Find a point on function graph that has a fixed arc-length distance from another point
Finding the inverse of the arc length function
Merging two pictures Is there a tool in Ubuntu to automatically merge two images having a common strip? I need to scan a large image, which will not fit at once in the scanner. I was thinking about scanning it in two parts and hand-editing the result in Gimp to join them. But probably an automatic tool can do the same more quickly and better.  EDIT I think I may have not made my point clear. My difficulty is not aligning two images. My problem is that one has to compensate for the rotation or distortion introduced by the manual process of putting the sheet into the scanner, and an automatic tool should obtain more precise results at analyzing common patterns in the two images to rotate and align them seamlessly. What is the best way to animate the camera path? I'm modeling a car driving along a road(speeds up, slows down, and stops at traffic lights to wait till the lights turn green, etc.) What is the best way to animate the camera path for the following scenario?   The camera starts moving from point A, and it takes 500 frames to get to point B. During this 500 frames, the camera first gradually speeds up, then moves at a constant speed, and finally slows down to a complete stop at point B. The next 50 frames, the camera will stay at point B. From frame 551, it takes another 500 frames to get to point C from point B. The camera experiences the same motion as described in #1 (speeds up, constant speed, slows down, then stop.) Again, the camera will stay at point C for another 50 frames.  Point C to D is a curve path ( added using Shift + A -> add path). I want the camera to move along the path from frame 1101 to frame 1200. The camera should have the same motion as before(speeds up, constant speed, slows down, then stop.)   What is the best way to animate the camera path in this case? Is there any Python scripts available and can be applied to case like this? Thank you all in advance for your replies. How can I attach a file to a post? I want to attach some files to a post on one of Stack Exchange sites. What is the best way to do this? Is there a better alternative to ambiguous for a word with a wide range of meanings, difficult to find, because they become different in connection with person's opinion. How to launch a command on network connection/disconnection? Should I install programs from a source tarball (`.tar.gz`), from the Ubuntu Software Centre, or from elsewhere? Why is the result of a raster calculation integer when it should be decimal? I'm trying to calculate the NDVI using raster calculator, but the result is integer instead of decimal.  NDVI = (NIR - RED)/(NIR + RED)   The result is normally in the range -1 to 1, but when i tried to calculate de result is -1, 0 and 1, and it does not have have any number in between like, -0.9 or 0.1. And i need those values so i can classify the result in term of soil occupation Ball swung in a horizontal circle, can the string ever by exactly horizontal to the ground? You swing a ball on the end of a lightweight string in a horizontal circle at constant speed.  Can the string ever by truly horizontal?  If not, would it slope above the horizontal or below the horizontal?  Why? Can a university revoke one's degree for his minor misconduct? WCF - Faults / Exceptions versus Messages 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&lt;T&gt; {     [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 Why doesn't attempting to edit count as a pass for a review audit? I just got a question in the review queue that, though poor, I thought was potentially salvageable via editing.  However when I clicked the Edit button I got the deleted post error.  Since the post was gone, I clicked I'm Done (what is there do do with a deleted post?) only to get the review audit failed message instead.  The current behavior is also problematic in that, now that I know about it, it's a risk-free way to check if a question is an audit and not an actual review. That allows me or anyone else who knows about it to detect audits without having to recognize that the question is bad. Does $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}=1$ imply that $a_n$ convergent? Does the condition $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}=1$ imply that $a_n$ convergent?  When I say convergent I mean to $L\in \mathbb{R}$ or to $\infty$ or to $-\infty$  I have a gut feeling this statement is false, just can't find a series which contradicts it.  Thanks a lot Assume that $A$ is an $n\times n$  real matrix, i.e. $$A^T=-A.$$  Since $\det(A-\lambda I)=\det(A^T-\lambda I)$, $A$ and $A^T$ have the same eigenvalues. On the other hand, $A^T$ and $-A$ also have the same eigenvalues. Thus if $\lambda$ is an eigenvalue of $A$, so is $-\lambda$. If $n$ is odd, $\lambda = 0 $ is an eigenvalue.  A curious search in Google returns  the nonzero eigenvalues of $A$ are all pure imaginary and thus are of the form $iλ_1, −iλ_1, iλ_2, −iλ_2,$ … where each of the $λ_k$ are real.   