APA6 Class: Manual line-break using "\\" or better solution?
Best choice between using \\ or leaving space after each paragraph to end the paragraph
My equation is not showing big bracket and not showing in next line Create custom fields with apex Anybody knows how to create custom text fields on salesforce.com objects using apex? Suppose f is a twice differentiable function with $f(0)=0$ and $f(1)=1$, $f'(0)=f'(1)=0$. Then show that $|f''(x)| > 4$ for some $x$ in $(0,1)$ Prove $\lim\limits_{n\to\infty}n^{-1/(p+1)}(1^{1^p}\cdot 2^{2^p}\cdots n^{n^p})^{n^{-p-1}}=e^{-1/(p+1)^2}$ Prove that for real number $p\geq  0$ we have   $$\lim_{n\to\infty}\frac{(1^{1^p} \cdot2^{2^p}\cdots n^{n^p})^\frac{1}{n^{p+1}}}{n^\frac{1}{(p+1)}} = \exp\left(\dfrac{-1}{(p+1)^2}\right).$$ novel with psi slavery How to install Google Chrome How do you install Google Chrome on Ubuntu? I had an article, but I lost it.  It showed and described a couple of C/C++ tricks that people should be careful. One of them interested me but now that I am trying to replicate it I'm not being able to put it to compile.  The concept was that it is possible to change by accident the value of a const in C/C++  It was something like this:  const int a = 3;          // I promise I won't change a const int *ptr_to_a = &amp;a; // I still promise I won't change a int *ptr; ptr = ptr_to_a;  (*ptr) = 5;               // I'm a liar; a is now 5   I wanted to show this to a friend but now I'm missing a step.  Does anyone know what's missing for it to start compiling and working?  ATM I'm getting invalid conversion from 'const int*' to 'int*' but when I read the article I tried and it worked great. Can Metamagic be used in Item Creation? What are the limits? One of my players has recently obtained the Craft Wondrous Item feat. In an attempt to prepare for what he may build I want to know the specific limits of Wondrous Items.  I know that someone can create an item for which they do not meet the prerequisites by adding +5 to the spellcraft DC, and that assistance is a thing.  Can someone use meta-magic when crafting a non-specific wondrous item?  Example: Amulet of Empowered Fire-Ball.  If so, can they use meta-magic feats they do not know, substituting for +5 DC?  Can the Spell Level exceed 9 for these items, as long as they add +5 for not meeting the CL requirements, and make the higher check?  Example: Amulet of Maximized Empowered Still Silent Disintigrate. Why is this true?  $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$ How can I use wget to get files recursively if the username contains an @? Firstly my main goal is to try and get FTP files recursively in Centos.  However the actual FTP login contains an @ which ruins the syntax.  Is there some way to place the username in "double quotes" or some such equivalent such that I can use @in the username? How to make foam with bubbles (beer, bath) My goal is create realistic foam. I mean really realistic foam with bubbles, no only SSS shader and done :-).   Use particle system's is not enough, because bubbles overlaps and black artifact's appear.  Any ideas? Some reference images and something about bubbles:    EDIT:  I want this for 360° turntable animation. Bubbles and foam does not to be animated, but should be good keep reasonable render time.  Of course, if someone know how to make it animated I glad to learn it and I'm sure I'm not only one. But my priority is realistic look, not animation.  Only for clarification: I don't need to know how to make bubbles in beer (there is very good tutorial by Andy Price), please focus only on foam. Beer is not important. For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists Show that $\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$ In a theoretical physics homework problem, I have to show the following: $$\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$$  Where $T$ is the Energy-Momentum-Tensor, $j$ the generalized current and $F$ the Field-Tensor. We use the $g$ for the metric tensor, I think in English the $\eta$ is more common.  I know the following relationships:   Current and magnetic potential with Lorenz gauge condition: $$\mathop\Box A^\mu = \mu_0 j^\mu$$ Energy-Momentum-Tensor: $$T^{\mu\nu} = \frac1{\mu_0} g^{\mu\alpha} F_{\alpha\beta} F^{\beta\nu} + \frac1{4\mu_0} g^{\mu\nu} F_{\kappa\lambda} F^{\kappa\lambda}$$ Field-Tensor: $$F^{\mu\nu} = 2 \partial^{[\mu} A^{\nu]} = \partial^{\mu} A^{\nu} - \partial^{\nu} A^{\mu}$$ d'Alembert operator: $$\mathop\Box = \partial_\mu \partial^\mu$$ Bianchi identity: $$\partial^{[\mu} F^{\nu\alpha]} = 0$$   So far I have set all the definitions into the formula I have to show, but I only end up a lot of terms from antisymmetrisation and product rule. I also drew all what I have in , but I still cannot see how to tackle this problem.  Could somebody please give me a hint into the right direction? Plotting several 2d functions in a 3d graph I am trying to reproduce a similar figure to the following one. My first guess was to use pgfplots but I didn't find any example that I could use as a starting point. At the moment I am unsure if pgfplots is actually the right package or I should rely on something else e.g. TikZ.   