$d(Tx, Ty) < d(x, y)$ does not guarantee existence of fixed point.

Let $T$ be a mapping of a complete metric space $X$ into itself. How do I show that the condition $d(Tx, Ty) < d(x, y)$, where $x \neq y$, does not suffice for the existence of a fixed point for $T$?


Can you sell your properties for cheap to another player in Monopoly?

Is it possible for example to sell a property you own to another player for 1$? I was playing with some friends and one of them had to pay me 1200$ and since he didnt have enough he sold all his houses reached 1200 gave me the money and then sold all his stuff for 1$ to another player.


"It's cold today" -- what term do linguists use to call "it" when it's used as the subject of a sentence, but has no real antecedent?

Could you please remind me what term linguists and the grammar people use to call it when it's used as a subject pronoun, but the funky thing is that it doesn't really refer back to anything in particular like he, she or we usually do which do refer back to a person or an animal that they stand for.  In grammar-speak, when it is used like that they say that it has no antecedent. I think I knew the term, but I unfortunately forgot it. I did a Google search, but the only thing I could find was empty subject. But the truth is that I don't think that's what they actually use in linguistics. Would you please refresh my memory?  Examples:        It's quite cold today outside. So, I don't really wanna go out.   Did I solve that math problem? Yes. Actually, it was very easy to get it cracked. There was really nothing to it!   Don't mention it! It's nothing. I really like to help people who are in need.


Minecraft * Line 1, Column 2 Missing ‘}’ or object member name error

I Typed In The Chat   /give @s skull 1 3 {SkullOwner:”TBNRfrags”}   And It Said     * Line 1, Column 2 Missing ‘}’ or object member name    in red. I Tried It Again In A Command block, and the same thing happened. I Played In Minecraft PE, BTW. Not Java. And TBNRfrags is one of my favorite YouTubers.


What causes the ? Here's my understanding of it: When a fluid flows around a curved surface it has high velocity and so low pressure its pressure will be lower than the atmospheric pressure and so it will be forced to follow the curve by the higher pressure of the atmosphere. If this above explanation is correct then how can flowing water have a pressure lower than the atmospheric pressure doesn't water have higher  pressure than the atmosphere even if it has high velocity? If this explanation is incorrect then please give me the right explanation.


PyQGIS QgsVectorLayer() Loading Invalid Layer in Standalone Python Script?

In my standalone python 3 script, QgsVectorLayer() is loading an invalid layer. When I use the exact same function and inputs in the QGIS GUI python console, the layer loads fine. I am not sure what is missing in my standalone script. I have double checked the paths and made sure they are correct. I used   QgsApplication.prefixPath()   to check the correct path for input in the   QgsApplication.setPrefixPath()   function within my standalone script. The path and inputs I use in the   QgsVectorLayer()   function in my standalone script are the same as those used in the GUI python console. I'm not sure why loading a vector layer in my standalone script it failing. The vector object is created, but .isValid() returns False.   Here is my standalone script:  import sys, os, time  sys.path.extend([r'C:\OSGeo4W\apps\qgis\python',r'C:\OSGeo4W\apps\Python37\Lib\site-packages'])  #modify environment variables to find qgis and qt plugins during qgis.core import os.environ['QT_QPA_PLATFORM_PLUGIN_PATH'] = r'C:\OSGeo4W\apps\Qt5\plugins' os.environ['QT_PLUGIN_PATH'] = r'%QT_PLUGIN_PATH%;C:\OSGeo4W\apps\Qt5\plugins;C:\OSGeo4W\apps\qgis\qtplugins;C:\OSGeo4W\apps\qgis\plugins' os.environ['PATH'] += r';C:\OSGeo4W\apps\qgis\bin;C:\OSGeo4W\apps\Qt5\bin;C:\OSGeo4W\\bin'  from qgis.core import * from qgis.gui import *  # supply path to qgis install location QgsApplication.setPrefixPath(r'C:\OSGeo4W\apps\qgis', True) #QgsApplication.setPluginPath('C:\\OSGeo4W\\apps\Qt5\\plugins\\platforms') #print(QgsApplication.systemEnvVars())  # create a reference to the QgsApplication # setting the second argument to True enables the GUI, which we need to do # since this is a custom application qgs = QgsApplication([], True)  # load providers qgs.initQgis()  ########################## # Write your code here to load some layers, use processing algorithms, etc. canvas = QgsMapCanvas() canvas.show() layer = QgsVectorLayer(r'C:\Users\Matt\OneDrive\FarmProject\Kankakee_Parcels\K3_TaxParcels.shp', 'Kankakee', 'ogr') if not layer.isValid():   print('Failed to open the layer')  # add layer to the registry add_layers = QgsProject.instance().addMapLayer(layer)  # set extent to the extent of our layer canvas.setExtent(layer.extent())  # set the map canvas layer set canvas.setLayers([add_layers]) canvas.refresh() time.sleep(30) ########################  # When your script is complete, call exitQgis() to remove the provider and # layer registries from memory qgs.exitQgis()


Is a subset of $\mathbb{R}^{n}$ that is homeomorphic to $\mathbb{R}^{n}$ necessarily open?

Let $A$ be a subset of $\mathbb{R}^{n}$, such that $A$ is homeomorphic to $\mathbb{R}^{n}$.  Is $A$ open in $\mathbb{R}^{n}$?


What's the difference between I've had and I've been having?

For example, what's the difference between:   I've had a wonderful time here and I've been having a wonderful time?  Does the present perfect simple indicate that the action is over?


If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $

Let $V$ be a subspace of $\mathbb R^3$ generated by the vectors $\{(1,1,1),(0,1,1)\}.$ There are $3$ vectors $u_1=(0,0,1),u_2=(1,1,0),u_3=(1,0,1)$.Then which of the following sets are connected?  $1.\left(\mathbb R^3\setminus V\right)\cup\{(0,0,0)\}$  $2.\left(\mathbb R^3\setminus V\right)\cup \{tu_1+(1-t)u_3:t\in [0,1]\}$  $3.\left(\mathbb R^3\setminus V\right)\cup\{tu_1+(1-t)u_2:t\in [0,1]\}.$  $4.\left(\mathbb R^3\setminus V\right)\cup \{(t,2t,2t):t\in \mathbb R\}$  Now $V$ is generated by two linearly independent vectors so is like $\mathbb R^2.$ So $\left(\mathbb R^3\setminus V\right)$ will be disconnected but giving the $(0,0,0)$ with them will make it connected.  No. $4$, I think will be connected also because $\{(t,2t,2t),t\in \mathbb R\}$ is in $V$ and contains the point $(0,0,0)$ Now, any neighbourhood of this point will have points from both $V$ and $\left(\mathbb R^3\setminus V\right)$ and so the union is connected.I'm not sure about no. $2$ and $3.$


After playing the game for a little while, I've noticed that Pokestops are chosen seemingly at random locations on the map. A few of them are even in inaccessible places; an abandoned church building, inside of an airforce base, etc. How are these locations chosen as Pokestops?


Prove the above by   by mathematical induction By any other method.   I was just asked to prove this so I thought of using mathematical induction.   My effort :   I started first by verification and the inequality was true for n=3, 4...  Then the assumption step $(k!)^ 2 \gt k^k$  But after that while proving it for n=k+1 I was getting stucked inthe very next step.


How Do I interpret HDD S.M.A.R.T Results?

My laptop has recently started to become a bit unreliable, and for some reason I started to suspect that my HDD was starting to fail. After a bit of hunting on the internet, I found Ubuntu's Disk Utility in the System menu and ran the long SMART diagnostics from this.  However, since the documentation for Disk Utility is very poor (palimpsest?), I'm not sure how to interpret the results:    For example, the Read Error Rate is over 50 million (!), yet the Assessment is rated "Good".   So would someone mind explaining to me how to interpret the results of these tests (especially the Normalized, Worst, Threshold and Value numbers)? And maybe tell me what they think of the results I got for my HDD? (Thanks)


$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$

Prove that if $p$ and $q$ are odd primes and $q$ can divide $a^p-1$, then either $q$ divides $a-1$ or else $q=2kp+1$ for some integer $k$.  I thought the supposition is $a\equiv 1 (mod\ q)$. So $$(a-1)(a^{p-1}+a^{p-2}+...+1) \equiv 0 (mod\ q)$$ Then I proved $q$ may divide $a-1$. But I don't know how to check that $q=2kp+1$. thks


How to use, and not to overuse, Insight skill checks?

I've recently begun DMing a 5th edition D&D campaign after a long time of quiescence as Dungeon Master. I really like this new take on D&D, but still, soon a problem has resurfaced, that is: the (paranoid) use of the Insight (or, as of 3rd edition, Sense Motive) skill, and I'm struggling to keep it in check.  I'm curious to hear how you handle this aspect of social interaction. When I'm interpreting an NPC, players often ask me if they can roll for Insight, and soon everyone at the table starts rolling. I'm thinking of outright disallowing such rolls, as (in my opinion) a player should only make a check when the DM calls for it. However, PCs should get to put their skills and proficiencies to use from time to time. So, this is what I've come up with:  1) Let them roll at most once per social interaction. Actually, I should be rolling for them behind my screen, so that they can't do metagame reasoning on a 1 or a 20.  2) Simply do not allow them to roll if they don't know the person they're interacting with to some minimal extent, or in cases where it is objectively not possible to draw a conclusion (for example, asking a guard if he has seen someone they're chasing, and the guard plainly replying "no").  3) Substituting most of the active Insight checks with passive ones. This would mean that the most empathic or intuitive PCs would sometimes sense something is amiss or tension coming from the NPC, or the like.   4) Only allow Insight checks if a PC clearly starts an interaction being suspicious of an NPC, otherwise not let it happen.  But still, I'm really not satisfied. What do you say to a player who failed or succeeded at the roll? To me, Insight should not be some kind of lie detector, but it often becomes one. Have you ever had this problem, too? What do you do?


Completely delete files from Trash on SSD

I've found a file with my personal information in it and I didn't want anyone to see them. So, I trashed the file and permanently deleted it.  Now, I've found out that when you delete a file from the Trash, you only remove a link to it (a pointer).  How do I completely remove it from my hard drive?   Should I make a very large file full of zeros to overwrite the sectors no longer in use, completely full up my hard drive, then delete it? Are there any free, open source tools to recover the file so I know it's gone or not?   I am using MacBook with a SSD drive. If this question is not suitable, please merge it.


Let $x_{n}$ be a monotonously decreasing sequence converging to $0$. prove $nx_{n}$ is also convergent to $0$.

Let $x_{n}$ be a monotonously decreasing sequence converging to $0$. The series $\sum x_{n}$ is convergent. Prove that $nx_{n}$ is also convergent to $0$. I‘m kinda stuck here. Help would be appreciated.


