Field inside a hollow sphere uniformly charged
Gravitational field intensity inside a hollow sphere
Let $f\colon\mathbb R\to\mathbb R$ be twice differentiable with $f(x)\to 0$ as $x\to\infty$ and $f''$ bounded. Show that $f'(x)\to0$ as $x\to\infty$. (This is inspired by  to a different question) Wiener Process $dB^2=dt$ Why is $dB^2=dt$? Every online source I've come across lists this as an exercise or just states it, but why isn't this ever explicitly proved? I know that $dB=\sqrt{dt}Z$, but I don't know what squaring a Gaussian random variable means. I need to format a drive containing an old install of Ubuntu 10.04, to install Vista (not my idea!) Vista setup apparently refuses to format non-FAT32 or NTFS partitions. However, I can't seem to format it from my live CD (Ubuntu 11.04) at all; I keep getting "device is busy" errors. What is the simplest way to format this drive? The number of 5-digit numbers such that their sum of digits is even is? I tried this problem by counting the number of 5-digit numbers and then dividing it by 2 just like we do for three digits. Please help. Thank you. I read a very special book a few years back. We follow a boy who lives in a world where, if one moves far enough in a direction, that person gets distended and changed in size.   The boy works on laying tracks for the train, on which his city is. The city has to continually keep moving or it also will get squashed.   It's like a world like if one end is pinched and then dragged out like a piece of rubber string or bubble gum.   The book is not older than 10 years I think.  Hope I was clear enough... Reapplying for a UK Standard Visitor visa after a refusal Move all files of type to a new folder in windows 7 Is it physically possible to build a long zoom (17-300 mm for example) at an aperture value of around 1.4 or 1.2? I'm curious if the physics allow a company to build such a lens of course with good IQ, minimal color aberration, maximum sharpness, and little to none lens vignetting or edge softness Having trouble indexing and executing a query in O (log n) time.  The query includes an INNER JOIN, an ORDER BY, and an equality operation. If I understand the laws of databases correctly, a query can be indexed and executed in O (log n) time (or thereabouts) if a non-equality operator is not used on more than one column. In this case, I believe the INNER JOIN does count as an equality operator and the non-equality operator would be the ORDER BY portion of the query. This table has upwards of 10,000,000 rows and needs to handle several reads and writes per second.  Using PostgreSQL. This is what the table looks like. As you can see, the column 'Names' is a list property and it is the column that the INNER JOIN goes against:  Age Names                       Date 34  ['carla', 'john', 'sam']    3/13/2011 26  ['json', 'cindy', 'joel']   3/13/2011 72  ['beth', 'amber', 'susie']  3/13/2011 14  ['john', 'jim', 'debie']    3/13/2011   This is the query that we are trying to do:  SELECT * FROM the_table WHERE Age==26 AND Names=='john' ORDER BY Date   My background is from using App Engine's Big Table, so I've used equality operators here to indicate that 'john' should be one of the names in the Names column. This would be an acceptable query in GAE's big table, it would execute in O (log N) time as all Big Table queries are reqyured to do. I am assuming there is a way to do this in PostgreSQL as well since PostgreSQL accepts list data types as columns.  Is this possible to do in PostgreSQL?  If so, how should the index be set up (we can't figure out how to set up an index that takes into account the three properties)? How do I create an internet shortcut within a folder? If all derivatives of $f$ are uniformly bounded by a common constant and $f(1/n) = 0$ for all $n$, is $f$ identically zero? $$ f: \Re \longrightarrow \Re \ \in C^{\infty} \\ \exists \ L&gt;0: \ \forall x \in \Re, \forall n\in N \\ |f^{(n)} (x)| \le L \\ f(\frac{1}{n})=0 \ \forall n\in N \\ f(x) \equiv 0  $$  Good morning,  Can you give me an help to make this proof?  This is my thought:   $\lim_{n \rightarrow +\infty } \dfrac{1}{n}=0=\theta$ $f(\theta)=0$ $f^{(n)} (\theta) =0\\f(x)=\sum_{k=0}^n \dfrac{f^{(k)}(x-\theta)^k}{k!}$  $f$ is analytic, the rest of Taylor's expansion is 0, because the derivatives are bounded, $f$ is null.   I have thought this reasoning, but I have difficulties to demonstrate part 3. Can you help me?  Is there any mistake?  Can I use an easier way to make the proof?  