Problem. Let $X$ be a non-empty set and $\beta$ be a  (in the linked definition of basis for a topology replace the term by basis set).  Then the set $\tau_\beta:=\left\{\displaystyle\bigcup_{B\in \beta_0} B: \beta_0\subseteq \beta\right\}$ forms a topology on $X$.   I have already shown that $\tau_{\beta}$ is a topology assuming that $\emptyset\in\tau_{\beta}$ but I can't show that $\emptyset\in \tau_\beta$. I think that it holds vacuously but I am not sure how to prove it. Can anyone help?

Indiscrete topology only has $\{\varnothing, X\}$ where $X$ is the entire space.  I know this is probably a dumb question. Why is the basis (according to wikipedia) for this topology just $\{X\}$ instead of $\{\varnothing, X\}$?  I understand that $\{X\}$ satisfies the definition. Suppose $\mathcal{B} = \{X\}$   Then $\mathcal{B}$ covers $X$ - Check! For all $B_1, B_2 \in \mathcal{B}, \ldots$ - Trivially satsifed since we don't have $B_1, B_2$   But how does this basis generate $\varnothing$?


i am Ambrose. I write from Nigeria. i tried to install acroread (Adobe reader) in ubuntu 18.04.2 LTS using a command i obtained from a You Tube video but something strange happened in the process. Presently, Sudo apt-get update does not work. if i do sudo apt-get update in the terminal, i get the the following; "E: malformed entry 51 in list file/etc/apt/sources.list(component)" "E: The list sources could not be read" Honestly, this is frustrating and this have hampered working with my machine and research.  Secondly, my machine (Laptop) can not detect Wifi in my place of work. Honestly, i bought the Laptop with Window 10 installed in it, but for the fact that my Ph.D research required me to use Ubuntu, the Window 10 was removed and Ubuntu 18.04.2LTS was installed and since then Wifi is not functional.  please, i need your assistance and help to solved the aforementioned problems. please, e-mail me to jerry410001@gmail.com  Thanks for your assistance.

I have unistalled and reinstalled the Ubuntu Software Center as per info I found in a similar thread and I got the same response about line 91 or something like that.  I just tried to upload a screen shot but since I'm new it won't allow me to.  I also can not figure out how to cut and paste anything so I have to hand type what the error screen says, both when I attempt to open the software center and nothing happens, when I try to enter commands into the terminal to uninstall, reinstall, whatever I get the same following:  COULD NOT INTITIALIZE THE PACKAGE INFORMATION An unresolvable problem occured while initializing the package information Please report t:his bug against the 'update-manager' package and include the following error message: 'E: Malformed line 91 in source list/etc/apt/sources.list (dist parse)  E: The list of sources could not be read.,  E: The package list of status file could not be parsed or opened.   How do I report bugs?  What can be done about this.  I have searched and everything everyone says to do leads me back to the same line error message.  So, I don't know how to get to line 91 in the source list; to tell you what it says. Sorry, I'm really new to this. That is what I need is to find out how to get there and fix what it says. I would really like to NOT have to re partition my hard drive and start from scratch, so I'm really looking forward to getting this problem solved. I need to be able to install new software.


My computer right now has Ubuntu 9.04, and I'm trying to install Ubuntu 14.10 using a bootable USB stick. If not mistaken, I did that process right, but the thing is when I boot the pen drive, a message shows up a little after:  SysLinux 3.64 Debian-2008-07-15 Ebios Copyright (c) 1994-2008 M. peter Anvin.   Missing parameter in configuration file.   Unknown Keyword in Configuration file.   Boot:   Now, 'Im using an old HP computer with the Windows Vista Basic sticker on it, not sure how old it is and what model, and I don't know if I'm making a mistake somewhere, does anyone know how to resolve this?

i'm on ubuntustudio and i want to format my hd and try kubuntu (install in my acer notebook, no partion, no double operating system problem, only istall it) i've downloaded iso file ( kubuntu-10.10-desktop-i386.iso ), insert usb pen drive, then: system > administration > startup disk creator erased usb pen content, and "make startup disk" finally, reboot computer with pen inside usb port  normal boot didn't start (as expected) but only black screen with this signal:  SYSLINUX 4.03 2010-10-22 EDD Copyright (c) 1994-2010, H. Peter Anvin et al unknown keyword in configuration file boot:   i've tried different usb pen stick and different iso files (ubuntu, kubuntu, netbook edition).. always same problem (sometimes only the first line without "unknow keyword in conf file" error)  some advice?? sorry for my bad english


Context of this question: This question follows from a post  and discusses on something different. Using calculation of variation we can find critical points of a function of a vaiable curve $\gamma$ with its end points fixed at $a,b$ and therefore defining geodesic on a manifold. (The rest of the paragraph is unnecessary reading for the question; it's mainly for the purpose of arranging my several posts on a topic.) Along the geodesic, exponential maps on a manifold project a tangent vector at a point $p$ (locally approximately linearly) to another point, as discussed here  (a related but different concept of exponential maps of Lie group is discussed here ). Geodesics have as such properties like the 'closed curve' {$\exp_p(v),\forall v$ of the same norm and belonging to $T_pM$} is perpendicular to all the geodesics passing through $p$, and is the shortest curve connecting $a,b$ (i.e. it's also a critical point for length). So we can say the 'closed curve' is very much resembles a circle, and a geodesic a radius or a straight line (We can perhaps even say that with geodesic and exponential maps we 'maps' projective geometry on to a manifold, similar to what we do when, with homeomorphism in definition of a manifold, we 'map' Euclidean space to a manifold). With the fact that geodesics is the shortest curve, we can define a metric (a measure of distance, NOT Riemannian metric which is an inner product and 2-tensor, as discussed here: ) on a manifold. The metric is homeomorphic to the original metric of the manifold, as discussed here . My question is as follows: A critical point of 'energy' (as Spivak calls it) $E(\gamma)=\int_a^b \langle \frac{d\gamma}{dt},\frac{d\gamma}{dt}\rangle dt$--where $\frac{d\gamma}{dt}$ is tangent vector along $\gamma$ at the point of $\gamma(t)$--is called geodesic. (I guess he uses the name 'energy' for in physics square of velocity is proportional to energy.) Why we define critical point for energy, instead of critical point for length $L(\gamma)=\int_a^b\sqrt{\langle \frac{d\gamma}{dt},\frac{d\gamma}{dt}\rangle} dt$, to be geodesic?

Is it true that applying the Euler-Lagrange equation to the integral  $E(\gamma)=\int_{t_1}^{t_2} g_{\alpha\beta}(\gamma^{\alpha})'(\gamma^{\beta})'\operatorname{d}\!t$ rather than the arc length integral $L(\gamma)=\int_{t_1}^{t_2} \sqrt{g_{\alpha\beta}(\gamma^{\alpha})'(\gamma^{\beta})'}\operatorname{d}\!t$ is just a mathematical trick for simplifying computation when parameterizing by arc length?  Isn't it true that if you are parameterizing a curve on a surface by something other than a constant multiple of arc length (for example, a curve $\mathbf{C}(x)=(x,y(x))$ in the parameter space of the hemisphere surface mapping $z=\sqrt{1-x^2-y^2}$), the critical point of $E(\mathbf{C})$ will not be a geodesic in general?


If you go in Google Analytics' Audience overview, you can Add segment:    Once done, click "Save". The new segment is now displayed:    Now close the browser, and open the browser again, Audience overview: the segment is no more there! You have to do Add segment once again manually!  How to add a segment once for all that will stay in Google Analytics' Audience overview?

I set up a segment that contains the data that my colleagues and I will want to be looking at 90% of the time. The All sessions segment contains superfluous data that we will generally not be interested in. However, every time I go to the GA, the All sessions segment is selected. I already know how to change/add the segments that I am looking at but is there a way for my segment to already be selected each time I arrive at GA?


When flagging a comment to be deleted, the possible flags are  "rude or offensive", "not constructive", "obsolete", "too chatty", and custom.  I'm trying to figure out what "not constructive" means in this context. AFAICT, there are two possibilities:  The comment is not particularly constructive. It doesn't add anything. In other words, roughly, it doesn't do what comments should do, viz attempt to clarify or improve the post or add relevant information. The comment is destructive. (In this view, "not constructive" is an instance of litotes, like "he's not very smart" to mean "he's quite stupid".)  Which leads me to three questions:  Which of those is the correct reading? If (as I suspect and as ) #1 is correct, then how is "not constructive" different from "too chatty"? They seem like synonyms. If (as ) #2 is correct, then can the flag be reworded from "not constructive" for clarity, please?