Why internal hard-disk is showing twice? Ubuntu 20.04

When I run sudo fdisk -l command, it's shows my internal hard-disk twice (sda2 & sda5). What could be the reason?. I'm on Ubuntu 20.04. Please tell me, if I need to share output of any other command. Thank You in advance. output of sudo fdisk -l | grep -A 7 /dev/sd Disk /dev/sda: 447.14 GiB, 480113590272 bytes, 937721856 sectors Disk model: Sandisk SD5SB3M2 Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0x36fc1339  -- /dev/sda1  *       2048   1050623   1048576   512M  b W95 FAT32 /dev/sda2       1052670 937719807 936667138 446.7G  5 Extended /dev/sda5       1052672 937719807 936667136 446.7G 83 Linux   Disk /dev/loop8: 65.1 MiB, 68259840 bytes, 133320 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes  -- Disk /dev/sdb: 931.49 GiB, 1000170586112 bytes, 1953458176 sectors Disk model: My Passport 0741 Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0x966accd6  -- /dev/sdb1        2048 1953458175 1953456128 931.5G  7 HPFS/NTFS/exFAT


I have a coding question with two compilable options. I want to ask which is better and why. Code review, programmers, stack exchange...im not really sure? Where is this question appropriate.   It may be an opinion based question and it may not. I don't really know until I know the answer. Like I said, both ways produce the same results, but I don't know which is the better practice.   What site does this belong on?


When I build complex design's markup, I can create deep level of nesting div's (15-20 nesting level). If it is impact bad on SEO?


How to color particles based on the texture of the object from which they are emitted, using the "grid" emission setting?

I am using Blender's particle system to try to voxelize my mesh. I'd like to color the voxels based on the diffuse color of the textured mesh at the closest location to each voxel. This is an image that shows what I'm trying to do:     explains how to color emitted particles based on the mesh from which they are emitted. The technique uses the "jittered" emission setting:    Using the technique in the post I linked to, here is what I get with "jittered" selected. You can see that the emitted cubes correctly match the color of the mesh:    When I change the emission setting to "grid", the cubes no longer match the color of the object:    I'd like to use the "grid" emission setting for voxelization, but can't figure out how to get the color of the emitted particles to correctly match the color of the mesh.   This is what my shader nodes look like for the cube which I am using as the dupli object:    I'd appreciate any help with this! Please let me know if there's something I can clarify.


Using a foreign driver's license in California when staying with a J-1 visa

I'm planning to attend a Californian university as a visiting scholar (not paid by the university) on a J-1 visa, for a total of four weeks; a colleague of mine will do the same, but for 12 weeks. I've been told (personally, ie. no citable sources) that, if you're staying on a J-1, you're effectively a California resident for the time you're there, and, therefore, need a Californian driver's license.  I've read up on this and found  that states:     If you are a visitor in California over 18 and have a valid driver   license from your home state or country, you may drive in this state   without getting a California driver license as long as your home state   license remains valid.      If you become a California resident, you must get a California driver   license within 10 days. Residency is established by voting in a   California election, paying resident tuition, filing for a homeowner's   property tax exemption, or any other privilege or benefit not   ordinarily extended to nonresidents.   I'm not planning to vote in any elections, nor will I own a home there, but I'm not sure what would constitute "privileges or benefits not ordinarily extended to nonresidents".  Do we need to get driver's licenses in California, or can we use our foreign licenses? How about day trips to Arizona or Nevada?  Note: this seems to be related to , but my question is specifically about staying there on a J-1.


Can anyone please explain when should i create communities, portals and sites for salesforce users?  How should i decide whether shoud i go with communities or portals?


Debian sleeps / hibernates only during remote desktop session using remmina

I am running Debian Buster. On my desktop settings/ Power, suspend and hibernate are deactivated. As expected the computer never sleeps/ hibernates. The problem: When working remotely, and the computer is idle then it enters into hibernation and it is unresponsive. The only way to get it back is to restart the computer locally. It looks 'sleep' and 'hibernate' are configured differently when the machine is used locally or remotely. Any idea what is going on? and how to solve it? thanks


How does static friction provide centripetal acceleration?

While reading about the motion of a car on a level road, I read that static friction provides centripetal acceleration? Please explain as simple as possible.


I'm sure that questions of this ilk have been asked before however I wanted to know if there is some advice for someone from my background. Recently, I've taught myself General Relativity (needed to fill time during lockdown, eh?), reading pretty much cover to cover 'Spacetime and Geometry' (Carroll) and coming up to finishing 'General Relativity' (Wald) in the same fashion, and I intend to read 'Large-Scale Structures of Space-time' (Hawking and Ellis) after. I'd really like to catch up on the Quantum aspect of everything, though. Context is, I'm a maths student and have covered a good deal of QM (although doing rel has made me a little rusty...) so I'd quite like to read something that doesn't really beat around the bush mathematically. I was wondering if there's anything that covers QFT and the Standard Model that's of similar difficulty to Wald in the context of GR, if that makes sense? I appreciate all help - the topic seems to be massive and I don't know what the 'industry standard' textbooks for this area are!


Special Relativity - What is an intuitive way to think about time dilation?

As objects move faster, their time slows down. I understand this, but what I'm having trouble with is intuitively grasping the concept of "time slowing down". A book I'm reading gave the following scenario:  Assume Person A is floating in space, while Person B flies past at a very high speed. If they were to communicate via radio (with electromagnetic waves moving at light-speed), Person A would hear Person B slurring their words.  Why does this happen?  Is it because Person B's time runs slower, and so from the reference frame of Person A, he talks slower? I'm sort of able to wrap my head around this, but I'm having a hard time doing it.  What would happen if Person A and Person B somehow had a conversation, while Person B was at their high speed and Person A was stationary (just as a thought experiment). When Person A spoke, would Person B take a long time to react (relative to Person A)? On the other hand, when Person B spoke, would it seem like Person A was speaking really fast (from B's perspective)?


Decompose ${\mathbb{Z}_n}^{*} / ({\mathbb{Z}_n}^{*})^2$ into a direct sum of cyclic groups.

Decompose ${\mathbb{Z}_n}^{*} / ({\mathbb{Z}_n}^{*})^2$ into a direct sum of cyclic groups,  Where $({\mathbb{Z}_n}^{*})^2 = \left\{a^2 \ : \ a \in {\mathbb{Z}_n}^{*} \right\}$,  A) when $n$ is an odd prime $p$,  B) when $n$ is a product of two distinct prime $p$, and $q$.  I think that they are just $\mathbb{Z}_2$.  Since, if $n=p$ an odd prime, ${\mathbb{Z}_p}^{*} = \left\{ 1, \ 2, \ ... , \ p-1\right\}$, then $({\mathbb{Z}_p}^{*})^2 = \left\{ 1^2, \ 2^2, \ ... . \ (\frac{p-1}{2})^2 \right\}$.  Then ${\mathbb{Z}_p}^{*} / ({\mathbb{Z}_p}^{*})^2 \cong \mathbb{Z} _2$  Similarly, if $n = pq$ for distinct prime $p$ and $q$, ${\mathbb{Z}_{pq}}^{*} = \mathbb{Z}_{(p-1)(q-1)}$.  And if $m \in \mathbb{Z}_{pq}^{*}$, then should $pq-m$ be too.  Clearly, their squares modulo $pq$ is exactly same. So $(\mathbb{Z}_{pq}^{*})^2$ should be $ \mathbb{Z}_{\frac{(p-1)(q-1)}{2}}$.  So is this case, $\mathbb{Z}_{pq}^{*} / (\mathbb{Z}_{pq}^{*})^2 \cong \mathbb{Z}_2$.  It seems to me, then, no matter what $n$ is, $\mathbb{Z}_{n}^{*} / (\mathbb{Z}_{n}^{*})^2 $ is congruent to $\mathbb{Z}_2$.  Where have I done wrong thing? What is wrong?


Are inline virtual functions really a non-sense?

I got this question when I received a code review comment saying virtual functions need not be inline.   I thought inline virtual functions could come in handy in scenarios where functions are called on objects directly. But the counter-argument came to my mind is -- why would one want to define virtual and then use objects to call methods?  Is it best not to use inline virtual functions, since they're almost never expanded anyway?  Code snippet I used for analysis:  class Temp { public:      virtual ~Temp()     {     }     virtual void myVirtualFunction() const     {         cout<<"Temp::myVirtualFunction"<<endl;     }  };  class TempDerived : public Temp { public:      void myVirtualFunction() const     {         cout<<"TempDerived::myVirtualFunction"<<endl;     }  };  int main(void)  {     TempDerived aDerivedObj;     //Compiler thinks it's safe to expand the virtual functions     aDerivedObj.myVirtualFunction();      //type of object Temp points to is always known;     //does compiler still expand virtual functions?     //I doubt compiler would be this much intelligent!     Temp* pTemp = &aDerivedObj;     pTemp->myVirtualFunction();      return 0; }


Born in the USA, have an expired USA passport and valid British passport

I was born in Pittsburgh, I have an expired USA passort and a valid British Passport. Do I need an ESTA to travel to USA?   I have two children with the same surname from my first marriage that are travelling with myself and my second wife (all British citizens with British passports). How do I apply for ESTAs for my two children and what do I need from their birth mother to allow them to tavel with me other than their British passports?


Override a new button by lightning component

I am working on a customer community using Customer Service (Napili) template. I have a requirement to override the new button of custom object so that some of the details can be auto-populated based on login user. I get to know standard new button cannot be overridden using lightning component the only way i could figure out is to disable the standard button and create a new Lightning component then add it to the custom content layout of record list view. Is there any better workaround to resolve this issue.


Rewrite Sharepoint URL (Sharepoint 2013)

I'd like to rewrite all my site urls in the way the the user can't figure out the exact name of the the page his viewing. let's say that my site is "www.justarandomsite.com"  and may page is "page.aspx" I' like to have instead of "www.justarandomsite.com/pages/page.aspx" sothing like this: "www.justarandomsite.com/skdhfjksdgfjksdgfjdsgvdjhsgfjdsdsjfgkdsjgfkdsgfjdsgfjkdsg"


How do you "control" for a factor/variable?

To my understanding, "Control" can have two meanings in statistics.   Control group: In an experiment, no treatment is given to the member of the control group.  Ex: Placebo vs Drug: You give drugs to one group and not to the other (control),  which is also referred as "controlled experiment".  Control for a variable: Technique of separating out the effect of a particular independent variable. Some of the other names given to this techniques are, " accounting for", "holding constant", "controlling for", some variable.  For example: In a Football viewing study (like or not like),  you may want to take out the effect of gender as we think gender causes bias, that is, male may like it more than female.     So, my question is for point (2). Two questions:  How do you "control"/ "account for" variables, in general. What techniques are used? (In terms of regression, ANOVA framework).   In above example, does choosing male and female randomly constitutes control? That is, is "randomness" one of the techniques for controlling other effects?


Omitting the auxiliary verb in short answers or titles

Please help me in this.  what do we call the composition of the short sentence below, where there's no auxiliary verb:  Request approved.  (subject + past participle)  and which of the following gives the same meaning?  The request got approved.  The request has been approved.  The request is approved.


What prevents continued hashing of a key from being used as a cipher when xored with plaintext?

