I'm currently implementing the Bentley-Ottman algorithm applied to spheres, involving intersections of many spheres on one sphere, circles in most cases of course. This requires locating "event" points on the sphere (ie: points where something "special" happened, such as extreme points of intersection circles or intersections between these).  My question is very similar to , mainly because I'm asking for the exact same thing : the eastmost and westmost points of a circle on a sphere, in my case named the start and end points of the circle. These points have the particularity of being the tangency points between the circle and a special longitude. The problem resides in finding these as exact coordinates.  I'm working with the  library, which provides a great deal of exact intersection primitives, and these are in my opinion probably the most appropriate way to find the exact start-end points.  So far I've tried to reduce the problem to a simpler one : instead of finding the longitudes of these points, I'm trying to find the height of the horizontal plane which contains these two points. Using the following notations :   S : start point E : end point C : center of the circle (not on the sphere of course) r : radius of the circle O : center of the sphere R : radius of the sphere h : height of the horizontal plane containing the start-end points H : intersection between the pole axis and the horizontal plane containing the start-end points phi : the latitude containing C phi' : the latitude containing the start-end points.   Starting out from the formula based on the Law of Sines, from the last post :  sin(phi') = sin(phi) cos(r/R)   We notably have :  h = R sin(phi') sin(phi) = OC / R   Giving finally :  h = OC cos(r / R)   This is as far as I've gotten, and I'm stuck on finding an algebraic form of this cosine.

There are few ways of articulating my question. It starts with a known circle on a sphere, i.e. a point-radius, and one that does not cover a pole.  I would like to calculate the point furthest west on this circle and the point furthest east. These points are the tangent points of lines of longitude which encircle the poles and are vertical.  These points are opposite each other along the vertical axis so there is one hard problem to solve from which the other is trivially determined.  This is highly related to calculating the minimum bounding lat-lon box of a circle.  I know how to determine the longitude delta from the center to the edges, which is:  asin( sin( dist_rad / cos(center_lat_rad) ) )   whereas dist_rad is the circle's radial distance is radians, and center_lat_rad is the latitude point of the circle's center in radians.  This equation was elusive to me until I discovered it with a wonderful explanation .  It contains a wonderful illustration:  .  The illustration shows T1 and T2 which are the points I am trying to calculate. What is left to figure out is at what latitude the eastern and western boundary meridians intersect this circle.  If the circle is at the equator, then it's zero, and if it's north of the equator, then this latitude is going to be higher than the circle's center latitude.


I have something like  \documentclass{article} \title{My title} \author{ABC\thanks{XYZ} \and DEF\thanks{UVW} \and GHI\thanks{KMN}} \begin{document} \maketitle \end{document}   and this produces footnotes on top of each other, like   * XYZ ** UVW *** KMN   However I am really struggling to find some extra space in my paper and I want to write all of them on a single line, together with their symbols:  * XYZ, ** UVW, *** KMN   Is there a way to do that?

For documents with a lot of footnotes, particularly if some are short, it can be nice to have multiple on the same line, e.g.:        this is the first footnote 2. this is the second footnote 3. this   if the third footnote 4. finally, we begin to wrap around.      Rather than having it:        First footnote   Second footnote   Etc.      Is there a way to achieve this in LaTeX?  (This is not a duplicate of  because I'm asking about regular full page environment.)


Let $$P_n=\frac{2^3-1}{2^3+1}\frac{3^3-1}{3^3+1}.....\frac{n^3-1}{n^3+1}$$ Prove that $\lim_{n \to \infty}=\frac{2}{3}$. I tried factorizing them but not much canceling or some other thing happened. What can I do?


I have following function to print bits:  void printBits(unsigned int num) {    for(int bit=0;bit<(sizeof(unsigned int) * 8); bit++)    {       printf("%i ", num & 0x01);       num = num >> 1;    } }   and I want to set bit number 5 as follow:  unsigned int DataInMemory = 0x00000000; DataInMemory |= (1<<5);   the result of printBites function is:     0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   it means that 1 << 5 set bit 6 not bit 5. Is it difference between bit position (indexes) and bit in programming nomenclature? How to set bit and print all bits in number using C?

How do you set, clear, and toggle a bit?


I'm trying to prove the expression ¬¬A→A. I can use 3 axioms:   A1: a→(b→a) A2: (a→(b→c))→((a→b)→(a→c)) A3: (¬b→¬a)→(a→b),   MP rule and deduction theorem.  What am I doing wrong?  ⊢ ¬¬A → A  ¬¬A ⊢A deduction th.  1.¬¬A  2.¬¬A→(¬A→¬¬A) [A1]  3.¬A→¬¬A [MP(1,2)]  4.(¬A→¬¬A)→(¬A→A) [A3]  5.¬A→A [MP(3,4)]

This is all in the context of a Hilbert system with modus ponens $A, A\to B \vdash B$ and axioms:  Axiom $1$: $A \to (B \to A)$   Axiom $2$: $(A \to (B \to C)) \to ((A \to B) \to (A \to C))$   Axiom $3$: $(\lnot B \to \lnot A) \to (A \to B)$  So I tried to prove double-negation elimination by doing the following:  \begin{array}{ccc} 1 & \{ \lnot \lnot a \} \vdash \lnot \lnot a & \text{Premise}\\ 2 & \{ \lnot \lnot a \} \vdash \lnot \lnot a \to (\lnot \lnot \lnot \lnot a \to \lnot \lnot a)  & \text{ Axiom } 1\\ 3 & \{ \lnot \lnot a \} \vdash \lnot \lnot \lnot \lnot a \to \lnot \lnot a  & \text{ Modus Ponens } 1, 2\\ 4 & \{ \lnot \lnot a \} \vdash (\lnot \lnot \lnot \lnot a \to \lnot \lnot a) \to (\lnot a \to \lnot \lnot \lnot a)  & \text{ Axiom } 3\\ 5 & \{ \lnot \lnot a \} \vdash \lnot a \to \lnot \lnot \lnot a  & \text{ Modus Ponens } 3, 4\\ 6 & \{ \lnot \lnot a \} \vdash (\lnot a \to \lnot \lnot \lnot a) \to (\lnot \lnot a \to  a)  & \text{ Axiom } 3\\ 7 & \{ \lnot \lnot a \} \vdash \lnot \lnot a \to  a  & \text{ Modus Ponens } 5, 6\\ 8 & \{ \lnot \lnot a \} \vdash a  & \text{ Modus Ponens } 1, 7\\ 9 & \vdash \lnot \lnot a \to a  & \text{ Deduction Theorem } \\ \end{array}  And then I continued on, to prove double negation introduction:  \begin{array}{ccc} 10 & \vdash \lnot \lnot \lnot a \to \lnot a & \text{Double Negation Elimination}\\ 11 & \vdash (\lnot\lnot \lnot a \to \lnot a) \to (a \to \lnot \lnot a) & \text{ Axiom } 3\\ 12 & \vdash a \to \lnot \lnot a & \text{ Modus Ponens } 10, 11\\ \end{array}  My questions:   Am I allowed to invoke the deduction theorem in the middle of a proof like this (step $9$)? Is this considered a context change? Is context-changing allowed? Are the proofs even right/correct? Assuming it's all correct: Are we able to combine them to say that $a \to \lnot \lnot a$ and $\lnot \lnot a \to a$, therefore $a \iff \lnot \lnot a$ or is this symbol not allowed? What ultimately let us say $\lnot \lnot a = a$, the use of the equal sign here?


I'm from Mumbai, India and will be visiting Vietnam later this year with my wife.  For the return flight, we are planning to book the flight via DMK.  Below is my flight plan.  Thai AirAsia Flight   Ho Chi Minh 21.35pm - Don Mueang 23.05pm  Transit Time at DMK - 3h 20min  Thai Lion Air   Don Mueang 02.25am - Mumbai 05.40am  I had couple of queries:  a. Do we need a transit visa at DMK ? Will onward ticket to Mumbai, although with a different connecting airline suffice ?  b. Is 3 Hours enough time to collect baggage and check-in for the Lion Air Flight? I'll probably be arriving and departing from Terminal 1.   Would really appreciate some help on this.  Thanks.

I am traveling from Chennai to Don Mueang International Airport, Bangkok, Thailand, and from there to Mandalay, Myanmar. In Bangkok, the layover time is 8 hours. Do I require transit visa?


I can't swim here. I am not able to swim here. I am unable to swim here.  I think these three sentences seem exactly simlilar. Is there any difference?

Which phrase is more suitable to convey one's inability to do something — "not able to" or "unable to"? For example,        not able to join the meeting   unable to join the meeting


I have a wide table, which by default makes the page look like:  |    xxxxxx         | |    xxxxxx         | |    ______________ | |    |             || |    |             || |    ______________ | |    xxxxxx         | |    xxxxx          |   I'd  like it look like:  |    xxxxxx         | |    xxxxxx         | |  ________________ | | |                || | |                || |  ________________ | |    xxxxxx         | |    xxxxx          |   I have tried setting the geomotry:  \newgeometry{left=0.2in, right=0.2in} \begin{table} ..... \end{table} \restoregeometry   But this will create a single page for the table.

I have a figure that is wider than the \textwidth of my document. (I don't want to change the \textwidth.) As a result, the leftmost part of the figure is flush with the left margin, while the rightmost part spills into the right margin too much. I'd like to center the figure, so that it will exceed the \textwidth equally on both sides.


We know that there are three distinct classes of private IP addresses that were created to avoid IP exhaustion of IPv4. Why were there three distinct ranges that were created?  Assuming that the largest organization would be able to fit all its devices in a 10/8 network, is there any reason to even have the other classes? If there is such a large organization that uses the entire 10/8 block, wouldn't it have been possible to just use the next sequential segment like 11/x? Could all home and SOHO routers simply just use a private ip address like 10.0.0.1?  Additionally, assume that you have a small network with no VLANs or other uses for private IP addresses, is there an issue with using the entire 10/8 in DHCP in a home network besides being just wasteful (performance degradation or otherwise)?  192.168.0.0 - 192.168.255.255 (65,536 IP addresses) 172.16.0.0 - 172.31.255.255 (1,048,576 IP addresses) 10.0.0.0 - 10.255.255.255 (16,777,216 IP addresses)

There is something I've always been mixed up about with IP addressing. When a company purchases internet access from an ISP and obtains their inside global IP address that they'll use for NAT (lets say they're just using PAT and only in need of 1 inside global address to make things easy), do your private IP address schemes have to stick within the class of network you purchased from your ISP? When purchasing internet access from your ISP, does it coincide with network classes?  I'm mixed up about the process itself, considering my public IP at home for instance is 24.x.x.x (which traditionally is a class A network 0-127 range), but at home obviously we all have class C networks, so I'm confused about the whole thing.  I notice most companies use a 172.16-31.0.0 private address scheme and subnet further from there. Which is a class B private address scheme, but is this because they purchased a class B network? Or as a result of CIDR, there are no classes of networks to be purchased, the internet access is the only thing needing purchasing which you will then be given a public IP from your ISP, and the private scheme is left up to the company and Network Engineers to determine. Could a company purchase internet access from their ISP for instance, then make the internal network 10.0.0.0 and subnet from there giving themselves as many subnets and host IPs they could ever use?  If you're totally confused by my questions by now, just to sum up, I want to know basically whether or not the public IP a company is administered from their ISP when they purchase internet access (inside global IP) has any influence on your private IP address scheme (for instance, having to use 172.16.0.0/16 as a starting point instead of being able to use anything I want because of your inside global address), and then subnetting from there.  Any clarity on this would be greatly appreciated.  I apologize for the enormous length of this post!  Thanks everyone.


