how can I update ubuntu v12.04 to v13.04 without using a internet connection?
How do I upgrade to a newer version of Ubuntu?
an "X is an X is an X" what does this mean? I am reading  (I must say, with great delight but that's not relevant) and  Canadian is a Canadian is a Canadian A citizen is a citizen is a citizen.  I do not understand this structure. Why not just &quot;A citizen is a citizen&quot;? What is the meaning of repeating this? $\mathbb R = X^2$ as a Cartesian product I wonder if it is possible to consider $\mathbb R$ as a Cartesian product $X\times X$ for some set $X$. From the point of view of the dimensionality, there are spaces with a Hausdorff dimension $1/2$ (sort of Cantor sets), but I guess there are other problems in this construction  unrelated to the dimension.  Edited: replying on the comment by Asaf. I want that for all $r\in\mathbb R$ there exists a unique representation $r=\langle x,y\rangle$ where $x\in X$ and $y\in X$. Also, what if we want to have $X$ to be a topological space and $h:X\times X\to\mathbb R$ to be a homeomorphism? It has come to the point in my computing program now where I have 5 swinging pendulums that are all modified at once by slider values. These values are drawn onto the from and passed through the class pendulum. To change the values the update button is run, and their is a default option to use a setup that works. The values are also shown on screen through some simple labels. The zero button sets all values (except length) to zero.  The values for each pendulum drawn is:   String length angle Acceleration (angular) Angluar velocity Damping or friction Gravity   My calcuations for these values: (Bob = the weight at the end of the string, and there are X and Y Co-ordiantes for it.  bobX = originX + (Math.Sin(angle) * length);         bobY = originY +(Math.Cos(angle) * length);   Caclulate Acceleration:  Angular Acceleration = (-1 * gravity / length) * Math.Sin(angle);    Increment Velocity:          Angular Velocity += Angluar Acceleration;   Increment Angle          angle += AngularVelocity;   Friction action, pendulum eventually 0's          AngularVelocity*= damping;   Now my next task is to make the pendulums collide "realistically" and recreate a newtons cradle type effect. I've looked into elastic collision solutions on particle e.g. here is an excellent example:    I've also looked at the raw physics behind it  but my brain couldn't get to grips with the raw physics side of things.  So I'm wondering if anybody could help me figuring out the theory for the collisions.  My current idea is when the co-ordinates meet the velocity will simply change polarity e.g. +10 to -10 in the opposing pendulum. Am I correct here?  If you are into code I've posted the code on stack overflow How to run scripts on start up? Contour integral of $\sqrt{z^2-1}$ on $|z| = 2$ I've been wrestling with this problem (available  ):  Evaluate the integral of $f(z) = \sqrt{z^2-1}$ around the circle $\{z: |z| = 2\}$, where the branch of the square root function is chosen so that $\sqrt{2^2-1} &gt; 0$.  I came up with the answer $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = \pi i$$ using the following argument, which seems a little like voodoo to me.  You notice that there are two points, at $z \pm 1$, where you might have to pick a branch of $log()$ to define the square root. Then, I convinced myself that as long as you exclude from your domain the real interval $-1 \le x \le 1$, the function $f(z)$ can be continuously defined (maybe the two branches somehow cancel?), and so is analytic on its domain.  Therefore you can shrink the contour of integration continuously using the Cauchy Closed Curve Integral Theorem, so that you wind up reducing it to the real integral $$2\int_{-1}^1 \sqrt{x^2-1} dx = \pi i$$  I'm not really sure the answer is correct, and I'm even less certain about the way I got it. I had a hard time convincing myself that $\sqrt{z^2-1}$ was not multi-valued on the domain. To try to get at that I tried $\sqrt{z^2-1} = \sqrt{z+1} \sqrt{z-1}$ and reasoned that the product makes the discontinuity disappear, using $$e^{\frac{\pi}{2}i}\cdot e^{\frac{\pi}{2}i} = -1 = e^{-\frac{\pi}{2}i}\cdot e^{-\frac{\pi}{2}i} $$ for the different branches of $log()$ you can choose.  I'd appreciate any input that would help me get a a better way to look at this.  Thanks!    EDIT  An attempt to use the Residue at infinity:  By substituting $z = 1/w$ you get \begin{eqnarray} \int\limits_{|z| = 2} \sqrt{z^2-1} dz &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1}{w^2}-1} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^2}\sqrt{\frac{1-w^2}{w^2}} dw \\ &amp;=&amp; \int\limits_{|w| = 1/2} \frac{1}{w^3}\sqrt{1-w^2} dw \end{eqnarray} The integrand is analytic in $|w| \le 1/2$ except at $w = 0$, so we can apply the Residue Theorem. Near $w = 0$, $\sqrt{1-w^2} = 1 - \frac{1}{2}w^2 + \dots$, so the residue of $\frac{1}{w^3}\sqrt{1-w^2} $ at $w = 0$ is $-\frac{1}{2}$. Then the integral is $$\int\limits_{|z| = 2} \sqrt{z^2-1} dz = 2\pi i \cdot (-1/2) = -\pi i$$ How do I say what is the current UTC in eastern zone Over the years I've written some libraries. These libraries sometimes depend on each other.  