Deterministic universe for dummies
Will Determinism be ever possible?
Effect of linear terms on a QFT I was told when first learning QFT that linear terms in the Lagrangian are harmless and we can essentially just ignore them. However, I've recently seen in the linear sigma model, \begin{equation}  {\cal L} = \frac{1}{2} \partial _\mu \phi _i \partial ^\mu \phi _i - \frac{m ^2 }{2} \phi _i \phi _i  - \frac{ \lambda }{ 4} ( \phi _i \phi _i ) ^2  \end{equation}  with $m ^2 =-\mu^2 &gt; 0$, adding a linear term in one of the fields $\phi_N$, does change the final results as you no longer have Goldstone bosons (since the $O(N)$ symmetry is broken to begin with).   Are there any other effects of linear terms that we should keep in mind or is this the only exception of the "forget about linear terms" rule? running rmi server, classnotfound How do I remove Ubuntu's password requirement? Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct? How to select a good non-stick pan, price point wise? If $f$ is a concave function and $f(0) \geq 0$ then $f(a+b) \leq f(a) + f(b)$ for all $a,b >0$ I have seen many folks doing this  concluding that shadow from point A on the Moon can travel to point B on the Moon faster than light.  What I fail to understand here (and I am sure I am wrong), is nothing can travel faster than light. I also read about Relativity where Einstein stated that every event happening for you depends on how fast the light gets from where the event is happening to you.  This is my particular problem with this Moon shadow experiment. You cannot make a shadow travel faster than light, because in order for the "disappearance" of light to get to the Moon, it has to travel at light speed.  Here is one way to understand my point. Consider we shine a flashlight on Moon, like the guy in the linked video did, we move the finger across the face of the flashlight, before we moved the finger it was casting the shadow at Point A on Moon, after we finish moving our finger, the shadow is at Point B on the Moon.  When the finger reaches the end of it's moving length, the light waves that have left the flashlight before the finger reached there will have to hit Point B and it will take them a second and a half to get there, and another second and half for us to see that shadow on point B, which makes it 3 seconds + finger moving time for us to actually see the shadow at point B. That means shadow traveled (say) across the diameter of the Moon in 3 seconds.   So. about 3000 Km in ~3 seconds make it 1000 Km per seconds which is very tiny compared to the speed of light. How can these experiments conclude that Shadow could be made to travel faster than light? What is the obvious clue that I am missing here? Difference between Simple Past and Past Perfect What is the difference in meaning between the two examples below?   When she returned home from office, she was shocked to see that her husband and daughter were missing. (Simple Past)  When she returned home from office, she was shocked to see that her husband and daughter had been missing. (Past Perfect)    FIRST QUESTION: For me example #1 gives only idea of Status of her missing husband and daughter and example #2 gives idea of completed action/situation of missing husband and daughter before she reached home. Is this right? SECOND QUESTION: Is example #2 past perfect or past perfect continuous? I received a table template, which I'm intended to generate dynamically with data using Java. But when the table becomes to large, the compilation with LaTeX fails. The specific about this template is, that it stretches the table width into the maximal page width and has same column widths for all data columns (except the first column).  Here is a minimal version of the full template, that still works fine:  \documentclass[final,authoryear,3p,twocolumn]{elsarticle}  \usepackage{amssymb,amsmath} \usepackage{calc} \usepackage{array} \newcolumntype{L}[1]{&gt;{\raggedright\arraybackslash}p{#1}} \newcolumntype{R}[1]{&gt;{\raggedleft\arraybackslash}p{#1}} \usepackage{eurosym} \usepackage{microtype} \usepackage{needspace} \usepackage{fp}  \usepackage{graphicx} \DeclareGraphicsExtensions{.pdf} \input{pgfexternal}  \newcommand\tabt{\rule{0pt}{2.6ex}} \newcommand\tabb{\rule[-1.2ex]{0pt}{0pt}}  \begin{document}  \begin{table*}[t]     \footnotesize     \begin{tabular*}{\linewidth}{@{}L{2em}@{}*9{R{(\linewidth-2em)/9}@{}}}\hline\tabt $i$ &amp; $1$ &amp; $2$ &amp; $3$ &amp; $4$ &amp; $5$ &amp; $6$ &amp; $7$ &amp; $8$ &amp; $9$\tabb\tabularnewline\hline\tabt $1$ &amp;  &amp; $48.87$ &amp; $0.01$ &amp; $0.05$ &amp; $1.23$ &amp; $0.00$ &amp; $0.20$ &amp; $5.67$ &amp; $2.35$\tabularnewline     \end{tabular*} \end{table*}  \end{document}   But when extending this example by another column, so that the table would look like the following example, it fails:  \begin{table*}[t]     \footnotesize     \begin{tabular*}{\linewidth}{@{}L{2em}@{}*10{R{(\linewidth-2em)/10}@{}}}\hline\tabt $i$ &amp; $1$ &amp; $2$ &amp; $3$ &amp; $4$ &amp; $5$ &amp; $6$ &amp; $7$ &amp; $8$ &amp; $9$ &amp; a\tabb\tabularnewline\hline\tabt $1$ &amp;  &amp; $48.87$ &amp; $0.01$ &amp; $0.05$ &amp; $1.23$ &amp; $0.00$ &amp; $0.20$ &amp; $5.67$ &amp; $2.35$ &amp; b\tabularnewline     \end{tabular*} \end{table*}   This fails, no matter how many columns I add. So far, it seems for me to be a problem with the division by 10. May it be, that LaTeX isn't able to handle that properly by default? How can I solve this problem and make even larger tables work using this template. Or is that to any other problem I don't see yet? Thanks for any help! Is there a third Holmes sibling? How can I set mouse sensitivity, not just mouse acceleration? See YouTube videos in Anaglyph mode How to see a YouTube video in  from a non-3D Android device? I am not able to enable Anaglyph mode from the YouTube application. Help with math symbols in BibTeX I am writing a PhD thesis using LaTeX. Every thing is going fine, but I have problem with the output of the mathematical symbols in the references lists. I copy one example from the Pdf file to make it clear for you. You can see that the fraction remains the same.      [1] Mezzacapo, F. and Cirac, J. I. (2010) Ground-state properties of   the spin-\frac{1}{2} antiferromagnetic Heisenberg model on the   triangular lattice: a variational study based on entangled-plaquette   states. New. J. Phys., 12,   103039.   You can see below the all the packages I use:  \documentclass[12pt,PhD,twoside,a4paper]{GB_muthesis}%[10pt,PhD, singlespace] \usepackage[pdftex]{graphicx} \usepackage[bookmarks=true,colorlinks=true,linkcolor=blue, urlcolor=blue,citecolor=blue]{hyperref} \usepackage[numbers,comma, sort&amp;compress]{natbib} \usepackage{amsmath} \usepackage{amssymb} \usepackage{mathtools} \usepackage{rotating} %\usepackage{GE_manthesis} \usepackage{GB_thesis} \usepackage{bm} \usepackage{fmtcount} \usepackage{setspace} \usepackage{chapterbib} \usepackage{subfigure}% allow subfigures \usepackage{amsfonts} \usepackage{url, enumitem} \usepackage{lscape} \usepackage{notoccite}%This package is for ingnoring the citation in the caption of the figures and tables. \begin{document} I'm having difficulty solving an exercise in my course.  The question is:      Prove that $n!\geq 2^n$.   We have to do this by induction. I started like this:   The lowest natural number where the assumption is correct is $4$ as: $4! \geq 2^4 \iff 24 \ge 16$. The assumption is: $n! \ge 2^n$.   Now proof for $(n+1)$ which brings me to: $(n+1)! \ge 2^{(n+1)}$  I think I can rewrite it somehow like this:  $$ {(n+1)} \times {n!}  \stackrel{\text{(definition of factorial)}}{\ge} 2^n \times 2 $$  $$ (n+1) \times 2^n \ge 2^n \times 2 $$  Then I think I can eliminate the $2^n$ and have something like this: $n+1 \ge 2$, or $n \ge 1$.  But I think I'm wrong here some where and was hoping somebody has some advice on this. How can I prove the above assumption?  Any help would be appreciated, kind regards. How do I effectively defeat the Wall of Flesh? I've been having trouble defeating this monster. Even with lots of buff potions, health potions, high tier armor (Molten), and ranged weapons with plenty of ammo (Minishark), I can't seem to kill this boss.  Worse, when I get it down to about 2000 hp, even if I'm fairly far away, it'll suck me in and continually rise towards the skybox, which doesn't allow me to do anything for some reason.  How do I defeat the Wall of Flesh? What gear should I be using and what kind of potions do I need? Can someone explain me this  please I am a bit confused?  