This is just an idea I had while looking through some threads so take it as you will.   Given a plaintext of any length and a key that a specific hash function is capable of taking as input(I mention this as I know bcrypt has issues with extremely large inputs), what would be the potential issues/attacks of hashing the key and then xoring the resulting key with a plaintext block of the same length? For the next block you would hash the previous hash created via the key and xor that with the next plaintext block. Repeat till you reach the end of the plaintext, pad it to the needed length, and commit the last xoring  I would imagine that it would make for a high speed stream cipher that is reasonably capable as long as the initial key is sufficiently strong.  Thanks.


I get low disk space warning after my last upgrade

I am using Linux mint 16 cinnamon. After my last upgrade free disk space dropped from 4.2GB to around 344MB. Don't know what happened. This is the output of df -h  Filesystem      Size  Used Avail Use% Mounted on /dev/sda10       10G  9.1G  329M  97% / none            4.0K     0  4.0K   0% /sys/fs/cgroup udev            1.7G  4.0K  1.7G   1% /dev tmpfs           345M  1.4M  344M   1% /run none            5.0M     0  5.0M   0% /run/lock none            1.7G  1.3M  1.7G   1% /run/shm none            100M   28K  100M   1% /run/user   How can I clear all the temporary files and folders.  Contents of var/log/dpkg.log for last upgrade are here:


How can I know what is the VH of nav bar/ footer etc?

I want to set that my first section (which does not include the navigation bar in code) will be 100% of the VH. So on my website, there will be - Navigation bar Main section I want both of them to be together 100% of the vh. How can I know how much VH each the navigation bar / other elements takes so I can modify my container to subtract the navigation bar VH so both of them together will be equal to 100vh? I was using WordPress and then this question came up, trying to code some stuff and didn't find a solution (unless I modify my self, but I want to know how can I actually know how much vh element takes without modify it). Thanks


Combinatorial proof for $2^n=1+\sum_{k=0}^{n-1}2^k$

I am looking to find a proof by double counting.   Logically concerning the left hand side I was thinking about the number of all subsets of a n-set.  On the right hand side following the same logic I see that with the same logic this will translate to summing up the number of subsets of all k-sets for k=0 to n-1 and then adding one more set.  This seems a bit counterintuitive as there are a lot of sets that will be counted double.  I looked at the building up of the subsets from k to k+1 and tried finding a recurrence relation.   I noticed that in fact the number of subsets of a n-set is equal to the amount of the subsets in n=0 to n-1 added together plus 1. But I cant see why this is true.  It makes more sense to me that $2^n$ is equal to the sum of all subsets of length $k=0$ to $n-1$ and then adding the set itself so plus 1 and thus having $2^n=1+\sum_{k=0}^{n-1}\binom{n}{k}$.  I am quite sure we could get from those binomial coefficients to the $2^k$ that we want to find. But this would not be a double counting proof anymore.  Maybe I need to look at the problem in another angle?


How to open same document as duplicate window in Photoshop

All I want is to have two different windows of the same document but at different zoom percentage that updates change in real-time, like one in 500% zoom for detailing work and other at 100% for the final result.


Shortest distance between skew line *segments*

The answer for the shortest distance between two skew lines has already been answered here and is also found on .   However, I need to apply a further constraint. I need to find the shortest distance between two skew line segments. Or, if it is easier, two rays, whose starting points are $P_1$ and $P_2$. How can I modify the equations for $c_1$ and $c_2$ in the wiki link to account for this? Or is this a far more complicated problem?


I Copied some database backups from one server to another server(new instance no databases are present).I tried restoring using below command   Restore database dbname from disk='g:\e2bak\dbname.bak' with  stats=10   It failed with below error     Directory lookup for the file "G:\MSSQL$s73g\MDF\dbname.mdf" failed   with the operating system error 3(The system cannot find the path   specified.)Msg 3156, Level 16, State 3, Line 1   Also server level default database settings are to store data and log in   G:\MSSQL10_50.SG\MSSQL   I can overcome the error by specfying move option. But my confusion here is  1.Why database .bak file is looking for G:\MSSQL$s73g\MDF\dbname.mdf",this is the path   of dbname database files in production from where we copied the .bak file  2.Also when I restored the database with move option and took a backup in same server,   I was able to restore the Database with below command  Restore database dbname  from disk='G:\e1ebk\dbname.bak' with replace,stats=10   Can you please help me understand why .Bak file location is pointing out to some other directory(which doesn't even exist in our server and existed only on production server) and in second case why this worked without move option.


text-align: center !important; is not working?

this is my CSS code, i do not understand why  text-align: center; is not working?  embed, iframe, object, video {     max-width: 98%;     min-width: 97%;     box-shadow: 0 0 20px #fff;     border: 1px solid #ffffff;     text-align: center !important; }


A word or short phrase for 'better in every way'?

When we're comparing two or more things, there are times when we have to weigh the advantages or disadvantages of each one.  There are other times when one of the things is better for every way in which it's being judged, and the final decision is not based upon trade-offs.  I know that I've heard a phrase for this (I want to say it was two words), but I've had no luck in remembering it.    I don't think 'clearly superior' or 'clear winner' quite fit the bill, as that might still suggest that the disadvantages are significantly outweighed by the advantages.  Is there such a phrase, or even a single word, that would convey this meaning without using idioms?


How to prove that a finite set is countable

How can I rigorously prove that a finite set is countable?   A set is countable if there exists a bijective mapping from this set to that of natural numbers.   Please anyone help me to prove it. Thanks in advance.


In the past, Blender (at least the Mac version) has had the ability to encode video files as .mov, the format used by Quicktime Player. However, with Blender 2.79 this feature seems to have vanished, for both the Internal and Cycles render engines. The release log happens to have the entry "Video encoding settings have been simplified, along with the addition of a Constant Rate Factor (CRF) mode" which I suppose could be the cause.  Does anyone know what happened—whether it is the aformentioned reason or something else—and how to export videos as Quicktime .mov in Blender 2.79?


Why can't Control Winds counter a breath weapon?

Related;   Could you cast Control Winds and direct it to be a gust towards say a dragon and counter the breath weapon? I find it hard that think that in the face of winds strong enough to cut one's movement in half that an exhaled attacks wouldn't just get blown back at the attacker.  The difference is that control winds is constant turbulence of wind as opposed to warding wind's simply circling the caster. This is a difference of a small barrier trying to counter a breathe weapon versus a constant force pushing in the opposite direction.  Am I missing something about the breath weapon? Does magic simply hold a red dragon's flames in that 15 foot cone in spite of the gale blowing in the opposite direction?   Counter to the answer given; We are talking about gale force winds countering a directional breath attack. Which consist of; fire, lightning, acid, poison gas, and cold AIR! The only one I can logically see not being effected too much by strong opposing winds is the lightning. Everything else by common sense should be pushed aside by winds traveling over 40mph/60kpm. So I ask, does the spell description lacking stating such bypass common sense?


Local explanation of the Aharonov-Bohm effect in terms of force fields

Here is an interesting paper for the Physics SE community:      On the role of potentials in the Aharonov-Bohm effect. Lev Vaidman. .  [quant-ph].   You should check it out because it's an amusing read, but I will summarise the argument to whet your appetite, assuming you have basic familiarity with the . In the traditional AB setup, one considers an electron in a superposition of paths, taking it in two opposite directions around a solenoid treated as a classical source of the electromagnetic field. The observable relative phase acquired between the electron's paths is attributed to the influence of the magnetic vector potential on the electron, which cannot be globally gauged away - despite the absence of a physical field anywhere along the electron's path(s) - due to a topological obstruction.  Instead, Vaidman considers the effect of the electron on the sources of the field, treating the latter as quantum particles. He shows that the relative phase between the two branches of the wavefunction can be considered as arising from the action of the physical field of the electron, which is not zero at the position of the sources. However, Vaidman uses highly contrived gedankenexperiments and completely semi-classical arguments, which begs a pair of concrete and related questions.  1) Can Vaidman's first, electric AB effect gedankenexperiment be described in a fully quantum manner, by solving (at least approximately) the three-particle Schroedinger equation? If not, why not?  2) Is it possible to explain within this formalism the experiments of Tonomura et al. (), who used a superconductor to completely shield the magnetic field of the source?


Add ability to flag answers as duplicates

While the etiquette of dealing with duplicate answers , there hasn't been a great way to deal with these, "Uh, yeah, I said this, too" types of behavior than the almighty downvote.   It would be nice to have a "Duplicate Answer" option on the flag menu. Five flags auto-deletes the answer, as with any other flag. In order to prevent abuse, the flagged answer would have to have the last owner edit (including original post) be younger than the original answer's original posting by at least 2 minutes.  Also, this ability should be a 5,000+ rep privilege, since we currently have no fanfare of rep from 3,001 to 9,999, and a power like this has a bit more umph than closing a question.  Thoughts?


How to compile creating externalized figures files from pgfplots in a given folder?

I'm working on a project on LaTeX which includes heavy externalization of pgfplots figures, so I've hidden everything in a tex subfolder of the main one and work only there. Every time, though, I have to scan through all the files (they're like an hundred or more) to search my .tex source or my custom .sty files.  I've found the option output-directory and I'm using it, but it only moves the main .log and .aux files, and the .md5 from the externalized figures, however every other .pdf and .log relative to any single figure created with pgfplots is still in the main directory.  I usually compile straight from the shell and use vim to write the files. Can I do this?


I have a php website hosted on IIS. App pool idle timeout is set to 0. Recycling is set to 3am daily.    After some time of inactivity (0 users on the website) First hit is very slow. (10-15 secods) vs normal 2 seconds.  I looked at the network tab in chrome and it shows that it spends most of the time on "Content Download" of js and css files (~500-600kb)  So, I'm wondering if there's a problem with static files, but not sure.


