I can't remember where I saw this but I don't understand what's going on here. What use does print(*x) provide? The following code:  x = [(1, 2), (3, 4)] print(x) print(*x)  y = [1, 2, 3, 4] print(y) print(*y)  z = 1, 2, 3, 4 print(z) print(*z)   Gives the following output:  [(1, 2), (3, 4)] (1, 2) (3, 4) [1, 2, 3, 4] 1 2 3 4 (1, 2, 3, 4) 1 2 3 4   I see what is happening but I don't know what is happening. In the previous cases, it just outputs them without any brackets or commas. But when I use this with a dictionary:  a = {1: "a", 2: [1, 2, 3], 3: (4, 5, 6)} print(a) print(*a)   I only get the keys back with the second print:  {1: 'a', 2: [1, 2, 3], 3: (4, 5, 6)} 1 2 3
In the following method definitions, what does the * and ** do for param2?  def foo(param1, *param2): def bar(param1, **param2):
Let $\pi : \widetilde{X} \longrightarrow X$ be the blow up morphism of $X$ a long of $Y \subset X$, with exceptional divisor $E$ and $\text{dim}Y &gt; 0$,   where $X$ and $Y$ are smooth projectives schemes.   For an answer to a question asked here in the forum (), Blowing up and direct image of line bundle), we have: $$\pi_{*}\mathcal{O}_{\widetilde{X}}(-E) = I_{Y/X} \tag{$**$}$$ here $I_{_{Y/X}}$ denotes the ideal sheaf of $Y$.  $(**)$ was obtained through the following exact sequence: $$0 \longrightarrow \mathcal{O}_{\widetilde{X}}(-E) \longrightarrow \mathcal{O}_{\widetilde{X}} \longrightarrow \mathcal{O}_{E} \longrightarrow  0$$  My doubt is: How to find $\pi_{*}\mathcal{O}_{\widetilde{X}}(-nE)$ for $n \geq 0$? What if $n &lt; 0 $?  Thank you. How does the PPA fit into the scenario of publishing an application to the Ubuntu Software Center? I've been going through docs for the past couple of hours but I haven't understood what the PPA is? I have a cross-platform Java application that I'd like to publish to the Ubuntu Software Center. My application is open-source and I'm using Github.   Apparently, publishing applications to the store isn't as simple as uploading a deb package - am I right? I need to create an account on Launchpad and put all my code there.  I don't intend to move from Git to Bzr merely for the sake of publishing to the app store but luckily, one is able to set up source-code mirroring from Github to Launchpad.  Since my application is still very premature, it'll have updates fairly often. When I build my application on my machine, do I simply go my Ubuntu App Developer page and upload the new DEB package or do they build my application from source?  What exactly is the PPA for? I don't think I'll need too many of the Launchpad features so I'd like to stick to Github if possible. FPDF error: Some data has already been output, can't send PDF Blackboard bold variants for Greek letters It is common (or it used to be) to use a blackboard-bold variant of \mu to denote roots of unity in some mathematical papers.  However, despite searching (several times, periodically over several years) I have never been able to locate any package or technique that makes this possible, other than using Metafont or possibly hunting through the font definitions to see if it is something I can create a variant of (along the lines of the suggestions in Section 8 of the Comprehensive LaTeX symbol list).  Thus far, I haven't been sufficiently motivated to learn how to do any of this (although it probably would have resulted in a net time savings), and I feel like I cannot be the only person who would have tried.  Is anyone aware of an existing way to produce this character? Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$. Finding a 2x2 Matrix raised to the power of 1000 How do I convert, NSDate to NSString so that only the year in @"yyyy" format is output to the string? I am writing a journal which has two column. I am using {figure} as well as {figure*} to place the figures in one column as well as stretch across two columns.   My problem is the order of the figures are not correct. e.g. their order of appearance is:                  Figure 1.                 Figure 2.                 Figure 5.                 Figure 3.                 Figure 4.   What should I do to make them appear in order? Java: GUI - JButton opening new JPanel and reading the JTextFields I have a TECNO Spark 2 running on Android 8.1 Oreo (Go Edition). Every time I try to install apps that require notification access, it says that the feature is not available.  How to fix it? Do there exist two primes $p<q$ such that $p^n-1\mid q^n-1$ for infinitely many $n$? We can prove that there is no integer $n&gt;1$ such that $2^n-1\mid 3^n-1$. This leads to the following question:     Is it true that for every pair of primes $p&lt;q$ there are only finitely many integers $n$ such that $p^n-1\mid q^n-1$? Are there two primes $p&lt;q$ and an integer $n&gt;p+q$ such that $p^n-1\mid q^n-1$?Is it true that if $n&gt;6$ then $2^n-1\nmid 5^n-1$?   Edit: Here are some examples: \begin{array}{ll} 2^{36}-1\mid 41^{36}-1, &amp;3^{12}-1\mid 97^{12}-1,\\ 5^{6}-1\mid 37^{6}-1, &amp;7^{4}-1\mid 151^{4}-1. \end{array}  Now I prove there is no integer $n&gt;1$ such that $2^n-1\mid 3^n-1.