Express $det(A \otimes A)$ using trace and det of $A$. I know that determinant is product of eigenvalues, and trace is sum. But i cannot procceed further. Any hints?

I'd like to know how can be shown that $\det(A \otimes B) = \det(A)^m \det(B)^n$ when $A$ and $B$ are square matrices of size $n$ and $m$ respectively and $\otimes$ represents the Kronecker product of $A$ and $B$.  I've seen some proofs using eigenvalues of $A$ and $B$, but since not every matrix has eigenvalues (at least not in all rings), I'd like a more intrinsic proof, maybe using the fact that $M_{(nm)^2} \cong M_{n^2} \otimes M_{m^2}$.   It all comes down to showing that $\det(A \otimes I) = \det(A)^m$ and using some smart property (e.g. $(A\otimes B)(C\otimes D) = (AC) \otimes (BD)$), but I wasn't able to do even that.


Background: In the next few months I will be applying for graduate school for a PhD program (or Master's if I have to go that way first). The degree will be Electrical Engineering focusing on Computational Electromagnetics (CEM). I have heard that the letters of recommendation are crucial, and should absolutely be written by people that personally know your work. Right now I have two candidates willing to write for me: (1) a tenure-track professor for whom I have worked for 2 years and although her expertise is not in CEM, the work I do for her requires a similar skill set. (2) a tenured faculty who has had me in a class, is a nationally recognized expert in CEM, and has worked on a project with me outside of school (specifically he was consulting where I was working over the summer).  Issue: For the third letter, the most readily available option would be my boss at my summer internship. He has known me for about 2 years now, he is a double major in Math and Comp Sci, and has a Masters in Comp Sci. He has also been doing work in CEM for a few years so he is an expert in that area as well. However, he does not have an appointment at a school right now (although he surely could), but instead works in industry. Keep in mind I will be applying to programs that are top 50-30 overall, but are top 25-10 in CEM (i.e. Ohio State, UTEP, U of Houston).  Would he be considered a strong letter writer, or should I seek another letter from a professor (who may not know me as well and/or may not be an expert in CEM)?  Note: although my internship is in industry, my job is to do research and development, so I am not questioning whether my background is strong, I am questioning whether the third writer's profile would be considered strong/adequate by the committees.

My background:   Final year computer science undergraduate in the UK. Spent one year working in a scientific facility developing software for scientists. My colleagues had previous academic experience (PhDs in math or physics). Researched for 3 months under professor N within my university. My dissertation begins in February, so cannot use my supervisor from that.   I want to pursue a PhD, and am at the stage of applying for programmes. However, each programme requires "two academic references", and am unable to come up with a second one (professor N being the first) that would provide the best application.  Giving many of you read references, and recruit PhD students, which of the following references would you prefer receiving:   A senior software developer where I previously worked (he has a PhD in physics), but I feel this is not "academic". My personal tutor (a professor who helps with any personal or professional problems), whom I have not seen in a few months, but have used for references before (to get the aforementioned job). Professor B who has taught me over the past three months, but whom I am not close with (on a personal or professional level).   I know my question is a bit specific, so perhaps to generalise:  Q. Is it acceptable to have industrial references when applying for PhD positions, or should I instead use university professors as reference? Even if they may result in a generic reference letter.  Q. How can I speak with professor B to avoid him writing a generic reference letter about me?


Evaluation of $\displaystyle \int\frac{1}{1+x^6}dx$   $\bf{My\; Try::}$Let $$I = \int\frac{1}{1+x^6}dx = \int\frac{1}{(1+x^2)(x^4-x^2+1)}dx$$  Using Partial fraction , above Integral is very lengthy, Can we solve it without using   partial fraction or any other way, Help me  Thanks

I came across following problem     Evaluate $$\int\frac{1}{1+x^6} \,dx$$   When I asked my teacher for hint he said first evaluate     $$\int\frac{1}{1+x^4} \,dx$$   I've tried to factorize $1+x^6$ as  $$1+x^6=(x^2 + 1)(x^4 - x^2 + 1)$$ and then writing  $$I=\int\frac{1}{1+x^6} \,dx=\int\frac{1}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx=\int\frac{1+x^2-x^2}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx$$ $$I=\int\frac{1}{x^4 - x^2 + 1} \,dx-\int\frac{x^2}{(x^2 + 1)(x^4 - x^2 + 1)} \,dx$$  However $$x^4-x^2+1=\left(x^2-\frac12\right)^2+\frac{3}{4}$$ But I can't see how it helps  I've also tried to reverse engineer the   And I need to have terms similar to $$\frac{x^2-1}{x^4-x^2+1} \quad , \quad \frac{1}{1+x^2} \quad , \quad \frac{1}{(x+c)^2+1}\quad , \quad \frac{1}{(x+c)^2+1}$$ in integrand, How can I transform my cute looking integrand into these huge terms?  Since in exams I will neither have access to WA nor time to reverse engineer the solution moreover it does not seem intuitive,is there any way to solve this problem with some nice tricks or maybe substitutions?


I have a problem in calling a template class I have. I declared a new type name Array, which is a template;  In the .hpp file:  template <typename T> class Array { public:    Array(); };   In the .cpp file:  template <typename T> Array<T>::Array() { //Do something }   In main:  Array<int> arr;   I get Linkage error: unresolved external symbol to the ctor.  Any Idea?

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


Why is the fermi level half-way between the conduction band and valence band?

What does it mean that the  for some semiconductors lie in the band gap?  Is Fermi level definition different from what is know as usual?  We define the Fermi level as the highest level of energy which is occupied by electrons.  Then what is missing here?


I had a Windows / Kubuntu dual boot. In Windows I added a new partition, however I had 4 partitions already. Therefore I think Windows changed all of my partitions' file systems to NTFS. Then all of the partitions appeared in "This PC". Up to that time I had not understood what Windows did with my partitions. I thought that I probably created two partitions instead of one, so I formatted them as Windows prompted. When I restarted my computer I got into rescue mode with a No such partition error. I repaired Windows with a disk installer. Unfortunately now I cannot install Ubuntu. I have one partition which was ntfs before this mess, where all of my important files are located. I have access to it, and I'm sure it's safe. I want to install Ubuntu, but keep that partition.  In the above screenshot, sdbs and sdc are two USB drives. I cannot resolve where my above-mentioned partition went. I can delete and I resized the sda4 partition in KDE Partition Manager, but when I try to install Ubuntu there I get The ext4 partition creation in sda4 failed. After that a window with following message appears:  ubi-partman failed with exit code 141. Further information may be found in /var/log/syslog. Do you want to try running this step again before continuing? If you do not, your installation may fail entirely or may be broken.

I would like to install Ubuntu alongside Windows 7 on a HP G62 Notebook. Although I have installed  Ubuntu in a dual-boot many times before, I found out that this model has already four partitions.    Partitions:   SYSTEM (NTFS, 199MB, used 66.59MB) Partition without any tag: NTFS (579GM, used 129GB)  RECOVERY (NTFS 16.74 GB, used 2.42GB)  HP_TOOLS (FAT32, 103.34 MB, used 13.23MB)   Since I am not an expert with partitions I would like to get advice on how to do this.  My first idea is this one:   Free some space from /dev/sda2 (I don't know if could also free some other space) delete the HP_Tools partition (I have already created a backup) create an extended partition with the free space in #1 containing three parititions: swap (1gb); / (EXT4, 30GB);  /home (EXT4, 120GB)   Another option is to use wubi instead.  What do you think? Is there any other way to achieve this?  PS: I really think this HP policy of using 4 partitions is not a coincidence  PS: I tried using gparted from the live CD and I got a warning message saying that if I freed some space from /dev/sda2 I could create serious issues in the system


Why is gravity called the weakest force? How do we even compare forces? I am not talking about the natural values of the forces that we normally experience in our daily lives.... I mean to say, we don't know the magnitude of any force to it's extremity, right? It can always be larger... So on what basis do we compare forces in general? What is the basis for a fair comparison in this case?

I can understand that on small scales (within an atom/molecule), the other forces are much stronger, but on larger scales, it seems that gravity is a far stronger force; e.g. planets are held to the sun by gravity. So what does it mean to say that "gravity is the weakest of the forces" when in some cases, it seems far stronger?


All I could find is that the genders of statues are reversed if your character/child in Rogue Legacy is gay. Is this really all that happens or is there any kind of additional trade off (benefit/loss) of any kind?  I only found an answer in Wiki so I wanted to double check this.

There seems to be a good amount of traits in this game, and some of them don't have description that actually lets you know what that trait does.  For the sake of proper answer write down all traits available in the game, their description, and their effect.


I was trying to write script using python. i need to avoid repetition of the same tasks and want to write in one.  catlist1 = ['s0.05-k5-a1.0' , 's0.05-k5-a3.0' , 's0.05-k5-a7.0' , 's0.05-k5-a10.0' ] catlist2 = ['s0.05-k7-a1.0' , 's0.05-k7-a3.0' , 's0.05-k7-a7.0' , 's0.05-k7-a10.0']  catlist3 = ['s0.07-k5-a1.0' , 's0.07-k5-a3.0' , 's0.07-k5-a7.0' , 's0.07-k5-a10.0' ] catlist4 = ['s0.07-k7-a1.0' , 's0.07-k7-a3.0' , 's0.07-k7-a7.0' , 's0.07-k7-a10.0']  catlist = [catlist1 ,catlist2 ,catlist3 ,catlist4 ]   i need to call each list inside the for loop. i call all lists inside this single loop. I can do it repititvily by writing multiple times for i in catlist1 and again in catlist2 ..  how could i solve this. thanks   for parName in catlist:               category = '/home/x/Desktop/rouge/ROUGE/Experiments/'       for root, subFolders, files in os.walk(category + parName):         #i = 0          (head, filename) = os.path.split(root)         print filename         #some function that is will re

