no of subspace in vector space V over finite field

Let $V$ be a vector space of dimension $n$ over $F_q$. Prove that no of the subspace of dimension $k(\leq n)$ is equal to no of the subspace of dimension $n-k$ in $V$.


SATA Drive is not detected when hotswapping

So from what I've read online, if AHCI is enabled in the BIOS, I should be able to hot-swap a SATA drive and it will supposedly "just work".  However, that has not been my experience.  When I hot-swap a SATA drive on my system, it is never detected. It doesn't show up in lsblk, it doesn't show up in Gparted, nothing even shows in dmesg.  So, I am wondering what the issue is?  I am using 16.04 on an Asus M5A97 R2.0    Edit to address Takkat's suggestion:  I have no such option:


Can you provide me historical examples of pure mathematics becoming "useful"?

I am trying to think/know about something, but I don't know if my base premise is plausible. Here we go.  Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because it has no practical utility, but I guess that according to the history of mathematics, the math that is useful today was once pure mathematics (I'm not so sure but I guess that when the calculus was invented, it hadn't a practical application).  Also, I guess that the development of pure mathematics is important because it allows us to think about non-intuitive objects before encountering some phenomena that is similar to these mathematical non-intuitive objects, with this in mind can you provide me historical examples of pure mathematics becoming "useful"?


In C++, 3.6.1 Main function     (3.6.1/5) A return statement in main has the effect of leaving the main function (destroying any objects with automatic storage duration) and   calling exit with the return value as the argument. If control reaches   the end of main without encountering a return statement, the effect is   that of executing return 0;   Can I do the following in C99 without return 0?  int main() { }


2D array in python changes the whole row when I only want to change 1 item(Is there a way around it?)

I wanted to create a 2D array that would have a number in each cell. I need to access specific cells and be ablt to change them.  def print_matrix(matrix):     #just to print it nicer     for x in range(0, len(matrix)):         print(matrix[x])  matrix = [] list = [] for x in range(0,10):     list.append(0)  for x in range(0,10):     matrix.append(list)  matrix[1][2] = 9   print_matrix(matrix)


Limit of $\frac{\tan(x)-x}{x^3}$ as $x$ approaches $0$ without L'Hospital's Rule

I am trying to find the limit of $\frac{\tan(x)-x}{x^3}$ as $x$ approaches $0$.  I know that this can be found by using L'Hospital's Rule 3 times.  Is there a way to solve this problem without using L'Hospital's Rule?  Please do not use Taylor series; I consider this to be an equivalent method.  I have noticed that the required number of applications of L'Hospital's Rule is precisely the order of the first non-zero derivative, which I think is essentially because a product is $0$ if and only if at least one factor is $0$.


Proving that even numbers equal the sum of two odd numbers.

Define E to be the set of even integers; E = {$x$ $\in$ $\mathbb{Z}$ :  $x$ = 2$k$, where $k$ $\in$ $\mathbb{Z}$}.   Define F to be the set of integers that can be expressed as the sum of two odd numbers.  Prove E = F.  My attempt: The only way I can figure out the solution is by providing numbers and examples. It's easy to see that two odd numbers will always equal an even integer. I just don't know how to write the proof for it.


Why do grape sodas taste radically different between US and Europe?

I am talking about these super sugary artificially flavored sodas, or candies for that matter.  When I was a child and we went from France to the United States, I had absolutely NO idea that I was drinking a grape soda because the flavors are so different there was absolutely no relation to any flavor I ever had.  Later, as a traveling adult, I noticed that this hasn't changed. The 'super artificial made for kids grape flavor' of US products does not exist at all in the EU countries I know well (France, Spain, Malta, Germany), I don't recall ever tasting it in any of the other EU countries as well (I've been to most).  The opposite is more nuanced; I've tasted some US products (that were more 'adult' flavors) that were closer to the European ones.  The question is why is there such a massive difference in taste to the point the flavors can't be recognized as the same fruit (in theory)? The opposite is almo


I tried to use the command \mathbb {R} in order to get the set of real numbers symbol in LaTeX. But, I just simply get the normal R.  How can I represent the set of real numbers in LaTeX?


Is a 1hr 3min layover at ORD (Chicago) enough when coming in international?

So I'm flying in from Ottawa, in Canada, and I have a 1 hour 3 minute "layover" between flights. Is this enough time? I booked through Expedia and it's both with United Airlines and I believe it'll be on one ticket because it's the same itinerary. I am not checking luggage, and as of tonight (flight is tomorrow morning), the gate I arrive at is F17 and I depart from F5. These are on the same terminal, but will I have enough time? I know the travel distance between the gates isn't bad at all as they're in the same big hallway, but I'm worried about customs/immigration time since I'm coming in from international.   I've never flown before and I'm worried about how long that would take. I heard that they give you customs forms to fill out on the plane, but I don't know if that would speed things up much. My plane is small (only 50 people) so I also don't think getting off the plane should take too long, but I do need to wait around for my carry on to be given back to me because it's "gate-checked" because it's a United Express flight and the overhead probably won't be able to fit it.  I apologize if this is just me being paranoid, but I want to make sure.


Links to the Wayback Machine are broken in chat transcript

is an example of the bug. It looks like this in regular chat:  That link points to: http://web.archive.org/web/20080409050311/http://personalpages.manchester.ac.uk/staff/daryn.lehoux/Tropes.pdf  In the transcript, it looks like this:  That link points to: http://web.archive.org/web/20080409050311/%3Ca%20href=  ... which doesn't work so well! Could this be fixed? I'm not sure if this impacts links to elsewhere.


Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.

Prove that the union of three subspaces of V is a subspace iff one of the subspaces contains the other two.  I can do this problem when I am working in only two subspaces of $V$ but I don't know how to do it with three.   What I tried is: If one of the subspaces contains the other two, Then their union is obviously a subspace because the subspace that contains them is a subspace. (Is this sufficient??).  If the union of three subspaces is a subspace..... How do I prove that one of the subspaces must contain the other two from here?  *When proving this for two I said that there is an element in one of the subspaces that is not the other and proved by contradiction that one of the subspaces must be contained in the other. How would I do this for three?


Find isomorphism from $F_5[x]/(x^2+x+2) \rightarrow F_5[x]/(x^2+4x+2) $ I realise both polynomials are irreducible therefore form fields, not sure how to form a isomorphism from one to the other, help please


I am trying to loop through a file to run commands remotely via SSH but its only sending the first command and stopping.  while read a b c; do ssh root@$remoteserverip "/usr/bin/mysql -e \"grant all privileges on $a.* to $b@'localhost' identified by '$c';\""  ; done < /dbusers.txt   MySQL logging shows:  Connect   root@localhost as anonymous on Query     select @@version_comment limit 1 Query     grant all privileges on db1.* to dbu1@'localhost' identified by 'passwd' Quit   and that's it.  Example contents of /dbusers.txt  db1 dbu1 passwd db2 dbu2 passwd db3 dbu3 passwd   If I use echo in front of ssh then it prints out all lines.


I'm getting 'Bad Login' when attempting to join multiplayer servers in Minecraft

I can login to minecraft fine through the launcher and play singleplayer just fine. But when I go into multiplayer it won't let me join any server. It just keeps saying "Bad Login".   I do have a paid account and this has never happened to me before. What could cause this?  I have no mods installed and the server is up to date


For $n$ sets with intersection of size at most $1$ sets we have $\frac{1}{n}\sum\limits_{i=1}^{n}|S_i|=O(\sqrt n)$

Suppose $S_1,\dots, S_n\subseteq[n]$ are such that $|S_i\cap S_j|\leq 1$ for all $1\leq i\lt j\leq n$. Show that in this case  $$\frac{1}{n}\sum\limits_{i=1}^{n}|S_i|=O(\sqrt n).$$


Question "Submit the assignment by February 10th." What does this statement mean? Possibility 1 The assignment should be submitted by February 10th, 23:59. Possibility 2 The assignment should be submitted by February 9th, 23:59.


Protagonist rebels with mutants to destroy a utopian culture only to find an authoritarian centralized brain controlling everything

I have a memory from my childhood of an animated film about a utopian culture. The protagonists and the female supporting character discover that their society is managed by mutated humans. The mutants do all the labor, and this is hidden from the rest of the community. The couple who discover that the underlying society is unjust rebel along with the mutants, but find a giant brain that created the social structure that they cannot defeat. This brain puts the protagonist to sleep under the sea for two thousand years with a large black poisonous thorn. His mission, when he awakes, is to kill the brain with the thorn. Two thousand years later, the hero awakens to find the brain created a new world with an army of robots. He has to defeat them. Eventually, the brain and the hero meet. The brain is much older and shows signs of atrophy. The hero kills the brain by stabbing it with the black thorn.   It may be possible that I watched two movies that day and melded them together. I've asked my father about this, but he has no recollection. I've gone to comic shops and discussed the plot with salespeople, to no avail. I search the internet. Nothing comes up that is similar to my description of this film. Perhaps you can help. The film could not have been produced later than 1990. My guess is that the date range to be considered is from the 1970s to the 1980s.   My best guess is that the origin of this animation is European. The subject matter, as I infer, relates to the Soviet Communist occupation. The large brain represents the authoritarian Communist regime that Europeans feared in the mid to late 1900s, and the protagonist represents the liberator of the machinery it builds. There are many films from France with this subject matter and themes relating to the social commentary of a utopian culture.


Use implicit function theorem to show $O(n)$ is a manifold

In class today our teacher mentioned that one can use the implicit function theorem to show that $O(n) \subseteq \mathbb{R}^{n^2}$ is a submanifold...that is, map $A \mapsto A^* A$, and set it equal to the identity matrix. There should be $n(n+1)/2$ equations in $n^2$ variables ($A^*A$ is always symmetric, so we only need $n(n+1)/2$ equations). When I asked how to show that the jacobian matrix of this transformation had full row rank (the condition of the implicit function theorem), my teacher said "take the derivative near the identity, and you see that the derivative is just a matrix plus its transpose ."  I wasn't sure what he meant. Can someone clarify?


If I build a package from source how can I uninstall or remove completely?

I used source code to build one package such as below:  ./configure --prefix=/usr --sysconfdir=/etc --localstatedir=/var --libexecdir=/usr/lib --with-package-name="Myplugin" --with-package-origin="http://www.ubuntu.org/" --enable-gtk-doc --disable-static make make install   But unfortunately, i discovered that its the latest version, and has lot of bugs, so i need to remove it/uninstall it. But how can i do so? I tried make clean; make uninstall but still i see it exist:  # pkg-config --list-all | grep Myplugin myplugin-.... $ ls /usr/lib/myplugin/libXYZ.so exist....   How do you remove this now?


When Corresponding Authors Don't Correspond

What are appropriate steps to take when the corresponding author of a paper one finds very interesting, and potentially very useful, but slightly puzzling (due to the enforced brevity of the publication format) in its nuts and bolts implementation doesn't correspond?  (I do not mean, 'Does not provide instant and copiously detailed answers,' I mean, 'Complete radio silence.')  Clearly, one does not send e-mail after e-mail after e-mail.  That is both rude and insane.  (Expecting different results from the same action.)  Clearly, one does survey that author's other literature (including past theses or dissertations, often the best place to find more verbose treatments of early papers) to see if the nuts and bolts questions are resolved there; one also surveys the literature of the non-corresponding co-authors for the same reason. (In fact, one does this, in my opinion, before contacting anyone in the first place.)  Clearly one does verify that the e-mail is up to date, to the best of one's ability.  When these options fail, and one is still extremely interested in a working implementation of a tersely published technique, are there any other reasonable strategies to apply?  Reasonable, as in, will not cause terrible reputation in the field.


