand, this question asks what would happen if the Dyson sphere, using mirrors, deliberately refocus a significant portion of the rays directly back at the star.


In my ArcGIS online map, I have two layers (morminte and layer2) related in a one-to-many relationship. For an item from the morminte layer I can have 0, one or two corresponding values from layer2. In the picture below it is shown the pop-up window for an item from morminte. In the pop-up, only the Nr. Mormant field is from the morminte layer. This is the only field that returns the right value.  The rest of the fields are from the related layer.  The fields NUME (surname) and PRENUME (name) should return text values, DATA_NASTERII and DATA_DECES -> date values and VARSTA->a number. Instead, if for the selected item I have one corresponding value from layer2, the pop-up returns "1", if I have 2 corresponding values, then I get "2" and if there is no value to be related, then I get "0".    Before uploading the map to ArcGIS Online, I made sure that both layers involved in the relationship class are configured properly in ArcMap. NUME and PRENUME are string fields, DATA_DECES and DATA_NASTERII are date fields and VARSTA is a short integer field.  In the Configure Attributes window for the morminte layer, I noticed that I can select only  count in the Statistic Operator tab. I don't know if it has something to do with this.    I also created a layer that has the fields NUME, PRENUME etc. as it's own. In this case, the pop-up shows the right values. But in my map I want to use two  related layers instead of one because is more advantageous for what I need to do.

I have an ArcGIS Online Map composed of three spatial feature classes and a table.  All three feature layers are related to the table and all the layers and table are housed within the same SDE.  I have enabled the popups for each layer using fields from the related table in the popup.  However, instead of showing the correct values from the related table I only see 1s and 0s as values.  If the value in the related table is NULL already the popup shows a 0 and if it is not NULL it shows a 1.  How can I resolve this issue so I can see my actual values in the popup?[


Suppose that we have two groups that they select N items. For example, in the table below, we have number of people from each group that have selected each item. items:  A   B    C   D      E       F   G   H    K      L G1:     3   4    52  633    1000    0   6   915  890    500 G2:     1   19   17  333    1000    25  6   110  951    510 Population of group 1: 1000 Population of group 2: 1050  Is there any test that determines the differences in which items are statistically/practically important/significant? Thanks very much.

Suppose that we have a population of $N= 1000$ people and they want to select 5 items (for simplicity) $\{A, B, C, D, E\}$ (but actually number of items is in the order of thousands). Number of selections for items is $\{3, 142, 52, 633, 800\}$. Each person (selector) is free to select as many items as they want. Selecting of one item may affect for selection of another item by one person. For example, if items are goods in a supermarket, the first person may select items $A$ and $C$. The second person may select all items. We want to find “the minimum number of selections”, named $T$, so that if number of selections for an item is larger than $T$, we can say that item is interesting or popular for the population since at least $T$ people have selected that item. We want to find this number ($T$) by “a statistical method”. As an another example, for each item, we can assign a value to it by the percentage of people who have selected that item. So, we have a range of 0 (no person has selected it) to 100% (all people have selected that item). Definitely, 100% means popularity or significance for that item for the population. But We want to find what is the minimum percentage so that we can say that item is still popular. In other words, is the range of popularity from 20-100% or 10-100% or ....? We want to find a statistical measure for defining popularity of significance. Thanks.


My attached image isn't shown. Neither are older images from another people.  Example where I don't see the image:

Which browsers are officially supported by Stack Exchange?  Also, what else is needed in order to use every feature of the site?


I ride a .  Yesterday morning I noticed (for the first time since purchase) that in my rear tire, the tire pressure has decreased to a flat. I thought it was a puncture, so I refilled the tire using a hand-pump and poured water over the tires expecting bubbles but didn't get any.  Then I took it for a ride, 20 kms and came back - nothing happened.  Then I came back in the evening to notice that the air pressure has decreased again, almost half. Then today morning it's a flat again.  Is it a puncture? I checked the tire's mouth valve, it's not leaking any air there. Should I get the tube out and check for a puncture?

I rode my road bike on Friday and the tyres were at the correct pressure then, around 100psi.  On Tuesday, I jumped on without checking them and quickly realised something was wrong with the rear tyre.  It wasn't completely flat but was fairly soft.  I hadn't gone far so went home and took the car to work instead.  When I got home later, I was surprised to find the tyre, while still soft, hadn't lost all pressure by any means.  It was around 40psi and felt the same as when I left it in the morning.  I decided there must be a slow leak somewhere, but I couldn't find one anywhere, putting the inner under water and going around it methodically looking for bubbles.  I've never failed to find a leak before that way.  I've switched it out anyway because I don't want to mess around with my commute, but I'm curious ... is there another explanation for that amount of pressure loss?  Or must there have been a puncture somewhere that I missed somehow?  The tyres (whole bike) are pretty new and in excellent condition.


I tried to install google chrome for ubuntu users from my Firefox web browser, but that did'nt work

How do you install Google Chrome on Ubuntu?


Prove using induction that every positive integer $𝑛>23$ can be expressed in the form $𝑛=5𝑎 +7𝑏$ for appropriately chosen non-negative integers $a, b$. What should I use? Mathematical Induction or Strong Induction? Can anyone help me solving this question? It confuses me a lot. Any help will be appreciated.

Can you check if my proof is right?  Theorem.  $\forall x\geq8, x$ can be represented by $5a + 3b$ where  $a,b \in \mathbb{N}$.  Base case(s): $x=8 = 3\cdot1 + 5\cdot1 \quad \checkmark\\ x=9 = 3\cdot3 + 5\cdot0 \quad \checkmark\\ x=10 = 3\cdot0 + 5\cdot2 \quad \checkmark$  Inductive step:  $n \in \mathbb{N}\\a_1 = 8, a_n = a_1 + (x-1)\cdot3\\ b_1 = 9, b_n = b_1 + (x-1)\cdot3 = a_1 +1 + (x-1) \cdot 3\\ c_1 = 10, c_n = c_1 + (x-1)\cdot3 = b_1 + 1 + (x-1) \cdot 3 = a_1 + 2 + (x-1) \cdot 3\\ \\ S = \{x\in\mathbb{N}: x \in a_{x} \lor x \in b_{x} \lor x \in c_{x}\}$  Basis stays true, because $8,9,10 \in S$  Lets assume that $x \in S$. That means $x \in a_{n} \lor x \in b_{n} \lor x \in c_{n}$.  If $x \in a_n$ then $x+1 \in b_x$,  If $x \in b_x$ then $x+1 \in c_x$,  If $x \in c_x$ then $x+1 \in a_x$.  I can't prove that but it's obvious. What do you think about this?


I was trying to come up with an interesting example (not like $(-1)^n$ or cyclic like $1,2,3, 1,2,3, 1,2,3, \ldots$) of a bounded not converging sequence with an explicit convergent subsequence.   I though of something like $x_n := \sin(n)$. Since $\sin(k\pi) = 0$ for every $k \in \mathbb{Z}$ I thought that the closer the argument of the sine was to a multiple of $\pi$, the closer sine of that argument should be to zero (continuity...). Therefore, the sequence $x_n := \sin(a_n \cdot 10^{n - 1})$, where $a_n$ are the first $n$ digits of $\pi$ should be converging to $0$, right? If yes, how can I show it?

Define a sequence $(a_n)_{n = 1}^{\infty}$ of real numbers by $a_n = \sin(n)$. This sequence is bounded (by $\pm1$), and so by the , there exists a convergent subsequence.  My question is this: Is there any way to construct an explicit convergent subsequence?  Naïvely, I tried considering the subsequence $$\sin(3), \,\sin(31), \,\sin(314), \,\sin(3141),\, \sin(31415),\, \dots$$ hoping it would converge to $0$, but I was unable to prove this (and I think it's probably not even true).


I have switched laptops recently, and I decided I want to make the switch from Windows to Linux (and have gone with Ubuntu for now).  I have the "old" SSD from my previous machine, which has a Windows 7 installation on it. I'm trying to install Windows 7 on VMWare so I can run some of the programs that are only available on Windows (that Wine can't handle).  I also have my Windows 7 key, but I don't know which "edition" it is (Home vs. Premium vs. Ultimate, etc.)  The furthest I've gotten is looking at explorer.exe's attributes to find this:     Product Version: 6.1.7601.17567   But I couldn't find what that means.  I have the SSD mounted and am able to read/access the old filesystem. How can I find out what Windows edition I need to install on VMWare?

I am attempting to recover an old computer that won't boot and I'm not sure what version of Windows it is running. How do I tell simply by examining the file system?  I am fairly confident it is either Vista or Windows 7. There is a small chance it is Windows Server 2008.


Say's that it is in line 11. Any help? I'm just trying to sort an array of 10 strings by length.  import java.util.*; public class lab10 {     public static void main(String[] args) {         Scanner key = new Scanner(System.in);          System.out.println("Enter 10 strings and I'll sort them by their length. Smallest to largest.");         String[] input = new String[10];         String smallest = input[0];          for(int i=0; i<10; i++){             if(input[i].length() < smallest.length()){                 smallest = input[i];             }             System.out.println(smallest);         }         key.close();     }    }

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


I came across this idiom recently:  \def\foo#{...}   That is, a hash but no parameter number. What might be the purpose of this?

In , Herbert uses a macro definition  \def\defpoint#1#{\expandafter\defpoint@i#1;;\@nil}   which Joseph Wright reports as having a "grab to #{" argument. How does this work? Where is it useful? Are there any restrictions? Does it extend in the same way nested macro definitions would? As in, using ##{ if redefining a macro within another one.