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


I wish to show a calculation and update a table to help keep track of things. I use siunitx and booktabs in my beamer presentation. I want to have the numbers in the table aligned on the decimal point, which I can do no problem. However, I want to uncover data in the table as I go along. There seems to be a problem with using siunitx.  MWE showing static table...  \documentclass{beamer} \usepackage{siunitx} \usepackage{booktabs} \usepackage{chemmacros}  \begin{document}  \begin{frame}{}  \begin{exampleblock}{Step 6 --- What is the Empirical formula?} Get smallest whole number ratio of moles \begin{table}[htbp] \centering \begin{tabular}{lS[table-format=3.2]S[table-format=3.2]S[table-format=3.2]S[table-format=3.2]} \toprule             &{C}        &{H}            &{O}    & {Totals}\\ \midrule moles (\num{d-4})   &1.417  & 4.25      &0  &0\\ ratio ($\div $ 1.417)   & 1 &2.99       &0  &0  \\  \bottomrule \end{tabular} \end{table}  Empirical Formula is \ch{CH3} \end{exampleblock}  \end{frame} \end{document}   Now if I try to uncover the values in the table...  MWE...  \documentclass{beamer} \usepackage{siunitx} \usepackage{booktabs} \usepackage{chemmacros}  \begin{document}  \begin{frame}{}  \begin{exampleblock}{Step 6 --- What is the Empirical formula?} Get smallest whole number ratio of moles \onslide<2->{\begin{table}[htbp] \centering \begin{tabular}{lS[table-format=3.2]S[table-format=3.2]S[table-format=3.2]S[table-format=3.2]} \toprule             &{C}        &{H}            &{O}    & {Totals}\\ \midrule \onslide<3->{moles (\num{d-4})} & {\onslide<3->{1.417}} &  {\onslide<3->{4.25}}     & {\onslide<3->{0}} & {\onslide<3->{0}}\\ {\onslide<4->{ratio ($\div $ 1.417)}}   & {\onslide<5->{1}  }& {\onslide<5->{2.99}}     &{\onslide<3->{0}}  &{\onslide<3->{0}}  \\  \bottomrule \end{tabular} \end{table} } \onslide<6->{Empirical Formula is \ch{CH3}} \end{exampleblock}  \end{frame} \end{document}   I lose the alignment on the decimal point as enclosing the \onslide<+->{...} in { and } treats the value as text and does not align it. If I do not enclose in parentheses I get an error saying too many $'s or extra}  Now I'm not too bothered about the alignment but if it could be done I would be grateful. I doubt the students would see the misalignment (probably querying why they decided to study chemistry...;>)

I try to make a table with siunitx column type in a beamer document with overlay. Here is a minimal non working example :  \documentclass{beamer} \usepackage{array,tikz}  \usepackage[%     locale=FR,%     detect-all,%     table-number-alignment = center-decimal-marker,     inter-unit-product = \ensuremath{{}\cdot{}},     group-minimum-digits=4]{siunitx} % \num{} ...  \begin{document}  \begin{frame}  \begin{tabular}{S} 3.25 \\ \visible<2->{50.2337} \\ \end{tabular}  \end{frame}  \end{document}   Produces this error message :  ! Extra }, or forgotten $. <recently read> }  l.20 \end{frame}   with the next correction :  \begin{tabular}{S} 3.25 \\ {\visible<2->{50.2337}} \\ \end{tabular}   No error message, but the result is not the one expected.


I am experiencing an issue when trying to simply detect a link button click through javascript. My nav html is spawned through javascript in this way: INDEX.HTML:

  NAV.HTML:

             Home

  INDEX.JS: $.get('/shared/nav.html', function(data) {     $("#nav").replaceWith(data); }); window.onload = function() {        const button = document.getElementById('home-button');      button.addEventListener('click', function() {         console.log("clicked");     }) }  THe javascript should execute after the html has been replaced and find the a element with "home-button" id, but button is always null for some reason... Any idea? Thanks. EDIT: Tried event delegation with no luck. INDEX.JS: $.get('/shared/nav.html', function(data) {     $("#nav").replaceWith(data); }); $("#nav").on('click', 'a', function(event) {     console.log('click.'); });  The rest of the code is identical. EDIT 2: Solution: replaceWith(data) in the javascript was removing the "nav" div, making it impossible to use event delegation. I changed from replaceWith to use innerHTML=... and the event delegation worked.

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I recently saw the following "proof" online, and couldn't pinpoint where the mistake was made:    From a well known property, $$1+2+3+\cdots = -\frac{1}{12}.$$  Multiplying both sides by $-1,$ we get $$-1-2-3-\cdots = \frac{1}{12}.$$  We can thus rearrange these equations as follows:   \begin{align*} 1+2+3+4+\cdots= \, -\frac{1}{12} \\ -1-2-3-\cdots= \; \: \, \, \frac{1}{12} \\ -1-2-3-\cdots= \; \: \, \, \frac{1}{12} \\ 1+2+\cdots =  -\frac{1}{12} \end{align*} Adding, the RHS clearly sums to $0$, while the LHS yields $1$, seemingly yielding that $0=1$. Where did this proof go wrong?

I am not mathematician by any means so this question might be rather stupid. I came across this Wikipedia article on  and found this bewildering formula,   $$1 + 2 + 3 + \dots  = - \frac1{12}$$  The article also says that "Ramanujan summation of a divergent series is not a sum in the traditional sense". I am wondering then what this summation actually implies?  Is there any interpretation of this confounding result in the physical world that someone not so math-savvy can understand?


Sometimes I am writing for two audiences. I have a complete document with extra footnotes and perhaps extra background paragraphs for an ordinary reader. And another version that omits this background detail which is considered assumed knowledge in the other audience.  Is there a latexy way to handle this kind of thing that is not overly cumbersome?  UPDATE: Sorry if this was a little unclear. I am not interested in working out how to manually 'comment out' sections of text.  I want to be able to setup a 'flag' of some sort which outputs a condensed version of the document with fewer footnotes, and an expanded version of the document with additional footnotes.

To "comment out" a line, I need to insert a % at the beginning of the line (so that the line will not be compiled). Is there a way to comment out a large section without having to manually place % in front of each line?


Please help me to find an example of a group epimorphism $f:G\to G$ which is not an isomorphism.   I understand that $G$ should an infinite group.

Let $G$ be any group such that  $$G\cong G/H$$ where $H$ is a normal subgroup of $G$.  If $G$ is finite, then $H$ is the trivial subgroup $\{e\}$. Does the result still hold when $G$ is infinite ? In what kind of group could I search for a counterexample ?


If $$a_nx^n+\cdots +a_0$$ is irreducible over some field, the polynomial $$a_0x^n+\cdots +a_n$$ with the coefficients reversed is irreducible over the same field as well.   Suppose the polynomial can be expressed as product of two polynomial the original polynomial will be reduced. Thats what I want to do but I ran out of idea. can someone help me?

Given that  $f(x)=\sum\limits_{k=0}^n a_kx^k$ is an irreducible polynomial, show that $g(x)=\sum\limits_{k=0}^n a_kx^{n-k}$ is irreducible too. I don't see how this specific coefficient exchange would preserve the irreducibility. Is there something else I should be looking at?


I Need to know how to Ungroup Meshes that were Previously joined Without Undoing History.   I Am attempting to ungroup things like . If you select anything on the models in there you will notice they are a big mesh made with the CTRL J Trick  I Need to know how to Ungroup it from that.  (Unless it can't be done. -_- and i have to try to recreate the meshes entirely)

I've just made a set of armor by using a male body mesh model I downloaded and selecting certain faces from the model and duplicating them to create viable armor pieces.   Since the pieces are just duplicated from the same mesh male model, then it's still part of the same object.   How do I separate the armor piece from the model to make the pieces separate?


I have an API which will create the report and we need to pass the JRXML content(whihc is passed as string from UI) for that,Now I want to compile the JRXML content before saving it into data base,One approach I have is that I can save the JRXML content into file system and then load that file and compile it,But I don't like it because if the compilation failed I need to delete that file from file system, So  wondering If I can compile the input JRXML content only before storing it into file.  I am passing the JRXML as a string to my method which should compile that JRXML string, but I don't want to store the content in file and then compile it

How can I transform a String value into an InputStreamReader?


I have a 3.46 overall gpa ( I'm retaking organic chemistry, so it should be closer to a 3.6 or a 3.7 by the time I graduate) and a 3.7 in my Biology major. My gre scores are pretty shoddy, not gonna lie. While I'm retaking it later on in the month, I'm currently in the 82nd and 86th percentiles for my verbal and writing respectively, but my quant is only in the 30th percentile. I have A's and B+'s in all my math courses, and I even work as a calculus tutor at my school. I have been doing independent research for the past 2 years and I've even participated in a 10 week research program at another university. I'm so worried that I won't get in anywhere. I really want to be out west, either at the University of Washington or OHSU but any funded program that has good research mentors will do. Do I have even a slight chance of getting in somewhere?

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


I have installed Ubuntu 17.04. For a while it worked great. Then I have installed a couple of packages which I don't remember. When I rebooted my laptop, I couldn't login from the default login desktop environment. Every time I try to login, it accepts the password, but loopsback to login screen again. But from the Unity8 desktop environment I can login without a problem. its not a startx, lightdm,owner problem etc..

My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M


I'm a PHP novice, trying to validate HTML form submission via PHP learned in a tutorial.   Code uses mysql_real_escape_string which PHP.net  is deprecated.  Here's an excerpt of that entire section:  /*Cleans an array to protect against injection attacks.*/ function f_clean($array) {     return array_map('mysql_real_escape_string', $array); }   What, if anything, should I add or change in the PHP in order maintain this security measure?

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


Has my iPhone been hacked?  Part I: The FaceTime Call  Yesterday evening, after turning on Do Not Disturb mode for the night, my phone begin to ring (an incoming FaceTime call) with a ringtone I have never used. The caller was not on my favorites list (so the call should not have made noise since I was on DND). That caller is my co-worker at the office, and claims to have not called me (and indeed his phone has no record of the outgoing call).  Part II: The Outgoing Text Messages  Today, I noticed an unsent text to several phone numbers I do not know (and a few I do know, some of my friends) with a political message I do not support. This wasn't me sending it, so what happened?  Part III: The Suspicious Calendar Events  As detailed in , I'm having spam calendar events appear as invitations.  Conclusion  I have no idea what is going on with my iPhone! Have I been hacked? What can I do to resolve this problem with my iPhone?

Today I've suddenly received spam calendar invitation for $19.99 Ray Ban sunglasses (never subscribed, checked, searched or visited any related site, so clearly spam) and it has other visible email accounts within the invitation. I'm wondering if I should be worried whether my accounts been compromised or a simple email from anywhere just plops this in my calendar without review. Questions to be answered:  What should I check/setup in order to make sure my iCloud account is safe? How can I delete this invitation without sending a notification to the sender, so as to prevent them from knowing my email address is live? How can I prevent these notifications in the future?  Here's an image:


I got this question after I leant about microscopes and telescopes from my textbook. In a simplified compound microscope, the objective has a smaller aperture and a smaller focal length compared to the eyepiece, as shown below:     In a simplified astronomical telescope, the objective has a larger aperture and a larger focal length compared to the eyepiece, as shown below:    In both simplified versions of a microscope and a telescope, there is one lens which has a larger aperture and a larger focal length compared to the other lens. In both of the these optical instruments the tube length could be adjusted. Whether the larger lens faces the object or the observer depends upon the use - whether it's to observe a distant star or a nearby bacteria.   So, theoretically, is it possible to use an astronomical telescope as a compound microscope and vice versa? I think the answer must be yes due to simple logic and principle of reversibility of light.    Please note: My question is different from this one -  - which asks about the reason due to which we choose different apertures and focal lengths of the objective and the eye piece. Further, from my initial Google search results, I found  Quora answer which states "...compound optics that magnify one way un-magnify in the other" but this contradicts my understanding of the principle of reversibility of light.  Both images are from Physics Part-II Textbook for Class XII (NCERT) |

In compound microscope, we take such an objective lens which has small focal length. While in astronomical telescope, we take such an objective lens which has large focal length.   Why don't we use same objective lens in both? The function of both the devices is to enlarge an object at infinity.


