E,F banach space, T $\in$ K(E,F) dim E= $\infty$ show R(T) is closed
When is the image of a linear operator (between Banach spaces) closed?
SharePoint 2013 Online - Missing Follow Link I am very new to R. I am learning machine learning right now. Very sorry, if this question appears to be very basic.  I am trying to find a good feature selection package in R.  I went through Boruta package. It is a good package but I read that it is only useful for classification.  I want to do implement feature selection in R for regression tasks. I went through the caret package documentation but for my level, it is very difficult to understand.  Can any one please point me to a good tutorial or list any good packages or most frequently used packages in R for feature selection.  Any help would be appreciated. Thanks in advance. Automatically make various multiple stroke colour the same as various underlying fill colours. I have auto traced a photograph in illustrator - its got thousands of vectors once I expand it and illustrator has converted each of them to a filled colour - I want to now trace the edges of them with a grungy brush but using the underlying fill colour. Where in illustrator can I stroke or outline these fills using the underlying colour - surely this is something that the program automatically does?   I've found this script online but don't know how to implement it. I'm new to this so any help appreciated. Many thanks.   James   var idoc = app.activeDocument;   var sel = idoc.selection;    for (i=0; i&lt;sel.length; i++) {       var ipath = sel[i];       ipath.stroked = true;       ipath.strokeColor = ipath.fillColor;   } Why am I getting a NoClassDefFoundError in Java? I am getting a NoClassDefFoundError when I run my Java application.  What is typically the cause of this? What is some good free software for doing physics calculations?  I'm mainly interested in symbolic computation (something like Mathematica, but free). Processor: PIC18F66K22 Compiler:  C18 (XC8 is fine also)   I've just made (and succesfully tested) code to measure the voltage on AN4 analog pin.  Now I want to try something else, not quite sure if it's theoretically possible.  My test-board has a PIC processor, with VDD,AVVD connected to a supply (ranging from 0(if the battery is empty/disconnected) to 4,2(full battery).  Can I use ADC to measure the VDD(-in) of my board?  Why not?:   It's not an ANx pin, not sure how to make the ADC measure it? (Channel?) If the voltage on VDD(-in) drops, will my ADC reference voltage also drop? (So when my PIC only gets 3,3V the ADC will still say it's 100% (as the max Voltage on the chip, also the reference is 3,3V).   Why/what do you ask?:   Can I just measure Channel 30 (VDDCORE)? Could I set my Vref to Vdd and measure a precision voltage reference with the A/D converter. (Not sure how) Or I could add a wire from VDD-in to an ANx pin? Will Internal VREF+ (4.096V) stay 4+V when the VDD-in is around 3,4V? Is there some kind of transformator that makes it so? Internal VREF+ (4.096V) is a bit lower than the max of the battery (4,2V), does this mean I can damage the ADC? Or just that the result will be max when the battery is full. (4,2V out of 4,096V)     Please mind that my knowledge of Electronics is "low". I've learnt way more about the software part in my education, but I'd like to know more about (Embedded) Electronics as it's a crucial part in Embedded Engineering. (It's sad how my school doesn't see this.) What is the difference between a class and a set? I know what a set is. I have no idea what a class is.   As best as I can make out, every set is also a class, but a class can be "larger" than any set (a so-called "proper class").  This obviously makes no sense whatsoever, since sets are of unlimited size. It's not like you get up to 25 elements and go "oh, hey, sets are limited to a maximum of 20 elements, so we'll have to call this 25-element thing something else".  Does anybody know what the actual difference between a set and a class is?  Several people have pointed out that you can write paradoxes which involve sets. I get that. But where do classes come into the picture? Algebraic closure of $\mathbb F_p$ I am able to use the split command successfully to split large file into multiple smaller files. This is being achieved by following command  split -b 1G $temp_path $final_filepath   But only caveat is that these files many times contain last line which is split across 2 files. Is there any way to avoid that using split or any other command ? Showing a set is nowhere dense in $C([0,1])$ /usr/bin/sudo must be owned by uid 0 and have the setuid bit set I have run following command accidentally   sudo chown [username] -hR /   Now sudo su getting error:  sudo: /usr/bin/sudo must be owned by uid 0 and have the setuid bit set   How to Solve This? Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$ I have trouble on this question: "Characterize the groups G for which the map $$\iota: G \to G$$ sending $$x \mapsto x^{-1}$$ for all $x \in G$, is an automorphism of $G$." From  post I have seen that $G$ must be abelian. Can anyone propose another characteristic of $G$ that I can derive from the given conditions besides abelian? Thank you so much!! How to set root password to null Number of solutions of $P(x)=e^{ax}$ if $P$ is a polynomial When you search on any of the SE network sites, with a tag (so that a description is shown); it shows the tag info content box, with the highlight-search-term span elements.  For eg. I searched ; ; and the results are as shown:                  Notice the &lt;span class='search-highlight'&gt; boxes around searched tag terms. What are good starting settings to store for exposure bracketing shots? I started experimenting with the Custom Functions (C1,C2,C3) on my Canon 7D and I decided a useful one to have may be setting it up for exposure bracketing. So it's a quick switch if I ever need it, as opposed to going through the menu to set it up.  I realize the settings would vastly depend on the situation, but do you have any suggestions for some good all round settings to program in as a starting point?    Examples: 1 stop vs 1 1/3 vs 2 stop brackets / ISO choices / Metering mode / shooting mode and so on. Positive correlation and negative regressor coefficient sign Is it possible to obtain a positive correlation between a regressor and a response (+0,43) and, after that, obtain a negative coefficient in the fitted regression model for this regressor?  I'm not talking about changes in the sign of the regressor among some models. The coefficient sign always remains.  Could  the remaining variables of the fitted model influence the changing of the sign? If $X$ is separated over $\operatorname{Spec} \Bbb Z$, is it separated over any other scheme? I use this program in Windows that's one-box and searches all of my drives. By default it lists all files, everywhere, in a single list. Is there a Linux graphical utility that does this? Sometimes I create Material Groups to be used as appendable reusable assets. Unfortunately sometimes parameters I want to control using a Group Node's slider are not available for routing to a Group Node's input socket. Some examples of these are the Color Ramp and the Mapping Node.  So here's what I want to do:    Can this be done? If so, how?  Thanks!