Following the idea at  I've used VMs personally, but can't seem to understand why it exists for any real world need. So I ask: why are virtual machines needed?  I can think two things. Testing compatibility support for different operating systems and 'isolation', a quarantine for someone to reverse engineer a virus or something. But are these really enough to justify the multiple projects dedicated to making good VM software? Where is the demand for these tools coming from?

I have been living under a rock for the past 5 - 8 years, and am just now getting up to speed with virtualization, virtual machines and platforms like VMware or VirtualBox.  I think I am starting to get them, but there are two concepts about VMs that I'm just choking on for some reason; one has to do with their intrinsic benefit to the enterprise, and the other has to do with their practicality when being used.  So I understand that you can have multiple VMs running on the same physical machine, all doing their own "thing" as if they were separate machines. So let's say I want to make a nice little virtual network of servers in my home office so I can have a big sandbox to play inside of for all my projects. I set up 2 physical machines as servers, and on each of them I have, say, 4 virtual machines running (1 might be an app server, another might be a RDBMS, another might be a message broker, etc.).   Besides saving me money (as I only have to provide 2 physical machines instead of buying 8 servers), what instrinsic benefit/purpose do these VMs serve here? I don't care how clever virtual machines are, if my computer only has 8GB of RAM, and I have 4 VMs running on it, those VMs only get 8GB of RAM to share between them. Putting 4 VMs on my server doesn't endow it with 4 times that amount of RAM! So, as far as I see it, VMs save you money on hardware, but just end up bogging down that hardware as you have multiple machines competing over the same pool of resources. What am I missing here? Can VMs communicate with each other over your network using high-level protocols like TCP/IP, HTTP, FTP, etc.? Otherwise, it just doesn't make sense to implement all these VMs if you have to feed them separate and independent chunks of data/requests to process.


I'm using the scrreprt package and I can't figure out how to use the "+" and the "&" symbol in the title of a subsection.  \documentclass[a4paper]{scrreprt} \usepackage{scrpage2} \usepackage[ngerman]{babel} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc}  \begin{document}     \section{Many supers}     Text     %Source of the problem     \subsection{Super+ & Hyper}     Text \end{document}   is what I'd use ideally, but that gives an error with a "misplaced alignment tab character"  I googled a lot and tried quite a lot of variations like:  \subsection{Super\+ \& Hyper} \subsection{Super\text{+ &} Hyper} \subsection{Super\[+ &\] Hyper}   and more - nothing I tried works. Especially the & poses a big problem. The + actually worked with   \text{+}   Does anyone have a solution?

I need to output the below text but since \ is a special character, I cannot:  [RegularExpression(@"\d+")]   Also sometimes I need use dollar sign $ as well but it seems to be a special char, too.  What is the way to escape those in LaTeX?  UPDATE:  I used \verb as suggested but I am unable to run commands inside it. Also, in the output the font and the opacity of the text is different than the default one:  \verb|[RegularExpression(\newline @"\d+")]|


I am taking this deep learning course from Andrew NG. In the 3rd lecture of 2nd week of the first course, he mentions that we can use RMSE for logistic regression as well but it will take a nonconvex form having a lot of local minima and so gradient descent may not be able to find the global minima. So why using RMSE as loss function makes the cost function as non-convex in logistic regression but convex in case of linear regression?

I am building a simple logistic regression model on 2D data. Here is the input I use.    I built a logistic regression model using this data and it successfully is able to find the discriminating line between these two classes. Here is the separating line found by my program:    Also, just for debugging, I plotted number of iterations vs J(theta), which also looks fine:    Now, confusing part comes into play. I am investigating the cost surface of this model that the logistic regressions is doing the gradient descent on. I am considering three different loss functions. Sum-of-squared loss, hinge-loss, log-loss.  Hinge loss:    Log-loss:    Sum-of-squared loss:    As far as I know, both hinge loss, sum-of-squared loss and log-loss should produce a convex surface. When I look at my surfaces, however, sum-of-squared surface does not look convex to me. Why is that the case?  For convenience, here is the two critical functions from my code:  function retval = J(X, y, theta)     M = size(y, 1);     % sum of squared error     retval = (1/(2*M)) * sum((h(X, theta) - y).^2);  endfunction  function retval = h (X, theta)     % logistic     retval =  1 ./ (1+ exp(-1 * (X * theta))); endfunction


How can I make a /testfor command emit a signal when there is only one player in the required area? I understand /testfor @a[x=,y=,z=,r=].

I want to run a command when there are only 10 entities left. I know you can use /execute unless entity to detect when all matching mobs have died, but it doesn't work if you want to run a command when there are for example 10 entities left.  A command like /execute if entity @e[limit=10] does not work, it also triggers if there is only one entity.  Such a counting system could also be used to determine once there is only one player left in an arena, meaning they have won a battle or similar.


Space has a constant density of dark energy, that means dark energy does not dilute with space expansion. By consequence, any space generated by space expansion does generate new dark energy.  Currently it is supposed that 70% of all energy is dark energy, and that dark energy will continue more and more to be the dominating energy of the universe. Where does this energy come from? Is the law of conservation of energy observed?

I understand that energy conservation is not a rule in general relativity, but I'd like to know under what circumstances it can still be possible. In other words, when is it possible to associate a potential energy to the gravitational field, so that the energy is constant in the evolution of the system?  Here are some examples, is there a convenient way to define energy in these scenarios?   Just a system of gravitational waves. A point mass moving in a static (but otherwise arbitrary) space-time. Equivalent (if I'm not mistaken) to a test mass moving in the field of a second much larger mass, the larger mass wouldn't move. Two rotating bodies of similar mass.   Overall, I'm trying to understand what keeps us from associating a potential energy to the metric. When we break the time translation symmetry of a system by introducing an electromagnetic field, we can still conserve energy by defining an electromagnetic potential energy. Why can't we do the same when we break TT symmetry by making space-time curved?


Recall the Fibonacci function defined by $f(0) = 0; \\f(1) = 1; \\f(n) = f(n-1) + f(n -􀀀 2)$  for all $n \ge 2$ Prove that $f(n) \cdot f(n + 1) = f(1)^2 + f(2)^2 + . . . + f(n)^2.$

The definition of a Fibonacci number is as follows:  $$F_0=0\\F_1=1\\F_n=F_{n-1}+F_{n-2}\text{ for } n\geq 2$$   Prove the given property of the Fibonacci numbers for all n greater than or equal to 1. $$F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$$  I am pretty sure I should use weak induction to solve this. My professor got me used to solving it in the following format, which I would like to use because it help me map everything out...  This is what I have so far:  Base Case: Solve for $F_0$ and $F_1$ for the following function: $F_nF_{n+1}$.  Inductive Hypothesis:  What I need to show: I need to show $F_{n+1}F_{n+1+1}$ will satisfy the given property. Proof Proper:  (didn't get to it yet)  Any intro. tips and pointers?


When using sudo apt-get install libxerces27 libxerces27-dev libopenal0a libglut /  libglut3-dev libfontcongfig1  It says for every package  E: Unable to locate package.   I am using precise distribution of linux 12.04  Please help.

When I try to install any package through the command line, I get an error.   $ sudo apt-get install <package> Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package <package>   Can anyone help me on this?


Ok, so I have searched and searched and cannot figure out what I did here. Most of my mp3, Libre Office, pdf, etc. files have missing icons. they look like this:   However if I access my network storage, I have exact copies of the same files in the photos btw, and they have the correct icons and look like     I am relatively new to Ubuntu, and I am sure that I did something wrong, but I have the system set up pretty much how I would like it for work and such, and would really hate to do a reinstall just for icons...  So if anyone could help it would be GREAT!

Like the title says, Nautilus is not generating thumbnails for any file types (pictures, documents, pdf, etc) after a clean install of 13.10.  I have checked the preferences and it is set to always generate thumbnails.  Help please!


If $p(x)$ is polynomial such that $$p(x^2+1)=(p(x))^2 +1$$ and $p(0)=0$ then $p'(0)$ is equal to _____.   Attempt  While looking on it and putting $x=0$ I got $p(1)=1$ and also the equation given had also the similar form (in comparison) of $$y^2+1=(y^2)+1$$. So, I put this polynomial in test and found that it satisfies this as  $p(x^2+1)=x^2+1$ and and $p(x)=x$ and hence it satisfied for every real x and so $p'(0)=1$. But I was not able to progress in the direction of correct solving.  Also, the given related problem is there on this site but, I have not been taught the coefficient determination and hence that answer there is out of my scope for now. But,I think there is this derivative method which I am currently learning and can understand about it.So, I would like to know how to approach this in derivative method and also if there is any other easier way without proving $p(x)$ to be the unique solution.  Also, it may happen that if any other exists,then many persons will get to know about the new method. It will be more helpful to them and me inlcuded.   So, is there any hints or suggestions on this problem?   Thanks for the help!

Find all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$  I' like a solution for this problem  and proof verification:  My proof:      Let $a_0=0$ and $a_{n+1}=a_n^2+1$, clearly $P(a_0)=a_0$ and if $P(a_n)=a_n$ then $P(a_{n+1})=P(a_n^2+1)=(P(a_n))^2+1=a_n^2+1=a_{n+1}$. So $P(x)=x$ for infinitely many values of $x$ (because $a_n$ is strictly increasing), hence $P$ is the identity polynomial, and it clearly works.


