I've just found out that one of my parents want a divorce.  They don't know that I know.  I am a young teen (about15) what should I do?

I am a young teenager, younger than 16. (I do not want to give my age online)    My dad told me he wants a divorce, but I don't want my parents divorced. My dad says he can't stand my mom anymore.  My dad is older than 45 and my mom is older than 40.    If it happens, I would choose to stay with my mom. My dad can cook and drive, but my mom can't. There's a school bus in high school though.    What can I do to prevent this divorce?


I'm wondering if this sentence makes sense. If more examples could be offered, that would be appreciated. Thank you.     As long as one has a pastor certificate and gifts and can analyze the Bible, it means they are approved and anointed by God.

Consider this example:     Sustainability management in large organisations is an important activity that helps to achieve one’s business goals while at the same time reducing their environmental impact and improving benefits to wider society."   Does it make sense to use both one’s and their to refer to organisations in the quoted sentence above?


This is happening when you ask questions.     I reproduced this on a different SE website and with the latest versions of Chrome and Firefox

I just edited an answer on Unix&Linux and when scrolling down, the semi-transparent right sidebar boxes "How to edit" and "How to format" kept their fixed positioning and overlapped with the page footer.     While posting this, I have seen several (not) duplicate questions about this issue, and although from my personal taste, I would prefer the boxes to stop scrolling before the footer is reached, I can accept the development teams decision to let it overlap.   However, on all those other posts, the boxes had an opaque background, so that the footer was hidden and the box content was readable. Here the boxes are transparent though, so the texts get mixed and are no longer well readable.


I'm trying to apply for a US visa from Singapore. When I get to the last step of the DS 160, where I'm required to upload my photo, I get an error saying 'An error occurred while processing your photo, please try again later'. To be clear, the photo passed all the checks in the previous stage and it says in green that the photo is ok, but on the next page it shows this error    I've been trying for about 20 hours now on several computers and mobiles and different browsers. None of it seems to work. Is anyone else facing this problem now and/or has figured out a proper solution to this? I tried calling the embassy, but we were told that they could not help.

I'm trying to apply for a B1/B2 US visa through the  but unfortunately can't get past the "Confirm photo" stage as I see the following error:    I've tried to re-upload the photo several times in both Chrome, Android Chrome and IE 11 to no avail. Is there something I can do so that I can complete my application?


I have the following piece of code:    $(document).ready(function() {   $("a[href*='window']").on("mouseover", function() {     $(this).css('color', 'green');   });   $("a:eq(2)").click(function() {     $(this).attr("href", "#window_1");   }); }); a {   padding-left: 20px; }  link 1 link 2 link 3 (click to add substring "window")     Here I'm basically trying to apply some css to a tags having the substring 'window' in their 'href' attribute on 'mouseover' event.  The code works fine for ones with predefined attribute (having the specified substring) but fails for dynamically added attributes.  How do I solve this issue?

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I'm trying to use drupal migration module with drush to migrate a database. I'm getting this error below.  Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 32 bytes) in /Applications/XAMPP/xamppfiles/htdocs/drupal-eight-iom/core/modules/migrate_drupal/src/Plugin/migrate/source/DrupalSqlBase.php on line 76  I have already tried editing the memory_limit on php.ini file  memory_limit=5024MB  Not sure what else I need to do in order to make it work. I'm using Drupal 8.4.4  $databases['default']['default'] = array (   'database' => 'drupal-eight-iom',   'username' => 'root',   'password' => '',   'prefix' => '',   'host' => '127.0.0.1',   'port' => '3306',   'namespace' => 'Drupal\\Core\\Database\\Driver\\mysql',   'driver' => 'mysql', );  $databases['upgrade']['default'] = array (     'database' => 'drupal-seven-iom',     'username' => 'root',     'password' => '',     'prefix' => '',     'host' => '127.0.0.1',     'port' => '3306',     'namespace' => 'Drupal\\Core\\Database\\Driver\\mysql',     'driver' => 'mysql',   );   $settings['install_profile'] = 'standard'; $config_directories['staging'] = 'sites/default/config'; $config_directories['sync'] = 'sites/default/files/config_zB_DnNUK68i5Owp5a8FzTiClQfp3d3jrwcy0_HuS1hNCGv9Y_Iva2Ahm8LCH-P0j0M2jwmQAsA/sync';

I've made a drush install of drupal 7.28 on my AWS server. I can confirm that the memory is set to 128M, all green on the reports -> site status page. The website will function normally and sporadically return no data, looking at the logs a tremendous amount of memory is trying to be allocated (assuming an infinite loop somewhere). Given that this is a basic install, no modules have yet been added what might be causing this?  PHP Fatal error:  Allowed memory size of 134217728 bytes exhausted (tried to allocate 140008587493184 bytes) in Unknown on line 0


I was wonder if it is possible to do mathematical operations like bits operations but with qubits. Is there a way to convert qubits to bits?

Currently, the  runs at 17.59 Petaflops, which consumes 9 megawatts of electricity. A qubit-based quantum computer has the potential to operate much more quickly for some operations than a classical computer would be able to (). In fact, classical computers face a major hurdle in computation speed due to the inherent capacitance of components. My question is: would a quantum computer able to compute things faster than a classical computer do so with less, about the same, or greater power draw for equivalent operations? Would that depend on its implementation?


In the following sentence are the words "senator and "representative" capitalized?  There are many special restrictions that senators and representatives must abide by.

I was taught at an early age in the USA that when we write about our President, we are supposed to capitalize the title in order to signify that it's on the federal level. Is it correct to always do this? And what about saying "the presidency" -- should that be "the Presidency"?


When a tag page is visited from mobile site, info option is missing from the dropdown. Mobile site:  Full site:

I was surfing SO on my iPhone, and wanted to see the info (tag-wiki) page for a tag, but didn't find it. Clicking on the tag always leads to the list of question, and there is no other link to the tag wiki. Is it not available on the mobile site?


I am examining the impact of 7 IVs on one DV using regression anaysis. Some of the IVs are significantly correlated with each other, which is consistent with theory.   While the single OLS regression between the individual IVs and the DV shows positive and significant effects in 4 out of 7 cases, multiple regression only finds 1 signigicant predictor.   As the first suspect in this case is multicollinearity, I applied a collinearity resistant Partial Least Squares Regression, which successfully identified 4 significant predictors.  However, when I conduct the VIF and Tolerance analysis, I don't find any indications for multicollinearity. VIF is below 1.7 for every variable.   Do I have multicollinearity in the data?   What else may explain this phenomenon?   (N = 80, survey data)

I have what is probably a simple question, but it is baffling me right now, so I am hoping you can help me out.  I have a least squares regression model, with one independent variable and one dependent variable. The relationship is not significant. Now I add a second independent variable. Now the relationship between the first independent variable and the dependent variable becomes significant.  How does this work? This is probably demonstrating some issue with my understanding, but to me, but I do not see how adding this second independent variable can make the first significant.


Apparently they've gotten rid of the COD Ghosts app so how am i supposed to create an account or a clan? When i click on barracks in the multiplayer menu the only thing it shows is Leaderboards and Reset Stats.

When I create a clan in the multiplayer menu, it says clan created but I cannot add or invite people to my clan. I go to create a new one assuming the request was canceled or not entered correctly, it says clan name already exists as if someone else created it.   Is this a bug? Did I do it wrong? Or am I missing something?   I'm on the PS3. Will this also happen on my Xbox 360 Version?


When I do algorithm exercises, I found many people like to transfer a string to charArray before do operations?   I don't understand why do we bother do that? I mean, I can use string.charAt(), why use string.toCharArray() and then charArray[i]? It's the same and even charArray use O(n) memory.  Can anyone explain that to me?

StringTokenizer? Convert the String to a char[] and iterate over that? Something else?


I have a java web application that allows users to search contents, when i try to sign-up a new user i get the following message! HTTP Status 500 – Internal Server Error  Type Exception Report  Description The server encountered an unexpected condition that prevented it from fulfilling the request.  Exception  java.lang.NullPointerException     DBConnector.queries.selectUserNamePass(queries.java:30)     Users.signupS.processRequest(signupS.java:42)     Users.signupS.doPost(signupS.java:109)     javax.servlet.http.HttpServlet.service(HttpServlet.java:647)     javax.servlet.http.HttpServlet.service(HttpServlet.java:728)     org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:52)  any one has an idea how to solve it?

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


What is the easiest way to convert a list of strings to a list of numbers so that those that look like integers converts to int and others to float?   Example:  list = ['1' , '2.2' , '3']   One way to convert is to define are they ints or floats:  list = [float(item) for item in list]   But in this example also obvious int would be converted to float as well.  One way could be to check variable type and convert case by case. Is there an easier way?    Edit:  A similar looking question  is a little hard to understand what the questions is, and accepted answer does not cover my case.  Another similar looking question  is a basic question of how to convert to int or float and my question went a little further than that.  I'll ask again in other words: How to convert a string (or list of strings) to just to a number (or list of numbers), whatever type, retain its type whether int, float (or complex). Usually conversion is made from string to a certain type of number, usually to int or float. Is there an easy and obvious way to convert a string to a number of any kind?

In Python, how can I parse a numeric string like "545.2222" to its corresponding float value, 545.2222? Or parse the string "31" to an integer, 31?  I just want to know how to parse a float str to a float, and (separately) an int str to an int.


Because I program a lot on my personal machine, sometimes I have a lot of windows open with articles on blogs etc that I would like to keep open as I'm working in addition to VS etc. Rather than turn my comp off at night or put it into hibernation (shudder), I simply leave it in standby or just plain on.   The problem is, every once in a while, Windows Update performs an update and automatically restarts my comp, which makes me lose everything. Where is the setting to prevent this from happening?

On XP Home how can I prevent Windows from ever trying to restart my computer after an update? XP Home has no Group Policy Editor.


Given $X, Y$ and $Z$ are three positive and non-equal natural numbers. If $\frac1X + \frac1Y + \frac1Z = 1$, then what's the value of $X + Y + Z$?   This is a question from my nephew, I cannot think of any such triples. Any idea guys?

