I've read about different experiences: someone's being blocked at the security check because "you can hit someone with that", and some others at the boarding because the helmet just doesn't fit with the "small bag" 35cm × 20cm × 20cm allowed dimensions.  Others were able to travel with a cabin bag AND their helmet (they had to put it under the seat in front of them).  Anyone here have an idea of what I should expect?
I'm planning a trip to recover a motorcycle from a distant city. The ideal trip would be flying to that location and coming back riding the bike, but that would require me to transport my riding gear with me in the plane: Leathers, boots, gloves, back protector and crash helmet.  All this is bulky and expensive stuff, and a crash helmet may be damaged if dropped or hit hard.   I don't expect any airline to allow me a crash helmet as hand luggage; and wearing it all the time is out of the question :-)   To complicate things, I would be coming back riding the bike, so any hard suitcase would have to be left behind.   How do people normally transport that kind of stuff?
How can I rotate about an arbitrary point in 3D (instead of the origin)? I have some models that I want to rotate using quaternions in the normal manner, except instead of rotation about the origin, I want it to be offset slightly. I know that you don't say, in 3d space, that you rotate about a point; you say you rotate about an axis. So I'm visualizing it as rotating about a vector whose tail is positioned not at the local origin.  All affine transformations in my rendering / physics engine are stored using SQT (scale, quaternion, translation; an idea borrowed from the book Game Engine Architecture.) So I build a matrix each frame from these components and pass it to the vertex shader. In this system, translation is applied, then scale, then rotation.  In one specific case, I need to translate an object in world space, scale it, and rotate it about a vertex not centered at the object's local origin.  Question: Given the constraints of my current system described above, how can I achieve a local rotation centered about a point other than the origin? Automatic upvote to anyone who can describe how to do this using only matrices as well :) I checked yesterday and today the new homepage in the Android app. Very surprised I saw that I would almost reach a silver tag badge, that confused be because I always take a look on possible badges I can get. However I compared the score with the website and I got a total different results. See this two screenshots: Let's fix some terminology first. A category $\mathcal{C}$ is preabelian if:  1) $Hom_{\mathcal{C}}(A,B)$ is an abelian group for every $A,B$ such that composition is biadditive,  2) $\mathcal{C}$ has a zero object,  3) $\mathcal{C}$ has binary products,  4) $\mathcal{C}$ has kernels and cokernels.  A category $\mathcal{C}$ is abelian if it is preabelian and satisfies:  5) every monomorphism is a kernel and every epimorphism is a cokernel.  Define the coimage of a map to be the cokernel of its kernel, and the image to be the kernel of its cokernel. We have the following commutative diagram:    where $\overline{f}$ is the only existing map (because of universality of kernel and cokernel).  I'm having trouble proving the following:     A preabelian category $\mathcal{C}$ is abelian iff $\overline{f}$ is an isomorphism.   The converse is easily shown, I'm having trouble proving $\Rightarrow$... translation invariant of integral on $\mathbb{R}$ Problem 1: Let $f\in L^1(\mathbb{R})$, show $\int_\mathbb{R}f(t)dt=\int_{\mathbb{R}}f(x+t)dt,\forall x\in (-\infty, \infty)$.  Problem 2: Let $f\in L^1(\mathbb{R})$,show $\displaystyle \lim_{t\rightarrow 0}\int_{\mathbb{R}}|f(x+t)-f(x)|dx=0$.  