This code is very slow:  DocumentBuilderFactory dbFactory = DocumentBuilderFactory.newInstance(); dbFactory.setNamespaceAware(false); DocumentBuilder dBuilder = dbFactory.newDocumentBuilder();  org.w3c.dom.Document doc = dBuilder.parse(new InputSource(new StringReader(content))); System.out.println(doc.toString()); // outputs [#document: null]   And not only that it's slow it does not even parse:  <!DOCTYPE en-note SYSTEM "http://xml.evernote.com/pub/enml2.dtd"> <en-note>

     <en-media hash="" type="application/octet-stream" />

This is my first Evernote blog with image/photo attached.

This is another line.

Some          formatting also for          some lines.
 </en-note>   What is the fastest way to parse this XML into a org.w3c.dom.Document?

When I parse my xml file (variable f) in this method, I get an error      C:\Documents and Settings\joe\Desktop\aicpcudev\OnlineModule\map.dtd (The system cannot find the path specified)   I know I do not have the dtd, nor do I need it.  How can I parse this File object into a Document object while ignoring DTD reference errors?  private static Document getDoc(File f, String docId) throws Exception{     DocumentBuilderFactory dbf = DocumentBuilderFactory.newInstance();     DocumentBuilder db = dbf.newDocumentBuilder();     Document doc = db.parse(f);       return doc; }


I guess this is a classic statistical question but I can not find any clear answers (or at least one that I can understand) about my problem on the net. I work in biology and I try to highlight a link between two variables. The first variable is a continuous quantitative variable (it is a measure of the intensity of a given signal, between 0 and 200). The second variable is a discrete quantitative variable (it is the number of stimulations that I do, between 0 and 4; so it is integer, count variable). For each stimulation, I have a number of measurements of my signal (between 4 and 15 measurements). I have illustrated the kind of measurements that I obtain using a boxplot representation.  I try to highlight the fact that the intensity of my (continuous) signal is correlated to my stimulation number (discrete). I do not think the Pearson or Spearman tests/coefficient are adequate in my case. Could you tell me what is the statistical approach to follow? Ideally, I would like to have a value, between -1 and 1, indicating if my variables are linked or not as well as a p-value to determine if they are significantly linked. Edit Thank you very much for your feedback and answers. To answer the different points, I went to the Department of Biostatistics and discussed with some folks there. Many of them told be that I cannot use the Pearson or Spearman tests/coefficient. I went then to the conclusion that "the Pearson or Spearman tests/coefficient are adequate in my case.". From my understanding, I cannot use the Pearson test because of the fact that my data are not normally distributed.. The student gave me this paper to read: . I have no mathematical background at all but my understanding is that I can use the coefficient but non the p-value of the test.. In my case, I really need to have the p-value. It seems that I cannot have/use the test if my data are not normal, so I need to transform them... I have no idea by what to start with.. For the Spearman coefficient and its associated p-value, the software that I am using do not want to provide me a results because of the ties.. I had the feeling that many people at the Department have an idea, but they all have a different solution. I am trying to see in the literature, if someone had the exact same problem ? Regarding the Binomial regression, will it provide me a coefficient and p-value?

Suppose we are dealing with this data set $(X_i, N_i)$ where $X_i$ is continuous variable (for example Exponential) and $N_i$ is discrete distribution (for example Poisson) for $i=1,...,n$. Let's say that $\rho$ is the correlation between $X$ and $N$. How can someone define $\rho$?


I'm working with a custom post type / custom taxonomy combo and I can't seem to get pagination to work properly.  I'm wanting to add an infinite scroll to the page, however I can't even get pagination to even show up in order to get the infinite scroll piece working.  Below is my loop:  <?php     $paged = (get_query_var('paged')) ? get_query_var('paged') : 1;          $args = array(             'post_type' => 'shows', // it's default, you can skip it             'posts_per_page' => '3',             'order_by' => 'date', // it's also default     'paged' => $paged,     'tax_query' => array(                 array(                         'taxonomy' => 'show',                         'field' => 'slug',                         'terms' => array(                              'anger-management'                          )                 )             )               );             $query = new WP_Query( $args );     ?>         <?php if (have_posts()) : while( $query->have_posts() ) : $query->the_post(); ?>              <div class="archive-item" style="background: url(<?php echo get('archive_image'); ?>) center center no-repeat;"><a href="<?php the_permalink(); ?>">

<?php the_title(); ?>

<?php echo get('location'); ?>  -  <?php echo get('date'); ?>

      <?php endwhile; ?>        <?php endif; ?>      <?php wp_reset_query(); ?>   Obviously, I've put in a pagination script after the endwhile, however it still does not work;  I've even tried a plugin just to see if it'd work, and it didn't.  I'm using the HTML5blank theme to build from, so here's the pagination script that comes built in:  function html5wp_pagination() {     global $wp_query;     $big = 999999999;     echo paginate_links(array(         'base' => str_replace($big, '%#%', get_pagenum_link($big)),         'format' => '?paged=%#%',         'current' => max(1, get_query_var('paged')),         'total' => $wp_query->max_num_pages     )); }   I'm not sure if I need to write a new one or not; to be honest, I'd prefer just to have basic "next posts" or "previous posts" links, but regardless, I just can't get the pagination to work AT ALL.  Any help would be much appreciated.    I guess I'm starting to wonder if I need to set some parameters for this type of loop that helps set up the pagination?  But I can't seem to figure that out if that's the case.

I have added a custom/secondary query to a template file/custom page template; how can I make WordPress use my custom query for pagination, instead of using the main query loop's pagination?  Addendum  I have modified the main loop query via . Why isn't pagination working, and how do I fix it?


I was wondering if we have two normal distributions of X,Y~N(0,1), why is then X-2Y~N(0,5)? I understand the mean of the X-2Y distribution, but why is the variance 5?

The question states:      Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is   normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$.   What is the mean and the variance of the random variable $Y$, where   $Y=X_1+...+X_n$.   How do I do this?


Drive history     My 16gb Kingston USB flash drive has been consistently giving   problems.  Under Windows XP it kept saying 'This storage media is   write protected' after copying over approximately 7 gigabytes worth of   files.  At first I thought this meant that one of the NAND chips are   not functioning properly(since it's only taking half the full   capacity), since the USB has two on either side.      I used to use the USB quite frequently as a bootable USB drive for   video editing, meaning that it got several gigabytes worth of data   written to it on a daily basis.   However, now I am on Windows 8, using it as a backup disk. It is repeatedly throwing "0x8000FFFF Catastrophic Failure" messages at Windows when I try to create a file after writing 128mb of data on it. Plugging the usb drive back in will allow another 128mb of data before it locks up again.   Error preview:    Trying to scan drive for errors:    Trying again to scan drive for errors, after unsafe removal:    Is there any way to fix this problem?

When I plug in my USB flash drive, it shows up on my computer as write-protected or read-only. I am unable to transfer data to it, nor can I modify or delete any files already stored on it. I also cannot repartition or reformat the drive using Windows Disk Management, DiskPart, GParted, or other tools. The drive does not have a write-protect switch.  Why did this happen and what can I do about it? Is there a way to remove the write protection?  (Note that this can happen with some memory cards, too, as they often use controllers similar to those used in flash drives. In some cases, the system may report that the drive or card was formatted successfully even though it was never actually formatted; the original data reappears when the device is reinserted.)     This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details.


I know that there's already another post that asked the same question. But I am trying to verify my understanding of the correct approach to this problem.  The problem: let $Y$ and $Y'$ be spaces obtained from attaching an n-cell to $X$ by homotopic attaching maps. Prove that $Y$ and $Y'$ are homotopy equivalent.  The approach I have in mind, described pictorially:  Let $f$ and $g$ be the corresponding attaching maps. The author gives the hint of considering the adjunction space $Z =:X \cup_{H} (\bar B^n \times I)$, where $H$ is the homotopy from $f$ to $g$.  This space is basically the disjoint union of different spaces obtained from attaching an n-cell, with the attaching map being a $H(u,t)$ with a fixed $t$.  We try to find a retraction from $Z$ to $X \cup_{H} (\bar B^n \times {0})$ which can be identified with $Y$ (Assuming $H(u,0) = f$).  And to define such a map, my idea was, every points that are in $\bar B^n \times I$ that are not on the boundary of $\bar{B^n}$, are not identified with any points in $X$, So any points that are either on the boundary, or on $X$, are identified with some points in $X$.  so for every fixed $t$, can we not just map $(x, (u,t)) \in Z$ to the points on $x \in X$ they are identified with in $X \cup_{H} (\bar B^n \times {0})$?  so in some sense, can we not define a retraction from $X \cup_{H} (\bar B^n \times I)$ to $X \cup_{H} (\bar B^n \times {0})$ by defining an "inclusion map" for each $X \cup_{H} (\bar B^n \times {t})$ into $X \cup_{H} (\bar B^n \times {0})$?  Sorry for the vague explanation of my approach, this is because I don't even know how to begin to construct such a map, or even know if this approach makes any sense.

Prove: If $f,g:S^{n-1} \to X$ are homotopic maps, then $X\sqcup_fD^n$ and $X\sqcup_gD^n$ are homotopy equivalent.   I think it can be proved by showing they are both deformation retracts of $X\sqcup_H(D^n\times I)$ where $H$ is the homotopy between $f$ and $g$.  However, I have difficult in proving that the deformation retracts are continuous map. In fact, I have difficulty in representing a map in quotient spaces like $X\sqcup_fD^n$. I think a map from $X\sqcup_fD^n$ to $W$ can be represented by two maps: $m_1: X\to W$, $m_2: D^n\to W$, where for $x\in S^{n-1}$, $m_1\circ f(x)=m_2\circ i(x)$.  Then I construct the deformation retract this way: $m_1: X\to X$. For $x\in H(S^{n-1},t)$, $m_1(x)=H(S^{n-1},0)$, otherwise $m_1(x)=x$.  $m_2: D^n\times I\to D^n\times {0}$: $m_2((D^n,t))=(D^n,0)$.  It is easy to verify that $m_1$ and $m_2$ define a map from $X\sqcup_H(D^n\times I)$ to $X\sqcup_fD^n$. As long as this is a continous map, obvioulsy then we find a deformation retract. But it seems such a map is not continous?


