There is resistance when you stretch a rubber band. That makes sense to me because the energy you exert is turned into potential energy of the rubber band, but if you hold the rubber band in the same stretched position, it requires constant energy from your body to keep it stretched, but the rubber band doesn't gain any extra potential energy. Where does that energy go?
I read the definition of  as  $$W ~=~ \vec{F} \cdot \vec{d}$$  $$\text{ Work  =  (Force) $\cdot$ (Distance)}.$$ If a book is there on the table, no work is done as no distance is covered. If I hold up a book in my hand and my arm is stretched, if no work is being done, where is my energy going?
I have two raster datasets, they have different projected coordinate systems; one in WGS_84_UTM_Zone_N34, another in Hungarian_1972_EOV,  they overlap each other perfectly if I open them in QGIS.   I would like to transform the coordinate system of the first raster into the second.  I tried Project Raster tool in Data Management toolbox (ArcGIS), it converted the first raster into Hungarian_1972_EOV, but it doesn't overlap with the second raster perfectly (There is a shift between two raster datasets fo about 10-15 meters).   Can anybody help me to find out what is the problem? Folland, "Real Analysis", Chapter 5.3, Exercise 36. Folland, "Real Analysis", Chapter 5.3, Exercise 36:     Let $\mathcal{X}$ be a separable Banach space and let $\mu$ be   counting measure on $\mathbf{N}$.  Suppose that   $\left\{x_n\right\}_1^\infty$ is a countable dense subset of the unit   ball of $\mathcal{X}$, and define $T \colon L^1(\mu) \to \mathcal{X}$   by $Tf = \sum_1^\infty f(n) x_n$.  (a)  $T$ is bounded.  (b)  $T$ is   surjective.   I have proved (a).  I would like help on (b).  Here are my ideas so far.    Say we want to show $y \in \mathcal{X}$ is in the image of $T$.  Reduce to the case $||y|| = 1$ and let $x_{n_m} \to y$.  My thought is to produce for each $N$ a function $f_N \in L^1(\mu)$ such that $||y - \sum_n^\infty f(n)x_n|| &lt; 1/N$ and also such that the $f_N$ converge in $L^1(\mu)$ to some $f \in L^1(\mu)$.  Then use the continuity of $T$ to conclude $T(f) = y$.    The way I have been setting up my inequalities is as follows. Pick $M_N$ such that for all $m &gt; M_N$, $||y - x_{n_m}|| &lt; 1/N$.  Then I want to define $f_N$ so that $$\sum_n^\infty f_N(n) = \sum_{m &gt; M_N}^\infty f_N(m) = 1, $$ hence $$||y - T(f_N)|| = ||\sum_{m &gt; M_N}^\infty f_N(m) y + \sum_n^\infty f_N(n)x_n|| \leq \sum_{m &gt; M_N}^\infty f_N(m) || y - x_{n_m} || &lt; \frac{1}{N}. $$  Presumably, if the $f_N$ are appropriately chosen, then I can find a dominating function and apply the Dominated Convergence Theorem to finish up.    However, getting all these hypotheses to hold simultaneously has been difficult.  In essence, the difficulty seems to be in requiring that the $f_N$ be "normalized" as well as possess a dominating function.  If this method is feasible, at least it seems to require a bit of analysis to show the desired series all converge.  Perhaps I am missing something cleaner.  If so, a simpler solution would be much appreciated.    -Thanks. Is -1 followed by a singular or plural noun? What are these cartridges that many characters have in the Star Wars movies? Admiral Ozzel has them on both sides of his uniform (upper chest).  Most Imperial officers seem to have them.  Han, pictured also here, has three such cartridges on his jacket.  I'd like to make such a jacket and use anything that looks like them.  I figure they are most closely related to cartridges for guns.  (which is what I imagine they are in the films).  But does anyone know the real scoop on them?  What is their purpose in the Star Wars universe?  Admiral Ozzel:    And Han Solo: How to make git mark a deleted and a new file as a file move? ffmpeg is not even cutting this and other mp4s to the nearest second What is the opposite of "personification"? I want a word that means the opposite of personification.  What is the correct word for describing people with the characteristics of an object/as if they are objects?  I found the word chremamorphism on some forums, but it doesn't seem to be included in the two online dictionaries I searched. Did English ever have a word for 'yes' for negative questions? The Germans have doch and the French have si as a word that means "yes" in response to a negative question, such as:     Don't you want some ice-cream?   Yes [I do]!   In English, we only have yes (as far as I know) and further clarification is required in order to be unambiguous.  Did we ever have such a word in English and, if so, what happened to it? If not, given the French and Germanic influences on English, any idea why not? What is the best way to store user settings for a .NET application? I have a .NET 2.0 Windows Forms application. Where is the best place the store user settings (considering Windows guidelines)?  