What is the minimal polynomial of $\sqrt{3} + \sqrt[3]{2}$ over  $\mathbb{Q}$?  I know the basic idea of what a minimal polynomial is--it is the lowest degree monic polynomial in $\mathbb{Q}[x]$ that has the above as a root. But how do you go about calculating it? How do you know intuitively if it does or doesn't exist?

Suppose I want to find the minimal polynomial of the number $\sqrt[3]{2} + \sqrt{3}$.   Now that means I want to find a  unique polynomial that is irreducible over $\Bbb Q$ such that $f(x)=0$. Now I know that because   $\sqrt[3]{2} + \sqrt{3}$ belongs to $\Bbb Q( \sqrt[3]{2} , \sqrt{3})$  it might be degree $2$, $3$ or $6$ and does not belong to $\Bbb Q( \sqrt[3]{2})$ so it cannot be of degree $3$ or  $\Bbb Q( \sqrt{3})$ so it cannot be of degree $2$.  So it is of degree $6$. I think my sayings are a bit intuitive and not formal and lack rigorous. Couldn't it belong to another extension of degree $2$? or $3$? I can't answer that. Why checking only those $2$ is enough? Or is it wrong at all to say that?


One of my players is considering multiclassing warlock/cleric. I have not played warlocks or had other players use them so I am looking into the casting mechanics. After looking at other threads I think I have the idea down. Something like a warlock 1/cleric 5 would have the cantrips and 1 warlock slot that can cast at first level and the cleric would provide up to 3rd level spell slots. my confusion comes from  Pact Magic: If you have both the spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the spellcasting class feature, and you can use the spell slots you gain from the spellcasting class feature to cast warlock spells you know.  so they would be able to cast warlock spells up to 3rd level with the cleric 3rd level slot, as evident from answers to , but would they also be able to cast fireball (in the case of a light domain cleric) using their warlock slot but doing so at 1st level? If so how would this translate to an end game build? would the cleric then have the equivalent to 2 9th level slots? I am assuming this does not work this way and the initial build listed essentially just has a slightly expanded spell list and an extra 1st level slot that comes back on a short rest, but I just want to make sure I am not missing something so I can explain this fully in the future.

Reviewing an answer to a recent question I posted, I had a thought about Armor of Agathys. In the event of a Sorcerer 18 / Warlock 2 build, would the character be able to cast Armor of Agathys with a 9th level spell slot, thus getting 45 Temporary Hit Points and dealing 45 damage when hit?   Is the spell in any way limited to being cast using Warlock spell slots or to a maximum of a 5th level spell slot?


guys! I apologize in advance if this question comes up often here. I'm a very beginner using Ubuntu and I'd appreciate any help to keep using it. I usually work with a mac and a windows computer, but now I've decided to install ubuntu on my windows laptop. It's been great so far (I've installed 12.04 precise pangolin). However I travel a lot and often I use some websites and softwares which do not work in the other countries where I've been travelling.  While using Windows I used FlyVPN and TunnelBear to fake an ip adress in USA or UK (where I currently live).  So, could you guys tell me how can I make the same? I've been searching on google for days and I still didn't find a solution.. maybe my lack of knowledge when it comes to ubuntu.. I appreciate any help! Thanks!

Goal: I want to be able to securely use the internet via my home PC while my notebook is connected to an open hotspot/access point.  I do know that I can use a SSH tunnel/SOCKS proxy, but I don't want to fiddle around with applications (making them use it, if even possible). I guess what I need is an OpenVPN setup, so I'm looking for a detailed guide on how to:   Install and setup the OpenVPN server Setup the OpenVPN client (NetworkManager)   Ubuntu versions this should work on are 10.10 and 11.04.


Stuck while doing question 10, can't proceed onto doing. Need some advice/solutions regarding this. Managed to solve question 11 already so don't need solution for that question anymore.  Thanks in advance!

How to integrate this?     Evaluate   $$\lim_{x\to0}\frac{\displaystyle\int_0^x(x-t)\sin t^2\ dt}{x\sin^3x}.$$   I've had difficulty in using L'Hopital rule. At the same time failed to really understand how to differentiate or evaluate the limit of the $x\sin^3x$ and $\int_0^x(x-t)\sin t^2\ dt$  Would like to appreciate your help


document.body.style.backgroundColor="#F00";   This statement styles the body background color as red.  In my original code I have a function that assigns elements by tag name to a global variable element. I've found after calling this function I can do this: element.style.backgroundColor="#F00";  However, there doesn't seem to be ANY way to substitute for the property section of the statement. Below I've produced the most obvious approach, though I have also tried assigning the parameters to variables and various combinations of quotation.    function assignStyle(value) {   document.body.style.backgroundColor = value; }  function attemptStyle(property,value) {   document.body.style.property = value; } button { font-family: monospace; } <button onmouseover="assignStyle('#131519');" onmouseout="assignStyle('#FFF');">   function assignStyle(value){} </button><br />  <button onmouseover="attemptStyle('backgroundColor','#137619');" onmouseout="attemptStyle('backgroundColor','#FFF');"> function attemptStyle(property,value){} </button>     Edit: This question is not a duplicate of . That question contains jQuery, which many people, including myself, know literally nothing about. My question is concerned with basic JavaScript. Also, I want to know how to add a property to an element, and so by means of passing an argument to a function parameter. As far as I'm concerned, variables complicate the question further.

I'm pulling items out of the DOM with jQuery and want to set a property on an object using the id of the DOM element.   Example  const obj = {}  jQuery(itemsFromDom).each(function() {   const element = jQuery(this)   const name = element.attr('id')   const value = element.attr('value')    // Here is the problem   obj.name = value })   If itemsFromDom includes an element with an id of "myId", I want obj to have a property named "myId". The above gives me name.  How do I name a property of an object using a variable using JavaScript?


I am a complete new-be when it comes to Linux and even more so when it concerns Ubuntu.  I want to configure the IPv4 settings to have automatic assigning of IP address but manual assigning for DNS. How do I do it?  Please teach me how to do it step by step.  Please take a look at the image to get an idea of what I am asking.  Thank you in advance.  Windows DNS settings example:

Is /etc/resolv.conf useless in  (Precise Pangolin)?  I see that the DNS server information is stored in  now. The nmcli command line tool can list that for you.  If I want to add one more  server, will adding it to /etc/resolv.conf by using the resolvconf package help?


Why wasn't Contance Spano, David Levinson's wife, in Independence Day: Resurgence? Did I miss a bit of exposition about her absence?

In the movie Independence Day (1996), there is a romantic subplot featuring David Levinson (played by Jeff Goldblum) and Constance Spano (played by Margaret Colin), leading to one of my favorite bits of dialog from the movie:     Julius Levinson: There was a lot of love there.   David Levinson: Love was never our problem.   In the movie Independence Day: Resurgence (2016), many actors from the first movie returned, and Jeff Goldblum was one of them.  But Margaret Colin did not return.  I'm actually interested in both the in-universe explanation and the real-world explanation.  Do we know either one?  Here's what I have found:   an  with Jeff Goldblum where he says there is an in-universe explanation but he doesn't say what it was. a  that says the character was killed in a car crash during the events of the novel Independence Day: Crucible.  Is that novel canon with the movie?


i would please to extend the size of nvme0n1p5 partition with the unallocated partition its on a dual boot machine. any suggestion please.

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


i was deported from uk in march 2015 on the basis of overstayer which occur after my ex wife age is not up to 21yrs by the time of marriage due to changing of marriageable age from 18-21yrs which my solicitor didn't informed us by then until my application was refused though they gave us a right of appeal but my solicitor kept it from us for a year until we decided to withdraw our file from him. we send for reconciliation which nothing happened for 4yrs till 2014 when i was served with a letter of liable to deportation/ detention without any criminal record atall. I have a daughter for a person settled in uk but not british yet and the child did not have a passport yet which i mentioned during the proceeding and obtain a court order under a family law that i'm the father of the child though she was in a relationship with an european citizen by the time of birth of the child which they are officially divorced now and i have a sister that has a british pp and children which i stayed with when i'm in uk which followed me to the proceeding during my hearing in court under appeal. pls when can i apply to see my daughter and is it best to apply to see my daughter or my family. please advice me on what to do and when can i apply to see my daughter not to stay but to see her maybe just for a week.

As I understand it, there are two mechanisms for throwing somebody out of the UK: deportation and removal. Informally, people seem to call both of these "deportation".  What are the differences between them? Who do they apply to? Do they have different effects on the person's ability to return to the UK later?


I'm looking for  a java regex that will return true if a string   contains any char[including special char _(underscore) and -(hyphen)]    more than 3 times.      example :  Heloooo --->True hellooo --->Flase  Heleoeoe---> False      got one \w{0,2}$ working fine for JS but not for JAVA Can anyone help,   thanks in advance?

What regex pattern would need I to pass to  java.lang.String.split()  to split a String into an Array of substrings using all whitespace characters (' ', '\t', '\n', etc.) as delimiters?


I am trying to figure out why I have white spaces in some of my table cells between some words. This is how the problem looks like:   This is the code that I use:  \begin{table}[ht] \centering \fontsize{9}{12}\selectfont \tabulinesep=1mm \begin{longtabu} to \textwidth {|l|X|X|X|l|l|} \hline   \textbf{Step No}   & \textbf{Test Cases}   & \textbf{Expected result}   & \textbf{Actual result}   & \textbf{Status} \endhead \hline 1 & The user starts the mobile application and performs 5 minutes of \textbf{walking}. & The system should recognise that the user is performing \gls{pa} and increments \textit{Active} time.  & Works as expected e.g., updates the \gls{ui} by adding 5 minutes to the \gls{pa} progress bar in \textit{Today} \& \textit{History} screens. & Pass \\ \hline 2 & The user starts the mobile application and performs 5 minutes of \textbf{running}. & The system should recognise that the user is performing \gls{pa} and increments \textit{Active} time.  & Works as expected e.g., updates the \gls{ui} by adding 5 minutes to the  \gls{pa} progress bar in \textit{Today} \& \textit{History} screens. & Pass \\ \hline \end{longtabu} \caption{Monitoring activity functional test snippet} \label{tab:monitoring-com-ft} \end{table}   Any ideas why this might be happening? Thank you in advance!

