While Wave says Grand Chariot is stronger, Incursio(Tatsumi) has more abilities, from what we see, and has the ability to adapt to any weather or situation, because of the beast used to make it. Its user, Tatsumi, also relies on his personal skill most of the time, Incursio there to just bail him out when he is in serious trouble, while Wave relies on Grand Chariot more than anything. But I could be wrong, so let me know your opinions.
Wave states with great confidence that Incursio is weaker than Grand Chariot, because Incursio was a prototype for Grand Chariot, etc.  The early clashes between Wave and Tatsumi can lead the viewer to such conclusion, but Incursio's has the ability to evolve (from the beast it was made of), while Grand Chariot doesn't.  If you watched to the finale, we can see that      Tatsumi causes Incursio to evolve so much during the fight against Shikoutazer that it even gains the ability to fly. While it is enough to defeat the emperor, unfortunately not enough to save Tatsumi's life.   Considering this, I don't think that Incursio was the weaker one. Is it so?
Prison problem: locking or unlocking every $n$th door for $ n=1,2,3,...$ Integration by partial fractions; how and why does it work? Could someone take me through the steps of decomposing  $$\frac{2x^2+11x}{x^2+11x+30}$$ into partial fractions?   More generally, how does one use partial fractions to compute integrals $$\int\frac{P(x)}{Q(x)}\,dx$$ of rational functions ($P(x)$ and $Q(x)$ are polynomials) ?    This question is asked in an effort to cut down on duplicates. See .  Also see . My issue is that I have a blender file in which cameras and lamps do not move when I attempt to rotate them using the mouse. If I select the objects (in object mode), press R, and move the mouse in the viewport, the lamps and cameras don't respond; they remain in the same orientation as when I started, no matter how vigorously I try to move the mouse. The values in the information bar show that the mouse is communicating. If, however, I manually enter a new value for the amount of rotation in the properties shelf of the viewport, the camera moves to the new orientation.  On a new default Blender scene, the cameras and lamps do respond to commands to rotate and scale using the mouse. I've compared all of the settings I can think of, and don't see anything obvious that corrects the problem.   is available. What is the advantage of using sudo apt-get autoremove over a cleaner app? Areas versus volumes of revolution: why does the area require approximation by a cone? Suppose we rotate the graph of $y = f(x)$ about the $x$-axis from $a$ to $b$.  Then (using the disk method) the volume is $$\int_a^b \pi f(x)^2 dx$$ since we approximate a little piece as a cylinder.  However, if we want to find the surface area, then we approximate it as part of a cone and the formula is $$\int_a^b 2\pi f(x)\sqrt{1+f'(x)^2} dx.$$  But if approximated it by a circle with thickness $dx$ we would get $$\int_a^b 2\pi f(x) dx.$$  So my question is how come for volume we can make the cruder approximation of a disk but for surface area we can't. Prove that there are infinitely many primes and non-primes in the numbers $10^n+1$, where $n$ is a natural number. So numbers are 101, 1001, 10001 etc. Why are my wrists the first part of my body to start aching during a long ride? Most riders seem to say it's their groin, neck or lower back that starts hurting first after a decent distance has been ridden. For me it is my wrists.  I have no history of wrist pain (strains, breaks etc) so it can't be explained by that and I try to adjust my hand positions across my handlebars as often as I can.  My question has 2 parts:   1. Is there anything I can do to minimise pain in terms of riding position, gloves, exercises etc which will reduce soreness?  2. Why might this pain be occurring?  *I do all of my riding on paved roads on a road (Specialized Allez) bike. Multiple Bluetooth speakers simultaneously I would like to pair two sticky dude Bluetooth speakers, at one time with my iPhone. With two of them at once it would be like stereo sound. Is there an app or something maybe? When is the move constructor called in the `std::move()` function? I'm reading  and I'm trying to understand the proof under "Degeneracy in One Dimension".  Here's what it says:     Considering a one-dimensional quantum system in a potential $V(x)$ with degenerate states $|\psi_1\rangle$ and $|\psi_2\rangle$ corresponding to the same energy eigenvalue $E$, writing the time-independent Schrödinger equation for the system:       $$-\frac{\hbar^2}{2m}\frac{ \partial^2\psi_1}{ \partial x^2} + V\psi_1 =E\psi_1$$       $$-\frac{\hbar^2}{2m}\frac{ \partial^2\psi_2}{ \partial x^2} + V\psi_2 =E\psi_2$$   Multiplying the first equation by $\psi_2$ and the second by $\psi_1$ and subtracting one from the other, we get:       $$\psi_1\frac{d^2}{d x^2}\psi_2-\psi_2\frac{d^2}{d x^2}\psi_1=0$$   Integrating both sides       $$\psi_1\frac{\partial \psi_2}{\partial x}-\psi_2\frac{\partial \psi_1}{\partial x}=constant$$   In case of well-defined and normalizable wave functions, the above constant vanishes, provided both the wave functions vanish at at least one point, and we find: $\psi_1(x)=c\psi_2(x)$ where $c$ is, in general, a complex constant. So, the two degenerate wave functions are not linearly independent. For bound state eigenfunctions, the wave function approaches zero in the limit $x\to\infty$ or $x\to-\infty$, so that the above constant is zero and we have no degeneracy.   Here are the parts I don't understand:   How does integrating $\psi_1\frac{d^2}{d x^2}\psi_2-\psi_2\frac{d^2}{d x^2}\psi_1=0$ yield $\psi_1\frac{\partial \psi_2}{\partial x}-\psi_2\frac{\partial \psi_1}{\partial x}=constant$.  