I am reading Hoffman & Kunze's chapter on linear transformations, with a view towards understanding dual spaces. (I primarily want to read Calculus on Manifolds; in the first chapter of that book, Spivak marks one exercise concerned with dual spaces as "soon-to-be-important". I never studied dual spaces in my linear algebra course, and I want to be sure I follow his development.)   H&K state the theorem that the space of linear transformations $L(V, W)$ from $n$-dimensional $V$ to $m$ dimensional $W$ has dimension $nm$. I am having a hard time understanding their proof; they basically just juggle $\Sigma$-notation. I somewhat follow the steps, which loosely are as follows: you let $\mathcal{B} = \{\alpha_1, ... \alpha_n\}$ be a basis for $V$, and $\mathcal{B'} = \{\beta_1, ... \beta_m\}$ a basis for $W$. For $1 \leq p \leq m$, $1 \leq q \leq n$, define  $$E^{(p,q)} : V \to W : c_1\alpha_1 + ... + c_q\alpha_q ... +c_n\alpha_n \to c_q\beta_p;$$  that is, let   $$E^{(p,q)}(\alpha_i) =     \left\{      \begin{array}{}        0, & i \neq q \\        \beta_p, & i = q       \end{array}    \right.$$  and put $E^{(p,q)}(\gamma) = \sum_{i=1}^n c_iE^{(p,q)}(\alpha_i).$ Fix some arbitrary l.t. $T: V \to W$ such that  $$T(\alpha_i) = \sum_{p=1}^m A_{(p,i)} \beta_p = A_{(1,i)}\beta_1 + A_{(2,i)}\beta_2 + ... +A_{(m,i)}\beta_m$$   for some weights $A_{(1,i)}, A_{(2,i)}, ... A_{(m,i)}, 1 \leq i \leq n$. Now consider   $$ T'(\gamma) := \sum_{p=1}^m\sum_{q=1}^nA_{(p,q)}E^{(p,q)}(\gamma).$$  On the one hand,  \begin{align} T'(\gamma) = \sum_{p=1}^m\sum_{q=1}^nA_{(p,q)}E^{(p,q)}(\gamma) &= \sum_{p=1}^m\sum_{q=1}^nA_{(p,q)}E^{(p,q)}(c_1\alpha_1 + ... + c_q\alpha_q ... +c_n\alpha_n)\\ & = \sum_{p=1}^m\sum_{q=1}^nA_{(p,q)}c_q \beta_p\\ & = \sum_{p=1}^m (\sum_{q=1}^nA_{(p,q)}c_q) \beta_p \end{align}  On the other hand,  $$ T(\gamma) = \sum_{i=1}^n c_iT(\alpha_i) = \sum_{i=1}^n c_i\sum_{p=1}^m A_{(p,i)}\beta_p = \sum_{p=1}^m(\sum_{i=1}^nc_iA_{(p,i)})\beta_p$$  so $T' = T$. Then you show that all the $E^{whatever}$ are linearly independent, and you are "done".    The problem with this is that I have no idea what's going on here. When I focus, I can make sense of the $\Sigma$-notation, but otherwise I don't follow the proof. So, I have to ask:   What is the intuition for why the theorem is true? Can anybody make the proof given more intuitive? (For example, what are the $E^{whatever}$ really doing? How did H&K know that we'd have $T' = T$ (how did they think of $T'$)?


I am using Ubuntu 16.04 on AWS EC2 instance which has been working fine until this problem.  My problem is that I've used 100% of available inodes, as I discovered with this command:  $ df -i Filesystem     Inodes  IUsed  IFree IUse% Mounted on udev           124464    360 124104    1% /dev tmpfs          126787    449 126338    1% /run /dev/xvda1     524288 522638   1650  100% / tmpfs          126787      1 126786    1% /dev/shm tmpfs          126787      5 126782    1% /run/lock tmpfs          126787     16 126771    1% /sys/fs/cgroup tmpfs          126793      4 126789    1% /run/user/1000   The main culprits I discovered:  $ find / -xdev -printf '%h\n' | sort | uniq -c | sort -k 1 -n    1155 /usr/src/linux-headers-4.4.0-62/include/linux    1155 /usr/src/linux-headers-4.4.0-65/include/linux    1155 /usr/src/linux-headers-4.4.0-66/include/linux    1155 /usr/src/linux-headers-4.4.0-70/include/linux    1155 /usr/src/linux-headers-4.4.0-71/include/linux    1155 /usr/src/linux-headers-4.4.0-72/include/linux    1155 /usr/src/linux-headers-4.4.0-75/include/linux    1155 /usr/src/linux-headers-4.4.0-78/include/linux    1155 /usr/src/linux-headers-4.4.0-79/include/linux    1155 /usr/src/linux-headers-4.4.0-81/include/linux    1155 /usr/src/linux-headers-4.4.0-83/include/linux    1155 /usr/src/linux-headers-4.4.0-87/include/linux    1155 /usr/src/linux-headers-4.4.0-89/include/linux    1155 /usr/src/linux-headers-4.4.0-91/include/linux    1155 /usr/src/linux-headers-4.4.0-92/include/linux    1514 /usr/src/linux-headers-4.4.0-62-generic/include/config    1516 /usr/src/linux-headers-4.4.0-65-generic/include/config    1516 /usr/src/linux-headers-4.4.0-66-generic/include/config    1516 /usr/src/linux-headers-4.4.0-70-generic/include/config    1516 /usr/src/linux-headers-4.4.0-71-generic/include/config    1516 /usr/src/linux-headers-4.4.0-72-generic/include/config    1516 /usr/src/linux-headers-4.4.0-75-generic/include/config    1517 /usr/src/linux-headers-4.4.0-78-generic/include/config    1517 /usr/src/linux-headers-4.4.0-79-generic/include/config    1517 /usr/src/linux-headers-4.4.0-81-generic/include/config    1517 /usr/src/linux-headers-4.4.0-83-generic/include/config    1517 /usr/src/linux-headers-4.4.0-87-generic/include/config    1517 /usr/src/linux-headers-4.4.0-89-generic/include/config    1517 /usr/src/linux-headers-4.4.0-91-generic/include/config    1517 /usr/src/linux-headers-4.4.0-92-generic/include/config    1517 /usr/src/linux-headers-4.4.0-93-generic/include/config   Is it safe to delete these files, and if yes could you please tell me the exact command or commands to use on my PuTTY client?


Cannot center a div inside a div? (html,css)

I am trying to center the items in a navbar (a div inside a div) but it either floats to the right or to the left, but never really in a center position.  (I'm using "navbar-default navbar-fixed-top" for the style of the navbar).  topnav2 is a "logo" that is perfectly placed to the left, but I want the items inside topnav to be placed in th center right next to the logo in topnav2.    .topnav a {     display: inline-block;   color: #777777;    padding: 14px 16px;   text-decoration: none;   font-size:22px;     letter-spacing: 1px;   }  .topnav2 a {   float: left;   display: block;   color: #777777;   text-align: center;   padding: 14px 16px;   text-decoration: none;   font-size:22px;     letter-spacing: 1px; }

         Projekt

         Home         Platzhalter 1         Platzhalter 2         Platzhalter 3

     like mentioned above, topnav2 is placed perfectly how I want it, but I somehow couldn't figure out how to center topnav next to topnav2


Examples of correlated Xs with opposite effect on Y

Could someone give me a simple real life example of how two things can be positively correlated, but they have different (opposite) effects on a third variable? I encountered this scenario and I'm trying to find a simple example to tell my boss that this is not unexpected.


Derivative of a determinant whose entries are functions

I do not understand a remark in Adams' Calculus (page 628 $7^{th}$ edition). This remark is about the derivative of a determinant whose entries are functions as quoted below.      $``$Since every term in the expansion of a determinant of any order is a product involving one element from each row, the general product rule implies that the derivative of an $n\times n$ determinant whose elements are functions will be the sum of $n$ such $n\times n$ determinants, each with the elements of one of the rows differentiated. For the $3\times 3$ case we have      $$\frac{d}{dt}\begin{vmatrix}   a_{11}(t) & a_{12}(t) & a_{13}(t) \\   a_{21}(t) & a_{22}(t) & a_{23}(t) \\   a_{31}(t) & a_{32}(t) & a_{33}(t) \end{vmatrix}=\begin{vmatrix}   a'_{11}(t) & a'_{12}(t) & a'_{13}(t) \\   a_{21}(t) & a_{22}(t) & a_{23}(t) \\   a_{31}(t) & a_{32}(t) & a_{33}(t) \end{vmatrix}+\begin{vmatrix}   a_{11}(t) & a_{12}(t) & a_{13}(t) \\   a'_{21}(t) & a'_{22}(t) & a'_{23}(t) \\   a_{31}(t) & a_{32}(t) & a_{33}(t) \end{vmatrix}+\begin{vmatrix}   a_{11}(t) & a_{12}(t) & a_{13}(t) \\   a_{21}(t) & a_{22}(t) & a_{23}(t) \\   a'_{31}(t) & a'_{32}(t) & a'_{33}(t) \end{vmatrix}."$$   It is not difficult to check this equality by simply expanding both sides. However, the remark sounds like using some clever trick to get this result. Can anyone explain it to me, please? Thank you!


To what extent can speed of light be reduced?

Light slows down upon entering different transparent objects, and the ratio is taken as  of the object. If light can be slowed down, then is there a limit up to which it can be slowed down? If yes, then what is the minimum speed?


Why does a class use so much memory compared to an array in c++

I want to store 3 properties of 1000 rectangles. I can do that in two different ways. I can use a structure or an array, but I try to find out which solution uses least memory. Here the code:  struct Figure {     unsigned int color;     virtual void foo() {} };  struct Rectangle : public Figure {     unsigned int width,height; };  int main() {     Rectangle r[1000];     unsigned int r2[1000][3]; //This take less memory, The first entry is rectangle number                         // the next is color, width and height std::cout<<"Type name is "<< typeid(r[0]).name() <<sizeof(r2)<<" "<<sizeof(r)<<std::endl; return 0; }   The output is:  Type name is 9Rectangle12000 24000  As you can see an array of objects of a structure uses twice as much memory as a plain array. Why is it so? I expected that an array of structures in my case would use more memory because of the polymorphic structure, but not that much.


C Programming: Does Modulus Ignore Leading Zeros in Result ? How Can I Stop It?

I'm programming a microcontroller in C and since the compiler or chip doesn't handle Floating Point numbers very well, it is recommended to scale the floating point value up enough to get rid of the decimal and then when outputting the number, scale it back down with a proportional division and use modulus to find and display the fractional part. Here's an example: Start with number 25.0625. Multiply by 10000 to get 250625. Good now we don't have a float anymore. Now to display this we use a line like this:  sprintf(buffer, "%li.%i", Temp / 10000, abs(Temp % 10000));   So we first get the 25 back out by / 10000, then we get the 0625 out by % 10000. Here's the problem though: It appears my modulus result ignores the leading zero in 0625 so when it concatenates the number back together, it becomes 25.625 instead of 25.0625. I can't count on there always being a leading zero, so stuffing a zero in there isn't the answer, and there could at other times be several leading zeros. My question is, how do I suppress the modulus from excluding leading zeros ? Thanks.


I'm teaching out of Rosen's discrete math book, and for mathematical induction he says:  "Why is mathematical induction a valid proof technique? The reason comes from the well-ordering property, listed in Appendix 1, as an axiom for the set of positive integers, which states that every nonempty subset of the set of positive integers has a least element. So, suppose we know that P(1) is true and that the proposition P(k) → P(k + 1) is true for all positive integers k. To show that P(n) must be true for all positive integers n, assume that there is at least one positive integer for which P(n) is false. Then the set S of positive integers for which P(n) is false is nonempty. Thus, by the well-ordering property, S has a least element, which will be denoted by m. We know that m cannot be 1, because P(1) is true. Because m is positive and greater than 1, m − 1 is a positive integer. Furthermore, because m − 1 is less than m, it is not in S, so P(m − 1) must be true. Because the conditional statement P(m − 1) → P(m) is also true, it must be the case that P(m) is true. This contradicts the choice of m. Hence, P(n) must be true for every positive integer n."  Everything makes sense except for this sentence:  "Furthermore, because m − 1 is less than m, it is not in S..."  That doesn't appear to be part of the well-ordering property, or anything else I could find in the book.  Where did that come from and how can it be explained?  I see no logical reason m-1 cannot be in S.


How to find number of keys in Javascript variable?

I have a variable as follows:  var keyValues={   key1:{   ----------   },   key2:{   ----------   } }   How can I find length of keyValues ? like I need keyValues.length=2.