I'm working with booktabs package. My goal is to get the same space between each word.   For example: LaTeX TikZ, tabular myframed titleps. \ Not like this one: LaTeX~~~~~TikZ,~~~~~tabular~~myframed~~~titleps .  Code sample:  \documentclass[twoside]{article} \usepackage[utf8]{inputenc} \usepackage[MeX]{polski}  \usepackage{array}% http://ctan.org/pkg/array \usepackage{booktabs}  \usepackage{tabularx} \usepackage{longtable}  \usepackage{xcolor}  \usepackage[left=4.50cm, right=4.50cm, top=3.50cm, bottom=3.50cm]{geometry} \frenchspacing  \makeatletter     \renewcommand\@seccntformat[1]{\csname the#1\endcsname.\quad}     \renewcommand\numberline[1]{#1.\hskip0.7em}     \renewcommand\quote{\list{}{\leftmargin=10pt\rightmargin=0pt}\item[]}  {\endlist}         \newcommand{\ra}[1]{\renewcommand{\arraystretch}{#1}}     \newcommand{\rr}{\raggedright}      \newcommand{\tn}{\tabularnewline} \makeatother  \begin{document}   \begin{table}[!ht]  \ra{2}  \setlength\tabcolsep{3pt}  \ignorespaces  {\setlength{\extrarowheight}{5pt}%  \begin{tabular}{m{\dimexpr.25\textwidth-2\tabcolsep-0.8pt}                 m{\dimexpr.35\textwidth-2\tabcolsep-0.4pt}                 m{\dimexpr.35\textwidth-2\tabcolsep-0.4pt}}\toprule    \textbf{Item 1} &\textbf{Item2}& \textbf{Item3 someLongerWord}\\ \midrule  \textbf{SubItem1 some text someLongerWord}\rr  & Lorem Ipsum jest tekstem  stosowanym jako przykładowy wypełniacz w przemyśle poligraficznym. Został po raz    pierwszy użyty w XV w. przez nieznanego drukarza do wypełnienia tekstem próbnej książki. & Lorem Ipsum jest tekstem stosowanym jako przykładowy wypełniacz w przemyśle poligraficznym. Został po raz pierwszy użyty w XV w. przez nieznanego drukarza do wypełnienia tekstem próbnej książki. Pięć wieków później zaczął być używany przemyśle elektronicznym, pozostając praktycznie niezmienionym.          \\  \addlinespace[4pt] \midrule   \textbf{SubItem2 some text} & Przeciwstawne wyobrażenia i~pojęcia występują razem i~mogą wzajemnie siebie zastępować. & Pogardzany nauczyciel wychowania fizycznego reprezentuje w~pamięci uwielbianego nauczyciela sztuki.\\   \addlinespace[4pt] \midrule    \textbf{Reprezentacja przez analogię bądź aluzję}\rr& Części obiektu bądź pamięci reprezentują całość. Podobne wyobrażenia są~wzajemnie swobodnie wymienianie. & Wyobrażenie huśtawki reprezentuje czas spędzony w dzieciństwie na zabawie z~ojcem.  \\\addlinespace[14pt] \midrule   \textbf{Płynność form}\rr& Wyobrażenia wrażeń zmysłowych odpowiadają słowom czy pojęciom. & Uczucie dreszczy z zimna reprezentuje gniew mężczyzny, który umówił się na randkę w ciemno i~czeka w padającym śniegu na~kobietę, która nie przychodzi.  \\ \addlinespace[4pt]\midrule   \textbf{No Time At All someLongerWord}\rr& Brak logicznego czy czasowego następstwa. Przeszłość, teraźniejszość a~nawet przyszłość stanowią jedną całość. & Obecny mąż pojawia się we~śnie odnoszącym się do~wcześniejszego etapu życia żony.  \\  \bottomrule  \addlinespace[10pt] %  \end{tabular}}  \small\caption{\small Charakterystyczne cechy poznawcze procesu pierwotnego}  \end{table} \end{document}


I'm writing my manuscript for my thesis and this the package that I'm using for the fonts :  \usepackage{lmodern} \usepackage{ae,aecompl}   I was reading a physical book and I want to know which type of font the author is using for his template.    Thank you

Is it possible to identify the font used in a specific document/picture?  Answers to this question should identify:   Possible methods to do this (perhaps one answer per method) and adequately describe how to use it (as opposed to merely stating it); Ways of finding the identified fonts, if possible (free or not); and Any prerequisites associated with the method used, if required (for example, "In order to use method X, your document has to be in format Y").   This question is meant as an FAQ, based on an . Its aim is to facilitate the community with the general procedures involved in font identification. Similar cases are solved on a per-usage basis on 's  tag.


Its a Problem from  Michael Nielsen quantum computation and quantum information

This question refers to Nielsen and Chuang's Exercise 4.22:   Prove that a $C^2(U)$ gate (for any single-qubit unitary U) can be constructed using at most eight one-qubit gates, and six controlled-not gates.    To prove this, I decomposed all $C(V)$ operations into $AXBXC$ form and ended up with 9 single-qubit gates and 8 C-NOT gates. So I need to now get rid of one single-qubit gate and 2 C-NOT gates. To do the former, I changed the order of $V's$ and got rid of 2 single-qubit gates with combining 2 pairs of single-qubit gates.  For example: as $C=R_z((\delta - \beta)/2)$ and $A=R_z(\beta)R_y(\gamma/2)$  became                 $CA=R_z((\delta - \beta)/2)R_z(\beta)R_y(\gamma/2)$   For the CNOT gates, I can't touch the 2 C-NOT operations on qubits 0 and qubit 1 because they are important for the functioning of $V^\dagger$. The only way then is to reduce the 4 CNOT gates that compose the 2 $C(V)$ gates. I am encountering some difficulty here. Any help/hint will be appreciated.   *This is not a homework question. I am self-studying from Nielsen and Chuang for an independent project.


I try to create a table like to one here:    I tried many options with \multirow and \multicolumn, however, after few hours I'm not even close to the final result.  Any ideas how could I achieve this?

When I used this piece down, I got.  \documentclass[a4paper,12pt]{report} \usepackage[inner=0.75in,outer=0.65in,top=0.75in,bottom=0.75in]{geometry} \usepackage{graphicx} \usepackage{url} \usepackage[sc]{mathpazo} %\usepackage{mathptmx} \usepackage{url} \usepackage[onehalfspacing]{setspace} \usepackage{parskip} \usepackage{paralist} \usepackage{multirow} \begin{document} \begin{table}[!htb] \centering \caption{Present Strength-Production} \begin{tabular}{|c|l|l|c|c|c|c|c|c|} \hline \multirow{2}{*}{Sl.No} &  \multicolumn{2}{c|}{\multirow{2}{*}{\textbf{Designation}}} &  \multicolumn{4}{c|}{\textbf{Shifts}} &\textbf{Leave/Off} &  \multirow{2}{*}{\textbf{Total}}\\ \cline{4-7} & & &\textbf{A} & \textbf{B} & \textbf{C}& \textbf{G}&\textbf{Reserve}&\\ \hline 1 & \multicolumn{2}{l|}{Plant Engineer} & & & & 1& & 1\\ \hline \multicolumn{3}{|l|}{\textbf{Sub Total}} & & & & \textbf{1} & & \textbf{1}\\ \hline 2&\multirow{2}{*}{Operator}&Work related to water regeneration&1&1&1&&1&  4\\ \cline{3-9} 3& & Work related to valve control& 1&1&1& &1&4\\ \hline \multicolumn{3}{|l|}{\textbf{Sub Total}}&\textbf{2}&\textbf{2}&\textbf{2}& &\textbf{2} & \textbf{8}\\ \hline 1 & \multicolumn{2}{l|}{Worker} &2 & 2& 2& & 2& 8\\ \hline \multicolumn{3}{|l|}{\textbf{Sub Total}} &\textbf{2}&\textbf{2}&\textbf{2}& &\textbf{2} & \textbf{8}\\ \hline \hline \multicolumn{3}{|l|}{\textbf{Total}} &\textbf{4} &\textbf{4} &\textbf{4}  &\textbf{1}&\textbf{4} & \textbf{17}\\ \hline \end{tabular} \label{tab:pro_pro} \end{table} \end{document}     Can anyone show me the right path?  Certain important things are   The starting place of Sub total and Total should be from the second column The vertical line in the Designation box Horizontal line between 2 and 3


Let $S$ be the set of all $3\times 3$ matrices over $\Bbb Z$ such that the product $AA^t=I$. Then find $|S|$?  Taking $A=$\begin{bmatrix} a & b &c \\d & e& f\\g & h & i\end{bmatrix} we get $3$ relations $a^2+b^2+c^2=1;d^2+e^2+f^2=1;g^2+h^2+i^2=1;$  How should I count from here?

Find three real orthogonal matrices of order $3$ having all integer entries.   I have no idea to solve the problem. I don't know how to start. If $A$ be such matrix then $AA^T=A^TA=I_3$. Please help me.


Is it calculated on the fly every time a reputation score needs to be displayed, or is every user's reputation stored as an integer in the database and updated as necessary?

I want to implement something similar to Stack Exchange's reputation system. What would be the better practice: using an SQL aggregate function to recalculate every time it changes, or storing reputations in a table and manually altering it every time reputation goes up or comes down? How does Stack Exchange's implementation work?


I have to find $$\sum_{n=1}^\infty \operatorname{arccot}(n^2-n+1)$$ and trying to compute sum of this series. I'm trying to take the derivative of member of the series and compute another sum, but this is not very successful.  Is it right way to try take the derivative or it is useless in this situation? I can't see how to simplify this monster.

This is from a GRE prep book, so I know the solution and process but I thought it was an interesting question: Explicitly evaluate $$\sum_{n=1}^{m}\arctan\left({\frac{1}{{n^2+n+1}}}\right).$$


Find all $n\in\mathbb{Z}^+$ such that the sum of the digits of $5^n$ equals $2^n$   Starting with a table of values, I found that $n=3$ works. Beyond this, it's hard to imagine any other number working. As $n$ gets larger, it seems to me that $2^n$ grows far more rapidly than the sum of the digits of $5^n$ would ever be able to "catch up" to.  My reasoning: multiplying by each $2$ doubles $2^n$, but multiplying by each $5$ adds (I think) at most $1$ digit to $5^n$, which would add at most $9$ to the sum of the digits of $5^n$. Another way of looking at it, suppose $n=1000000$. Notice that $5^{1000000}<10^{1000000}$, which is $1$ with $1000000$ zeros. Thus $5^{1000000}$ has at most $1000000$ digits, and the sum of its digits would be maximized if those digits were all $9$s. Then the sum of the digits of $5^n$ would be $9\cdot1000000=9000000$, which is far less than the number $2^{1000000}$.  But is there a way to prove this using theory?