It's from a texbook I am reading (block cipher companion)  it says that:      each weak key has  $2^{32}$ fixed points $m$ where $\operatorname{DES}_w(m) = m$ ( $w$ is a DES weak key). In other words encrypting a fixed point gives exactly the same point. To see this consider the $2^{32}$ ciphertexts after 8 rounds of encryption for which the two 32 bit halves are equal. For a weak  DES key, the round keys of the eighth and ninth rounds are equal. Thus the intermediate texts after seven rounds and after nine rounds of encryption will be equal. Since the round keys of the 7th and the 10th rounds are equal, the intermediate texts after 6 rounds and after 10 rounds of encryption will be equal. Continuing like this it follows that the plaintext will be equal to the ciphertext.    Now did not quite get :   Why are there $2^{32}$ fixed points?  And why after the eighth round of encryption the two halves must be equal? What does the author mean by the intermediate texts exactly? And how are they being equal?   P.S.: This question is not asking for what the weak keys are. I am asking for "fixed points" not exactly weak keys. For this reason I think it is not a duplicate of any other question. There is one similar question to what I've asked for which I have checked and saw that no satisfactory answer has been given there either.  Here is the similar question with no proper answers: I'm embarking on a journey to create a conference abstract book using XeTeX and got stuck within five minutes:        The missing 'g' in 'somethin' influences the line height of the following line. How can I correct this?  At the end I want to be able to include the abstracts and corresponding information through our online registration system, so this should be a global setting.  My MWE:  \documentclass[10pt, a5paper]{article} \usepackage{fontspec}  %% GEOMETRY \usepackage[left=2cm, right=1.5cm]{geometry} % to change the page dimensions  \newenvironment{AbsHead} {     \fontsize{16}{22}\headfont\noindent }% {     \vspace{0.5 cm} }  \newenvironment{AbsAuthors} {     \fontsize{12}{14}\authorfont\noindent }% {    \vspace{0.5 cm} }  \begin{document}  ￼￼￼￼\setmainfont{Minion Pro} \newfontfamily\authorfont{Helvetica Neue Light} \newfontfamily\headfont{Helvetica Neue Condensed Bold}  \begin{AbsHead}The XIAP  something something something somethin somethin somethin somethin somethin somethin somethin something something\end{AbsHead}   \begin{AbsAuthors}Somebody Someone\end{AbsAuthors}   \noindent Purpose: Lorem ipsum \end{document} How can I increase memory security in Delphi? Is it possible to "wipe" strings in Delphi? Let me explain:  I am writing an application that will include a DLL to authorise users. It will read an encrypted file into an XML DOM, use the information there, and then release the DOM.  It is obvious that the unencrypted XML is still sitting in the memory of the DLL, and therefore vulnerable to examination. Now, I'm not going to go overboard in protecting this - the user could create another DLL - but I'd like to take a basic step to preventing user names from sitting in memory for ages. However, I don't think I can easily wipe the memory anyway because of references. If I traverse my DOM (which is a TNativeXML class) and find every string instance and then make it into something like "aaaaa", then will it not actually assign the new string pointer to the DOM reference, and then leave the old string sitting there in memory awaiting re-allocation? Is there a way to be sure I am killing the only and original copy?  Or is there in D2007 a means to tell it to wipe all unused memory from the heap? So I could release the DOM, and then tell it to wipe.   Or should I just get on with my next task and forget this because it is really not worth bothering. Control Cycles/Eevee material nodes and material properties using python? I uploaded a pre-print of an article on arXiv 1 year ago. The article was accepted in SCI journal and currently available online. However, I found a typo mistake in one equation and want to add more discussion related one figure (On researchgate I am receiving a lot of queries regarding that figure). Should i upload a new version of pre-print on arXiv? (How citations will work in this case? as arxiv version is more advanced compare to Journal version) OrI may upload a short document on arXiv as an errata/correction with extra discussion?Or I may address errata and discussion in online page of journal? Actually this journal allows the registered users to comment and start discussion related to published article.