How to add label to index the rows and columns of the matrix ? because I want to number the line outside the matrix       \[     \begin{array}{lc}       \ Mat_{\varPhi to M} & \left(\begin{array}{@{}ccccc@{}}             1 & 1 & 1 & 1 & 1 \\             0 & 1 & 0 & 0 & 1 \\             0 & 0 & 1 & 0 & 1 \\             0 & 0 & 0 & 1 & 1 \\             0 & 0 & 0 & 0 & 1               \end{array}\right) \\[15pt]     \end{array}     \]


Please don't judge me for believing stuff like horoscopes and astrology, though I did not send any amount nor my bank account number. But she knows my birthday, full name and address. What could possibly happen to me? I used an alias on the first month, but I don't know it's like demons really know how to persuade a person who is currently in an unfavorable situation which led me to give my real name and current address. Please enlighten me or tell me if I should worry because my anxiety is killing me.

Updated question because old one was embarassing: I saw a spam email from "PayPal" and I didn't realize that it was a phishing attempt. I gave the phishing site my name, telephone number, and email. What could he do with them?  Old question: Well, I saw a spam email, but I didn't realize that it's really a scam at first. I gave him my telephone number, address, and name. What would he do with them? Could he ruin ALL of my reputation with it?


I have an external drive that has only my user with read-write (all other groups as read-only).   So when I mount it on another computer, I can't write to it. Yet, even though I am the owner, I can't change permissions to read-write for all, even if I sudo chmod.  Disk /dev/sdb: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders, total 1953525168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x00012a16     Device Boot      Start         End      Blocks   Id  System /dev/sdb1               2  1953525167   976762583    7  HPFS/NTFS/exFAT

I have a script that I need to execute on an NTFS partition. The script's permission is set to 600.  I attempted to modify the permissions by running chmod 755 script.sh, which doesn't report a failure or anything - but it also doesn't change the permissions on the file:  $ stat script.sh    File: `script.sh'   Size: 297070      Blocks: 584        IO Block: 4096   regular file Device: 811h/2065d  Inode: 35515       Links: 1 Access: (0600/-rw-------)  Uid: ( 1000/  xxxxxx)   Gid: ( 1000/  xxxxxx) Access: 2010-09-30 14:05:16.041621000 -0700 Modify: 2010-09-30 14:05:05.070157000 -0700 Change: 2010-09-30 14:05:05.070475000 -0700  $ chmod 755 script.sh $ stat script.sh    File: `script.sh'   Size: 297070      Blocks: 584        IO Block: 4096   regular file Device: 811h/2065d  Inode: 35515       Links: 1 Access: (0600/-rw-------)  Uid: ( 1000/  xxxxxx)   Gid: ( 1000/  xxxxxx) Access: 2010-09-30 14:05:16.041621000 -0700 Modify: 2010-09-30 14:05:05.070157000 -0700 Change: 2010-09-30 14:05:05.070475000 -0700   As you can see, it remains unchanged.


A Banach space $X$ is said to be injective if every linear continuous $T:Y\to X$, with $Y\subseteq Z$ Banach spaces, has a linear continuous extension $T^*:Z\to X$ with the same operator-norm.  My question is: is every finite-dimensional normed space $X$ injective?  All examples I know are infinite-dimensional and besides they're not so simple.   Any hint? Thank you.

Here is a problem in functional analysis from Folland's book:     If $\mathcal{M}$ is a finite-dimensional subspace of a normed vector space $\mathcal{X}$, then there is a closed subspace $\mathcal{N}$ such that $\mathcal{M}\cap \mathcal{N} = 0$ and $\mathcal{M}+\mathcal{N} = \mathcal{X}$.   I tried the following approach: I am trying to define a projection map $\pi_{\mathcal{M}}$ from $\mathcal{X}$ to $\mathcal{M}$, which would be continuous and hence taking the inverse of any closed set would give a closed set in $\mathcal{X}$. I am confused about what the projection map would be. Please suggest some approach.


I've taken a look at the related questions , , etc. This case seems slightly different.  A user has asked the same question twice with slightly different wording, but there is absolutely no extra information. The newer question clearly says:     Sorry for the duplicate question as I am not getting any reply.   How do we handle this case? The user seems fairly well-established (>500 rep). Do we just mark as dupe or is there a specific mod request? Do you see an opportunity to educate?  Here are the questions:

I got  question in review. First sentence is:     I know there is a  question, but no answers.   And indeed the two questions are virtually identical. I started to flag as duplicate - but the original question had no answer at the time, so it wouldn't be correct and apparently . (I didn't go so far as to try to submit the flag).  What is the proper action here? How do we want such a question to be handled? Should both (or more) questions stay open indefinitely until either is answered and somebody gets the good idea to do the duplicate linking?   As the new question is essentially a bump to the front page (perhaps with re-tagging), especially in the case where the OP knows that a previous question exist, perhaps something should be done to enable bumping re-emphasizing without writing the new question.  As I wrote this,  actually got an answer. So the old one should now be closed as a duplicate of the new - but my question remains for the case where all known/found duplicate questions have no answer?  Ironically, just before asking this, the "Questions that may already have your answer" gave me ... (Although the suggestion has no answer). So it has been asked before - the comment there even suggest the ability to re-emphasize.


The lifetimes of batteries are independent exponential random variables, each having parameter λ. A flashlight needs 2 batteries to work. If one has a flashlight and a stockpile of n batteries, what is the distribution of time that the flashlight can operate?  My friend said this was a gamma distribution with parameters (n/2, λ). But what does that even mean? I honestly have no idea where to begin. I know the distribution for an exponential random variable, $λe^{-λx}$, but other than that, not much. Help

The lifetimes of batteries are independent exponential random variables , each having parameter $\lambda$. A flashlight needs two batteries to work. If one has a flashlight and a stockpile of n batteries, What is the distribution of time that the flashlight can operate?  What I have so far:  Let $Y$ be the lifetime of the flashlight; $Y_1=min(X_1,...,X_n)$ where $X_i$ is the lifetime of a battery ($1\le i\le n$), and $Y_2$ the second smallest of the $X_i$ (so $Y_1\le Y_2$)  I wanted to compute: $P[Y\le t]=P[Y_2\le k+m|Y_1\le m]$ where $k+m=t$ then we have that $$P[Y_2\le k+m|Y_1\le m]={P[Y_2\le k+m, Y_1\le m]\over P[Y_1\le m]}={P[Y_2\le k+m] P[Y_1\le m]\over P[Y_1\le m]}=P[Y_2\le k+m=t]$$ (because of the independence of the random variables)  So $P[Y_2\le t]=P[min(X_1,...,X_{j-1},X_{j+1},...X_n)\le t]$ (assuming $X_j=min(X_1,...,X_n)$) hence:  $$P[min(X_1,...,X_{j-1},X_{j+1},...X_n)\le t]= 1-P[min(X_1,...,X_{j-1},X_{j+1},...X_n)\ge t]=1-P[X_1\ge t,...,X_{j-1}\ge t, X_{j+1}\ge t,... X_n\ge t]=1-e^{(n-1)\lambda t}$$  I would really appreciate if you can tell me if this is the correct approach :)


Lets say my opponent have  in play. Then proceeds to use instant spell that target Zada to trigger its effect. Then i play  in response to his instant spell. Does Zada, Hedron Grinder still resolves even if my Stasis Snare resolves first by exiling Zada? If its effect still resolves, how do you prevent Zada from using its ability if i have the instant removal (stasis snare, lightning axe, grasp of darkness etc...) in my hand that can be played in response ?

Player A taps  targeting Player B; its "deals 1 damage to target player" ability is placed on the stack.  Player B gets priority and responds with , targeting Goblin Fireslinger.  Both players pass priority. Snap resolves, and Goblin Fireslinger is returned to its owner's hand.  Does Player B still take 1 damage from Goblin Fireslinger's activated ability?  I know that if the creature had been killed/sent to the graveyard, the ability would still resolve, but I was told recently that because a player's hand is a private zone it couldn't. If anyone could confirm or deny this for me, it would be most appreciated.


The night on the first part at the Two Pine mall and when all the ruckus happened, Doc Brown already programmed the time machine to go to Nov 05 1955.  Why so? I mean, I don't recall if there is a reason for that or it was only chance or no reason at all. If this was the first time tested, perhaps he could have gone to the Old West, or wherever.  But why, in-universe, did he choose that time? Does it have to do with the flux capacitor?

Is there any significance to the date November 5, 1955 that was chosen in Back to the Future? Is it one of the directors birthday or something like that or were there specific real life events that day in history?   I am not looking for in-universe answers.


My question is around Error handling in a WCF service and passing error information back to the calling client. I do know that we can use the FaultContract as part of the ServiceContract while defining the interface.  What if i dont want to use the FaultContract and as part of my DataContract response i include the Error response or success response as an object of type Result?   What is the difference in the two approaches? Especially in terms of internally any extra channels used?   I have tried both approaches and both work. What i know so far is that approach 2, does not need the client to know what error to trap, he can just investigate the Result object to see.  Example of a FaultContract Code  public interface ICalculator {     [OperationContract]     [FaultContract(typeof(MathFault))]     int Divide(int n1, int n2); }   My Error Handling Code  public interface ICalculator {     [OperationContract]     Result Divide(int n1, int n2); }  [DataContract] public class Result  {     [DataMember]     public bool Success { get; set; }     [DataMember]     public string ErrorNumber { get; set; }     [DataMember]     public string ErrorMessage { get; set; }  }

We're currently having a debate whether it's better to throw faults over a WCF channel, versus passing a message indicating the status or the response from a service.  Faults come with built-in support from WCF where by you can use the built-in error handlers and react accordingly. This, however, carries overhead as throwing exceptions in .NET can be quite costly.  Messages can contain the necessary information to determine what happened with your service call without the overhead of throwing an exception. It does however need several lines of repetitive code to analyze the message and determine actions following its contents.  We took a stab at creating a generic message object we could utilize in our services, and this is what we came up with:  public class ReturnItemDTO<T> {     [DataMember]     public bool Success { get; set; }      [DataMember]     public string ErrorMessage { get; set; }      [DataMember]     public T Item { get; set; } }   If all my service calls return this item, I can consistently check the "Success" property to determine if all went well. I then have an error message string in the event indicating something went wrong, and a generic item containing a Dto if needed.  The exception information will have to be logged away to a central logging service and not passed back from the service.  Thoughts? Comments? Ideas? Suggestions?  Some further clarification on my question  An issue I'm having with fault contracts is communicating business rules.  Like, if someone logs in, and their account is locked, how do I communicate that? Their login obviously fails, but it fails due to the reason "Account Locked".  So do I:  A) use a boolean, throw Fault with message account locked  B) return AuthenticatedDTO with relevant information


I'm planning on self-studying linear algebra, and trying to decide on a book.  I'm thinking of using Hoffman and Kunze.   What sort of experience is required to handle Hoffman and Kunze?  So far, I've read most of Axler's Linear Algebra Done Right. (It was for a class in high school, so we just worked through it and got as far as we got.) I feel like I understand it pretty well, and I really liked it, but I've read that it has a rather unusual approach and I would like to try something different.  I've read that Hoffman and Kunze is good, but that it is heavy on the algebra.  I'm not sure how do calibrate that, though.  Does it mean "Don't use it for linear algebra for engineers" or "You should have a year of algebra, but if you have that, it's not a big deal".  (I guess it's somewhere in between.)  I specifically like that it includes a strong emphasis on matrices, which are pointedly ignored in Axler, without devolving into being just a manual for computation.  This is my impression of the book from having read around (mostly here), but if something of it is wrong, please correct me.  I have very little experience to provide comparison and normalize the different recommendations I've read.

