Conclude the number of elements in $H$ divides the number of elements in $G$.
Intuition behind why order of a subgroup divides order of a group.
A regular expression to exclude a word/string How do i know which wheels will fit my bike? my bike is:  and everything I have came with the bike, only now the axle of the rear wheel bent and the skewer has lost its grooves.  and I would like to replace the rear wheel with the 12 x 142mm version of:   I want to reuse the old casettes and disc break. I was told to buy new rotor bolts, will these do?   Will I be able to migrate all my previous parts onto this new wheel and will the wheel fit onto my bike?  update: A replacement axle would be prefered. What axle would work for my bike? Bootable USB of Ubuntu Minimal CD I want to burn Ubuntu Minimal CD ISO to an old, 1 GB USB thumbdrive. Regular ISO doesn't fit. I already tried Startup Disk Creator and Unetbootin but both failed. I tried installing GRUB and pointing it to boot like this:  insmod part_msdos linux /linux initrd /initrd.gz   but it doesn't work. I also tried dd but I ended up with not bootable drive.  Rufus worked on Windows with the same thumbdrive but I no longer use Windows.  What else can I do? Why are these numbers not equal? has been solved, in XeTeX, by this code:  \def\kright#1{\leavevmode #1\kern-\XeTeXglyphbounds3 \the\XeTeXcharglyph`#1 } \def\kleft#1{\leavevmode \kern-\XeTeXglyphbounds1 \the\XeTeXcharglyph`#1 #1}   which allows me to align text more precisely to the ink by accessing the side-bearing measurements (\XeTeXglyphbounds1 and 3).  This XeTeX dependency is currently the only thing stopping me from moving to LuaTeX (mainly for microtype). Is an equivalent function available in LuaTeX, or planned?    After reading a bit more on microtype, could the equivalent effect be achieved by an appropriately-tailored set of character protrusions? That way, my move to LuaTeX might be a lot simpler. Is there a systematic way of solving cubic equations? In my text book, to solve cubic equations, I need to    find by trial &amp; error what $f(a)$ will make the equation 0. The factor will be $(x-a)$ then the other factor will be $Ax^2+Bx+C$ then I can solve using compare coefficient   But for te first part, is there any other way apart from trail &amp; error? Or is there some technique to guess the factor of an equation?   The question I am currently doing happens to be $2x^3+3x+4=9$   UPDATE:  $2x^3+3x+4=9$ should be $2x^3+3x+4=9x^2$   UPDATE 2  So I am going to try substituting   $x=\pm{1}, \pm\frac{1}{2}, \pm{2}, \pm{4}$  When $x=-\frac{1}{2}$, one of the provided answers,   $2(−0.5)^3−9(−0.5)^2+3(−0.5)+4=-18.75\neq 0$   did I make a mistake? When playing as a spellcaster, is it valid the use of the Ready action to prepare Dispel Magic to counter a spell cast by an opponent? In the same vein, when declaring said action, do I have to specify which spell slot I will use when Readying the Dispel Magic spell? If that is the case, does this tactic nullify an opponent's spell? I get the impression that this is basically turning Dispel Magic into a spell with a casting time of &quot;1 reaction&quot;. Is my reading of the rules accurate? Genes and Intelligence Assuming that intelligence has a genetic component,   • do we know which genes contribute to it?   and, if so,  • can we predict intelligence from genomic analysis? What happens when ability scores reach 0? D&amp;D 5E does not seem to have rules for ability score damage (that I could find), although it does mention that if CON is decreased, your maximum HP is reduced. In addition, the Shadow monster in the Monster Manual has a Strength Drain attack that deals 2 Strength damage. The attack says that if a character's Strength reaches 0, the character dies. Are there any general rules for ability damage in 5th Edition? How can I find out which process is locking a file or folder in Windows?  For instance, when trying to delete a folder, Windows reports this:     The action can't be completed because the folder is open in another program   Happens the same with a file, but how do I find out what program or application is currently using it and preventing me from deleting the file or folder? Extending an enum via inheritance I know this rather goes against the idea of enums, but is it possible to extend enums in C#/Java?  I mean "extend" in both the sense of adding new values to an enum, but also in the OO sense of inheriting from an existing enum.    I assume it's not possible in Java, as it only got them fairly recently (Java 5?).  C# seems more forgiving of people that want to do crazy things, though, so I thought it might be possible some way.  Presumably it could be hacked up via reflection (not that you'd every actually use that method)?  