If $\frac{a}{b}<\frac{a'}{b'}<\frac{a''}{b''}$, with all values positive, then $\frac{a}{b}<\frac{ab+a’b’+a’’b’’}{b^2+b’^2+b’’^2}<\frac{a’’}{b’’}$
Inequality from Challenge and Thrill of Pre-college Mathematics
What is meant by a continuous-time white noise process? Literal &#39; appears in flag panel instead of being escaped How to make password-less login work I generated a key and copied it to my target:  ssh-keygen ssh-copy-id username@hostname   I left the the location of the key as default and did not set any passphrase.  For a small while after that, I was able to ssh username@hostname without being prompted for a password, and then it stopped working for some reason. I am trying to make folder that everyone can view and can't copy,modify.    For all answers.I thinking about specially ms office files. I tried following methods  Software  - copy protect    - anti copy    This method can't protect save as and upload  MS office macro    Users can enable,disable macros.  MS office restriction    This is best choice but can't protect from file uploading.   Almost I found the solution. Way is combination of MS office restriction and restrict access from browsers using firewall or antivirus. But I don't exact how to do this. "He added" vs. "Did he add" (inversion after negative adverb) Pokemon GO isn't working at all for me right now. I'm in one of the following circumstances and can't do anything:   My game is displaying a "Try Again" message I'm stuck on the Loading Screen When I sign in I get a message that the servers are experiencing problems. I see the map but nothing is loaded, and my team color is wrong The "loading" Pokeball just ends up spinning and I can't catch or interact with things When I try to catch a Pokemon, the Pokeball just sits on my screen doing nothing Gym opponents will drop to 1 HP and won't take any more damage or attack When I open a pokestop, the pokestop image and the name of the pokestop does not load.   What's causing this? Is there a way to fix it? How to link dataframes in ArcGIS or QGIS? The below image shows a layout in ArcGIS 10.1 with four dataframes.  Each dataframe is of the same geographic area, although they are different images. For example, the top left image is a 1989 DOQ, the top right image is a reversed 1989 DOQ, the bottom left image is a 2012 DOQ, and the bottom right image is a reversed 2012 DOQ.   Is it possible to link the dataframes so that panning the image in one dataframe pans the images in all of the other dataframes (i.e. similar to how you can "Link Views" in Erdas Imagine)? Is this possible in QGIS? I have seen a "Universal Laptop Adapter" sold in a computer shop before. I am thinking of getting one for a laptop. Is it safe to use? What differences are there between one of these and a typical laptop adapter? Show that  $$t(n) = 1 + \sum_{ j=0}^{n-1} t(j)$$  is the same as  $$t(n) = 2^n$$  Initial condition $t(0) = 1$ Page to Run Classes I have a urgent requirement to make a page in which list of all classes be there with the check box embedded and having button Run. If i select one or more than one classes and click on run button(Run Test) the test class associate with the particular class should run. please help me out of this requirement.  PageLayout "Users" folder shared with everyone Today I found something strange on my newly installed Windows 7 OS - my "users" folder C:\Users was shared and "Everyone" had full access... I disabled that and now it seems fine, however I'm a bit scared actually, I'd like to know what caused that and if my system is compromised. I'm trying to typeset some python code, and I would like integer literals to be highlighted. I've come up, after about two hours of fighting with the documentation and various other questions here and on SO, with the following:  \lstset{ %     language=Python,     otherkeywords={1, 2, 3, 4, 5, 6, 7, 8, 9, 0},     morekeywords=[2]{1, 2, 3, 4, 5, 6, 7, 8, 9, 0},     keywordstyle=[2]{\color{orange}},     keywordstyle=\color{blue}\bfseries,     stringstyle=\color{red}, }   Unfortunately, that doesn't work. Numbers found in strings are also highlighted, which is rather annoying, and not only are they highlighted: they are highlighted in blue. Numerals in regular program text, on the other hand, are rightly highlighted in red.  Help?  EDIT: Thanks Peter Grill for your very nice solution. Is there a way to not break string colouring, though? When I use you code, the stringstyle=\color{red} doesn't seem to work anymore (strings are just plain black). Similarly, comments can be enclosed in triple quotes in python, and if I adapt your quote to detect """ blocks, then the corresponding  comments are not highlighted anymore. Inequalities for combinations of $\int f $ and $\int (1/f)$ where $m\le f\le M$ on an interval Motivation behind standard deviation? Is it possible to get back your deleted Terraria character? Has the disputed flag message changed? I know how disputed flags work. Today, I reviewed a "not an answer" flag and marked it as invalid.   I've later seen a disputed message with this reason:     invalid flag         disputed - a moderator reviewed your flag, but found no evidence to   support it   Given that disputed flags are in the ,  Is this message applicable only to my flag or is this message also for the original flagger?  Or put otherwise, are all disputed flags now shown this message (or similar decline reason)?  I've run out of flags for today to test this further. Are there any Combinatoric proofs of Bertrand's postulate? I feel like there must exist a combinatoric proof of a theorem like: There is a prime between $n$ and $2n$, or $p$ and $p^2$ or anything similar to this stronger than there is a prime between $p$ and $(\prod_p p) + 1$ (Euclid's theorem).  I was trying to prove one by the Sieve on this grid      1     2     3     4 ... p   p+1   p+2   p+3   p+4 ... 2p  2p+1  2p+2  2p+3  2p+4 ... 3p ........................... ........................... ........................... p^2 p^2+1 p^2+2 p^2+3 p^2+4 ...   but it did not work.  Do any good arguments like this exist? I don't expect anything as strong as Prime Number Theorem or even Bertrand, but surely a direct combination proof can prove that there are lots of primes? I want to find an example of a homomorphism $f:G\to H$ such that $A$ is a normal subgroup of $G,$ but $f(A)$ is not so in $H.$  I know that if $f$ was onto $f(A )$ must be normal , but otherwise i want to find an example! Why doesn't "System.out.println" work in Android? It seems that they can all mean "easily provoked to anger"  irascible：Easily provoked to outbursts of anger; irritable.  fractious：Irritable; argumentative; quarrelsome.  irritable：1.Capable of being irritated. 2.Easily exasperated or excited.  atrabilious：1.Characterized by melancholy. 2.ill-natured; malevolent.