I can't join any servers and it says the authentication servers are currently offline

It shows - "the authentication servers are currently offline servers are currently offline". I just got Minecraft yesterday.


How do i get python to write swedish letters(åäö) into a html file?

So the code I have copied an HTML file into a string and then changed everything to lower case except normal text and comments. The problem is it also changes the åäö into something the VS code can't recognise. What I can find is its a problem with the encoding but can't find anything about it on py3 and the solutions I found for py2 didn't work. Any help is appreciated and if you know how to improve the code plz tell me. import re import os   text_list = []  for root, dirs, files in os.walk("."):     for filename in files:          if (             filename.endswith(".html")         ):             text_list.append(os.path.join(root, filename))  for file in text_list:      file_content = open(f"{file}", "r+").read()      if file.endswith(".html"):         os.rename(file, file.replace(" ", "_").lower())         code_strings = re.findall(r"<.+?>", file_content)         for i, str in enumerate(code_strings):             new_code_string = code_strings[i].lower()             file_content = file_content.replace(code_strings[i], new_code_string)      else:         os.rename(file, file.replace(" ", "_").lower())         file_content = file_content.lower()      open(f"{file}", "r+").write(file_content)


A question about infinity orders in set theory

I would like to ask this question and i hope it is not obvious or rediculus.  We know about cardinal numbers in set theory and that this ''numbers'' are equivalence classes.  In other words two sets are equivalent(or equipotent) if there exists a bijection from one set to another.This relation is an equivalence relation.  Thus the equivalence classes are the cardinal numbers.  We also know that there are infinitely many cardinal numbers.  For instance $\aleph_0<c<2^c<2^{2^c}<....< $ where $c=2^{\aleph_0}$  My question is that can we form a set that has as its elements all cardinal numbers?  If such set exists then what is its cardinality?(maybe it does not exist because in some way we may derive the existence of the set of all sets..im not sure)  Thank you in advance!  My question is not an exact duplicate of the mentioned question.In the question Cardinality of the set of all cardinals the user assumes that there exist a set of all cardinals and i ask if there exists such set.


Question is :  You have a 5 card hand from randomly shuffled standard deck of 52 cards. P - Event that hand exactly contains one spade. Q - Event that hand exactly contains one ace.    Calculate : a. Prob[P] b. Prob[Q] c. Prob[P intersection Q]    I've faced this kind of problem for the first time. Can anyone please guide me ?


I would like to replace the version of Firefox that is already installed with Firefox ESR on Ubuntu 18.04.  I have downloaded it from   But I couldn't configure it successfully as I could in Ubuntu 14.04:  sudo tar -xvjf firefox-x.x.tar.bz2 -C /opt sudo ln -s /opt/firefox/firefox /usr/bin/firefox   So I have reinstalled Ubuntu completely.  How can I achieve this?


Bus conductor's change maker used for magic?

This was part of a weird dream I had but I've a vague recollection that it's based on a book that I read a long time ago, in my youth; a character had one of those change-makers that bus conductors used to wear with 'pods' of some description in each column. They then click for change that dispenses the pod into their hands which they then cast.  My feeling is that the story was similar to the Spellsinger series, where somebody from our world crosses over to a magical realm and I probably would have read about the same period, mid to late eighties.


Insert into select into multiple related tables using INSERT_IDENTITY

Okay setting the scene. I have three tables, (Table1, Table2 and DataTable) and I want to insert into Table1 and Table2 using DataTable as source. So for every row in DataTable I want a row in Table1 and Table2, and Table2 needs to have the inserted id (PK) from Table1...  If I were to do this...  INSERT INTO Table1 SELECT A, B, C FROM MyTable INSERT INTO Table2 SELECT IDENTITY_INSERT(), D, E, F FROM MyTable   I'd get the ID of the last inserted record into Table1.  Is a CURSOR or WHILE loop the only ways to do this?


Lost my old passport for Schengen visa application

I am a British resident and applying for Schengen visa to France. I am preparing my documents for application and as stated they require old passports and previous issued Schengen visa. However I realised I have lost my old expired passport which has my 3 previous (expired) Schengen Visas issued in the past 3 years.   Can I still apply in this case? Will I get rejected?


"Trojan:Script/Cloxer.A!cl", any info on this virus? what does this virus do?

Windows Defender identified and removed a threat on my Win10Pro PC called "Trojan:Script/Cloxer.A!cl". But there is no information on the web on this trojan, searching for this yields little/nothing. The Windows Defender info on this is only that they consider it severe and: This program is dangerous and executes commands from an attacker and the .   How can I get more details on what this virus does/did? What are the commands it may have run? Does is try to obtain user names and passwords? Does it find and upload files someplace? Is it a crypto miner? Spyware? DoS zombie? How was my system impacted? Should I totally wipe and re-install?  I'd just like to know what this Trojan does/could do so I can gauge the impact of it and I'd like to know the vectors it uses as to how it got on my system.  I do keep my system up to date (on Win10 Pro V 1709 Build 16299.248) and my Defender is up to date and I run it often, but I have no other protection.  UPDATE: On the point that this post may be a duplicate - I disagree and feel this is NOT a dupe. Mainly I am looking for specific details on the Cloxer virus, not how to remove it (but that referenced post is good and a logical next read for viewers of this post).


What is the sequence loading linux kernel module on startup? How priority is set to them?

I have a Linux kernel module which I compiled dynamically. How is it added to startup? There are lot of .ko files in /lib/modules. How is priority set for loading these modules?


I am trying to UV Wrap the can in the image but I am struggling with how to design my label so it fits the correct curve of the UV map.  I tried warping my image in Photoshop but I just couldn't make it look prefect. Is there an easier way in Blender?


How to Solve The Redundant Literal Rule (OR)?

I found on the internet this rule (A + B = A + A̅ B) and its called Redundant Literal Rule. this is it's OR form. But I want to know is this really form of the Redundant Literal Rule?. I saw in a website there are 2 Types in this Law. What do you think about that. Is that true? (proves can add as comments)


gcd between powers of two co-prime numbers

Is it true that $\forall x,y,n\in \mathbb{Z}$, if $\gcd(x,y)=1$ then $\gcd(x^n, y)=1$? If not, is there a counterexample?


Mapping building to only one grid which contains more than half of its area using QGIS?

I have a shapefile of a city map and I have created vector grid as polygons.   After intersecting the two shapefiles, a building will map to all the grids it overlaps.   However, if I just want it to map to the one grid which contains the majority of the building (>50%), how could I achieve it?   Is there a function or plugin in gqis for this task? Or do I have to write my own code to do this?  I am new to QGIS.


Sum of nucleus less than sum of neutrons & protons?

The mass of a nucleus is less than the sum total of the individual masses of the protons and neutrons which form it.  How this is possible?


Let $A$ be a commutative ring, prove that if $x \in A$ is nilpotent then $1-x$ is an invertible element in $A$.  I need help with this one.


How do I delete file named -?]d?j??.? from system?

I cannot remove such file, I get error message. file name is      -?]d?j??.?   and I want to remove it. I try rm -?]d?j??.? but it gives error.


I am working on a development website which involves users posting their favourite content of their book on to the webpage and all the data gets stored in the database and gets displayed on the website. However whenever i try to post big paragraphs using the form I created and php scripts which processes the form, it doesn't give any error but it doesn't store the values to the database as well. It works okay if the content to process is short. Please help me the code is below. Any suggestions would be appreciated.  <?php $hostname = "localhost"; $username = "root"; $password = ""; $database = "library"; $conn = mysql_connect($hostname,$username,$password)or die('Cannot connect'); mysql_select_db("library", $conn); ?>  <?php $title = $_POST['title']; $author = $_POST['author']; $content = strval($_POST['content']); $description = $_POST['description']; $category = $_POST['category'];  if (isset($title) && !empty($title)){     $sql = "INSERT INTO books(title,author,description,content,category) VALUES('$title','$author','$description','$content','$category')";     mysql_query($sql);     echo 'Successfully Added the book'."
Check it out here"; } else{     echo 'Title is missing'; } ?>   Thanks.


What is the right SE site for Kuali apps related questions?

Under the Kuali suite there are various university enterprise applications including a framework/middleware for development of these applications.  These are created through community efforts as open source.  A collaboration of universities across the globe are developing and implementing them at their institutions.  What would be the best stack exchange site for questions regarding implementation, configuration, and customization of these applications?  Questions will easily overlap topics of such sites like  and . I can easily see the questions to be flagged as off-topic in any of these sites and that's why I'm asking.  We started an area 51 proposal for a specific stack exchange site for these questions but reluctantly came to the conclusions that the bars for the site requirements are quite high and not likely for us to meet. This effort did give us a nice list of  for reference to the kind of questions I'm inquiring about.


parts of my models are disappearing as my scene gets bigger

As I navigate around my growing scene parts of my models disappear. Is this a settings issue or is it because my computer doesn't have enough power?


Does there exist a continuous function $f: \Bbb R\to \Bbb R$ that is rational at (Lebesgue) almost every irrational, and irrational at every rational?

Does there exist a continuous function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ that is rational at (Lebesgue) almost every irrational, and irrational at every rational?  Some thoughts: for some $q\in \mathbb{Q}$, $f^{-1}(q)$ is a closed set of positive measure disjoint from the rationals. But of course that's possible.  Though it does at least mean that the null set of irrationals where $f$ is irrational is dense in $\mathbb{R}$, by the Baire Category theorem, since the set is the complement of the countable union of nowhere dense sets: $$\big(\mathbb{Q}\cup(\cup_{q\in\mathbb{Q}} f^{-1}(q))\big)^c$$  Also if it exists, $f$ can't be injective on any open interval. So the Cantor function comes to mind, but that obviously doesn't work since it's locally constant on an open set. Maybe a "nowhere injective" function is guaranteed to be locally constant somewhere?  I have no idea.   (I saw this asked on reddit, and after thinking for a while I'm too curious not to ask here.)


How to make a "fat jar" of a Maven project?

Using IntelliJ I just created a new Maven project and added the following to the pom file  and the following to a Main.java file   Now if I run the code all works well, but how do I make this as a "fat jar" that will contain all the dependencies in the pom file and that I'll be able to run by just java -jar my.jar ? Like you are able to do with a Spring Boot app.


Where to place $(document).ready(function()?

We often read here and there, that we must place our js code either on the page head section or before (sorry) the end body tag. Discussions about this aside, I'm just looking to know what are the reading order for such things by the browsers (taking that they do act as equals here):  Can we place:  $(document).ready(function(){   No matter where on the page structure, because we are using $(document).ready or should we still place it on the head section ?  Can anyone please clarify this.  If my question isn't clear, I can rephrase.


If you let a person in, make sure to see their ID first.   Is it grammatically correct to use a plural determiner for a singular noun in situations like this when it implies that “person”, “client”, “tenant” etc. can be either he or she?


Apparently the expansion to this function is equal to the following -   $(1-\phi{z})^{-1} = 1 + \phi{z} + \phi^{2}z^{2} + ....$  But I can't see why that is. I have a feeling the answer is extremely trivial and obvious.  Thanks for your help!


Could we recognize our galaxy by looking at it from a different place in the universe?