Find all $n\in\mathbb N^+$ such that the sum of the digits of $5^n$ is equal to $2^n$.   I've solved this, but I think the proof is a bit weird and I wonder if there's a better one.    My proof:  We can see that $n\neq 1$, $n\neq 2$, $n=3$, $n\neq 4$ and $n\neq 5$.  Let $n>5$. Notice that $5^6$ has $5$ digits, while $\frac{2^6}{9}=7\frac{1}{9}$, so $5^6$ has to have at least $8$ digits in order for the sum of the digits to be able to at least reach $2^6$.  Everytime $1$ is added to the exponent of $5$, the amount of digits $5^n$ gets is at most $1$, while $\frac{2^{n+1}}{9}-\frac{2^n}{9}=\frac{2^n}{9}>3$, so the lowest amount of digits it has to have to reach $2^n$ becomes higher by at least $4$.  When $n=6$, the amount of digits $5^n$ has is already lower than the amount it has to have in order to reach $2^n$, and I've just proved that the amount it has to have in order to reach $2^n$ grows faster than the amount of digits $5^n$ has, therefore $5^n$ will never be able to reach $2^n$ when $n>5$.  Hence the only solution is $n=3$.


If so, why would you apply another rotation after you already found the "variance-maximizing" - and in that sense optimal - rotation. Wouldn't the second rotation lead to a - again - non-variane-maximizing situation?  Please enlight me.

As far as I understand,  principal components are obtained by rotating the coordinate axes to align them with the directions of maximum variance.   Nevertheless, I keep reading about "unrotated principal components" and my statistics software (SAS) gives me varimax-rotated principal components as well as the unrotated ones. Here I am confused: when we compute principal components, the axes are already rotated; so why is there another rotation needed? And what does "unrotated principal component"  mean?


I used the following code to introduce to logo in my document:   \titlegraphic{\includegraphics[width=2.5cm]{lit}\hspace*{5cm}~%    \includegraphics[width=3.5cm]{uvt2} }   how should i proceed such that the two logos to be on the first slide at the same position.  Now I obtained the following picture:

In a beamer presentation, I am using the following code to add logos on my title page:  \titlegraphic{   \includegraphics[width=3cm]{logo-lirmm.png}   \hspace*{0.75cm}~%   \includegraphics[width=3cm]{logo-york.png}   \hspace*{0.75cm}~%   \includegraphics[width=3cm]{logo-dc.png} }   This code aligns vertically the three logos at the bottom. How can I center them vertically?


Like If I have :     1st line (keep)   2nd line (keep)   3rd line (keep)   4rth lines (delete)   5th (del)   6th (keep)   7nth (keep)   8th lines  (keep)   9th (del)   10th (del)   11th (keep)   12th (keep)   13th (keep)   14th (del)   15th (del)     etc....

I have a large file and I would like print from each sequential 50 lines , the 15th and 25th lines.  sed -n '15,25p' inputfile   How to modify this command to print only lines 15 and 25 and to loop over each 50 lines in the file.


Sorry for the elementary question on here, but I am trying to wrap my hand around why we define the p-value as the probability (assuming the null hypothesis is true) that we obtain a result as or more extreme than our observed result. I am specifically puzzled about this "or more" part. Why are we concerned with values that are more extreme than our result and not just as extreme? We do not observe values that fall within the region described by the p-value, so why use this approach? I understand that it is impossible to define an area under the curve of the assumed distribution at a single point, and so that we need to look at a region of the curve in order to talk about probability. Given this, it is much more intuitive to me to define a rejection region (e.g. the combined 5% of the area of the curve at either tail) before obtaining the results, and reject the null hypothesis if our observed result falls within that region. In short, why do we employ a statistic that is necessarily defined by more extreme values than our result if in fact we do not observe those more extreme values? Hope this all makes sense.

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests.  It seems that students easily learn how to perform the calculations required by a given test but get hung up on interpreting the results.  Many computerized tools report test results in terms of "p values" or "t values".  How would you explain the following points to college students taking their first course in statistics:   What does a "p-value" mean in relation to the hypothesis being tested?  Are there cases when one should be looking for a high p-value or a low p-value? What is the relationship between a p-value and a t-value?


So, I've been trying to set up a game over LAN with my brother. We're both running our own accounts, both on the same network, using Update 1.6.4. However, I'm running on Linux Mint while he's running on Windows 7. When he sets up a LAN game, I can see it in the multiplayer menu but when I try to connect it gives me the error:   io.netty.channel.connecttimeoutexception connection timed out:     This is the only text on the screen, besides the cancel button. When I try to set up a LAN game, I click Open to LAN but it doesn't show up on his list of servers.  Any help would be much appreciated.

My LAN server won't let my cousin join me or me join my cousin. It won't show up on the multiplayer screen - it keeps saying "scanning for LAN servers" but it never finds it. I am at his house and we use different computers but it won't connect. How can I fix this?


Current situation   Tags should not into titles. In an opened question, tags are shown at the very bottom of the question.   Problem   If a question was opened via a websearch site (which does not show tags): One has to scroll down all the way until the end of the question, to see if the question really affects oneself   Suggestion   Move the list of tags right below the title. Maybe like this:

It happens to me rather often that I look at a question such as "How to do whatever with Collections" and while that's what I'm looking for in Java, it's useless if the question refers to, for instance, C#.  So, this is purely a UI thing: how about putting the tags right under the question title, rather than arbitrarily far under the question text itself?  EDIT: here's what I mean


I would like to ask why the following sentence is only possible according to grammatical rules:     I'm reading a novel of Steinbeck's   What's wrong with "I'm reading a novel of Steinbeck" or "I'm reading Steinbeck's novel"?

As  shows, we nearly always use the possessive form of personal pronouns for friend of mine/his/ours/etc.  But when it comes to actual names, we prefer  without the possessive apostrophe. That preference is even more marked with, say, . Not that I think the usage itself is particularly American - it's much the same with .  Personally, I find friend of him grates. In general I've no strong feelings either way as to whether it's friend of Peter or friend of Peter's (though I deplore the possessive in ), but in line with many others, I really don't like the possessive in relation to things like countries.  Why is this?   Edit: Noting an apparent "progression" (pronoun -> person -> nation) marked by reduction in use of the possessive, I checked at a finer "granularity". NGram shows that although it does occur,  virtually "flatlines" against friend of mine. But the bias reduces through of you, of us, and by the time I get to  it's much less extreme. There seems to be something "egocentric" about the double possessive.  Presumably when babies learn to speak, they soon notice that possessive pronouns, possessive apostrophes, and the word "of", all do the same job. Parents would correct a child who says "of mine's", but probably wouldn't even notice the same "redundancy" in "of Peter's". Younger speakers are unlikely to even be talking about something "of America's". Perhaps as we mature we tend to discard the "double possessive" for the more "distant" things that only adults are likely talk about, but we keep it for "closer" people because that's how we spoke when we were younger.  EDIT2 I note that I'm a great fan of him is vanishingly rare compared to ...fan of his, but with ...fan (of John) the double possessive occurs far less often than ...friend (of John's). Usage seems to be affected by the noun before "of" as well as the one after it. This is getting complicated...


Given $X$ a topological space and $A\subset X$, find an example where there exists $x ∈ \overline{A}$  which no sequence in A converges to $x$

Let $(X,\tau)$ be a topological space, $\emptyset\neq A\subseteq X$ and $(x_n)$ be a sequence in $A$. I could easily show that any limit of $(x_n)$ belongs to $\overline{A}$. My note says that if $x\in\overline{A},$ $x$ is not necessarily a limit of a sequence in $A$. But I cannot find a counterexample. Now in my attempt to find a counterexample, which I failed, I could conjecture that if the topological space is metrizable then, if $x\in\overline{A}$ then $x$ is a limit of a sequence in $A$. Is my conjecture true? And how would you find a counterexample to the original problem? Please help. Thanks.


While doing inequality problems from a exercise I stuck on the following two problems.   $1.$ If $a,b,c$ be positive real numbers, such that the sum of any two is greater than the third, prove that $a^2 (p-q)(p-r)+b^2 (q-p)(q-r)+c^2 (r-p)(r-q)>0$ for all real $p,q,r.$  $2.$ If $a,b,c$ be positive real numbers, not all equal, and $n$ is a negative rational number, prove that $a^n (a-b)(a-c)+b^n (b-a)(b-c)+c^n (c-a)(c-b) >0$ No need of a full solution. Just give me some hint. I want to do this myself

If $a,b,c$ are the sides of a triangle and $p,q,r$ are positive real numbers then prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$  After modification. I have to prove $(a^2 p^2+b^2 q^2 + c^2 r^2) \ge pr(a^2+c^2-b^2)+qr(b^2+c^2-a^2)+pq(a^2+b^2-c^2)$


So I used to hate Ubuntu Software Center (SC) in 14.04 and 16.04 because it was very buggy and nothing really worked. Now with 18.04 everything works perfectly and installing flatpak plugin for it opens the door to a lot more software and newer. So, snaps, flatpaks, and the other ones, SC is a great and super easy tool to find pretty much anything. I moved away from installing via the terminal as I used to, but I lack something now: I used to also backup my sources.list so when I would install Ubuntu again I could easily reinstall all of my software again. Not anymore now since I install them via SC.  My question is: how do I backup all of my installed software that is done via SC? Would love to see something as simple as "reinstall all your apps" option. SC should have such an option.  Thanks!

I know, I just can hit Super+A to see all installed apps in Ubuntu, but I need a command to list their names. The command  dpkg --get-selections | awk '{print $1}'   is also not an option because it shows all installed packages and it contains drivers, kernels and libraries.


I'm working on a code in C that returns the index of the left most 1. It will also need to return -1 if there are no 1 in the binary number. My code resulted in error message from the terminal:  warning: control reaches end of non-void function [-Wreturn-type]

what I'm after is something I can feed a number into and it will return the highest order bit.  I'm sure there's a simple way.  Below is an example output (left is the input)  1 -> 1 2 -> 2 3 -> 2 4 -> 4 5 -> 4 6 -> 4 7 -> 4 8 -> 8 9 -> 8 ... 63 -> 32


I was trying something and I ran into this problem:  <?php     echo 100 - 99.9; // gives: 0.099999999999994   can anyone tell me why this happened and how can I fix this?

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


How do I join someone else's LAN world on Minecraft? My brother and I are trying to join each others worlds on it and are having trouble.


.bashrc and bash.bashrc include:  [ -z "${debian_chroot:-}" ]  Bash manpage states the following on parameter expansions of the following form: ${parameter:-word}  If parameter is unset or null,  the  expansion of word is substituted. Otherwise, the value of parameter is substituted. Why write   "${debian_chroot:-}"   and not simply  "${debian_chroot}"   ?   Answer I'm going with:

In my terminal prompt definition in my .bashrc file, among other things, I have this snippet of code:  ${debian_chroot:+($debian_chroot)}   What does this do, and do I need it?