The problem Comments are terrible; no one agrees on what they're for, or how long they should be kept. Comment flags are equally terrible, because if no one's on the same page as far as what should be posted in the first place then no one can agree on what should be removed either. On top of that, we have this confusing set of flags where two mean "noise", one means "vile", one means "moderator, help!" and one means nothing at all - the end result is that it's all but impossible to even analyze comment flagging. The solution (or, part of it) Two years ago, in a fit of rage, I . Nothing got done. As always, everyone has a different idea of how things are supposed to work, and I'd bitten off more than I could chew. So, here we are, two years later, and comment flags still suck. So let's start by just cutting the fat: if we can trim down the list of flags to a set of clearly distinct problems, we might have something we can build on. Here's what I'm proposing, based on the past two years of discussion:   Re-word the "rude or offensive" flag to read,  rude or abusive: this comment violates .   Remove the "not constructive", "obsolete" and "too chatty" flags.  Add a new comment flag:  no longer needed: this comment is obsolete, chatty or otherwise unnecessary   Re-word the "other..." flag:  in need of moderator attention: these comments require action by a moderator. Be specific and detailed!    That's it; that's all I'm proposing to start out - simplify things so that we have something to build on. See also:


I get notifications of elections from every single community I've joined, even if it is just for a single question and I have no interest in the community whatsoever. I know that they don't come super often, but it is still annoying, since I see the badge on my inbox and think "Ooh, a new message, I wonder what it is?", but then disappointment that it was just a reminder for an election I'm not at all interested in.

Please add some way to opt out of moderator election notifications.  I don't have time to research who deserves my vote and therefore I will never vote.  Since I'm not taking part, I don't want election reminders to show up in my Stack Exchange inbox. They add up the more communities you take part in and almost every notification I've received in the last two months has been related to elections.


We know reputation is recalculated for questions. My reputation also increased in all the sites and updated in the hamburger where you put list of the sites.    My reputation on Science Fiction & Fantasy is also recalculated to 1547.    This change. still showing the old reputation. This is only the issue with a single site.   Should I blame the cache?

So just a little while ago i was flipping out because i was 2 rep away from my 10k rep goal    but then all of a sudden it was then 10,008 rep because someone upvoted me. however i didn't get any notification about this +10  [    now as you can see in the screenshots above, over the past 2 days i got 2 upvotes to a question i posted, however the notifications only shows 1 +10 notification. and they system knows i got the upvote because i knew that i now have access to mod tools.  I am on a Windows 10 Laptop using Chrome 78.0.3904.97 (Official Build) (64-bit)


In algebra, one lesson we took was about logic. We learned that it is a true statement or logical expression to say that if a Beijing was the capital of the US then the moon existed last night, as this is convenient with a false statement implying a true one being a true statement. Agree?

I am studying entailment in classical first-order logic.  The Truth Table we have been presented with for the statement $(p \Rightarrow q)\;$ (a.k.a. '$p$ implies $q$') is: $$\begin{array}{|c|c|c|} \hline p&q&p\Rightarrow q\\ \hline T&T&T\\ T&F&F\\ F&T&T\\ F&F&T\\\hline \end{array}$$  I 'get' lines 1, 2, and 3, but I do not understand line 4.      Why is the statement $(p \Rightarrow q)$ True if both p and q are False?  We have also been told that $(p \Rightarrow q)$ is logically equivalent to $(~p || q)$ (that is $\lnot p \lor q$).  Stemming from my lack of understanding of line 4 of the Truth Table, I do not understand why this equivalence is accurate.       Administrative note. You may experience being directed here even though your question was actually about line 3 of the truth table instead. In that case, see the companion question  And even if your original worry was about line 4, it might be useful to skim the other question anyway; many of the answers to either question attempt to explain both lines.


I'm reading through Derek Goldrei's "Propositional and Predicate Calculus" book and I've come across an exercise problem that states to show the derivation of "$\vdash{(\lnot\lnot{p}\to{p})}$" using these three axioms:  $$(\phi\to{(\psi\to{\phi}))}$$ $$((\phi\to{(\psi\to{\theta}))}\to{((\phi\to{\psi})\to{(\psi\to{\theta})})}$$ $$((\lnot\phi\to{\lnot\psi})\to{(\psi\to{\phi})})$$  As well as the deduction theorem. I searched through Stack Exchange and found some answers. However, the note the author gives states:     Our private solution includes use of Ax 1, Ax 3, Modus Ponens, and the deduction theorem.   And so far every solution posted here contains solutions that either use lemmas not yet introduced, or the use of other axioms. My question is how would one derive the formula using only the first and third axiom, modus ponens, and the deduction theorem only. This is what I have so far:  $$\begin{align} &(0)\quad\vdash{(\lnot\lnot{p}\to{p})}&&\text{. . .}\\ &(1)\quad\lnot\lnot{p}\vdash{p}&&\text{Deduction Theorem}\\ \\ &(2)\quad\lnot\lnot{p}&&\text{Assumption}\\ &(3)\quad(\lnot\lnot{p}\to{(p\to{\lnot\lnot{p}})})&&\text{Ax 1}\\ &(4)\quad(p\to{\lnot\lnot{p}})&&\text{MP 2, 3} \end{align} $$  I just feel stuck as to where to go next, or if I even started off correctly. A solution is not required, just a step in the right direction could help.

This is all in the context of a Hilbert system with modus ponens $A, A\to B \vdash B$ and axioms:  Axiom $1$: $A \to (B \to A)$   Axiom $2$: $(A \to (B \to C)) \to ((A \to B) \to (A \to C))$   Axiom $3$: $(\lnot B \to \lnot A) \to (A \to B)$  So I tried to prove double-negation elimination by doing the following:  \begin{array}{ccc} 1 & \{ \lnot \lnot a \} \vdash \lnot \lnot a & \text{Premise}\\ 2 & \{ \lnot \lnot a \} \vdash \lnot \lnot a \to (\lnot \lnot \lnot \lnot a \to \lnot \lnot a)  & \text{ Axiom } 1\\ 3 & \{ \lnot \lnot a \} \vdash \lnot \lnot \lnot \lnot a \to \lnot \lnot a  & \text{ Modus Ponens } 1, 2\\ 4 & \{ \lnot \lnot a \} \vdash (\lnot \lnot \lnot \lnot a \to \lnot \lnot a) \to (\lnot a \to \lnot \lnot \lnot a)  & \text{ Axiom } 3\\ 5 & \{ \lnot \lnot a \} \vdash \lnot a \to \lnot \lnot \lnot a  & \text{ Modus Ponens } 3, 4\\ 6 & \{ \lnot \lnot a \} \vdash (\lnot a \to \lnot \lnot \lnot a) \to (\lnot \lnot a \to  a)  & \text{ Axiom } 3\\ 7 & \{ \lnot \lnot a \} \vdash \lnot \lnot a \to  a  & \text{ Modus Ponens } 5, 6\\ 8 & \{ \lnot \lnot a \} \vdash a  & \text{ Modus Ponens } 1, 7\\ 9 & \vdash \lnot \lnot a \to a  & \text{ Deduction Theorem } \\ \end{array}  And then I continued on, to prove double negation introduction:  \begin{array}{ccc} 10 & \vdash \lnot \lnot \lnot a \to \lnot a & \text{Double Negation Elimination}\\ 11 & \vdash (\lnot\lnot \lnot a \to \lnot a) \to (a \to \lnot \lnot a) & \text{ Axiom } 3\\ 12 & \vdash a \to \lnot \lnot a & \text{ Modus Ponens } 10, 11\\ \end{array}  My questions:   Am I allowed to invoke the deduction theorem in the middle of a proof like this (step $9$)? Is this considered a context change? Is context-changing allowed? Are the proofs even right/correct? Assuming it's all correct: Are we able to combine them to say that $a \to \lnot \lnot a$ and $\lnot \lnot a \to a$, therefore $a \iff \lnot \lnot a$ or is this symbol not allowed? What ultimately let us say $\lnot \lnot a = a$, the use of the equal sign here?


Why "==" or equals method doesn't work ?           String levelSetting = ManageLogFile.getLevel();          if (levelSetting != Log.Level.DEBUG.toString()) {             System.out.println(Log.Level.DEBUG.toString());             System.out.println(levelSetting);             log.setData(null);             }   With Result displayed :   DEBUG DEBUG   It's the same String... But != doesn't work... I have also tried with equals method.. and same problem I have compare lenght and it's 5 for both.

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?


What's the shortcut to select the current suggested user when tagging hir in a comment?

While commenting on posts, when we start typing @ and a few characters that match one of the earlier commentators, a suggestion appears above the comment text area. Is there a shortcut to accept that suggestion?