I'm looking for a book to learn Algebra. The programme is the following. The units marked with a $\star$ are the ones I'm most interested in (in the sense I know nothing about) and those with a $\circ$ are those which I'm mildly comfortable with. The ones that aren't marked shouldn't be of importance. Any important topic inside a unite will be boldfaced.  U1: Vector Algebra. Points in the $n$-dimensional space. Vectors. Scalar product. Norm. Lines and planes. Vectorial product.  $\circ$ U2: Vector Spaces. Definition. Subspaces. Linear independence. Linear combination. Generating systems. Basis. Dimesion. Sum and intersection of subspaces. Direct sum. Spaces with inner products.  $\circ$  U3: Matrices and determinants. Matrix Spaces. Sum and product of matrices. Linear ecuations. Gauss-Jordan elimination. Range. Roché Frobenius Theorem. Determinants. Properties. Determinant of a product. Determinants and inverses.  $\star$ U4: Linear transformations. Definition. Nucleus and image. Monomorphisms, epimorphisms and isomorphisms. Composition of linear transformations. Inverse linear tranforms.  U5: Complex numbers and polynomials. Complex numbers. Operations. Binomial and trigonometric form. De Möivre's Theorem.  Solving equations. Polynomials. Degree. Operations. Roots. Remainder theorem. Factorial decomposition. FTA. Lagrange interpolation.  $\star$ U6: Linear transformations and matrices. Matrix of a linear transformation. Matrix of the composition. Matrix of the inverse. Base changes.   $\star$ U7: Eigen values and eigen vectors Eigen values and eigen vectors. Characteristc polynomial. Aplications. Invariant subspaces. Diagonalization.   To let you know, I own a copy of Apostol's Calculus $\mathrm I $ which has some of those topics, precisely:   Linear Spaces Linear Transformations and Matrices.   I also have a copy of Apostol's second book of Calc $\mathrm II$which continues with   Determinants Eigenvalues and eigenvectors Eigenvalues of operators in Euclidean spaces.   I was reccommended Linear Algebra by Armando Rojo and have Linear Algebra by , which seems quite a good text.   What do you reccomend?


I know '==' is used to check the equality of two values and 'is' is used to test the identity of objects in Python as pointed out in  post. However they can be both used for comparing numbers besides their other applications. I did some tests using both of them to compare two integers and 'is' appears to run faster. Why is that? and if that's true is there any other reason to use '==' for number comparisons at all?  timeit.timeit('1 is 1', number=10**8) 2.3460144830169156  timeit.timeit('1 == 1', number=10**8) 2.9029528259998187

My  has failed me.  In Python, are the following two tests for equality equivalent?  n = 5 # Test one. if n == 5:     print 'Yay!'  # Test two. if n is 5:     print 'Yay!'   Does this hold true for objects where you would be comparing instances (a list say)?  Okay, so this kind of answers my question:  L = [] L.append(1) if L == [1]:     print 'Yay!' # Holds true, but...  if L is [1]:     print 'Yay!' # Doesn't.   So == tests value where is tests to see if they are the same object?


So I'm doing some work on Jim, about to texture, and boom, these crazy artifacts on some randomly selected faces...   I've tested the .blend file on my laptop and it all seems fine, and I've tested new .blend files and they tend to do the same. The texture shows fine in Cycles and I haven't done anything to the material except plug in the texture, I have also tried reinstalling Blender completely with no luck...  I do have a fairly old IMac, mid 2011 21.5", which might be the thing causing it, but any insight would be amazing <3  Any ideas?  Edit: I also get some weird stuff in shading mode too (black model, weird light sphere   )

I am experiencing some weird lighting And rendering issues on blender under Linux.  This is what I get on Linux:    And this is what I am supposed to get:    My OS is Linux Mint 19.1 Cinnamon with Linux kernel 5.3. iam using Blender 2.8.1 I tried loads of different Linux kernels but ended up with The same results. I tried Upgrading My kernel Downgrading My kernel. Installing Updates. I tried Everything Nothing is Working. Also I got the output when running Blender from Terminal.  Received X11 Error:     error code:   182     request code: 156     minor code:   34     error text:   GLXBadFBConfig  Received X11 Error:     error code:   8     request code: 156     minor code:   34     error text:   BadMatch (invalid parameter attributes) Error: Not freed memory blocks: 2, total unfreed memory 0.000458 MB  Blender quit


We know from the , that: $\displaystyle \large {m+n \choose r}=\sum_{k=0}^r{m \choose k}{n \choose r-k}$ I want to find the sum of only those terms where $k$ is odd. What's the closed form of that? If there's no closed form, what's the simplest possible simplification of the sum?

How do I simplify: $$\sum_{r = 0}^{\lfloor \frac{k}{2} \rfloor} \dbinom{k}{2r} \cdot \dbinom{n-k}{k-2r}?$$ Basically, the sum is: $\dbinom{k}{0} \cdot \dbinom{n-k}{k} + \dbinom{k}{2} \cdot \dbinom{n-k}{k-2} + \dbinom{k}{4} \cdot \dbinom{n-k}{k-4} \cdots.$ This seems very similar to Vandermonde's Identity but because we skip two everytime instead of one, I don't see how I can apply it to this problem.


Let {a_n} be a sequence such that lim a_2k = L = lim k→∞ a_(2k+1) Prove that lim n→∞ a_n = L.  I know that I'll have two limits set up, |a_2k - L| < ε and |a_(2k+1)-L| < ε and then I'll have two inequalities, k ≥ N_1 that comes from n = 2k and k ≥ N_2 that comes from n = 2k+1. So in total I'll have two cases. I just don't know how to fill in my proof with the language it requires to make sense. Can someone please help me?

Given a sequence $a_{n}$, if I know that the sequence of even terms converges to the same limit as the subsequence of odd terms:    $$\lim_{n\rightarrow\infty} a_{2n}=\lim_{n\to\infty} a_{2n-1}=L$$  Is this sufficient to prove that the $\lim_{n\to\infty}a_{n}=L$?    If so, how can I make this more rigorous?  Is there a theorem I can state that covers this case?


There are some languages that get highlighted incorrectly. Is it possible to specify a code block that does not have any highlighting when it gets displayed?  Here is an small example of CSS that is getting highlighted as if it was C/C++.  #div.a {   background-color: #000000; }  .static { }

Do you think it would be worthwhile to provide hints as to what language to use for the syntax highlighting?  Sometimes I find the highlighting on SQL or VB.NET answers is more distracting than helpful; for example:       to pick the two I've been looking at recently.


I have a problem when trying to execute a model builder through C# the application throws:     an error has occurred error hresult e_fail has been returned from a   call to a COM component   Note : ArcGIS 10.1 and .NET 2010  CODE :    using System; using ESRI.ArcGIS.esriSystem; using ESRI.ArcGIS.Geoprocessing;  namespace GeoprocessingInDotNet2008 {     class Program     {         private static LicenseInitializer m_AOLicenseInitializer = new GeoprocessingInDotNet2008.LicenseInitializer();      [STAThread()]     static void Main(string[] args)     {         // Load the product code and version to the version manager         ESRI.ArcGIS.RuntimeManager.Bind(ESRI.ArcGIS.ProductCode.Desktop);          //ESRI License Initializer generated code.         //m_AOLicenseInitializer.InitializeApplication(new esriLicenseProductCode[] { esriLicenseProductCode.esriLicenseProductCodeArcInfo },         //new esriLicenseExtensionCode[] { });          // Create geoprocessor. Overwrite true will replace existing output         IGeoProcessor2 gp = new GeoProcessorClass();         gp.OverwriteOutput = true;          // Get the workspace from the user         string wks = @"C:\Users\AmineMed\Documents\ArcGIS\LYDEC\DataBases";          // set the workspace to the value user entered         gp.SetEnvironmentValue("workspace", wks + "\\" + "Temp.mdb");          // Add the custom toolbox to geoprocessor         gp.AddToolbox(@"C:\Users\AmineMed\Documents\ArcGIS\LYDEC\ConverterTool.tbx");          // Create a variant - data are in the workspace         IVariantArray parameters = new VarArrayClass();         parameters.Add(@"C:\Users\AmineMed\Desktop\mise à jour\El Mejjatya\Plan topo Al Wiam\Plan topo Al WiamT15071c.dwg");         object sev = null;         try         {             gp.Execute("Creation", parameters,null);             Console.WriteLine(gp.GetMessages(ref sev));         }         catch (Exception ex)         {             Console.WriteLine(ex.Message);             string errorMsgs = gp.GetMessages(ref sev);             Console.WriteLine(errorMsgs);         }         finally         {             Console.WriteLine("Hit Enter to quit");             Console.ReadLine(); // pause the console to see messages         }          //ESRI License Initializer generated code.         //Do not make any call to ArcObjects after ShutDownApplication()         m_AOLicenseInitializer.ShutdownApplication();     }

How can I execute ModelBuilder in ArcMap 10.1 using .NET 2013 C# classes?


I'm now a second year math student at a top uni, and in the summer of my first year, I was a part of a small research team where we proved various new results related to Random Matrix Theory and wrote 2 papers on them. Now those papers are up on arXiv, but it hasn't been accepted to a peer-reviewed journal yet. My question is that when I'm applying for summer research programs etc should I list these as "preprints" on my CV even if they haven't been accepted to a journal yet?

Assume a search committee is reading my CV and in the publication section they notice some of my papers are only submitted or claimed to appear in a journal (or accepted for publication in a journal). Sometimes the journal which has accepted the paper for publication lists the title of accepted articles before actually publishing them, but in the rest of cases there is no evidence to prove that the referee process of the paper is over and the journal has accepted the paper for publication. Also assume preprints of my papers are available in ArXiv. So, my questions are:   How a search committee interprets and evaluates those papers which are just submitted or are claimed to appear?  Does a search committee consider these types of publications less valuable than the published ones (assuming the same quality)?  Does a search committee refer to my preprints in ArXiv to evaluate my submitted or accepted papers?


