Removing non numeric characters from text file Python 3.3
Removing non numeric characters from a string
Given function $g$ continuous in line $[0,\infty)$, positive and strongly increasing that upholds $\lim_{t\to\infty}  g(t) = L$. Calculate the limit:  $$ \lim_{n\to\infty} \int\limits_1^2 g(nx) \, dx. $$  At the moment what I think that I should do is swap the $g(nx)$ with $L$ as it approaches infinity but from there on I am just not sure whats my next step is. Finding a closed form for a recurrence relation $a_n=3a_{n-1}+4a_{n-2}$ Consider the sequence defined by $$ \begin{cases} a_0=1\\ a_1=2\\ a_n=3a_{n-1}+4a_{n-2} &amp; \text{if }n\ge 2 \end{cases} .$$ Find a closed form for $a_n$.    I tried listing out examples, but I don't see any common pattern between them.  All solutions are greatly appreciated. I keep running into areas where I see a chest in a section of the room that seems completely walled-off. Is there any way to get to these, or is that just the randomly generated dungeon being a tease?  I had to splice two screenshots together to show an example of what I'm talking about:   Is there any way to get in there? Possible to get type of an aliased type in c#? Type.GetType("System.String")   Is there a lookup for the aliases available somewhere?  Type.GetType("string")   returns null. Adding columns to production tables What's the best way to add columns to large production tables on SQL Server 2008 R2? According to Microsoft's books online:     The changes specified in ALTER TABLE are implemented immediately. If the changes require modifications of the rows in the table, ALTER TABLE updates the rows. ALTER TABLE acquires a schema modify lock on the table to make sure that no other connections reference even the metadata for the table during the change, except online index operations that require a very short SCH-M lock at the end.   (http://msdn.microsoft.com/en-us/library/ms190273.aspx)  On a large table with millions of rows, this can take a while. Is taking an outage the only option? What's the best way to handle this kind of situation? Launch app only if not already open An  is defined as $p = q\times d$ (for two point charges $\pm q$ separated by a distance $d$).    What is the physical meaning of this quantity?  Why does the direction of the electric dipole moment go from the negative charge to the positive charge? Another way of saying this, why electric dipole moment is a vector quantity? Operator precedence in a find command? See below example:  $ ls -1p appledir/ applefile orangedir/ orangefile $ find . -type f -name apple\* ./applefile $ find . -type f -name orange\* ./orangefile $ find . -type f -name apple\* -o -name orange\* ./applefile ./orangedir ./orangefile $ find . -type f \( -name apple\* -o -name orange\* \) ./applefile ./orangefile $    I was surprised to discover I needed the parentheses for this to work as expected; apparently I haven't internalized the rule of precedence by which find evaluates its arguments.  How can I easily predict when I will and when I will not need to use parentheses to explicitly group find primaries?  Put another way, what are the rules by which I can imagine find inserting parentheses into the commands I give it, which will allow me to accurately predict how it will evaluate ungrouped expressions? What do you call a response which does not address the question? When some one is asked a question, sometimes if they are trying to avoid answering the question, they respond with something unrelated. What is the word for that response?  Eg. A: Why were you late?     B: This bagel tastes good.  What I am looking for is the name of that response, not the action. How to preserve custom number formatting after closing a workbook? In Section 9 of Chapter 6, Lang constructrs for the first time a non-abelian extension as a splitting field $K$ of $X^n - a$ when the ground field $k$ does not contain primitive $n$-th roots of unity $\zeta_n$. He constructs an injective homomorphism of the Galois group $G(K/k)$ into the matrices of type   $$ M=\begin{pmatrix} 1 &amp; 0 \\ b &amp; d \end{pmatrix} \quad \hbox{with}\ b\in \mathbb{Z}/n\mathbb{Z} \quad \hbox{and} \quad d\in (\mathbb{Z}/n\mathbb{Z})^*,$$  where $(\mathbb{Z}/n\mathbb{Z})^*$ the multiplicative group of integers modulo n.  Afterwards, he states in Theorem 9.4 that if $n$ is an odd positive integer prime to the characterstic and $[k(\zeta_n):k]=\varphi(n)$ (i.e, the primitive roots of unity are not in the ground field), then the above homomorphism is, in fact, an isomorphism. Besides, the commutator group is $G(K/k(\zeta_n))$, so $k(\zeta_n)$ is the maximal abelian subextension of $K$.  Lang proves the theorem inductively over the number of prime factors in the decomposition of $n$ (i.e. if $n=9= 3\cdot 3$, then the proof "would take two steps" to complete). The induction start with $n$ prime is written clearly and I agree with it.   Now come the questions:   I do not understand Lang's argument to prove that the commutator subgroup is the subgroup $\begin{pmatrix}1 &amp; 0 \\ b &amp; 1\end{pmatrix}$, $b\in \mathbb{Z}/n\mathbb{Z}$. What is this projection on the diagonal and how does one see that the factor group of the commutator group is isomorphic to $(\mathbb{Z}/n\mathbb{Z})^*$?   By the way, direct computation of $x\, y\, x^{-1}\, y^{-1}$ for two arbitrary matrices $x=\begin{pmatrix} 1 &amp; 0 \\ b &amp; d \end{pmatrix}$, $y=\begin{pmatrix} 1 &amp; 0 \\ c &amp; e \end{pmatrix}$ yields a matrix $\begin{pmatrix} 1 &amp; 0 \\ b(1-e)+c(d-1) &amp; 1 \end{pmatrix}$. As $n$ is odd, $2 \in (\mathbb{Z}/n\mathbb{Z})^*$, so taking $e=1$ and $d=2$, we indeed reconstruct the above-mentioned group.   