Find all solutions of  ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$ , where $x,y,z$ are positive integers.  Found ten solutions $(x,y,z)$ as ${(3,3,3),(2,4,4),(4,2,4),(4,4,2),(2,3,6),(2,6,3),(3,6,2),(3,2,6),(6,2,3),(6,3,2)}$.  Are these the only 10 solutions? First, none of $x$, $y$ or $z$ can be $1$ ($x$, $y$ and $z$ are positive integers)  If I let $x=2$, then finding all solutions to $1/y+1/z = 1/2$    leads to $(4,4), (3,6)$ and $(6,3)$ which gives me $(x,y,z)$ as $(2,4,4), (2,3,6), (2,6,3)$ but this also means $(4,4,2), (4,2,4), (3,2,6), (3,6,2), (6,2,3), (6,3,2)$ are all valid triples for this equation. If I let $x=3$, the only different values of $y$ and $z$ are $(3,3)$ How do I prove these are the only ten solutions? (without using any programming)  Known result:  If we denote $d(n^2)$ as the number of divisors of $n^2$, then the number of solutions of ${\frac {1} {x} }+{\frac {1} {y} } = {\frac {1} {n} }$   =  $d(n^2)$  (For positive $x$, $y$)  For ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$  $z = \frac{xy}{y(x-1)-x}$ where $xy \neq 0$ What happens after that?  Question is: how do we sho there are the only ten solutions?  I'm not asking for a solution.  Assuming $x \le y \le z$  $1 \le y \le \frac{xy}{y(x-1)-x}$   $\Longrightarrow 1 \le x \le y \le \frac{2x}{x-1} $   Got the answer.  I'll probably call @mathlove's answer. (Any additional answers I'll view later) Liked @user44197 answer.


I have always been confused between these two. From what I understand, methods always use dot notation like:  $( "li.third-item" ).nextAll().addBack().css( "background-color", "red" );   In this case, nextAll(), addBack() and .css() are all methods.  Similarly, functions are called directly. Like,  make_tea();   I want to know with certainty whether something is a function or a method by looking at how it is used. Does using PersonOne.run_now() always guarantee that run_now() is a method? Can run_now() still be a function if we are using a . to access it?  My question is "Does a function become a method when we are using . to call it?"

Can someone provide a simple explanation of methods vs. functions in OOP context?


The  spell description says:  You ward a creature within range against attack. Until the spell ends, any creature who targets the warded creature with an attack or a harmful spell must first make a Wisdom saving throw. On a failed save, the creature must choose a new target or lose the attack or spell. This spell doesn't protect the warded creature from area effects, such as the explosion of a fireball. If the warded creature makes an attack, casts a spell that affects an enemy, or deals damage to another creature, this spell ends.  My question is whether I ruled the above spell correctly based on the scenario below:  Character A casts sanctuary on Character B Creature 1 tries to attack Character B, and fails its Wisdom save against sanctuary. Creature 1 sees that it has enough remaining movement available to reach Character C, and thus moves to Character C and attacks (regardless of whether it has multi-attack or not).  The player who controls Character A (the one who cast sanctuary) feels that since Creature 1 failed the Wisdom saving throw, the attack was wasted and Creature 1 should not have been able to attack Character C. They concede that Creature 1 can move to Character C, but disagree that it should have been able to attack them. However, based on the wording of:  On a failed save, the creature must choose a new target or lose the attack or spell.  ...I feel that a creature can move and make an attack as it does not specify anything about movement speeds, and clearly states that another target must be sought. Was my ruling correct? If not, please explain why.

Take a simple scenario as an example:  A cleric casts sanctuary An enemy wielding a spear attempts to make a melee attack at the cleric with his spear The enemy fails his Wisdom save, and thus can't attack the cleric  Now what? According to the  spell description:  On a failed save, the creature must choose a new target or lose the attack or spell.  No one else is currently in melee range, but others are within move distance. What happens to the enemy's intended attack, after failing the Wisdom save?  Do they simply lose the attack if there is no other target immediately in range, causing that spear attack to be wasted? Does the enemy now get to "hold" the melee spear attack, use movement to get in melee range with someone else, and then resume the same melee spear attack on the new target? Can the enemy choose to make a different kind of attack with the same weapon, and decide to throw the spear instead (at someone else)? Can the enemy choose to attack with a different weapon, such as a shortbow, and attack someone else instead (either before or after moving)? Can the enemy choose to cast a spell instead of making a weapon attack?


I want to disassemble a broken hair dryer (just to see what's inside), but I just found out it uses a weird tamper-proof screw I had never seen in my life. Trying to google for it doesn't help much; I still could not find its official name.  It's like a standard flat screw, where the central part has not been cut, and looks like this from above:    It looks a bit like an "H", so I tried looking for "H screw" and got a  Google , but I find very few of them, and they look mostly related to watches.  I find it appalling that Philips (the hair dryer manufacturer) needs to put such tamper-proof protection on such a common household appliance, but I suppose they have their legal reasons to do so. However, without knowing the name of the screw, I can hardly find where to buy a screwdriver for it!  If there is an official name for this screw, please enlighten me. I found a  on the Internet, but it seems to be small and related to watches. My screw is a "standard small appliance size".

A previous owner fitted the light fitting pictured above, and has not left me a tool to remove the bolt. The bulb has blown so I need to get in to the unit. The head diameter is about 12mm and the gap between the two notches is about 6mm. I would like to remove it with some technique involving more finesse than simply smashing up the fitting and/or drilling out the bolt.  I hope someone can recognise the bolt and give me a search term which will let me cheaply buy a bit for this bolt from somewhere like Ebay UK.


I have a paginated table of items. We can do some bulk actions ( like delete) on items. User selects some items on page 1 and goes to next page and selects some items on page 2. is it better that bulk actions work per page? Or work on all selected items in all pages?

I have a list which is paginated in a webpage. It also has a function to select the number of entries per page. A bulk update on all is required.   What would be the best approach to this? My concern is that a user would doubt if we refer to the current page or to the whole list. Would a confirmation window with details or an info message to detail it would suffice?  This is how it looks for now:


Hi I just installed Ubuntu 20.04LTS.  I am unable to view .dwg files which I receive in any of the available platform like Qcad, Librecad, zwcad, Freecad.  Please suggest me way out as otherwise I am finding ubuntu 20.04LTS extremely good.

I'm looking for a utility or a program for Ubuntu, and possibly even for Windows that is able to convert a CAD file format .DWG to PDF.   My need is to provide a preview of CAD files, and I thought that the easiest way is to convert them into PDF format, but I'm open to suggestions, even if there is only the possibility to convert them to JPG image file type or PNG would be fine.  What interests me is only to find some solution, no matter if it is commercial or free


Mind Spike says  On a failed save, you also always know the target’s location until the spell ends, but only while the two of you are on the same plane of existence.  DnD Beyond lists this having a range/area of 60ft. Does this mean if my target teleports (remaining on this plane of existence) away I stop knowing where they are outside of the 60ft? Or is that the initial range?

Does going outside the range of the spell or breaking line of sight between the caster and target break concentration or otherwise affect control over the spell?  For example, a Heat Metal spell has a range of 60 ft. If I cast the Heat Metal spell on a an armored foe, and that foe runs outside the range of the spell (60 ft), or around the corner, does that break concentration and end the spell? Heat Metal also allows you to use a bonus action to cause the 2d8 of damage — would exercising that option be prevented by being out of range or line of sight?


I need to prove that if $A,B,C,D$ are sets, $(A \times B) \cap (C \times D)=(A \times D) \cap (C \times B)$  I am trying to show that if for all $x,y$ in LHS, it is also an element of RHS.   $(x,y) \in (A \times B) \cap (C \times D) \iff$ $(x,y) \in (A \times B)$ and $(x,y) \in (C \times D)$  $\iff x \in A, y \in B$ and $x \in C, y \in D$  $\iff x \in A, y \in D$ and $x \in C, y \in B$    (Am I allowed to change the order of $y$ as above?) and if so, what law allows me to do that?.

The question goes: Let $A,B,C,D$ be sets. Prove that $\big(A\times B\big)\bigcup \big(C\times D\big)=\big(A\bigcap C\big)\times \big(B\bigcap D\big)$ I started with the definition of the cartesian product $A \times B=\left\{\big(a,b\big): a\in A \wedge b \in B\right\}$ The union of $A\times B$ and $C \times D$ would be a set of coordinates where $\big(x,y\big): x\in A\bigcup C \wedge y\in B\bigcup D$ I am stuck here because the union of the two cartesian products on the left doesn't seem to imply that $x\in A\bigcap C$ and $y \in B\bigcap D$. Could anyone give me a hint or a possible step I might not be seeing? Please and thank you.


In the Deathly Hallows book/movie, Voldemort 'kills' Harry with the avada kedavra curse. But if Harry was a Horcrux, then why can't the other horcruxes be destroyed by Avada Kedavra? It might be because they're not alive, but then why didn't Harry die with the Horcrux?

In The Deathly Hallows Hermione says this about destroying Horcruxes:     “It doesn’t have to be a basilisk fang,” said Hermione patiently.   “It has to be something so destructive that the Horcrux can’t repair   itself. Basilisk venom only has one antidote, and it’s incredibly   rare—"      "That’s a problem we’re going to have to solve though, because ripping, smashing, or  crushing a Horcrux won’t do the trick. You’ve got to put it beyond magical repair.”   Mad-Eye Moody from The Goblet of Fire tells us this about Avada Kedavra,     ...there's no countercurse. There's no blocking it.   but also that,      Avada Kedavra's a curse that needs a powerful bit of magic behind it - you could   all get your wands out now and point them at me and say the words, and I doubt   I'd get so much as a nosebleed.    Harry is also seen once attempting to use Crucio on Bellatrix Lestrange in The Order of the Phoenix out of anger at the death of Sirius, but he fails. She tells him,     "You need to mean [Unforgivable Curses], Potter! You need to really want to cause pain - to enjoy it - righteous anger won't hurt me for long - I'll show you how it is done, shall I? I'll give you a lesson -"   Even if Harry and company are not powerful enough to perform the curse themselves, they know several powerful wizards (Kingsley, Lupin, et al.) who could likely perform the curse.  Lastly we know that Voldemort himself destroyed the last bit of his soul that was inside Harry with Avada Kedavra.  Could the Horcruxes be destroyed with Avada Kedavra as well?


void f(string message) {     string.Format(message,"x",y"); }   f() is called by g:  g() {    f(SomeJson+"{0}"); }   the curly braces in json are being interpreted as placeholders for values by string.format() in f(). IS there a way to have the curly braces escaped?