I am reading and extracting some filenames from a directory and trying to add them into an array. The given directory has duplicate files so I would be extracting some duplicate file names also. Original file names in the directory as: 100_abc strategy-42005_04May2020_0000-04May2020_first_file.csv    100_abc strategy-42005_04May2020_0000-04May2020_second_file.csv    101_xyz statitics strategy_04May2020_first_file.csv  Script used:  #!/bin/bash  c=0  for filename in /home/vikrant_singh_rana/testing/*; do         #stripping a file name          GroupName=$(basename "$filename" ".csv" | awk -F "_" '{print $2}' | awk -F "-" '{print $1}')         echo "$GroupName"          var=["$c"]="$GroupName"         c=$(($c+1)) done echo "print my array" echo "${var[*]}"   the file name it extracts from directory contains spaces with them. for example. abc strategy abc strategy xyz statistics strategy  so when I print my array it would be printing like as abc strategy abc strategy xyz statistics strategy  above code is adding same file name again to array if it encounter same file again while reading. so I have added a if statement in order to prevent that, which is not working as expected. I was expecting that array should have unique file name as an element only. for filename in /home/vikrant_singh_rana/testing/*; do         GroupName=$(basename "$filename" ".csv" | awk -F "_" '{print $2}' | awk -F "-" '{print $1}')          if [[  "${var[@]}"  =~ "$GroupName" ]]; then                 echo "I am here "                 c=$(($c+1))                 var["$c"]="$GroupName"         fi  done

Help for a simple script  #!/bin/bash  array1=( prova1 prova2 slack64 )  a="slack64" b="ab"  if [ $a = $b ] then       echo "$a = $b : a is equal to b" else       echo "$a = $b: a is not equal to b" fi     This script simply doesn't work, I want a script which check if slack64 is present in a list(i use an array),and simply give me, yes is present,or no. I don't know how to compare an array with a single variable.


Looking for a short story, potentially by Kurt Vonnegut, about a world in which people's jobs are increasingly specialized which leads to a lack of poets and other artists.  At some point there's a general who realizes that what is needed is a poet, which leads to the realization that none exist (or potentially there's only one?)

Story where a traumatised soldier in a hospital vanishes. ‘Experts’ don't understand that poets did this all the time and not a poet can be found anywhere. The story was in English. Perhaps it was by  Asimov.


I want to install an app from Google Play, where it's said it has 14.99MB.  However, when I click on Install, it says "Insufficient storage".  When I click View Storage, there says 180MB available.  Why can't I just download it to the SD Card?  As I see, this has been a persistent error, though in other posts people are talking about 15 MB of free space. I got more than 10 times that, so isn't it strange?  Also, the Storage screen don't show the available space as part of the bar "Device Memory", above. Does that happens with anyone else?  I'm using a Sony Xperia.  Thanks in advance.

I have a Motorola phone, with 8GB of internal memory.  To my surprise, in a few days, I had 474MB of free space, but couldn't install a 338KB app!! So, clearly the limit of ~25MB referred to in some comments ( and ) are not always the case. A user just told me the following:     Actually it's "25MB or 10% of the storage", whichever is hit first. So   with e.g. 10 GB internal storage, it would hit you as soon as you drop   below 1 GB free. Crazy, but that's what it is.   Actually, that's not correct, because I didn't have to free up 1GB of internal memory. But anyway, half a gigabyte is enough to run a full operational system. I've seen similar complaints of hundreds of MB not enough to install apps ~ 1MB or similar small operations ( and ).  What's wrong here?


my laptop battery got empty soon and I installed bumblebee and tlp, now I have about 3hour battery energy more than before on my laptop. and now I found there is an other powermanagement for ubuntu laptop-mod-tools. which one is the best for powermanagement on ubuntu 13.04 ? tlp or laptop-mod-tools?

I'm trying to install the Jupiter power settings app but, I read it is no longer compatible with the new kernel. Is there a similar program or a way to manage the power settings on 13.04?


Please help, this will be an easy and obvious problem but im new to coding and im teaching myself online. My program should ask the user to enter an amount, it should then ask the user to enter an account type, and it should then output the value of the amount with a years interest.   import java.io.IOException; import java.util.Scanner;   public class BankInvestment {      private static final String Account = null;      public static void main(String[] args) throws IOException {         // TODO Auto-generated method stub         int S = 3;         double D = 0.5;         double C = 1.5;         int L = 4;         @SuppressWarnings("resource")         Scanner input = new Scanner(System.in);         @SuppressWarnings("resource")         Scanner user_input = new Scanner( System.in );         int n = input.nextInt();         int Output = 0;         String Accounttype = null;          System.out.println("Please Enter Account Type(S,D,C,L): ");         Accounttype = user_input.next();          if (Accounttype == "S"){             Output = n / 100 * S + n;             System.out.println(Output);         }         else if (Account == "D"){             Output = (int) (n / 100 * D + n);             System.out.println(Output);         }         else if (Account == "C") {             Output = (int) (n / 100 * C + n);             System.out.println(Output);         }         else if (Account == "L"){             Output = n / 100 * L + n;             System.out.println(Output);         }     } }

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


i have a table in aws athena as shown below.   and i want to get rows for each device id with highest timestamp.

Table:   UserId, Value, Date.   I want to get the UserId, Value for the max(Date) for each UserId. That is, the Value for each UserId that has the latest date. Is there a way to do this simply in SQL? (Preferably Oracle)  Update: Apologies for any ambiguity: I need to get ALL the UserIds. But for each UserId, only that row where that user has the latest date.


I am new to statistics and it this the first time I am trying to normalise variables. Thus, sorry for my incompetence.  My goal is to classify the landscape by cluster analysis (using kmeans in R) and see if there is a relationship between species distribution and type of the landscape.  However, some of the variables (totally there are 10 variables) I am using are strongly correlated. Thus, I decided to do PCA and run cluster analysis with principal components. I tried to do it without normalising variables before PCA (however, I standardised them with data.frame(scale(data,center=T,scale=T)) function), but the results I got didn't impressed me, since, I observed stronger and more interpretable relationship, when I tried to run cluster analysis with 4 uncorrelated and hypothetically the most important variables (also standardised). So now I want to normalise the variables and try to rerun PCA and cluster analysis. But to make matters worse, some of the variables I am using are far from normal, the sample sizes are large (n=40038) and I've got no experience in transforming the data.  I have read that tests of normality are useless in cases of large samples and, generally, for deciding if one is able to use parametric methods for his data. So I am inspecting normality visually and by values of kurtosis and skewness. So for example, I have one, very problematic variable with many zero values which looks like to follow gamma distribution:    I transformed the variable to the power of 0.3 (x^0.3) and got the following results:  Skewness= 0.5006657 Kurtosis= 3.255236    I also tried other transformations and yeo.johnson() function, but none of them produced me a better result. However, I see that the result I have is far from normal. Nonetheless, maybe it is still fair enough approximation of normal distribution for PCA, as this method doesn't have a strict requirement for it? And to rephrase this question - what will happen if I run PCA with that kind of variable, while other variables follow more or less normal distribution, and later use k means to classify principal components' values? Finally, maybe there is a better way to transform this variable?

We want to apply PCA to monitor our process testing data. After we plot the density of the testing data and do normality tests, we found them to be definitely not normal, but still symmetrical and long tailed.  What distribution can these be?  If they are not normal, is PCA still be applicable? If not, what other monitoring technique could be used?   We have too many of those testing data, so eyeballing them 1 by 1 is definitely not a good choice.    shapiro test   ARM_Z  RAMP_Z  DISC_Z RAMP_Z8  ARM_Z1  ARM_Z2   0.0000  0.0032  0.0000  0.0724  0.0246  0.0000   adf test   ARM_Z  RAMP_Z  DISC_Z RAMP_Z8  ARM_Z1  ARM_Z2     0.01    0.01    0.01    0.01    0.01    0.01   jarque-bera test   ARM_Z.X-squared  RAMP_Z.X-squared  DISC_Z.X-squared RAMP_Z8.X-squared  ARM_Z1.X-squared  ARM_Z2.X-squared             0.0000            0.4580            0.0003            0.8591            0.0029            0.0000    They are more peaked than corresponding fitted normal distributions.


This question is a very basic one, We are told that that current is produced because of flow of electrons but it is stated that the flow of current is opposite to the direction of the flow of electrons if the electrons are the body which moves which further produces current then how can current move to the opposite direction (is current is basically flow of electrons)

I recently came to know about the Conventional Current vs. Electron Flow issue. Doing some search I found that the reason for this is that Benjamin Franklin made a mistake when naming positive and negative charges. There is even this little comic about that   My question is, how can a naming convention be wrong? Perhaps I don't understand what is the actual mistake here, I don't know. But I don't see how a naming convention could be wrong or right. There is no right and wrong about that. It could've been any other name, like charge A and charge B.  I'll appreciate anyone can help me understand what is wrong in all this.


I use WinEdt Build 20131031 (v. 8.1) 64-bit with Windows 7 and MikTeX. My slides have been made with the seminar package and contain a lot of eps files. I compile the tex document in the following order: LaTeX -> dvips -> ps2pdf.  My problem is that I want to turn off the autorotate in ps2pdf. Otherwise a number of slides that contain the eps plots are incorrectly rotated. How can I do this with WinEdt?  By the way, I already tried to write "-dAutoRotatePages=/None" into Options -> Execution Modes -> ps2pdf -> Executable -> Switches, but without success.

Consider the following example:  \documentclass{article}  \usepackage{pstricks-add}  \def\RPut(#1)#2{%   \rput[r]{90}(!#1 1980 sub 2 div 0){#2 \quad}   \rput[l]{90}(!#1 1980 sub 2 div 0){\quad #1} }  \begin{document}  \psset{unit=0.78} \begin{pspicture}(-0.1,-2.9)(14.7,1.3)   \psaxes[     labels = none,     Dx = 2,     dx = 1,     Ox = 1980,     yAxis = false   ]{->}(15,0)   \RPut(1980){Lake Placid}   \RPut(1984){Sarajevo}   \RPut(2006){Torino} \end{pspicture}  \end{document}   If I compile using xelatex everything is fine but if I compile using latex --> dvips --> ps2pdf the figure is rotated 90 degrees clockwise.  How do I compile using latex --> dvips --> ps2pdf but without getting the rotation?


I would like to make a pattern.  For example, my input is   string str = "15-16-00-014716 AND15- [  ] (5) Description of 16-00-014715";   Expected output is  15-16-00-014716 AND15-16-00-014715   I tried below regex:  Regex.Replace(YourString, @"\s+\[.*(?=\b\d+)","");   But the output is like   15-16-00-014716 AND15-0-014715

For example, this regex  (.*)<FooBar>   will match:  abcde<FooBar>   But how do I get it to match across multiple lines?  abcde fghij<FooBar>


I have a  which sides consist of parts of rays, and I only know the coordinates of two points on each ray.  I need to determine if a point $(x,y)$ lies in such quadrangle.  , I painted the sides of the quadrangle red in case you don't understand about what quadrangle I'm talking.