Suppose we're in an unknown place in the universe, only knowing that the Milky Way is somewhere is the sky (but of course, younger that it actually is, due to unknown distance light has to travel to reach our position).  Under detailed observation, could we recognize our galaxy?  Our galaxy alone would probably look like just another younger spiral galaxy. But, its vicinity would also include younger Magellanic Clouds, Andromeda galaxy, etc. And maybe other properties that could hint that galaxy being ours.    Note: I severely edited the initial post to keep the core question, as comments and the proposed "duplicate question" kept focusing on the background, rather than the actual question. I know these kind of edits are discouraged as they can invalidate answers, but the only answer so far is not affected by the edit.


Cannot install DB2 Express C 10.1 on Mac OS X 10.7.5

When I invoke ./db2setup it cannot find the JRE where it expects it.  Binary for Java not found as follows:  /private/tmp/db2/expc/db2/macos/install/db2setup: line 606: /tmp/db2.tmp.740/db2/macos/install/../java/jre/bin/java: No such file or directory  I successfully installed DB2 Express C 9.7 last summer before when I was still using the Apple JDK.  I am now getting the JDK from Oracle as it is the only source I know of.  How do I tell the DB2 install where to find Java?


I recently bought a wifi adapter(Astrum NA150) which is not supported by linux out-of-the-box. But in the cd there are drivers for win,mac,linux and android. They also have makefile. But as i know make is not supported by android.How can i install them. Link to the drivers:


use of graphics stock icon (spoon,fork,skull head) for logo

I am a new graphics designer I want to  use skull head, spoon icon, fork, etc in my logo from free stock but I don't know how to avoid copyright issue


Why is a Coulomb not a fundamental unit?

Why is a coulomb not a fundamental unit but an ampere is considering that a coulomb is more ' fundamental '?


Punctuation with "The question is..." '.', '?' or ' "... ?" '

Possible Duplicate:          Take this statement for example:     That's not the question. The question is what was Colonel Mustard doing in the bedroom with the revolver.   or      That's not the question. The question is what was Colonel Mustard doing in the bedroom with the revolver?    or     That's not the question. The question is "what was Colonel Mustard doing in the bedroom with the revolver?"


Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$

Let $m$ be a positive integer and $n$ a nonnegative integer. Prove that $$(n!)\cdot(m!)^n|(mn)!$$  I can prove it using , but I have to use the lemma that $$ \dfrac{\displaystyle\left(\sum_{i=1}^na_i\right)!}{\displaystyle\prod_{i=1}^na_i!} \in \mathbb{N} $$ I believe that it can be proved using the lemma, since  he has mentioned so at the end of his answer. Any help will be appreciated. Thanks.


SQL Server date conversion fails due to some user/db setting

Which user/db setting would cause the date conversion here to fail with Conversion failed when converting date and/or time from character string?  SELECT     -- This works:     CONVERT(datetime2, '01 ' + LEFT([MonthName], 3) + ' ' + CAST([Year] as char(4)), 106)      -- This doesn't:     ,CONVERT(datetime2, '01 ' + LEFT([MonthName], 3) + ' 2018', 106)   [Year] is of type int NOT NULL.  [MonthName] is of type nvarchar(100) NOT NULL and its collation is SQL_Latin1_General_CP1_CI_AS.  DBCC USEROPTIONS shows this:  language   | us_english dateformat | mdy   I tried creating another table with seemingly the same settings and the query works there. Something is obviously different but I can't figure out what.  EDIT  Doing a SELECT DISTINCT [Year], [MonthName] reveals that there's data only for 'December', 2017. So yes, the month name is in English.  Leap years can't be the problem because of the previous point but also because I'm forcing the day to be 1.  Interestingly, TRY_CONVERT doesn't return NULL for any row. I did a  WHERE TRY_CONVERT(datetime2, '01 ' + LEFT([MonthName], 3) + ' 2018', 106) IS NULL   I'm suspecting that inputting the ' 2018' causes the resulting string to be of some other collation (or something) which makes SQL Server expect the date format to be something different.  Here's the weird part. The query works if it's like this:  SELECT DISTINCT     CONVERT(datetime2, + LEFT([MonthName], 3) + '01 2018', 106)     ,CONVERT(datetime2, '01 ' + LEFT([MonthName], 3) + ' 2018', 106)     ,[Year]   But removing either the [Year] or the DISTINCT will again produce the same error.  The query has only two tables joined in the FROM clause and no WHERE clause. The [MonthName] comes from the second table and the [Year] from the first.


Numpy module not found, but I have installed numpy

I am using Windows 10 and Ubuntu 20.04. I am trying to install some software (python-fsps) using sudo SPS_HOME=$SPS_HOME python3 setup.py install. However, this gives me the error ModuleNotFoundError: No module named 'numpy'. I really should have numpy installed, becasue I can use it in sessions on Anaconda. Also, running pip3 install numpy, tells me Requirement already satisfied: numpy in /home/lzucker1/.local/lib/python3.8/site-packages (1.18.5). I have also tried conda install -c anaconda numpy, but it does not recognize conda, which is also weird becasue I do have conda on my computer. I have tried defining export PATH=$PATH:$HOME/anaconda3/bin in my ~/.bashrc file, but that does not change anything. I would greatly appreciate any advice.


When I am running sudo apt-get -f install, it shows dpkg: error processing. Please find the complete logs below and advise how to solve this. Should I remove the old version?      Reading package lists... Done     Building dependency tree            Reading state information... Done     Correcting dependencies... Done     The following additional packages will be installed:       cuda-cublas-9-1     The following packages will be upgraded:       cuda-cublas-9-1     1 upgraded, 0 newly installed, 0 to remove and 553 not upgraded.     1 not fully installed or removed.     Need to get 50.1 MB of archives.     After this operation, 56.2 MB of additional disk space will be used.     Do you want to continue? [Y/n] y     Get:1 http://developer.download.nvidia.com/compute/cuda/repos/ubuntu1604/x86_64  cuda-cublas-9-1 9.1.85.3-1 [50.1 MB]     Fetched 50.1 MB in 21s (2,313 kB/s)                                                 (Reading database ... 415420 files and directories currently installed.)     Preparing to unpack .../cuda-cublas-9-1_9.1.85.3-1_amd64.deb ...     Unpacking cuda-cublas-9-1 (9.1.85.3-1) over (9.1.85-1) ...     dpkg: error processing archive /var/cache/apt/archives/cuda-cublas-9-1_9.1.85.3-1_amd64.deb (--unpack):      trying to overwrite '/usr/local/cuda-9.1/lib64', which is also in package cuda-cudart-9-1 9.1.85-1     Errors were encountered while processing:      /var/cache/apt/archives/cuda-cublas-9-1_9.1.85.3-1_amd64.deb     E: Sub-process /usr/bin/dpkg returned an error code (1)


Solve: $T(n) = T(n-1) +(1/n)$ by iteration


Why will this plan for a perpetual motion device not work?

I have made a plan for a perpetual motion device, but I am sure that it won't work because otherwise the world would be relying on it right now. I know that perpetual motion defies the laws of physics.    The blue represents a container of water, the brown wheel is made of wood, halfway into the water.  Half of the wheel is in the container of water, and half is not. This seems like it should work to me (a complete noob at physics), because the part of the wheel that is in water will always try to float upwards, and the side outside of the water will be pulled on by gravity and try to fall downwards.  Assuming that we found a way to not let any water leak out of the container, why wouldn't this work? Extra credit to anyone who can make a explaination without using equations or complicated terms, so I (a noob) can understand. Thanks!!  NOTE:  This question is different from the one it is marked as duplicate of because that one has an answer that is explaining to someone that has experience with physics, whereas I have none. Also, the main question of that question is about Buoyancy, whereas mine is about the machine itself.


How do I actually disable Wi-Fi or Bluetooth in iOS 11 Control Center?

In iOS 11, I can't disable Bluetooth or Wi-Fi using the redesigned Control Center. It disconnects from any Bluetooth/Wi-Fi devices but the radios are still on, draining battery. It also doesn't disable AirDrop either. If I disable Bluetooth or Wi-Fi using settings this shows:     How can I quickly disable Bluetooth/Wi-Fi without having to go to settings?


How can i fix the damaged area on varnished hardwood floor?

The area was damaged when a bottle of black mould killer tripped over. I hadn't realised till it was too late. Any recommendations on how to fix it without redoing the floors would be greatly appreciated.


What is the equivalent of the C++ Pair in Java?

Is there a good reason why there is no Pair<L,R> in Java? What would be the equivalent of this C++ construct? I would rather avoid reimplementing my own.  It seems that 1.6 is providing something similar (AbstractMap.SimpleEntry<K,V>), but this looks quite convoluted.


Is possible to use 2 Xbox 360 wireless controllers in PC, using just one receiver?

Recently, I bought an Xbox 360 wireless controller for PC, which comes with the USB receiver...  I want to play ''Rayman Origins'' in co-op with my girlfriend, and I want to know if it is a good idea to buy a normal Xbox 360 wireless controller (for Xbox) and if it would work as a second player using the same USB receiver?  Or do I need to buy another Xbox 360 wireless controller for PC, and use the same receiver? Or use 2 receivers?


From tree, I cannot make arrows from each node and give the color for each floor and give a layer to that

I want to draw a tree like the below.    \documentclass[article] \usepackage{tikz} \usetikzlibrary{shapes,arrows,trees}  \begin{document} \begin{tikzpicture}[level distance=2cm, level 1/.style={sibling distance=1.5cm}, level 2/.style={sibling distance=1.7cm}, ] \node {$f$} child {node {$|f \ast \psi_{\lambda_i}|$  }} child {node {} } child {node {}  } child {node {$|f \ast \psi_{\lambda_1}|$} child {node {$||f \ast \psi_{\lambda_1}| \ast \psi_{\lambda_j}|$}} child {node {}} child {node {}} child {node {$||f \ast \psi_{\lambda_1}| \ast \psi_{\lambda_2}|$}} child {node {}} child {node {}}} child {node {}} child {node {}};  \end{tikzpicture} \end{document}   I tried like this.    First of all, I cannot make arrows from each node. and how can I give the color like the first image. Also, how can I make the block or grouping or make an layer to distinguish each group as I grouped in the first image..  Thanks.


`who am i` after `su` not showing new user id?

Why is it that when I switch user su <username> and then execute who am i is outputs the previous user which I was logged as and not the one I've switched to?


What do you call a **person** who is capable of doing anything and everything, humanly possible?

What do you call a person who is capable of doing anything and everything, humanly possible?


Import and export data from SQL Server table using query

I need to import and export data from a table using a SQL query so I need query example for importing and exporting data. I don't want to export it to txt file as the data is not getting aligned. I have read that this can done manually but I want to do this dynamically. You can see below manually import and export data.


How do you change the starting rotation on imported OBJ file?

When I import my obj file into Blender the rotation of the actual object is not correct (like when you look in Transform > Rotation; the X value is at 90 degrees while the others are at zero) Do you know how to change this starting value so that my object is straight? This has become an issue since the measurements in Transform > Dimensions are not correct since blender measures the object upon initial import and now after I rotate the object to it's proper orientations.