How can brackets be escaped in using string.Format? For example: String val = "1,2,3" String.Format(" foo {{0}}", val);  This example doesn't throw an exception, but it outputs the string foo {0}. Is there a way to escape the brackets?


First up, I know there are a lot of similar questions with 24, not 12. So bare with me please :)  What is the Question?  Consider the following numbers of the form $p^2 - 1$ where $p$ is prime.  $$5^2 - 1 = 24$$ $$7^2 - 1 = 48$$ $$11^2 - 1 = 120$$  Each of these numbers is divisible by 12. Prove or provide a counter example to the following statement: "If $p > 3$ is prime, then $12 $ | $p^2 - 1$"  What have I tried?  Okay so off the cusp I know two methods that might help.   Modular Arithmetic And that any prime $\geq$5 can be represented as $6k \pm 1 $   I'm only just catching up on course content and modular arithmetic so I don't really know where to start.   I assume because 12 | 24, the proof will be very similar to the ones provided on this forum for that question  I guess I wan't to make sure.

Let $p>3$ be a prime. Prove that $24 \mid p^2-1$.   I know this is very basic and old hat to many, but I love this question and I am interested in seeing whether there are any proofs beyond the two I already know.


I'm looking for a one (two might be ok) word description for a person who doesn't want anyone else to have a better life than himself. This is the type of person who will break your crayon on purpose because he accidentally broke his own. He's not inherently mean; if his own life is going well, then yours can, too.   To make this a little stronger, here's another example. Describe (in one or two words) a person who, after being born with only one arm, goes around chopping off other people's arms because he thinks it isn't fair that they all get to have two.  So far, the best I have is bitter or malcontent, but neither of these is strong enough in my opinion.   For context, I'm writing a log line and having trouble getting a strong enough adjective to describe the antagonist.

The German word schadenfreude is often used in English to express the pleasure derived from seeing misery in others.   From dictionary.reference.com     schadenfreude noun. satisfaction or pleasure felt at someone else's misfortune.    For example quite harmlessly, finding it funny when someone trips over, or more dramatically the pleasure derived when seeing your ex-partner go through a messy break up.   Is there a word for wanting bad things to happen to others? The context would typically a bit a jilted lover or a jealous person.  For example hoping someone's holiday goes badly, or hoping the company project goes badly after you leave.


I'm revising for an exam - two questions:  i) What's the cardinality of the set of strict total orders on $R$?  This is a subset of the power set of $R$ (because $|R|=|R.R|$), so I know its cardinality is less than this - but I can't find a way to show its cardinality is equal to this, i.e. an injection from the power set into the set of strict total orders.  ii) What is the cardinality of the set of countable subsets of F, where F is the set of functions from $R$ to $R$?  Cardinality of F is same as cardinality of power set of $R$ (one way given by reasoning above, and the other way by the fact that $|P(R)|=|2^R|=|R^R|$. The set of countable subsets of this I am not sure how to calculate though.

For a finite set $S$ there are $\vert S\vert!$ orderings of its elements.  What is the cardinality of all orderings of $\mathbb{N}$?  What would $$\vert \mathbb{N}\vert!$$ mean?  Is it $\prod_{n\in\mathbb{N}} \aleph_0=\aleph_0^{\aleph_0}=\aleph_1$?   says the "equivalence classes of well-orderings of the natural numbers" has cardinality $\aleph_1$.  But I can't put together in my mind the connection between well-orderings of $\mathbb{N}$ and all orderings of $\mathbb{N}$.  (Are there non well-ordered orderings of $\mathbb{N}$?)  This leads to wondering what the cardinality of all orderings of $\mathbb{R}$ is.  (Actually my thought process went in the other direction, from $\mathbb{R}$ to $\mathbb{N}$.)  I think knowing the answer to the above question will teach how to determine what $$\vert \mathbb{R}\vert !$$ means, if anything.  I will be happy if you assume the continuum hypothesis to be true for the purposes of this question, but any level of completeness is welcome.


I installed Ubuntu 19.04 this morning and i've been trying to download lots of apps but its challenging and frustrating but not like wine.So these are my errors root@miarhpe:/home/ephraim# sudo apt-add-repository 'deb https://dl.winehq.org/wine-builds/ubuntu/ disco main'  Ign:1 http://ppa.launchpad.net/noobslab/apps/ubuntu disco InRelease             Ign:2 http://security.ubuntu.com/ubuntu disco-security InRelease                Hit:3 http://ppa.launchpad.net/videolan/master-daily/ubuntu disco InRelease     Err:4 http://security.ubuntu.com/ubuntu disco-security Release                    404  Not Found [IP: 91.189.88.152 80] Hit:5 https://dl.winehq.org/wine-builds/ubuntu disco InRelease                  Ign:6 http://ng.archive.ubuntu.com/ubuntu disco InRelease                       Ign:7 http://ng.archive.ubuntu.com/ubuntu disco-updates InRelease               Ign:8 http://ng.archive.ubuntu.com/ubuntu disco-backports InRelease             Ign:9 http://ppa.launchpad.net/webupd8team/atom/ubuntu disco InRelease          Err:10 http://ng.archive.ubuntu.com/ubuntu disco Release   404  Not Found [IP: 91.189.88.152 80] Err:11 http://ng.archive.ubuntu.com/ubuntu disco-updates Release                  404  Not Found [IP: 91.189.88.152 80] Err:12 http://ppa.launchpad.net/noobslab/apps/ubuntu disco Release         404  Not Found [IP: 91.189.95.83 80] Err:13 http://ng.archive.ubuntu.com/ubuntu disco-backports Release   404  Not Found [IP: 91.189.88.152 80] Err:14 http://ppa.launchpad.net/webupd8team/atom/ubuntu disco Release   404  Not Found [IP: 91.189.95.83 80] Reading package lists... Done N: Skipping acquire of configured file 'main/binary-1386/Packages' as repository 'http://ppa.launchpad.net/videolan/master-daily/ubuntu disco InRelease' doesn't support architecture '1386' E: The repository 'http://security.ubuntu.com/ubuntu disco-security Release' no longer has a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. N: Skipping acquire of configured file 'main/binary-1386/Packages' as repository 'https://dl.winehq.org/wine-builds/ubuntu disco InRelease' doesn't support architecture '1386' E: The repository 'http://ng.archive.ubuntu.com/ubuntu disco Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'http://ng.archive.ubuntu.com/ubuntu disco-updates Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'http://ppa.launchpad.net/noobslab/apps/ubuntu disco Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'http://ng.archive.ubuntu.com/ubuntu disco-backports Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'http://ppa.launchpad.net/webupd8team/atom/ubuntu disco Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.  Please help me out what's going wrong

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


In order to change my laptop from Ubuntu to windows I changed my filesystem from ext4 to NTFS. Now it is showing error unknown file system(Grub rescue). Is there any way I can exit from that.

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


Assume the following script:  $ cat test.sh #!/bin/bash echo $PATH   This happens:  $ echo $PATH /usr/local/bin:/usr/bin:/usr/local/sbin:/usr/sbin:/home/<user>/.local/bin:/home/<user>/bin $ sudo ip netns exec blue echo $PATH /usr/local/bin:/usr/bin:/usr/local/sbin:/usr/sbin:/home/<user>/.local/bin:/home/<user>/bin $ ./test.sh /usr/local/bin:/usr/bin:/usr/local/sbin:/usr/sbin:/home/<user>/.local/bin:/home/<user>/bin $ sudo ip netns exec blue ./test.sh /sbin:/bin:/usr/sbin:/usr/bin   Why. It's breaking my scripts ecosystem because it means they cannot see many of my binaries.  Out of the two distributions I've tested this in, Fedora 24 is the only one that does it. Ubuntu 14.04 echoes all $PATHs the same as I expect.  I tried adding to the script  $ sudo ip netns exec blue PATH=$PATH   But it errors out, presumably because PATH=etcetc is not really a command.  What is the correct way to do it?

I have a program that is installed in a custom directory under /opt. To make it easier to run it, I edited my bashrc to add said directory to my path: export PATH=$PATH:/opt/godi/bin:/opt/godi/sbin  This works fine if I want to run the program without sudo. However, if I try to run it with sudo it fails with a "command not found" error. $ sudo godi_console sudo: godi_console: command not found  Inspecting the PATH variable after using sudo reveals that its not including the same PATH I have as a normal user: $ sudo sh # echo $PATH                  /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin  Why is the PATH not the same? Am I doing something wrong? I'm on Debian Jessie, if it makes a difference. One thing I tried was to invoke /opt/godi/sbin/godi_console directly, passing the absolute path to the executable. Unfortunatelly, that didn't help in this particular case because godi_console itself depends on the PATH being correctly set.


@Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     setContentView(R.layout.activity_log);      Name = (EditText)findViewById(R.id.ETNAME);     Password = (EditText)findViewById(R.id.ETpassword);     Info = (TextView)findViewById(R.id.TVinfo);     Login = (Button)findViewById(R.id.BTlogin);      Info.setText("No of attempts remaining: 5");      Login.setOnClickListener(new View.OnClickListener() {         @Override         public void onClick(View v) {             validate(Name.getText().toString(), Password.getText().toString());         }     }); } private void validate(String UserName, String UserPassword){      if((UserName == "Starlite") && (UserPassword == "abc123")){         Intent intent = new Intent(LOGActivity.this, InterfaceActivity.class);         startActivity(intent);      }else{         counter--;         Info.setText("No of attempts remaining: " + String.valueOf(counter));          if(counter == 0){             Login.setEnabled(false);         }     }  }   }  This is my code and I created it to log to a profile. But I can not login with it. What is the error of it? The following are the top code. I done with it with tutorials. But it not working.It was verified in 5 times. But can not log to it.

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Is an academic probation for not finding a research advisor in time considered "disciplinary sanctions by any university"?  This is asked in a graduate school application.  Does "sanction" mean penalty?  Does "disciplinary" include the issue of finding a research advisor in time?  Thanks!

