Is there an easy way (i.e. without using TikZ, say) to write a line of text backwards? By which I roughly mean, the entire text is reflected about the y axis.  I only need it for a Beamer heading, not anything more general like a hyphenated paragraph.   may be related.
The following  (links to pdf) in the  has no provided source. The book  by Ash and Gross seems to use a similar style. Where can I find hints for typesetting publication standard articles/books as above in TeX. I looked around a bit but couldnt find much from else from keyword searches.  Particularly, I am looking at the chapter headings, title page design, and the mirror effect. Sorry for the title, as I dont really know what its called.
Get referenced node fields in twig In Drupal 8, I have a content type, that has an "entity_reference" field and I wish to access the referenced node's fields in twig template. the kint() output for the field is:   In this list I can't find the referenced node's field values. How can I (if at all possible) load the node or node fields/values in twig?  Best,  Alari If $A = \tan6^{\circ} \tan42^{\circ},~~B = \cot 66^{\circ} \cot78^{\circ}$ find the relation between $A$ and $B$ My trigonometric problem is:     If $A = \tan6^{\circ} \tan42^{\circ}$ B = cot$66^{\circ} \cot78^{\circ}$ find the relation between $A$ and $B$.    Working :   $$B = \cot 66^{\circ} \cot78^{\circ} = 1- \frac{\tan24^{\circ}+\tan18^{\circ}}{\tan42^{\circ}}$$  $$A= \tan6^{\circ} \tan42^{\circ} = 1- \frac{\tan6^{\circ} +\tan42^{\circ}}{\tan48^{\circ}}$$  but it seems  this is the wrong way of doing this...please suggest. Thanks! Formula across objects Do you ever center AND standardize variables in multiple regression? Do you ever center AND standardize variables in multiple regression? It seems as if standardization would automatically center variables...is this true? This is the proof from the book:     Theorem. There are infinitely many primes of the form $4n+3$.    Lemma. If $a$ and $b$ are integers, both of the form $4n + 1$, then the product $ab$ is also in this form.  Proof of Theorem: Let assume that there are only a finite number of primes of the form $4n + 3$, say  $$p_0, p_1, p_2, \ldots, p_r.$$ Let $$Q = 4p_1p_2p_3\cdots p_r + 3.$$ Then there is at least one prime in the factorization of $Q$ of the form $4n + 3$. Otherwise, all of these primes would be of the form $4n + 1$, and by the Lemma above, this would imply that $Q$ would also be of this form, which is a contradiction. However, none of the prime $p_0, p_1,\ldots, p_n$ divides $Q$. The prime $3$ does not divide $Q$, for if $3|Q$  then $$3|(Q-3) = 4p_1p_2p_3\cdots p_r,$$ which is a contradiction. Likewise, none of the primes $p_j$ can divides $Q$, because $p_j | Q$ implies $p_j | ( Q - 4p_1p_2\cdots p_r ) = 3$, which is absurd. Hence, there are infinitely many primes of the form $4n +3$.   END  From "however, none of the prime ...." to the end, I totally lost!    My questions:   Is the author assuming $Q$ is prime or is not? Why none of the primes $p_0, p_1,\ldots, p_r$ divide $Q$? Based on what argument?     Can anyone share me a better proof?     Thanks. Application is "Ready to Sale" but not reflected on iTunes Store What sci-fi novel has the moon split into 7 pieces by an asteroid, threatening life on earth? I am looking for the title of a novel that I only caught part of on audio. It takes place within our current time frame and deals with the Moon getting struck and fragmented into (initially) 7 pieces by a high-speed asteroid that they called "The Agent".  Within a few weeks of this episode, scientists figure out the the Moon will continue to break down in a cascade reaction over the next couple of years until the planet gets bombarded by so much debris that it sterilizes Earth. The governments of the world frantically start to build a series of ships using swarming concepts to evacuate the planet as much as possible... and that's all I have heard so far.  Thanks for any info. Introductory measure theory textbook I would like to teach myself measure theory and I am looking for a good introductory textbook at the advanced undergraduate or early graduate level. A reader-friendly text with plenty of examples would be ideal. Can't install php5 on Ubuntu 16.04 so I've recently installed my first Ubuntu, to be precise, a daily build of 16.04, on my new laptop since the hardware was to new for 15.10. Now I'm in the process of setting it up and I want to install php5 and some extensions.  When I execute sudo apt-get install libapache2-mod-php5 I get the error message that there is no installation package available for php5 and libapache2.  The error message is in german, so I doubt that this would help, but anyways here it is. :-) E: For package »libapache2-mod-php5« existiert kein Installationskandidat.  Do I need to add a apt-get repository? Or what am I doing wrong? sum of the residue at all poles of the rational function p/q is 0. We are given two polynomials p, q with deg(q)>1+deg(p). Show that the sum of the residue at all poles of the rational function p/q is 0.   How do I go about solving this? Does Auto White-Balance Really Work? How? How does the Eco-Cooler air conditioner really work? describes a device for developing countries which apparently cools the air by 5 °C without electricity. According to , it works by lowering the pressure to drag in the ambient air. Wouldn't the ambient air be at the same temperature?  