In the context of predictive modeling, when comparing clasification models, What statistic should be considered more important over the others: Accuracy, sensitivity, specificity, or area under ROC curve? Would you suggest other statistics?  Thanks & regards.

This is a general question that was asked indirectly multiple times in here, but it lacks a single authoritative answer. It would be great to have a detailed answer to this for the reference.  , the proportion of correct classifications among all classifications, is very simple and very "intuitive" measure, yet it may be a . Why does our intuition misguide us here and are there any other problems with this measure?


On Travel.SE we often see questions about a person (usually a love interest) asking for money to pay for airfare, visas, permits and other expenses. For example        What general advice can be given in such situations to the person asking the question? Is it all a scam or can there be legitimate situations in which an online friend could be asking for money?

Woman planning to visit me from Ukraine to the US applied for a visa and such, claims to have paid for the visa but needs 500 dollars more for the airfare from Ukraine to the US. She says strict rules apply that the airfare cannot be purchased by US person, and must be purchased in Ukraine by person applying for the visa because of terrorist issues, etc..   Is there truth to such?


Is there an issue when Stack Overflow is used with Firefox on Mobile devices? A few weeks ago the design suddenly changed, now it looks pretty much like the desktop version, see screenshot. The nice and useful mobile theme disappeared. Of course, in my Firefox settings I did not set "Show desktop version" - anyway there is almost no difference. With the Chrome browser it looks much better (like it was looking in Firefox earlier times), see the second screenshot. Firefox Screenshot:  Chrome Screenshot:

I have mobile safari on my iPhone 5, but I don't get the mobile theme on Stack Overflow.    Is there any way to force mobile theme? The regular theme is causing me an issue for Ask Different. Ask Different Meta is Mobile theme for me.


All emails I send from my new server go to spam in Gmail (and sometimes yahoo).  I've never before sent out mass email or spam.  What I've already done:   Configured reverse DNS Enabled DKIM Verified my IP is not on spam lists Verified I'm not an open relay   Here are the headers from the received message:   Really, can't seem to figure out why the mail just doesn't come through.  I'd really appreciate your help. Thank you!

This is a  about how to handle email sent from your server being misclassified as spam.  For additional information you may find these similar questions helpful:                    Sometimes I want to send newsletters to my customers. The problem is, that some of the emails get caught as spam messages. Mostly by Outlook at the client (even in my own Outlook 2007).  Now I want to know what should be done to create "good" emails. I know about reverse lookup etc., but (for example), what about a unsubscribe link with an unique ID?  Does that increase a spam rating?


I am using the figure environment to place my figures in my document. At this point, I am using the [hbt] option because I don't necessarily care about where the figure is placed --- so long as it is placed AT/AFTER where I declare it.  Is there a way to ensure that the figure is placed at/after where I declare it while still allowing it to float to the best location ([hbt])?

AFAIK a figure or table should always be placed after the first reference to it in the text.  So I always place the code for my figures and tables after the paragraph which contains the first reference \ref to them. When I then use the command \begin{figure}[t], it is possible that the figure is placed at the top of the same page where it is referenced, so IMHO that is against the rule mentioned above.   Is there a way to force pdflatex to place the floats after the paragraph which precedes them in the source text? (so in my example that would be at the top of the following page or later)


I just bought a house and want to replace the locks. Unfortunately, on door has what appears to be an older Schlage double cylinder deadbolt that I can't figure out how to remove. I've tried prying faceplates off with no success. Internet searches talk about screw caps but these don't seem to be capping anything and I can't pry them out. I tried going in from the door edge, but the plate there seems to be attached to the inner mechanism and I couldn't get it out. Does anyone know how I can remove this lock with destroying the door? Image of the inside attached. The outside looks the same but without the two depressions on either side of the key.

Does anyone know how to remove this dead bolt that has no screw heads to use a screw driver? Here's a picture below.


Question: $f$ is a bounded real-valued function defined on $\mathbb{R}$. $A=\left\{x \in \mathbb{R}:\lim_{y\rightarrow x}f(y)=f(x)\right\}$, prove $A$ is a Borel set. I have no idea where to begin for I only know Borel sets can be formed by countable union/intersection/complement of open/closed sets and don't know how to connect it to the problem. My attempt: I tried to construct $B_n=\left\{|f(x)-f(y)|\geq\frac{1}{n}\right\}$ then I got stuck.

Let $f:X \to \mathbb R$ be a function where $X$ is a metric space. Is the set of points at which $f$ is continuous a Borel set?  i.e. Is the set $\{ x \in X : f$ is continuous at $x \in X$ $\}$ a Borel set in $X$?  (Maybe separability of $X$ is needed?)


A question may sometime be a combination of dupes of multiple other questions. If that happens, it should be possible - both before and after the question is closed as a dupe (with a dupehammer or otherwise) - for a moderator to add questions to the "list of dupes".   I know a "list of dupes" exists since I've seen questions marked as dupes of more than one question. So - why not make it editable with sufficient privileges?  This is motivated by  (see the comments for the two dupes).

When searching for duplicates of a question often multiple ones turn up, but when voting to close only one of them can be specified.  It would be useful to be able to add more than one duplicate link when voting to close.  This is not a duplicate of  as that feature only allows gold-badge users to add multiple targets; this proposal would allow everyone to propose multiple duplicates.


In the duplicate bridge game yesterday, I was the declarer and the contract was 3D. My LHO led a H and the RHO won the trick. She led back a H and RHO ruffed with D5. The were 3 hearts in dummy an I said 'small'. My partner, a sweet old lady, played D6 instead of a small H. Nobody noticed this and the LHO led a club which I won. At that point I noticed the mistake, and called the director. What should be the ruling?

I failed to have the dummy follow suit because the remaining card of that suit was accidentally hidden under a card of another suit. This was discovered later in the game, and treated as a . Should the penalty have been reduced because the dummy is face up and everyone (opponents included) failed to notice that it had only 12 visible cards to begin with?


Recently some app started opening new firefox tabs with the adress 'livemobilesearch.com'. I uninstalled the most recentently installed apps, but the problem still persists. I assume the pages get opened when I unlock my phone from standby, because sometimes after I unlock the phone the screen flashes for a second and if I open the firefox after that, a new tab with said webpage is open. I already deleted the 'cache' and 'data' of the firefox app but nothing changed. Also I tried an anti virus and malware software called "Malwarebytes Security: Virus Cleaner, Anti-Malware", but it didn't find anything. I have two ideas / questions to find out what causes this problem:   Does the firefox app have a logfile that tracks from where pages are openend? Is there a way to see a list of receivers that are 'subscribed' to the SCREEN_ON Event?   If anyone has another idea to how to fix my problem I'd be glad to hear it.  Thanks in advance.  EDIT: I've read and followed the instructions of the related articles from the comments. dumpsys activity activities shows the following:  * TaskRecord{3bf05cb #1075 A=com.android.chrome U=0 StackId=1 sz=1}   userId=0 effectiveUid=u0a103 mCallingUid=u0a103 mUserSetupComplete=true mCallingPackage=com.android.chrome   affinity=com.android.chrome   intent={act=android.intent.action.VIEW dat=https://livemobilesearch.com/?utm_campaign=dist&utm_source=foobar flg=0x14002000 pkg=com.android.chrome cmp=com.android.chrome/org.chromium.chrome.browser.ChromeTabbedActivity}   realActivity=com.android.chrome/org.chromium.chrome.browser.ChromeTabbedActivity  ....  * Hist #0: ActivityRecord{bbeee47 u0 com.android.chrome/org.chromium.chrome.browser.ChromeTabbedActivity t1075}       packageName=com.android.chrome processName=com.android.chrome       launchedFromUid=10103 launchedFromPackage=com.android.chrome userId=0       app=ProcessRecord{408bf79 18941:com.android.chrome/u0a103}       Intent { act=android.intent.action.VIEW dat=https://livemobilesearch.com/?utm_campaign=dist&utm_source=foobar flg=0x14002000 pkg=com.android.chrome cmp=com.android.chrome/org.chromium.chrome.browser.ChromeTabbedActivity (has extras) }       frontOfTask=true task=TaskRecord{3bf05cb #1075 A=com.android.chrome U=0 StackId=1 sz=1}       taskAffinity=com.android.chrome       realActivity=com.android.chrome/org.chromium.chrome.browser.ChromeTabbedActivity   The way I understand the output is, that the tabs were opened from chrome. I've disabled chrome for now, as I can't uninstall it.   EDIT 2:  The problem still persits. Even though I followed the steps in the similar thread in the comments, the unwanted page still gets opened. I can't uninstall Chrome since it is a system app (I have a sony xperia x compact on Android 8.0.0).   After I disabled Chrome the unwanted page is still opened. It now states in the dumpsys: "launchedFromPackage=org.mozilla.firefox". It would appear, that the solution form the comments is in my case not working.  Any advice would be much apreciated.