I'm wondering whether dismissal / withdrawal from a PhD program should be listed as disciplinary action on subsequent applications. A Master's program application usually asks questions like:     Have you ever been found responsible for a disciplinary violation at any post-secondary institution you have attended, whether related to academic misconduct or behavioral misconduct, that resulted in a disciplinary action?   I was academically dismissed from a PhD program after four semesters for not being able to maintain the minimum GPA. I plan to fully include this information in my application (e.g. through transcripts from the institution from which I was dismissed), and address why I was dismissed (and what steps I have taken to address academic concerns) in my Statement of Purpose.    Q: However, I am not sure if my dismissal counts as one that is due to "disciplinary violation" related to "academic misconduct or behavioral misconduct". I was simply dismissed due to not being able to maintain the required grades. Should I answer the above question in the negative?


Am using Bean class to get/set value for the attributes. In some cases am gettig Exception in thread "main" java.lang.NullPointerException error due to the value is null. What will be the best practice to handle null pointer exception when we get/set values from/to bean class.  Is that ternary operator is good to use or any other suggestions?  Please find the below line of code where am getting null pointer exception.  doc.setCatalog_title(sourceAsMap.get("catalog_title").toString());

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Does anyone has a way to produced something alike the following, I saw this first .  and the titles have this presentation (like centered):

Is it possible to identify the font used in a specific document/picture?  Answers to this question should identify:   Possible methods to do this (perhaps one answer per method) and adequately describe how to use it (as opposed to merely stating it); Ways of finding the identified fonts, if possible (free or not); and Any prerequisites associated with the method used, if required (for example, "In order to use method X, your document has to be in format Y").   This question is meant as an FAQ, based on an . Its aim is to facilitate the community with the general procedures involved in font identification. Similar cases are solved on a per-usage basis on 's  tag.


What happens with  in the case of a board wipe? I know that all the creatures die at the same time, so do I still get zombies or is that ability mulled by the fact that Overseer is now gone?

is a creature with the ability "Whenever a nontoken creature an opponent controls dies, put a 2/2 black Zombie creature token onto the battlefield tapped"  Now, lets say 3 of my opponent's creatures die either through combat, spells, or sacrificing. Could I put the triggered ability on the "stack" so to say in order to get 3 2/2 black zombies for each non token creature that died that my opponent controlled, or am I forced to put one and only one despite 3 creatures dying?


I have set up sql server 2008 in windows server 2008 r2 and it works fine. However, I have deleted the my user from logins in the sql server accidentally and now I cannot find a way to log in to the sql server and I believe I did not set up any other user well. Think of it as I just installed and removed the user.  Is there anyway that I can add an account?

I have inherited a Windows 7 Professional pc with an existing instance of SQL Express 2008. I have local admin rights on the machine. I do not know the SA password. I am unable to create databases or logins, or modify the SA login's password. I would like to grant my domain account SYSAdmin privileges.  I have tried the following, in both situations I right clicked and ran SQL management studio as Administrator, and used Windows authentication to log in to the local SQL express.  I created a local admin account, with administrator privileges and logged in to my PC as that. I have logged to my PC as a Domain Admin.  I understand that if I log in as an administrator using windows authentication I should have full privileges, what can can be stopping me from getting this access?


When you are about to walk into someone (generally a stranger), you anticipatory move, say left, to avoid a crash. The other person too does the same but to his right. So in essence the anticipation on both sides was futile (your left is his right). Then you go right and the other guy responds with a left. This carries on twice or thrice until it ends with a smile and a consensus as to which way to go. Finally you part ways.  This whole 'process' seems very intriguing to me and I'm sure has not just happened to me, hence, I expect there must be some word for it.

Is there a word or expression in English, which describes the situation, when you can't pass a  stranger, who is walking towards you on the street, because you both start to step the same direction?  I'm pretty sure I've heard one once. As I remember, it was including "dancing" reference, but in more specific way.


How can I access all files and folders on my user  username/media/ directory?  I'm using Ubuntu 18.04.3 LTS.   Ubuntu's Nautilus can indeed access all files and folders in all locations. However, Ubuntu's software that I have downloaded (e.g. KRITA, WPS WRITER etc) can NOT access any file or folder on the /media directory. Thanks in advance.

I have Ubuntu 18.04 LTS installed. I inserted USB-flash to my laptop. It was automounted to /media/username/DISKLABEL and opened in Nautilus. I can read and write objects to it. How can I access it from the application, which is installed as Snap? I tried snaps of the following applications such as gedit, arduino-mhall119, organize-my-files. All them show me errors if I navigate to /media folder:    Could not read the contents of Media Error opening the directory of '/media': permission denied  Output of active Snap  is below: $ snap interfaces  | grep -v ".*-$" Slot                             Plug :browser-support                 organize-my-files :core-support                    core:core-support-plug :cups-control                    gedit :desktop                         gedit,organize-my-files :desktop-legacy                  gedit,organize-my-files :gsettings                       gedit,organize-my-files :home                            arduino-mhall119,gedit,organize-my-files :network                         arduino-mhall119,gedit,organize-my-files,pulsemixer :opengl                          organize-my-files :pulseaudio                      organize-my-files,pulsemixer :unity7                          arduino-mhall119,gedit,organize-my-files :wayland                         gedit :x11                             arduino-mhall119,organize-my-files,pulsemixer gnome-3-26-1604:gnome-3-26-1604  gedit gtk-common-themes:gtk3-themes    gedit gtk-common-themes:icon-themes    gedit gtk-common-themes:sound-themes   gedit -                                arduino-mhall119:serial-port -                                gedit:avahi-observe -                                gedit:mount-observe  Updates:  connecting mount-observe to Gedit with snap connect gedit:mount-observe does not help. it seems that we need special Snap with support of  interface.


Let $a,b,c,d \in \mathbb{Z}$. If $\gcd(ac,bd)=1$, then $\gcd(a,b)=\gcd(c,d)=1$? Couldn't find any counterexample for that affirmation, all I can find is examples of it working. Like we having: $$\gcd(24,35)=1 \text{ and } \gcd(4,5)=\gcd(6,7)=1 $$ How can I prove it?

So far I have that $a|b$ implies $b=ax$ for some x in the integers and $c|d$ implies that $d=cy$ for some y in the integers.  From here I can see that $gcd(a,c)|gcd(b,d)$ is logically equivalent to $gcd(a,c)|gcd(ax,cy)$ but I am not sure where to go from there.


I have been provided with the following sentence by a native English speaker  Successful coalitions carefully choose the brands that they think are the best fit for their programme both in terms of value and benefit to their customers.  I am not a native English speaker so a bit hesitant to point out that the correct placement of the word "both" should be as below. Am I right?  Successful coalitions carefully choose the brands that they think are the best fit for their programme in terms of both value and benefit to their customers.

Truffles are among the world’s most valuable commodities, in terms of both economic and ecological worth. Truffles are among the world’s most valuable commodities, both in terms of economic and ecological worth.   Is one preferred over the other?  If so, why? A colleague indicated that 'both in terms of' was grammatically incorrect, but could not state why.


Currently, when I restart from Windows to Ubuntu, or if I hibernate Windows and boot Ubuntu, I can't access my Windows partition.  I have to restart from Ubuntu to Windows, then shut down Windows, then boot Ubuntu again.  Is there another way around this?  Error mounting /dev/sda5 at /media/user/Windows8_OS: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda5" "/media/user/Windows8_OS"' exited with non-zero exit status 14: Windows is hibernated, refused to mount. Failed to mount '/dev/sda5': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option.

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


I'm an intern in a company that sells about 900 products.   We are trying to forecast our sales for the next year. I already have the monthly data for the 3 previous years, cleaned it, and analysed the trends plus various kinds of seasonality.   I tried both Holt-Winters and SARIMA. I ran quite a lot of tests through Excel plugins PEERforecaster and Real-Statistics, plus a manual Excel model developped by Régis Bourbonnais, PhD to compute the data with Holt-Winters, and the automatic forecasting method included in Excel 2016.   Of everything, the automatic excel forecasting method included in Excel 2016 seems to be the most accurate, but works only for very few products.   Did I miss anything ? Is there anything that I should try instead ?  If you could give me any guidance, I would be grateful. Thank you.

Imagine a standard machine-learning scenario:     You are confronted with a large multivariate dataset and you have a   pretty blurry understanding of it. What you need to do is to make   predictions about some variable based on what you have. As usual, you   clean the data, look at descriptive statistics, run some models,   cross-validate them etc., but after several attempts, going back and   forth and trying multiple models nothing seems to work and your   results are miserable. You can spend hours, days, or weeks on such a   problem...   The question is: when to stop? How do you know that your data actually is hopeless and all the fancy models wouldn't do you any more good than predicting the average outcome for all cases or some other trivial solution?  Of course, this is a forecastability issue, but as far as I know, it is hard to assess forecastability for multivariate data before trying something on it. Or am I wrong?   Disclaimer: this question was inspired by this one  that did not attract much attention. It would be nice to have detailed answer to such question for reference.


I am a little bit confused on the first principal directions. Say I have three points in a two dimensional euclidean space: (1,1), (2,2), and (3,3) and I want to calculate the first principal component.  First I see that the center is (2,2) so I move all points to the origin. Now (2,2) is like (0,0) and (1,1) is (-1,-1) and (3,3) is (1,1). This is the mean shift. Now, I know that the first principal component is $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})^{T}$ from matlab. But, how is it calculating this? What does this mean?  Do you compute the covariance matrix then find the eigenvalues then the eigenvectors. This eigenvector is the direction? Then you normalize?  So we have our points after the mean shift at (-1,-1), (0,0), and (1,1). We now compute the covariance matrix  c(x,x) c(x,y)  c(y,x) c(y,y)  which is [0 1; 0 1] we then look at the largest eigenvalue 1 and compute the eigenvector which is [1;1]. Then we normalize so divide by $\sqrt{1^2 + 1^2}$?

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.   I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it.        I strongly believe in the following quote:     You do not really understand something unless you can explain it to your grandmother. -- Albert Einstein   Well, I can't explain these concepts to a layman or grandma.   Why PCA, eigenvectors & eigenvalues? What was the need for these concepts? How would you explain these to a layman?