As a result, the "tex" directory is structured as follows:  tex ├── library |   ├── library1.sty |   ├── library2.sty |   └── library3.sty ├── project1 |   ├── master.tex |   ├── chapter1.tex |   └── chapter2.tex ├── project2 |   └── article.tex └── project3     └── paper.tex   The libraries depend on each other. As a result, in every library that depends on another library, this is part of the header:  %library2.sty \ProvidesPackage{library2} \RequirePackage{../library/library1}   In other words, the library is imported from the "root of every project". This is not a good design choice. What if someone copies the libraries in the folder of the root of a project, or what if the folder "library" is renamed...  It is however reasonable the "active directory" still remains in the project root.  What can be done to resolve such library dependencies? How to make a figure span on two columns in a scientific paper? Can the 5E abjurer wizard recover temp hp on his arcane ward any time it is below max or only when it reaches 0? On p115 of the PHB under Arcane Ward there are a few facts that I think are clear:   The ward is created by the first abjuration spell you cast in a day It has a max hp of level &times; 2 + int modifier. The ward does not absorb damage once it reaches 0 hp, but it remains until you take a long rest The ward can be recharged by casting abjuration spells, at a rate of 2 x spell level worth of hp 3.   However, the way they wrote the paragraph about recharging seems unclear to me. Can you recharge the ward whenever it is below max hp or only when it is at 0? My understanding of temporary hp would say it is the latter, but the writing on this ability infers the former.  An example.  If I were a level 10 abjurer with 20 int and cast Mage Armor, it would give the ward 25 hp. If I took 30 damage from an enemy, the ward would absorb 25 damage, leaving it at 0, and I would take the remaining 5 damage. If I cast Stoneskin (level 4 abjuration) the ward would be recharged with 8 hp. If I then cast Planar Binding (level 5 abjuration) which would be correct?   The ward remain at 8 hp The ward would recharge an additional 10 hp to a total of 18 hp What's this? What is it? but not What's it? - Why? Can anyone give a cogent, simply described explanation of why the verb BE in:  What is it?  ... doesn't seem to be able to be contracted with the subject:  What's it? *  Compare the sentences above with:  What's this? What's that?  These are perfectly fine. In fact, the contractions here should be expected in almost all examples of spoken English. Answers with references to authoritative vetted sources would be greatly appreciated. I know that for a Banach space $X$ and a linear functional $T:X\rightarrow\mathbb{R}$ in its dual $X'$ the following holds: \begin{align}T \text{ is continuous } \iff \text{Ker }T \text{ is closed}\end{align} which probably holds for general operators $T:X\rightarrow Y$ with finite-dimensional Banach space $Y$. I think the argument doesn't work for infinite-dimensional Banach spaces $Y$. Is the statement still correct? I.e. continuity of course still implies the closedness of the kernel for general Banach spaces $X,Y$ but is the converse still true? When will my device get the Android 5.0 update (Lollipop)? parallel thermostat I have a venter room heater in a cabin. It uses a milivo;t thermostat. I am hooking it up to a wifi thermostat using a relay and 24 volt power supply. My concern is that if the power goes off that the thermostat will not power the unit on. I currenty have a digital thermostat that controls the unit and works great. can I wire the current thermostat to the wifi in parallel so if power goes off it will still allow the heater to turn on. If I can how do I wire it? Can you claim a Double Sacrifice Bonus? Two very closely related questions:  If a card has two different "Sacrifice this creature for X" abilities on it, does sacrificing it give both benefits?  Likewise, if a card requires a creature to be sacrificed, but that creature has a "Sacrifice this creature for X" ability, do you get the sacrifice benefit when you sacrifice it for the other requirement? I would like to restore LightDM to its default state, because for some reason /etc/lightdm/unity-greeter.conf is now an empty file.  Deleting /etc/lightdm/unity-greeter.conf and then running sudo apt-get install --reinstall unity-greeter doesn't create a new config file as you might expect.   How can I restore a missing config file? What is the difference between Set and SetDelayed? How to count the number of occurrences of an element in a List I have an ArrayList, a Collection class of Java, as follows:  ArrayList&lt;String&gt; animals = new ArrayList&lt;String&gt;(); animals.add("bat"); animals.add("owl"); animals.add("bat"); animals.add("bat");   As you can see, the animals ArrayList consists of 3 bat elements and one owl element. I was wondering if there is any API in the Collection framework that returns the number of bat occurrences or if there is another way to determine the number of occurrences.  I found that Google's Collection Multiset does have an API that returns the total number of occurrences of an element. But that is compatible only with JDK 1.5. Our product is currently in JDK 1.6, so I cannot use it. How to draw Brownian motions in tikz/pgf Can I make my Ubuntu make sounds when I press Caps Lock etc.? How to customize the package editor interface?