So $\Delta x$ and $\Delta p$ are uncertainties in quantum mechanics. What exactly does the term "uncertainties" mean?

So, as your usual physics undergrad, I read Griffiths's derivation of the general   uncertainty principle. I understood it but there was no physical intuition given behind it in the book. It was basically a bunch of manipulations and inequalities used to get just the right result.  Other than "It's because of the statistical interpretation." is there a more intuitive reasoning behind uncertainty. Like commutators, behavior of particles, etc.  Thank you for the replies and as always, much obliged.


I have some problems after installing the latest 64bit-MiKTeX as well as the latest packages through the package manager. It seems that there is a problem with the combination of fontspec and expl3 from the l3kernel. I read about errors with newer version of fontspec in combination with expl3 and had a look at different workarounds, but I think that this one is different.  The log is below.  Any hint is welcome!  Bye Holger  LuaTeX: beta-0.80.0 (MiKTeX 2.9 64-bit) (rev 5238)  l3kernel, l3packages etc: packaged on 2015-11-05  complete log file:   example:   \documentclass[12pt, a4paper]{article}  \usepackage{fontspec}  % workaround for suppressfontnotfounderror \ifdefined\suppressfontnotfounderror   \expandafter\let\csname xetex_suppressfontnotfounderror:D\endcsname     \suppressfontnotfounderror \else   \expandafter\let\csname xetex_suppressfontnotfounderror:D\endcsname     \luatexsuppressfontnotfounderror \fi   \newfontfamily{\Arial} [Ligatures=TeX,UprightFont=arial.ttf]{arial}  \begin{document} \Arial Some text in Arial...  \rmfamily Some text in regular font...  \end{document}   some of the errors:  Undefined control sequence. ...\c_e_fp { 2.718 2818 2845 9045 } Undefined control sequence. ...\c_e_fp { 2.718 2818 2845 9045 } LuaTeX error [\directlua]:1: invalid escape sequence near '\s'. ...\c_e_fp { 2.718 2818 2845 9045 } Missing number, treated as zero. ...\c_e_fp { 2.718 2818 2845 9045 } Undefined control sequence. \fp_const:Nn \c_one_fp { 1 } Undefined control sequence. \fp_const:Nn \c_one_fp { 1 } LuaTeX error [\directlua]:1: invalid escape sequence near '\s'. \fp_const:Nn \c_one_fp { 1 } Missing number, treated as zero. \fp_const:Nn \c_one_fp { 1 } Undefined control sequence. ...\c_pi_fp { 3.141 5926 5358 9793 } Undefined control sequence. ...\c_pi_fp { 3.141 5926 5358 9793 } LuaTeX error [\directlua]:1: invalid escape sequence near '\s'. ...\c_pi_fp { 3.141 5926 5358 9793 } Missing number, treated as zero. ...\c_pi_fp { 3.141 5926 5358 9793 } Undefined control sequence. ...one_degree_fp { 0.0 1745 3292 5199 4330 } Undefined control sequence. ...one_degree_fp { 0.0 1745 3292 5199 4330 } LuaTeX error [\directlua]:1: invalid escape sequence near '\s'. ...one_degree_fp { 0.0 1745 3292 5199 4330 } Missing number, treated as zero. ...one_degree_fp { 0.0 1745 3292 5199 4330 } Undefined control sequence. { \i } Undefined control sequence. { \i } LuaTeX error [\directlua]:1: invalid escape sequence near '\i'. { \i } Missing number, treated as zero. { \i } Undefined control sequence. { \q_recursion_tail } Undefined control sequence. { \q_recursion_tail } LuaTeX error [\directlua]:1: invalid escape sequence near '\q'. { \q_recursion_tail } Missing number, treated as zero. { \q_recursion_tail } Undefined control sequence. { \q_recursion_tail } Undefined control sequence. { \q_recursion_tail } LuaTeX error [\directlua]:1: invalid escape sequence near '\q'. { \q_recursion_tail } Missing number, treated as zero. { \q_recursion_tail } Undefined control sequence. { \q_recursion_tail } Undefined control sequence. { \q_recursion_tail } LuaTeX error [\directlua]:1: invalid escape sequence near '\q'. { \q_recursion_tail } Missing number, treated as zero. { \q_recursion_tail } Undefined control sequence. { \q_recursion_tail } Undefined control sequence. { \q_recursion_tail } LuaTeX error [\directlua]:1: invalid escape sequence near '\q'. { \q_recursion_tail } Missing number, treated as zero. { \q_recursion_tail } Undefined control sequence. { \textsigma }

Every once in a while after updating MiKTeX, the installation gets into an inconsistent state. This might be a problem with the packages (an example is described in ), but sometimes packages are split or renamed. The cases I remember are when  and when miktex-etex-base-2,9 was renamed to miktex-etex-base-2.9 (if I recall correctly; I am sure it was either that or something very similar). In each case the MiKTeX Update process suggested to remove the "old" packages but it didn't give the user any hints about him having to manually add the respective replacement packages back in the package manager to get one's MiKTeX installation back into a usable state.  What are best practices for keeping MiKTeX up to date? Note that I'm not asking about installing new packages or fonts in general; there are other questions covering this area.   In which order should one execute the Update process and the Synchronization of the repository? , it is recommended to check the MiKTeX homepage before updating. What else should one do? When and in which order (and why) should one execute the "Refresh FNDB" and "Update Formats" processes within the MiKTeX Options menu? What else can happen? Other advice?


How can I add images taken from my device (an Android phone) to my questions on Stack Exchange? Whenever I try to upload one it says image_mime_type must be set. I haven't learned JS, so I don't understand this error. Please tell me what I can do.

When I try to insert an image in my post, this message appears at the top of the SE app:     image_mime_type must be set   What does it mean and why does that message appear?   SE version: 1.0.85 Android Marshmallow MiUi 7   I used the default MiUi gallery.


I have often read that it is less precise to state the chain rule using Leibniz's notation as opposed to Lagrange's notation. I don't understand this claim because it seems to me that the two statements are identical, and, if anything, Leibniz's formulation is 'cleaner'. If $y=f(u)$, and $u=g(x)$ (and $f$ is differentiable at $u$, and $g$ differentiable at $x$), then $$ \frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx} $$ Equally, we could write $$ (f \circ g)'(x) = (f' \circ g)(x)g'(x) $$ It seems simple to show that these two statements mean the same thing: $$ \frac{dy}{dx}\equiv(f \circ g)'(x) $$ because they both refer to the change in $y$ (where $y=(f \circ g)(x)$) divided by the change in $x$. More formally, they both refer to the same limit expression: $$ \lim_{\Delta x \to 0}\frac{f(g(x+\Delta x))-f(g(x))}{\Delta x} $$ We can also verify that $\frac{dy}{du}\equiv(f' \circ g)(x)$ and that $\frac{du}{dx} \equiv g'(x)$. However, the fact that the two notations refer to the same statement does not mean that we can't prefer one over the other. So what dangers are there in using Leibniz's notation for the chain rule? I have always found it to be simpler and more intuitive, but perhaps there are things which make Leibniz's notation misleading.

One problem I have found when learning calculus is that there are many different ways to denote the derivative. If $y=f(x)=x^2$, then we could write \begin{align} f'(x)&=2x \\ y'&=2x \\ \frac{df}{dx}(x)&=2x \\ \frac{df(x)}{dx}&=2x \\ \frac{d}{dx}f(x)&=2x \\ \frac{dy}{dx}&=2x \end{align} And this is just Lagrange and Leibniz's notations alone. What I find troubling is that they all seem to be suggesting subtly different things about what the derivative actually is. Is it a function, a limit of a quotient, or both? In the interests of keeping my post brief, I'll focus my attention on $f'(x)=2x$ and $\frac{dy}{dx}=2x$, as these seem to be the most common notations.  $$ f'(x)=2x $$  It does make sense to think of the derivative as the gradient function: $$ f'\colon x\mapsto\lim_{\Delta x \to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x} $$ In this case the limit expression is equal to $2x$, and so we can write $$ f' \colon x \mapsto 2x $$ However, this notation seems a little counter-intuitive when we consider what it means to differentiate a function with respect to a variable other than $x$. If I ask what is the derivative of $f(x)$ with respect to $\frac{x}{2}$, does this question make sense? Is it simply $f'(\frac{x}{2})$? Or do we have to express $x^2$ in terms of $\frac{x}{2}$? And how can we can express this derivative using Lagrange's notation?  $$ \frac{dy}{dx}=2x $$  There are many things which are nice about Leibniz's notation, including the fact that it is explicit which variable you are differentiating with respect to. However, in this case, it is unclear whether we are talking about a function, or something else entirely. There are other issues. Some people say they dislike the Leibniz formulation of the chain rule $$ \frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx} $$ saying that they find it to be inaccurate. I don't really understand why this is the case. Could someone please elaborate?


How I can have an object in the foreground with a transparent background? I do not want to have a background that is just keyed out because that always leaves halos even when I do the correct lighting. So how would I go about having a background that is transparent alpha channel and all? Also what video file do I have to use to preserve the alpha channel?

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


I am looking for a way to get the length of an array for the pointer address.  An example:  int *a = (int*)malloc(sizeof(int)*2);// will be an array.  *(a+0) = 1; // values of the array *(a+1) = 2;   Is there a way to detect how much memory is allocated by this pointer? We suggest that there are no empty elements in this array. If I know how much memory is allocated, I should be able to get the size of an array (deviding by sizeof(int));

I've allocated an "array" of mystruct of size n like this:  if (NULL == (p = calloc(sizeof(struct mystruct) * n,1))) {  /* handle error */ }   Later on, I only have access to p, and no longer have n. Is there a way to determine the length of the array given just the pointer p?  I figure it must be possible, since free(p) does just that. I know malloc() keeps track of how much memory it has allocated, and that's why it knows the length; perhaps there is a way to query for this information? Something like...  int length = askMallocLibraryHowMuchMemoryWasAlloced(p) / sizeof(mystruct)   I know I should just rework the code so that I know n, but I'd rather not if possible. Any ideas?


It leads to "not found".  For example:     App Version: 1.0.89 Device Manufacturer: Samsung Device Model: SM-N910V   OS Version: 6.0.1 (N910VVRS2CPL1)

The link to the recommended job in the app brings you to a page with the text: Not Found    Looking at the link it seems like after changing the URL structure in Stack Overflow Jobs they have not been updated in the apps.  For the job in the screenshot this is the used URL in the app:    The correct URL is:


I am trying to make an executable file of my Java Application but I don't know how to do that.  I know how to generate an executable jar file, but I want to make an executable application.  I'm using eclipse indigo to make the java application and to generate the jar file.  How to make the executable?

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


I've created index with makeidx package. It works. I just need to print the first letter above every group of keys. My problem is the same cited here () but the solution given is for a Linux system not Windows.  I created the .ist file. But the command "makeindex -s test.ist test.idx" is not a solution since i work on a windows system.  Can anyone help me?

