I am looking for a noun that means firstness as exemplified in the following  Examples   Roger Bannister was the first person to run a mile in under four minutes.  Not many of us can achieve firstness in something.  Neil Armstrong exhibited firstness by being the first person on the moon.  Some people prefer to answer first in a quiz, even if they get the answer wrong. They prefer firstness over correctness.  I thought of primacy. However the dictionary meaning doesn't fit -- primacy refers to importance rather than temporal 'firstness'.  I specifically want it to mean that the person achieves or completes something sooner than anyone else. Not that they achieve it better or to more acclaim.  Question: What is a noun (or failing that a short phrase) that means 'firstness' and would fit into those sentences without changing any other words?
What do you call a person who started something that is later followed by everyone? For example, someone started to stay late at night till 8 p.m. and later everyone started to stay till 8 p.m..
How can I get the size of an Amazon S3 bucket? An unclear sentence in the book "Griffiths, Harris-Principles of algebraic geometry" Let $X$ be a complex manifold and consider a holomorphic vector bundle $\pi:E\to X$ of rank $r$. By the usual correspondence between vector bundles and locally free sheaves, we consider $E$ as a sheaf by abuse of notation. We denote with $\mathscr A_X^{p,q}$ the sheaf of $C^\infty$ $(p,q)$-differential forms on $X$ and we define: $$A^{p,q}(E):=\Gamma(X,\mathscr A^{p,q}\otimes_{\mathscr O_X} E)$$ $$A^k(E):=\bigoplus_{p+q=k}A^{p,q}(E)$$  Now suppose that $\nabla:A^\bullet(E)\to A^\bullet(E)$ is a linear connection on $E$, then the curvature operator is defined as: $$\nabla^2:A^0(E)\to A^2(E)$$ where $\nabla^2$ is the composition of the maps $\nabla: A^0(E)\to A^2(E)$   and $\nabla: A^1(E)\to A^2(E)$. One can show that $\nabla^2$ is $C^\infty(X)$-linear.    I don't understand the following sentence from the Griffiths-Harris book at page 75 (I rephrase it by using my notation):     Since $\nabla^2$ is $C^\infty(X)$-linear, then it is induced by a bundle map $E\to\bigwedge^2T^*X\otimes E$, or in other words, $\nabla^2$ corresponds to a global section $\Theta$ of the bundle $\bigwedge^2T^*X\otimes\operatorname{Hom}(E,E)$.   I absolutely don't understand how I can see the operator $\nabla^2$ as the section $\Theta$. Google Sheets Customize View Using Create Custom Menu and Hiding/Showing Specifc Columns Trying to determine a way that I can use a custom menu (.createMenu) with views that will allow me to show / hide specific columns.  I need the capability to pick specific multiple columns and not ranges.  In the example below how can you pick a custom view from the menu (say "Customer Info") that will only show columns A, B, C, and H?  Maybe another view could show "Financial". There have been a number of cases where I would like to thank someone for providing me with a thorough response and give them feedback beyond the vote up. Often I wish people would tell me why they voted me up. Not that the thank you part is necessary but it sets it apart from the other comments related to answering the question itself.  In this type of situation is a "Thank you" acceptable in a comment?     For more information, see  in the . By definition a matrix representing a Lorentz transformation is orthogonal, so that its inverse is equal to its transpose.   Consider a pure boost in the t-x plane; $$\Lambda_x=\begin{pmatrix} \cosh(\gamma) &amp;&amp; \sinh(\gamma) &amp;&amp; 0 &amp;&amp; 0\\ \sinh(\gamma) &amp;&amp; \cosh(\gamma) &amp;&amp; 0 &amp;&amp; 0\\ 0 &amp;&amp; 0 &amp;&amp; 1 &amp;&amp; 0\\ 0&amp;&amp;0&amp;&amp;0&amp;&amp;1 \end{pmatrix}.$$ $\Lambda_x$ has inverse  $$\Lambda_x^{-1}=\begin{pmatrix} \cosh(\gamma) &amp;&amp; -\sinh(\gamma) &amp;&amp; 0&amp;&amp;0\\ -\sinh(\gamma) &amp;&amp; \cosh(\gamma) &amp;&amp; 0&amp;&amp;0\\ 0 &amp;&amp; 0 &amp;&amp; 1 &amp;&amp;0\\ 0&amp;&amp;0&amp;&amp;0&amp;&amp;1 \end{pmatrix}$$ but tranpose  $$\Lambda_x^T=\begin{pmatrix} \cosh(\gamma) &amp;&amp; \sinh(\gamma) &amp;&amp; 0&amp;&amp;0\\ \sinh(\gamma) &amp;&amp; \cosh(\gamma) &amp;&amp; 0&amp;&amp;0\\ 0 &amp;&amp; 0 &amp;&amp; 1&amp;&amp;0\\ 0&amp;&amp;0&amp;&amp;0&amp;&amp;1 \end{pmatrix}.