Does the constriction compress the air and temporarily increase the pressure and so temperature, which then dissipates heat because it is hotter than surroundings; then after passing the constriction, the pressure returns to almost ambient but the temperature drops to below ambient?  How does the Eco-Cooler air conditioner actually work, if at all? What's the 'correct' way of registering/installing an Assembly to the GAC? Show that $PF.PG=b^2$ in a hyperbola If the normal at P to the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ meets the transverse axis in G and the conjugate axis in G' and CF be the perpendicular to the normal from the center C then show that $$PF.PG=b^2\space and \space PF.PG'=a^2.$$ We know that the equation of the normal at parametric point $P\equiv(a\sec\theta,b\tan\theta)$ is given by  $$a\,x\cos\theta+b\,y\cot\theta=a^2+b^2$$   Equation of the transverse axis is $y=0$ and that of the conjugate axis is $x=0$.   Hence   $$G\equiv(\frac {a^2+b^2}{a}\sec\theta,0), \, G'\equiv(0,\frac {a^2+b^2}{b}\tan\theta)$$  C is the origin and CF is perpendicular to the normal. Hence   $$ CF\equiv b\,x\sec\theta-a\,y\tan\theta=0\implies y=\frac {b\,x\sec\theta}{a \tan\theta}$$   Substituting this in the equation of the normal we get   $$a\,x\cos\theta+b \,\cot\theta\,\frac {b\,x\sec\theta}{a\,\tan\theta}=a^2+b^2\ $$   implies  $$ (a^2 \cos\theta \sin^2\theta+ b^2\cos\theta)x=(a^2+b^2)\sin^2\theta$$  After finding the coordinates of F, the calculation becomes very complicated. So is there an easier way to approach the problem? I would love to see a pure geometric solution to this problem. Should players get a surprise attack by interrupting a villain's speech? Just before confrontations with the "boss" of a dungeon or adventure, I often like to ham it up a bit and let the BBEG-of-the-week gloat a bit about how brilliant their plan is, or what a thorn in the side the PCs have been, or about how the PCs will never win, etc. Usually this is pretty brief, but it sets the tone of the encounter, and generally allows the players a window to say anything they wanted to say before we start the final combat. It also gives the players a chance to ask questions in case they missed something about the plot and they'd like it cleared up in-game.  Usually this goes just fine, and the players seem to generally like it, but sometimes a player who doesn't quite fit the narrative-focused mindset of the rest of the party gets a little restless and throws the first punch. Again, usually this doesn't happen, but occasionally it does.  If a player decides to do this in a given speech, how should I respond? I've defaulted to making everyone roll initiative when a player says they attack in a situation like this. After all, I don't really want to reward the players for attacking in the middle of dialogue, since I (and most of the players) find the dialogue to be really fun, and it mostly exists for the players' benefit, anyway. Besides, when the villain finally attacks, they don't get a surprise round -- their attack just means everyone has to roll initiative.  On the other hand, I feel like the player who threw the first punch might feel a little cheated in not getting a free shot off. They might be trying to have a cool moment of emulating Han Solo, blasting the enemy when they're caught off-guard gloating. Since I make them roll initiative, though, I rob them of this moment and Greedo might get the first shot off, anyway.  So, in this situation, should the player who fires first get a surprise round, or am I handling it correctly in making everyone roll initiative?  5e is the relevant edition, here. Quoting the rules is nice, but I'll take a well-reasoned argument for one way of playing or the other over a strictly RAW answer. Inertial forces and centre of mass Is inertial force always attached to the centre of mass of the object? Why? What rules cause this to happen?  See the  below of the leaned bike in a corner.    The force $m\frac{v^2}{r}$ pointing to the right is the centrifugal force (inertial force - because it's a rotating reference frame, therefore a non-inertial reference frame). It is attached to the centre of gravity of the bike.  I'm thinking that inertial force is attached to the centre of mass because of the fact that it should simply avoid creating a torque on the object. That's intuitive, but there must be a general rule that allows us to conclude that. Why "themselves" and "himself" Possible Duplicate:          I would like to use round parentheses () instead of square brackets [] for citations in a document that I'm working on.   I figured out how to get them in the text using the round option with natbib.  I can't figure out to have the generated bibliography to show () instead of [] when it lists the references.  What do I need to change to fix the way it formats the bibliography? Compare classifiers based on AUROC or accuracy? I have a binary classification problem and I experiment different classifiers on it: I want to compare the classifiers. which one is a better measure AUC or accuracy? And why?  Raondom Forest: AUC: 0.828  Accuracy: 79.6667 %            SVM: AUC: 0.542  Accuracy: 85.6667 % What was the point of testing carbonite-freezing technology on Han Solo? Darth Vader tested carbonite-freezing technology on Han Solo because he didn't want to kill Luke who was precious to the emperor. But, why was it necessary? Wasn't it already a tested and proven technology? Even Darth Vader (when he was Anakin) himself used it along with others decades ago (Star Wars: The Clone Wars S03E18).