I vaguely remember watching this as a child in the mid nineties. It might be possible that this was not an anime, but something non-Japanese.  I remember there were at least two characters in a space ship stranded in space. A regular looking human guy and a robot or cyborg looking woman. I'm pretty sure the woman had a human looking head with hair but the rest of her body was mechanical. The characters both had pale skin, the robot woman had blonde hair.   At some point the robot woman goes outside to fix the space ship by herself. While she's working a creature that looks like a sunny side up egg attacks her (probably the reason I remember this because I was extremely confused as to why an egg was attacking a robot). The egg crawls inside the robot woman and she faints/stops working.  Thinking about this some more I'm starting to recall a few more details. The alien egg creature doesn't outright attack the robot woman. It's sneaky and attaches itself to her head first without her noticing. Kind of absorbing into her skull after that. I have a feeling this means that there's some sort of possession plot.  The next scene I remember is just the regular looking guy standing over the robot woman looking confused. I guess she made it back inside the space ship before she broke down/fainted. He attempts to revive her by attaching wires to her chest.  I'm not sure if this is useful, but here's some added context. I lived in Russia when I saw this. My father loved anything sci-fi and would watch any movies he could get his hands on. My best guess is that I would have watched this in 1995-96. I'm certain that this wasn't a Russian made cartoon.  The original language or country this cartoon would have been from is hard for me to identify for a few reasons. First, most VHS tapes wouldn't have been originals. It was common for people to sell pirated copies converted into a format that local VHS players could play. Second, these tapes rarely had box art or accurate/correctly translated titles. Unfortunately I don't remember what the title was, and there was no artwork on the VHS tape's box.

What is the name of an anime from 80s-90s movie/series in which there is a scene, maybe the end, where a girl (who has an armor) exchanges age with a dying man in a beach, so the man transforms into a baby and the girl grows to a woman?


Currently, the button to "start a bounty" seems to be suffering from Windows 8-syndrome—it looks a bit more like text than an actual button.        This issue isn't specific to Meta.SE either—it's a network wide problem with the new-style designs.  The old designs had nice little backgrounds around the buttons to make it more clear they were... well... buttons.        Can we possibly bring that back?

This may be me being silly, but has the start a bounty text colour changed?  I distinctly remember it being the same colour as the add comment text?


So I am having trouble getting the sum of the series:  $1 + 2\left(\frac32\right) + 3\left(\frac{3^2}{2^2}\right) + ... + k\left(\frac{3^{k-1}}{2^{k-1}}\right)$  I cant figure out for the life of me how to figure out the sum of this.

How can I evaluate $$\sum_{n=1}^\infty\frac{2n}{3^{n+1}}$$? I know the answer thanks to , but I'm more concerned with how I can derive that answer. It cites tests to prove that it is convergent, but my class has never learned these before. So I feel that there must be a simpler method.  In general, how can I evaluate $$\sum_{n=0}^\infty (n+1)x^n?$$


I am a second year Geo student.  I was tasked with creating a sea surface temperature grid from a colour profile, which I have completed, but I am required to drop the land based cells through the use of a shoreline shapefile.    I have dissolved the shoreline (which I am hoping is the right move), but can't seem to find a way to move forward.

I have a shapefile of Lakes over my study area. Each polygon has attribute information of each lake, name, shape etc. Actually I want to eliminate all lakes from analysis. In other word, I want lakes to have 0 value and the area that out of boundary of lake to have their orginal pixel values. when I do subset using this shapefile, the output is not I want because my shapefile deoesn't have any value outer boundary of lake.   How can I build a proper mask file (inner part of lake has 0 value, outer is 1) using this shapefile in ArcGIS Desktop?


I just start using the text-based Lynx browser, and a part of the interface is very hard to read like you can see on this screenshot:    How can I fix that?

As you can see my lynx's bottom part is hard to read. How can I change the color? I use Solarized Dark on iTerm2.


I want to make a new OS based on Ubuntu (for banks, and higher end businesses in the beginning... with home users and even a server version later on...) I am willing to hire qualified people to help, or possibly partner with someone. Essentially I want to make a hardened version of Linux, similar to Ubuntu. I can base it from Ubuntu or another flavor.   I haver some coding knowledge, but most recently have been in data science and cyber security. I also have a moderate amount of experience with Ubuntu and Ubuntu Server.  Thoughts? Recommendations? Where is a good place to begin?

I want to create an Linux distro based of Ubuntu 14.04 with a graphical user interface(GNOME) and cool terminal theme.


I attempted a solution using this version of Taylor's Theorem, \begin{align*} |f(d) - P_n(d)| &= \left| \frac{f^{n+1}(t)}{(n+1)!} \right| |d-c|^{n+1} \\ |f(d) - f(c) - f'(c)(d-c)| &= \left| \frac{f''(t)}{2} \right| |d-c|^2 \end{align*} Letting $d=1$ and $c=1/2$ and using the triangle inequality, I get $$ \frac{|f''(t)|}{4} - \frac{|f(d)-f(c)|}{|d-c|} \geq -|f'(c)| $$  The negative sign on the RHS is throwing me off because otherwise I could easily achieve the desired result. Am I attempting using the wrong theorem or are there any glaring mistakes in my process?

Suppose that $f(x)$ is differentiable on $[0,1]$ and $f(0) = f(1) = 0$. It is also   known that $|f''(x)| \le A$ for every $x \in (0,1)$. Prove that   $|f'(x)| \le A/2$ for every $x \in [0,1]$.   I'll explain what I did so far. First using Rolle's theorem, there is some point $c \in [0,1]$ so $f'(c) = 0$.  EDIT: My first preliminary solution was wrong so I tried something else. EDIT2: Another revision :\  I define a Taylor series of a second order around the point $1$: $$ f(x) = f(1) + f'(1)(x-1) + \frac12 f''(d_1)(x-1)^2 $$ $$ f(0) = f(1) + f'(1)(-1) + \frac12 f''(d_1)(-1)^2 $$ $$ |f'(1)| = \frac12 |f''(d_1)| <= \frac12 A $$  Now I develop a Taylor series of a first order for $f'(x)$ around $1$: $$ f'(x) = f'(1) + f''(d_2)(x-1) $$ $$ |f'(x)| = |f'(1)| + x*|f''(d_2)|-|f''(d_2)| \leq \frac{A}{2} + A - A = \frac{A}{2} $$  It looks correct to me, what do you guys think?  Note: I cannot use integrals, because we have not covered them yet.


How to calculate the A(n) Vandermonde matrix determinant if the column with powers n-1 is replaced with powers n?

Let $x_1,...,x_n $ are distinct real numbers.  Is it a formula for the Vandermonde type determinant $V(x_1, \cdots,x_n)$  whose last column is $x_1^k,\ \cdots,\ x_n^k$, where $k \geq n$, instead of $x_1^{n-1},\ \cdots,\ x_n^{n-1}$?  Thanks


Is it possible to add new values to a picklist from apex code. I my trigger I am getting a set of picklist values now I need to add all these values to a picklist field on my object. Please help me out to get the solution for this issue.

I have queries pulling all of the information correctly but what I can't seem to find was a way to add new options to a picklist using APEX.  I currently have   Package__c.Products__c.add(new Schema.PicklistEntry(products[j].Name));   Package__c is my custom object, and Products__c is the picklist. products[j] is pulling a list of products pulled from our products page.  And I've tried adding it as a select option, or even casting the variable type.  And this information has to go to the actual picklist within a custom object, and not within a visual force page or anything like that.


On the desktop site, this isn't a problem, but on mobile it gets a little annoying  After tapping here to load more comments:        The text field is shown, given focus, and then pushed out of view by the new comments.  What's left is a partially zoomed in view of the new comments, with a keyboard that can't be hidden until you scroll to find the text field.        It's great that the field is shown, but can we not give it focus automatically?  Tested in Safari on iOS 7.1.1

On the mobile-web version of Stack Exchange sites, clicking the "add / show X more comments" link always zooms the "new comment" field into focus and opens the keyboard.  It also scrolls the page towards the top a bit so the new comments appear off the bottom of the screen.  Most of the time, when clicking on that link, I just want to read the hidden comments.  It's annoying when I have to dismiss the keyboard, zoom out and scroll back.  It should simply reveal the new comments and the keyboard should not show up unless I decide to tap inside the "new comment" field.  This is observed with the latest version of Mobile Safari in the latest iOS, although it's likely an issue on all mobile devices whenever the mobile version is displayed.    EDIT:  This question was closed with this reason:     "This question has been asked before and already has an answer. If those answers do not fully address your question, please edit this question to explain how it is different or ask a new question."   However, the original question does not already have an answer with a solution nor even an explanation.  like mine.  I don't dispute that I accidently posted the same complaint.  However, based on the wording of the closed reason, it would seem to imply that duplicates are allowed in situations when the original does "not fully address" the question.


I need to change the length of the horizontal line that separates text body from footnotes. I want  length of footnote line is as much as width of footnote text. I can the following codes:      \def\footnoterule{   \hrule \@width 4in \kern 4\p@}   but in this case, length of footnote line is fixed. Can you help me?

I am using pdflatex and just want to know how to change the footnote line (thickness, length).  Besides that: How can I set the distance between text-lines in the text.


recently I have been hacking few psu and have to deal with some high voltage caps. It sort of scared me, but thinking about it, what is the chance of it really killing me.    Is it safe to touch one terminal of a charged and opened 120v cap? I mean the other terminal is opened, and connected to nothing, so there is no current flow, so it should be safe. Touching 2 terminals of a charged cap with one of your finger will give you a shock in your finger, but since no current go through your heart, it will not kill you. am I correct?  The only scenario a charged cap could kill you is when you touch one terminal with one hand, and other terminal with other hand, and the shock go through your heart. but still, what is the chance of that tiny 120v killing you if you are a health person. I think doctors use high voltage to save people.    Is a tiny 120v charged cap really that intimidating?