I have made my own Morse Code translator where you can enter the code and the corresponding letter prints out. However, what I want to do is that whenever I enter a letter, the code prints out. Here's my code:  MorseCode = {'.-':'A',             '-...':'B',             '-.-.':'C',             '-..':'D',             '.':'E',             '..-.':'F',             '--.':'G',             '....':'H',             '..':'I',             '.---':'J',             '-.-':'K',             '.-..':'L',             '--':'M',             '-.':'N',             '---':'O',             '.--.':'P',             '--.-':'Q',             '.-.':'R',             '...':'S',             '-':'T',             '..-':'U',             '...-':'V',             '.--':'W',             '-..-':'X',             '-.--':'Y',             '--..':'Z',             '.----':1,             '..---':2,             '...--':3,             '....-':4,             '.....':5,             '-....':6,             '--...':7,             '---..':8,             '----.':9,             '-----':0 }  print "Type 'help' for the morse code." print "Type 'end' to exit the program.\n" while True:     code = raw_input("Enter code:")     if code in MorseCode:         print MorseCode[code]   So the question is: Is there a way to somehow invert this dictionary so whenever I enter 'A', '.-' will print out? I'm only studying python for two weeks now so I'm still mastering the basics before I move on to the more advanced levels. Thank you!

Given a dictionary like so:  my_map = {'a': 1, 'b': 2}   How can one invert this map to get:  inv_map = {1: 'a', 2: 'b'}


I would like to get the elevation of different point in the digital elevation model means around 4000 points would any one please tell me how can it be possible.

I have an ArcMap 10 project with multiple layer groups. One layer is a raster DEM, another layer group is a bunch of vector shapefiles (including points, lines and polygons). The client wants all vector data to contain Z values.  Populating the attribute tables for the vector data with X and Y values is easy enough but how do I populate the Z values?   Is there a way that I can use Field Calculator to "grab" the height values from the DEM layer for each vector feature?   I should add that we don't have a licence for the 3D Analyst or Spatial Analyst extensions.


I had a working view. I have tried to modify it by removing the the relationships then it crashes. Now I am not able to edit the view.  How to revert back the previous changes of view.  Here is the error appearing in edit page of view  Notice: Undefined index: field_product_overview in Drupal\views\Plugin\views\HandlerBase->getEntityType() (line 700 of core/modules/views/src/Plugin/views/HandlerBase.php). Drupal\views\Plugin\views\HandlerBase->getEntityType() (Line: 250) Drupal\views\Plugin\views\field\EntityField->access(Object) (Line: 1047) Drupal\views\ViewExecutable->_initHandler('field', Array) (Line: 898) Drupal\views\ViewExecutable->initHandlers() (Line: 1230)

This is one of those times when I tried to add something and realized that I've got it applied to all displays. This time it was a vocabulary filter, so I clicked cancel and it didn't register so I clicked back to site.  After that I tried to edit and it returned     The website encountered an unexpected error. Please try again later.   The log shows this:     Exception: No entity type for field vid on view VIEW in   Drupal\views\Plugin\views\HandlerBase->getEntityType() (line 712 of   /PATH/core/modules/views/src/Plugin/views/HandlerBase.php).   I checked the active config and couldn't find anything with a vid. Clearing cache and reimporting the view config didn't fix it. So, is there a way?


What's the use of C# keyword fixed/unsafe?  For example,   using System;  class Program {     unsafe static void Main()     {         fixed (char* value = "sam")         {             char* ptr = value;             while (*ptr != '\0')             {                 Console.WriteLine(*ptr);                 ++ptr;             }         }     } }   Why do I need to fix it in the first place? Thanks

Can someone give an example of a good time to actually use "unsafe" and "fixed" in C# code? I've played with it before, but never actually found a good use for it.   Consider this code...  fixed (byte* pSrc = src, pDst = dst) {     //Code that copies the bytes in a loop }   compared to simply using...  Array.Copy(source, target, source.Length);   The second is the code found in the .NET Framework, the first a part of the code copied from the Microsoft website, .  The built in Array.Copy() is dramatically faster than using Unsafe code. This might just because the second is just better written and the first is just an example, but what kinds of situations would you really even need to use Unsafe/Fixed code for anything? Or is this poor web developer messing with something above his head?


I've spent all my morning trying to get rid of all fireflies in the final render, but the result still shows too much noise. How can I fix it (without changing materials)?  Thank you.

I know that this question is a bit old or maybe overdone, but I'm running the latest edition of Blender and when I use the Cycles engine I get really fuzzy results and I can't find a simple, non-compromising solution to the quality.  I don't know exactly what I'm doing wrong here, but I'm sure others share my frustration.  Leaving everything in default settings, I started a new project and switched to the Cycles render.  I duplicated the cube and set colors for two Diffuse BSDF shaders, then went ahead and made walls and a floor all sharing the same diffuse shader.  I made two windows to emit blue light.  The screenshot has gaps between the walls because of the setup:  I'm aware that it's considered very incomplete and many have come to terms with some amount of noise, but is this normal?  Furthermore, with default settings or not, I can't change the amount of noise produced.  Supposedly, using "progressively refine" in the rendering tab should make it refine itself indefinitely, however Cycles only counts to 10 refines and then stops, creating a render which is a pixel-perfect match of the ordinary rendering method when it's completed.  I understand that there are tricks that can be used to reduce noise, but at the cost of extra processing time and usually small quality conflicts, like blurring.  My question essentially boils down to is this Cycles' current limit?


How does one draw a horizontal parabola, left or right oriented? I can easily draw:  \draw[blue, line width=1.75pt, domain=-2.00 : 3.00, samples=1500] plot[smooth](\x, {\x*\x - \x - 2});   and even trick a horizontal parabola in origin using two radicals:  \draw[magenta, line width=1.75pt, domain={0.00}:{3.0}, samples=1500] plot[smooth]( \x, {pow(\x, 0.5)} ); \draw[magenta, line width=1.75pt, domain={0.00}:{3.0}, samples=1500] plot[smooth]( \x, {- pow(\x, 0.5)} );   But I cannot make it do this (true horizontal parabola):  \draw[red, line width=1.75pt, domain={-4.10}:{4.0}, samples=500] plot[smooth]( \y, {\y*\y - \y - 2} );   Any idea? Here's my MWE:  \documentclass{standalone}  \usepackage{mathtools} %includes amsmath \usepackage{mathabx} \usepackage{tikz} \usetikzlibrary{patterns,calc,arrows} \usepackage{pgfplots} \pgfplotsset{compat=1.10} \usepgfplotslibrary{fillbetween}  \begin{document}  \begin{tikzpicture}[>=triangle 45, cap=round]  \draw[->] (-4.0,0) -- (4.0,0); % Ox \node[below] at (4.0, 0.0) {\textit{x}}; \node at (-0.2,-0.3) {\textit{0}}; \draw[->] (0,-4.0) -- (0,4.0); % Oy \node[left] at (0.0,4.0) {\textit{f(x)}}; \filldraw [red] (0.00, 0.00) circle(3pt);  \draw[blue, line width=1.75pt, domain=-2.00 : 3.00, samples=1500] plot[smooth](\x, {\x*\x - \x - 2}); %\draw[red, line width=1.75pt, domain={-4.10}:{4.0}, samples=500] plot[smooth]( \y, {\y*\y - \y - 2} );  \draw[magenta, line width=1.75pt, domain={0.00}:{3.0}, samples=1500] plot[smooth]( \x, {pow(\x, 0.5)} ); \draw[magenta, line width=1.75pt, domain={0.00}:{3.0}, samples=1500] plot[smooth]( \x, {- pow(\x, 0.5)} );  \end{tikzpicture}   \end{document}

pgfplots is not quite comfortable plotting sqrt(x) near x=0. The graphic can be improved by setting samples=2000 (not less), but this seems overkill to me.  Is there a way to plot x as a function of y, while keeping the x axis horizontal and the y axis vertical? This would solve the issue of plotting sqrt(x) by simply replacing it with x=y^2.  \documentclass{article}  \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture}  \begin{axis}   \addplot[] {sqrt(x)};   \addplot[] {-sqrt(x)};  \end{axis} \end{tikzpicture}  \end{document}


Could someone explain why my variable x returns to it's former ID after these steps:  >>> x = 10 >>> id(x) 497834400 >>> x = str(x) >>> id(x) 48840576 >>> x = int(x) >>> id(x) 497834400

Why does the following behave unexpectedly in Python?  >>> a = 256 >>> b = 256 >>> a is b True           # This is an expected result >>> a = 257 >>> b = 257 >>> a is b False          # What happened here? Why is this False? >>> 257 is 257 True           # Yet the literal numbers compare properly   I am using Python 2.5.2. Trying some different versions of Python, it appears that Python 2.3.3 shows the above behaviour between 99 and 100.  Based on the above, I can hypothesize that Python is internally implemented such that "small" integers are stored in a different way than larger integers and the is operator can tell the difference. Why the leaky abstraction? What is a better way of comparing two arbitrary objects to see whether they are the same when I don't know in advance whether they are numbers or not?


One process in particular is using a lot of CPU (100% and raising temps to 95C) which needs to run for long period of time(~3 hrs). Using this  helped limit the usable bandwidth of CPU to 50%. But unfortunately it slowed that process considerably(~9hrs), is it ok if I raised the CPU rate limit to higher number mid process.  Process does not allow changing affinity or priority!

I have noticed that from some time my system is freezing and its probably caused by the high CPU usage which is caused by the system process.  All applications I'm running is the Skype, TeamSpeak and Chrome so it definitely shouldnt eat that amount of CPU.  You can see the problem itself and running processes in the screenshot below:    Sometimes CPU usage is reaching 90%, but the average usage is like 40-65%.  My PC parameters:   Windows 8 (customer preview) Intel Core i3 - 2350M 8 GB RAM   I'd appreciate any help attempt! Regards.  --UPDATE--  As the user below posted a great answer, I have noticed that the process that is eating the most CPU in the system is called Arthurx.sys, simple google tells that it's a TPLink driver (an wifi adapter, I have bought like 2 weeks ago!) drivers has been installed from the Windows MSDN, but also tried to install the drivers from the attached CD, but it doesn't help. From the system start, it is using like 5% of the CPU only, but after 2-4 hours of working it is growing up and reaching 40-60% of the CPU usage.  Device name: TPLink WN722N


I've found myself in quite the unusual situation, through my own thoughtlessness. Using a computer of which I do not have an (or the) administrative account on, went to msconfig, to 'boot' and selected the option to force the computer to launch in safe-mode.  Now, as of restarting the computer, it launches in safe-mode though I am then requested to log in, before I can return to the dialogue and deselect the safe-mode option. However, as I explained, this is not quite possible.  Are there any buttons I can press when the computer is launching that will give me an option to return to standard booting? I am not to use any methods such as using a restore point, restoring to factory default, deleting the administrator's account, create a new administrator account, change the password, etc. etc. - I am simply wondering if there is a method to achieve a standard boot-up, probably using an F1-12 key, and what it would be.  Many features on my environment have been disabled, so even if an answer is proposed there is a chance I will be unable to use it. Therefore, the more alternatives the better, granted they do not violate the above examples.  Using - Windows 7, Acer Travelmate B113.