Since I don't really know where to start, I would appreciate any piece of code that points me in the right direction.    EDIT  Here is some dummy data for the plots.  plot1   plot2   plot3   plot4 0       0       0       0 3.466   2.058   0       0 4.262   2.976   0.001   0 3.822   3.168   0.006   0.008 2.953   2.936   0.019   0.063 2.065   2.492   0.046   0.265 1.332   1.977   0.092   0.734 0.797   1.478   0.164   1.508 0.443   1.045   0.268   2.44 0.228   0.698   0.412   3.219 0.107   0.438   0.598   3.524 0.046   0.256   0.831   3.219 0.017   0.138   1.109   2.44 0.006   0.067   1.429   1.508 0.002   0.029   1.78    0.734 0       0.01    2.141   0.265 0       0.003   2.479   0.063 0       0.001   2.736   0.008 0       0       2.808   0 0       0       2.465   0 0       0       0       0 I have been reading Geoff Cumming's 2008 paper  [~200 citations in Google Scholar] -- and  am confused by one of its central claims. This is one in the series of papers where Cumming argues against $p$-values and in favour of confidence intervals; my question, however, is not about this debate and only concerns one specific claim about $p$-values.   Let me quote from the abstract:     This article shows that, if an initial   experiment results in two-tailed $p= .05$, there is an $80\%$   chance the one-tailed $p$-value from a replication will fall in   the interval $(.00008, .44)$, a $10\%$ chance that $p &lt; .00008$,   and fully a $10\%$ chance that $p &gt; .44$. Remarkably, the   interval—termed a $p$ interval—is this wide however large   the sample size.   Cumming claims that this "$p$ interval", and in fact the whole distribution of $p$-values that one would obtain when replicating the original experiment (with the same fixed sample size), depend only on the original $p$-value $p_\mathrm{obt}$ and do not depend on the true effect size, power, sample size, or anything else:     [...] the probability distribution of $p$ can be derived without   knowing or assuming a value for $\delta$ (or power). [...] We do not assume any prior knowledge   about $\delta$, and we use only the information $M_\mathrm{diff}$ [observed between-group difference] gives about $\delta$ as   the basis for the calculation for a given $p_\mathrm{obt}$ of the distribution of   $p$ and of $p$ intervals.      $\quad\quad\quad$    I am confused by this because to me it seems that the distribution of $p$-values strongly depends on power, whereas the original $p_\mathrm{obt}$ on its own does not give any information about it. It might be that the true effect size is $\delta=0$ and then the distribution is uniform; or maybe the true effect size is huge and then we should expect mostly very small $p$-values. Of course one can start with assuming some prior over possible effect sizes and integrate over it, but Cumming seems to claim that this is not what he is doing.  Question: What exactly is going on here?    Note that this topic is related to this question:  with an excellent answer by @whuber. Cumming has a paper on this topic to:  -- but that one is clear and unproblematic.  I also note that Cumming's claim is repeated several times in the 2015 Nature Methods paper  that some of you might have come across (it already has ~100 citations in Google Scholar):     [...] there will be substantial variation in the $P$ value of repeated experiments. In reality, experiments are rarely repeated; we do not know how different the next $P$ might be. But it is likely that it could be very different. For example, regardless of the statistical power of an experiment, if a single replicate returns a $P$ value of $0.05$, there is an $80\%$ chance that a repeat experiment would return a $P$ value between $0$ and $0.44$ (and a $20\%$ change [sic] that $P$ would be even larger).   (Note, by the way, how, irrespective of whether Cumming's statement is correct or not, Nature Methods paper quotes it inaccurately: according to Cumming, it's only $10\%$ probability above $0.44$. And yes, the paper does say "20% change". Pfff.) How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$ If $f(x)$ is a continuous function on $(-\infty, +\infty)$ and $\int_{-\infty}^{+\infty} f(x) \, dx$ exists. How can I prove that $$\int_{-\infty}^{+\infty} f(x) \, dx = \int_{-\infty}^{+\infty} f\left( x - \frac{1}{x} \right) \, dx\text{ ?}$$ Where are the save files in Skyrim? Search [tag1] OR [tag2] Is there a way to search questions that are tagged with either tag1 or tag2?  Actually, I would like the general filter,      ([tag1] AND [tag2], ...) OR ([tag3]   AND [tag4], ...) OR ...   And even     [tag1] AND ([tag2] OR [tag3])   I need that because I'm looking for interesting questions and I have to search for each tag separately. Mathematics for Quantum Mechanics What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation. Short story that takes place off planet, involving sun and rain I read this short story about 20 years ago, and I'd love to find the title and author. This is what I can recall about the story:   It takes place in a classroom full of kids (around 10 years old?) The planet always gets rain The kids lock the main character (a girl, I think) in the closet during the very rare occurrence of sunlight and she misses the entire event.    I know it's not much to go on, but I hope it rings a bell for someone!