Convert a 2 Dimentional array to a single dimention
How to Flatten a Multidimensional Array?
What is the norm of this bounded linear functional? Let $a$, $b$ be two arbitrary but fixed real numbers such that $a &lt; b$, let $C[a,b]$ denote the normed space of all continuous real (or complex) valued functions defined on $[a,b]$ with the maximum norm, and let $f$ be the functional defined on $C[a,b]$ as $$f(x):= \int_{a}^{b} x(t) x_0(t) dt $$ for all $x$ in $C[a,b]$, where $x_0$ is a fixed element of $C[a,b]$.   Now $f$ is evidently linear and bounded. How to compute the norm of $f$? What is this norm?   And what is the norm of the bounded linear functional $g$ defined as follows: $$g(x):= \int_{a}^{(a+b)/2} x(t) \cdot dt - \int_{(a+b)/2}^{b} x(t) \cdot dt$$ for all $x$ in $C[a,b]$? For users running Java application or applets in the browser, what difference does it make running either Sun Java or OpenJDK?  EDIT  Oracle will be , and basing the proprietary implementation on OpenJDK. Can we expect similar experience in running Java apps using either OpenJDK or Oracle JDK? Problems with Curve Modifier Every time I think I have the curve modifier mastered, it throws me a another curve ball (no pun intended).  Why in  can I not get the lights to follow the spiral curve? When the modifier is activated, the lights are stretched and distorted along the curve.  I created the curve by converting it from a mesh (string of verts). Why does it not display like a normal Bezier? Is that related to my problem?  I am following all the "rules" that I am aware of, as detailed here: . The curve seems to run in the correct direction. The origin point is at the first point of the curve. The curve modifier on the lights is set to -Y which is the local orientation of the curve's direction.  What am I missing? Methods to work around the problem of missing data in machine learning Virtually any database we want to make predictions using machine learning algorithms will find missing values ​​for some of the characteristics.  There are several approaches to address this problem, to exclude lines that have missing values ​​until they fill with the mean values ​​of the characteristics.  I would like to use for a somewhat more robust approach, which would basically run a regression (or another method) where the dependent variable (Y) would be each of the columns that have missing values ​​but only with the rows of the table that contain all the data , and predict the missing values ​​with this method, complete the table by the table and move to the next 'column' with missing values ​​and repeat the method until everything is filled.  But that gives me some doubts.  Why any column start? I believe that the one with the smallest missing values ​​until the one with the most  Is there any threshold of missing values ​​that is not worth trying to complete it? (for example, if this characteristic only has 10% of the values ​​filled would not it be more interesting to exclude it)  Is there any kind of implementation in traditional packages or other methods that are robust to missings? Is there a way to take a screenshot using Java and save it to some sort of image? A closed subset of an algebraic group which contains $e$ and is closed under taking products is a subgroup of $G$ A closed subset of an algebraic group which contains $e$ and is closed under taking products is a subgroup of $G$.   Denote this set as $X$. If the condition of $X$ being closed is dropped, this statement does not hold. The set of nonzero integers in $\mathbb{G}_m$ over $\mathbb{C}$ is a counterexample.  It suffice to prove that for any $x \in X$, $x^{-1}X = X$. As $X$ is closed under taking products, it is clear that $X \subseteq x^{-1}X$. In order to prove the inverse inclusion, the closedness of $X$ (under Zariski topology) must be used.   Let $\phi: G \rightarrow G, y \mapsto x^{-1}y$ is a homoemorphism of $G$ as an algebraic variety. So $x^{-1}X = \phi(X)$ is a closed subset of $G$ containing $X$. But Why are they equal?  Thanks very much. How to create vector graphics In Photoshop? I know people prefer using CorelDraw or Adobe Illustrator, but I want to know if there is a technique I can follow to use Adobe Photoshop to make vector Images. I carry a small 2-AA flashlight, and a few times, I have accidentally left it on in my holder.  Each time it dies completely, so that no light is emitted, but if I turn it back off and wait for a few minutes, the light works weakly again.  The longer I leave it off, the longer the dead battery lasts.  I've noticed similar patterns in my mobile phone battery.    Why does this happen? Entry to The US before 30-day grace period for student visa The F student visa allows me to enter the US up to 30 days before the program starts. For starting to set up things it is of my interest to arrive sooner than that. How hard is it to travel there beforehand with a tourist visa (waiver) and leave to, say Mexico, to then re enter on a proper date within the 30 days with the student visa? This seems easier than requesting for a status change inside the US from tourist to student.. Are "w/o", "w/", "b/c" common abbreviations in the US? How do i convert a binary int into a string? For me, it is pretty clear that $a + \overline{a}*b = a + b$, because the first $a$ in the or will make sure that if the second term must be 'evaluated', $a$ will always be false, and therefore won't matter in the and - probably because I'm a programmer and it is very common to see this unnecessary cluttering in long if-else structures.  I can easily prove it with the truth table as well, just make both expressions', and turns out they are identical.  