I've recently bought a new Android smartphone. After setting it up and loading my contacts onto it I thought that would be it.  Now after some days, every time I unlock the phone it takes a few seconds before it opens the default browser and opens some spam website. I tried to see what was causing it. I removed any apps I didn't know I could trust, but the problem persisted. After trying to solve it for some time I gave up and reset the phone to factory default. Now after having it reset to the default it ran without issues for roughly a week before the problem reappeared.    I tried to uninstall some apps in order to see if they were to cause of it, but nothing changed after doing so. However I did notice that if I turn off the wifi it won't even try to open the browser (I haven't tried mobile data since I don't have a bundle). This makes me feel like it might be related to something on the network but that wouldn't explain why only that phone would have the issue when there are at least 6 android phones on that very same network.  I hope that there is someone who can help me find the cause of this issue and help me solve it.  TL;DR When unlocking my phone, it opens the browser and tries to open a spam website. But only does so while connected to the wifi.  Things I've tried so far:   Factory reset (only helped for a limited time) Clearing the browser cache and all related data  Removing any app I don't know to be reliable Attempting to find what triggers it (seems like some type of internet connection is required??)   The device is the Doogee Shoot 1. As for the browser, the default is set to be the Android browser, but if I change the default it would use Chrome just as well. It seems to really just use the browser that is set to default.


I'm learning formatting expressions from a book and i have a question:  '{num} = {title}'.format(**dict(num=7, title='Strings'))   in the line above why are there two * before dict?? what do they represent?  the book didn't even mention this type of formatting expression and suddenly it was in the examples!!

In the following method definitions, what does the * and ** do for param2?  def foo(param1, *param2): def bar(param1, **param2):


Is it possible to map quantum states of different physical (quantum) systems to the same Hilbert space? For example if I consider two different molecules  in the ground state, may I represent them as kets in the same Hilbert space? I am not considering to construct a tensor product of their own Hilbert spaces like in the case of composite systems.  If I am not wrong, I recall that in S matrix scattering theory, different colliding particle are mapped to kets in the same Hilbert space.   If it is correct, may I think that a mixture state of a quantum system is a result of a statistical ensemble of states of different (quantum) physical systems?

I think in quantum mechanics we assign to each system a specific Hilbert space i.e. if systems are different then their Hilbert spaces are different. Is this true? If not why? For differernt system I mean their hamiltonians are different.


I'm trying to find a word that best describes someone who secretly causes problems for other people. Sort of like a shit-stirrer or trouble maker but specifically for when the identity of the trouble-maker is unknown.  Any help is greatly appreciated!  Have a great day.

What would you call someone who does things knowing specifically that his/her actions will cause pain and/or conflict or completes an action just to get someone in trouble or hurt them?   For example, in  there are two people that are in love, but the Colonel goes out of his way to tell the father of the girl that the boy is a thief and would be bad for their reputation.   What is a word that would describe him?


I was wondering if the following is good for SEO. I have a webshop with categories and products. Products can contain - themselves.  For example, one of the URLs would be:  http://SITE/products/CATEGORY/this+is+something+1-layer   Where the product name is "This is something 1-layer"  Now, I understand it's better to use - as space replacement, but since my product names can contain a - I was wondering if just using + would be good.  If not, what would be a better way to display it?

Which is better for search engines?   example.com/my_cool_page.html example.com/my-cool-page.html  example.com/my+cool+page.html


For Gamma function's duplication formula $$\Gamma (z)\;\Gamma \left(z+{\frac  {1}{2}}\right)=2^{{1-2z}}\;{\sqrt  {\pi }}\;\Gamma (2z)$$ , if limit $z$ to real numbers, i.e. $z\in \mathbb R$, is it possible to prove it using basic analysis, i.e. not relying on complex analysis or beta, zeta etc functions?

He says:     Prove the formula of Gauss:   $$ (2\pi)^\frac{n-1}{2} \Gamma(z) = n^{z - \frac{1}{2}}\Gamma(z/n)\Gamma(\frac{z+1}{n})\cdots\Gamma(\frac{z+n-1}{n}) $$   This is an exercise out of Ahlfors.  By taking the logarithmic derivative, it's easy to show the left & right hand sides are the the same up to a multiplicative constant.  After that I'm lost. It's easy using another identity when $n$ is even to use induction. But when $n$ is odd I am lost.  It's obvious when $n$ is a power of 2.


SOLVED: I mis-installed it. Thanks David. I installed Ubuntu 20.04 alongside a preexisting Win10 installation. Now, neither OS recognizes the other's presence. I can miraculously use both, but it's a hassle and all the fixes I've found haven't worked. I have tried various fixes for both issues: When I boot and go into startup menu > boot device options, I'm faced with  (first image) the bottom option "Notebook hard drive" starts GRUB and I can get into Ubuntu normally. But why isn't it recognized as Ubuntu? If I don't go into the boot menu and let the computer do its thing, it goes to Windows automatically. The second image shows what happens if I go into the BIOS boot options. There's that "notebook hard drive" option under "Legacy boot order", but I can't seem to turn that on. I already have secure boot turned off, as you see. Getting the computer to start directly into GRUB would presently be disastrous anyway, because GRUB in turn doesn't recognize Windows and I'd be unable to use it! I've tried  (second answer, "If the os-prober method doesn't work...") and indeed, now there's a Windows 10 entry. But selecting it gives me a black screen with the text An operating system wasn't found. Try disconnecting any drives that don't contain an operating system. Press any key to restart Note that I don't actually have any rows in my lsblk output with /boot/efi in them, but /dev/sda2 has an appropriate label: NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT loop0    7:0    0  55,5M  1 loop /snap/core18/1988 loop1    7:1    0  55,5M  1 loop /snap/core18/1997 loop2    7:2    0   219M  1 loop /snap/gnome-3-34-1804/66 loop3    7:3    0  64,8M  1 loop /snap/gtk-common-themes/1514 loop4    7:4    0    51M  1 loop /snap/snap-store/518 loop5    7:5    0  31,1M  1 loop /snap/snapd/11036 loop6    7:6    0  32,3M  1 loop /snap/snapd/11588 sda      8:0    0 447,1G  0 disk  ├─sda1   8:1    0   499M  0 part  ├─sda2   8:2    0    99M  0 part  ├─sda3   8:3    0    16M  0 part  ├─sda4   8:4    0 186,3G  0 part /home/kilian/Windows ├─sda5   8:5    0   603M  0 part  ├─sda6   8:6    0 186,3G  0 part / └─sda7   8:7    0    15M  0 part  sr0     11:0    1  1024M  0 rom  /dev/sda2: UUID="C495-5A59" TYPE="vfat" PARTLABEL="EFI system  partition"PARTUUID="6795db25-5a95-4724-a256-4b7cf3c60931"  Last thing I tried just now was the boot-repair tool suggested below the custom GRUB entry in the AskUbuntu post I linked. I got this: WindowsEFI detected. Please disable BIOS-compatibility/CSM/Legacy mode in your UEFI firmware, and use this software from a live-CD (or live-USB) that is compatible with UEFI booting mode. For example, use a live-USB of Boot-Repair-Disk-64bit (), after making sure your BIOS is set up to boot USB in EFI mode. Anyway, before I continue trying out fixes that work on either problem in isolation - is this even two separate problems? Or are both linked to the same issue, did I do something fundamentally wrong when partitioning my SSD? Has anyone encountered this particular problem?

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


How do I show that in a normed space $| (\|x\|-\|y\|) | \leq \|x-y\|$  I need to use normed space axioms but I'm unable to figure it out. I think the scalar axiom and triangle inequality are helpful.

I've seen the full proof of the Triangle Inequality  \begin{equation*} |x+y|\le|x|+|y|.  \end{equation*} However, I haven't seen the proof of the reverse triangle inequality:  \begin{equation*} ||x|-|y||\le|x-y|. \end{equation*} Would you please prove this using only the Triangle Inequality above?  Thank you very much.


I'm trying to make a login screen by fetching Card No and PIN from database using xampp for ATM app by giving input as Card No and PIN then it is showing error as:  Exception in thread "AWT-EventQueue-0" java.lang.NullPointerException at Atmcardno.jButton1MouseClicked(Atmcardno.java:228) at Atmcardno.access$300(Atmcardno.java:15) at Atmcardno$4.mouseClicked(Atmcardno.java:128)   My jButton1 code for login and fetching the Card No and Pin is shown below. I've been programming in java swing and need help.      System.out.println("Starting...");            if(((cardno.getText()).equals("")) && (pwd.getPassword().equals("")))           {            JOptionPane.showMessageDialog(this,"Please enter ATM Card No and PIN No.","Warning!!!",JOptionPane.WARNING_MESSAGE);        }           try{               System.out.print("Starting1...");                 int foundrec=0;                 Class.forName("com.mysql.jdbc.Driver");                 Connection con= DriverManager.getConnection("jdbc:mysql://localhost:3306/atmdb","root","");                 System.out.println("Connected to database.");       PreparedStatement ps= con.prepareStatement("select* from accountdetail where atmno='"+cardno.getText()+"' and pinno='"+pwd.getPassword()+"'");                 ResultSet rs= ps.executeQuery();                 while(rs.next())                 {                     atno=rs.getInt(1);                     System.out.println(atno);                     acno=rs.getInt(2);                     System.out.println(acno);                     pno= rs.getInt(3);                     System.out.println(pno);                     String cardname= rs.getString(5);                     System.out.println(cardname);                     String expdate= rs.getString(7);                      try                     {                         SimpleDateFormat sdf= new SimpleDateFormat("yyyy-mm-dd");                         Date d1= sdf.parse(curdate);                         Date d2= sdf.parse(expdate);                          System.out.println("Expiry date of ATM card is "+sdf.format(d2));                         System.out.println("Today's date is "+sdf.format(d1));                          if(d1.compareTo(d2)>=0)                         {                             JOptionPane.showMessageDialog(null, "Hello "+cardname);                       //      new AccountType().setVisible(true);                         }                         else if(d1.compareTo(d2)<0)                         {                             JOptionPane.showMessageDialog(this, "Your ATM card is out of expiry date, please visit nearest branch for more information.","Warning",JOptionPane.WARNING_MESSAGE);                             new Welcome().setVisible(true);                           this.setVisible(false);                           }                      }                     catch(ParseException pe)                          {                               System.out.println("Exception in date format. "+pe);                               pe.printStackTrace();                          }                     foundrec=1;                 }                  if(foundrec==0)                 {                     JOptionPane.showMessageDialog(null, "Invalid ATM card no. or PIN no. ","Warning",JOptionPane.WARNING_MESSAGE);                  }              }             catch(Exception e) {                 e.printStackTrace();             }

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


I have the following code  import pandas as pd df = pd.DataFrame(columns=['var1', 'var2','var3']) df.loc[0] = [0,1,2]  def RS():     x = 123     y = 456     z = 'And some more random shit'     return x+y  def BS():     x = -890     y = (456*1)+90     z = 'And some more random shit'     return x-y  def MyCompute(srt, srt_string):     df[srt_string] = srt()     df['1min' + srt_string] = 1-df[srt_string]  MyCompute(srt=RS, srt_string='RS') MyCompute(srt=BS, srt_string='BS')   Is there a way to avoid the double RS and double BS in calling the MyCompute function?