My try for Problem 1:  Consider $\displaystyle \int_{\mathbb{R}}f(t)dt=\lim_{n\rightarrow \infty}\int_{-n}^nf(t)dt=\lim_{n\rightarrow \infty}\int_{\mathbb{R}}f_n(t)dt$, where $f_n(t)=f(t)\chi_{[-n,n]}$.  And since $dt=d(x+t)$, we have $\displaystyle \int_{-n}^nf(x+t)dt=\int_{-n+x}^{n+x}f(t)dt$.  So for each $x\in (-\infty,\infty)$,  $$ \begin{split} \int_{\mathbb{R}}f(t)-f(t+x)dt &amp;=\lim_{n\rightarrow \infty}\int_{\mathbb{R}}f(t)(\chi_{[-n,n]}-\chi_{[-n+x,n+x]})dt\\ &amp;=\lim_{n\rightarrow \infty}\int_{\mathbb{R}}f(t)(\chi_{[-n,-n+x]}-\chi_{[n,n+x]})dt\\ &amp;=\lim_{n\rightarrow \infty}\lim_{k\rightarrow \infty}\int_\mathbb{R}\varphi_k(t)(\chi_{[-n,-n+x]}-\chi_{[n,n+x]})dt\\ &amp;=\lim_{k\rightarrow \infty}\lim_{n\rightarrow \infty}\int_\mathbb{R}\varphi_k(t)(\chi_{[-n,-n+x]}-\chi_{[n,n+x]})dt \end{split} $$ where $\varphi_k(t)$ is simple function pointwise converges to $f(t)$, simple function vanish out of set of finite measure, so $\varphi_k(t)(\chi_{[-n,-n+x]}-\chi_{[n,n+x]})$ vanishes when $n$ big enough(is this right?)    Another try:  Since $f\in L^1$, $f$ is bounder a.e. so can be approximated by simple functions, and $\chi_{A+t}(x)=\chi_A(x-t)$,thus $$\int f(t)=\lim_n\int\varphi_n=\lim_n \sum_{i=1}^nc_i\mu(E_i)=\lim_n \sum_{i=1}^nc_i\mu(E_i-x)=\int f(t+x)$$  For problem 2, I guess they share the same method.   Any help or correction about these two problems? Thanks. How to help a toddler overcome the fear of water on head? Can I get smaller tires without changing my rims? I currently ride a hybrid that came with 700x32c tires. Can I swap out a narrower tire without changing the rims, or do rims only fit a specific size of tire?   How small can I go before I have to buy new rims?  I hear having narrower tires makes you go quite a bit faster.  Does it really help that much? I have 28,000 files of size 6.7 GB in the directory aaa/input. I need create TAR files in the directory aaa/output, such that each TAR file cannot exceed 1.9 GB, so I have to tar the 28,000 files into 4 TAR files (6.7/1.9) as Log_(current date)_01.tar Log_(current date)_02.tar ... etc.  such that each tarball is less than 1.9 GB. Is there a way to do this using a Unix script? I am using ArcMap 10.2 and want to represent a layer in a rotated dataframe with chart (graph) symbology. The problem is that the charts do not rotate with the dataframe:     I thought I could convert to graphics and rotate each chart individually, but   that is very tedious I don't find an option to convert a layer to graphics, works for the legend but not for the actual layer symbology The general consensus on a similar question,  is that "highly significant" is a valid, though non-specific, way to describe the strength of an association that has a p-value far below your pre-set significance threshold. However, what about describing p-values that are slightly above your threshold? I have seen some papers use terms like "somewhat significant", "nearly significant", "approaching significance", and so on. I find these terms to be a little wishy-washy, in some cases a borderline disingenuous way to pull a meaningful result out of a study with negative results. Are these terms acceptable to describe results that "just miss" your p-value cutoff? reCaptcha v1 is shutting down on March 31, but SEDE still uses it You have already activated X, but your Gemfile requires Y How do I escape a single quote ( ' ) in JavaScript? Drawing on an image with TikZ Recently I have learned how to draw simple stuff with TikZ. I really like it. Now I wonder if it is possible to draw with TikZ on a image. Instead of pasting a image in Illustrator and adding some vectors to point something in the picture I would like to do it using TikZ. Is it possible?   