The second (inductive) part of the proof is a complete mystery to me with virtually every sentence being a Theorem which needs an extra proof. Can someone give me some hints?   2.a. Lang writes $n=p\,m$ and takes $\alpha$ to be the root of $X^n-a$. It is clear that $\beta=\alpha^p$ is a root of $X^m -a$. Now comes the argument "By induction we can apply the theorem to $X^m-a$". I agree that we can apply it here but the result is that $K=k(\beta,\zeta_m)$ is the splitting field of $X^m-a$. In the diagram below, there appears $k(\beta,\zeta_n)$ out of nowhere.   2.b. Now Lang proceeds to apply the theorem on $X^p-\beta$ over $k(\beta)$. Bergman's "Companion" reminds to check that $[k(\beta,\zeta_p):k(\beta)]=\varphi(p)$ before applying the theorem and gives a hint "$[k(\zeta_p):k]$ and $[k(\beta):k]$ are relatively prime". I disagree with this hint. Take $n=21= m p$ where $m=3$ and $p=7$. Then $[k(\zeta_p):k]=\varphi(p)=p-1=6$ but $[k(\beta):k]=m=3$ and both are not co-prime. Can we apply the theorem here at all? Or if so what is the argument? If Bergman's argument is valid, where is the fault in my logic?  2.c. Even assuming that we can apply the theorem in 2.b., then we can say something about $k(\alpha, \zeta_p)$ and not $k(\alpha,\zeta_n)$. How do we proceed to checking everything Lang states in the last section of the proof (basically, everything after the diagram)?  EDIT: I have found the essentially same question How to downgrade a package via apt-get? How can I downgrade a package to an older version via apt-get?  Other tools are also acceptable but apt-get is preferred. Whether the players killed a mage and got his spellbook(s) or they met with a nice wizard who let him or her learn a spell from his spellbook, can a player prepare a spell from a spellbook that isn't his or hers?  I'm asking because the PHB p. 114 says:     [...] Preparing a new list of wizard spells requires time spent studying your spellbook and memorizing the incantations and gestures you must make to cast the spell: at least 1 minute per spell level for each spell on your list.    emphasis mine   Further, the block on the left as a Copying a Spell into the Book ("the" Book as in "your" Book, since it appears in the block titled Your Spellbook), which explains how you can copy a spell from one book to another, assuming the book is from a stranger, it cost more and takes more time. It actually says:     [...] deciphering the unique system of notation used by the system of notation of the wizard who wrote it. [...]   It continues saying that you have to learn the various parts of the spell (verbose, material, gesture.)  This makes it sounds like a wizard would have a really hard time to prepare a spell from another's spellbook. Is that the case? Book about a teenager programmed to be an assassin and trying to get back at the people responsible I read this book a few years back (around 5?). It was part of a multibook series but I have only read one book.  It's about this teenager who I think had been programmed to be an assassin but then somehow retained his conscience and was out to get the people responsible for that.  I briefly remember a girl, and this one part where he realizes he can ride a horse and then there's a chase too. I think the guy's name was Jim or Jimmy, but not quite. I'm also quite sure he was either part computer, or had a chip or something in his brain which had been programmed to give him a host of mental and physical abilities which he retained and used as well as the series progressed. Hydrostatic pressure - doesn't density vary with depth? Our class is learning about hydrostatic water pressure and we have been told that we can calculate the force of the liquid on an object at any depth using "the density x 9.8 x the depth". However, as the depth increases, wouldn't the density of the liquid increase because of the weight of the liquid above it compressing it? So should't there be something in the equation to account for the varying density? To me, "density x 9.8 x depth" seems like it is saying that the density will be constant... Android: How to open a specific folder via Intent and show its content in a file browser? What is meant by "object serialization"? Can you please explain it with some examples? multiline command chunks in bash history into multiple lines In Bash (as well as Bash in WSL), multiline written commands can call-back with up/down arrows correctly also built-in history command report them correctly (until I'm still logged-in in bash). But after exiting from bash and press up/down arrows, multiline commands appears each as separate entries and that's because cat ~/.bash_history has chucked the command on multiple separate entries and writing problem here; the history command result messed too. I have set these options in ~/.bashrc shopt -s cmdhist lithist HISTTIMEFORMAT='%F %T '  and now writing problem fixed but history command still report in multiple line and separate entries (reading problem now). Bash version is 4.3, same issue on v4.4 there is  since a long years but no solution yet. Update: it's also to mention that below multiline command as an example is correctly displaying even after exit Bash: for i in {1..10} do echo $i done  but this is failing: awk ' { print $1}' &lt;&lt;&lt;'first last'  Update 2: the issue mentioned above is fixed in Bash v5.0.0+ that changed to recognize entries between &quot;timestamp as delimiter&quot; as single entry of command (HISTTIMEFORMAT, cmdhist and lithist must be set). Is the expression "yesterday afternoon" correct? Is it proper to use the following expressions  I started to London yesterday afternoon . I started to London yesterday morning  I ask because it is supposedly correct to say 'last night'. Why don't we say 'last afternoon' or 'last morning'? TinyMCE disable escaping