I've created index with makeidx package. It works. What really need is to print the first letter above every group of keys (i.e. referring to the image I want to print the red letter, that I have manually inserted).


I have been hit with a Virus that disables Windows Security by removing all its components (Windows 10). Startup Repair fails to run and I don't have a system restore that dates back before this (or even the virus somehow survives system restores not sure). The virus also disguises as the winrmsrv service and tries to get firewall access (I denied that).  I've downloaded MalwareBytes and scanned for malwares, the threats were detected and removed but the security components are still missing. Previously, I've resorted to resetting the PC which fixed the issue but now it's back again (after around 6 months) and I can't find the source of it. My initial thought is that the malware could be up within a removable flash drive (I got an infection previously within a drive but it was scanned and removed before opening anything within the drive). But upon further inspection, all other laptops within my home are not affected and we use the flash medias interchangeably so it must be still stuck somewhere within my PC. The Defender Firewall appears to be running but can only be accessed from the start menu, and I get this message as well (screenshot below). In control panel, the firewall appears to be working.   My question is: How it is coming back after a PC reset? Is there something that I'm missing or misunderstanding? In addition, can I fix missing components in Windows without resorting to a factory reset?

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


If the tree isn't watered, it (dies - will die).   This sentence seems very confusing to me, I don't know whether to choose dies or will die because zero conditional is used when the result will always happen. I heard from a friend of mine that if we talk about specific things we use first conditional.  What's the best choice for this sentence?

If the tree isn't watered, it (will die - dies - would die).    I know zero conditional should be about facts. In the example above I'm confused whether to choose will die or dies.


Find all primes $p>2$ such that $\frac{2^{p-1}-1}{p}$ is a perfect square.   My try: Since $p>2$, we can write   $\frac{2^{p-1}-1}{p}=\frac{(2^{\frac{p-1}{2}}-1)(2^{\frac{p-1}{2}}+1)}{p}=n^2$ Now since p is a prime one of the $(2^{\frac{p-1}{2}}-1)$ and $(2^{\frac{p-1}{2}}+1)$  case-1  $p|(2^{\frac{p-1}{2}}-1)$      $(2^{\frac{p-1}{2}}-1)=pk$  hence $n^2=k(pk+2)$  writing   $k=m^2t$ where $t$ doesn't contain any perfect square divisor  $a^2=t(pm^2t+2)$  This indicates that t is either $1$ or $2$.  Putting $t=1$  $a^2=pm^2+2$  hence   $a^2=2^{\frac{p-1}{2}}+1$  $(a-1)(a+1)=2^{\frac{p-1}{2}}$  It can easily be shown that $a=3$ is the only solution to this equation hence $p=7$ is the only solution in case-1.(putting $t=2$ doesn't give any solution.)  Similar method gives $p=3$ in case-2  But someone told me there is an elegent and novel method to solve it. I tried but i didn't get it. Please help.

Find all primes $p$ such that $(2^{p-1}-1)/p$ is a perfect square. I tried brute-force method and tried to find some pattern. I got $p=3,7$ as solutions. Apart from these I have tried for many other primes but couldn't find any other such prime. Are these the only primes that satisfy the condition? If yes, how to prove it theoretically and if not, how to find others? Thanks in advance!


I am storing some calendar items in an array like so,  [  {'CALENDAR': 'HOME',   'SUMMARY': vText('b'Run''),   'LOCATION': vText('b'''),   'START': datetime.datetime(2017, 9, 29, 18, 0, tzinfo=<DstTzInfo 'US/Pacific' PDT-1 day, 17:00:00 DST>),   'END': datetime.datetime(2017, 9, 29, 18, 45, tzinfo=<DstTzInfo 'US/Pacific' PDT-1 day, 17:00:00 DST>)},  {'CALENDAR': 'HOME',   'SUMMARY': vText('b'Tacos''),   'LOCATION': vText('b'''),   'START': datetime.datetime(2017, 10, 2, 19, 0, tzinfo=<DstTzInfo 'US/Pacific' PDT-1 day, 17:00:00 DST>),   'END': datetime.datetime(2017, 10, 2, 20, 0, tzinfo=<DstTzInfo 'US/Pacific' PDT-1 day, 17:00:00 DST>)},  {'CALENDAR': 'WORK',   'SUMMARY': vText('b'Work''),   'LOCATION': vText('b'3740 West Market Center Drive\\, Riverton\\, UT\xc2\xa0 84065''),   'START': datetime.datetime(2017, 8, 21, 8, 0, tzinfo=<DstTzInfo 'America/Denver' MDT-1 day, 18:00:00 DST>),   'END': datetime.datetime(2017, 8, 21, 17, 0, tzinfo=<DstTzInfo 'America/Denver' MDT-1 day, 18:00:00 DST>)}  ]   I am wondering if there is a way that I can sort the array by the dictionary value 'START' so that the earliest event is listed first in the array and I can print the information I want to from there, any thoughts?

I have a list of dictionaries and want each item to be sorted by a specific value. Take into consideration the list: [{'name':'Homer', 'age':39}, {'name':'Bart', 'age':10}]  When sorted by name, it should become: [{'name':'Bart', 'age':10}, {'name':'Homer', 'age':39}]


I wonder if there exists any system to make LaTeX print different versions of each letter randomly. The idea is to make a realistic handwritten or typewritten document where almost every «a» is a bit different from each other. Are there any font with dynamic parameters, such as the thickness of each part, to emulate this way different pressure patterns in a typewriter, for example?

I was reading  on this site, and this was a sample of a cursive font from that discussion:     I really like it, but immediately noticed that it could not have been written by a human, because of how perfectly similar all of the t's and d's looked.   I think that creating convincing "dynamic" typefaces would be an interesting challenge. I don't know of any particularly good applications for it, other than to help out those folks with terrible handwriting, who don't have artistic skill, or who have disabilities (hooray for speech recognition!).   There should be a set of several glyphs for each character, so that they may be randomly chosen when typeset.   In order to get letters to flow together (as they should when using a cursive style) it seems like there needs to be ways to specify "regions" where lines can be bent to accomodate different combinations.   When not dealing with cursive, it is a much simpler problem, but I still don't know of any systems which focus on facilitating the creation of "variable" print. It would be dead simple: an extended font file, and a RNG.    So what I want to know is, has anybody else ever been bothered by this issue, where no cursive font has ever looked convincing? Are there any typographical systems which do these things I describe?


When I tried to use arrow keys in insert mode in vi editor the following characters are being inserted in the editor:   for ↓ I get B, for ↑ I get A, for ← I get D, for → I get C.   Please help me in resolve this problem.

I am open a file in vi:  vi index.php   Here the problem is: when I press the down arrow and it prints 'B'. Why it prints 'B'?


Every time I activate the Broadcom wifi driver my ethernet stops working and I still don't have wifi. I have to use Sudo apt-get remove --purge bcmwl-kernel-source and restart to get the ethernet back. Any ideas? I have a Dell Inspiron 1501.

I updated Ubuntu to 14.04 LTS and I can no longer see my network - No network devices available shows in the network drop down menu. Networking is enabled and if I choose to boot my Dell Inspiron 1300 from the network I do see some activity on the card but none in Linux. Both lights on the nic stay on permanently.   I don't know where to look for the equivalent of event viewer or similar to even start to troubleshoot, having only about two hours with the install before I updated. Original install was last October.   Any pointers on where to look in logs etc would be gratefully received.   02:00.0 Ethernet controller [0200]: Broadcomm Corporation BCM4401-B0 100base-tx [14e4:170c] (Rev 02) Subsystem dell Device [1028:01c9]  cat /etc/modprobe.d/blacklist-bcm43.conf # Warning: This file is autogenerated by bcmwl. All changes to this file will be lost.  blacklist b43  blacklist b43legacy  blacklist ssb  blacklist bcm43xx  blacklist brcm80211  blacklist brcmfmac  blacklist brcmsmac  blacklist bcma  blacklist b44  install wl  modprobe -r b43 b44 b43legacy ssb; modprobe --ignore-install wl ; modprobe --ignore-install b44


In Schwartz' and Peskin's QFT books, when trying to deal with representations of the Lorentz group the authors study the representations of the Lie algebra of such group.  By definition, if $SO(1,3)$ is the Lorentz group, the Lie algebra is $\mathfrak{so}(1,3)$ defined as the set of all left-invariant vector fields on $SO(1,3)$ which in turns is equivalent to the tangent space at the identity of $SO(1,3)$.  Now, $SO(1,3)$ is a real manifold. Hence its tangent space at the origin is a real vector space.  Anyway, the books say that there are elements on this Lie algebra called generators defined by some complex matrices $J_i$ and $K_i$ such that any group element is  $$\Lambda = \exp(i\theta^i J_i+i\beta^i K_i)$$  and such that  $$[J_i,J_j]=i\epsilon_{ijk}J_k$$  $$[K_i,K_j]=-i\epsilon_{ijk}J_k$$  $$[J_i,K_j]=i\epsilon_{ijk}K_k$$  Now there's something quite wrong here. There are two main points I've noticed:   How can the elements of $\mathfrak{so}(1,3)$ be complex matrices if this is a real vector space? The matrices certainly need to be real. Unless one is hidden a complexification somewhere, but this isn't made clear in the books. If that's the case, where and why does one use a complexification? It is not true that all elements of the group can be recovered by exponentiation, if I'm not mistaken. I really don't remember this quite well, but claiming that all elements have that form seems wrong. Furthermore, the exponentiation I know about is the map $\exp : \mathfrak{so}(1,3)\to SO(1,3)$ defined by  $$\exp(A)=\phi^{X^A}_1(e),$$  where $X^A$ is the associated left-invariant vector field, $\phi^{X^A}_t$ is its flow and $e\in SO(1,3)$ is the identity. If I'm not mistaken this exponential map isn't surjective. How the author is justified to say that any group element is of this form?   In summary how to connect the physicst's approach the author presents to the usual Lie group / Lie algebra theory?

The exponential map for the restricted Lorentz group is surjective. An outline of why is shown on the wiki page .  Is there a more general theorem that states that for some class of Lie groups or Riemannian manifolds (which includes the restricted Lorentz group), the exponential map is surjective?  There is a theorem stating that compact, connected Lie groups have surjective exponential maps. But as the restricted Lorentz group is not compact, this isn't applicable.


We are designing an application which has multiple tables and there are multiple action items like the view, edit, etc.   Placing the action buttons on the right side of the table will not be the best option as the number of columns increases the width of the table increases which introduces a vertical scroll that hides the buttons.    So, keeping the action buttons on the right-hand side will be user-friendly? Or it has to be kept on the left-hand side so the buttons are always visible.

One of the pages in our web app includes a table that typically has a few dozen rows for each user, and it takes most of the page's width (5-8 columns).   For each row, users can perform 3 possible actions.  What's the recommended way to let users perform these actions? We've considered a few options:   3 small action buttons on the left-hand side of each row  3 small action buttons on the right-hand side of each row Drop down with the three actions Other approaches?   I saw other questions with a great discussion on  , but in this case, I'm more interested in the right place to put them.   Thanks!  Option 1 Illustration


I was wondering is it possible to prove 1+0=1(or 0+1=1)? If yes! how does it look like! Does it even make sense to ask for proof here? My google searches didn't turn up anything.  Thanks.