I'm looking for guidelines on how to identify capacitors which have the potential to cause pain, injury or death due to electrical shock if not handled correctly.  I recently purchased a "getting started with electronics" kit from Radio Shack. It contains an electrolytic capacitor of 1,000 µF and 25 V. I'm assuming this particular capacitor doesn't have the potential to cause such harm because it was included in an introductory kit. However, at what point does a capacitor have the potential to cause pain, injury or death due to electrical shock?  Ideally, I'd like links to reference material on the subject.


Suppose I have a 3D data set (3 features) and $c=2$ classes. If we perform LDA, we will only get 1 LD since the maximum number of dimensions is $c-1$. I understand from the math derivation of why this is the case, but still can't visualize why we can't have a 2D plane where we can project the 3D data and have maximum separation of the classes.  Imagine the picture below with only 2 classes (2 spheres) instead of 3 classes. Can't we find a plane for LDA instead of a line in this specific case?      Update:  Roughly speaking, this is the mental picture that I get so far:   Imagine the above picture with only 2 spheres Imagine a Linear Discriminant line in the 2D plane on the left Then, all the 2D planes that I was looking for are those planes with the LD line as the axis of rotation. So, there are infinite number of those planes. As @ttnphns mentioned, the planes are thus unnecessary as the line can separate the 2 classes.

I am working with dimensionality reduction algorithms. Linear Discriminant Analysis (LDA) is a supervised algorithm that takes into account the class label (which is not the case of PCA for example). I am using Python to do a comparative study between some algorithms.  Why with two classes (k = 2), regardless of the data dimensionality, LDA gives one dimension, i.e. the new subspace is composed of only one dimension? For example if I try to project my dataset (of 100 attributes and 2 classes) to 10-dimensional space by using LDA(n_components=10) I only obtain 1 dimension?  For k>2 I can obtain the number of discriminant vectors that I specified as n_components. How can I get n_components dimensions for k=2?


As mentioned in , I can't install a Linux subsystem on my Windows-10 machine, as the version is too old (1709 while at least 1903 is needed). I thought that I could solve this, using a simple Windows upgrade, but this seems not to work. Why is that? Are there limitations to Windows-10 version upgrades (it's the computer of my employer, not my own)? First edit: The last package my computer is trying to install, is the following one (sorry for the Dutch): 2019-04 Cumulatieve update voor op Windows 10 Version 1709 for x64 gebaseerde systemen (KB4493440)  After having tried this (without succeeding), this is the message I see on my Windows update screen: Er wordt een update voorbereid voor uw apparaat, maar dit is nog niet gereed. We blijven het proberen, maar u kunt het ook zelf nu opnieuw proberen.  Freely translated: An update is prepared for your device, but this not ready yet. We keep trying, but you might try it yourself too.  I'm already seeing this message for several days now. Edit after some more investigation: As mentioned on , I've stopped the Windows update service, cleaned the datastore directory (%windir%\SoftwareDistribution\DataStore) and restarted Windows update service again, but the problem still appears. (I checked the mentioned directory and the files Datastore.edb and Datastore.jfm have been re-created.) I also performed a system file check, which mention everything being ok: sfc /verifyonly  Beginning system scan.  This process will take some time.  Beginning verification phase of system scan. Verification 100% complete.  Windows Resource Protection did not find any integrity violations.  What can I do?

I have been trying to update my pc from 20h1 to 20h2 but the windows update shows error message 80007002 and when I manually install the update using windows 10 update assistant it downloads completely and then even starts install and gets stuck at 87 percent on the screen where it says do not turn off. What to do? This is the log file. Matching Profile found: FindRollbackFailure - 3A43C9B5-05B3-4F7C-A955-88F991BB5A48 SetupDiag version: 1.6.0.0 System Information:     Machine Name =      Manufacturer =      Model =      HostOSArchitecture = 1033     FirmwareType = UEFI     BiosReleaseDate = 20160513000000.000000+000     BiosVendor = A12     BiosVersion = A12     HostOSVersion = 10.0.19041     HostOSBuildString = 19041.1.amd64fre.vb_release.191206-1406     TargetOSBuildString = 10.0.19041.621 (vb_release_svc_prod1.201014-1758)     HostOSLanguageId =      HostOSEdition = CoreSingleLanguage     RegisteredAV = Quick Heal Internet Security     FilterDrivers = FileInfo     UpgradeStartTime = 12/20/2020 2:54:38 PM     UpgradeEndTime = 12/20/2020 5:30:40 PM     UpgradeElapsedTime = 02:36:02     CV = Pi3IdU3SlEqpFx93     ReportId =    Error: SetupDiag reports rollback failure found. Last Phase = Pre OOBE Boot Last Operation = OOBE boot apply Error = 0xC1900101-0x4000D LogEntry:   Refer to "https://docs.microsoft.com/en-us/windows/desktop/Debug/system-error-codes" for error information.  Last Setup Phase: Phase Name: Pre OOBE Boot     Phase Started: 12/20/2020 4:37:50 PM     Phase Ended: 1/1/0001 12:00:00 AM     Phase Time Delta: 00:00:00     Completed Successfully? False   Last Setup Operation: Operation Name: OOBE boot apply     Operation Started: 12/20/2020 4:37:50 PM     Operation Ended: 1/1/0001 12:00:00 AM     Operation Time Delta: 0:00:00:00.0000000     Completed Successfully? False


My quetion is - how I can enter "new line" symbol using android voice input? For example I tyr to create shopping list using Evernote and voice, but to create new item in list I must switch to keybord, and press enter. How to do that using only my voice?

I've found I can make punctuation happen by saying "comma", or "period", but I can't find the word for new line.  I tried "paragraph", and "line break", but it just prints those words.


We have a rocket in Space that accelerates with 10m/s². Our engine requires one Unit of Energy each second, while expelling neglible amounts of mass¹. Well assume the rocket has a mass of 100kg aswell as an inital speed of 0. Scenario A: After 1 second the rocket has achieved a speed of 10 m/s while using 1 Unit of Energy. Scenario B: After 10 seconds the rocket has achieved a speed of 100 m/s while using 10 Units of Energy. Now introducing the formula for kinetic energy: kinetic energy is 0.5 * mass * velocity squared $$ KE = \frac{1}{2}m\cdot v^2 $$ Applying this to our Scenarios: Scenario A: $$ 0.5 \cdot 100\mathrm{kg}\cdot (10\frac{\mathrm{m}}{\mathrm{s}})^2 = 50\mathrm{kg}\cdot 100\frac{\mathrm{m}^2}{\mathrm{s}^2} = 5000\frac{\mathrm{kg}\cdot\mathrm{m}^2}{\mathrm{s}^2} $$ Our rocket now has 5 000 Joules of kinetic Energy, which was achieved using one Unit of Energy. Thats 5000 Joules per Unit of Energy! Scenario B: $$ 0.5 \cdot 100\mathrm{kg}\cdot (100\frac{\mathrm{m}}{\mathrm{s}})^2 = 50\mathrm{kg}\cdot 10.000\mathrm{m}\frac{\mathrm{m}^2}{\mathrm{s}^2} = 500.000\frac{\mathrm{kg}\cdot\mathrm{m}^2}{\mathrm{s}^2} $$ Our rocket now has 500 000 Joules of kinetic Energy, which was achieved using one Unit of Energy. Thats 50 000 Joules per Unit of Energy! My Problem is the discrepancy in how many Joules one Unit yields between the two Scenarios. After (unsuccessfully) trying to research the topic, I think that my mistake must lie within the first part describing my understanding of how a rocket works. Though if i try to transfer the kinetic energy formula onto my understanding of the rocket, i have to assume an exponential increase in the energy required to double the speed of an object. The problem is that this would be at odds with how real world rockets appear to work. It is not that their TWR drops while they easily go Hypersonic. Trying to explain this with the use of reaction mass is also not helpful because the fuel consumption is linear. Thus i found myself here, asking the question of what i could be missing. [1] e.g. an ion drive.

Lets say that hypothetically we have a rocket with constant mass, and an engine providing a constant force. I understand that it is unrealistic to have a rocket of constant mass with a rocket engine that ejects mass to accelerate, however this simplifies the problem. As the rocket accelerates the force from the engine will be travelling at a larger speed, therefore increasing the power of the rocket engine, since $W=Fm$, and this makes sense due to the constant acceleration that would occur with a constant force, since $E=\frac{1}{2}mv^2$. The rate of fuel flow into the engine will remain constant, so the chemical energy that is going into the engine will remain constant. This seems to contradict the increasing power from the force of the engine.