I was not able to boot in safe mode on my Windows 7 PC, so I went into boot manager and checked off boot into safe mode to see if that would fix the issue. Unfortunately it did not, and now my PC seems only to be able to keep trying to boot into safe-mode. Is there a way to set it back to regular normal boot from outside of Windows?


In Java, How do I get the current index for the element in Java?  for (Element song: question){     song.currentIndex();         //<<want the current index. }   In PHP you could do this:  foreach ($arr as $index => $value) {     echo "Key: $index; Value: $value"; }

Is there a way in Java's for-each loop  for(String s : stringArray) {   doSomethingWith(s); }   to find out how often the loop has already been processed?  Aside from using the old and well-known for(int i=0; i < boundary; i++) - loop, is the construct  int i = 0; for(String s : stringArray) {   doSomethingWith(s);   i++; }   the only way to have such a counter available in a for-each loop?


Not , but ... single or multiple repositories, GitHub-style documentation, etc.

There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.


I cannot find a way to install Avast Internet Security 6.0.1367.exe from the exe file directly.  I would like to know how to install it on my computer, to know the right commands to install it from terminal.

What antivirus programs are available for Ubuntu?  We previously used Symantec Endpoint Protection but it does not work in Ubuntu.


According to my knowledge dy/dx is not a ratio. Then while solving the problems of integration by substitution how can we use it as ratio. Because of we have dx/dt =f(x). Then while shoving it by substitution why do we take it as dx=dt•f(x).

In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $dy/dx$ is not a ratio. Couldn't it be interpreted as a ratio, because according to the formula $dy = f'(x)dx$ we are able to plug in values for $dx$ and calculate a $dy$ (differential). Then if we rearrange we get $dy/dx$ which could be seen as a ratio.   I wonder if the author says this because $dx$ is an independent variable, and $dy$ is a dependent variable, for $dy/dx$ to be a ratio both variables need to be independent.. maybe?


I am currently trying to label an line in an align* environment using \tag; however, the tag appears on the left side of the line instead of on the right. How do I move this label to the right side?  Thank you!   %latex \documentclass{amsart} \usepackage{amsmath} \usepackage{amssymb} \usepackage{pgfplots}  \begin{document} \begin{proof}     We begin by formulating the profit maximization problem and taking the first order condition.     \begin{align*}         \max_q \left(pq-C(q)\right) \\         \max_q \left(pq-10q-q^2 \right) \\         \frac{\partial \pi}{\partial q}=p-10-2q=0 \tag{First-Order Condition}     \end{align*}     We then formulate market balance by substituting $nq$ in for $Q$.     \begin{align*}         p=100-6Q \\         p=100-6nq \tag{Market Balance}     \end{align*}     Lastly, we write the expression for profits for a firm and set this equal to zero.     \begin{align*}         pq-C(q)=0 \\         (100-6nq)q-10q-q^2=0 \tag{Equilibrium Entry}     \end{align*} \end{proof} \end document

I am new to TeX and am using  to write a maths paper. When I put the followng code, the equation number is automatically displayed on the left, instead of in the right as is usually done. What is the problem and how do I fix it?  \documentclass[12pt,oneside]{amsart} \usepackage{amssymb} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \begin{document} Let us consider a spherical symmetric metric in curvature coordinates: \begin{equation}  \label{metric} ds^2=-e^\lambda dr^2-r^2(d\theta^2+\sin^2\theta d\phi^2)+e^\nu dt^2 \end{equation} \end{document}   The output I get is


The problem is described in the picture, the solution is suppose to be a constructive proof, so you need to find an algorithm that works regardless of stuff like running time. Any help would be grate I can’t solve this and I’ve trying for a while EDIT: My main direction was changing the sign on every raw with negative sum, now every raw is complete and the sum of all entries is nonnegative (since the sum of all raws is now nonnegative)

Real numbers are written on an $m\times n$ board. At each step, you are allowed to change the sign of every number of a row or of a column. Prove that by a sequence of such steps, you can always make all row sums and column sums non-negative.   I am supposed to find an algorithm to prove this statement. Nevertheless, I tried induction on $m$ and $n$, but that did not work out well.  My first instinct was to make all the row sums non-negative. Now, we start to make the column sums non-negative. Take the first column. Call it $C_1$. If it is already non-negative, then move on. If not, then switch the sign of every number in this column. Note that this might make some row sums negative. Let these rows be called $R_1,\cdots R_k$. Note that after the switch, $C_1\cap R_i$ must be a negative number. To see why this is so, simply assume to the contrary and note that if it were positive, the row sum of $R_i$ has increased from its previous value, and hence can't be negative. So switch all the $R_i$. Clearly, this makes all the rows non-negative again. $C_1$ also remains non-negative, because switching all the rows turn the $C_1\cap R_i$ into positive numbers, and hence the column sum of $C_1$ increases, and hence remains non-negative.  I have also figured out an algorithm to turn the second row non-negative without altering any of the rows or the first column, but I am stuck here.  I also thought about using the extremal principle. Simply consider the configuration of the board which maximizes the number of positive rows and columns, but I haven't been able to proceed.  Any help will be appreciated.


Ash/Satoshi is the Alola region's Champion, so in the episode where he went back to Alola, I expected that someone would refer to him as the Alolan Champion, but nobody did. In another recent episode, Ash went back to the Unova region to fight Iris, and it was revealed there that Iris is now the Unova region's Champion, but Ash never tells her that he is also now a Champion. Why isn't Ash's Pokémon League win ever acknowledged?

I was watching Pokemon Sun Moon. In the answer to this question  it says that Ash never age so obviously he didn't became child.  But why did he need to go to Poke-school? He knows a lot on Pokemon and he went on till the finals in last league (Kalos)


Can you use the Adobe Creative Clouds apps, the desktop version, on an iPad Pro?  Possibly through mirroring the display ( desktop to iPad)?

Are there and apps/programs that allow an iPad to be used as a drawing tablet? I've tried Duet Display and Chrome Remote Desktop, which are great apps, but are not helpful with my situation. They don't allow you to click and drag with a stylus, pen, or finger - you can only click. I have a good drawing app on my iPad but it has limitations and my software is just sitting on my desktop unused. I do not like the Adobe apps available and I don't have a CC subscription anyways.


I understand question deletion by moderators, but I cannot understand why this question was deleted by the Community user:   Please could somebody explain this to me.

The  was deleted last night by the Community user.    Normally, I wouldn't see an issue with this, but for this particular deletion, I can see three issues:   We try not to delete good content There are multiple upvoted answers We often use previous answers on Meta (as well as badly asked questions) to form the precedent (and to use as duplicates) when users ask questions like this in the future   On a personal note, I find it easier to link to one of my previous answers whenever possible.  This seems like a bug with the deletion algorithm, , the deletion algorithm should never delete questions with upvoted answers.  I'm going to go ahead and undelete it, but I'm bringing this up in case there was either:    A policy change A bug   So is it either of the above or something else?


I wish to find out the class of compact sets in $\mathbb{R}$ which are supports of continuous functions.  To my solution I have an idea that the support will be finite union of closed and bounded sets in $\mathbb{R}$ but I am not sure about the answer and if it is correct then i have no explicit form to prove it. can anyone help me in doing so.

An exercise of Rudin's Real and Complex Analysis says:     Is it true that every compact subset of $\mathbf{R}^1$ is the support of a continuous function? If not, can you describe the class of all compact sets in $\mathbf{R}^1$ which are supports of continuous functions? Is your description valid in other topological spaces?   I proved that, in every metric space, a set (not necessarily compact) $A$ is the support of a continuous function if and only if it is the closure of an open set.  However, I don't think that this characterization holds for every topological space.  So, in order to find a counter-example, I tried to use the discrete and the trivial topologies. However, the discrete topology is metrizable and this characterization holds for topological spaces with the trivial topology.  Is this result true for any topological space? If not, what would be a counter-example?


Can no longer scale objects in object-mode though it works in edit-mode. I feel like I noticed the appearance of these gray nodes around the 3D view around the same time that these issues began occurring.

My issue is that I have a blender file in which cameras and lamps do not move when I attempt to rotate them using the mouse. If I select the objects (in object mode), press R, and move the mouse in the viewport, the lamps and cameras don't respond; they remain in the same orientation as when I started, no matter how vigorously I try to move the mouse. The values in the information bar show that the mouse is communicating. If, however, I manually enter a new value for the amount of rotation in the properties shelf of the viewport, the camera moves to the new orientation.  On a new default Blender scene, the cameras and lamps do respond to commands to rotate and scale using the mouse. I've compared all of the settings I can think of, and don't see anything obvious that corrects the problem.   is available.


I have a long equation (but that fits in just one line), with three terms:  \begin{equation*}\label{eq:threeterms} A = \underbrace{A_1}_{(1)} + \underbrace{A_2}_{(2)} + \underbrace{A_3}_{(3)}. \end{equation*}   The equation is not numbered, as it barely fits on the line, and I use hand-written references $(1)$, $(2)$ and $(3)$ in all the text to refer to the three terms. I would like to be able to define three (non displayed) tags for the three terms, and refer to them with \eqref{eq:term1} (etc), to have a nice link to the equation and not just the text $(1)$.  Is this possible? I tried naively with three \tag{1}, \tag{2} and \tag{3} (or \tag*) commands but I cannot attain what I would like.