Thanks. What is "#!' in a script file? $cat shebang.sed  #! /bin/sed -f s/red/xxx/ s/BLUE/1234/  $./shebang.sed rgb lower (#1): "xxx green blue" UPPER (#2): "RED GREEN 1234"  $sed -f shebang.sed rgb lower (#1): "xxx green blue" UPPER (#2): "RED GREEN 1234"   I may guess what #! is doing. However, I don't say I know it. what is "#!"? Is there an editor or IDE (or a script) for substituting the TeX-Commands $ and $$ for opening and closing math regions into the corresponding LaTeX-Commands \(,\) and \[,\]? I'm sure there is a tool - and I'm searching for. I think, this will result in better readable code. A simple search and replace wont do that - but with regular expressions, that should not be problem. I simply do not want to invent the wheel a second time. How to to calculate the hash of an unordered set Suppose I have a set of elements, with known hash (e.g. SHA-2). How can I calculate the hash of the set? With it I mean an unordered set, so the order of elements is undefined and shall not play any role in determining the hash of the set.  In theory any commutative operation applied to the hashes should be fine, but I have the strong feeling that XORing all of them together is quite unsafe. An attacker could add an element to the set to produce a hash collision, although finding an element with that wanted hash is as hard as breaking the hash of the whole set.  Anything better solution than the trivial one of sorting the elements into a list, calculating their hashes and then calculating the hash of the hash list?  I think Merkle trees can't help here if they are based on some sort of ordering of the elements. fitting a smaller range when we bought our house, it had a very used 40" gas range. now that range has died. replacing with a new 40" range is very pricey ($2k+), and our cooking needs don't justify the size anyhow.  i'm looking for ideas on how to fit a smaller range. i would imagine that extending the counter top and cabinets would be a pretty extensive change. we've found we can get a 36" range for around 1/2 the cost. would it be feasible to add some sort of storage along side the smaller range to fill in the space?  thanks. i know this is an open-ended question with no specific answer, i'm just looking for ideas. Trying to find a TV show about an event that leaves everyone dead apart from people who died at the moment of the event? This was a TV show aired in the UK probably sometime between 1990 and 1993, if memory serves it was only a one-off. The plot starts with the protagonist waking up in bed and being disappointed. He eventually goes outside and everyone is dead, whatever they were doing at the time they died doing it (driving, working, etc.) The protagonist is in a state of panic running around town (I seem to remember it being set in the UK) and he discovers that he's is 'alive' because he'd attempted suicide and died at the exact moment this mysterious event happened. I think he encounters others that 'died' at the time of the event and that's when he realises. I think the protagonist was a bald, white man, probably mid-thirties. Sorry for any vagaries, I was VERY young when it was on. Until recently I assumed it was The Quiet Earth but I've checked and it definitely isn't. It was in colour and was contemporary at the time so it would have been made around 1990. How can I change the language for dictation on the fly? With English not being my first language, I usually need support for at least two languages when using features like auto-correct and dictation.  Is it possible to toggle the language which is used for dictation via a shortcut?  As of now, I always have to manually navigate through the menus in the System Preferences which if far from convenient. I've tried to see if there are any pre-defined actions in Automator, but found none. I have a list with a people column called AssignedTo.  I'm making a rest call:  .../_api/web/Lists/GetByTitle('listname')/Items?$expand=AssignedTo&amp;$select=*,AssignedTo/Title   Which is successfully returning the name of the person the item was assigned to. I'm trying to get other user information like email or their user id.  Most tutorials online show how to expand ID and Title (Name) and  I found a list of these properties that can be expanded:   ID FirstName LastName Title Department SipAddress   And those all work. But I can't find the email and or the login ID. I've tried $select=AssignedTo/LoginName and several other variations on that, but they all return that the field is not valid. I was hoping $select=AssignedTo/* would expand all the fields, but that doesn't rework either.  Anyone know if the above are the only fields that can be expanded off a people column? identifying which item is clicked in a multi level list using jquery Is "TABLESAMPLE BERNOULLI(1)" not very random at all?