So my computer had a no signal black screen for almost 8-9 maybe 13 years finally got the black screen off and turns out my aunt who I let use my pc put a  password on my admin account. So I've looked up all the ways to  bring up the CMD on lock screen and no matter how I follow the steps perfectly. In system 32 I can not find the sethc  and all my files has DII behind them. I see no sethc.exe or anything close to it. I'm so lost and I don't wanna clean my PC because I'll have to redownload my Vista and anything else. That might be vital to my gaming. So any help will be a big help

I got a brand new Windows 7 machine, installed the operating system, created one account and forgot its password. What can I do?  There is no external CD, the operating system is loaded from somewhere inside the machine.  I already tried to remember passwords and tried all candidates with all possible combinations of caps lock, num lock etc.


If time does not pass for a photon traveling at the speed of light, which can only occur when traveling in a vacuum, what happens when it is slowed down by traveling through non vacuum space like water, does it time pass for it then?

I know that if we solve the Maxwell equation, we will end up with the phase velocity of light being related to the permeability and the permittivity of the material. But this is not what I'm interested in - I want to go deeper than that. We know that the real speed of light is actually not changing, the decrease in speed is just apparent. Material is mostly empty, the light will still travel with $c$ in the spacing. The rare atoms will disturb the light in some way. So I am interested in how the atoms affect the light. Photon absorption-emission theory Some textbooks that I read explain it in a way kind of like this: In a material the photons are absorbed by atom and then re-emitted a short time later, then they travel a short distance to the next atom and get absorbed&emitted again and so on. How quickly the atoms in a material can absorb and re-emit the photon and how dense the atoms decides the apparent speed of light in that material. So the light appears slower because it has a smaller “drift speed”. Interference theory But recently I realize an alternative explanation: Atoms respond to the light by radiating electromagnetic wave. This “new light” interferes with the “old light” in some way that results in delayed light (advanced in phase), this can easily be shown by using simple phasor diagram. Consequently effectively the light covers a smaller phase each second, which gives the impression of a lower phase velocity. However the group velocity is changing in a complicated way. I think that the first explanation does not explain the change in phase velocity of light. if we consider light travelling into a slab of negative refractive index non-dispersive material, let’s say the light is directed perpendicular to the slab. The phase velocity’s direction will be flipped, but group velocity’s direction in the material will not change. Only the second explanation can explain the flipped phase velocity direction. I guess that the velocity that we get in the first explanation is actually belongs to the group velocity. It makes sense to me that the front most of the photon stream determines the first information that the light delivers. So the question is What really cause the phase velocity of light to be decreased?  "drift velocity" of photons (they aren't the same photons, they are re-emitted all the time) phase difference between absorbed and emitted light something else  And also, I still don't really understand detailed explanation of the absorption-emission process for small light's wavelength (for large lambda compare to the atoms spacing, the photons will be absorbed by the phonons). The dispersion relation that we know is continuous and also some material is non-dispersive, therefore the absorption process must occur in all frequency for a certain range. So definitely it doesn't involve the atomic transition, otherwise it will be quantized. My guess is that the relevant absorption process gets smooth out by the dipole moment. What makes the spectrum continuous? EDIT: link for dispersion relation:


The land and forests encompassing Amon Lac appear to have been constantly part of the realm of the Silvan Elves from the start of the First Age until the second millienium of the Third Age. Aside from some bands of woodsmen, the race of Men seem to have avoided, or at least ignored the area, as it lay outside the reach of Numenor (later, of Gondor or Arnor). The same seems true of the Dwarves, who besides building a trade road through, preferred to stay in their mountain halls.  Then suddenly into the tale appears the Fortress of Dol Guldur Was it a mini-Barad-Dur, or a hole in the ground there lived a corrupted Maiar? It IS described as a 'fortress', it had dungeons, and was large enough to serve as a garrison for a force of orcs strong enough to threaten both Lorien and the Woodland Realm simultaneously. Did Sauron and his servants construct a new entity, or simply occupy an existing one dating from earlier history?

Who built the fortress of Dol Goldur, and when was it built? And was it always a place for evil, or Sauron just occupied it?  Despite the fact that Mordor is much better fortified; artificially by the old fortifications,  and geographically, as it is surrounded by the mountains. Also considering the presence of mount doom that seem to enhance Sauron's power, Sauron chose to start his campaign from Dol Goldur, despite Mordor being ready for quite some time.  Why did he choose this enigmatic fortress, and not go straight for Mordor or even go earlier?


As I remember the unified key, but the problem is i search this forum and the whole youtube and evrything possibe to recover my partition .   This is exactly what happened:   I got a live Dvd to install the ubuntu, but before installation of ubuntu it asked whether you want to replace the windows 8, and i thought that it will delete the windows c folder and will replace the ubuntu latest 16  !! Then i installed the ubuntu  with warning that it will remove the windows and replace the ubuntu. And after sucessful installation of ubuntu now i faced the really painful situation that i didn't have my partition of 1 terabyte.  It has to be 2 partions on my windows. After getting this problem i searched and researched the whole internet and i got nothing but somewhere it mentioned that use testdisk but the fact is i don't have any idea with the terminal window . Since i seached officially the software database but there is so such software found. i downloaded it from the internet from their site but i don't know how to install a zip file even after extracting it. But i got the Gparted and after opening it says like this:     I have many important things on my drive so I really need to recover it!

I have a Toshiba satellite A-200 laptop with a Vista OS on it with 4 NTFS partitions  (C:) Vista  (D:) Entertainment  (E:) Work  (F:) Sources   and I wanted to start using Ubuntu instead. So I tried it first from the live CD and everything was OK and all the partitions were shown and working and so I decided to install Ubuntu to replace Vista on the (C:) drive. After I did that I can no longer find my folders and files on the (D:), (E:), (F:) partitions and the only file system that is shown is one 198 GB although my HDD is 320 GB.  I can't access the lost data on the remaining 120 GB which I hope is still there and not totally lost  I am now working from the live CD but I am unable to install testdisk. Can I recover the Vista partitions by the product recovery CD to get my laptop back to the factory settings? Can I recover the NTFS partitions using a recovery program for Windows or will that make the problem worse?   I need these data badly as I don't have a backup for them.


Very basic question.  Please show where I'm wrong in the following reasoning.  The movement of an object in function of time could be described as $$ x(t) = v t + x_{i} $$ if velocity is constant.  If velocity is not constant then $$ x(t) = v(t)\cdot t + x_{i} $$ where $$ v(t) = a t + v_{i} $$ with a being constant.  Now if I substitute $v(t)$ in $x(t)$ it results $$ x(t) = at^2 + v_it + x_i $$  But the general equation for an accelerated object is $$ x(t) = \frac{1}{2}at^2 + v_it + x_i $$  Where does the $\frac{1}{2}$ come from?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?


I have multiple text inputs on a HTML page with the class="min_value", I need to add some validation to these text inputs with jQuery, the basic validation is shown, essentially is a value is entered below 250.00 the value of the textbox is set to 250.00 .  This works well with a single text input with the class "min_value" but not when multiple text inputs exist with the class name. Is it possible to alter this code so the validation is done on each text input, and only the value of that text input is changed?  jQuery(function ($) {      $(".min_value").each(function(){          $(".min_value").change(function(){               var min_value = $(".min_value").val();              if(min_value <= 250){                 $(".min_value").val('250.00');                   alert('The Minimum Value can not be less the 250.00');             }         });     }); });

I have HTML code like this :
        Link A1        Link A2        Link A3

        Link B1        Link B2        Link B3
   When user clicks a link from above HTML, I want to get the jQuery object of the corresponding  element, and then manipulate its sibling. I can't think of any way other than creating an ID for each  element, and passing that ID to an onclick event handler. I really don't want to use IDs.   Any suggestions?


I am trying to generate a .txt file on my Windows 10 PC of Arduino serial terminal data. I am not using SD card on Arduino Mega board just need to send commands to Arduino baord from serial terminal and save the generated results in .txt file on PC.   Please guide for best possible solutions.  Thank you....

How can I save data retrieved from a sensor to a text file on the computer?


So I have a lot of partitions on my computer. (came partitioned with the backup and then windows 10 created more). I just installed Linux on my dual boot. I can run both Windows 10 and Linux perfectly. The issues is this though. In order to install from USB I had to boot legacy. Now when I boot legacy I see the grub menu and it has Linux and some Windows 10 restore partitions but not the actual windows 10 os. In order to switch between the two I have to go into bios click boot to UEFI first and then windows. Boot into legacy first boom Linux. Anyone know how to fix this so that Grub shows both.  The grub that I installed was part of the linux install.  I know there are multiple dual boot topics but i haven't seen one mentioning legacy and UEFI and i am not sure if that is what is messing me up.

I followed this  to install Ubuntu as dual-boot with Windows 8.1 pre-installed as(UEFI),but I am not able to dual-boot and tried    I first burned an Ubuntu ISO on a blank DVD-R to create the LiveCD. Even with secure boot disabled, when I tried restarting my computer, it never booted to the installation screen, and it just skipped to Windows.  After a lot of skimming, I thought I had to put my computer in Legacy Mode in order to get give my CD/ROM drive priority. I installed Ubuntu and used my existing EFI partition. Ubuntu works, but Windows doesn't, probably because my laptop is stuck in Legacy Mode. I tried switching back to UEFI using boot-repair on the Linux Terminal, and going into Advanced Properties -> Grub Location -> Ticking the checkbox for EFI, but it says I need to be in an EFI session, and now I'm just really lost and confused at what I've all done. I can see my Windows8.1 OS on a partition but I want to dual-boot Windows 8.1 along with Ubuntu?   Did I just brick my computer?