$$ These are not equal. Where have I gone wrong? I've got bunch of files with ill-formed numbering:  prefix-#.ext       | for files with number 1-9 prefix-##.ext      | for files with number 10-99 prefix-###.ext     | for files with number 100-999   Due to further processing I need all of their names to be in format: prefix-###.ext. Is there any easy way to do that? What is an uninterruptible process? Sometimes whenever I write a program in Linux and it crashes due to a bug of some sort, it will become an uninterruptible process and continue running forever until I restart my computer (even if I log out).  My questions are:   What causes a process to become uninterruptible? How do I stop that from happening? This is probably a dumb question, but is there any way to interrupt it without restarting my computer? How do moving charges produce magnetic fields? I'm tutoring high school students. I've always taught them that:     A charged particle moving without acceleration produces an electric as well as a magnetic field.   It produces an electric field because it's a charge particle. But when it is at rest, it doesn't produce a magnetic field. All of a sudden when it starts moving, it starts producing a magnetic field. Why? What happens to it when it starts moving? What makes it produce a magnetic field when it starts moving? Can I see a list of gyms I left a pokemon at? Can I use SharePoint Designer 2013 to edit SharePoint 2010 sites? Can I use SharePoint Designer 2013 to edit SharePoint 2010 sites?   Couldn't find this info in the web. Is it possible to do The Pitt without a slave outfit? Time reversal symmetry and T^2 = -1 Until recently  had one single reputation point, you can see it in this old screenshot:    Now it has over 2K reputation all of a sudden.. what has caused this? Has it affected "real" members as well? What should I opt for?   Option A) very well paid PhD, around €3000 per month at a respectable university or;  Option B) a non-paid PhD, where I have to pay €2000 per year at one of the top 10 universities of the world?  EDIT: Actually they are both UK universities, Option B  is ranked between the top 10 in the world in engineering and tech, and I do get a scholarship that pays 18000 pounds which covers the difference between international student tuition and EU tuition. In Option A, I will be doing research in a good university and will be working alongside giants in the industry. Mounting Disk Image in Raw format While Trying to mount a disk image in Raw(dd) format using the following command  mount  nps-2010-emails.dd /media/manu/   I get the following error message   mount: you must specify the filesystem type   I know that using -t we can specify the file system but what is the terminology for  a RAW (dd) file, which can pe passed as an argument to the mount command. If my method to mount this file system is wrong please help me out in doing the same.  On typing the command file -s nps-2010-emails.dd  The output is as follows:  nps-2010-emails.dd: x86 boot sector; partition 1: ID=0xb, starthead 254, startsector 1, 20479 sectors, extended partition table (last)\011, code offset 0x0 The final state of 1000 light bulbs switched on/off by 1000 people passing by There are  1000  light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8... tutor 3 then 3,6,9...etc until all 1000 tutors have done this.  What is the status of light bulb 25? 93? 576?  Is there a general solution to find out the status of any light bulb?  How many light bulbs are on after all 1000 tutors have gone by?  Not homework but a UK university interview question. Please help. Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$? I have 24 reputation points, but SO chat is still giving me the message "you must have 20 reputation...." Why can't I join the chat? Why exactly is work a path function? This might be a stupid question, but why exactly is work a path function?  In school, my teacher said it’s because it depends on the path. She gave an example of walking up a mountain, and said the work you expend depends on the path you take (straight path up or circling up around the mountain). But isn’t the work expended just equal to $E= mgh?$ Closing jFrame after clicking JButton