Is it possible to prove that $1+1 = 2$? Or rather, how would one prove this algebraically or mathematically?


For example, is the following sentence grammatically correct in terms of the usage of the article?   There was an s-t-r-e-e-t in London.

In the following example, is it appropriate to use a or an as the indefinite article, and why?     He ate __ green apple.   I know that in the case of just "apple", it would be "an apple," but I've heard conflicting answers for "green apple," where the noun is separated from the article by an adjective.  Also, which is more appropriate in this case:     He ate  __ enormous Pop-Tart.


$X$ is a Banach space. $f$ is a function (may not linear) on $X$.We call $f$ is weakly lower semicontinuous if the set $\{x:f(x)≤c\}$ is weakly sequently closed.We call the set $A$ is weakly sequently closed if any ${x_n}$ belongs to $A$,$x_n$ weakly converge to $x_0$,then $x_0 ∈ A$.  Show that $f$ is weakly lower semicontinuous iff $x_n ∈ X$, $x_n$ weakly converge to $x_0$ implies $f(x_0)≤$the lower limit of $f(x_n)$. $f$ is continuous (may not linear) and convex $$(0≤t≤1,f(tx+(1-t)y)≤tf(x) + (1-t)f(y))$$ imply that $f$ is weakly lower semicontinuous.

I have seen that if a set $K$ on an Hilbert space $H$ is convex and strongly sequentially-closed, it is weakly closed. The teacher said that if you take a convex and weakly lower semicontinuous functional $F$, using the fact that the sets $F^{-1}(-\infty, \lambda]$ are convex and that closure implies weak closure, it is easy to conclude that convexity and strong lower semicontinuity imply weak lower semicontinuity. I do not see how to do that though. I would like to see a proof not involving weak topologies etc. The way he said it menat it was supposed to be done using only the definitions, or little more.


Is the set $\{\big(x,\sin(1/x)\big):x\ne 0 \}$ connected in usual metric of $\mathbb R^2$ ?   I tried writing it as a union of two connected sets , or otherwise as a union of two disjoint non-empty open sets without any success , Please help . Thanks in advance

I just came across the example of the topologist's sine curve that is connected but not path-connected. The rigorous proof of the non-path-connectedness can be found .   But how can I prove that the curve is connected? To be honest, even intuitively I am not being able to see that the curve is connected. I am thinking if it is proved that the limit point of $\sin(1/x)$ as $x \to 0=0$, then it would be proved. But, why is this true? IMO, this limit doesn't exist. Intuitively also, it seems that the graph would behave crazily and not approach a particular value as a tends to $0.$  EDIT (Brett Frankel): There are a few different working definitions of the topologist's since curve. For the sake of clarity/consistency, I have copied below the definition used in the linked post: $$ y(x) = \begin{cases} \sin\left(\frac{1}{x}\right) & \mbox{if $0\lt x \lt 1$,}\\\ 0 & \mbox{if $x=0$,}\end{cases}$$


I know monoalphabetic ciphers are weak, but my message recipient doesn't like taking the time for the decryption process. I've tried Vigenere, Gronsfeld, Beaufort and Digraphic Ciphers, but he doesn't decrypt them. What is a good choice for speed and enough security against novice cryptanalysts? One-Time-Pad is highly impractical, and Solitaire takes too much time, what is the best bet? Your suggested answer gives me systems that are impractical and slow. I don't need high security, merely simple yet strong ciphers not mentioned above.

By "hand cipher", I mean a symmetric cipher for which encryption and decryption can can both be performed with a pencil on graph paper, consuming about 10-20 seconds per character by a proficient user. Additional simple tools, e.g. a deck of cards or a multiplication table, may be used to expedite the process. No mathematical proficiency is required other than mental addition, subtraction, and maybe multiplication.  Basically, it should be a cipher that someone of average mathematical abilities can master, and it should require no digital technology or cryptographic tools that cannot be constructed out of paper.  For example, four-square in CBC mode seems secure to me because CBC is a well established mode of operation and four-square seems to be a good block cipher as it accommodates large keys and seems to produce a random-looking output. However, the fact that four-square in CBC was never widely adopted before digital encryption became a consumer technology leads me to believe that someone broke the cipher and thus discouraged people from using it.  So is there any hand cipher that the best supercomputers would take years to cryptanalyze? If not, then for which hand cipher is the best known attack the most complex?


Hi i am getting the error below when i try and update my ubuntu server through command line:     Reading cache      Checking package manager      Cannot upgrade      An upgrade from 'zesty' to 'bionic' is not supported with this tool.   i used the following commands to try and update:  sudo apt update  sudo apt dist-upgrade  sudo apt autoremove do-release-upgrade   im trying to upgrade from 17.04  my sourcelist content is:  ## EOL upgrade sources.list # Required deb http://archive.ubuntu.com/ubuntu/ artful main restricted universe multiverse deb http://archive.ubuntu.com/ubuntu/ artful-updates main restricted universe multiverse deb http://archive.ubuntu.com/ubuntu/ artful-security main restricted universe multiverse  # Optional deb http://archive.ubuntu.com/ubuntu/ artful-backports main restricted universe multiverse

I've installed ubuntu 17.04 and I want to upgrade it to 18.04. When I tried to do:   sudo do-release-upgrade   I got a message saying An upgrade from 'zesty' to 'bionic' is not supported with this tool. Need inputs to proceed on this.  sudo do-release-upgrade Checking for a new Ubuntu release Your Ubuntu release is not supported anymore. For upgrade information, please visit: http://www.ubuntu.com/releaseendoflife  Get:1 Upgrade tool signature [819 B]                                            Get:2 Upgrade tool [1,257 kB]                                                   Fetched 1,258 kB in 0s (0 B/s)                                                  authenticate 'bionic.tar.gz' against 'bionic.tar.gz.gpg'  extracting 'bionic.tar.gz'  Reading cache  Checking package manager  Can not upgrade   An upgrade from 'zesty' to 'bionic' is not supported with this tool.


There is a way to dynamically enlarge a page in a LaTeX document? the thing I want is to have a document which will always have a single page, so the page should increase in height to hold all the document contents.

Well, may be this is not really useful, but I've thought if it was possible to put all the document in one long page. I mean, if your document is going to be read in a computer, mix all the pages in a continuous page. If your document has 90 pages (A4), where each one is 21cm by 29.7cm the continuous document should be (more or less) one page which is 21cm by 90 · 29.7 = 2673cm. Is this possible? EDIT: Some things I would like to achieve:  The \newpage, \chapter{}, \part{}, etc. shouldn't go to a new page, they should only add more vertical space. The package pdfpages should add the pages continuously with almost no space between them. The titlepage, in this case, has a different color, so it could go alone in a basic A4 page (just to make things easier).  Question Is this possible?


Failing Case I ran across an UnboundLocalError exception that I could not understand. I isolated the simplest chunk of the code: def wrapper_func():    x = 0    def test_unbound():        x += 1        return x    return test_unbound()  Then if I call it: >>> wrapper_func() Traceback (most recent call last):   File "<stdin>", line 1, in <module>   File "<stdin>", line 6, in wrapper_func   File "<stdin>", line 4, in test_unbound UnboundLocalError: local variable 'x' referenced before assignment  But as I understood it, x should be available to the inner function. Functioning Case I tested it by doing something almost identical: def outer_func():    x = 1    def inner_func(val):       print(val + x)    inner_func(2)  If I test this out, no error: outer_func() 3  What Am I Missing? Can someone help me understand why the failing case fails and the successful case works?

The following code works as expected in both Python 2.5 and 3.0:  a, b, c = (1, 2, 3)  print(a, b, c)  def test():     print(a)     print(b)     print(c)    # (A)     #c+=1       # (B) test()   However, when I uncomment line (B), I get an UnboundLocalError: 'c' not assigned at line (A). The values of a and b are printed correctly. This has me completely baffled for two reasons:   Why is there a runtime error thrown at line (A) because of a later statement on line (B)? Why are variables a and b printed as expected, while c raises an error?   The only explanation I can come up with is that a local variable c is created by the assignment c+=1, which takes precedent over the "global" variable c even before the local variable is created. Of course, it doesn't make sense for a variable to "steal" scope before it exists.  Could someone please explain this behavior?


I am using Slackware 13.1 (kernel 2.6) with FVWM as my desktop manager.  I have frequently had issues when coding where my over-sensitive mouse registers a middle-button (mouse-wheel) click while scrolling with the mouse-wheel.  Is there any way to modify the shortcut so that middle-click no longer pastes using the built-in clipboard with X11/Xorg/Xfree86? I would prefer if it were re-mapped to something like +MiddleClick, or something similar.  I have searched through the forums already, and have found some suggestions using XMODMAP, but none have worked so far.  Thank you all in advance for your time and assistance.

I don't like having the middle mouse button paste, because I often end up with uncompilable code in Eclipse. How can I turn this off (in all programs)? I'm running Fedora.


I am the top-level organization owner. An employee who was the administrator of a Trello board left recently and I am unable to rename or delete the board. I have already removed his account from the organization.   Is there a way to rename and/or preferably delete the board?

One of our programmers decided to leave us. We took him off the group, but his board that he is the only admin of is still hanging around. How do I remove it?


I need to get just HH:MM to the code work but if I do echo %TIME%  the variable is HH:MM:SS, how can I break the string or make it show just hours and minutes?

Update: Now that it's 2016 I'd use PowerShell for this unless there's a really compelling backwards-compatible reason for it, particularly because of the regional settings issue with using date. See @npocmaka's     What's a Windows command line statement(s) I can use to get the current datetime in a format that I can put into a filename?  I want to have a .bat file that zips up a directory into an archive with the current date and time as part of the name, for example, Code_2008-10-14_2257.zip. Is there any easy way I can do this, independent of the regional settings of the machine?  I don't really mind about the date format, ideally it'd be yyyy-mm-dd, but anything simple is fine.  So far I've got this, which on my machine gives me Tue_10_14_2008_230050_91:  rem Get the datetime in a format that can go in a filename. set _my_datetime=%date%_%time% set _my_datetime=%_my_datetime: =_% set _my_datetime=%_my_datetime::=% set _my_datetime=%_my_datetime:/=_% set _my_datetime=%_my_datetime:.=_%  rem Now use the timestamp by in a new ZIP file name. "d:\Program Files\7-Zip\7z.exe" a -r Code_%_my_datetime%.zip Code   I can live with this, but it seems a bit clunky. Ideally it'd be briefer and have the format mentioned earlier.  I'm using Windows Server 2003 and Windows XP Professional. I don't want to install additional utilities to achieve this (although I realise there are some that will do nice date formatting).


In the sentences like these:     I thought of my new watch as crippled.       The girls perceived the school as decisive.      I thought of this as damaged.   Word "as" is followed by adjectives. I knew that it is possible, but I am more familiar with the "as" followed by nouns like "I thought of my new watch as a crippled watch." What makes it possible? Is there a official rule that enables me to do this? Or is ellipsis used?