Some people pointed to Application.LocalUserAppDataPath. However, that creates a folder structure like:     C:\Documents and Settings\user_name\Local Settings\Application   Data\company_name\product_name\product_version\   If I release version 1 of my application and store an XML file there, then release version 2, that would change to a different folder, right? I'd prefer to have a single folder, per user, to store settings, regardless of the application version. ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ In the two following snippets, is the first one safe or must you do the second one?  By safe I mean is each thread guaranteed to call the method on the Foo from the same loop iteration in which the thread was created?  Or must you copy the reference to a new variable "local" to each iteration of the loop?  var threads = new List&lt;Thread&gt;(); foreach (Foo f in ListOfFoo) {           Thread thread = new Thread(() =&gt; f.DoSomething());     threads.Add(thread);     thread.Start(); }   -  var threads = new List&lt;Thread&gt;(); foreach (Foo f in ListOfFoo) {           Foo f2 = f;     Thread thread = new Thread(() =&gt; f2.DoSomething());     threads.Add(thread);     thread.Start(); }   Update: As pointed out in Jon Skeet's answer, this doesn't have anything specifically to do with threading. Is the question mark misused in affirmative sentences? Cannot login to chat.meta.stackexchange.com; server error when trying to access chat homepage I just recreated my MSE account after having deleted it a few years ago. Now, I'm trying to log in to Meta Stack Exchange Chat, and whenever I try to do so, it just fails silently and I'm still logged out.  Additionally, in the same browser session that I'm supposedly logged out, I get a server error when accessing the chat homepage or the chat profile page of any user. I don't get any errors when trying to access any of these pages in a private session. I also was able to sign in to Stack Exchange Chat and Stack Overflow Chat without problems, since my accounts on SO and my parent site for SE chat haven't been deleted.  I think it might be because it's trying to sign me in to my old chat profile, which was not deleted, but that is associated to my old, deleted site account, which clash and thus cause it to fail. How to boot from a USB drive in VirtualBox? The question is simple and straight forward:  How to boot from an USB drive in VirtualBox?  EDIT:  I have attached usb to VirtualBox as shown in the screenshot.    But it is not possible to boot from an USB drive even when attached  .  So I would like to know if there is any other possiblity to boot from an USB drive? move file by list in file (with leading whitespace) antonym for beneficiary Is there an antonym for beneficiary that is not simply "giver" or "payer"? I'm looking for a word that roughly mean someone who loses financially in the case of an event. S. Weinberg, “The Quantum theory of fields: Foundations” (1995), Eq. (9.2.15) In Weinberg's book The Quantum Theory of Fields, Volume 1 on p.388 (Chapter 9), the following identity is used (with $f$ being any "reasonable" function):  $$f(+\infty) + f(-\infty) = \lim_{\epsilon \rightarrow 0^+} \epsilon \int_{-\infty}^{+\infty} d\tau f(\tau) e^{-\epsilon |\tau|}.\tag{9.2.15} $$  I don't understand the identity in a qualitative / heuristic way. Upon realizing it is a sarcophagus, he decides to sacrifice himself (I think by disconnecting his air) and exist in it for eternity along with the original creature. It may have been in an old Omni magazine, or some other periodical. I thought it may have been in the anthology "Dead Astronauts" but I did not find the story in there. Why do I have two docks in Ubuntu desktop (with GNOME 3) after installing Dash to Dock? I have a polygon shapefile of many lakes, I also have a point shapefile of locations on those lakes where fish were caught.  The point shapefile contains the attributes: Fisherman_iD, Fish_Caught, Lat, Long.  The polygon shapefile contains the attributes Lake_name, Points_per_polygon(PNTCNT)  Each point obviously has differing entries under the fish_caught field.   What I want to get is the average fish caught per lake (polygon).  So I need to have a total number of fish caught, per individual polygon, and then I can divide that by the PNTCNT file I create using the Points in a Polygon tool.  Ideas? I am relatively new to QGIS. I need to add 30 minutes to values in a Oracle date column.  I do this in my SELECT statement by specifying   to_char(date_and_time + (.000694 * 31)  which works fine most of the time.  But not when the time is on the AM/PM border.  For example, adding 30 minutes to 12:30 [which is  PM] returns 1:00 which is AM. The answer I expect is 13:00.  What's the correct way to do this?