I'm not necessarily interested in implementing any given method, it just provoked my curiosity when it occurred to me :-) Is list::size() really O(n)? Recently, I noticed some people mentioning that std::list::size() has a linear complexity. According to  , this is in fact implementation dependent as the standard doesn't say what the complexity has to be. The comment  says:     Actually, it depends on which STL you   are using. Microsoft Visual Studio V6   implements size() as {return (_Size);   } whereas gcc (at least in versions   3.3.2 and 4.1.0) do it as { return std::distance(begin(), end()); } The   first has constant speed, the second   has o(N) speed    So my guess is that for the VC++ crowd size() has constant complexity as Dinkumware probably won't have changed that fact since VC6. Am I right there? What does it look like currently in gcc? If it is really O(n), why did the developers choose to do so? I have a class like this:  public class myClass {   public List&lt;myOtherClass&gt; anewlist = new List&lt;myOtherClass&gt;;    public void addToList(myOtherClass tmp)   {     anewList.Add(tmp);   }  }   So I call "addToList" a hundred times, each adding a unique item to the list.  I've tested my items to show that before I run the "addToList" method, they are unique.  I even put a line in to test "tmp" to make sure it was what I was expecting.  However, when I do this (lets say myClass object is called tmpClass):  int i = tmpClass.anewList.Count(); for (int j = 0; j&lt;i; j++) {    //write out each member of the list based on index j... }   I get the same exact item, and it's the last one that was written into my list.  It's as if when I add, I'm overwriting the entire list with the last item I've added.    Help?  This makes no sense. I've also tried List.Insert, where I'm always inserting at the end or at index 0.  Still no dice.  Yes, I'm doubly source my indexing is correct and when I do my test I'm indexing through each of the elements.  :)  UPDATE: Okay, I tried this and still had the same problem:  foreach(myOtherClass tmpC in tmpClass.anewList) {         Console.WriteLine(tmpC.theStringInMyClass.ToString()); }   and still for each of the 100 items, I got the same string output... I'm sure I'm doing something completely stupid, but I don't know what yet. I'm still 100% sure that the right string is getting passed in to begin with.  -Adeena    Okay, I tried this and still had the same problem:  foreach(myOtherClass tmpC in tmpClass.anewList) {     Console.WriteLine(tmpC.theStringInMyClass.ToString()); }   and still for each of the 100 items, I got the same string output...  I'm sure I'm doing something completely stupid, but I don't know what yet. I'm still 100% sure that the right string is getting passed in to begin with.  -Adeena What is the definition of a "feature map" (aka "activation map") in a convolutional neural network? Intro Background Within a convolutional neural network, we usually have a general structure / flow that looks like this:  input image (i.e. a 2D vector x)   (1st Convolutional layer (Conv1) starts here...)  convolve a set of filters (w1) along the 2D image (i.e. do the z1 = w1*x + b1 dot product multiplications), where z1 is 3D, and b1 is biases. apply an activation function (e.g. ReLu) to make z1 non-linear (e.g. a1 = ReLu(z1)), where a1 is 3D.   (2nd Convolutional layer  (Conv2) starts here...)  convolve a set of filters along the newly computed activations (i.e. do the z2 = w2*a1 + b2 dot product multiplications), where z2 is 3D, and and b2 is biases. apply an activation function (e.g. ReLu) to make z2 non-linear (e.g. a2 = ReLu(z2)), where a2 is 3D.    The Question The definition of the term &quot;feature map&quot; seems to vary from literature to literature. Concretely:  For the 1st convolutional layer, does &quot;feature map&quot; corresponds to the input vector x, or the output dot product z1, or the output activations a1, or the &quot;process&quot; converting x to a1, or something else? Similarly, for the 2nd convolutional layer, does &quot;feature map&quot; corresponds to the input activations a1, or the output dot product z2, or the output activation a2, or the &quot;process&quot; converting a1 to a2, or something else?  In addition, is it true that the term &quot;feature map&quot; is exactly the same as &quot;activation map&quot;? (or do they actually mean two different thing?)  Additional references: Snippets from :  *The nomenclature is being used loosely here. In particular, I'm using &quot;feature map&quot; to mean not the function computed by the convolutional layer, but rather the activation of the hidden neurons output from the layer. This kind of mild abuse of nomenclature is pretty common in the research literature.   