Frequently, I suggest a post author to make a particular change.  The author makes the change, then notified me in a comment to inform me.  I delete my comment (which is now obsolete) and flag the other comment for being obsolete as well.  Then a moderator needs to come along, verify the comment is indeed obsolete, and delete it.   The moderator workload would be reduced significantly if the comment author was notified as well.  The comment author will probably have the conversation in fresh memory.

Simple enough:   The OP is the best judge of whether the comment is obsolete, and has no particular incentive to be unscrupulous in leaving an old comment - and even if they did, chances are this feature will lead to more obsolete comments being cleaned up than status quo in my estimation Right now there's no real way for two users to jointly clean up an obsolete comment thread.  If I delete mine, I need to let the conversation partner know they can cleanup their half...  but then my "notification" comment remains, and there's in general no way out of this loop If OP doesn't take action in, say, 2 days, can notify mods anyway It proselytizes itself:  if 100 people on meta see this thread, when they flag other comments as obsolete, they are educating the rest of the user base that it's okay to flag comments as obsolete. Plus there is already some badge-incentive regarding flags to help encourage people It solves the problem we have that it's impossible for an OP to notify a downvoter (who comments) or commenter that the improvement has been made with no weight added to our UI   So yep, sounds like an easy enough win to me.


Suppose that $\sum\limits_{n=1}^{\infty}a_n$converges.Prove that if $b_n$ monotone increasing to infinity and $\sum\limits_{n=1}^{\infty}a_nb_n$converges,then $b_n\sum\limits_{k=n}^{\infty}a_k\to0(n\to\infty)$.I made the following attempts. Let $R_n=\sum\limits_{k=n}^{\infty}a_k$,so $\lim\limits_{n\to\infty}R_n=0$.then we know that $\{\frac{1}{b_n}\}$ monotonic decreasing and $\frac{1}{b_n}\to0(n\to\infty)$.So we have $$\sum\limits_{k=n}^{\infty}\dfrac{a_k}{b_k}=\sum\limits_{k=n}^{\infty}\dfrac{1}{b_k}(R_k-R_{k+1})\implies\left|\sum\limits_{k=n}^{\infty}\dfrac{a_k}{b_k}\right|\leqslant\sum\limits_{k=n}^{\infty}\dfrac{1}{b_k}|R_k-R_{k+1}|\leqslant\dfrac{1}{b_n}\sum\limits_{k=n}^{\infty}|R_k-R_{k+1}|\leqslant\dfrac{1}{b_n}R_n.$$ So we can get it $b_n\sum\limits_{k=n}^{\infty}\dfrac{a_k}{b_k}\to0(n\to\infty)$.I'd like to know how to proceed. Thank you.

Suppose that $\Sigma_{k=1}^\infty a_k$ converges. Prove that if $b_k\uparrow \infty$ and $\Sigma_{k = 1}^\infty a_kb_k$ converges, then   $b_m \Sigma_{k = m}^\infty a_k → 0$ as $m → \infty$.  Attemtp: Suppose $\Sigma_{k=1}^\infty a_k$ converges, and $\Sigma_{k = 1}^\infty a_kb_k$ also.Then we know by Abel's Formula that the sequences converge only iff its partial sums converge. If we let $\Sigma a_k = \Sigma \frac{a_kb_k}{b_k}$, then because $b_k$ is increasing we have $\frac{1}{b_k}$ is decreasing to zero. So we almost have a telescoping series.   Then let $c_k = \Sigma_{ j = k}^{\infty} a_jb_j$. Then $\Sigma_{k = n}^m a_k = \Sigma \frac{a_kb_k}{b_k}= \Sigma_{k = n}^m \frac{c_k - c_{k+1}}{b_k}$  I don't know how to continue. I am having trouble applying Abel's Formula and the subscripts are confusing. Can someone please help me? I am suppose to use Abel's Formula.  Thank you very much.  Abel's Formula: Let $a_k,b_k$ be real sequences, and for each pair of integers $n \geq m \geq 1$ set $A_{n,m} = \Sigma_{k =m}^n a_k$ $\Sigma_{k = n}^m a_kb_k = A_{n,m}b_n - \Sigma_{k = m}^{n-1} A_{k,m}(b_{k+1} -b_k)$


I cannot find this article the beneficial effects of bacterial infections on host resistance to cancer :end results in 449 cases, HC Nauts, 1980, Cancer Research Institute on the internet, and I am seeking help from others. Where (which Stack Exchange) should I ask this type of question?   And yes, I know it's stupid.

Questions like looking for css templates, blog templates, icons ... In general, resources (let's leave the licensing terms aside for now) which you might need when building a project of your own. Where should those questions go?  They're definitely not on-topic on Stack', SuperUser maybe although I doubt it. Webapps? Hmm, probably not.  Is there a place where they would be on-topic on the SE network?


What will be the value of this limit?  $$\lim_{n\to\infty}n\cdot\sin(2\pi\ e\ n!)$$  Any help on how to proceed?

I tried and got this   $$e=\sum_{k=0}^\infty\frac{1}{k!}=\lim_{n\to\infty}\sum_{k=0}^n\frac{1}{k!}$$ $$n!\sum_{k=0}^n\frac{1}{k!}=\frac{n!}{0!}+\frac{n!}{1!}+\cdots+\frac{n!}{n!}=m$$ where $m$ is an integer. $$\lim_{n\to\infty}n\sin(2\pi en!)=\lim_{n\to\infty}n\sin\left(2\pi n!\sum_{k=0}^n\frac{1}{k!}\right)=\lim_{n\to\infty}n\sin(2\pi m)=\lim_{n\to\infty}n\cdot0=0$$  Is it correct?


In the given question we have to find equivalent capacitance across A and C .  I do not understand how can we convert the given circuit into a simpler one or if that can not be done how do we find the equivalent capacitance of such a complex circuit .

I simply can't figure out what the capacity of this circuit is.  I can do the math myself, I just need a hint how to create an equivalent circuit where it is obvious what is parallel and what is in series...


Example process waiting an input sent to background  $ read -p "Input text and hit ENTER to exit" &   I try to write to stdin (fd/0) with \n  $ echo -e "ok\n" > /proc/$!/fd/0   but  $ fg  read -p "Please hit ENTER"   so the process is still running, then string "ok\n" never reach it  How can I send a string+ENTER to another process STDIN?

In my Ubuntu, i run java application in background. I use bash script to run it and now it looks like:  nohup java -jar app.jar & exit 0   The problem that i want to be able to write an input string to my application, without making it foreground, from different terminals/sessions. Something like  echo "mytext" > /appdir/in   How should i change my script?


I am trying to get current android device time, and convert it into UTC timezone, then i need to convert it into Unix Timestamp.   I google it, found some solutions, tried few, but nothing helping me here.  This is what i am doing now.    Date date;   SimpleDateFormat dateFormatGmt = new SimpleDateFormat("yyyy-MMM-dd HH:mm:ss");   dateFormatGmt.setTimeZone(TimeZone.getTimeZone("UTC"));    SimpleDateFormat dateFormatLocal = new SimpleDateFormat("yyyy-MMM-dd HH:mm:ss");    date=  dateFormatLocal.parse( dateFormatGmt.format(new Date()) );    date.getTime();   Output:   date(Its returning the correct UTC date time) Thu Jan 26 08:06:20 GMT+05:00 2017 date.getTime() returns 1485399980000   When i put this Timestamp in online tools, Its not returning right output.  Kindly guide me how to convert current  UTC time into UnixTimestamp

When I create a new Date object, it is initialized to the current time but in the local timezone. How can I get the current date and time in GMT?


The prominently displayed feature request tag on this site should be removed immediately. A Q&A site does NOT mix well with feature requests. A Q&A site correctly punishes duplicate questions because duplicate questions lower the quality of the site. But this mindset of seeking to shoot down duplicates is exactly the opposite of what is needed for consideration of feature requests. The latter is best served by an open and creative mindset that will consider the feature request on its own merits with intent of actually hearing the unmet need rather than seeking to punish the person providing feedback. Including the feature request tag on meta is a mistake. People who express their unmet needs via feature requests are likely to be punished for doing so by the duplicate eradication mindset. This punishing of good behavior harms Stack Exchange in 2 ways.  It creates a strong negative experience of the person reporting their unmet need. It robs Stack Exchange of the feedback it needs to keep innovating to better meet the needs of users.