I would like to tag two parts of a huge equation using underbraces (and call them, say term A and term B).  Later in the text, I want to talk about term A and term B.  Is there a way to tag and label A and refer to it using ref later?  Currently, I'm having to manually type in A, B, C, etc. and keep referring to check if I'm referring to the right tag.  \documentclass{article} \usepackage{amsmath} \usepackage{mathtools}  \begin{document}  \begin{equation*} \sum_{i=1}^n (i + i^2) = \underbrace{\sum_{i=1}^n i}_{A}  + \underbrace{\sum_{i=1}^n i^2}_{B} \end{equation*}  Later in the text, I want to talk about term A and term B.  Is there a way to tag and label A and refer to it using ref later?  Currently, I'm having to manually type in A, B, C, etc. and keep referring to check if I'm referring to the right tag.  \end{document}   I want to replace _{A} with something like _{\tag{A}\label{eq:term1}}.  And then, later in the text say Term~\ref{eq:term1} is blah blah blah (where of course, blah blah blah is $n*(n+1)/2$.)


I want to calculate the sum \begin{align*}    \sum_{k=1}^{n-1} \frac{1}{k(n-k)}. \end{align*} I already tried some things but I think it has a nicer form than \begin{align*}    \sum_{k=1}^{n-1} \frac{1}{k(n-k)} = \sum_{k=1}^{n-1}  \frac{1}{n}\bigg(\frac{1}{k} + \frac{1}{n-k}\bigg) = \frac{2}{n}\bigg(H_n - \frac{1}{n}\bigg). \end{align*}

I am trying to compute $$\sum_{k=1}^{n-1} \frac{1}{k(n-k)}$$ using a term by term partial fraction decomposition and also with generating functions, but I'm stuck.


Could you please provide me with a book of calculus containing the concepts of trigonometry, hyperbolic functions, and complex numbers? thank you very much.

This question is a  of the common question asking for calculus references. It is here to  away the repetition, and give a canonical resource for calculus references.      I'm looking for a resources to learn single-variable calculus.


I have a Python script which takes command line arguments.  When I want to run the script I have to navigate to its directory and run:  python myscript.py [arguments]   How can I run it like:  myscript [arguments]   Do I have to create a package? If so, how?

Hi I would like to run a script from the terminal, is there anyway to do that? For example : if I have a python script I would normally run it with this command :    python script.py   How can I run this script just by typing in the filename of the script in the terminal (even if i'm in another directory) ?  Another answer I found pretty helpful :    You can just create symlink. Create it in /usr/local/bin. All you need is to run command:  sudo ln -s /full/path/to/your/file /usr/local/bin/name_of_new_command   After that you should make your file executable:  chmod +x /full/path/to/your/file   Now you should be able to run name_of_new_command at any time in your terminal.  Note that this is good solution only for home usage of Linux.


In this curve, there's a pretty big difference between validation and training accuracy in the end. Does that mean it's overfitting?

Consider error of hypothesis h over training data errortrain(h) and error over entire distribution D of data errorD(h). Hypothesis h in H overfits training data if there exists an alternative hypothesis h´ in H such that:   errortrain(h) < errortrain(h´) errorD(h) > errorD(h´)   I am struggling to find literature on that topic.  Is there a more formal (or more detailed) definition of overfitting?


GA Z170-HD3P-mobo Intel 6500 3.2 - CPU NVIDIA Gtx 770 - GPU 250GB SATA - hard drive 750W - PSU some fans OS Ubuntu 16.04 LTS    Although I've read that all the hardware is compatible, Ubuntu is not recognizing the GPU and when I go to the NVIDIA GEFORCE website for the most recent driver for this card and run the file it tells me that there was an error in the Text to run the file.   After attempting to install through ppa, i see a list of drivers in the "Software and Updates" to choose from. all binary drivers, however after selecting one and trying to apply the changes, when done the changes are not made and it is still stuck "using X.Org X server-Nouveau display driver from xserver-xorg-video-nouveau(open source)"   may i ask for some assistance on what i should do next?

I'm on Ubuntu 16.04 and I notice that in the "Additional Drivers" tab of "Software & Updates", the latest versions of NVIDIA drivers I can install are   version 367.57 from nvidia-367 (proprietary) version 370.28 from nvidia-370 (open source)   Aside from the fact that I don't know what "proprietary" and "open source" mean here, I also don't see an option to select the driver version based on my actual graphics card. I'm using GTX 1080 and the current Long Lived Branch version is 375.20; will the Ubuntu graphics PPA be updated eventually, or will I have to manually install 375?


I want to center a div container on a page, in the css I am using  margin-left:auto;   does not seem to work.  Anything goes here  Thanks

How can I horizontally center a
 within another
 using CSS?

Foo foo


My wife has several files and folders that somehow ended up having filenames that have caused them to be undeleteable (can't be deleted) by normal means or via the command line. I believe the filenames are too long due to the depth of the folder structures. Does anyone know of a good utility for cleaning up files like this?

Windows seems to have a length limit on file names when trying to delete, though it won't prevent those files from being created.  Our build process creates a number of temporary files (many build off of a WSDL) that run afoul of this limit.  Our ant script is somehow able to delete them when doing a clean, but sometimes I need to delete the workarea directory (where all the temp files go) without actually doing a full clean from ant.  This is the same errors , but the answers there don't really work for me as I'm dealing with a directory, not a file, and I don't always know what specific files or subdirectories are causing the problem.  And I'm trying to avoid any manual process (other than triggering a single command) to actually delete them.  If I try deleting the directory from Explorer I get the error   Cannot delete [file name]: The file name you specified is not valid or too long.   Specify a different file name   Trying Remove-Item in powershell gives the following error:  Remove-Item : The specified path, file name, or both are too long. The fully qualified file name must be less than 260 characters, and the directory name must be less than 248 characters. At line:1 char:12 + Remove-Item  <<<< -force -Recurse <directory>   Does anyone know of any tools or easy ways to get around this delete error without having to manually find the problem files and move/rename them?


If I have two algebraic numbers $\alpha,\beta$ such that $A(\alpha) = 0$ and $B(\beta)=0$ where $A,B \in \mathbb{Q}[x]$ are the minimal polynomials of $\alpha$ and $\beta$ respectively. Knowing only the coefficients (and degree) of $A$ and $ B$ is there an algorithm for generating the minimal polynomial of $\alpha+\beta$?  I asked a professor and he recommended computing powers of $A(x) + B(x)$ and claimed there was a way to reduce it to get the appropriate polynomial however I'm not seeing his method.

Suppose $E/F$ is a field extension and $\alpha, \beta \in E$ are algebraic over $F$. Then it is not too hard to see that when $\alpha$ is nonzero, $1/\alpha$ is also algebraic. If $a_0 + a_1\alpha + \cdots + a_n \alpha^n = 0$, then dividing by $\alpha^{n}$ gives $$a_0\frac{1}{\alpha^n} + a_1\frac{1}{\alpha^{n-1}} + \cdots + a_n = 0.$$     Is there a similar elementary way to show that $\alpha + \beta$ and $\alpha \beta$ are also algebraic (i.e. finding an explicit formula for a polynomial that has $\alpha + \beta$ or $\alpha\beta$ as its root)?    The only proof I know for this fact is the one where you show that $F(\alpha, \beta) / F$ is a finite field extension and thus an algebraic extension.


For $\varepsilon$-$\delta$ proofs, basically we need to find a $\delta$ such that $|F(x)-L|<\epsilon$ whenever, $0<|x-a|<\delta$ (for a small positive number $\epsilon$).  To prove L'Hospital's rule (for when numerator and denominator function both tend to $0$ as $x\rightarrow a^{+}$)  let us assume $F(x)=\frac{f(x)}{g(x)}$. Where, $\lim_{x\rightarrow a^{+}}f(x)=0$ and $\lim_{x\rightarrow a^{+}}g(x)=0$.   I claim that $L=\lim_{x \rightarrow a^{+}}\frac{f'(x)}{g'(x)}$. Now I need to prove this $L$ is indeed the limit.  $$\left|\frac{f(x)}{g(x)}-\lim_{x \rightarrow a^{+}}\frac{f'(x)}{g'(x)}\right|<\epsilon.$$  But after this I cannot understand how to find $\delta$ as a function of $\epsilon$, so that I can complete the proof. How should I proceed?

The following is an excerpt from Bartle and Sherbert's Introduction to Real Analysis:        Okay. I am having a little trouble following this proof. What is $c$ and why is it in $(a,b)$? What confuses me is that there is no reference to any $\delta$ nor any reference $x$ such that $0 < x - a < \delta$. They just simply write $L - \epsilon \le \frac{f(\beta)}{g(\beta)} \le L + \epsilon$ and claim that the conclusion follows. I suspect they are using $\beta$ in place of $x$, but this still doesn't account for the absence of a $\delta$ and why $\beta$ wouldn't satisfy $0 < \beta - a < \delta$.   On second thought, perhaps $\beta$ and $c$ are intended to stand for the typically used $x$ and $\delta$, respectively. It seems that what the authors have shown is that for every $\epsilon> 0$, there exists a $c > 0$ such that if $\beta$ satisfies $a < \beta \le c$, then $|\frac{f(\beta)}{g(\beta)} - L| \le \epsilon$. Even on that interpretation, why is $c$ (i.e., $\delta$) in $(a,b)$? In fact, if $a$ and $b$ are negative, this doesn't make much sense...  EDIT:  Okay. I think I follow what you, @Jack, are saying. However, there is one last thing giving me trouble. Just before equation (2), the authors claim that there exists a specific $u \in (\alpha, \beta)$ by the Cauchy Mean Value theorem such that equation (2) holds. Now, in order to validly substitute this in the inequality below (2) to obtain inequality (3), we need that that specific $u$ is in $(a,c)$, but this has not been demonstrated. All that we have is that if $u \in (a,c)$, then $L - \epsilon < \frac{f'(u)}{g'(u)} < L + \epsilon$, but how do we know that the specific $u$, guaranteed to exist by the Cauchy Mean Value theorem, falls in the interval $(a,c)$?  Also, it doesn't seem that we merely want to assume that $\beta \in (a,b)$ but that $\beta$ is arbitrary in $(a,c)$, right? Or may be it doesn't matter, since if we have "$\beta \in (a,b) \implies |\frac{f(\beta)}{g(\beta)} - L | <\epsilon$", then we would clearly have "$\beta \in (a,c) \subseteq (a,b) \implies |\frac{f(\beta)}{g(\beta)} - L | < \epsilon$". Am I thinking about this correctly?