$  Proof: Denote $A=2^n-1$ and $B=3^n-1$. If $n$ is even then $3$ divides $A$ but not $B$, a contradiction.  If $n$ is odd then $A\equiv -5\pmod {12}$. Since every prime greater than $3$ is $\equiv \pm1,\pm5 \pmod {12}$, some prime factor $p$ of $A$ must be congruent to $\pm5 \pmod {12}$. As $p \mid B$, we have $3^{n+1}\equiv 3 \pmod p$. Since $n+1$ is even, we get $(\frac{3}{p})=1$, a contradiction again. For the following block of code:  For I = 0 To listOfStrings.Count - 1     If myString.Contains(lstOfStrings.Item(I)) Then         Return True     End If Next Return False   The output is:  Case 1:  myString: C:\Files\myfile.doc listOfString: C:\Files\, C:\Files2\ Result: True   Case 2:  myString: C:\Files3\myfile.doc listOfString: C:\Files\, C:\Files2\ Result: False   The list (listOfStrings) may contain several items (minimum 20) and it has to be checked against a thousands of strings (like myString).  Is there a better (more efficient) way to write this code? Replace \input{fileX} by the content of fileX automatically Suppose I have a document with multiple include or input statements  \input{fileA} \input{fileB}   etc.   Is there an easy way to generate a single .tex file where \input{fileA} is replaced by the actual content of fileA etc. without copying it manually? When we push a box, the box applies an opposite force on my hand, but why does my hand move with the box as I push the box if the net force of my hand is 0? What is happening? Is there a way to see what were the Candidate Execution Plans generated by the Query Optimizer? The Query Optimizer creates more than one possible execution plan. How can I see all the plans generated before the executed one was chosen?   :     The Query Optimizer must analyze the possible plans and choose the one   with the lowest estimated cost.   Please, notice that I'm not talking about , I'm talking about candidate execution plans, the ones that were generated but not selected to be executed.  According to Benjamin Nevarez's article :     The generation of candidate execution plans is performed inside the   Query Optimizer using transformation rules, and the use of heuristics   limits the number of choices considered in order to keep the   optimization time reasonable. Candidate plans are stored in memory   during the optimization, in a component called the Memo.   Would it be possible to visualize the candidate plans rendered the way we can ? Kindle for PC via Wine I really want to get the Kindle PC program running on my computer so I can download, read, and manage my e-books. I realize that Calibre can be used to manage e-books and I do have that downloaded. However, Amazon won't let me download ebooks unless my PC is registered in their Kindle program and I'd like to just keep things streamlined.  I've viewed many tutorials and advice for setting it up. I have Wine, I have Kindle for PC, I set it to Win98, all of that. However, when I try to open KindlePC from the Wine menu or from the desktop icon, nothing happens. No error messages, nothing. I don't know what might be wrong. How can I make it work? I have continuous problems of network dropping connections on wifi with ubuntu 16.04, I have an ASUS R510J, this is my network card:  ##### lspci #############################  03:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821AE 802.11ac PCIe Wireless Network Adapter [10ec:8821]         Subsystem: AzureWave RTL8821AE 802.11ac PCIe Wireless Network Adapter [1a3b:2161]         Kernel driver in use: rtl8821ae  04:00.1 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [10ec:8168] (rev 12)         Subsystem: ASUSTeK Computer Inc. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller [1043:200f]         Kernel driver in use: r8169   sudo service network-manager restart doesnt's help, as I never regain internet connection after it drops, and I have to restart the PC. On Ethernet cable I have no problem.  What do you think is the issue? drivers?  thank you $$\frac{1}{n+1}&lt; \log(1+ 1/n)$$  Any ideas? I tried estimating the difference between $1/n$ and the logarithm and comparing with $1/n-1/(n+1)$ but I miserably failed. Inner Product on $\mathbb{R}$ and on $\mathbb{C}$ This is a question of the book Linear Algebra of Kenneth Hoffman.  Describe explicitly all inner products on $\mathbb{R}$ and on $\mathbb{C}$.  I think that if $&lt;,&gt;$ is one inner product on $\mathbb{R}$ (or $\mathbb{C}$) then $&lt; ,&gt;=K[,]$, where $[,]$ is the standard inner product. Is that correct? The volume on my macbook pro has suddenly become greyed out. I haven't installed any updates or made any modifications to the computer, it just suddenly became greyed out after waking the macbook up from sleeping.  I've tried resetting the PRAM, but I don't hear any chime at all when I start up my computer, no matter how long I wait/how many times the computer re-restarts itself.  There also seem to be no internal speakers detected when I go into system preferences. For both input and output the computer detects 0 devices.  Thanks so much in advance for any help!!