I have an idea or subject that should have a Q&A, and want to propose a new site. How can I do this?  Related:


In following MWE, \newcommand is used to create \myFoo macro which just forwards its unique argument, then \NewDocumentCommand is used to create \myBar with the same behavior. The former accepts \par in its argument but not the latter. \documentclass{minimal} \begin{document} \newcommand\myFoo[1] { #1 } \myFoo {\par\noindent Foo } \NewDocumentCommand\myBar { m } { #1 } \myBar {\par\noindent Bar } \end{document}  There is an error that I do not understand at line 6 Runaway argument? { ! Paragraph ended before \myBar  was complete. <to be read again>                     \par  l.6 \myBar {\par                 \noindent Bar }  What is wrong here?

Leaving blank line break simple macro but % terminating it fixes it. What's going on? I know one is supposed to use %, but I can't have any blank lines in the macro without it complaining. A blank line essentially terminates the macro and TeX complains about a mixing }. Using etoolbox also produces the same problem so it seems it is an issue with xparse. Is there any way to fix xparse package so I don't have to litter my code with %s? \documentclass{book}  \usepackage{xparse, ifthen, etoolbox}   \NewDocumentCommand\iftb{m m G{\relax}}{\ifthenelse{\boolean{#1}}{#2}{#3}}  %\NewDocumentCommand\iftb{m m G{\relax}}{\ifbool{#1}{#2}{#3}} \newboolean{A}\setboolean{A}{true} \newboolean{B}\setboolean{B}{true}   \begin{document}  \iftb{A}{% % <- remove all text on this line breaks macro (keep blank line)     \iftb{B}{%         asdffdsasdff         % <- same here         asdf     } }  End \end{document}


Would you write  The cruise liner Titanic hit an iceberg.  Or  The cruise liner, Titanic, hit an iceberg.  Thanks

On the freelancing website Upwork, there is a US Punctuation and Mechanics test one can take to boost credibility on one's profile for potential clients. These tests are administered by third-party companies that often hire non-native English speakers, so they're known to have some inaccuracies. Unfortunately, because you're allowed to retake the exams after a certain period passes, the correct answers are never revealed. One of the questions on this exam is the following:  Richard’s wife(A) Abigail(B) is an incredibly talented cook(C) and gardener. Comma at (A) Comma at (B) Comma at (C) Comma at (A) and (B) No commas needed  I answered "No commas needed", but I suspected afterwards that the answer key was looking for the answer choice above it, "Comma at (A) and (B)". After searching this question online, I found a website with answers for the various questions on the test, and the site claims that "Comma at (A) and (B)" is in fact the correct answer for this particular question. Is the answer key wrong? I feel like there's really no need for any commas, but on the other hand, the appositive Abigail isn't restrictive because it doesn't offer terribly "essential" information, suggesting it could be set off by commas.


So I have this block of code:  public Student(String name, String subject) {         if(subject.substring(17,18) == "e"){             subjectName = "English";         }else if(subject.substring(17,18) == "m") {             subjectName = "Math";         }         studentName = name;     }   I am feeding the Student in a name as a string and then a subject which is in a form like this:  ..\text\students\english\grades   Now I use substring on it and get only the first letter of the subject. If the letter is e then the lesson name is english and so on.  But for some reason my IF checks dont pass at all, if I throw a sysout in them, nothing happens, the check never passes while it should...  What could be the problem here?

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?


Suppose you have mass of 1kg as you start to move it at a speed which is 90% of the speed of light then what will happen to that mass? Will it increase?

Some people say that mass increases with speed, some people say that the mass of an object is independent of its speed.  I understand how some (though not many) things in physics are a matter of interpretation based on one's definitions. But I can't get my head around how both can be 'true' is any sense of the word.  Either mass increases or it doesn't, right?  Can't we just measure it, and find out which 'interpretation' is right? e.g.: (in some sophisticated way) heat up some particles in a box and measure their weight?  ------------------------------  UPDATE  Right, so I've got two identical containers, each with identical amounts of water, each on identical weighing scales, and each in the same g field. If one container has hotter water, will the reading on its scale be larger than the other? If the answer is yes, and g is constant, does this mean that the m in w=mg has got bigger?


I have used LYX for several months to write my paper and I really love this software. Next month, I am  going to write my thesis (using my school latex template). Now I had my friend thesis folders written by latex, it has a lot of .tex file, for example: mythesis.tex, frontpage.tex, table of content.tex, chapter1.tex, chapter2.tex and so on.  I try to import it to LYX but it can not run properly. Please help me add this thesis template into LYX. Thank you so much!

I tried googling this elsewhere but I'm new to LaTeX and extremely confused about certain things. Basically I downloaded MikteX and I'm using the latest version of Lyx with it. Now all I basically know how to do is make pretty looking mathematics and add contents pages/titles/references/etc.  I'm looking to make a dissertation and my unviersity provides a template,  (available for download at that link).  So, what exactly do I need to do (and please be super specific as I am totally clueless to all the jargon I read).   Basically, I need to download ociamthesis.cls in the first line of that webpage. Does it matter where I save it? What exactly do I do next?


I spent the entire day yesterday til 3am trying to fix this, and all the possible solutions you can find on the web just don't work for me.  I agreed to some regular updates on Ubuntu 16.04.4 LTS, all worked fine. Ever since starting back up, only the stuff that was lying around on my Desktop is to be seen. One of the "fixes" even caused a blackscreen and I couldn't even boot my OS anymore, I had to start a Ubuntu safe session and reconfigure lightdm in the terminal to even make my OS work again. I'm also still confused on why it allows you to choose between lightdm and gdm as a manager.   I checked the .xsession-errors file and it reports  ... upstart: unity7 main process ended, respawning upstart: unity7 main process (4644) terminated with status 1 ...   metacity --replace & disown at least temporarily allows me to minimise, drag and close windows.  ccsm won't apply any changes made at all after I close it.  I've tried everything google can find for you...  dconf reset -f /org/compiz setsid unity unity --reset-icons reinstall unity reinstall ubuntu desktop initctl restart unity-panel-service update, upgrade, dist-upgrade aptitude etc....   Absolutely NOTHING works!!  Any ideas?

When I login, nothing happens.   I am presented with my desktop wallpaper.    No Dash, no Launcher, nothing.


$u_i$ are complex roots of 1, but of n+1 degree (excluding $u_0$ = 1)  My attempts, I don't know if it leads anywhere or what to do next: We can tell that $u_i = (u_1)^{i}$ so we have: $(2 - u_1)(2 - u_1^2)...(2 - u_1^2)$ Supposing n+1 is odd number (even case is similar), we can tell that half of this roots is equal to its conjugate, so: $ 2 - u_i = \overline{2 - u_{n-i}}$. Because $z\overline{z} = |z|$ are equation reduces to: $|2 - u_1|^2 |2 - u_1^2|^2 \dots |2 - u_1^{\frac{n+1}{2}}|$  So this means imaginary part is 0? What about real part? I don't know what I can do next or this is all wrong.

Let $n \ge 1$ and $u_{1},u_{2},...,u_{n}$ are all root of unity for $n+1$ and there are different from $1$.(a) Find polynomial $f \in \mathbb R[x]$ of degree $n$ for which: $f(u_{k})=0$ for $k=1,2,...,n$.(b) Calculate real coefficient and imaginary part for $(2-u_{1})(2-u_{2})\cdot...\cdot(2-u_{n}).$    I have a knowledge about root of unity but I completely don't know how to do it because I think that I need some extra trick to do it but my ideas finished. I know that $\varepsilon_n^{(k)} = \cos\left(\tfrac{2k\pi}{n}\right) + i\sin\left(\tfrac{2k\pi}{n}\right) = e^\frac{2\pi i k}{n}$ and for $n>1$ $\sum _{{k=0}}^{{n-1}}e^{{\frac  {2\pi ik}{n}}}=0$ but I think it is too little knowledge to solve this task.Can you help me?


I cannot get my insert function working. I have used this frame work.     The error i get is   Fatal error: Call to a member function insert() on a non-object in /home/hghdigib/public_html/backup/feed/classes/xml_upload.php on line 39  I have stripped lost out to make it easier to follow.   Any help would be much appreciated been scratching my head for a while.   My Global Class File   require_once("classes/database.php"); require_once("classes/xml_upload.php"); $db = new Mysqlidb('localhost', '', '', ''); $dataupload = new DataUpload($db); $dataupload->getAllProducts($db);   My xml_upload.php class  class DataUpload {      public $db;     public $xml_upload;      function __construct($db) {         $this->db = $db;     }         public function getAllProducts() {         foreach ($propertys as $results)         {             $insertData = array(                 'prop_id' => $results['prop_id'],                 'lastchanged' => $results['lastchanged'],                 'url' => $results['url']             );              if($db->insert('propertie_ids', $insertData)) echo 'success!';         }      }         }

So I'm refactoring my code to implement more OOP.  I set up a class to hold page attributes.  class PageAtrributes  {   private $db_connection;   private $page_title;      public function __construct($db_connection)      {         $this->db_connection = $db_connection;         $this->page_title = '';     }      public function get_page_title()     {         return $this->page_title;     }      public function set_page_title($page_title)     {         $this->page_title = $page_title;     } }   Later on I call the set_page_title() function like so  function page_properties($objPortal) {         $objPage->set_page_title($myrow['title']); }   When I do I receive the error message:     Call to a member function set_page_title() on a non-object   So what am I missing?