Question      Let $n$ and $k$ be integers such that n is even, $n\ge2$ and $1\le k\le n$. You are having a party where $n$ students attended.       a) $k$ of these $n$ students are politically correct and, thus, refuse to say Merry Christmas.   Instead, they say Happy Holidays.      b) $n - k$ of these $n$ students do not care about political correctness and, thus, they say Merry Christmas.      Consider a uniformly random permutation of these n students. The positions in this permutation are numbered as $1,2,…,n$.       Define the random variable $X$,       $X$ = the number of positions with $i$ with 1<=$i$<=$\frac{n}{2}$ such that both students at positions $i$ and $2i$ are politically correct.       What is the expected value $E(X)$ of the random variable $X$? (Use indicator variables)      Options:      a) $n$ $.$ $\frac{k(k-1)}{n(n-1)}$      b) $n$ $.$ $\frac{(k-1)(k-2)}{n(n-1)}$      c) $\frac{n}{2}$ $.$ $\frac{k(k-1)}{n(n-1)}$      d) $\frac{n}{2}$ $.$ $\frac{(k-1)(k-2)}{n(n-1)}$      answer is c).   Attempt:  Indicator Variable:  $X$ $= 1$ if  $i$ with 1<=$i$<=$\frac{n}{2}$ such that both students at positions $i$ and $2i$ are politically correct.   $X=0$ for all other cases  We need $E(X)$ = $\sum_{k=0}^{n/2} k . p(k)$   We have $\frac{n}{2}$ positions? but I can’t seem to find $p(k)$  There’s so much information given in this question that Im confused on how to break it down beyond the basic initial expected value steps.

Question      Let $n$ and $k$ be integers such that n is even, $n\ge2$ and $1\le k\le n$. You are having a party where $n$ students attended.       a) $k$ of these $n$ students are politically correct and, thus, refuse to say Merry Christmas.   Instead, they say Happy Holidays.      b) $n - k$ of these $n$ students do not care about political correctness and, thus, they say Merry Christmas.      Consider a uniformly random permutation of these n students. The positions in this permutation are numbered as $1,2,…,n$.       Define the random variable $X$,       $X$ = the number of positions with $i$ with 1<=$i$<=$\frac{n}{2}$ such that both students at positions $i$ and $2i$ are politically correct.       What is the expected value $E(X)$ of the random variable $X$? (Use indicator variables)      Options:      a) $n$ $.$ $\frac{k(k-1)}{n(n-1)}$      b) $n$ $.$ $\frac{(k-1)(k-2)}{n(n-1)}$      c) $\frac{n}{2}$ $.$ $\frac{k(k-1)}{n(n-1)}$      d) $\frac{n}{2}$ $.$ $\frac{(k-1)(k-2)}{n(n-1)}$      I think the answer is c).   Attempt:  Indicator Variable:  $X$ $= 1$ if  $i$ with 1<=$i$<=$\frac{n}{2}$ such that both students at positions $i$ and $2i$ are politically correct.   $X=0$ for all other cases  We need $E(X)$ = $\sum_{k=0}^{n/2} k . p(k)$   We have $\frac{n}{2}$ positions? but I can’t seem to find $p(k)$  There’s so much information given in this question that Im confused on how to break it down beyond the basic initial expected value steps.


I need to determine all positive integer solutions for the equation:  $$\frac 1x + \frac 1y + \frac 1z + \frac 1{xy} + \frac1{yz} + \frac 1{xz} + \frac 1{xyz} = 1.$$  This is how I have tried to do it:   Mulitiplied both sides by $xyz$ to get $$yz+xz+xy+z+x+y+1=xyz.$$  Factor it: \begin{align} x(y+z+1-yz)+yz+y+z &= -1   \\ x(y(1-z)+z+1)+y(1+z)+z &= -1 \end{align}  If $z=0$, we get \begin{align} x(y+1)+y=-1 &\iff xy+x+y=-1   \\ &\iff (x+1)(y+1)=0, \end{align} which gives us $x=y=-1$.  Is this all positive integer solutions? Or have I missed something?  EDIT: I am stupid.   New attempt.   If $z=1$, I get $2x+2y=-2 \iff x+y=-1$.  Then there is no solutions of positive integers for both $x$ and $y$ at the same time.    If I try for $z=2$, I get \begin{align} x(y(1-2)+2+1)+y(1+2)+2=-1 &\iff x(3-y)+3y+2=-1   \\ &\iff 3x+3y+3-xy=0 \end{align} and I won't get a solution where all the variables are positive integers.

Can any one help me with this?  Determine all integer triples $(x,y,z)$ such that $1 ≤ x ≤ y ≤ z$ and $x + y + z + xy + yz + xz = xyz − 1$.  I thought of Vieta's formula but don't let me lead you into a dead end.


Using cat index.html | grep 'src.*js' I got these results:  <script src="/c/dam/cdc/j/adrum.js"></script> <script type="text/javascript" src="/c/dam/cdc/j/targeter-bundle_min.js"></script> <script type="text/javascript" src="/etc.clientlibs/clientlibs/granite/jquery.min.js"></script> <script type="text/javascript" src="/etc.clientlibs/clientlibs/granite/utils.min.js"></script> <script type="text/javascript" src="/etc.clientlibs/clientlibs/granite/jquery/granite.min.js"></script> <script type="text/javascript" src="/etc/clientlibs/foundation/jquery.min.js"></script> <script type="text/javascript" src="/etc/clientlibs/foundation/shared.min.js"></script> <script type="text/javascript" src="/etc.clientlibs/clientlibs/granite/lodash/modern.min.js"></script> <script type="text/javascript" src="/etc/clientlibs/foundation/personalization/kernel.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/clientlibs/responsive/js/foundation.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/dmr/context-banner/clientLib.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/dmr/libs/u.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/dmr/libs/nmsp.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/dmr/libs/log.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/dmr/libs/metrics.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/dmr/libs/utils/dynamic-video-init.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/dmr/libs/base.min.js"></script> <script type="text/javascript" src="/etc/designs/cdc/dmr/bundles/dmr.min.js"></script> <script src="/etc/designs/cdc/dmr/libs/dmimg.min.js"></script> <script src="/c/dam/assets/dmr/three-marquee/dmh-marq3_min.js"></script> 100 48065    0 48065    0     0   140k      0 --:--:-- --:--:-- --:--:--  140k<script type="text/javascript" src="/etc/designs/cdc/dmr/mosaic/clientLib.min.js"></script> <script id="sprinklr-embed-loader-1035-ZW1iZWQ6NWJjZjJhZDAxNjIzYWUxYTM0YzRlOTg0" type="text/javascript" src="https://gallery.sprinklr.com/clients/1035/embeds/ZW1iZWQ6NWJjZjJhZDAxNjIzYWUxYTM0YzRlOTg0/script.js"> <script type="text/javascript" src="/etc/designs/cdc/clientlibs/responsive/js/homepage.min.js"></script>   But I want to extract the strings that begin with src= and end with .js.   Like this:  src="/etc.clientlibs/clientlibs/granite/jquery.min.js"

I am trying to find data from files using grep, but grep usually prints out the filename as well as the line where the term is found.  In this case, I am looking for a special regexp and I want grep to print all items matching the regexp, not the line or the filename. In other words, I want to see only the matched regular expression.


When the post title is long enough then such string occupies too much space in profile page on the post section. For example in :        As you can see the “Q” icon is obscured by the post score indicator, and post date is wrapped to two lines.

I think that the post date on user profiles looks messy: it sometimes looks right-aligned (as in the posts on October 2), and it sometimes ends up in a strange left-align (the dates which wrap into a new line). Can this be resized such that all dates show up in just one line, with everything right-aligned? I observed this on Vivaldi 2.0 and Brave 0.24 for Windows 10, on the Physics profile page of .


Tom Riddle says to Harry, that they are both probably the only Parselmouths in Hogwarts since Salazar Slytherin.  Parselmouth is said to be a rare gift, but is it really so rare? Are there really no mentions of other Parselmouths than those 3?

Was Salazar Slytherin the first Parselmouth, or did somebody else use it before him?  I’ve read the books, but I can’t find any examples.


$\max\{a,b\} = \frac12(a+b+|a-b|)$ and $\min\{a,b\} = \frac12(a+b-|a-b|)$  how would you go about solving this?  I started with suppose $a \leq b$  Also, show min{a,b,c} = min{min{a,b},c}.  How would I go about showing that?

Show that the $\max{ \{ x,y \} }= \dfrac{x+y+|x-y|}{2}$.   I do not understand how to go about completing this problem or even where to start.


Let $|a|>3$, $n\geq1$, $n\in\mathbb{N}$,    then the function $$f(z)=e^z-az^n$$    has exactly $n$ roots in the disc $\{z\mid|z|<1\}$, and that they are all simple.      Hint: look at $f(z)-f'(z)$   I am not sure how do I even approach proving existence of roots, rather then proving maybe that the function is not vanishing (and then it has logarithm, and root, but how do I show existence of n roots?)  I thought also of maybe using somehow Rouche's Theorem, since:  $$f(z)-f'(z)=az^{n-1}\cdot(n-z)$$  and from there, that showing that $f$ has $n$ roots in the disk.  Thank you!

Rouché theorem : Let $D \subset \mathbb{C}$ a domain and $f,g: D \to \mathbb{C}$ two holomorphic functions in $D$. Let $C$ a closed path contained in the interior of $D$. If $|f(z)+g(z)| < |f(z)|+|g(z)|$, $\forall z \in \mathbb{C}$, then $f$ and $g$ have the same number of zeroes in the interior of $C$.  Question : Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk.  So I've taken $f(z)=-az^n+e^z$ and $g(z)= az^n$ in using the closed path $C : |z|=1$. I obtained $|-az^n+e^z+az^n|= |e^z| \leq |-az^n+e^z|+|az^n|$, $\forall z \in C$. How could I prove that $|e^z| \not= |-az^n+e^z|+|az^n|$?


I am looking for such textbook or notes. Thanks in advance for sharing links or sites or any related questions!

What are some of the best books on graph theory, particularly directed towards an upper division undergraduate student who has taken most the standard undergraduate courses? I'm learning graph theory as part of a combinatorics course, and would like to look deeper into it on my own. Thank you.