In Python, how do I get a function name as a string, without calling the function?  def my_function():     pass  print get_function_name_as_string(my_function) # my_function is not in quotes   should output "my_function".  Is such function available in Python? If not, any ideas on how to implement get_function_name_as_string, in Python?


this is function to make line with 4 points that give it place and name   int counter=0;  public void CreateALine(double po1, double po2, double po3, double po4)     {         // Create a Line         Line redLine = new Line();         redLine.X1 = po1;         redLine.Y1 = po2;         redLine.X2 = po3;         redLine.Y2 = po4;          // Create a red Brush         SolidColorBrush redBrush = new SolidColorBrush();         redBrush.Color = Colors.Red;          // Set Line's width and color         redLine.StrokeThickness = 3;         redLine.Stroke = redBrush;          // Add line to the Grid.         LayoutRoot.Children.Add(redLine);         LayoutRoot.RegisterName("readline"+counter, redLine);         counter++;                 }   I want to create more than one line,  Could i access to any line by its name? to make an event or control its Visibility like this :        redline0.Visibility = Visibility.Collapsed;       redline1.Visibility = Visibility.Visible;

I need to search a WPF control hierarchy for controls that match a given name or type. How can I do this?


I have a document template in Catalan  using \usepackage[catalan]{babel}. I want to write the document in Spanish, but when I change that line to \usepackage[spanish]{babel} it throws an error:     ./main.aux:3: Package babel Error: Unknown language `catalan'. Either you have    (babel) misspelled its name, it has not been installed,    (babel) or you requested it in a previous run. Fix its name,    (babel) install it or just rerun the file, respectively.   What do I have to do?

I've been trying to change the language of my LaTeX document by replacing \usepackage[swedish]{babel} with \usepackage[english]{babel} but I only get this message:  ! Package babel Error: You haven't loaded the option swedish yet.   I've read in an other question at this forum that compiling enough would solve the problem, but that doesn't work for me. Does anyone know what I should do?


I have shapefile with polygons and lines. There are attributes for: layer, lineweight, colour: Red, colour: Green, colour: Blue. (colour values are from 0-255).  Is there a way to read values from attributes, and assign colour and lineweight to polygons and/or lines? After that I would like to use the save layer option to save symbology.  I'm using ArcMap 10.3.

I have an excel file with 2 attribute columns, 1-feature info 2-Number of color (RGB) that the current feature should be symbolize. This file file can be joined with the layer using the "feature info" field which is unique (join by attribute table). So i have as attribute the color number attribute for every polygon feature.  How can  i use this this information to symbolize every feature with their attributed color already imported from the excel sheet?


I wanted to edit  replace the bulleted list with a table. The answers to   that this isn't supported by markdown. I tried to make an HTML table, but I couldn't get that to work either.  Given that tables have no markdown support, are there any other ways to make tables on SE sites?

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


I am installing an overhead automatic garage door opener.  My only power source close to where I will be hanging the motor is an overhead light socket that is operated by a switch on the wall next to the house entry door.  I wanted to know if it is possible to rewire the light socket with a standard electrical plug outlet AND to remove the switch & wire it to provide constant power to the new outlet.  The overhead light is on my 15A garage GFI circuit & the opener lists 120V/6A as its power requirements.  Thank you

I am installing an overhead automatic garage door opener. My only power source close to where I will be hanging the motor is an overhead light socket that is operated by a switch on the wall next to the house entry door.   I wanted to know if it is possible to rewire the light socket with a standard electrical plug outlet AND to remove the switch & wire it to provide constant power to the new outlet. The overhead light is on my 15A garage GFI circuit & the opener lists 120V/6A as its power requirements.  I live in the US.


I have a problem with my brother DCP-1510 printer and need to ask to some wise folks of stackexchange about it. In particular, it was supposed to be a multipurpose printer(allowing scanning as well) but now there were issues with the driver installation. I was able to search for the driver using the device manager, but the scanning function is not functional. Please, recommend me the site in which I can ask this question.

Where do questions along the lines of "how do I get my scanner (model number here) to work over the network with the latest OS X ?" (and similar questions) go? (Obviously, they don't go on Stack Overflow.) Is there a master list somewhere?


I am currently modelling traffic and my map of roads consists of nodes connected with lines. For each road there is maximum capacity and amount of traffic and each road therefore has a utility value between 0 and 1.  To my question; I am wondering whether there is a colouring method for my lines in tikz that defines the colour by a value. For example I may want a high utility value to be red and a low utility level to be green and values in between are gradients of the booth. Is this possible in some way?  EDIT: The answer in the link is useful. I am now updating all my values to my lines manually; is there perhaps a way to retrieve them from a vector?

I am trying to draw rectangles, each of which has a corresponding value, which will be mapped into a color from a color map based on the value. This is how I want the write the code. What is missing is the mapping from \myvalue to \mycolor.  \documentclass{standalone}  \usepackage{colortbl} \usepackage{pgfplots} \usepackage{pgfplotstable}  \pgfplotsset{compat=1.9}  \newcommand*{\ListOfRectanglesColor}{%   0/0/1/1/blue,   1/1/2/2/red, }  \newcommand*{\ListOfRectanglesValues}{%   0/0/1/1/0.3,   1/1/2/2/0.6, }  \begin{document} \begin{tikzpicture}   \foreach \sXa/\sYa/\sXb/\sYb/\mycolor in \ListOfRectanglesColor {     \fill[\mycolor] (\sXa, \sYa) rectangle (\sXb, \sYb);   }   %\foreach \sXa/\sYa/\sXb/\sYb/\myvalue in \ListOfRectanglesColor {   %  what code will define \mycolor as a color based on \myvalue?   %  and a specified color map?   %  \fill[\mycolor] (\sXa, \sYa) rectangle (\sXb, \sYb);   %} \end{tikzpicture} \end{document}   Edited in response to comment  Question: How do I map values to colors? I would appreciate it if the TeX code were commented so that I could understand how the code works.  For simplicity, the mapping function will be of the form  \valuetocolor{value-min}{value-max}{color-min}{color-max}{value}   The floating point numbers value-min and value-max will be mapped to two defined colors color-min and color-max respectively. We can assume that value-min ≤ value-max. I want to map the floating point number value to the linear interpolated value between color-min and color-max. More precisely, let λ be the value such that value = λ value-min + (1 - λ) value-max. Then I want \valuetocolor{value-min}{value-max}{color-min}{color-max}{value} to return the color λ color-min + (1 - λ) color-max.    Related TeX.SX Question  I am aware that there is a related question  where there is TeX code that accomplishes a mapping from value to color for a more complicated color map. Unfortunately, with my limited TeX/PGF knowledge, I can't understand how the code works.


Similar to how you can place random points within lines and within a polygon.

I have GPS coordinates which identify aid projects in Africa. Now, I want to re-locate these projects, such that each project is re-located by 100 km in a random direction from its original location. (Extra: I have country layers; can I force QGIS to re-locate only within the original country?) I tried the Virtual Layer & Geometry Generator, both didn't work so far. Any leads? I use QGIS 3.14.15.


I am new to regex and i want to extract strings from file path. Below is the mentioned filepath from which i want to extract string:  input : c://dev-dl-data-d2-us=east-1-5148727/all/stage/clinical/cro/raw/c/ca209_040/2018/08/02/aesae.csv  Output: ca209_040,aesae.csv

I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them?


I have 2 drives:  - HDD - holds a windows 10 installation that got corrupted  - SSD - holds a fresh installation of windows 10  So since the OS on HDD got corrupted I had to install a new one on SSD, but now every time I boot I get a dual boot screen, asking me to chose between the 2 OSes. The Windows folder in HDD is not renamed to Windows.old so it's still active... What can I do so only the SSD installation is recognized? P.S. except formatting, I have some data there... If there's no other way I'll move the data and format...

I installed Windows 7 on one partition and formatted the other where I had Windows 10 installed leaving only that one Windows 7 OS on my drive, but I still have two OSs offered in Windows Boot Manager. What is even weirder is that their names are reversed, when I choose Windows 10, it's Windows 7 that gets loaded.