What will happen if all the population all over the world jumped together at the same time in sea?

What can happen if a magnitude of such huge force is applied over the sea water of earth? Force applied will be average mass of each person *7 billion *9.8 .


When trying to print out questions, why is the content shifted to the left?

I am not interested in a plugin to do a fancy print, I'd just like for the content to be spread out on the page.   I have hopefully attached a page from each of the four sites I recently joined to illustrate the issue. I print because, so far, I find no bookmark capability here.  Instead I have found if I record the question number. Google will find it usually first: sustainability 4974 or for sure with: sustainability "/questions/4974"


Possible Duplicate:          $$\int_{0}^{1} dx\frac{\log(1+x)}{1 + x^2}$$  I am having a hard time deriving the answer, $\frac{\pi}{8} \log(2) $.  I have tried Taylor expansion of both numerator and denominator, both seem too complicated and fruitless.


Is coherent light required for interference in Young's double slit experiment?

In , a home experiment is presented which appears to produce a very good double-slit interference pattern with normal sunlight.  The experiment is an empty cardboard box with a visor and a placeholder for a microscope slide with two slits on one side. This is arranged with the slits and visor facing the Sun, so the interference forms on the bottom of the box.    They claim to observe a good interference pattern from the two slits:    Discussions of interference in optics textbooks often stress that coherent light is needed to produce such patterns, and that sunlight and other thermal sources of light do not have such coherence. How, then, is this possible?


My question is about free fall from an airplane. Lets say your seat detaches from the plane and you follow a standard free fall.  $$v^2=v_0^2+2g\Delta x=\sqrt{0+2\cdot 9.8\,\mathrm{m/s^2}\cdot 10000\,\mathrm m}=443\,\mathrm{m/s}$$  Now, let's say that right before hitting the ground, you jump up from your seat (using the seat as a hard surface to jump from) to reduce the impact velocity of your body.  Here's were I'm lost: how would you calculate that? I was trying to calculate the force needed for your muscles to spring up, which should equal the force of gravity. In this case:  $$F_{muscle}= -mg= -100\,\mathrm{kg}*9.8\,\mathrm{m/s^2}= 980\,\mathrm N$$  Then what? In short, how much would the velocity be reduced by jumping up from the chair right before impact (assuming you can exert $980\,\mathrm N$ on the chair), if any at all?


Importing raster adf files with the additional files

I am trying to import a  in Esri GRID format from the USDA into QGIS.  One file ("w0001.adf") can be added using "add raster", but the attribute table and other info register as error or errors.  Using the "ArcInfo/Binary directory" does not work either.


If mobiles internert is off and i saved any contact on google account,then where it is stored actually before getting sync?


I wrote text on an object, but it is visible on the backside of the object i.e. Image:


Using short adjectives as adverbs, such as "easy" & "short"

I know that some adjectives (such as easy & short) can be used as adverbs in some situations, but when can this happen and what adjectives does this apply to?  This definitely works: "He stopped short" But does this?: "He fell pretty hard"


Problem playing online videos on Ubuntu 16.04

I have the latest, Ubuntu 16.04, with the latest Firefox and Adobe Flashplayer version 11. Videos from YouTube, Vimeo, etc. are working fine. But no video from  will play. Why is this and how can I fix it?


Is there a goto on error/warning type of deal in bash?

Ok so I saw at work a script which is on OpenVMS using the DCL scripting language that they have a way to do a catch all for warnings or errors etc...  There is a page about it here.  basically its ON warning THEN GOTO sendfailemail or something like that. I was wondering without using a bunch of if statements is there a way to do such a thing in bash?  I am looking for something that can do a trap not just based on ERR but return code. What is nice about vms is that you can do on warning which on vms is exit status 0 vs error which is exit status 2. So I know I can do trap ... ERR but I wanted something that could trap exit status 1 or 2 specifically.


How can I find the location of a regex match in Perl?

I need to write a function that receives a string and a regex. I need to check if there is a match and return the start and end location of a match. (The regex was already compiled by qr//.)  The function might also receive a "global" flag and then I need to return the (start,end) pairs of all the matches.  I cannot change the regex, not even add () around it as the user might use () and \1. Maybe I can use (?:).  Example: given "ababab" and the regex qr/ab/, in the global case I need to get back 3 pairs of (start, end).


According to the tab on the right I can ask question.   But we would never say that. I can ask a question. However, question is neither an an abstract nor uncountable noun.   I also noticed the same rule in an online system I use - I can add order.   Are these phrases incorrect or is it a rule that justifies omitting the articles?


We're building an app that has an element that performs some specific set of actions. The element itself is new, and tests are very conclusive: for the target the app is directed to, the affordance is clear (while for other targets, it's not, but this is basic in Gibson's theory).  So I'm writing the documentation for the app, and came to the part where I have to describe this element, and I was simply explaining the fact that affordances had yet to be discovered but test are conclusive, providing all the theoretical background and testing results at hand. Then I thought that instead of having to re-create the wheel, I could simply include existing research on the concept of "yet to be discovered affordances" itself (assuming it exists).   Note: Of course I'm aware about Nielsen's UX Discoverability and Gaver's False affordances concepts, so this NOT what I'm asking. In some way, I think it's the state previous to UX Discoverability.   Anyways, maybe it's just that I can't think the proper words, but my question is "Is there a concept for "yet to be discovered" affordances?"


How can I disable a particular interrupt in Windows 10?

It seems to be caused by the SSD disk installed instead of an optical drive, in the relevant questions about Linux the suggested solution is like:  echo "disable" > /sys/firmware/acpi/interrupts/gpe13   How can I disable such an interrupt in Windows?


I really want to open up root mode on this phone, but everything that I have tried says root unavailable. Can someone point me in the right direction?


Every group of order $14077=7 \cdot 2011$ is cyclic (use Sylow Theorem)

I know that I can use Sylow's theorem because $7$ is prime, and so is $2011$. So, $14077$ has the form $p^{a}m$ where $p \nmid m$ for some $a$ and $p$ is prime. Moreover, we know from previous results that there are exactly two subgroups of the group of order $14077$, one subgroup for each divisor of $14077$.  Both of those subgroups then, call them $Q_{7}$ and $Q_{2011}$ would be cyclic because each has prime order. So...is this good enough to prove that the group of order? I feel like I am missing a step, and I have seen other problems use external direct products.  Do I need to do that here to show $Q_{14077}=Q_{7}$ X $Q_{2011}$?


Generate a regex to find sub strings with certain number of occurrences of certain characters

Suppose I have a string "IICCIICCIICBIICCIICDII". The string is of the pattern II[CBD][CBD]II[CBD][CBD]II... It is a repeated pattern. Now I am trying to find all overlapping substrings which satisfies following condition:   Substring does not start or end with letter I. Suggested solution: (?<=[CBD]), (?=[CBD]) Substring contains at least(but as less as possible) certain number of occurrences of letter C, B, and D. These letters can exist in any permutation and can have different number of occurrences. Suggested solution: something along the lines of [C]{m, n}?  These pre-defined numbers are variable so that I can dynamically generate regex with change in requirement for these variables. Order and number of occurrences of letter I doesn't matter Adding to condition 1: Start/end of a substring can't have two occurrences of [CBD] (e.g., CCIIB or BIICC is an invalid match) (sorry about that)   For example, for a pattern with at least 2 Cs: CIIC (three of them), 2 Cs and 1 B: CIICBIIC, BIICCIIC  I do not think my question is similar to the question quoted in one of the answers. I have looked at that question (titled "shortest repeated substring"). My question differs in the sense that repeated pattern needs to have a certain number of occurrences of certain characters. The question quoted is just finding shortest repeating pattern. That question IS helpful though.  Let me know if the question is clear and not a duplicate. Thanks.


90s sci-fi series with an episode where a boy goes into VR and fights a Medusa-like monster

I am looking for an animated series, shown in the 90s. I remember an episode where the boy went into VR and fought a medusa-like monster.  It may be that this was the premise for the whole series: That the children heroes go into VR every time to fight the evil guys.   I am not sure if the whole series were computer-animated but surely there were such elements together with classic animation.  The style of the series was quite dark and cool for teenage boys.


Tell rate-limited users how long they have to wait before asking a new question

New users are limited to one question per an hour, but once they'll hit this limit, all they see is You can only post once every 60 minutes. I think it would be very appreciate to change / extend this message, adding You need to wait next xx minutes. I saw similar solutions on many forums.  Would it be hard to implement something like that?  EDIT: It could be either added as extension to above mentioned warning message or as red-colored reminder above Title field. Or even as an explanation message, preventing user from clicking on a Ask Question button? Anything would be good, to not let user write the question (can be time consuming) only to hit the wall of limit. This can be a little bit annoying or frustrating, don't you think?


Algorithm to Create All "Spot it!" Cards

"Spot it!" is a fun card game, played with 55 cards, each having eight symbols. There are more than 50 symbols in all. There is always one, and only one, matching symbol between any two cards, and this is the feature on which all the games playable with these cards are based. Some mathematical aspects of the game are discussed  before.    Here's my question: How are these cards designed?! Put in a more mathematical way, is there an algorithm (not a brute-froce on!) to find all subsets of size $k$ of a set of size $n$, so that each two subsets have exactly one element in common?  Thanks.  Upadte: It seems that my question has been answered .


I learned today that there are digraphs in C99 and C++.  The following is a valid program:  %:include <stdio.h>  %:ifndef BUFSIZE  %:define BUFSIZE  512 %:endif  void copy(char d<::>, const char s<::>, int len) <%     while (len-- >= 0)     <%         d<:len:> = s<:len:>;     %> %>   My question is: why do they exist?


How to change the Dash Button in Unity Launcher?

I don't like the default Dash Button (also known as BFB in short of "Big Freakin Button") in Unity Launcher. It's pretty inconsistent with Faenza icon theme and I would like to change it. How can I do that?


To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$

My Approach. To prove the given statement it is sufficient to show that $$\exists \epsilon > 0, \exists x \in [0,1], \forall N \in \mathbb{N}, \exists n > N $$ $$ \Rightarrow | f_n(x) - f(x)| > \epsilon$$    Let $\epsilon = \frac{1}{10}, x = \frac{1}{n}, n =N+1$. Hence $| f_n(x) - f(x)| = \frac{1}{2} > \epsilon = \frac{1}{10}$. Hence, we have shown for every $N \in \mathbb{N}$, how to choose $n$ such that $| f_n(x) - f(x)| > \epsilon$. Thus, $f_n(x)$ does not converge uniformly on $[0,1]$.    Is there any logical flaw or wrong steps in my proof. Any help would be appreciated.