Gold or silver badge for multiple daily votes

There is a badge for using 30 votes (Suffrage) in a day.  There is also a badge (Vox Populi) for using the maximum 40 votes in a day.  However, there are no badges for doing either of these multiple times.  What I am suggesting implementing a silver badge for using 30 votes in a day 100 times and a gold badge for using 30 votes in a day 300 times.  It has frequently been my observation that people tend to get the Vox Populi and Suffrage badges and then just kind of slack off of voting.  It would be substantially beneficial to the community if people were out trying to get more voting badges.  And yes, there are definitely people who spend enough time on some of the stacks to warrant getting a badge for 30 votes 300 times without randomly voting up whatever material comes to mouse.


If you run a code snippet, a hat still appears (hats are above snippets in the Z-order)

If you run a code snippet, a hat still appears. Steps to repro:  Go to a question where there is a snippet and where the OP wear a hat well, if you find that hard, just go here.  (BTW, it's my answer)  Then, run the snippet.      Or just see here:   Winter Bash 2020!


Proving existence of $\gcd$: Artin exercise 2.3.3

I am trying to solve this exercise in Artin.     (a) Define the greatest common divisor of a set $\{a_1, \ldots, a_n\}$ of $n$ integers. Prove that it exists, and that it is an integer combination of $a_1, \ldots, a_n$.      (b) Prove that if the greatest common divisor of $\{a_1, \ldots, a_n\}$ is $d$, then greatest common divisor of $\{a_1/d, \ldots, a_n/d\}$ is $1$.   I am having difficulty getting started, and am really just looking for a hint and some clarifications on interpretation. My thoughts on this at the moment are:   1) My first instinct is to induct on $n$. I don't think we can define the $\gcd$ of an empty set or of a single element, so the base case would would have to be $n = 2$.    2) It doesn't seem that I have any information on these integers. Can we define the $\gcd$ of $0$ or negative integers? Surely the $\gcd$ itself is greaeter than or equal to $1$.   3) I cannot figure out how to 'prove' existence. If we have two integers, the $\gcd$ "exists by definition." If the integers are relatively prime, their $\gcd$ is $1$. If not, there exists some integer $d > 1$ that divides both. There's certainly a finite number of such elements because the distance between any two integers is finite, so taking the maximum gives the $\gcd$.   4) The $n \implies n + 1$ inductive step seems to just be invoking this same $n = 2$ argument I just made.


If coprime polynomials divide another polynomial, then their product divides the polynomial

Let $k$ be a field and let $f\in k[x]$. Let's say that there are some $g, h\in k[x]$ such that $\gcd(g, h)=1$, $g|f$ and $h|f$. I want to show that $gh|f$.  Since $g|f$ and $h|f$, we may write $f=gu$ and $f=hv$ for some $u, v\in k[x]$. Now, $\gcd(g, h)=1$ implies that there are some $\alpha, \beta \in k[x]$ such that $\alpha g+\beta h=1$. We may now write that $gu=hv\implies \alpha gu=\alpha hv \implies (1-\beta h)u=\alpha h v\implies u=h(\alpha v +\beta u)$. Thus, $f=gh(\alpha v + \beta u)$, so $gh |f$. Is this correct? I remember hearing this fact in high school, but in my abstract algebra course from this year the lecturer never mentioned it, even though it would have made some things easier. This is why I tried to prove this myself.


Is a ring of integers necessarily Noetherian?

Let $K$ be an algebraic extension field (not necessarily finite) of $\mathbb{Q}$. Let $\mathscr{O}_K$ be the integral closure of $\mathbb{Z}$ in $K$.  Then, is $\mathscr{O}_K$ Noetherian?  If $K$ is a finite extension of $\mathbb{Q}$, then $\mathscr{O}_K$ can be shown to be Noetherian. However, if we do not assume that finiteness condition, is it still true?  (It can be shown that $\mathscr{O}_K$ is an integrally closed domain of Krull-dimension $1$. Hence, if it is Noetherian, it is a Dedekind domain.)


How to group the result of a SQL Server query (group by not working)

Got this query:  SELECT TOP 100      i.item_id ,      i.item_description,      part.part_number  FROM       i  LEFT JOIN       part ON part.item_id = i.item_id   An item usually have multiple part number. It is possible to modify my query to get a grouped result?  without to add any subselects. Group by is not working. I tried to add FOR XML PATH('') but it transform all columns in xml, not only part number


I need to use a calculator to find trigonometric ratios like $\sin(41),\cos(32)$.  How do calculators work for trigonometry? Also, as calculators are invented by the human mind can we do it mentally? Is there any binary trick or something like that?


How are objects able to move even after newton's third law of motion

I can't understand at all why objects move even though after newton's third law.I also have a doubt in following example  If we apply a force on an object the object applies a backward push on us according to newton's third law of motion.let us now put the force vector applied by the object to its back. Now we can cut off Its forces then how is the object able to move.


List of mathematical notations - International convention

I'm wondering if exist a list of mathematical notations accepted internationally (book, handbook, textbook etc.). I tried to search online, but without success.


8 letter word beginning and ending on triple word scores

I played the 8 letter word emerging, using the middle e already on the board, and starting and ending on triple word scores.  Is the score tripled, and then tripled again before adding the 50 pt bonus, or is it 6 times the word score before the bonus?


Concatenating two columns in ArcGIS 10.2.1: "no records within table"?

I am trying to merge two text columns (consisting of 2 digit and 3 digit numbers respectively) into one in ArcGIS 10.2.1 desktop version, but unable to do so. I have added a new field and kept it as text. On using arc toolbox > data management tools > calculate field, I am trying to merge the two columns into the newly created column.   Example:   I have the following two columns in the shapefile - Code1 (text, 10) and Code 2 (text, 10). I want to concatenate the values in these two columns in a new data field Key (text,11) that I have already created.  Code1 Code2  Key                                                                          015   21     21015                                                                                647   19     19647                                                                                213   05     05213    When I try to use field calculator I get the error no records within table. See below:


Recurrence relation for binary string with $n$ digits such that $11$ doesn't appear in the string

I wanted to understand how to solve these types of questions in Combinatorics in which there is a recurrence relation. For example, this question states:  Consider a binary string which consists only of digits 0 and 1, let an be the number of such strings with $n$ digits such that 11 doesn't come anywhere in the string. Find the relation between $a_n, a_{n-1}$ and $a_{n-2}$.  Now I have no idea how to solve this question, any help or solution would be much appreciated.


Simultaneous Users ( 2 - 4 Users ) on a MAC PRO

With the up-coming high end Mac Pro, how would I share it with different people? Assume I have a keyboard, mouse and monitor for everyone.  I am involved in a setup in which there are 4 Users (3D Game Developers). I am considering the option to not purchase 4 iMacs separately for each user.  Thanks!


"Big" and "Diminutive" are what kind of words...?

What do you call a word that look different than it means? For example, the words "big" and "diminutive"?


I am using a fantastic  to try and generate a CV. I have installed Tex Live 2016 this morning.  When I try and compile the cv.tex document, I am prompted with the following error:  "fontspec error: "font-not-found" The font FontAwesome cannot be found...."    on Line 164. The document successfully compiles with the Educations, Skills, Experience sections but does not include the heading (persons name and contact details).  Following this , I tried to place the relevant .ttf files in my local directory, using  ~texmf\tex\xelatex\fonts\truetype\awesomefont   But this has not helped.  A contributor to the github document informed me that the fontawesome package is installed with a default TeX Live installation. . He then suggested I compile the following example  \documentclass{article} \usepackage{fontspec} \RequirePackage{fontawesome} \begin{document} \faCodeFork \end{document}   For which I generate a blank document. So where must I place the .sty or .ttf files so the document can be successfully compiled?


Second order partial of $f(x,y)=\frac{xy(x^2-y^2)}{x^2+y^2}$

Consider the function $f(x,y)=\dfrac{xy(x^2-y^2)}{x^2+y^2}$ for $(x,y) \neq (0,0)$, $f=0$ otherwise.  I have to compute $\dfrac{d^2f}{dydx}(0,0)$.  I know that I have to calculate $\frac{df}{dx}$ first. But that is ,  $\frac{df}{dx} = \frac{\partial f}{\partial y}\frac{dy}{dx}+\frac{\partial f}{\partial x}$. When I put it in wolframalpha, it gives me this calculation, and also just $\frac{\partial f}{\partial x}$ as an alternative form.   Why do I just ignore the y'? I don't know what y(x) is, as a function of x.  y and x are independent functions, no?


I have a document, where I want to use $\tau_{ff}$. If this is rendered it looks like a space is inserted between the two f's. $\tau_{rl}$ looks fine ...   Where does this additional space come from and how can I avoid it being inserted?  (Miktex 2.9 on windows, if this is relevant).


Converting a character array to a string

Why is the toString method returning jibberish?  char[] arrays = {'a','b','c'};   { a, b, c } arrays.toString()   "[C@6519ceb1"


I looked for a phoenix in the Monster Manual, but I can't seem to find anything. I want to see if I can use one in my adventure, but I couldn't find a phoenix anywhere. Are there phoenixes in D&D 5E?


I am computer scientist and not a physicist, but I really like physics One question popped into my mind recently about gravity. General theory of relativity describes gravity not as a force but as a curvature of space-time. So if gravity is not a force but just illusion caused by curvature of space-time then why do we consider it to be a fundamental force And why are searching for force carrying particle for gravity if it is not a force?


Numbers till 400 divisible by 2, 3, 5, 7

I stumbled upon the following in a book:     till 400 all even numbers will be divisible by 2 ( 200 even numbers)   remaining 200 odd numbers  1 3 5 7 9 ..... 399 200/3 = 67 will be   divisible by 3, as we have discarded all even numbers and out of   remaining numbers 2nd number is 3 then 1 + 198/3 = 67 numbers are   divisible by 3      now we have discarded all multiples of 2 and 3 remaining numbers will   be  200 - 67 = 133;   1 5 7 11 13 ... so on out of these 133 numbers 2nd   number is 5 so numbers divisible by 5 will be 1 + 131/5 = 1+26 = 27      now remaining numbers = 133 - 27 = 106; 1 7 11 13 .. so on again 2nd   number is 7 , so numbers divisible by 7 = 1 + 104/7 = 1+14 = 15      total numbers from 1 - 400 divisible by any of 2 3 5 7 = 200+67+27+15   = 309   But I can't seem to understand how the following is derived? :     as we have discarded all even numbers and out of remaining numbers 2nd   number is 3 then 1 + 198/3 = 67 numbers are divisible by 3   How does the result come out to be "1 + 198/3" ?


Can I install Windows 7 on my Mac mini Server?

I have a Mac mini server and I want to install Windows 7 on it. How can I do this?