I'm building a quite simple web application, and need to get some rough understanding of how much load my server can take.  Of course, this depends on a whole lot of factors, but I just need a rough idea if we're talking about ten or ten thousand users, because at the moment I have no idea.  Standard LAMP-setup, with a quite small database and a reasonably simple and fast PHP. Each non-static request requires about 20 simple SQL queries. With no load, the runtime for such a request is around 50 ms. No explicit caching.  Current hosting is on a VPS w/ 1GB RAM and unknown CPU.  Is it possible to give a rough estimate given this? What is the bottleneck? CPU, RAM? Does 50 ms / request mean 20 requests per second? How much can caching help (factor 10? 100? 1000?)? Where would caching make most sense? How do I perform load-testing?  Uuh, lots of questions, not expecting detailed replies but would greatly appreciate pointers to where I can go from here to read up on system requirements/testing/possible ways of scaling up!

This is a  about  Related:      I have a question regarding capacity planning. Can the Server Fault community please help with the following:   What kind of server do I need to handle some number of users? How many users can a server with some specifications handle? Will some server configuration be fast enough for my use case? I'm building a social networking site: what kind of hardware do I need? How much bandwidth do I need for some project? How much bandwidth will some number of users use in some application?


My whirlpool side by side is not cold or making ice I have tried to reset the filer and it didn't fix the problem?

My whirlpool side by side refrigerator is not cold and freezer is cold but not making ice?  I have replaced the relay switch on compressor, I have taken the back off inside the freezer and the fan is working, I have taken the damper off and it is working, I have been told if fans are working the control panel is working, I have cleaned the coils (the best I can), the fan is working to cool compressor.  Don't know what else it could be, help! please


Following this almost 3 years old question    What is the state of the art for forecasting time series in 2019 or 2018?  What's the best and simplest method that is easy to learn and has great performance in term of accuracy? And also what's the best framework to work with?

Suppose I have a set of measurements taken at regular intervals, and I want to predict future values of one of those measurements. There are relationships between the variables being measured. For example, some variables may tend to rise together, or one variable might tend to fall when another rises. What are the state-of-the-art methods for this type of forecasting?


I've been developing an application in C# (using VS2008) for quite sometime now and about a week ago, 'Edit and Continue' has stopped working for me. I can edit the code while debugging, but any little change that I make to the code now forces me to stop the project and restart it. The message that I get is this:  Modifying a 'method' which contains a lambda expression will prevent the debug session from continuing while edit and continue is enabled.  Oddly, I'm not even using lambda's when this happens. Modifying the same chunk of code last week while in debug mode allowed me to continue with no problems. I've done various searches on the internet to find out what I could have done to cause this change in behavior. The only help I can find on the web is directly related to debugging ASP.NET web projects. However, this portion of my solution is a Windows Forms project.  What could the problem be? Is there a way to fix this? I would greatly appreciate any help.

So, every time I have written a lambda expression or anonymous method inside a method that I did not get quite right, I am forced to recompile and restart the entire application or unit test framework in order to fix it. This is seriously annoying, and I end up wasting more time than I saved by using these constructs in the first place. It is so bad that I try to stay away from them if I can, even though Linq and lambdas are among my favourite C# features.  I suppose there is a good technical reason for why it is this way, and perhaps someone knows? Furthermore, does anyone know if it will be fixed in VS2010?  Thanks.


Using integration by parts find a recursive formula of $\int cos^n(x) dx$ and use it to find $\int cos^5 x dx$  I have no idea how to do this and my knowledge does include integration by parts etc. I just do not know what to do. Thanks!

This question is just a soft question, about can we compute a general formula for everything? Or it has some restrictions?  Like $\int x^ndx=\frac{x^{n+1}}{n+1}+C$.  I am not able to deduce a formula for both.  I dont know where to start, so please guide me?


Why does this only print arg out once?  $ alias test="echo $1 $1 $1" $ test arg arg   This is on GNU bash, version 4.2.25(1)-release (x86_64-pc-linux-gnu).

I want to set an alias to start nedit together with command line option -noautosave (due to text files up to 500MB). What seemed to be easy:  alias nn="nedit -noautosave $1 &"   just raises some error "Permission denied" of a different file and another error about unexpected EOF while looking for matching "'" and "unexpected end of file".  One solution I found after a Google Search would be to check the quotes, but I can't see any possible errors with them.  I also tried declaring a function:  function nn () { nedit -noautosave $1 &}   which also failed with same errors.


I constantly reboot between Adobe and Ubuntu when I need to so dome graphic design and UI work. Or should I just switch to a Mac? Is it possible to have Adobe on Linux?

Can .exe and .msi files (Windows software) be installed in Ubuntu?


Rookie Question! I have a shapefile in QGIS 1.8.0 of a country with 20000 divisions. I need the area of each division, but this is not a given attribute. When i click on a district, the "Identify Results" panel shows a "Derived" value for the area of each district along with the feature id. Can somebody tell me how I could extract these area values to a data file? Thanks!!

I cut a part out of one feature and added it to another feature in a polygon shapefile.  My problem now is that both features has the same values in the area-, perim-, p2a-, width- and length-columns?  The features are very much different in size, how do I get QGIS to sort of "re-calculate" the areas etc?


How do I show that $\int_{0}^{1} \frac{1}{x^{x}} = \sum_{k=1}^{\infty} \frac{1}{k^k}$. Also, how do I show that $\int_{0}^{1} \frac{1}{1-x} + \frac{1}{ln(x)} dx = \lim_{n \rightarrow \infty} (\sum_{k=1}^{n} \frac{1}{k}) - ln(k)$

I'm trying to find $\int x^x \, dx$, but the only thing I know how to do is this:  Let $u=x^x$.  $$\begin{align} \int x^x \, dx&=\int u \, du\\[6pt] &=\frac{u^2}{2}\\[6pt] &=\dfrac{\left(x^x\right)^2}{2}\\[6pt] &=\frac{x^{2x}}{2} \end{align}$$  But it's certain that this isn't the correct way to evaluate that, and the answer must be wrong.


Let there be $A,B$ matrices.  Let $C=A+B$  $Span(Col(C))\subseteq Span(Col(A))$ because C is a linear combination of A . $Span(Col(C))\subseteq Span(Col(B))$ because C is a linear combination of B .   Therefore $Span(Col(C))\subseteq Span(Col(A))+Span(Col(B))$ and $Rank(A+B)\leq Rank(A)+Rank(B)$

Let $A,B$ be matrices $m\times n$ $(A, B \in M_{m\times n}(R))$. How can we prove that $$\operatorname{rank}(A+ B) \le \operatorname{rank}(A) + \operatorname{rank}(B)\ ?$$


How can you run an application as another user in Windows 7? The only catch is that I don't want to have to hold down the shift key, right click on the application and choose Run as different user. I need it to automatically login using the login credentials I specify.

How do I run as a different user on a shortcut in Windows 7?   On Windows XP, I had the ability to mark a shortcut as being run by a different user, so that every time I ran it it would prompt me for a username/password. This let me have two shortcuts for things like , one for my normal account and one for my domain administrator account which has access to production servers.  I can get to the 'Run as different user' option with Shift + right-click, but I can't see an option anywhere that would let me mark the shortcut as doing this every time.


I am running Ubuntu 16.04 on my windows pc using Oracle VirtualBox.   I've recently tried installing Octave on my Ubuntu platform, but after a few steps it is showing some error saying unable to fetch archives.   What should I do? I've posted the image here.

I get this error whenever I try to install programs using the terminal:  home@ubuntu:~$ apt-get install myunity E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   Also I'm unable to install updates using the terminal.


In a regular question, it is assumed that comments notify the OP, even though you can explicitly tag the OP, evident by the tag suggestion/auto-fill.  I find myself wanting to message the bounty awarding user, who has placed a bounty on a buried post, where the OP may or may not be active.  But there is no autofill tag suggestion for the bounty user.  Is it implicit?

are described at length, but don't address bounties.   If I put a bounty on someone else's question, will I be notified of undirected comments? Can people notify me via @-replies even if my only involvement with the question is putting a bounty on it?   If the answer to one or both is no, could we get a new feature putting anyone with a bounty on a question on par with the question's author for the purposes of comment @-replies?  Or, if not, at least add them to the list of @-reply targets to allow messaging them?  This was all prompted by  from DanQ that had a bounty put on it by rabidsnail, presumably because she had the same problem.  Once it showed up on the Featured Questions list, people asked for more information in comments.  DanQ never responded, and may well not have cared about the question by that point.  Presumably rabidsnail cared, but did she get any notification about the comments requesting more info?  (I assume rabidsnail checked in on the question at some point, and obviously didn't add more info then, but maybe she would have had she known sooner.)  There's also the question of proper etiquette when elaborating on a question that's not yours, but that's beyond the scope of this question.


How could I animate a plane that transforms to a sphere using Blender ? I know you can transform a cube to a sphere using shape keys, but is this possible for a plane ?

How to make a grid-to-sphere animation like this?


When one deals with a dispersion relation of the form $$\epsilon(\vec{k})=\epsilon(|\vec{k}|)$$ then a simple transformation in polar/spherical coordinates is enough to find the density of states.  I read that for electrons in an arbitrary dispersion relation the DOS is given by $$D(\epsilon)\propto\int_{\epsilon(\vec{k}=\textrm{const.})}\frac{dS_\epsilon}{|\nabla_\vec{k}\epsilon(\vec{k})|}$$ Where $dS_\epsilon$ is a surface element of the surface of constant energy. How does on proof this?