I wanted to install python 3.4.2 through the terminal and it asks for my password. I started to type but nothing appears. how do I give my password?


meaning of iris_dataset.data[:,:2] in jupyter notebook

Can you please tell the meaning of """iris_dataset.data[:,:2]""" in jupyter notebook python


Different output from a function with the same arguments

Why is my function 'increment' return different values for matrix that i create by other function and different for manual matrix?  n = 2 m = 3 indices = [[0,1],[1,1]]  def matrixpopulation(n,m):     row=[]     matrix=[]     row+=(0  for _ in range(0,m))                 matrix+=(row for _ in range(0,n))     return matrix  def increment(indices,matrixa):     for v,k in indices:         for i in range(3):             matrixa[v][i]+=1         for i in range(2):               matrixa[i][k]+=1     return matrixa  matrixa=matrixpopulation(n,m) filled_matrix=increment(indices,matrixa)  print(matrixpopulation(n,m)) print(filled_matrix)  manualmatrix=[[0,0,0],[0,0,0]] print(manualmatrix) print(increment(indices,manualmatrix))


I know that on 32 bit system max number of memory cells in RAM is 2^32. But RAM in my computer show not exactly this size. Can someone explain why on 32 bit system size of RAM not equal max size of cells but varies(3.2 - 3.6 Gb)?


I am looking for a more elegant term to replace 'playgirl'.  Playgirl (n); a woman who pursues a life of pleasure without responsibility or attachments, especially one who is of comfortable means.  The word should be suitable to replace 'playboy' in, for example;      "Genius, billionaire, playboy, philanthropist” line in by Ironman.


I had the Facebook and Instagram apps installed on my iPhone (latest iOS). I deleted both apps and checked that there was no data from either app stored on iCloud (I went to Settings - iCloud - Manage storage and there was no mention of them storing anything on iCloud). Then I reinstalled Instagram, opened it, clicked on Login and the page still showed “Login as MYFACEBOOKNAME”.   How is this possible? How can I delete my FB login info once and for all on my iPhone?


I need to create a letter using the scrlettr2 package. For this purpose, I wrote the LaTeX document given below.  But when I compile it I see marks on the side (see 3 red ellipses on the left).    How can I remove them?  Here's the source code:  % koma_env.tex \documentclass[a4paper,backaddress=off]{scrlttr2} % \usepackage{lmodern} \usepackage[utf8]{inputenc} % \usepackage[T1]{fontenc} % \usepackage[english]{babel} % \usepackage{url}    \setkomavar{fromname}{\{\{Landlord Name\}\}} \setkomavar{fromaddress}{\{\{Landlord Name\}\} \\ \{\{Landlord Correspondence Address Line 1\} \\ \{\{Landlord Correspondence Line 2 (if applicable)\}\} \\ \{\{Town/City\}\} \\ \{\{County\}\} \\ \{\{Postcode\}\}}  \begin{document}  \begin{letter}{\{\{Tenant Names\}\} \\ \{\{Property Address Line 1\}\} \\ \{\{Property Address Line 2 (if applicable)\}\} \\ \{\{Town/City\}\} \\ \{\{County\}\} \\ \{\{Postcode\}\}}  \KOMAoptions{fromphone=false,fromfax=false} \setkomavar{subject}{Pre Check-Out Inspection at \{\{1st line of Property\}\}}  \opening{Dear \{\{Tenant Names\}\}}  Your tenancy is due to come to an end on \{\{date\}\}. I would like to arrange an inspection at the property before the tenancy ends to identify anything that may lead me to retain some of your deposit if not addressed by the time I retake possession.  Carrying out this inspection prior to the tenancy ending will give you the opportunity to tackle anything raised and ensure I can return the maximum amount of deposit to you when the tenancy ends  I would like to carry out the inspection on \{\{date\}\} at \{\{time\}\}. It would be best if you were present then if anything is identified we can discuss this and be clear on what would be required to rectify it. Please can you contact me as soon as possible to confirm whether or not this is convenient.  If you do not wish to be present I have a set of keys to access the property and will send you the results of the inspection. Please let me know either way at your earliest convenience.  \closing{Kind Regards}  \end{letter}  \end{document}


Clash Royale How and Where to Find Free and Open Tournament List

Please read my question before you say it's duplicates. I think many of you have the same problem as I do. As the clash royale has not implemented search or filter function to the tournament tab, there isn't anyway that you can find an open tournament. Based on others answered questions, it seems like betting on luck by trying different key words is the way, but the truth is the odds are not in my favor. Not to mention trying to figure out the password to a password protected tournament.  Anything helps.


Is this how eigenvalues of some matrix $A$ are related to the inverse of $A$?

Let $A$ be an invertible $n\times n$ matrix. If $$Av = \lambda v \qquad (1)$$ for some $v$ and $\lambda$ then $\lambda$ is an eigenvalue of $A$ and $v$ a corresponding eigenvector. Equation $(1)$ may be written as $$Av = \lambda v = \lambda Iv \quad\Leftrightarrow\quad Av - \lambda I v = 0 \quad\Leftrightarrow\quad (A - \lambda I)v = 0$$ where $I$ is the identity matrix. The last equation can be used to find correct $\lambda$'s via the fundamental theorem of algebra (first take determinant).  On the other hand, it is also possible to write $$Av = \lambda v \quad\Leftrightarrow\quad A^{-1}Av = A^{-1}\lambda v \quad\Leftrightarrow\quad Iv - A^{-1}\lambda v = 0 \quad\Leftrightarrow\quad (I - A^{-1}\lambda)v = 0$$ since it was assumed $A$ is invertible.  Now, since $(A - \lambda I)v = 0$ and $(I - A^{-1}\lambda)v = 0$ it must be that $$A - \lambda I = I - A^{-1}\lambda$$ which connects the matrix $A$ to its inverse via the eigenvalues of $A$.  I did some calculations and it seems this works for some invertible matrices $A$ but not all. Am I doing a mistake somewhere?


Equivalence of definitions of prime ideal in commutative ring

Could someone prove that in a commutative ring $R$ the following two definitions of prime ideal are equivalent:  1) An ideal $P$ is prime if $P\neq R$ and if for all ideals $A,B$ of $R$ with $AB\subseteq P$ we have that $A \subseteq P$ or $B \subseteq P$.  2) An ideal $P$ is prime if $P\neq R$ and if $ab \in P \implies a \in P$ or $b\in P$.  I have read (in Artin as well as online) that these are equivalent, but I cannot find a suitable proof.  Artin's proof of $1) \implies 2)$ is one line: Take $A=(a)$ and $B=(b)$. I do not see how this is a proof. If someone could explain the implication as if I were a complete novice to ring theory (which I am), that would be most helpful.  Note: I am not assuming that $R$ is unital, only that it is commutative.


How to make sure that Thinkpad discharges external slice battery first?

The thing is that when an external slice battery pack is connected, the laptop first discharges the internal one. This is a problem because then it is impossible to switch between multiple external battery packs without powering off the laptop. It is also not possible to just disconnect the external battery pack when you e.g. need to insert it into a docking station.  Thus, my question: how to change the discharge order under Linux?  For my use cases following order would make much more sense: when an external slice battery is connected, first discharge it completely before using power from the internal battery.  Background: For some Thinkpad models (e.g. X220) there are slice battery packs () available that you can connect to the bottom of the laptop (similar to a docking station).  They seem to be supported well on Linux - e.g. the Gnome Shell battery applet includes both batteries (internal and external) when connected - including displaying the current capacity for each.


Do polygon pours have to be either ground or supply voltage?

I was wondering if it is possible to have polygon pours but not connected to anything. Will that affect the circuit in some manner ? Because for the pcb I'm designing, if I use polygon pours as ground planes it results in a large number of isolated islands.  So is it better to send the pcb design off without any polygons or is it ok to send it with non-connected polygon pours? Many Thanks


How should I undo this connection? It doesn't seem to unscrew, though part of it will move down towards the boiler although this doesnt seem to make it disconnect (I havent tried forcing this though as I don't want it to break)  Its the mains cold water inlet to a small boiler by the way.  Many thanks]


Typesetting in the style of mobile phone texts

I would like to include into a "traditional" text document an environment that mimics the graphical style of basic text on mobile phones:  author 1 text left adjusted, on red blocks with rounded corners; author 2 text right adjusted, on green blocks with rounded corners, and so forth.  Something with a syntax similar to this:  \begin{phonetext} \authorleft{my text} \authorright{your text} \authorleft{my next text} \end{phonetext}   The ideal would be to be able to choose colors of the backgrounds (e.g., red on left, green on right) and other font size and related information.  I don't need the ability to include photos, video frames, audio recording icons, posting date and time, and such, but perhaps someone else would use such options.


Difference between one-tailed and two-tailed testing?

While studying for my stats course, I was trying to understand the difference between one-tailed and two-tailed hypothesis tests. Specifically, why does the one-tailed test reject the null while the two-tailed one does not?   An example:


Prove by induction $\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}{4}$ for $n\ge1$

Prove the following statement $S(n)$ for $n\ge1$:  $$\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}{4}$$  To prove the basis, I substitute $1$ for $n$ in $S(n)$:  $$\sum_{i=1}^11^3=1=\frac{1^2(2)^2}{4}$$  Great. For the inductive step, I assume $S(n)$ to be true and prove $S(n+1)$:  $$\sum_{i=1}^{n+1}i^3=\frac{(n+1)^2(n+2)^2}{4}$$  Considering the sum on the left side:  $$\sum_{i=1}^{n+1}i^3=\sum_{i=1}^ni^3+(n+1)^3$$  I make use of $S(n)$ by substituting its right side for $\sum_{i=1}^ni^3$:  $$\sum_{i=1}^{n+1}i^3=\frac{n^2(n+1)^2}{4}+(n+1)^3$$  This is where I get a little lost. I think I expand the equation to be  $$=\frac{(n^4+2n^3+n^2)}{4}+(n+1)^3$$  but I'm not totally confident about that. Can anyone provide some guidance?


Where can I ask questions about Joomla! CMS?

Sometimes I want to ask questions about Joomla! CMS. I see a  site on the network. Where can I ask my questions about Joomla! CMS?


Why is my peripheral vision better for seeing in the dark?

I often walk around my house at night with the lights turned off and one night I noticed that looking straight at an object with very little light available made the object disappear from sight but if I directed my visual else where I could clearly see the object in my peripheral


In the second edition of Awodey's Category Theory he suggests visualizing a cone as a many sided pyramid. I'd much like to make the proper commutative diagrams, but I don't know how to make a many sided pyramid. The first diagram is just a many sided pyramid, while the second is a superposition of two such pyramids (sharing the same base), only with different apexes along with an arrow between them.  Edits: This is more or less the first diagram I'd like to make, except I'd like my pyramid to be symmetric. Preferably, in black and white, with the vertical arrow to the vertex remaining red and the pyramid faces slightly bluish (but still transparent).   The second diagram would have another pyrmaid with translated apex at the same height, superimposed over the one in the first diagram.


Today i was at a arena. A player from the red team put a Grimer there, which causes my game to crash every time I select the arena (Samsung Galaxy S4 mini). All other pokemons i saw so far did not make any problems  I searched a bit, and found out that this is a known bug, e.G.:   Now my question, is there a way to battle in the arena or even select it without crashing my app? Some option like "hide model in arena",changing some smartphone-settings or another trick? Or do i have to wait till a bugifx from niantec comes or somebody else which has a handy which dont crashes with grimer clears the arena, before selecting the arena?  Because somebody could place him there i guess this is only a bug for specific smartphones, but this could be used to exclude a lot of players from arenafighting by only placing grimers in arenas to let the game crash for them, are there some official notes about this from niantec or how to avoid the crash?