There is a point $(x,y)$, and a rectangle $a(x_1,y_1),b(x_2,y_2),c(x_3,y_3),d(x_4,y_4)$, how can one check if the point inside the rectangle?


When I start the OS this is what I get after I login in (see the pic). I can't get into the desktop. I think the problem started when I uninstall python3 but I couldnt find any solution. I'm using a virtual machine, but I dont wanna loose my files. Any help would be usefull.

I am a new Ubuntu user running Ubuntu 13.04.  I've been trying to install and use a DeDRM tool, but I've been having problems doing so. I was following some directions that said I needed a version of Python 2.7, but not anything Python 3.0 or later (because 3.0 versions are missing some necessary libraries?). I tried to install Python 2.7.5.6, but it didn't work. I thought it was probably because I had the later version of Python, so I went through terminal and removed Python 3.3, so I could install the earlier version of Python.  Now that I've uninstalled Python 3.3, a lot of applications no longer work, including the terminal and the Ubuntu Software Center. I have no idea how to fix this problem now.


Q) Suppose that $f$ is a simple Lebesgue measurable function on $R^n$. Show that there exists a Borel measurable function $g$ such that $f(x) = g(x)$ for almost every $x \in R^n$. I know that a simple Lebesgue measurable function takes finitely many values on Lebesgue measurable sets. But I'm not sure how I can find an appropriate Borel measurable function $g$, i.e. function wherein the pre-image of every open set is Borel measurable, which is the same as $f$ except atmost on a countable set?

Suppose $(\mathbb{R},\Sigma(m),m)$ is our measure space, where $m$ is Lebesgue measure.  Also, suppose $f : \mathbb{R} \to [-\infty, \infty]$ is a Lebesgue measurable function.  The problem:     Prove that $f$ is equal almost everywhere to a Borel measurable function.   My attempt:  We only have to prove this assertion for a non-negative Lebesgue measurable function $f$ because the result will follow for all Lebesgue measurable functions.  Furthermore, since any Lebesgue measurable function can be approximated by a sequence of non-negative, monotonically increasing, Lebesgue measurable simple functions $s_{n}$, we only need to prove the claim for an arbitrary Lebesgue measurable simple function.  So, let $s: \mathbb{R} \to [-\infty, \infty] $ be a Lebesgue measurable simple function.  We can write $s$ canonically as $$ s(x) = \sum \limits_{i = 1}^{n} \alpha_{i} \chi_{A_{i}}(x)$$ where $\alpha_{i} \in [-\infty, \infty]$, $\bigcup \limits_{i = 1}^{n} A_{i} = \mathbb{R}$, and $A_{i} \cap A_{j} = \emptyset$ if $i \neq j$.  For each $i$, since $A_{i}$ is Lebesgue measurable, we can find a Borel set $B_{i}$ such that $A_{i} \subseteq B_{i}$ and $m(B_{i} \setminus A_{i}) = 0$.  Clearly, this implies that $\bigcup \limits_{i = 1}^{n} B_{i} = \mathbb{R}$.  Now we just need the $B_{i}$'s to be pairwise disjoint, with each $B_{i}$ still retaining $A_{i}$.  To make them pairwise disjoint, I constructed the following sets:  $\tilde{B_{i}} = [B_{i} \setminus (\bigcup \limits_{j \neq i} B_{j})] \cup A_{i}$.  This construction gives us that the $\tilde{B_{i}}$'s are pairwise disjoint (I think....) and $A_{i} \subseteq \tilde{B_{i}}$.  But I don't know that $\tilde{B_{i}}$ is necessarily still a Borel set. :( :(  Am I approaching this problem all wrong?


(\x)^2 will plot correct parabola, while \x^2 will have negative x branch upside down. Why () are required for this formula to work?  \documentclass[10pt]{article} \usepackage[utf8]{inputenc} \usepackage{tikz} \usetikzlibrary{shapes.geometric} \usetikzlibrary{shapes.misc}  \begin{document} \begin{figure}[!htb]     \begin{tikzpicture}         \draw[very thin,color=gray] (-4.1,-4.1) grid (4.1,4.1);         \draw[->] (-4.2,0) -- (4.2,0) node[right] {$x$};         \draw[->] (0,-4.2) -- (0,4.2) node[above] {$f(x)$};          \draw[thick,purple,domain=-3:3,smooth] plot (\x,{0.5*\x^2});         \draw[thick,brown,domain=-3:3,smooth] plot (\x,{0.2*\x^3});     \end{tikzpicture}  \caption{$y=1/2 x^2, y=1/5 x^3$} \end{figure}  \end{document}

I have some files with TikZ graphics that have suddenly changed appearance since I upgraded to PGF-2.10.  Here is a minimal example:  \documentclass{minimal} \usepackage{tikz} \begin{document} \pgfversion\par \begin{tikzpicture} \draw[blue] plot[domain=-1:1] (\x,{\x^2 + \x^3}); \draw[xshift=4cm,blue] plot[domain=-1:1] (\x,{(\x)^2 + (\x)^3}); \end{tikzpicture} \end{document}   In PGF 2.00 I had this:    while in 2.10 I have this:    The one on the left in PGF 2.10 looks like the graph of y=x^3 but could also be y=x^3 + x|x|.   This has been  on sourceforge and  on the pgf-users mailing list.  Although I haven't checked myself yet, the bug remains open and some of the commenters below report that problems still exist in the CVS version.   Geoffrey Jones notes the bug is in the 2.00 CVS version:     Hi Matthew, not an answer, just an FYI   that's too large for the comment box.   My compile of your code through pgf   v2.00 produces the result you see with   v2.10, above:       I.e., the difference you observe seems   to pre-date v2.10.   There is a workaround by inserting parentheses.  But since I have so many old lecture files I'd rather find a solution that doesn't involve rewriting my TikZ code.  And I'm squeamish about using the CVS bleeding edge code even if it were fixed, since I don't want to introduce other problems.  Ideally I'd like a simple patch that I can stick at the preamble, or just fix one file in the PGF distro.


I have been given a shapefile which is supposedly in a NAD1927_Zone16 projection. I need to align it with a raster image in a Lambert Conformal Conic (NAD 1927) projection.  I've tried to use the Project and Define Projection tools to verify that this shapefile is in NAD1927_Zone16, but when I compare to other data it is no where near where it should be (leading me to believe that the projection indicated on the shapefile is not correct).   In addition, I've edited the Standard Paralell and Latitude of Origin and Central Meridian values as per:    And I've also tried loading in a custom projection from a .prj file downloaded from the following site:   I haven't done much with projections or transformations before, but I really didn't expect it to be this complicated when I agreed to the task.

I have a Shapefile but its coordinate system is Unknown, and there is no *.prj file.   How can I identify it now?


html code   <input type="text" id="cal" />

   function js  function show_calendar () {                 $("#output").html("

" + title_month + " " +year+ "

");                  var thead = $('

')                 for (var i=0; i<=6; i++) {                 thead.append(""+week_days[i]+"	");                 }                 $("#output table").append(thead);                 //other code here ...                 tr.append(""+days_count+"	");                 //other code here ...   jquery code  $(document).ready(function() {             $("#cal").click(function() {                 $("#output").toggle("slow", function () {                     show_calendar();                  });             });              $("td").click(function() {   //it doesn't work                 alert("clicked");             });         });   When I click on a td element in my table it doesn't work. Why?  How can I fix?

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I was trying to make a list with genericity, and when I try to compile this is what it says:  Undefined symbols for architecture x86_64:   "List<int>::List(int)", referenced from:       _main in main.cc.o   "List<int>::~List()", referenced from:       _main in main.cc.o   This is what I have typed in my .cc and .h  node.h  #ifndef __NODOS_LISTA_DOBLE__ #define __NODOS_LISTA_DOBLE__ #include <vector> template<class T> class Node{ private:     Node<T>* back;     Node<T>* next;     T key; public:     Node (T key);     virtual ~Node(); }; #endif   node.cc  #include "node.h" template <class T> Node<T>::Node(T key){     this->head=nullptr;     this->heap=nullptr;     this->key=key; } template <class T> Node<T>::~Node(){}   list.h  #ifndef __LISTA_DOBLEMENTE_ENLAZADA__ #define __LISTA_DOBLEMENTE_ENLAZADA__ #include "node.h" #include <vector> template<class T> class List { private:     Node<T>* head;     Node<T>* heap; protected: public:     List (T key);     List (std::vector<T>& v);     virtual ~List();     void MakeListNull(); }; #endif   list.cc  #include "list.h" template <class T> List<T>::List (T key){     head=new Node<T>(key);     head->back=nullptr;     heap=head;     heap->next=nullptr; } template <class T> List<T>::List (std::vector<T>& v){     if(v.size()>0){         head=new Node<T>(v[0]);         head->back=nullptr;         Node<T>* nx=head;         for (int cont=1;cont<v.size()-1;cont++){             nx->next=new Node<T>(v[cont]);             nx->next->back=nx;             nx=nx->next;         }         heap=new Node<T>(v[v.size()-1]);         heap->next=nullptr;     } }  template <class T> List<T>::~List(){     this->MakeListNull(); }  template <class T> void List<T>::MakeListNull(){  }   main.cc  #include <iostream> #include "list.h"  int main (int argc, char** argv){     List<int> miLista(5);     return 0; }   I have been looking all the evening on internet and don't know why that error keeps popping, if anyone could help me I would be so grateful.

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I use MiKTeX 2.9 and use{imakeidx } for doing list of indexes in beamer. but I have the message in log: No file "DM2019_7 (2)".ind. [103  ] In texstudio it works . Please help.  Example :      \documentclass[mathserif,12pt,aspectratio=169]{beamer}   \usepackage[T2A]{fontenc} \usepackage[russian]{babel} \usepackage[utf8x]{inputenc} \usepackage[scaled=0.95]{PTSans} \usepackage{graphicx} %\usepackage[usenames,dvipsnames]{xcolor} \usepackage{epstopdf} \usepackage{algorithm} \usepackage{algorithmic} \usepackage{latexsym,amssymb,amsthm}     \usepackage{multicol}   \newenvironment{theindex}{}{} \usepackage{imakeidx} \renewenvironment{theindex}{%     \let\item\par   % definitions for subitem etc     \let\subitem\par     \let\subsubitem\par } \makeatletter \def\@idxitem{\par}  \def\imki@firstpagestyle{empty} \makeatother \newcommand\indexspace{} \makeindex  \begin{document}  \begin{frame} \index{apple} \end{frame} \begin{frame} \index{Algorithm} \end{frame} \printindex \end{document}

I tried to create an index to a document I write, but when viewing the .pdf output there was no index. Also no error messages were displayed. I managed to find this in the LOG FILE: No file "Actual Document".ind. ("Actual Document.aux") ) Indeed, when I check the folder supposed to have these files, I found only a file Actual Document.idx with all my indices, but no .ind file. Changing the extension .idx to .ind produced an error. Here is what I have written:  \documentclass[12pt]{book} \usepackage{makeidx} \makeindex \begin{document} continuous \index{continuous} \clearpage \printindex \end{document}   What have I done wrong and what is going on with these files?