Snippets from :  In this paper we introduce a visualization technique that reveals the input stimuli that excite individual feature maps at any layer in the model. [...] Our approach, by contrast, provides a non-parametric view of invariance, showing which patterns from the training set activate the feature map. [...] a local contrast operation that normalizes the responses across feature maps. [...] To examine a given convnet activation, we set all other activations in the layer to zero and pass the feature maps as input to the attached deconvnet layer. [...] The convnet uses relu non-linearities, which rectify the feature maps thus ensuring the feature maps are always positive. [...] The convnet uses learned filters to convolve the feature maps from the previous layer. [...] Fig. 6, these visualizations are accurate representations of the input pattern that stimulates the given feature map in the model [...] when the parts of the original input image corresponding to the pattern are occluded, we see a distinct drop in activity within the feature map. [...]  Remarks: also introduces the term &quot;feature map&quot; and &quot;rectified feature map&quot; in Fig 1.  Snippets from :  [...] One dangerous pitfall that can be easily noticed with this visualization is that some activation maps may be all zero for many different inputs, which can indicate dead filters, and can be a symptom of high learning rates [...] Typical-looking activations on the first CONV layer (left), and the 5th CONV layer (right) of a trained AlexNet looking at a picture of a cat. Every box shows an activation map corresponding to some filter. Notice that the activations are sparse (most values are zero, in this visualization shown in black) and mostly local.   Snippets from   [...] Every unique location on the input volume produces a number. After sliding the filter over all the locations, you will find out that what you’re left with is a 28 x 28 x 1 array of numbers, which we call an activation map or feature map. How do I copy a folder keeping owners and permissions intact? So I was going to back up my home folder by copying it to an external drive as follows:  sudo cp -r /home/my_home /media/backup/my_home   With the result that all folders on the external drives are now owned by root:root. How can I have cp keep the ownership and permissions from the original? All I want to see are the specs Is there a way to see the processor and speed of a Cisco UCS B230 Blade Server without the enclosure that runs it? The enclosure that we have does not power on and all I need is to see what cpu and processor speed is in it. Why don't the Ubuntu repositories have the latest versions of software? Why are packages in the official Ubuntu repositories older than the latest (upstream) versions from Debian Sid, PPAs, the authors, etc.? Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not? Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not? I feel like there should be some easy example showing that it is not, but I can not think of one. Implement MicroController Power Switch and re-use the button for other features This is similar to other questions, but I feel it is different because of the reuse of the "power" button.   I want a "latching" Momentary Power button.  Behavior:   User Pushes momentary button, holds down as long as necessary and the device powers up. Between Power On and Off the same button will be re-used for other functions  When it is held down for 5 +/- seconds the MicroController will turn itself off.    Design Constraints:   Battery provides between 3.7V to 2.9V during it's usable life The Voltage regulator requires Vin +/- 0.3V on the Enable Pin, 3.1V output. MicroController operates at 3.1V MicroController Output Pin High state is 2.7V Max   Debouncing: In this case I'm not concerned about debouncing the switch, if the user doesn't hold it down long enough for the MicroController to set it's Digital Output pin  High the device doesn't power on.  I've worked up the following schematic, which kind of works.    It assumes 3.7V from the battery. Uses an Analog Input for the Power button, which then uses the variation in voltage to determine if the button has been pressed. In the current design the difference is 0.12 V (from 3.4 to 3.52), but the MicroController has a 12 bit ADC so that shouldn't be a problem, in addition I can adjust the sensitivity range of the ADC.   Questions:  What is the difference between reality and the simulator?  Is there a better way?  How can I get a greater voltage difference on the button input? I've tried many different combinations but they increase the voltage range above the 3.6V Input High Maximum specified in the datasheet.  I'm not excited about the "Leakage current" when the uC Controlled Power Pin is Low, any suggestions?   Thank you for any ideas/suggestions/answers. Travelling as unmarried couple in Dubai I'd wish to visit Dubai with my girlfriend, but after reading  and  I started to get a little worried about it. How should I book an hotel? Must I book two singles? Could it be a problem if we walk together in the city and go together to restaurants and malls without being married?