Suggested edits: Better visual indication of whether edit is to a question or an answer

Could we please have a clearer visual indication of whether the suggested edit is an edit to a question or an answer?  Currently the only way I distinguish between the two is to look for the (very light gray) text asked or answered next to original poster's name.


I have recently got the urge to install and test different devices on uncommon OS markets.  I have discovered that I still have an old Samsung Jet S8003, and would like to install Android Gingerbread on the device. First and foremost, is it possible and would it be able to operate fine without bugs?  Second, could I install a later version of the Android OS like Jellybean or Kit-Kat?  I have tried  but have failed as the OS loads up in ssh and then it says that it cant load from ext2.


How does one use a variable in a bash for loop? If I just use a standard for loop, it does what I expect  for i in {0..3} do    echo "do some stuff $i" done   This works fine.  It loops thru 4 times, 0 to 3 inclusive, printing my message and putting the count at the end.  do some stuff 0 do some stuff 1 do some stuff 2 do some stuff 3   When I try the same thing with the following for loop, it seems to equal a string, which is not what i want.  length=3 for i in {0..$length} do    echo "do something right $i" done   output:  do something right {0..3}   I've tried   for i in {0.."$length"} and for i in {0..${length}} (both output was {0..3})   and  for i in {0..'$length'} (output was {0..$length})   and they both don't do what I need.  Hopefully someone can help me.  Thanks in advance for any bash expert's help with for loops.


How can I secure SSH access to a linux box running Ubuntu k for multiple users?  This server will be for a web app but I'm not sure how to evaluate the tools to perform this task. I have tried a few tools in the past but not sure how they stack up against each-other. How can I evaluate my SSH security and the tools and utilities that I would use to perform that securing?


Unlike rdesktop, when I press ALT + F4 in remmina, it doesn't react in the Windows system, but instead closes the remmina window.  Any thoughts?


Analogue of "orphan" for someone who's lost their siblings

As per title - is there such a word?  Either a noun:     John is an ??????  (his only brother died when he was 3)   or verb (or past tense as an adjective):     John  was ????ed today (his only sister died today)


In some of the previous posts, I read we should say "something is available TO someone" (when talking about people). Yet, I have just come across this statement: "Special rates are available for school groups" (when talking about admission to galleries etc.) and now I am confused. Any explanation? Should we used to or for?


What happens in electron-electron collisions?

What are the results of high energy electron electron collisions?  Are other particles created?


Proof that every repeating decimal is rational

claims that every repeating decimal represents a rational number.  According to the following definition, how can we prove that fact?  Definition:  A number is rational if it can be written as $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.


Summing numbers in javascript gives unexpected value

Strangely enough, when I try to add "9333852702227980 + 7", it returns me "9333852702227988" and not "9333852702227987". I cannot figure out why! Any ideas and how to go around this problem?    alert((9333852702227980 + 7).toString());


I get the error  mlabel command not found   I tried using sudo apt-get install mlabel, but it said unable to locate package mlabel.  Any ideas how to get this working?


Connected to wifi successfully, but no internet connection

I'm a relatively new macOS user. Let me try to describe the problem I'm facing as succinctly as possible  Just this morning, when I'm unable to get any internet connection even though WiFi is connected (full strength). All my other devices has no issues when connected to the same network (it's my home network)  I've logged into the router, and checked, there are no blacklisted IP/MAC addresses.  Additional information   I'm using a tMBP 15" for over a year I've had no issues with any WiFi connectivity to my home network before today. ping from terminal doesn't work as well. I'm able to connect to my phone's hotspot, and get internet from my MBP.  I have bootcamp set up. When I boot into Windows, I'm able to get internet access through my home WiFi   How can I troubleshoot this to get to the root cause of the problem?


Evaluating the sum $\sum_{n=1}^{\infty}\dfrac{(-1)^{n}}{n^{2}}$

I am tasked to evaluate the sum  $$\sum_{n=1}^{\infty}\dfrac{(-1)^{n}}{n^{2}}$$ Using contour integration. This is what I've done so far.   Let $C_{N}$ be the square defined by the lines $x=\pm(N+\tfrac{1}{2})\pi$ and $y=\pm(N+\tfrac{1}{2})\pi$. Let $f=\tfrac{1}{z^{2}\sin(z)}$. I was able to prove that  $$\int_{C_{N}}\dfrac{1}{z^{2}\sin(z)}dz=2\pi i\left[\dfrac{1}{6}+2\sum_{n=1}^{N}\dfrac{(-1)^{n}}{\pi^{2}n^{2}} \right]. $$  By Cauchy's residue theorem. So now if I could prove that he integral converges to zero then I would be done. The problem is that I can't seem to get an upper bound on the integral. I've having trouble with the fact that $|f|$ is unbounded within $C_{N}$ so ML inequality doesn't help me. Any hints would be great. Thanks.


Continued fraction for $[1,2,3,4,5,6,\dots]$

Any continued fraction that does not terminate or repeat can't be rational or a quadratic irrational.  It is not hard to write something that does not fit these two categories.  Can we still get a closed form for something like: $$ [1,2,3,4,5, \dots ] = 1 + \cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{\dots}}}$$


I am level 24. Got the Blank Lexicon and Attunement Sphere from Septimus. Both of these items are in my inventory, so clearly I can't drop them.   For whatever reason, the actual pedestal that you're supposed to place the Blank Lexicon in isn't there... I obviously haven't gotten the Elder Scroll yet, because I need to use the Lexicon to do so (but again, I can't because the freaking pedestal isn't physically there...). I have both Elder Knowledge and Discerning the Transmundane in my quests.   Have no idea what the problem is.. On top of that, my last Save (not quick save) is from when I was like level 5, so if I load I have a hell of a lot to make up. I always quick save because I'm an idiot I guess.   I play on PS4 and use mods, but nothing I use should affect the game this tremendously.


Book(s) recommendation: Multivariable calculus

Yes, there are many threads seeking book recommendation on multivariable calculus. Me personally enjoyed "Differential and Integral calculus - Piskunov" and looking something similar in writing on multivariable calculus at any level (intermediate to advance)  Any recommendation will be appreciated.


How can i get the height of a dynamicly varying div using javascript?

Is there anyway to get the height of a dynamic div using javascript?I have a dynamic div which is populated by contents dynamically.I want to know div's height each time. Can anybody help me to figure it out?


couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)

Fresh install of Lubuntu  Installed updates from synaptic  Installed wine and components from synaptic, upon what I assume is completion it popped this error code.   Is it something I should rush to fix?


Use letter keys to input number without Fn function

My keyboard does not have a Fn key, nor a number pad. But I would like to input lots of number with a number pad layout. I wonder if there is an application, which can change some letters, say, 890-iop-kl; as a number pad when I activate the option.   I use Debian Jessie system. It will be better if the function is realized by command-line like things so that I could extend it to what I want.   Thanks very much.


What does the With Editor status mean for an Elsevier journal after being with the Managing Editor (ME)?

I submitted a paper to an Elsevier journal, but it was not assigned to a reference number. They sent me a mail stating that the paper with the managing editor for initial evaluation . After tow weeks later, I got mail stating that the paper is with the Editor. And it was assigned to a reference number. What does this mean? Thanks in advance.


In HP7, Umbridge, with the locket, says that she is related to Selwyn with the "pure-blood chains."  Is this true?


Advice on how to remove these weird black shadow things?

I am not sure what to do with these vertices to fix this weird pinch I have. It creates weird shadows and looks bad. Here are some images.      I could probably just delete a big chunk and try again but maybe this will be a good learning experience for the future to learn other ways to fix this. Thanks a lot for the advice!


existence of antiderivative of a complex analytic function

$(a)$ Show that there is a complex analytic function defined on the   set $U=\{z\in\mathbb{C} \ | \ |z|>4\}$ whose derivative is   $\displaystyle\frac{z}{(z-1)(z-2)(z-3)}$.      $(b)$ Is there a complex analytic function on $U$ whose derivative is   $\displaystyle\frac{z^2}{(z-1)(z-2)(z-3)}$?   The problem clearly reduces to find a analytic function $f(z)$ on $U$ such that $f'(z)=\displaystyle\frac{z}{(z-1)(z-2)(z-3)}$. But if I integrate both sides over the contour of $U$, the RHS is analytic on $U$. So $f(z)=0$. But this result is too absurd to consider. Again same goes for $(b)$, but which is not the case since we have to prove no such $f$ would exist. I considered the CR-equations but the given function is too large to handle for this. What is the best approach for this problem? Any help is appreciated.


How to show that... $$x^4-10x^2+1$$ is reducible modulo $p$ for every prime $p$. I can show it, for say $2$,$3$....but should one proceed if he has to show for all primes.  Just don't seem to get it. Can somebody help me?


Are $\log_1 1$ and $\log_0 0$ indeterminate forms?  Whenever I ask someone about these indeterminate forms, they deny by saying either $\log$ is neither defined at base $0$ nor at base $1$, or they say $\log$ is a function so these must not be included in fundamental indeterminates.  But, we know division by zero is not defined, yet $0/0$ is indeterminate; and many others. And, actually, $\log$ is more a binary-operator that is the inverse operation of power/exponent operator.


Finding limit of $\frac{x^2y^2}{x^3+y^3}$ as $(x,y)\to (0,0)$

Here, if we go along $x=-y$ then the function itself is not defined, and limit seems to exist for all other paths of approach  Putting in another way, if we use polar coords, limit is:  $$\lim_{r\to 0} \frac{r^4 \sin^2\theta\cos^2\theta}{r^3(\sin^3\theta + \cos^3\theta)}$$  which is zero only when $(\sin^3\theta + \cos^3\theta)$ is nonzero, and function itself is not defined for values where $(\sin^3\theta + \cos^3\theta) = 0$  So here, what do we say? Does the limit exist? or does it not exist  (Additional Question)  Suppose that limit is being calculated $(x,y) \to (0,0)$. Then can we choose one of the paths as, say $x=0$, although in limit we only let variables to "tend" to a value? Is it allowed to use this path?


How do I prove/disprove that $F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$, where $F_n$ is the $n$th Fibonacci number?


I recently noticed that when i open a program (that opens a window), the window has a border on top, naming the app. For example, on Firefox it says: "ask Ubuntu - Mozilla Firefox" that has the regular 3 buttons(minimize, maximize and close) and a forth one that just minimizes the window while also letting the "ask Ubuntu - Mozilla Firefox", with those 4 buttons on. This annoys me tbh. Does anyone know any way of getting rid of it and why it has appeared?