I've made some strange experiences ever since I upgraded from Ubuntu 16.04 to 18.04: Small vertical red lines are occuring next to (random) letters in almost every word that is displayed in any program. This is kind of annoying, since it renders a text hard to read. Changing of fonts does not help. Does anyone know what might cause this problem and could give me a hint regarding a possible solution?  I would highly appreciate that.

In System Info in 11.10, the graphics driver wasn't detected. I use ACER Aspire 4750 with Intel Core i3-2340M and Intel HD Graphics 3000 graphic card  How to install the driver for my Ubuntu?


The Mobile feat appears in the Player's Handbook (PHB, p.168) and would be generally accessible to all classes and races as long as DM agrees to allow feats at the table.  You are exceptionally speedy and agile. You gain the following benefits: • Your speed increases by 10 feet.  There are certain class or sub-class features that allow a PC to have increase in movement (walking) such as: a Barbarian's Fast Movement (+10 feet), a Monk's Unarmored Movement (+10 to +30 feet), or a Druid's Wildshape (walking, depending on the beast), a Scout Rogue's Skirmisher (reaction, moves half their speed). There are also certain class or sub-class features that modify existing or provide additional movement options other than walking, such as: Swarmkeeper Ranger's Writhing Tide (10 feet flying), Twilight Cleric's Steps of the Night (10 feet flying), or a Ranger's Deft Explorer (+5 feet; climbing/swimming speed sam as walking), a Druid's Wildshape (swimming/flying, depending on the beast), Phantom Rogue's Ghost Walk (10 feet flying), The Fathomless Warlock's Gift of the Sea (40 feet swimming). I'm looking for an answer for this specific question with relation to how the Mobile feat interacts with class/sub-class features which provide adjustments to movement speeds. From what I gather all these class/sub-class features would add a +10 feet movement, e.g. a Warlock with the The Fathomless sub-class who takes the Mobile feat would have a 50 feet swimming speed. Is this correct? Thanks for the clarification/confirmation on this.

A monk's Unarmored Movement class feature increases the monks speed by 10 feet at level 2, and further at higher levels. According to , this stacks with an Aarakocra monk's fly speed, because that fly speed is innate to the race. However, how does this interact with fly speeds gained from other sources, such as the Fly spell? That spell specifically states that "the target gains a flying speed of 60 feet for the duration." Can this gained flying speed then be improved by a monk's Unarmored Movement, giving a level 2 monk a flying speed of 70 feet while the Fly spell is active on them?


I am using an iPad and they are using an iPhone.I tried a lot of things.

So my brother and I have been playing Minecraft together on our iPads for years now, but in September I got a new iPad Pro 3rd Generation and I’ve been having issues with Minecraft ever since. Every time we have tried to join each other’s worlds we get the message “Unable to connect to world”. Recently after the update on December 16th, it worked for about a week without having any issues, but now it has gone back to not letting us connect to the worlds. Both of us are able to connect to other people’s worlds, but not each other’s, we’ve tried many things to fix this but so far nothing has worked. If you have any ideas for what we should do please let me know, thank you so much!


I've tried almost everything to make proper dualboot in my notebook. Will be happy with any help you can provide.   Notebook Acer Aspire E5-553G-15CK 2 OS installed - Windows 8.1 x64 (was installed first) and Ubuntu 16.04 desktop x64. Disk is in the GPT partition.  Both OS were installed under UEFI with secureboot disabled. UEFI bios version is InsydeH20 v5.0.   There is no option in boot menu in bios to choose "Ubuntu", only "windows boot manager". Also, I didn't saw even once grub2 loader window while rebooting. Notebook just boots into windows directly. Fast boot is disabled in windows/power management. Also, I've tried bcdedit /set {bootmgr} path \EFI\ubuntu\shimx64.efi - didn't helped. Tried boot-repair - didn't helped.  Additional info is in full report .  Is there any other way to get grub2 loader boot first instead of windows boot manager?

I installed Ubuntu 14.04 onto my Acer Aspire E15. The PC has a 500 Gigabyte HDD.   During the installation it divided the HDD into separate partitions. However every time I turn on the PC it goes directly into Windows 8.1. It doesn't allow you the opportunity to select which OS you want to use.   Question 1: How do I set the PC so it will allow me to select the OS?  Question 2: And if #1 isn't possible. How to I remove Ubuntu from the PC and recover the partition for Windows


I recall watching a youtube video about a ball with a spring on the idea propelling themselves through stable fluids without any assistance, even if we make sure the spring isn't moving in the beginning. It'd be a great help to get an explanation as to why this happens since I haven't been able to find the video after searching for quite a long time. Since soap molecules also share the same shape as a ball and a spring, it may be possible that soap molecules could propel themselves as well.

I saw the latest video from Sixty Symbols . At the end of the videos he says that we do not know how to calculate the movement of the little swimmers. He says(6:14-6:40 in video) that mathematicians derive formulas for small velocities and that they do not work for this experiment. This got me thinking.  Is the speed really that high? Have a look at visualization of the flow behind the swimmer, time in the video 4:32-4:47. The flow looks calm, there is no turbulence. Therefore the argument that the velocity is too high might not be the right one.  Stokes, Oseen, ... drag: I did the calculation for Stokes and Oseen drag and yes you get that the swimmer should not move. Even more, if you assume the drag force as any function of velocity, than the calculation says the swimmer should not move. Therefore deriving more accurate drag formulas for constantly moving sphere in liquid does not help.  Acceleration is too high, not the velocity: Next step in approximation is to derive drag force on single oscillating sphere in fluid. The question is, what is the drag force on the sphere which is moving with velocity $\mathbf{v} = \mathbf{ v}_0(1 + a \sin(\omega t))$?  Will this drag force predict movement of the swimmer? If not than it can be tested in the experiment by making the spring really long and no movement should be seen.    $ \newcommand{bm}{\mathbf} $ My calculations:  Center of mass of the whole system, its velocity and total mass are $x, v,m$  Position, velocity, radium, mass of $i$-th sphere are $ x_i,  v_i, r_i, m_i$.  Since $\bm x$ is center of mass than \begin{align} m_1  x_1 + m_2  x_2 &= m x \\ m_1 + m_2 &= m \end{align} Spheres are oscillating with frequency $\omega$ $$ x_1 - x_2 = L(1+\alpha \sin(\omega t)) $$ $L$ is rest length of spring, $\alpha$ is relative extension of the spring.  Thus \begin{align} x_1 &= x + \frac{m_2 L}{m}(1+\alpha \sin(\omega t)) \\ x_2 &=  x -\frac{m_1 L}{m}(1+\alpha \sin(\omega t)) \\ v_1 &= v + \frac{m_2\omega L}{m}\alpha \cos(\omega t) \\ v_2 &= v -\frac{m_1\omega L}{m}\alpha \cos(\omega t) \\  \end{align}  The force on the system is sum of forces on those two spheres \begin{align} F &= F_1 + F_2 \\ F_i &= f(v_i,r_i) \end{align} Force on the single sphere is a function $f$ of its velocity and its radius.  Stokes drag: $$ f(v,r) = 6\pi \mu r v $$ Thus $$ F_i = 6\pi \mu r_i \left( v + \frac{m_2\omega L}{m}\alpha \cos(\omega t) \right) $$ Averaging over period and assuming that the CoM velocity is constant over the period. $$ \hat F_i =\frac{\omega}{2\pi} \int_t^{t+\frac{2\pi}{\omega}} F_i = \frac{\omega}{2\pi}  \int_t^{t+\frac{2\pi}{\omega}} 6\pi \mu r_i \left( v + \frac{m_2\omega L}{m}\alpha \cos(\omega s) \right) ds = 6\pi \mu r_i v  $$  So the averaged force over the time period is the same as if no oscillation is happening.  In general Suppose that the swimmer is not moving, $v=0$. Again assume that the velocity is constant over period. Then averaged force over period is $$ \hat F_i = \frac{\omega}{2\pi} \int_t^{t+\frac{2\pi}{\omega}} F_i =  \frac{\omega}{2\pi} \int_t^{t+\frac{2\pi}{\omega}} f(v_i,r_i) =  \frac{\omega}{2\pi} \int_t^{t+\frac{2\pi}{\omega}} f\left( \frac{m_2\omega L}{m}\alpha \cos(\omega t),r_i\right) $$ But drag force always acts in opposite direction to the velocity and its magnitude does not depend on the direction. We have to get $$ \frac{\omega}{2\pi} \int_t^{t+\frac{2\pi}{\omega}} f\left( \frac{m_2\omega L}{m}\alpha \cos(\omega t),r_i\right) = 0 $$  Possible flaw in the calculation I assumed that the acceleration of the swimmer is much smaller than acceleration of individual spheres. Thus I could treat $v$ as constant in the integration.


I am looking for a word which means "term for inhabitant of". An example sentence would be:     The _________ of London is Londoner.   This is not a duplicate of the marked question as it asks what is a "term for inhabitant of", the answer being demonym - this is completely different to the supposedly duplicate question and I would appreciate these requests being retracted.

Citizen: 1. A legally recognized subject ornational of a state or commonwealth, either native or naturalized. 2. An inhabitant of a particular town or city.  Denizen: 1. An inhabitant or occupant of a particular place.  Same thing?


I've killed the Wall of Flesh twice now on Android, but I've never been able to get or even see the Pwnhammer, so now I'm stuck and I can't get any better ores.

So.. I spent a good week and a half playing terraria on my android and met with some friends to join me. We finally managed to get to the Wall of Flesh, and me and my friends died quite a few times. Finally, I managed to defeat him by myself and was extrememly disappointed when I couldn't get the Pwnhammer. Did I do something wrong, or is this a bug of some sort?


Does Gauss law hold in all cases, including the ones where charges are moving at speeds comparable to light? What I think: Gauss law does not hold true when charges are moving at very high speeds. For example, assume a sphere and a charge kept midway between the center and a point on the sphere. If the charge moves towards A, then, the increase in electric field is communicated to the region near A quicker than the decrease in the field near the diametrically opposite end of A is communicated, so the flux should be more than expected at that time. Obviously, this is just a thought and may be wrong.

My text claims that Gauss's Law has been proven to work for moving charges experimentally, is there a non-experimental way to verify this?