For example, on a picture of a computer (PNG,etc) I would like to draw some arrows and labels saying "Keyboard", "Monitor", etc. Prove that $T(n) = T(n/3) + T2n/3) + 5n$ is $O(n log n)$ I love R. Courant and F. John's Introduction to Calculus and Analysis because of its wide coverage, precise description and friendly written style.  Are there any classic textbooks like it on ODE/PDE?  thanks. How we fix (La)TeX math coding to be left aligned In display math (employing $$...$$) content normally gets aligned centered. But, I need it to be left aligned. Any suggestions?  Example  $$f(x) = \frac{{{{\sin }^2}x{\mkern 1mu} \cos x}}{{\sin x + \cos x}} -          \frac{1}{4}\tan (\frac{\pi }{4} - x){\mkern 1mu} {\mkern 1mu}           \forall {\mkern 1mu} x \in R - \{ n\pi  - \frac{\pi }{4}\} ,n \in I$$ How to remove `t=canonical` from Firefox browser searches made on DuckDuckGo? Bounding box is larger than expected when drawing a curved path I have been working on logo for my department and I have the following code. The problem is that whenever I compile the diagram seems to be larger than the actual logo. I do not know what is the problem. I know the numbers I have selected are not the best but any insights into the matter will be highly appreciated.   \documentclass[letterpaper]{article}  \usepackage[top=2cm,bottom=2cm,left=2cm,right=2cm]{geometry}  %\usepackage{amsmath,amssymb,units}  %\usepackage{enumitem,multicol}  \usepackage{tikz}  %\usetikzlibrary{arrows}  \usepackage{lipsum}   \begin{document}   \lipsum[1-2]  \begin{tikzpicture}[y=0.80pt, x=0.8pt,yscale=-1]  \path[draw=black,fill=white]    (258.9527,290.5199) .. controls (173.9885,538.4766) and (568.5860,261.2969) ..    (306.5098,257.1141) .. controls (44.4337,252.9312) and (429.9845,542.5624) ..    (352.9767,292.0206) .. controls (275.9689,41.4788) and (119.6549,497.6604) ..    (334.1376,346.9999) .. controls (548.6203,196.3394) and (66.4622,188.6439) ..    (276.0276,346.0724) .. controls (485.5930,503.5010) and (343.9169,42.5633) ..    (258.9527,290.5199) -- cycle;  \end{tikzpicture}  \lipsum[1-2]  \end{document}    See image below: I am using texlive 2013, and just ran the following command to update the packages.  sudo ./tlmgr update  -all   After it finished, I tried to compile tex documents that uses tikz package as the following MWE shows:   \documentclass{article}  \usepackage{tikz}  \begin{document}       aaaa  \end{document}   Then pdflatex complains; it said:   (/usr/local/texlive/2013/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty  (/usr/local/texlive/2013/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex  ! I can't find file `pgfutil-common-lists.tex'.  l.556 \input pgfutil-common-lists.tex   The problem is that, pgfutil-common-lists.tex is indeed in the directory:   /usr/local/texlive/2013/texmf-dist/tex/generic/pgf/utilities/   Why is that? pdflatex should be able to find it, right? I even download the  again, and replace the pgf directory in   /usr/local/texlive/2013/texmf-dist/tex/generic/   Nothing changed at all........... Any idea? Thank you for your critics.  %=====================================================================  Then followed the comments, I type the following command in the terminal:    sudo mktexlsr gives me command not found;  mktexlsr gives me:  mktexlsr: /usr/local/texlive/2013/../texmf-local: directory not writable.     Skipping...  mktexlsr: /usr/local/texlive/2013/texmf-config: directory not writable. Skipping...  mktexlsr: /usr/local/texlive/2013/texmf-dist: directory not writable. Skipping...  mktexlsr: /usr/local/texlive/2013/texmf-var: directory not writable. Skipping... mktexlsr: Done; Forkpsewhich pgfutil-common-lists.tex, nothing pops up. Ubuntu 18.10 Cosmic not starting GNOME session on bootup