Bash ping script file for checking host availability

I am trying to write a bash script in a file that would, when run start pinging a host until it becomes available, when the host becomes reachable it runs a command and stops executing, I tried writing one but the script continues pinging until the count ends,  Plus I need to put that process in the background but if I run the script with the dollar ($) sign it still runs in foreground,  #!/bin/bash ping -c30 -i3 192.168.137.163 if [ $? -eq 0 ] then /root/scripts/test1.sh exit 0 else echo “fail” fi


Investigating the convergence of a series using the comparison limit test

Actually not sure how to approach this... but I may be missing something:  Replacing the sequence:  $x_{n}=1+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{n}}-2\sqrt{n},\,\,\,\, n=1,2,....$  By the corresponding series, invesigate it's convergence.  Hint: Take $a_{1}=x_{1}$ and $a_{n}=x_{n}-x_{n-1}$ for $n>1$. Then $x_{n}$ is a sequence of partial sums for $\sum_{k=1}^{\infty}a_{k}$. Use an expicit formula for $a_{n}$ and use the comparison in limit test to show that the series converges.  Note: This looks easy, but as I said... there's something not quite connecting. When writing out the summation, I'm not entirely sure if they're compatible, as one would go from k=1 to n, and the other would go from k=1 to n-1, yet still vary with k... so do I need to use another pronumeral for it? Or can I simply use k-1 instead of k?


Link to "an account" in "add comment" is dead

When I am viewing a question while not logged in, it shows, under the question:     add comment (requires  with )   However, the link to  is dead.      Here's a screenshot to the result 404 page:    Same 404 page on   Chrome (Normal Mode / Incognito Mode) Opera 12.16 (Private Browsing Mode) IE 10 (Normal Mode / InPrivate Mode)


I am really annoyed because I recently switched to GNOME and I lost a command, Super + Q, that I had with a special application.   Now, it shows the side menu (Ubuntu Dock) and numbers the applications.   I tried to change it at the keyboard options but the command is not even there!   I assume that it's a GNOME issue. But I am not very experienced and it is really annoying that I can't see the command in the Keyboard Command window.  This in on a XPS 13, Ubuntu 17.10, GNOME 3.26.1.


What are units of Distance Matrix tool results in QGIS?

I have a point data set. Now there are cluster of points based on a field. So I take out one such cluster which has points with same field.I want to find distance between all the points in cluster and find out if any point is far away so that I can check if that point is faulty.  Ok to elaborate more on the above one, I have say just 4 points and I have tried to use the distance matrix from the ftools plugin in QGIS.I have chosen the linear matrix and got a csv output. The distance which gives it here what would be the unit for it.


If $a_n$ is a sequence of real numbers, then I know the following result:   If    $\underset{n\to\infty}{\lim} a_{n}$ exist then $$\lim_{n\rightarrow\infty} a_{2n} \quad \text{and} \quad \lim_{n\to\infty} a_{2n-1} \quad \text{and} \quad  \lim_{n\rightarrow\infty} a_{3n}$$ exist and equal. Now what can I say about the converse? i.e.  if I know that $$\lim_{n\rightarrow\infty} a_{2n} \quad \text{and} \quad \lim_{n\to\infty} a_{2n-1} \quad \text{and} \quad  \lim_{n\rightarrow\infty} a_{3n}$$ exist, what can i say about $\underset{n\to\infty}{\lim} a_{n}$?


Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS?

Perhaps a very basic question but one that has me confused. Say, in a correlation table the relationship between A and the DV (B) is .351, but -.150 in the OLS model (where you have added C, D and E variables), what does this then mean? In other words: if the C to E variables not only change the coefficient of A but even make it go from negative to positive, does that indicate an undesirable interaction effect between the variables used in the OLS? I have been checking the VIF scores for this but based on low VIF I have no reason to fear multicollinearity. What (if anything) is wrong?  I'm trying to wrap my head around this constructing a simple example for myself to understand. Say A is a person's height and B is the distance this person jumps. There probably is a positive correlation (higher means longer legs, means longer distance jumping). What variables C to E would offset this person's height, even to the extent that this person's height is working against him when jumping (making the coefficient between A and DV B in the OLS negative)?


Google is using RC4, but isn't RC4 considered unsafe?

Why is Google using RC4 for their HTTPS/SSL?  $ openssl s_client -connect www.google.com:443 | grep "Cipher is" New, TLSv1/SSLv3, Cipher is RC4-SHA   Isn't RC4 unsafe to use?


How can I abstract building maps from SObject Lists in a good way?

I frequently find I want/need to map a list of SObjects by a value other than it's own Id.  So, I'd like to abstract this process to make it reusable.  For example, I might want to map Contacts by Account Id.  So I've created a method mapBySpecifiedIdField:      public static Map<Id, Set<SObject>> mapBySpecifiedIdField (List<SObject> homogeneousSObjectList, SObjectField idField) {     if (homogeneousSObjectList == null || homogeneousSObjectList.isEmpty()) {         return null;     }      Map<Id, Set<SObject>> sObjectSetBySpecifiedIdMap = new Map<Id, Set<SObject>>();     for (SObject sObj : homogeneousSObjectList) {         Id specifiedId = (Id) sObj.get(idField);         if (!String.isBlank(specifiedId)) {             if (!sObjectSetBySpecifiedIdMap.containsKey(sObj.Id)) {                 sObjectSetBySpecifiedIdMap.put(sObj.Id, new Set<SObject>());             }             sObjectSetBySpecifiedIdMap.get(sObj.id).add(sObj);          }     }      String mapType = 'Map<Id, Set<' + homogeneousSObjectList[0].getSObjectType() + '>>';     Map<Id, Set<SObject>> concreteSObjectSetByIdMap = (Map<Id, Set<SObject>>)Type.forName(mapType).newInstance();     concreteSObjectSetByIdMap.putAll(sObjectSetBySpecifiedIdMap);      return concreteSObjectSetByIdMap; }   I'd prefer to invoke it with:  Map<Id, Set<Contact>> mapContactSetByAccountId = (Map<Id, Set<Contact>>) MapHelper.mapBySpecifiedIdField(contactList, Contact.AccountId);   But first, I'll get a compile error:     Incompatible types since an instance of Map<Id,Set<SObject>> is never an instance of Map<Id,Set<Contact>>   If I change my invocation to:  Map<Id, Set<Object>> mapContactSetByAccountId = MapHelper.mapBySpecifiedIdField(contactList, Contact.AccountId);   But this results in a runtime error:     System.TypeException: Invalid conversion from runtime type Map<Id,Set<Contact>> to Map<Id,Set<SObject>>   Is there any way I can make this work?


In any triangle, prove that: $a\cos A+b\cos B+c\cos C= 4R\sin A.\sin B.\sin C$  My Attempt: $$L.H.S=a\cos A+ b\sin A+ c\sin C$$ $$=2R.\sin A. \cos A+ 2R\sin B\cos B+2R\sin C\cos C$$ $$=R.\sin (2A)+R.\sin (2B)+R.\sin (2C)$$ $$=R(\sin (2A)+\sin (2B)+\sin (2C)$$


What is Ubuntu's status on the Meltdown and Spectre vulnerabilities?

Any questions relating to status updates, or asking if anything is going to be patched for these vulnerabilities should be closed as duplicates of this question.    are in the news right now and sound pretty severe. I don't see any security updates from Ubuntu that cover these vulnerabilities.  What is Ubuntu doing about these vulnerabilities, and what should Ubuntu users be doing?  These are CVE-2017-5753, CVE-2017-5715 and CVE-2017-5754.


Bash 'unbound variable' error when variables are referenced in multiline comment (set -u)

I have an unexpected behaviour- following snippet fail with 'unbound variable' error:  #!/bin/bash set -u <<EOF a=a b=$a EOF   Tested on:  GNU bash, version 4.4.12(1)-release  GNU bash, version 4.2.46(2)-release


Is it wrong or looked upon to acknowledge God on Master's thesis paper?


I'm looking for a simple word to use as the name of a function in a computer program that widely employs a naming metaphor. For this reason, I need a simple verb that can substitute (the instruction) "Become born."


A grey wedge appears on the screen I've uploaded a picture of what keeps happening, I keep masking out part of the scene and can't figure out what keys i'm pressing, any help really appreciated! Thanks.


value zero generated numerously using random function()

/*This is my function code*/ Random random = new Random(); int randomInt = random.nextInt()%200;  String imgName = "img" + randomInt;  int ImageId = getResources().getIndentifier(imgName,"drawabale",getPackageName()); myImage.setImageResourse(ImageId);      Previously in my drawable folder there are      200 images already inserted using img1,img2.....img199  like nomenclature...     every time I call random function mention below to generated one      random number and form a string name starting from      "img" and some number. But most of time only 0 is generated by random function and id set to      image is display 0th image constantly..at some point it successfully display other images but most of time it generated zero value continuosly.   Thanks in Advance !


In Microscope are Light and Dark used for anything?

I was teaching a game of Microscope today and I kept seeing references to light and dark. While expressing the tone of periods, events, and scenes is good, I remember from the playtest that a parent element's lightness or darkness somehow contributed to its children's tones.   In Microscope, how are the markers of Light and Dark used?


When user enters from php page to mysql it makes wierd characters like Pyr«±n«±es, ????? etc, when typing ' æøå éá etc.  I have tried anything now.   PHP files is saved as UTF8 without bom. Altered all tables, database and converted to UTF8 HTML META charset utf8 Form has "accept-charset="utf-8" Right after connection: mysql_query SET NAMES UTF8 PHP Header with charset: utf-8   What to do? When it's going to database it makes those annoying characters.  Please help me.


Why are there so many virtual terminal devices?