If I have a 3D dispersion relation   $E=E(k_x, k_y, k_z)$ I have an equation for the density of states, which is   $D(E)=\frac{1}{\nabla_k E}\int\frac{dS}{(2\pi)^3}$  1) I am confused about the integral. What am I integrating over, exactly? It must have units of the $k$ vector, so it's a k-space integral, but what is the surface that is relevant?  3) Where does that equation come from, how is it derived?


When I run this query on  for Stack Overflow:  select Id, ProfileImageUrl from Users where Id= 13   the imageURL for the user with userID 13 is not returned even though the user has a profile image. May I please know what am I missing here?

I noticed that in the StackOverflow data dump many profiles miss the ProfileImageUrl column. What is the reason for this, because I could still get this data by scraping all profiles that I am interested in, but I guess that is not something StackExchange would want me to do (and it also takes a lot of time, which the data dump could have reduced drastically...)? EDIT: See this query of my profile on StackOverflow:  EDIT2: In case some troll edits that query: SELECT ProfileImageUrl FROM Users WHERE DisplayName = 'jabbink'  Result: empty


Some journals ask to put the references in thebibliography environment. It is easy to do this using bibtex. One just finds the bbl file and paste everything in there, to the main text.  However, I could not find a similar way to do same when bibliography is generated by biblatex.   Any ideas?

Suppose that I moved from BibTeX to biblatex. With BibTeX I just copied the content of .bbl file into final version of my paper before submitting it to a journal. What should I do at same stage having .bbl file produced by biblatex? It is of quite different format.


I have a plan to self-study real analysis,but I'm not sure about myself I complete read Calculus,linear Algebra ,Number theory. But I saw in some thai textbook mention about topology.Is it important for real analysis ? I have more question . Is calculus by spivak will help for studying real analysis?

Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction to Analysis" by Gaughan.   While it's a good book, I'm not sure it's suited for self study by itself.  I know it's a rigorous subject, but I'd like to try and find something that "dumbs down" the material a bit, then between the two books I might be able to make some headway.


Dont know how to delete this thing, there's a face or dot showing in the middle and I think this is the reason why my model look like ugly when I turn submesh

So I have been following the Blender Guru modeling tutorial with minor changes every thing looked OK till he added the sub-surf modifier and I have no idea how to fix  (followed tutorial  )  this is my edit view with and with out sub surf     and this is how it should look like


Let $A$ be a unit commutative ring and $S:= \{a^n | a \in A, n\geq 0\}$. With $S^{-1}A$ the localization of $A$ over $S$.  I'm having some problems on proving that $$S^{-1}A \cong A[X]/(1-ax)$$ I'm not searching for a complete solution maybe just some hints, thank you very much.

I am having trouble with the following problem.      Let $R$ be an integral domain, and let $a \in R$ be a non-zero element. Let $D = \{1, a, a^2, ...\}$. I need to show that $R_D \cong R[x]/(ax-1)$.    I just want a hint.  Basically, I've been looking for a surjective homomorphism from $R[x]$ to $R_D$, but everything I've tried has failed. I think the fact that $f(a)$ is a unit, where $f$ is our mapping, is relevant, but I'm not sure. Thanks


DJB described curve25519 in his paper which can be found  (PDF). It seems that the main purpose was for Diffie-Hellman key exchange. I think this means that Discrete Log is supposed to be hard on curve25519.  My questions is whether DDH (Decisional Diffie-Hellman) assumption is conjectured to hold on curve25519 too so that we can use it for building an ElGamal encryption scheme. Some quick investigation shows that DDH are assumed to be hard on elliptic curves with large embedding degree () and it seems that most elliptic curves have large embedding degree except those constructed for pairing based crypto.   So, I guess the answer should be “yes”. But still I would like to get some expert knowledge to confirm that one can securely build ElGamal encryption on this curve.

I know the usual way of using getting shared secrets for encryption with ECC is DH, however, this only works with two keypairs of exactly the same kind, for example two curve25519- or two p256-keypairs.    With ElGamal, one can get a symmetric key for a recipients public key no matter which kind of key they are using themselves. This works great if users don't have the same kinds of keys, and it doesn't use the same shared secret each time. This behaviour makes development and use of an application using ECC for encryption much easier and probably even is more secure (as the shared secret is different each time), so I'd prefer using ElGamal if possible.    However, it only seems to work for Short type curves - NIST, SECG, brainpool and so on. (My javascript implementation (1) is based on SJCL's implementation, but uses "elliptic" as a library, which supports Short, Montgomery and Edwards curves, while SJCL and JSBN only know Short.)    I don't really get this, as the logic behind ElGamal is really simple:    public_key = curve_param_G * secret_key     tag = curve_param_G * random_secret     key = public_key * random_secret = curve_param_G * secret_key * random_secret     key = tag*secret_key = curve_param_G * random_secret * secret_key       The implementation of multiplication for Montgomery and Edwards curves seems to be different from the multiplication function of Short curves. Still, shouldn't it work?    Is there any change to make ElGamal work with Montgomery curves like curve25519, or Edwards type curves like ed25519, and is it just implementations fault? Or is there any reason this actually isn't possible?    Reasearching on this topic doesn't bring much detailed information(, unless you get the exact math behind Montgomery and Edwards curves, which I don't at the moment, I'm just using the elliptic library for a simple app).    Thank you for your answers :)    (1) Some pseudocode (simplified):    Get a symmetric key for a known public key (to get a symmetric key only the recipient will be able to find out knowing a public key):    ec = curveobject(curve_the_pubkey_is_on);     secret = random_secret_key();     tag = ec.g.mul(secret); // pass along with the message     key = public_key.mul(secret); // use for symmetric encryption         Get a symmetric key for a known tag (to get the symmetric key knowing the tag and own private key):    key = tag.mul(private_key); // can decrypt message with


I'm new to Ring Theory and I'd like to check if I'm on the correct track with this.  Wolfram defines a PID as "an integral domain in which every proper ideal can be generated by a single element".  As I understand it, an ideal is something like a normal subgroup in group theory. So, if let's say I have a ring defined by all one-variable real coefficients of polynomials denoted $k[x]$ where $k \in \mathbb R$, an ideal $I$ would be addictive subset of $k[x]$ when $k.i \in I$, where $k \in K$ and $i \in I$. How can I go about thinking of such an ideal? Just off my mind, there seems to be no suitable candidates (other than the trivial ones, $0$ and $k[x]$) that can form an ideal.   Also, is my thinking correct on this? $k[x]$ is a PID because for $x \in k[x]$, I can generate all the possible polynomials in $k[x]$ by simply multiplying $x$ by itself to reach the degree of $k[x]$. As I can add $x$ of whichever power I like together, I can get any polynomial in $k[x]$. For instance, if you gave me something like $x^3+2x$, it can be generated by the polynomial $x$ by mutiplying $x$ by itself $3$ times and adding that to $2x$. Is my intuition correct for this? Otherwise, how can you prove that $k[x]$ is a PID?  Thanks for all the help.

I want to show that if $K$ is a field then $K[x]$ is principal  Here is what I did:  I took 2 polynomial p(x) and q(x). Since we're on a field we can do a euclidean division of polynomials:  $q(x) = p(x)a(x) + r(x)$ with $deg(r) < deg(p)$  Now if $r= 0$ we obviously have $p \in (q)$   But I don't know how to show that it is principal if $r \neq 0$  Also I would like to show that the assertion is false if we replace "$K$ is a field" by "$K$ is a principal domain and an integral domain". I can't figure out how to do that


I'm doing the following exercise and I don't know how to prove it.  Suppose $a,b \in \mathbb{Z}$, and $d=\gcd(a,b)$. I have to prove that if $x\equiv y \bmod d$, then the system   $$X\equiv x \mod a$$  $$X\equiv y \mod b$$  has a solution.  I don't even how to start...  Thanks for your help :)

We want to find the solution $x$ to the congruence system  $$\begin{align} x &\equiv r_1 \!\!\!\pmod{\!m_1}\\ x &\equiv r_2 \!\!\!\pmod{\!m_2}\end{align},\ \ {\rm where}\ \  \gcd(m_1, m_2) = 1$$  These can be rewritten as  $$\begin{align} x &= r_1 + m_1 j\\ x &= r_2 - m_2k\end{align}$$  for unknown integers $j, k$. So we set those two equations as equal and rearrange them to  $$m_1j + m_2k = r_2 - r_1$$  Now assume we perform $\text{egcd}(m_1, m_2)$, which gives us the solution to  $$m_1u + m_2v = \gcd(m_1, m_2)$$  Let the integer $\,h\,$ make $\,h \gcd(m_1, m_2) = r_2 - r_1$.  Then $\qquad hm_1u + hm_2v = h\gcd(m_1, m_2) =  r_2 - r_1 = m_1j + m_2k$  At this point I am lost because I don't think we can just assume  $hm_1u = m_1j$ and extract $j = hu$.   How do I get the values of $j$ or $k$ so I can get the value of $x$?


When Hermione uses the Time-Turner she is making her 24 hour day even longer by going back into the past a few hours.  Let's say her time spent in the past has added up to one year (I know it couldn't possibly, but other wizards may have). If Hermione was supposed to die in 2100, would she still die in 2100 or would she now die in 2099 from using the Time-Turner?  A.K.A. is Hermione aging equivalent to the hours she has gone back, or does her body "reset" to the age it was at the hour she has gone back to?

In her third year at Hogwarts, Hermione is given a time-turner so she can take more classes. Several of her classes are concurrent to each other, so she attends one class (for 1-2 hours) goes back in time, and attends a different class during the same time frame.  But from an aging point of view, she should age 4 hours in relation to the 2 hours everyone else ages. How much older should Hermione be relative to everyone else after using the time-turner for an entire school year?