Constant Jerk Relativistic Rocket
How to describe arbitrary accelerations in special relativity
For what $n$ is $U_n$ cyclic? Bootstrap CSS Active Navigation Switching back to last *used* tab on Chrome wpf combobox binding Launcher Icons disappear The full prophecy by Trelawney, the part my question is about in bold:     "The one with the power to vanquish the Dark Lord approaches ... born to those who  have thrice defied him, born as the seventh month dies ... and the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not ... and either must die at the hand of the other for neither can live while the other survives ... the one with the power to vanquish the Dark Lord will be born as the seventh month dies ..."    – Sybill Trelawney (to Dumbledore)    I am interpreting      for neither can live while the other survives   as: Harry can't live while Voldemort survives and vice versa. But why? It clearly worked until the end of book 7. One could argue with Dumbledore's thery of the self-fulfilling prophecy. But clearly Voldemort was smart enough to see that there was no mechanism that would kill him just because Harry stayed alive.    and either must die at the hand of the other    Again: Why? If somebody else destroyed all Horcruxes and then killed Harry, Voldemort would be just as vulnerable and could be killed by anyone. On the other hand, Harry could have been killed by anyone - his mum's protection transferred to Voldemort by Harry's blood was only helping against Voldemort.  I guess that I am interpreting this part of the prophecy in the wrong way or maybe there is an alternate, less obvious and more tricky one. So my question is: What exactly does the highlighted part of Trelawney's prophecy state? Java - when to use 'this' keyword Let $R$ be the subring of $M_2(\mathbb{R})$ defined by $$R=\left\{\begin{pmatrix}a&amp;b\\0&amp;d\end{pmatrix}\mid a\in\mathbb{Q},b,d\in\mathbb{R}\right\}$$  Show that $R$ is right-Artinian but not left-Artinian.  The "obvious" approach to show it is not left-Artinian is to find an $A\in R$ such that $$RA\supset R(A^2)\supset R(A^3)\supset\dots$$  is an infinite decreasing chain of proper left submodules of $R$ (as a module over itself). However, after spending a lot of time in this endeavor I've come to the conclusion that no such element $A$ exists (I can post a proof if anybody is interested but it'd be long and not worth the time for me otherwise). Does anybody have an idea for another approach I can take to this? I have no idea what else submodules of $R$ would look like. I have always taken these kinds of things for granted. Well of course $a(b+c)=ab+ac$! But why? The thought randomly popped in my head, and I realized that I could not prove it.  Perhaps we should take some time to prove these "obvious" things. I feel like if I cannot prove it, then I do not fully understand it. I would really like a proof of this most basic law, because I have been pondering over it for quite a while. Thanks!  Edit: This proof is for real numbers. Is there a way to change the process group of a running process? Is there a way to change PID, PPID, SID of a running process? It would make sense for the answer to be no, but I'd like to make sure. Which comes first: cat or dog? Which comes first in a sentence?  I know some word pairs such as bacon and eggs, where bacon always comes first. E.g:     Make me bacon and eggs for dinner, honey.   Cats and dogs are the two most common pets I know of. What is the preferred order?   Dogs are superior.     Don't put dogs and cats together, they might fight!  Cats are superior.     Don't put cats and dogs together, they might fight! Why don't the Google Docs CTRL + ALT shortcuts work? I'm currently using Google Docs, but when I try to use the keyboard shortcuts like Ctrl+Alt+M it gives µ instead.    Is Chrome (9) overruling Google Docs in some way?  How can I get these shortcuts working?  I'm using Chrome dev 9 on a Dutch Windows 7 with a US-layout keyboard Question concerning linear combinations of vectors and linear independence in Linear Algebra. Matrix Multiplication in context of row and column vectors I am curious about the proof of these two integrations. It would be great if you could point me in the right direction : $ \int{e^{ax}\cos({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\cos(bx)+b\sin(bx)] + C $ &amp; $ \int{e^{ax}\sin({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\sin(bx)-b\cos(bx)] + C $ Prove: If a sequence converges, then every subsequence converges to the same limit. I need some help understanding this proof:  Prove: If a sequence converges, then every subsequence converges to the same limit.  Proof:  Let $s_{n_k}$ denote a subsequence of $s_n$. Note that $n_k \geq k$ for all $k$. This easy to prove by induction: in fact, $n_1 \geq 1$ and $n_k \geq k$ implies $n_{k+1} &gt; n_k \geq k$ and hence $n_{k+1} \geq k+1$.  Let $\lim s_n = s$ and let $\epsilon &gt; 0$. There exists $N$ so that $n&gt;N$ implies $|s_n - s| &lt; \epsilon$. Now $k &gt; N \implies n_k &gt; N \implies |s_{n_k} - s| &lt; \epsilon$.   Therefore: $\lim_{k \to \infty} s_{n_k} = s$.   What is the intuition that each subsequence will converge to the same limit I do not understand the induction that claims $n_k \geq k$ Software for Calendar Designing Which is the best software of making a calendar. Coreldraw or Illustrator? What is the standard size of calendar? And is there any inbuilt format or template fro making calendar in both Corel or Illustrator? Also, even though Photoshop is a rasterised software but still wanted to ask can it be designed in Photoshop also? wp_customize_image_control default value I am trying to create a custom theme using Wordpress 3.4's customization options. I would like to create an option to change the theme's logo, but I would like to also display a default logo image.   I am using the following code in my function.php page:  $defaultbranding = "get_bloginfo('template_directory') . '/images/logo.png";      $wp_customize-&gt;add_setting( 'change_branding', array(         'default' =&gt; get_bloginfo('template_directory') . '/images/logo.png',     ) );      $wp_customize-&gt;add_control( new WP_Customize_Image_Control( $wp_customize, 'change_branding', array(         'label'   =&gt; 'Image Control',         'section' =&gt; 'theme_settings',         'settings'   =&gt; 'change_branding',     ) ) );   And in the theme's header.php page:  src='&lt;?php echo get_theme_mod( 'change_branding' , 'default' ) ?&gt;'   I would like the 'default' value on the front end to be:  get_bloginfo('template_directory') . '/images/logo.png'   Is there some way I can achieve this?  Thanks in advance for any help. Why are we in love "with" someone? The verbs dare and need do not require auxiliaries when used in the interrogative; for example, “need I?” is as acceptable as “do I need?”  Excluding the auxiliaries themselves (like be, do, have), are there any other such verbs that work that way?