I've been reading the  and it mentions about virtual terminals which, if I understood it correctly, it is a Linux-specific feature (not in Unix) to allow multiple login consoles in a non X11 system. You create virtual terminals by pressing ALT-F2. I'm running Linux Mint and in my /dev folder though I see many tty devices and I don't know what they are for. Here is the grepped output:  crw-rw-rw-  1 root tty       5,   0 Jan  2 19:45 tty crw--w----  1 root tty       4,   0 Jan  2 19:10 tty0 crw-rw----  1 root tty       4,   1 Jan  2 19:10 tty1 crw--w----  1 root tty       4,  10 Jan  2 19:10 tty10 crw--w----  1 root tty       4,  11 Jan  2 19:10 tty11 crw--w----  1 root tty       4,  12 Jan  2 19:10 tty12 crw--w----  1 root tty       4,  13 Jan  2 19:10 tty13 crw--w----  1 root tty       4,  14 Jan  2 19:10 tty14 crw--w----  1 root tty       4,  15 Jan  2 19:10 tty15 crw--w----  1 root tty       4,  16 Jan  2 19:10 tty16 crw--w----  1 root tty       4,  17 Jan  2 19:10 tty17 crw--w----  1 root tty       4,  18 Jan  2 19:10 tty18 crw--w----  1 root tty       4,  19 Jan  2 19:10 tty19 crw-rw----  1 root tty       4,   2 Jan  2 19:10 tty2 crw--w----  1 root tty       4,  20 Jan  2 19:10 tty20 crw--w----  1 root tty       4,  21 Jan  2 19:10 tty21 crw--w----  1 root tty       4,  22 Jan  2 19:10 tty22 crw--w----  1 root tty       4,  23 Jan  2 19:10 tty23 crw--w----  1 root tty       4,  24 Jan  2 19:10 tty24 crw--w----  1 root tty       4,  25 Jan  2 19:10 tty25 crw--w----  1 root tty       4,  26 Jan  2 19:10 tty26 crw--w----  1 root tty       4,  27 Jan  2 19:10 tty27 crw--w----  1 root tty       4,  28 Jan  2 19:10 tty28 crw--w----  1 root tty       4,  29 Jan  2 19:10 tty29 crw-rw----  1 root tty       4,   3 Jan  2 19:10 tty3 crw--w----  1 root tty       4,  30 Jan  2 19:10 tty30 crw--w----  1 root tty       4,  31 Jan  2 19:10 tty31 crw--w----  1 root tty       4,  32 Jan  2 19:10 tty32 crw--w----  1 root tty       4,  33 Jan  2 19:10 tty33 crw--w----  1 root tty       4,  34 Jan  2 19:10 tty34 crw--w----  1 root tty       4,  35 Jan  2 19:10 tty35 crw--w----  1 root tty       4,  36 Jan  2 19:10 tty36 crw--w----  1 root tty       4,  37 Jan  2 19:10 tty37 crw--w----  1 root tty       4,  38 Jan  2 19:10 tty38 crw--w----  1 root tty       4,  39 Jan  2 19:10 tty39 crw-rw----  1 root tty       4,   4 Jan  2 19:10 tty4 crw--w----  1 root tty       4,  40 Jan  2 19:10 tty40 crw--w----  1 root tty       4,  41 Jan  2 19:10 tty41 crw--w----  1 root tty       4,  42 Jan  2 19:10 tty42 crw--w----  1 root tty       4,  43 Jan  2 19:10 tty43 crw--w----  1 root tty       4,  44 Jan  2 19:10 tty44 crw--w----  1 root tty       4,  45 Jan  2 19:10 tty45 crw--w----  1 root tty       4,  46 Jan  2 19:10 tty46 crw--w----  1 root tty       4,  47 Jan  2 19:10 tty47 crw--w----  1 root tty       4,  48 Jan  2 19:10 tty48 crw--w----  1 root tty       4,  49 Jan  2 19:10 tty49 crw-rw----  1 root tty       4,   5 Jan  2 19:10 tty5 crw--w----  1 root tty       4,  50 Jan  2 19:10 tty50 crw--w----  1 root tty       4,  51 Jan  2 19:10 tty51 crw--w----  1 root tty       4,  52 Jan  2 19:10 tty52 crw--w----  1 root tty       4,  53 Jan  2 19:10 tty53 crw--w----  1 root tty       4,  54 Jan  2 19:10 tty54 crw--w----  1 root tty       4,  55 Jan  2 19:10 tty55 crw--w----  1 root tty       4,  56 Jan  2 19:10 tty56 crw--w----  1 root tty       4,  57 Jan  2 19:10 tty57 crw--w----  1 root tty       4,  58 Jan  2 19:10 tty58 crw--w----  1 root tty       4,  59 Jan  2 19:10 tty59 crw-rw----  1 root tty       4,   6 Jan  2 19:10 tty6 crw--w----  1 root tty       4,  60 Jan  2 19:10 tty60 crw--w----  1 root tty       4,  61 Jan  2 19:10 tty61 crw--w----  1 root tty       4,  62 Jan  2 19:10 tty62 crw--w----  1 root tty       4,  63 Jan  2 19:10 tty63 crw--w----  1 root tty       4,   7 Jan  2 19:10 tty7 crw--w----  1 root tty       4,   8 Jan  2 19:10 tty8 crw--w----  1 root tty       4,   9 Jan  2 19:10 tty9


Too many revision when post status is changes

When ever i update the custom post type it generates too many revision which crashed the website.  ( memory exceeded) How can i debug this issue?    Update :  I was able to find the culprit. Will it be possible for some one to detect what i did wrong in the below code :  if (class_exists('wpprolister_core')) {      add_action('wp_insert_post', 'wpprolister_updated_to_publish', 10, 3);      function wpprolister_updated_to_publish($post_id, $post, $update)     {          if (get_field('wpprolister_advanced_option_edit_seo', $post_id)) {              $metatitle     = get_field('wpprolister_seo_title', $post_id);             $metadesc      = get_field('wpprolister_seo_meta_description', $post_id);             $metakeywords  = get_field('wpprolister_seo_keyword', $post_id);             $content       = get_field('wpprolister_description', $post_id);             $image         = get_field('wpprolister_listing_slider_image', $post_id);             $attachment_id = $image['ID'];              if (!empty($image)):                 $size  = 'medium';                 $thumb = $image['sizes'][$size];                 if (defined('WPSEO_VERSION')) {                     update_post_meta($post_id, '_yoast_wpseo_title', $metatitle);                     update_post_meta($post_id, '_yoast_wpseo_metadesc', $metadesc);                     update_post_meta($post_id, '_yoast_wpseo_focuskw', $metakeywords);}                 //also update the content and featured image                 $my_post = array(                     'ID'           => $post_id,                     'post_content' => $content,                 );                 wp_update_post($my_post);                 update_post_meta($post_id, '_thumbnail_id', $attachment_id);              endif;          }     } }   How i solved the problem (please let me know if i did wrong ):  remove_action('wp_insert_post', 'wpprolister_updated_to_publish');             $my_post = array(                 'ID'           => $post_id,                 'post_content' => $content,             );             wp_update_post($my_post);             add_action('wp_insert_post', 'wpprolister_updated_to_publish');


Is it a bad idea to connect two Li-ion batteries in parallel?

Suppose I have two Li-ion batteries for smartphones. One could say that if they are connected in parallel, then the voltage given to the device would be the same, but the capacity would be doubled, hence doubling the lifetime of the total battery (i.e. more time to use the smartphone without charging it).  However, this seems a bad idea to me. The first thing that crosses my mind is that doing this would lead to huge currents between the two batteries if the voltages are not exactly the same.  Would this approach work? If not, are there any other drawbacks on top of the one I described?


Which Ubuntu version that support HP 14-bw001au?

I want to remove the Windows 10 from my laptop and switch to Ubuntu. But I am not sure which Ubuntu version that support the laptop.  The laptop is HP 14-bw001au.  Thank you.


I am trying to solve this problem:      Let $ R_1,...,R_n$ be rings with identity. Every ideal of $R=\prod_{i=1}^n R_i$ is of the form $\prod_{i=1}^n I_i$  where $ I_i$ is an ideal of $R_i$.    The first part is clearly if $J$ an ideal of $R$ then $J\subset \prod_{i=1}^n I_i$, but i can complete the rest..any help..


Is the sentence "Why C treats array parameters as pointers?" correct?

Why C treats array parameters as pointers?   It sounds quite wrong to me. I would have been happier to hear      Why does C treat array parameters as pointers?   instead.  Is the first sentence correct?


Making code print in the same line without repetitions in python

I am a beginner to python and this is one of the assignments my teacher has given me. "Given an integer input, AND a list of numbers (you need a single input then the new list input), Then print yes if the input is present in the list and then print all the index positions that it appears! If the given integer is not present, just print no" I'm pretty sure i've gotten the code right but the tests keep failing because my output is not printing in the same line. This is my code:     N = int(input())     a = [int(s) for s in input().split()]      for N in a:       for i in range(0,len(a)):         if a[i]==N:           [print("Yes",i)]       else:        print("no")  i'm posting an image of the tests to give more context of what the problem i'm facing is.  I hope this is enough context for ya'll to help me out.


A war on a planet where time passes slowly at the poles

The story is set on a planet where time passes much more slowly at the pole. A soldier is near one of the poles and a major offensive seems to be building up with his side firing into some kind of grey curtain, a horizon caused by the extreme time "gradient".  The other side is firing back.  He is fetched from his post as his discharge has come up and travels to the equator where he starts a new life. 20 years pass when 2 officers approach him, they had left to get him back only a few minutes after he has left and he returns to his post some 10 or so minutes after he had left.  He realizes that the weapon fire they are getting from across the void is just there own stuff coming back.  I have always taken it as an analogy for lots of tit for tat wars, but cannot find the story.


If $I = [a,b] $ and suppose $f : I → R $ is increasing in $I$, then $f$ is continuous in $a$ if and only if $f(a)$ = $inf$ $\{f(x):x ∈→ (a,b)\}$ I've solved it this way, okay? If not, please help me correct it. Let $f$ continue en $x=a →$ lim $x_→a^+$ $f(x)=f(a)$ Let's suppose $inf\{f(x)/ x ∈ ]a,b[\}) = L ≠ f(a)→L>f(a)$ lim $_{x→a^+}$ $f(x)=f(a)→$ si $\varepsilon = \frac{f(a)-L}{2}>0, \exists \delta$ $> 0 / a<x<a + \delta →|f(x)-f(a)|<\varepsilon →$ $|f(x)-f(a)|< \frac{f(a)-L}{2}→f(x)-f(a) <\frac{f(a)-L}{2}→ 2f(x)-2f(a)<f(a)-L→$ $f(x)<\frac{3f(a)-L}{2}→ f(x)<\frac{3f(a)-f(a)}{2}→f(x)<f(a)$ contradiction then $ x>a$


Maybe some kind of virus? Cannot open AntiVirus www sites

Win XP. Any browser (Firefox, Opera) cannot open several antivirus sites:   eset.com drweb.com freedrweb.com avira.com bitdefender.com   (but usual sites are all OK opened.) I checked: hosts file is clean; ping for AV sites doesn't work too (all packets lost); inet connection to these sites ok from another PC; Windows safe mode: all is OK, sites work.  I have ESET Smart Security on this PC. I performed full check with:    ESET SS  DrWeb CureIt (I could copy it from another PC),  Avira (could copy it too) MS Sec Essentials.    No resuts. What can be a reason?


what advantage are AT-ATs (they're rubbish)

In Starwars during the battle of Hoth, the empire made what i believe to be a hilarious strategic miscalculation and sent vehicles with only forward facing firepower (unimpressive firepower at that), are easy targets, and are slow moving, up against the stronger, more agile squadrons of rebel fighters which consequently result in massive imperial AT-AT casualties.   The rebels had previously illustrated a proficiency at fighter based combat and rely upon them heavily. Fighters appear to be the perfect counter to an AT-AT assault.   So why would any general in his sane mind deploy them? granted, i recognise that their firepower was sufficient to breach the rebel defences, would likely impose a significant psychological effect on the enemy, would act as overwatch due to heigh and acted as troop carriers. However they were completely vulnerable to the obvious rebel fighter counter and appear to be totally impractical anyway: They are slow moving, easy targets and possess obvious weak spots around the cockpit and leg joints.   What ever happened to tanks, which would be the far more logical alternative, especially when supported with ground to air/air-air defences, and why would the empire use AT-ATs?


I read in some website that during the period of inflation, the expansion of the universe underwent incredibly fast, and its size increased by a factor of $10 ^{50}$,   In this field, I think, there is nothing for sure, but if there was really inflation, what does it mean that the size increased by a factor of $10 ^{50}$, but from what extent? From 1 mm? Or from the Planck length? Or something else?  Has it been established that (whatever was the original measure) the factor is increased by $10 ^{50}$, and not for example of 40 or $10 ^{50^{60}}$?


Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$ by defining a bijection $f:A^{B \cup C} \rightarrow A^B \times A^C$.  Any hints on this one?  Thank you!


charset=iso-8859-2 webpage displays with UTF-8 header - question marks (�) instead of accented letters

I have a webserver administration question. In this website:   All PHP generated pages contain the following line:  <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-2" />   But this is somehow disregarded probably via the php-apache processing and the page displays in browsers with an UTF-8 header. As a result of that question marks (�) are shown in the page text instead of accented characters (éáöőóüűúí). I tested this in Firefox, IE, Chrome and Seamonkey.  The strangest in this phenomenon, that this symptom started only yesterday, after I upgraded my server to Debian 8.0 Jessie from 7.0 Wheezy. During the upgrade I also upgraded all other packages as well, including apache, php, and so on, and selected "yes" for overwriting config files with factory default ones. After this I fine-tuned my config files to have everything the way I like, but I did not find a way to fix this. Before the upgrade, the page displayed just fine.  Here is a screenshot, where you can see that Firefox sees the "charset=iso-8859-2" definition, but still displays the page with UTF-8 encoding.    My suspicion is, that this is a server configuration issue, but it could also be, that one part of the processing component (Apache, php) changed due to the upgrade in some way, resulting this strange behavior. The problem is, I can't pinpoint, what could possibly cause this problem.  Can anyone solve this mistery? What could be possibly going wrong during the processing of the page?


I have some classes A and B:  struct A {     typedef int value_type; }; struct B {     typedef float value_type; };   I want to make a tuple of A::value_type and B::value type via variadic template. I am expecting something like this:  template<typename ...T> struct my_tuple {      typedef std::tuple<T::value_type...> tuple_type; };   This doesnt compile. How can I make such kind of tuple?


What is the fastest algorithm for finding the natural logarithm of a big number?

Like for $\pi$, we have an algorithm/infinite series that can give us the first 50 decimal places in about 3 terms. So if I wasn't to calculate like $\ln(25551879\cdots)$ (a really huge integer, most likely a prime), upto 100 decimal places, what will be the algorithm I should use or is used worldwide and how efficient is it? I know that the Taylor series is rather slow in its work, so any other algorithm in which this is computed?


I was writing to a friend of mine, back and forth, and suddenly I am getting the following message back:  <email@example.com>: host mx1.example.com[123.123.123.123] said: 554 5.7.1 Spam     detected by content scanner.  Message rejected.  (in reply to end of DATA     command)   This is strange, because I am not even using words or phrases that are "SPAMMY."  I tried to re-send the message with a slight change in the content, but I get the same reply.  Could it be that this has not something to do with the content but with something else, such as my server reputation?  As a note, I am using a local mail server here, not GMAIL or something.


Is the 5-foot range of the Help action my range to the ally, the enemy, or both?

A player in our group that knows much more than me explained the Help action during game, but then after the game I read the PHB and not sure if he's using it correctly.  I thought I needed to be within 5 feet of the enemy. He said I need to be within 5 feet of the ally.  The  action says:     You can lend your aid to another creature in the completion of a task. When you take the Help action, the creature you aid gains advantage on the next ability check it makes to perform the task you are helping with, provided that it makes the check before the start of your next turn.      Alternatively, you can aid a friendly creature in attacking a creature within 5 feet of you. You feint, distract the target, or in some other way team up to make your ally’s attack more effective. If your ally attacks the target before your next turn, the first attack roll is made with advantage.   Does the ally, the enemy, or both need to be within 5 feet of me when I take the Help action?


\hphantom in \tabulary produces extra vertical space instead of horizontal

Inserting an \hphantom to indent a table row works in tabular, but in tabulary it produces extra vertical space instead.   Since these are left-aligned L columns I would expect the space at the left edge to be preserved, while the space on the right is variable. Why does this happen and how could I fix it?  \documentclass{article} \usepackage{tabulary}  \newcommand{\sator}{Sator arepo tenet opera rotas} \newcommand{\tabindent}{\hphantom{em}}  \begin{document}  \section{Tabular}  \begin{tabular}{ll} \sator  & \sator\\ \tabindent\sator & \tabindent\sator\\ \end{tabular}  \section{Tabulary}  \begin{tabulary}{\textwidth}{LL} \sator  & \sator\\ \tabindent\sator & \tabindent\sator\\ \end{tabulary}  \end{document}


My Disk Utility is showing me some Weird Stuff.  My current startup partition is showing as 155 GB, with (I was shocked to discover) 344 GB of unpartitioned free space:    I can try to resize the first partition by removing the "Free space" section, then hit "Apply", but then I get this error:    Actually, if I try this a few times, I get variously different errors.  Sometimes it even says it succeeds, but the partition size doesn't seem to have changed.  When I retry this same sequence after booting from my recovery partition, basically the same result happens, except that now I have two "Free space" partitions, both showing 344 GB, in addition to the 155 GB startup partition.  What's going on here, and how can I take advantage of my full 500 GB disk?  Or do I not actually have a 500 GB disk??  Here's the Disk Utility info for the physical disk - notice that it says it's 500 GB, but the 155 GB partition takes up the whole blue bar:    I'm using High Sierra 10.13.6, on a Late 2011 MacBook Pro 13".


If you toss $1000$ fair coins $10$ times each, what is the probability the *some* coin will get $10$ heads?

The answer to this is supposedly close to $0.63$. However, I get approximately $0.9765625$ for the following reason:  The probability of a fair coin flipped $N$ times resulting in all heads is $1/2^N$. In this case, $1/2^{10}=1/1024$. If I flip $M$ coins, $N$ times each, there are $M$ ways for some coin to result in all heads (from the binomial coefficient "$M$ choose $1$"), so the probability of some coin resulting in all heads is $M(1/2^N)$. In this case, $1000\times 1/1024 \approx 0.9765625$.  Can someone please explain the flaw in my reasoning?


Proving a scalar function is differentiable at the origin but that its partial derivatives are not continuous at that point.

Let $f: \mathbb R^2 \to \mathbb R$ defined as   $f(x,y)=(x^2+y^2)\sin(\dfrac{1}{\sqrt{x^2+y^2}})$ if $(x,y) \neq (0,0)$, $f(x,y)=(0,0)$ if $(x,y)=(0,0)$  Prove that $f$ is differentiable at $(0,0)$ but that the partial derivatives of $f$ are not continuous at the origin.  The attempt at a solution:  I had some problems at the first part of the exercise:  I've calculated $\dfrac{\partial f}{\partial x}(0,0)$ and $\dfrac{\partial f}{\partial y}(0,0)$, both exist and are equal to $1$.  So, to prove $f$ is differentiable at the origin, I have to show that   $\lim_{(x,y) \to (0,0)} \dfrac{|f(x,y)-(f(0,0)+<\nabla f(0,0),(x,y)>)|}{\|(x,y)\|}=0$ But $\lim_{(x,y) \to (0,0)} \dfrac{|f(x,y)-(f(0,0)+<\nabla f(0,0),(x,y)>)|}{\|(x,y)\|}$ equals  $\lim_{(x,y) \to (0,0)} \dfrac{|(x^2+y^2)\sin(\dfrac{1}{\sqrt{x^2+y^2}})-(x+y)|}{\|(x,y)\|}$. I don't know how to show this limit equals $0$.  For the second part (I've only analyzed $\dfrac{\partial f}{\partial x}$ since both cases are the same), what I did was try to show that $\lim_{(x,y) \to (0,0)} \dfrac{\partial f}{\partial x}(x,y) \neq \dfrac{\partial f}{\partial x}(0,0)$   I thought of considering the curve $\phi(t)=(t,0)$, so   $\lim_{t \to 0} (f\circ \phi)(t)=\lim_{t \to 0} 2t\sin(|t|^{-1})-\dfrac{t\cos(|t|^{-1})}{|t|^{-1}}$. But $\lim_{t \to 0^{+}} \dfrac{t\cos(|t|^{-1})}{|t|^{-1}}=\lim_{t \to 0^{+}} \cos(\dfrac{1}{t})$ and this limit doesn't exist, so the original limit doesn't exist. This shows the partial derivative with respect to $x$ at the point $(0,0)$ is not continuous.   I would appreciate if someone could help me to finish the first part and tell me if what I did in the second part of the problem is correct.


If an atom absorbs an electron it must re radiate it but many times it is said that so along with absorption we must see emission lines but we see missing lines in abortion spectrum so where absorbed photon goes if it convert into heat energy how it take place


Let p be a prime and let $a \in \mathbb Z$. Prove that the congruence $x^x \equiv a\pmod p$ is solvable.


Im new to python and got stuck while processing a .bat file  1) I have a .bat file that contains the following lines:  set local_dir=%~d0%~p0  set LVMain_StartAddress=0xfaff set LVMain_EndAddress=0x0f4ff set HVMain_StartAddress=0x01d00 set HVMain_EndAddress=0x095ff set LVMain_StartAddressMerged=0x0D000 set LVMain_EndAddressMerged=0x0fcff set HVMain_StartAddressMerged=0x01001d00 set HVMain_EndAddressMerged=0x010095dd   2) A python script runs through the file to look for the line "set LVMain_StartAddress=0xfaff"  3) When it finds the line, I want to replace the hex address with a new one. Sometimes the new hex address is 5 characters long  4) Below is the python code I wrote to do this:  # write LVMain start address in .bat file with open("..\..\..\Tools\Scripts\GenerateRomTestChecksums.bat", "r+") as f:      #read lines individually until we find where to write LvMain Start address     BatFileLine = f.readline()     while( (LVMain_StartPattern in BatFileLine ) == False ):         BatFileLine = f.readline()      #set marker back to the beginning of the line     LineMarker = int(f.tell()) - (int(len(BatFileLine)) + 0x01)     f.seek(LineMarker)      #split string where address starts to write new address in file     name, hex_address = BatFileLine.split('0x')     #append new address and carriage return     name = name + APPL_End_address + "\n"     print(len(name))       contents = f.read(len(BatFileLine)).replace(BatFileLine,name)     f.seek(LineMarker)     f.write(name)   This is part of a larger function and "APPL_End_address" is given as a  parameter  5) When I run this code, and the new hex address is 5 hex digits wide, I get the following output:   It seems the new hex address is written correctly, but the first character of the next line erased. Any ideas why?


what the mening of (+) in BETWEEN function

Recently I observed the following syntax:  AND TRUNC (SYSDATE) + 1 BETWEEN a(+) AND b(+)   I know that the (+) sign is used to address left or right join in conditions like:  and a = b(+)   ... but I have no idea what it means in the BETWEEN function.  Can someone explain, please, or better give an example using BETWEEN function?  Thank you,


I beg your pardon for such a silly question, but I've never really understood the explanation they gave in the Geography textbooks. If the slanting Sun's rays due to the Earth's axial tilt can cause such a huge temperature difference, why isn't all our ocean get frozen when the Earth is farthest from the Sun (in the Earth's orbit)?  Earth revolves around the Sun in an elliptical orbit with a mean eccentricity of 0.0167. As a result, Earth's distance from the Sun (center-to-center) varies with mean values of 0.9832899 AU (147,098,074 km) at perihelion (closest) to 1.0167103 AU (152,097,701 km) at aphelion (most distant). If the slanting solar rays can freeze water at the poles, this difference should cause the entire water body to freeze, isn't it? I'm definitely missing something here. Can anyone please help me?


when I export my data genereated with the openLayers using Atlas rendering is always incomplete. Atlas is rendering too fast so that the data from openLayers is not completely loaded.   Do anyone knows how to handle this?