Consider:  All cases involving children are treated as urgent. The man was described as tall and dark, and aged about 20.  How "as" can collocate with adjectives here? If I omitted "as" or replaced "as" with "to be", would these two examples still be correct and acceptable?


See his .  Why is it showing like that?  All his profiles are showing like this. See his .

It seems that my profile no longer shows other accounts that I have in Stack Exchange:   You have no other accounts on the    I haven't checked all my accounts, but it's happening at least in Stack Overflow, Meta and Board and Card Games. This morning, I could see my other accounts just fine. It's a bit of a bother because I use those links to change between my accounts.


In the code below, I need to print out the first 5 lines from the CSV file "winners.csv" and I don't know how to do it. I just know that lines 4-5 will cause all lines in the csv file to print. The code in question: wins = open("winners.csv", "r") csv1 = csv.reader(wins, delimiter=",") sort = sorted(csv1,key=operator.itemgetter(1),reverse=True) for eachline in sort:     print(eachline) wins.close()

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


I am converting a high-dimensional model to a lower dimensional model by fitting a sliding window of it to a linear (parametric) model and looking at the evolution of parameter values over time.  I'm going from 6.3 million points to about 2500 values of 6 parameters.  Physics says the intercept should be a constant value, but when I use LM it moves around.  I think the motion is because of noise, and that it causes other parameter values not to indicate properly.  I would like to set it to a known constant value.  How do I make a linear model in R that has a prescribed intercept (not zero).  Current code:  for (i in 1:(n-k)){    fit <- lm(y ~ x1 + x2 + I(x3^2) + x4 + x5 + x6 , data=data[i:(i+k),])    #STORE PARAMETERS INTO VARIABLES ...  #truncated for brevity }   Code that doesn't do the job:    fit <- lm(y ~ I(9.81) + x1 + x2 + I(x3^2) + x4 + x5 + x6 , data=data[i:(i+k),])   fit <- lm(y ~ 9.81 + x1 + x2 + I(x3^2) + x4 + x5 + x6 , data=data[i:(i+k),])   Question:   How do I prescribe the constant? I tried searching for this both at google and CV - is there a vocabulary that I am missing? Can you comment on how something like AIC or R2 are impacted by this model? I prefer to use AIC or BIC and I think that, as model selection criteria they should account for parameters, but the R2 changes (I think) in a fundamental way between the two. I tried searching in CV for an answer to this question, but did not find it.  One alternate solution was suggested but its form is substantially different than what was requested.  It is about massaging the inputs, not about formatting the command without fundamentally altering the data. The answer that I liked (and found most useful) is about the form of the formula entered, not about creating new variables.    As usual, comments and suggestions are solicited.

I know how to perform a linear regression on a set of points. That is, I know how to fit a polynomial of my choice, to a given data set, (in the LSE sense). However, what I do not know, is how to force my solution to go through some particular points of my choosing. I have seen this be done before, but I cannot remember what the procedure was called, let alone how it was done.   As a very simple and concrete example, let us say that I have 100 points scattered on the x-y plane, and I choose to fit a whatever-order polynomial through them. I know how to perform this linear regression very well. However, let us say that I want to 'force' my solution, to go through, say, three of my data points at x-coordinates $x=3$, $x=19$, and $x=89$, (and their corresponding y-coordinates of course).  What is this general procedure called, how is it done, and are there any particular pitfalls I need to be aware of?  Edit:  I would like to add, that I am looking for a concrete way to do this. I have written a program that actually does the linear regression in one of two ways, inverting the covariance matrix directly, or through gradient descent. What I am asking is, how, exactly, step by step, do I modify what I did, such that I force the polynomial solution to go through specific points?   Thanks!


I was building a mob zoo and my bats got out and they fly around and annoy me. How do i remove them?

So, my friend just implemented a bunch of new mods into his SMP server, which meant a host of new commands to play with.  I thought I'd give the /mobspawn command a few goes, and see what I could achieve.  So I headed off to the server's jail (I forget why this particular location compelled me), and gave it a few spins.    I seem to have made a bit of an error in judgement.     What can I do to get rid of this mess?  Is there a command or some other technique I can use to clear out any mobs in my immediate vicinity?


As I'm going through the Feistel network in the DES algorithm.  While encryption uses a Feistel Network, the input block is divided into two halves left ($L$) and right half ($R$). In each round, the right half $R$ goes through unchanged. But the left part $L$ goes through an operation $F$.  I didn't understand why right halves is kept unchanged in a Feistel Network. Can anyone explain?

In a Feistel cipher structure, what exactly does the "round function $F$" do to the right half of the data, before taking XOR of the output with the left half of the data?


If I send money from US to India in my parent's saving account will I have to pay tax in India?

I am planning to transfer around $8K-10K in my parent's bank account(Joint bank a/c) in India . I have read a lot of posts(like )  but I am still not sure if my parents will need to pay taxes on the money that I send them since it is not a NRI/NRE/NRO account?


I edit e-books in e-pub format. I use CSS to do the book layout. I am confronted with a table column alignment problem, and I have no cue as to how to deal with it. The table has text headings for each column, and then numerical content of the cells. The column width is set by the heading, which makes in some cases the column very wide as compared to the cells contents.  I want to right-align the numbers in the column to their last digit. But I would like them to be placed more to the center of the column. The "text-align: right" command aligns the numbers at the right side of the cell. Is there a way to shift all the numbers towards the center while keeping them all right-aligned to the last digit?

In an HTML table, the cellpadding and cellspacing can be set like this:  <table cellspacing="1" cellpadding="1">   How can the same be accomplished using CSS?


I hope you can help me. I have recently found this sentence "improving safety should not be considered merely a law obligation, but also a concrete economic opportunity". I was wondering if the position of merely is correct. Thank you.

Which is grammatically correct?  I can only do so much in this time.  or  I can do only so much in this time.


Recall that an $AR(p)$-process (with mean $0$) is defined by the following recurrence relation $$ X_t = \phi_1X_{t-1} + \cdots + \phi_pX_{t-p} + Z_t $$ where $Z_t$ is i.i.d. white noise. If we use the backshift operator $$ B(X_t) = X_{t-1} $$ then we can rewrite this recurrence relation as a polynomial in the operator $B$ $$ \phi(B)X_t = Z_t $$ I keep running into the technical claim that the process is stationary if the roots of $\phi(B)$ (when considered as a complex valued polynomial) lie outside of the complex unit circle $e^{i\theta}$. Why is this true?

I'm sorry if this is a duplicate, but I can't seem to find the answer to this.  If $Z_t$ is a white noise process and $X_t$ satisfies  $$ \phi(B) X_t = \theta(B) Z_t $$  (where $B$ is the lag operator), then when is $X_t$ stationary?  If $\theta(z)$ and $\phi(z)$ have no common roots and $\phi(z)$ has a root with $|z| = 1 $ then $X_t$ is necessarily non-stationary [Brockwell and Davis, Remark 3 in Chapter 3].  I also know that a moving average of a stationary process with absolutely summable coefficients is also stationary [Brockwell an Davis, Proposition 3.1.2]. So if $\phi(z)$ has no roots in with $|z| \leq 1$ then the Maclaurin series for $1/\phi(z)$ has radius of convergence greater than 1. Therefore $X_t$ is a moving average of $\theta(B) Z_t$ with absolutely summable coefficients, and hence stationary.  By stationarity, I mean weak (=second order) stationarity.  The lecturer has a habit of putting this on the final, so I'd like to know if there's a general theorem governing it.  From a past paper:


I had a some blocks on the dashboard page.  Then I created a new role with fewer permissions and wanted to show only a couple of them on the dashboard.  I edited all blocks and restricted the access by role.  Now all the blocks with restricted content are still visible in the dashboard but they all have the "(empty)" text on it.  How can I get rid of these blocks completely ?

I created a View called Recent comments and added a block to my dashboard. Afterwards, I deleted the View, which results in an empty block on my dashboard    and the following error message:     Notice: Undefined index: recent-comments-block in   dashboard_page_build() (line 192 of   C:\wamp\www\mysite\modules\dashboard\dashboard.module).   I tried to drag the empty block away after clicking Customize dashboard, but every time I hit Done, it is displayed again. Clearing caches did not help either.  What should I do to get rid of the empty block?


Is there any rule which tells when to use a particular measure of central tendency.

How would you explain the concept of mean, median, and mode of a list of numbers and why they are important to somebody with only basic arithmetic skills? Let's not mention skewness, CLT, central tendency, their statistical properties, etc.  I have explained to somebody that mean is just a quick and dirty way to "summarize" a list of numbers. But looking back, this is hardly illuminating.  Any thoughts or real world examples?


I have tried searching and used without the solution mentioned here:  I have this query: $sql = "UPDATE factuur_toekomst SET             fac_datum = CONCAT(DATE_FORMAT(DATE_ADD(fac_datum, INTERVAL ".$add_regels_interval." MONTH), '%Y-%m-'), '01'),             prijs = '".$add_bedrag."',             uitgevoerd = (SELECT uitgevoerd+1 FROM factuur_toekomst AS temp WHERE id = '".$add_regels_id."'),             user_id = '".$_SESSION['user_id']."'             WHERE id = '".$add_regels_id."'             ";  That responds with error:  #1093 - Table 'factuur_toekomst' is specified twice, both as a target for 'UPDATE' and as a separate source for data  Using uitgevoerd = (SELECT (uitgevoerd+1 FROM factuur_toekomst) AS temp WHERE id = '".$add_regels_id."'),  or uitgevoerd = ((SELECT uitgevoerd+1 FROM factuur_toekomst) AS temp WHERE id = '".$add_regels_id."'),  Is responding with an syntax error. Any suggestions? UPDATE factuur_toekomst SET fac_datum = CONCAT(DATE_FORMAT(DATE_ADD(fac_datum, INTERVAL 1 MONTH), '%Y-%m-'), '01'), prijs = '0', uitgevoerd = (SELECT uitgevoerd+1 FROM factuur_toekomst AS temp WHERE id = '14'), user_id = '1' WHERE id = '14'

I have a table story_category in my database with corrupt entries. The next query returns the corrupt entries:  SELECT *  FROM  story_category  WHERE category_id NOT IN (     SELECT DISTINCT category.id      FROM category INNER JOIN         story_category ON category_id=category.id);   I tried to delete them executing:  DELETE FROM story_category  WHERE category_id NOT IN (     SELECT DISTINCT category.id      FROM category        INNER JOIN story_category ON category_id=category.id);   But I get the next error:      #1093 - You can't specify target table 'story_category' for update in FROM clause    How can I overcome this?


Are there any terse, accessible books that are geared specifically at learning these two formalisms and how to effectively use them? So far I've only see either topic introduced as a part of another book, like QM or classical mechanics. I was hoping for something focused more or less exclusively on these formulations that would then go on to explain important nuances and limitations, and then systematically show how to apply them effectively.

