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UTF-8 all the way through
Meaning of "kernel" In analysis, there are at least three kinds of "" concepts:   In probability theory, there is a concept called , also called probability kernel, from one measure space $X$ to another $Y$. It is actually a family of measures on $Y$, indexed by members of $X$. It can transform a measure on $X$ to a measure on $Y$, in terms of integration.  A special case is  of probability density function in statistics, where the  is actually a probability kernel. In real/complex analysis, there is a concept called  from a product space $X \times Y$ to $\mathbb{R}$ or $\mathbb{C}$. It can transform some special function: $X \to \mathbb{R}$ or $\mathbb{C}$ to another one:$Y \to \mathbb{R}$ or $\mathbb{C}$. This is used for defining integral transformation In Hilbert space theory, there is concept called , which is a family of bounded mappings for a family of Hilbert spaces. For every two Hilbert spaces $X$ and $Y$ in the family, there are exactly two members of the kernel, one mapping from $X$ to $Y$ and the other from $Y$ to $X$.   I wonder    Are they related concepts, since they seem to share some indescribable similarity? Can they be unified?   In particular, the first two are similar to each other as the kernels induce transformations on measures and on functions in terms of integrals.  It is however not obvious to me how the third one, i.e. the Hilbert space one, is related to the second one. Are they related to the  concepts? Or even to the  concept?   I feel like some insights and references for catching the general ideas shared across as many kinds of "kernels" as possible.  Thanks and regards! How to handle trigger recursion I have two objects A(parent) and B(child) related by a lookup relationship. I  need to update records in object A using data loader. There is an after update trigger on object A which updates some fields on related records of object B. On object B as well there is an after update trigger which updates a field on parent object A. How can i handle recursion. What are our policies regarding self-harm and suicide? What should I do as a Moderator when I encounter situations regarding self-harm and suicide? Does ClamAV Scan Windows virus? I'm new to Ubuntu.  I'm now setting up an OwnCloud server which supports ClamAV file scan.  Since most of the users connected to the server uses Windows OS, can ClamAV scan for Windows virus?  I also did some research that such as BitDefender. It clams that it scans real time, if someone upload files to the server, will BitDefender scan the file even OwnCloud doesn't support?  By the way, I heard that if I update the system frequently, I don't have to install any antivirus that scan for Linux virus. Is that right? Prove that $\overline {A^\complement} = (A°)^\complement $   To show that $\overline {A^\complement} \subseteq  (A°)^\complement$   We first show $A^\complement \subseteq  (A°)^\complement ...(*) $  We know that since $ A°\subseteq A \qquad (*)$ is automatically follows .  The part I didn't understand is the following:     Then we conclude that since $ (A°)^\complement$ is closed    $\therefore \overline {A^\complement} \subseteq  (A°)^\complement$ How do I make the method return type generic? Consider this example (typical in OOP books):    I have an Animal class, where each Animal can have many friends. And subclasses like Dog, Duck, Mouse etc which add specific behavior like bark(), quack() etc.  Here's the Animal class:  public class Animal {     private Map&lt;String,Animal&gt; friends = new HashMap&lt;&gt;();      public void addFriend(String name, Animal animal){         friends.put(name,animal);     }      public Animal callFriend(String name){         return friends.get(name);     } }   And here's some code snippet with lots of typecasting:  Mouse jerry = new Mouse(); jerry.addFriend("spike", new Dog()); jerry.addFriend("quacker", new Duck());  ((Dog) jerry.callFriend("spike")).bark(); ((Duck) jerry.callFriend("quacker")).quack();   Is there any way I can use generics for the return type to get rid of the typecasting, so that I can say      jerry.callFriend("spike").bark(); jerry.callFriend("quacker").quack();   Here's some initial code with return type conveyed to the method as a parameter that's never used.   public&lt;T extends Animal&gt; T callFriend(String name, T unusedTypeObj){     return (T)friends.get(name);         }   Is there a way to figure out the return type at runtime without the extra parameter using instanceof? Or at least by passing a class of the type instead of a dummy instance. I understand generics are for compile time type-checking, but is there a workaround for this? How does Hextech Crafting work? How do you earn free loot?  