How to change terminal screen size/resolution on Ubuntu 19.04 Server with VirtualBox?

I installed Ubuntu Server 19.04 from VirtualBox on Windows Host. I have a terminal screen 800x600. VirtualBox does not provide me an option to change resolution.  How do I change the terminal resolution?  Tried:  1)  Downloaded VirtualBox Guest Additions from virtualbox.org, mounted media, and installed.  2)  sudo apt-get install virtualbox-guest-additions-iso  Wonder if the problem is because it's the Server version, and there's no graphic interface or X11.  Guest Additions installed:  $lsmod | grep vboxguest  vboxguest     331776     1  Looks like GRUB might have something to do with it.  Looks like I need a graphical terminal.


Are cropped images from a full-frame sensor equal quality to full APS-C images despite the lower resolution?

If I put a DX lens on a Nikon D700, it will reduce megapixels to 5.1.  I understand that FX pixels are about 2.5 times larger than DX pixels. Would I be correct to assume that, therefore, my FX image using 5.1 megapixels will produce quality equivalent to at least a 10 megapixel image on a DX camera, all other things being equal?


Does a tapped or removed attacking creature still deal its damage?

If an attacking creature gets tapped, removed from the game, returned to hand, put in the library or destroyed during combat, does its damage still get through to the blocking creature or player?


Real Analysis Inequality Proof Involving Reals and Rationals $0 < |r - q| < \varepsilon$

I'm having difficulties making progress in proving: $$\forall \varepsilon > 0, \ \exists q \in Q  \text{ where } 0 < |r - q| < \varepsilon $$  To clarify, $r$ is a real number and $q$ is a rational number.   Is there some theorem I should be using? This exercise is presented in the same section/chapter as the Completeness Axiom (each nonempty set has a least upper bound or supremum), the Archimedean Property of Real Numbers ($ \exists n \in Z^{+}$ such that $na>b $ for positive real numbers $a$ and $b$), and a theorem stating there is a rational and irrational number between any two distinct real numbers.  I'm just not seeing the connection (if any at all). Any help in the right direction would be much appreciated. Thank you!


Maybe I am not the first one who got this idea.  There are many programming questions asked and answered on these sites. My idea is when the question or answer consists of a lot of code and the user wants it, he must copy-paste it. So how about providing a download button which will download the code as a file?


Any detriment to hanging a bike by its front wheel?

I came across the below image today and thought it a great idea for storing bikes. However I wasn't sure if literally hanging a bike by its front wheel might cause undue stress to either the wheel itself or the front forks. Has anyone else done this to no ill effect? In the image below the back wheels don't even seem to be touching the floor, which I would have thought would take some of the weight.


Comment on the monotonicity of $g(x)={f(x)\over x}$

If $f(x)$ is a real valued function defined on $[0,\infty)$ such that $f(0)=0$ and $f''(x)>0$ for all $x$.  Consider a new function $g(x)={f(x)\over x}$. I want to comment on the monotonicity of function $g$. I mean I want to find whether $g$ is increasing or decreasing and where.  Here are the things I observed. Don't know if it can help or not.  We can find that $g(0)=f'(0)$  Since second derivative of $f$ is positive, it means $f'$ is an increasing function.   $g'(x)=\dfrac{xf'(x)-f(x)}{x^2}$  But I am not able to proceed.  Thanks for hint.


Help identifying unknown fantasy movie/show where prisoners are punished with immortality?

I've been looking for years - only things I have are, the protagonist is a man, he's friends with a young man who can shape shift - at one point the man talks to a jaguar like creature thinking it's the young man, while he's actually off to the side telling the man not to stop talking, or the cat will tear his throat out.  There's a weird prison, the warden is a large, Jabba the Hutt like creature to my memory and he loves a female prisoner sentenced with immortality. He lets her out once every.... Blank years to walk on the beach.  I'm not sure if this is some obscure b-movie or awful sci-fi channel series or maybe a mini-series? But any help would be appreciated.


Is Happiness of a pokemon the same as Affection?

OK, I just started playing Pokemon-Y. In PokemonAmie there are ways to increase the affection of your pokemon. Is this the same thing as Pokemon Happiness that is used for happiness evolutions?  If not, is there a character that tells you how happy your pokemon is?


Why isn't the nominative case generally used with "to be"?

In German, constructions with sein, which is uninflected infinitive meaning "to me", seem to generally use the nominative case. For instance, this is a dog translates to das ist ein Hund, and ein here is in the nominative. In German,  seems related to what the subject of the sentence is.  In any case, I was thinking about this and wondered about why in constructions like it is [inflected pronoun], using the nominative case for the pronoun instead of an objective case seems slightly overly formal.  That's not to say that the nominative case is never used. For instance, from the book of John:     Then Jesus, knowing all that was to happen to him, came forward and asked them, “Whom are you looking for?” They answered, “Jesus of Nazareth.” Jesus replied, “I am he.”   (This is from the New Revised Standard Version, but the King James Version gives the same.) Now, this seems grammatically correct to me, but it probably seem unnatural to the casual listener if, upon asking who Jane Doe is, I answered with "I am she" instead of "I'm her."  Why is this the case? Has this just always been the case in more informal English? Or have there been shifts in usage?


I have one table in Postgres which has following columns:  processtransactionid bigserial, TenantID uuid, ProcessInstanceId bigint attributename varchar(250), attributevalue varchar(250),   createddate timestamp, queueid int   The attributename contains values like 'filename', 'documentstatus', 'batchImportdate', etc. and attributevalue columns contains corresponding values of the attribute, like filename = abc.jpg, documentstatus ='Present' & batchImportdate='2019/08/26 12:57:51'  I want output in the following way:   ProcessInstanceId filename  documentstatus batchImportdate        queueid     6008            abc.jpg   Present        '2019/08/26 12:57:51'  2    6008            abc.jpg   Absent         '2019/08/26 12:57:51'  3   grouping of the records to be done by ProcessInstanceId, queueid  I am able to create query in SQL Server using the PIVOT keyword but facing a problem in creating the same query in Postgres.  Could you please help me write the Postgres query?


I'm using the only open source firewall for Android:  and would like to use a VPN in addition. Is this possible? If so: how?  Both types of apps typically use virtual VPN tunnels. NetGuard has network settings too.


I am having some issues related to the precision with Decimals. Let's take a look at the following scenario:  Decimal total = (5 / 3) * 3; System.debug(total) // this will print 4.9999999999999999  total = 5 * 3 / 3; System.debug(total) // this will print 5   The reason seems that in the first operation, the number that arrives at the multiplication is 1.66666666666666666 (Decimal precision)  Is there any know bug from salesforce with this? Because in other languages I don't observe this behavior.


What does the Eye icon mean on LG phones?

I see an eye icon at the top of my screen, but without the phone around it, what does the eye icon mean, just the eye icon.


Topology Book Recommendation other than Munkres

Could anyone recommend a good text on topology which would offer a higher level of abstraction than Munkres(and possibly cheaper)? I'd like to start with point set topology, but if the book could touch upon more subfields, that would be a plus. I'm an undergraduate who has taken courses in real analysis (on the level of rudin), combinatorics, complex analysis (Bak & newman), linear algebra and differential equations.


Prove that $\sqrt[n]{n!}$ is increasing and diverges

I have to prove that $a_n$ is (strictly) increasing and diverges  $a_n = \sqrt[n]{n!}$ ;  n $\in$  $\ \mathbb{N}$  From sequence I see that $a_n$ increasing to infinitive.  $\sqrt[1]{1!}=1 ,\  \sqrt[2]{2!} \approx 1.41, \  \sqrt[3]{3!}  \approx 1.81 ,...,  \sqrt[n]{n!} $


How can only the change in direction can be called acceleration?

Why does the change in only the direction leads to acceleration of a body. I mean acceleration of body implies that it is moving fast or getting slow with respect to its initial speed. But i dont think that change in direction affects any of it?


A Question on Shakespeare's use of conditionals

The following is a big question, but I am really confused by the use of conditional in this Shakespearean excerpt.   From The Taming of the Shrew, Act I, Scene I:     142   I am agreed; and would I had given him the best      143 horse in Padua to begin his wooing that would      144   thoroughly woo her, wed her and bed her and rid the      145   house of her!   Can someone help me parse out this conditional sentence? It seems that the modern English equivalent would be "I would give the best horse to him who could woo her if I found this chosen man who can do so successfully."   If my reading is correct, here is my doubt: Shakespeare uses  A) would I had given as if he means it as the dependent clause whereas we, in MoE, usually change the word order this way in the dependent clause, as in: "Had I known of the matter, I . . ." Is there something I don't understand?   B) Since the time reference is the future, why would . . . had in the first place? Shouldn't it be "I would"?   D) would . . . had? Was this an 16th century equivalent to would . . . have?


How does centering the data get rid of the intercept in regression and PCA?

I keep reading about instances where we center the data (e.g., with regularization or PCA) in order to remove the intercept (as mentioned in ). I know it's simple, but I'm having a hard time intuitively understanding this. Could someone provide the intuition or a reference I can read?


\mid, | (vertical bar), \vert, \lvert, \rvert, \divides

What's the difference between the different vertical bars?  $S = \{\, x \mid x \not= 17 \,\}$ $a \vert b$ implies $a \leq b$ when $b \ne 0$ $a|b$ implies $a \leq b$ when $b \ne 0$ $\lvert x \rvert$ is always non-negative     Are all of these uses correct?


Option to get inbox notifications for new meta posts

Currently, moderators get an inbox message for each new post submitted to a per-site meta they moderate, SO excluded.  I would like to have that, please.  The reason is, I like to know what's going on. I usually read all of meta anyway, when I notice that there's something new, so I figure I might as well get notified about it as soon as it happens.  And there's already a system that delivers new meta posts to certain inboxes.  (This might not be a good idea for MSO in particular though, at least until .)


Since the split, the  tag is no longer relevant, but people are still using it to tag new questions here. Back when this site was Meta Stack Overflow, this tag was used to indicate if a question specifically applied to the Stack Exchange network of sites, while the  tag was used to indicate Stack Overflow-specific questions. However, this site's scope is now the entire Stack Exchange network, making it redundant.  Can it be mass-removed?


Is this box bonded properly to the ground?

The receptacle is from the mid-1950's and my multimeter shows that it is grounded. There are a solid 120 volts when testing between live and ground. I noticed a bare copper wire coming from the cloth wiring in the back tied to a screw connected to the box. I looked around for usable screw holes in the box to screw a ground screw into but they were all way too large. Does this look okay? I get good continuity here between the green insulated copper ground wire I added and the rest of the box.  The green wire goes to the ground screw on the new outlet in this case.


Why is the localization at a prime ideal a local ring?

I would like to know, why $ \mathfrak{p} A_{\mathfrak{p}} $ is the maximal ideal of the local ring $ A_{\mathfrak{p}} $, where $ \mathfrak{p} $ is a prime ideal of $ A $ and $ A_{\mathfrak{p}} $ is the localization of the ring $ A $ with respect to the multiplicative set $ S = A -\mathfrak{p} $ ? Thanks a lot.  N.B. : I have to tell you that I'm not very good at Algebra, so please, be more kind and generous in your explanation, and give me a lot of details about this subject please. Thank you.