I'm taking a course on  and  Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics.  So far at my university library, I have found many books on both subjects, but not ones with good practice questions and answers. I have Schuam's outline of Lagrangian Dynamics, but didn't really find a lot of practice questions.  Any suggestions would be greatly appreciated!


len() built-in function in python is called like this: mylist = "Hello" x = len(mylist)  On the other hand, the string built-in functions of str class are called using object with dot operator like this: a = "Hello, World!" print(a.lower())  Could someone please explain the reason of this difference in invocations of len() and other str methods like lower()?

I know that python has a len() function that is used to determine the size of a string, but I was wondering why it's not a method of the string object.  Update  Ok, I realized I was embarrassingly mistaken. __len__() is actually a method of a string object. It just seems weird to see object oriented code in Python using the len function on string objects. Furthermore, it's also weird to see __len__ as the name instead of just len.


I have a PDF A.pdf and B.pdf and would like to merge them both to AB.pdf, where each page is merged alternately so that page 1 in AB.pdf would be the first page of A.pdf and page 2 in AB.pdf would be the first page of B.pdf etc.  I would like to achieve that with an handy command in bash on macOS 10.14.5. How can I do that?

I would like to merge 4 pdfs, pdf1.pdf, pdf2.pdf, pdf3.pdf pdf4.pdf together so that the pdfs are spliced, i.e. the first page will be the first page of pdf1, the second the first of pdf2, the third the first of pdf3, etc.  The pdf files are with plain images, no table of contents.  How would I accomplish this? It would be nice to do it from Terminal as well.


A charge $Q$ is places at the corner of a cube of side $a$. What is the electric flux through all the six faces of the cube? What is the electric flux on each one of it's faces?   I am aware of Gauss' Law, but, I don't know how the charge being in the corner of the cube instead of the center of a sphere affects things.

I am looking at Griffiths introduction to Electrodynamics 3rd ED.  Problem 2.10 asks for the flux of $E$ through the right face of the cube, when a charge $q$ is in the back left corner of the cube.  The solution manual says it should be $\frac q {24\epsilon _0}$ but I think it should be $\frac q {6\epsilon _0}$ because each side should experience the same flux, and the face of the cube represents 1/6th of the cube.


I'm not personally interested in such a feature, but I just want to put forth the idea of an optional, possibly monetize-able,  romantic relationship matching feature for SE users. Is this a bad idea? If so, why not?

No, not like this:    Hear me out!  As Stack Overflow grows, it becomes increasingly ridden with extremely newbie and mediocre questions. It's just natural. The team are fighting hard to keep the crap out, but there are many very basic questions that are okay on their own. They don't deserve to be kicked out* - they are just very, very, very basic and/or localized.   Too much basicness tires users who are interested in discussing more advanced topics.  As has been discussed many times over, the voting system is not suited to identify advanced questions due to what is known as the . A group of people will vote on what they understand, which puts truly expert questions at a natural disadvantage that a democratic voting system can't overcome.  Now, there is a small number of users on Stack Overflow who I, as a user, know share my basic values (like, teaching a man to fish rather than fishing for them); I also know they are experts in their fields. It is safe to assume that what these users regard an interesting question worthy of attention, is likely to be interesting to me as well.      The idea is to introduce an opt-in "follow" mechanism that allows followed users to share what they find interesting, with very little fuss and on a purely opt-in basis.   Allow every SO user to follow any other SO user with a certain minimum rep, say 3000.   To every user who is being followed (or every user), display a new link underneath every question, "Recommend".    Introduce a new filtered view somewhere, named "Recommended". The view will show me all questions that my followed users are recommending.   Whenever I browse a list of questions, highlight those questions that have been recommended by my followed users. (I haven't put much thought into how to implement this graphically - you get the drift.)      I'm not especially fond of social networking, and I think most of it doesn't have a place on SO. But I'm starting to think this specific thing could be the right way to go in order to tell apart expert content from the 10000th dreary "how do I upload a file" question.  This is an entirely opt-in feature - unless I actively follow some users, I will never notice this.   Maybe for a bit of ego-stroking, the profile page can show how many users follow you. Or even who. Everything else would simply be kept under wraps - no publication of follower data in the data dump, no follower leagues or anything like that.      * At least not under current SO rules. Maybe those rules need to be changed - but that is a different discussion.


I am troubleshooting a backup script (bash), and I have limited working knowledge of the current configuration since the last 3 predecessors did not leave any documentation. I do know that my server is running MySQL Server 5.5.37 on a Debian machine. I'm manually testing the script and found mysqldump to be the problem. I realize there are very many posts on this same error message (, , , ), but none of them have worked for me. Running this command mysqldump -uroot -p******** --all-databases > backup.all.sql 2> backup.all.err  produces the following error: Got error: 1045: Access denied for user 'root'@'localhost' (using password: YES) when trying to connect  Here's a summary of what I've tried.  Verifying that root user can log in, and is being logged in correctly (ie. USER(), CURRENT_USER();).  I can log in to mysqlwith root user and supplying the -p flag. Yet if I supply the password as part of the cmd (ie. mysql -uroot -p********) I receive the same error as above. ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)   Verified that every user has a password, there are no anonymous users, and root is in the users table with the normal hostnames (list below, shortened). +-------------+--------------+ | user        | host         | +-------------+--------------+ | root        | 127.0.0.1    | | root        | localhost    | +-------------+--------------+   I can run mysqldump -p --all-databases with limited success but will not work for my use case because I'd like the script to run automatically without the need for user interaction (eg. supplying the password before proceeding with the backup process).  Root user has all privileges on all dbs. +-------------------------------------------------------------------+ | Grants for root@localhost                                         | +-------------------------------------------------------------------+ | GRANT ALL PRIVILEGES ON *.* TO 'root'@'localhost' IDENTIFIED BY   | | PASSWORD '*********' WITH GRANT OPTION                            | +-------------------------------------------------------------------+   Values in /etc/mysql/my.conf all seem to be pretty standard and are probably default. There are no additional .conf files.  Tried forcing a connection to localhost (which also forces use of the TCP protocol) mysql -h localhost -uroot -p********    Reviewed and tested each of the  from the MySQL 5.5 docs.  Reset root password (not OS root user) using dpkg-reconfigure mysql-server-5.5  Flushed privileges, just in case, using mysqladmin flush-privileges  Ran mysqlcheck --all-databases in case mysql was corrupted. No errors were found.   Is there any reason why 'root'@'localhost' would still be denied when supplying the password for both mysql and mysqldump? Could both modules be ignoring the password I'm supplying and, if so, why? Lastly, is there anything else that I can try in order to allow me to log in by providing a password as part of the cmd?

I am trying to set a cron job for taking backup from my slave machine. So I need to stop the slave  I issued a command   mysqladmin --user=root --password=test_pass stop-slave   But it is throwing error:      mysqladmin: connect to server at 'localhost' failed error: 'Access   denied for user 'root'@'localhost' (using password: YES)'   Now I tried with the command  mysqladmin --user=root --password stop-slave   It prompts for password and I gave as test_pass and everything was fine.  Why so happened? What is the alternative?  NB: BTW my mysql version is mysql-5.0.95-5, it it make any sense.


First of all, related:    Here it is said how to fix a position to the exact place you position it in the latex document. I was wondering if it is also possible to float it within a \section or \subsection, but keep it fixed to that (sub)section. In other words: let it float within only a certain (sub)section and not the entire document, so I am certain table X will end up somewhere in section X and table Y will end up somewhere in section Y.   EDIT The question was already answered here:

I would like to place figures in my document in certain subsections. Normally I would achieve this with float using [H]. But this would mean, that the figures are at fixed points in my text and sometimes this just doesn't look good.   I already found this question:   How can I tell LaTeX use subsections as float barriers instead of sections.


How do i run a file named start.sh file on startup if im on ubuntu server? i decided to install ubuntu server on a pc that i rarely use so i can have my minecraft server on it ... and i want to be able to add plugins and such on it without having to go to that computer all the time (switch screens and such) and just use ftp and transfer all of the files that way and then restart my computer then the new plugins are loaded. can someone please help me with this? :)  (sorry if this was confusing its really late here atm)

How can I run scripts automatically when Ubuntu starts up so I don't have to run them manually after startup?


I want to create a go back button on a single.php in WordPress. I know I can easily do that with window.history.go(-1) but in the case of the visitor come from another site, I want to redirect to the homepage of my site.  In other words: How can I know if the previous page is an internal link to my site? And if not, redirect to the homepage?

Some e-Marketing tools claim to choose which web page to display based on where you were before. That is, if you've been browsing truck sites and then go to Ford.com, your first page would be of the Ford Explorer.  I know you can get the immediate preceding page with HTTP_REFERRER, but how do you know where they were 6 sites ago?


I want to rename some fileds on a SHP file, (the fields on the DBF file), using ArcCatalog (ArcGIS Desktop v10.2.2).  From ArcCatalog, right click on a SHP file -> Properties... -> Fields. Then the program let you rename the field and change the data type... apparently.    When I hit Enter or click Apply, an error appears: Failed to alter the name of the field.  The file is not in use, nor read only, and the name of the field is under the 10 character limit.  Ironically, I can do it with gvSIG!

How can I change the field names (not the alias) in ArcGIS 10.2? I already found this page on ArcGIS support: "" but there is is not "Defense Mapping" on Customized Mode Categories In my ArcCatalog! Without access to Defense Mapping, how can I change the field names?


Having trouble installing ubuntu. I downloaded the 12.04.3 desktop i386 iso image, used the universal installer to put it on a USB drive (the netbook does not have a CD drive). netbook- acer aspire one with amd arm c-60 processor 1mhz with 4GB ram.  I changed the boot order to USB and I get:  SYSLINUX 4.06 EDD 2012-10-23 Copyright 1994-2012 H.Peter Anvin et al  _ and cursor flashing but you cant write anything, no buttons work you have to do a hard shutdown to leave.   I tried the same procedure with the amd64 iso and get same results.   why did it not boot?

I would like to see a full how-to guide on how to install Ubuntu.


Helping others is a good habit.   Which part of speech is "Helping" & "others" here? I think helping here is noun & others is pronuoun.

Given the following sentences:        I have even started using them in normal writing.   People can understand your writing better.      Are using and writing gerunds, verbs, or some other part of speech?  Context:  I am prefixing the words in some phrases with abbreviations. Some of the words are giving me trouble in classification. (The message is supposed to be an implicit proof of why adding prefixes to table names in a database is terrible. But I'd like to get it right.)  Here's the full set of sentences for your amusement. However, please restrict your comments to the stated question, for the most part.        com-Don't ver-Listen prep-To adj-Those adj-Other nou-People.    pro-You aux-Should adv-Always ver-Use nou-Prefixes prep-With pro-Your adj-Table nou-Names.    pro-I aux-Have adv-Even ver-Started ver-Using pro-Them prep-In adj-Normal nou-Writing.   com-See adv-How adj-Effective pr-It ver-Is?    nou-People aux-Can ver-Understand pro-Your nou-Writing adv-Better!      (where com means command verb)  This question is part of 3 related questions:     This question   It originally came from