Here is my question:     How can I prove the fact that "the nonzero eigenvalues of $A$ are all pure imaginary"? How to fix a stripped pedal crank The threads on my bike's pedal crank just became fully stripped and the pedal fell off, though the pedal itself is fine. Is there any way I can fix this without fully replacing the pedal crank? Does %* in batch file mean all command line arguments? Can the present perfect continuous construct be used in passive voice? Can the passive voice be used for sentences in the present perfect continuous?  I understand the present perfect and its passive voice (have/has built, has been built). However, the passive voice of present perfect continuous is unclear:   Active: They have been building this house for years. Passive: ???   I have seen suggestions of “This house has been being built for years,” but it sounds awkward and I don't recall anywhere else where two be verbs follow one another. Is this the right form to use? What's the function of the "|" (pipe) operator? Trying to identify a story about breaking out of a predefined path and no one notices I vaguely remember reading a short story many years ago where something happens and the protagonist gets a bit "out of step" with the rest of the world.  Everyone else keeps acting as if he's still doing what he would have been doing before the event, to the point of carrying on one-sided conversations and the like.  I can't remember much of the plot, but the premise stuck with me.  Edit: To try and explain it more clearly, based on the comment I just wrote, I think everyone else was effectively acting like they were robots with a prerecorded program.  If someone would normally wake up, drink coffee, put on pants, then walk out the door to catch a bus, then if the protagonist broke his coffee cup, stole his pants, and jammed the door, the victim would pour coffee into a broken/nonexistent cup, walk out pantsless, but when he got to the jammed door he might suddenly realize something was up (and thus being "out of step" spreads) or he might continue to go through the motions.  In either case, no one else would notice that the victim was pantsless (or that he didn't make it to work)...  How much of this actually came up in the story, I don't remember. General solution to the PDE $xU_x+yU_y=0$ Solve the equation $xU_x+yU_y=0$.   From Partial Differential Equations: An Introduction, 2nd Ed. (Strauss, pg. 10). There are no boundary conditions.  Solution: The PDE can be written $(x,y)\cdot\nabla U(x,y)=0$, implying that the vector $(x,y)$ is tangent to the PDE's characteristic equation. Then I can write $dy/dx=y/x$, and to solve this ODE,  $$\frac{dy}{dx}=\frac yx \\ \ln y=\ln x+c_1 \\ y=cx \\ y/x=c$$  Hence, the PDE is dependent on $c$ and I can write $U(x,y)=f(y/x)$ for some function $f$, solving the problem.  Question: Is this solution correct? The hint for the question (supplied by the professor) said I should use a substitution of variables, but this seems reasonably valid. What exactly happens to the signals hitting a common mode choke? I'm trying to better understand the principles behind the common mode choke. I made a few drawings to clarify.  &nbsp; Differential Mode Signals  Differential currents (driven by differential voltages) create equal but opposite magnetic fields B in the inductor core:    These magnetic fields cancel each other out, so the net flux in the core is zero. As such, these differential currents don't "feel" any impedance.  &nbsp; Common Mode Signals  In contrast, common mode currents generate equal and additive magnetic fields in the core. That's why they "feel" a high impedance, and cannot get through (or getting through means they are highly attenuated).    But what exactly happens? I have several theories, which I will describe below.  &nbsp; Common Mode Signals - Theory 1  My first thought would be that the common mode signal hits the choke and creates a magnetic flux inside. By doing this, lots of energy is lost (hysteresis and perhaps other effects) as heat. Only a small part gets through:      What kind of common mode choke would behave in this particular way? "Burning up" the voltage spike seems a very desirable effect to me.  &nbsp; Common Mode Signals - Theory 2  Perhaps the voltage spike doesn't really get the chance to build up much magnetic flux in the core, or maybe the core is simply not "lossy" enough. The voltage spike bounces off the core and turns back. Only small part gets through:    Although the system on the right side of the choke is protected, the system on the left has to deal with reflected signals. Nasty things like standing waves might appear.  &nbsp; My questions  I've got a few questions for you:   Do you think theory 1 or theory 2 is most plausible? Do you think certain types of common mode chokes tend to behave as described in theory 1, others like in theory 2? Perhaps both of my theories are just plain wrong. If so, what actually does happen?   Please enlighten me.