Without having explicit formulas for $\psi_1(x)$ and $\psi_2(x)$, how do we just apparently pull them both out of the integral? I don't understand how the constant in the last equation vanishes just because $\psi_1$ and $\psi_2$ vanish at infinity. Even if it does vanish, how does that imply $\psi_1=c\psi_2$? I have looked at other questions on this site (e.g. "why does space expansion affect matter") but can't find the answer I am looking for.  So here is my question: One often hears talk of space expanding when we talk about the speed of galaxies relative to ours. Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object.  If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it.  I have a few potential answers for this, which raise their own problems:   Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance Fundamental particles are curled up in additional dimensions a la string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me. How do I add myself into the sudoers group? Possible Duplicate:          I've added myself back into the admin's group I think, by following   But I still can't do commands like:  sudo aptitude update   I get the message  oshirowanen is not in the sudoers file.  This incident will be reported.   How do I add myself into the sudoers group now that I am in the admin group? proving topological equivalence How would I show that $$d_E = \sqrt{\sum_{i=1}^n(x_i-y_i)^2}$$ and $$d_\infty= \sum_{i=1}^n|x_i-y_i|$$ and $$\sup\{|x_1-y_1|,|x_2-y_2|,...,|x_n-y_n|\}$$ are topologically equivalent on $\mathbb{R}^n$? I can do it for $\mathbb{R}^2$, but I'm not sure how a generalization looks like. Git keeps prompting me for a password How do I unit test (using xUnit) a class that has internal private methods, fields or nested classes? Or a function that is made private by having  (static in C/C++) or is in a private () namespace?  It seems bad to change the access modifier for a method or function just to be able to run a test. I was compiling a tool called Rejoystick so I installed a few packages and dependencies. But now I don't need it any more so I removed those packages. Running apt-get shows that I have some packages that are automatically installed and are no longer needed.   But I have a bad experience with apt-get autoremove. It broke my desktop environment when I uninstalled wine some time ago. Luckily, I had a clonezilla partition backup then, but this time, I don't have a backup. So I'm cautious. Running apt-get shows these packages are orphaned     gir1.2-gtk-2.0 libasound2-dev libavahi-client-dev libavahi-common-dev   libcaca-dev libcairo-script-interpreter2 libdbus-1-dev libdrm-dev   libexpat1-dev libfontconfig1-dev libfreetype6-dev libgl1-mesa-dev   libglu1-mesa-dev libharfbuzz-dev libharfbuzz-gobject0 libice-dev   libpcre3-dev libpcrecpp0 libpixman-1-dev libpng12-dev libpthread-stubs0-dev   libslang2-dev libsm-dev libx11-dev libx11-doc libx11-xcb-dev libxau-dev   libxcb-dri2-0-dev libxcb-dri3-dev libxcb-glx0-dev libxcb-present-dev   libxcb-randr0-dev libxcb-render0-dev libxcb-shape0-dev libxcb-shm0-dev   libxcb-sync-dev libxcb-xfixes0-dev libxcb1-dev libxcomposite-dev   libxcursor-dev libxdamage-dev libxdmcp-dev libxext-dev libxfixes-dev   libxft-dev libxi-dev libxinerama-dev libxrandr-dev libxrender-dev   libxshmfence-dev libxxf86vm-dev mesa-common-dev x11proto-composite-dev   x11proto-core-dev x11proto-damage-dev x11proto-dri2-dev x11proto-fixes-dev   x11proto-gl-dev x11proto-input-dev x11proto-kb-dev x11proto-randr-dev   x11proto-record-dev x11proto-render-dev x11proto-xext-dev   x11proto-xf86vidmode-dev x11proto-xinerama-dev xorg-sgml-doctools xtrans-dev   zlib1g-dev   I'm not sure if I should run apt-get autoremove. I was searching details related to each of these packages so that I can understand which ones are needed but they all seem important e.g.     gir1.2-gtk-2.0    I have Cinnamon, GNOME and Unity installed, I think apt-get autoremove will break something. Any help will be appreciated.   Thanks for reading. (Almost) double light speed Linear Transformations: Proving 1 dimensional subspace goes to 1 dimensional I am having trouble understanding this whole question, and how to prove it.  Let $F:\mathbb{R}^n\to\mathbb{R}^m$ be a linear transformation. Prove that if $L$ is a $1$-dimensional subspace of $\mathbb{R}^n$, then  $F(L)=\{y\in\mathbb{R}^m: y=F(x)\text{ for some }x\in L\}$  the image of $L$ under $F$ is a subspace of $\mathbb{R}^m$ with dimension $1$ or $0$. Hence prove that if the kernel of $F$ is $\{0\}$, then the image of $L$ is a $1$-dimensional subspace of $\mathbb{R}^m$ (and so, in this case, $F$ takes lines in $\mathbb{R}^n$ to lines in $\mathbb{R}^m$). Is there a good equivalent implementation of strptime() available for Windows?  Unfortunately, this POSIX function does not appear to be available.   - summary: it converts a text string such as "MM-DD-YYYY HH:MM:SS" into a tm struct, the opposite of strftime(). Why use a certain measure of forecast error (e.g. MAD) as opposed to another (e.g. MSE)? MAD = Mean Absolute Deviation MSE = Mean Squared Error  I've seen suggestions from various places that MSE is used despite some undesirable qualities (e.g. , which states on p8 "It is commonly believed that MAD is a better criterion than MSE. However, mathematically MSE is more convenient than MAD.")  Is there more to it than that? Is there a paper that thoroughly analyzes the situations in which various methods of measuring forecast error are more/less appropriate? My google searches haven't revealed anything.   A similar question to this was asked at , and the user was asked to post on stats.stackexchange.com, but I don't think they ever did.