But I was looking for a 'algebraic' way to prove it. That is, something using the basic operations properties like the fact that they are transitive, commutative, associative, etc. For example, if I was to prove this other simple identity $a + a*b = a$ I would simply do something like:  $a + a*b = a*(1 + b) = a*1 = a$.  Is there a way to also prove the former using this algebraic operations, without resorting to the truth table? We have the following points: $$ (0,0)(1,51.8)(1.9,101.3)(2.8,148.4)(3.7,201.5)(4.7,251.1)  \\ (5.6,302.3)(6.6,350.9)(7.5,397.1)(8.5,452.5)(9.3,496.3) $$ How can we find the best fitting line $y=ax$ through the points? My calculator has the option to find the best fitting line $y=ax+b$ through these points, which is:  $$y = 53.28x + 0.37$$  How can I find the best fitting $y=ax$? It seems to me we can't just remove the $0.37$ without compensating in the $a$? Biblatex + Xelatex does not display accents Run a web server from any directory Repeated Iteration of a 2x2 matrix Suppose I am given a $2$x$2$ matrix $A=$ \begin{pmatrix} a &amp; b \\ c &amp; d \end{pmatrix}  And an initial vector $x_n$ = \begin{pmatrix} x_0 \\ y_0\end{pmatrix}.  Under repeated iteration $x_{n+1} = Ax_n$, we find that $x_{n+1}$ converges to a line in the direction of the $eigenvector$  of $A$ of the form $X$= $[u,mu]$ where $m$ is the slope of the line.  I know that this process somehow also involves the largest $eigenvalue, \lambda,$ of $A$, though I am unsure how it connects.  My question is: How does the largest eigenvalue connect to this repeated iteration, how do I find the slope of the line of convergence $m$, and what is meant by the "direction of the eigenvector"? Determining the number of bit strings of length n that contains no adjacent 0s • $C_n =$ this number of bit strings  • A binary string with no adjacent 0s is constructed by   Adding “1” to any string w of length $n-1$ satisfying the condition, or Adding “10” to any string v of length $n-2$ satisfying the condition   I still don't find that intuitive at all. Why adding up $C_{n-1} + C_{n-2}$ results in $C_n$? I have tried my best and asked my friends for help, but they find the formula unintuitive as well. Could anyone here come up with a clear explanation? Thanks! I had posted a  last week about customizing a ToolValidator class and got some very good answers.  In working with the proposed solutions, I have created a custom module that performs queries on a db, and will be called by both the ToolValidator class (to provide values for the drop-down lists) and later in the geoprocessing script (to get other parameters based on items selected in drop-down lists).  However, I can't seem to actually call the custom module in the ToolValidator class.  I have been trying to append to path with no luck.  When I try to apply these changes to the script, I get a runtime error:  [Errno 9] Bad file descriptor.  If I comment out import line, no errors.  sys.path.append('my_custom_module_directory') import my_custom_module   Many of you may be asking why don't I just implement a custom tool with ArcObjects.  The reason is that my end users don't have the privleges necessary to register ANY dlls on their computer.  UPDATE:  This was happening to me in ArcGIS 10.  Interestingly enough, I was initially appending to the path inside of the initialiazeParameters function of the ToolValidator class.  If I do the append outside (i.e., on top of) of the ToolValidator class, everything works as expected.  sys.path.append('C:/Working/SomeFolder') import somescript --------&gt;THIS WORKS  class ToolValidator:   """Class for validating a tool's parameter values and controlling   the behavior of the tool's dialog."""    def __init__(self):     """Setup arcpy and the list of tool parameters."""     import arcpy     sys.path.append('C:/Working/SomeFolder')     import somescript -------&gt; THIS DOESNT WORK     self.params = arcpy.GetParameterInfo()   UPDATE 2:  I think I found the true cause of my problem.  In the code snippets in this post, I have been appending what appear to be real paths (ex C:/Working/SomeFolder) to the sys.path.  In my actual ToolValidator class, I was constructing a relative path using os.path.dirname(__file__) +"\my_special_folder...".  I was anticipating that os.path.dirname(__file__) would return the path of the toolbox, since that contains the ToolValidator class.  I have come to find this is not the case.  As far as I can tell, the ToolValidator class is never actually written to a .py file, and I speculate the the this code is passed to the python interpreter in memory, so __file__ is useless, or some temp script is persisted and then execfile(path_to_script) is called, again rendering __file__ useless.  I'm sure there are other reasons I am missing as well.    Long story short, if I use a hardcoded path, the sys.append works anywhere, relative paths don't work so well in the ToolValidator class. I've followed this tutorial to install Ubuntu 15.10:    After restarting my computer I got to the grub menu and chose Ubuntu. Shortly after that I got this error:  /run/lvm/lvmetad.socket: connect failed: No such file or directory WARNING: Failed to connect to lvmetad. Falling back to internal scanning.   These messages keep adding up on a black screen every second. After a while,  I get access to the initramfs ash console.  what am I doing wrong? Installing Cygwin packages from the command-line Possible Duplicate:        I'm looking for a "yum"-link method to install additional Cygwin packages from the command-line. Let's say I want to add the package "Math/bc", then ideally I'd like to be able to do it  using one command as in:  yum install bc   Currently the only way I've found to install new packages is to locate and run the installation file SETUP.EXE file and then scroll to the relevant package, add it, etc. This is  quite cumbersome so I'm sure there is a smarter command-line way to add an additional package.