What's the deal with essences and why are they so important?  What do the different options mean when dealing with Redeeming Rerolling Disenchanting and Upgrading?  How does it all work? How can you change the href for a hyperlink using jQuery? Unable to format internal drive as APFS on 2018 MacBook Pro I have some Python code that makes Raster Attribute Tables for GeoTiffs using GDAL.    In ArcGIS I can see these attribute tables fine and they behave how I like (as classifications) but in QGIS the whole concept of an attribute table seems to be missing.    Is there any way to access a RAT in QGIS? Coming from Eclipse and having been used to duplicate lines all the time, it's pretty strange finding out that Xcode has no such function. Or does it?  I know it's possible to change the system wide keybindings but that's not what I'm after. Ignore citations in captions in list of figures when numbering I'm having some difficulty understanding how to interpret variable importance output from the Random Forest package. Mean decrease in accuracy is usually described as "the decrease in model accuracy from permuting the values in each feature".   Is this a statement about the feature as a whole or about specific values within the feature? In either case, is the Mean Decrease in Accuracy the number or proportion of observations that are incorrectly classified by removing the feature (or values from the feature) in question from the model?   Say we have the following model:  require(randomForest) data(iris) set.seed(1) dat &lt;- iris dat$Species &lt;- factor(ifelse(dat$Species=='virginica','virginica','other')) model.rf &lt;- randomForest(Species~., dat, ntree=25, importance=TRUE, nodesize=5) model.rf varImpPlot(model.rf)     Call:  randomForest(formula = Species ~ ., data = dat, ntree = 25,  proximity = TRUE, importance = TRUE, nodesize = 5)  Type of random forest: classification Number of trees: 25 No. of variables tried at each split: 2          OOB estimate of  error rate: 3.33% Confusion matrix:           other virginica class.error other        97         3        0.03 virginica     2        48        0.04     In this model, the OOB rate is rather low (around 5%). Yet, the Mean Decrease in Accuracy for the predictor (Petal.Length) with the highest value in this measure is only around 8.   Does this mean that removing Petal.Length from the model would only result in an additional misclassification of 8 or so observations on average?   How could the Mean Decrease in Accuracy for Petal.Length be so low, given that it's the highest in this measure, and thus the other variables have even lower values on this measure? Are there any good tools besides SeleniumRC that can fetch webpages including content post-painted by JavaScript? I need a compact representation of an array of booleans, does Python have a builtin bitfield type or will I need to find an alternate solution? Considering this code, can I be absolutely sure that the finally block always executes, no matter what something() is?  try {       something();       return success;   }   catch (Exception e) {        return failure;   }   finally {       System.out.println("I don't know if this will get printed out"); } Inset in Blender not coming out even "Temporarily unreachable" when using fetch as Googlebot from Webmasters Tools The page I'm trying to fetch is public.  The server logs show no request.  Google reports that any page on my site is "Temporarily unreachable". It won't even fetch the verification file, a static HTML file that was successfully used to verify with the webmaster tool application itself.   My site is running on the .  What is causing this? Which folder is recycle bin in on Win7? How to check files there? I was using another account before. Let me call it account A. And I deleted a lot of files to the Recycle Bin at that time. But before I removed account A I forgot to empty the Recycle Bin.   My question is, are my files still there? I've searched and found that the Recycle Bin may live in $Recycle.Bin, but I can't open files there so I can't know what they are. Any help how to open deleted files or how to delete them permanently? How many throws of a die until every possible result is obtained? A die is thrown until every possible result (i.e., every integer from 1 to 6) is obtained. Find the expected value of the number of throws.   How do I do that? I understand that probability for the single result is $\{1, 5/6, \ldots , 1/6\}$, but what about the expected value?