Properties of $\liminf$ and $\limsup$ of sum of sequences: $\limsup s_n + \liminf t_n \leq \limsup (s_n + t_n) \leq \limsup s_n + \limsup t_n$

Let $\{s_n\}$ and $\{t_n\}$ be sequences.  I've noticed this inequality in a few analysis textbooks that I have come across, so I've started to think this can't be a typo:  $\limsup\limits_{n \rightarrow \infty} s_n + \liminf\limits_{n \rightarrow \infty} t_n \leq \limsup\limits_{n \rightarrow \infty} (s_n + t_n) \leq \limsup\limits_{n \rightarrow \infty} s_n + \limsup\limits_{n \rightarrow \infty} t_n$.  I understand the right two-thirds of the equation, and can prove it.  I'm stuck on the far-left third.  I don't understand how that is true.


Is it possible to overfit a logistic regression model? I saw a video saying  that if my area  under the ROC curve is higher than 95%, then its very likely to be over fitted, but is it possible to overfit a logistic regression model?


Computing the number of nonisomorphic finite abelian groups of order $n$

Let's say I'm given a number $n = p^{3}q^{4}r^{2}s$ and I want to find the number of (non-isomorphic) abelian groups of order $n$. How I'm computing the number is basically partitioning, that is, I'm just looking at it and saying that I have $\mathbb{Z}/p^{3}q^{4}r^{2}s\mathbb{Z}$, $\mathbb{Z}/p^{2}q^{4}r^{2}s\mathbb{Z} \times \mathbb{Z}/p\mathbb{Z}$, and so on. Then I count the number of groups I've written down. However, I've found that I'm quite prone to error when I do this. Is there a faster way of doing this? If not, is there a systematic trick/way I could use to make this easier?


I have a dumb problem that I'm hoping that someone can point me in the right direction on. I'm trying to install ubuntu 16.04.1 on a windows10 machine. I've followed all the steps correctly (I think) all the way up to the point where I am supposed to go through the install program on the thumb drive. The first problem is that it does not show the option screen that has the partition the hard drive options (see here: ). The next page (here:) only shows that my "device for boot loader installation" is the thumb drive itself.  I'm confused. I've made sure that there is in windows a free partition with no drive assigned and every other step up till the point where I reach this dead end I've followed correctly seemingly. Can anyone tell me what's going wrong?


Is $\mathbb{Z}[x]$ an integral domain? If so, why?

I'm trying to solve a larger problem about maximal and prime ideal, and knowing if $\mathbb{Z}[x]$ is an integral domain would really help me


Getting hyperref to work with \citeyear and \citeyearpar in biblatex

When used in concert with the hyperref package, biblatex automatically creates hyperrefs for citations but not if they are inserted using \citeyear or \citeyearpar. Is it possible to add a hyperref to year only citations?  \documentclass{article}  \usepackage[backend=biber,natbib=true, style=authoryear-comp]{biblatex}  \usepackage{filecontents}  \begin{filecontents}{\jobname.bib} @article{ref1,   author = {Doe, John D.},   title = {Hyperrefs to citations},   journaltitle = {Links Everywhere},   volume = {1},   date = {2000},   pages = {1--2}, }  \end{filecontents}  \addbibresource{\jobname.bib}  \usepackage{hyperref}  \begin{document}  citet -- \citet{ref1}  citeyear -- \citeyear{ref1}  citeyearpar -- \citeyearpar{ref1}  \printbibliography  \end{document}


I have done the following code in JavaScript to put focus on the particular element (branch1 is a  element),  document.location.href="#branch1";   But as I am also using jQuery in my web app, so I want to do the above code in jQuery. I have tried but don't know why its not working,  $("#branch1").focus();   The above jquery (focus()) code is not working for div, whereas If i am trying the same code with textbox, then its working,  Please tell me, how can I put focus on a div elemnt using jQuery?  Thanks!


What does "@" at the beginning of a command name mean?

The  mention commands such as \@author and \@director, and latex.ltx is full of them. However, when I use \@author in my document, it just outputs the word "author". What does the @ in command names mean?


"Failed to start session" after interrupted upgrade to 14.04

While upgrading to 14.04 using sudo do-release-upgrade my network connection was interrupted and several packages failed to upgrade.  Running do-release-upgrade again reported No new releases found but apt-get listed many packages "kept back", so it seemed the system was in an intermediate state. I ran apt-get dist-upgrade which installed those packages again, then apt-get autoremove after which apt seemed happy.  However, after restarting I cannot log in at the GUI prompt. After entering my password the error "Failed to start session" appears in red. I am still able to log in from the command prompt, but I don't know what to do to solve or debug the GUI log in failure.


Roblox age restriction not lifted when I turn 13

I had turned 13 last month and entered the exact date I was born in at Roblox, but Roblox still didn't lift the age restrictions. Is this an error, bug or what? I was looking forward for this restriction lift but it doesn't seem to happen somehow.


"Had been planning" or "were planning" What is the difference?

We_________(had been planning /were planning) to felicitate John at   our annual cultural fest when the news of his death______(had arrived   /arrived).   Can someone tell me which one to use and why, and why not?


In a twosided scrbook, I am aligning all my figures and tables on top of the page (via [!t]). As a result, the upper edge of the figures is higher than the upper edge of the table caption. This can be seen in the image below which I took from the answer to     My editor asks me to change this so that all pages start at the same height. As far as I understand, the space between captions and text is adjusted with belowskip -- but that would change it for both figures (space below the caption) and tables (space above the caption). So can I adjust the space above table captions only?


I put together a build, and I'm having some issues. When I boot up the PC all fans and LEDs come on, but nothing ever pops up on the screen.   The manual states I should be prompted with a BIOS screen. It also says some beeps should come through my audio, but there's been no sound. I've tried taking the GPU out and booting that way, but there's no change except that a white LED on the motherboard stays on.   From what I've read that'll stay on until a GPU is installed. I've also tried replacing the RAM with RAM from a different computer, but there's still no change. I've also tried booting with a single stick of RAM. Customer support stated that my RAM is likely the issue, but there wasn't much more said than that.   Does anyone have some other troubleshooting or likely causes that I should look into? It seems like everything is starting up as intended and that it just doesn't display anything on the monitor.   Specs:     CPU: AMD - Ryzen 7 1700X 3.4 GHz 8-core processor   RAM: G.Skill - Ripjaws V Series 16 GB (2 x 8 GB) DDR4-3200 memory   SSD: Samsung - 860 EVO 500 GB 2.5" SSD   PS: Corsair - RMx (2018) 750 W 80+ gold certified fully modular ATX power supply   Motherboard: Asus - ROG STRIX B450-F gaming ATX AM4 motherboard   CPU Cooler: Thermaltake Frio silent 14   GPU: MSI Armor Radeon RX570    Link for pictures of the build ?


How does rolling two d20 and taking the higher affect the average outcome?

D&D 5E has an "advantage" concept where instead of rolling 1d20, you roll 2d20 and take the higher. Likewise, disadvantage means rolling 2d20 and taking the lower.  How does this affect the expected average outcome of the roll?


I have a database of invoices. Some of these are to be paid by us. These are called expenses. Some are to be paid us by others. How should I call those? I want a word that is fit to use for invoices and that is the same like expense other way around.


System tray icons disappeared after upgrading Ubuntu

I have many applications with tray icons like davmail, hardware monitor. I miss this feature on Ubuntu 14.04. Does anyone have a solution?  There are some tools like Skype indicator, but I need a general solution for this problem so that I can add application icons to the system tray.


let $f$ be a entire function and $B$ is bounded open set. $\partial(f(B)) \subset f(\partial B)$.

let $f$ be a entire function and $B$ is bounded open set.  Then is it true that   $\partial(f(B)) \subset f(\partial B)$.  Hint is given that use open mapping theorem . But i got stuck how to use it. please provide some hint


Accessing and controlling iPhone via MacBook

My iPhone is charging on my table but it lies beyond stretch of my hand. I feel lazy to stretch out to pull it up.    I want to check iPhone's battery charge level from my MacBook Pro. Is it possible to do so? Is there any macOS app that acts as a client for my iPhone on my MacBook Pro?  Not only would I like to check iPhone's battery level from my MacBook Pro, but also launch or close other apps, change settings, etc, on the iPhone. Is it possible?


Integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$

I am trying to compute the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i].$ I have managed to show that $\mathbb{Z}[i]$ is inside the integral closure, and I suspect it is the entire thing. Can someone give me a nudge in the right direction?


Can you intentionally fail a skill check?

This comes up to me in the context of the 3.x/PF/d20 Fly skill, even when I simply read about it: Can you intentionally fail a Fly skill check, or any other skill check for that matter, if you, or your character for that matter, decides that the effects of failing the check are what is desired in the situation?  Example:  Take a a shapeshifted Draconian cruising at high altitude, with a few friends on his back who have some means of breathing air supply, whether it be mundane or magical.  Now lets say that the air supply goes kablooie, similar to a decompression or all-packs-trip in an airliner.  For the sake of the folks on his back -- if not himself, depending on if dragon forms need supplemental air to fly at such high altitudes, the Draconian has to lose altitude, and fast.  Considering that by RAW, a Fly check failure leaves yourself falling, would saying "I initiate a rapid descent" be enough to treat the next Fly check as an intentional failure, or would you have to roll a 'reverse' Fly check, where failing the check gives you the desired outcome of a rapid descent, and succeeding leaves you stuck at altitude?  P.S. I added the rules-as-written tag because a RAW answer is highly desired here, albeit not mandatory.  I can already mostly figure it out from a simulationist standpoint, but that answer involves going in-depth into airline flying and non-normal procedures.


Why is quantum mechanical momentum the derivative of the wave function with respect to the position?

In classical mechanics the momentum is defined as mass times the time-derivative of position.  In quantum mechanics, however, the time-derivative of the wave function is the hamiltonian, while the momentum is defined as $i\hbar \frac{\partial}{\partial x} \Psi(x) $, which is a space-derivative and not a time-derivative.  Note that I understand why momentum is an operator on the wave function (it's a measurable quantity, so it's an operator as per a postulate of QM). I understand the derivation from spatial translation, but I don't understand why it's an equivalent of the classical momentum as it's a space derivative and not a time derivative.


A more formal English expression for K-12 (in the US)?

This is US-specific.  I had mistakenly believed that grade school meant K-12. Turns out it refers only to elementary school. Is there a more formal (but fairly succinct) English expression for K-12?


Is their a better way to implement class in c++?

When we write class in c++ we divide class into two part that header file and cpp file. In header file we define class and prototype  Class.h  class A{ public: void functionName(); };   Then we define what the function actually does in cpp  Class.cpp  #include<iostream>  void A:: functionName(){  do something; }   then in main function we do  #include "class.h"  using namespace std; int main() {   A a;   a.functionName();   return 0; }   Is their a better way to do it?. Somthing similar to java(that's the language i currently work with). I think doing things like this(cpp way) in big projects will be Messy to work with


What is Kylo Ren's relationship with Darth Vader?

If       Han Solo   is Kylo Ren's father, then how is      Darth Vader Kylo Ren's grandfather?


My monitor is turned off after 1 mintute,But my computer doesn’t sleep after 1 minute(longer than 1 minute) So what should I do!?


How can I install the latest apt package for Cockpit with apt?

I'm running 18.04TLS, and have Cockpit version 164-1.  If I go to  I see there's a new package 170-1, but I can't install it, because it is not Stable.  Is there any workaround to use these packages to install the new version? I don't want to build it from source.