I wrote this sentence:  Because of his low weight, Gabe was still being nurtured instead of being named.  And Word underlined the bold part saying I was using passive voice and I don't know how to fix it.  Passive voice is not part of the assignment, but I need two prepositional phrases.

Whenever I create a document in Microsoft Word, it complains about a lot of my sentences being in passive voice. But, when I read that sentence aloud, it sounds fine to me. I am not sure if it is just me and will a statement in passive voice sound strange to a native speaker?  So, my question is, is it considered bad form to use passive voice generally? Or in some specific cases like written communications only?  Edit: If it is ok to use passive voice, then why does MS-Word complain?


I wanted to add a Isocam into my scene so I searched for it online and what I found out is here: But It says to install it from prefrences but when I open the given link I find out that it show a script That is here:  But I don't know how to apply into it? Can someone give me direction? here Isocam tool also not shows up and it shows blender 2.8x required when I have 2.90.2

There is this addon that was built called Window Generator 2. It can be . However, when I go to the download link it shows up in a new tab as a bunch of code.  How can I download and use this addon in Blender?


I recently installed 12.04, but I had the same problem in 11.10. When I watch a video, VLC suppresses the monitor being turned off. In older (pre-Unity) Ubuntu versions, this would only be in effect while the video was playing. Now VLC is disabling the turning off of the monitor regardless of if it is playing or not.  Is there a way to fix this? Or a less quirky shell? Or a video player that doesn't exhibit this behaviour?

I am using Ubuntu 11.10 and my screensaver keeps coming on while I'm watching a movie.  I don't remember this happening in 11.04 and can't remember how to stop it?


(/usr/local/texlive/2018/texmf-dist/tex/generic/oberdiek/etexcmds.sty))) (/usr/local/texlive/2018/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty) (/usr/local/texlive/2018/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg)) *geometry* driver: auto-detecting *geometry* detected driver: pdftex ) Runaway argument?  Extension-1, SH Hall\\ \end {tabular} \end {center} \vspace *{\fill \ETC. ! File ended while scanning use of \Gin@iii. <inserted text>                  \par  <*> delete.tex  ?   Without scale code runs well.  \documentclass{article} \usepackage{fontawesome,caption} \usepackage{graphics} \usepackage[left=0.5cm,right=0.5cm,top=0.5cm,bottom=0.5cm]{geometry} \captionsetup[figure]{labelformat=empty} \begin{document} \pagenumbering{gobble} \vspace*{\fill} \begin{center}   \begin{figure}      \includegraphics{example-image-a} % this runs well   %  \includegraphics[scale=1]{example-image-a} % this not run     \caption{Taken from Internet(black and white image)}   \end{figure}   {\Huge\textbf{To Buy}} \\   \LARGE \vspace{2cm}   \begin{tabular}{l}     \faPhone{} \textbf{01515-611989}\\     \faHome{} Room - \textbf{1406}, Extension-1, SH Hall\\   \end{tabular} \end{center} \vspace*{\fill}  \end{document}

\documentclass[a4paper,12pt]{article}  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[french]{babel} \usepackage{amssymb} \usepackage{amsthm} \newtheorem{montheoreme}{Théorème}[] \newtheorem{monlemme}{Lemme}[] \newtheorem{mondem}{Démonstration}[] \newtheorem{moncorol}{Corollaire}[] \newtheorem{mondefin}{Définition}[] \newtheorem{chapter}{Chapitre} \newtheorem{monremarq}{Remarque} \newtheorem{monpropos}{Proposition} \newtheorem{monexpl}{Exemple} \usepackage{graphics} \begin{document}  \begin{Large}  \textbf{Biographie :} \end{Large} \\  \includegraphics[scale=0.1]{800px-Karl_Weierstrass.jpg} \textbf{Karl Theodor Wilhelm Weierstrass :} habituellement appelé Karl Weierstrass, orthographié Weierstraß en allemand, né le 31 octobre 1815 à Ostenfelde (Westphalie), mort le 19 février 1897 à Berlin, était un mathématicien allemand, lauréat de la médaille Copley en 1895.\\ Il a étudié les mathématiques à l'université de Münster et obtint une chaire à l'Université technique de Berlin. Il fut immobile les trois dernières années de sa vie et s'éteignit à Berlin à la suite d'une pneumonie.\\ Karl Weierstrass est souvent cité comme le « père de l'analyse moderne ». Il consolida des travaux de Cauchy sur les nombres irrationnels et leur amena une nouvelle compréhension. Ses travaux les plus connus portent sur les fonctions elliptiques.


I am having trouble understanding the hyphenation rules of "babel". According to , selecting either UKenglish or british should result in Oxford dictionary type hyphenation. But it doesn't:  \documentclass{article} \usepackage[UKenglish]{babel}  \begin{document} Foobar foobar foobar foobar foobar foobar foobar foobar foobar foobar produce foo bar. \end{document}   This hyphenates pro-duce:   Which is in accordance with American English, e.g., , whereas according to  it should be prod-use.

Now I know there are hyphenation differences between British and American English but in no dictionary, British or American, could I find the word "alternate" to be broken down to al·tern·ate instead of al·ter·nate (). And yet:  \documentclass[a5paper]{article} \usepackage[british]{babel} \begin{document} alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate alternate \end{document}     If you remove the babel line or change it to american, the hyphenation will be correct:    So how does the British hyphenation work? Is it a complete reimplementation that can be buggy? Or is it just a list of exceptions where British syllabification differs from American? If it is the latter, why would a wrong hyphenation of "alternate" be made part of that word list?


I have recordings of intensities of two fluorescent antibodies on a 2d image $2^{10} \times 2^{10}$ pixels in size, giving me $2^{20}$ pairs of numbers.   What is the best way to find the best straight line approximation in the plane, in the sense that the sum of squares of Euclidean distances from the points to the straight line is minimized? Is this given by PCA?  What is "orthogonal regression"? Is PCA the same as "orthogonal regression"?

I always use lm() in R to perform linear regression of $y$ on $x$. That function returns a coefficient $\beta$ such that $$y = \beta x.$$  Today I learned about total least squares and that princomp() function (principal component analysis, PCA) can be used to perform it. It should be good for me (more accurate). I have done some tests using princomp(), like:  r <- princomp( ~ x + y)   My problem is: how to interpret its results? How can I get the regression coefficient? By "coefficient" I mean the number $\beta$ that I have to use to multiply the $x$ value to give a number close to $y$.


Do developers have to implement upvoted feature request? How long should I wait before developers implement feature request?

There are lots of questions tagged  that don't have a  response.  How do we interpret this? Is it because they are declined by default? We just have to wait for a response (the team is very busy)? Is Jeff the only one that reviews this questions?  I suppose the ones that have negative votes may (or may not) be declined by default, but there are quite a few with some to a lot upvotes that should have an official answer.


I executed the following line:  git rebase -i dev --onto master    I figured this would cut my dev branch and paste it on top of my master branch. And the -i would let me collapse the changesets.  But when it brought up the editor, I did not see any of the changesets. All I saw was "noop". So I just exited it. And then I look at my git history, all my changes are gone. My dev branch is at the same place my master is at!  Can some one help me recover? Thanks!

Does anybody know how to easily undo a git rebase?  The only way that comes to mind is to go at it manually:   git checkout the commit parent to both of the branches  then create a temp branch from there cherry-pick all commits by hand replace the branch in which I rebased by the manually-created branch   In my current situation this is gonna work because I can easily spot commits from both branches (one was my stuff, the other was my colleague's stuff).  However my approach strikes me as suboptimal and error-prone (let's say I had just rebased with 2 of my own branches).  Any ideas?  Clarification: I'm talking about a rebase during which a bunch of commits were replayed. Not only one.


We know that since $f$ is analytic on $E$ we have  $$u_x=v_y \quad u_y=-v_x$$  We have $f^*(z)=u(x,-y)-iv(x,-y)$  Essentially we are going from   $$E^* \stackrel{\overline{z}}{\rightarrow} E \stackrel{f}{\rightarrow} \mathbb{C} \stackrel{\overline{z}}{\rightarrow} \mathbb{C}$$  and $f$ is analytic on $E$. While $z \mapsto \overline{z}$ is not analytic we are doing that mapping twice so it may not disturb analyticity?  I know I need to consider the Cauchy-Riemann equations on $f^*$ but I'm not sure how to get there. Thanks for the help!

I'm doing a bit of self study, but I'm uncomfortable with a certain idea. I want to show that $f(z)$ is analytic if and only if $\overline{f(\bar{z})}$ is analytic, and by analytic I mean differentiable at each point. Here $f$ is a complex valued function.  What I do is write $f(z)=u(x,y)+iv(x,y)$, where $u$ and $v$ are real functions of two variables. Then $\overline{f(\bar{z})}=u(x,-y)-iv(x,-y)$.  These two forms look very similar, in the sense the one function being differentiable should immediately imply the other is differentiable, since the only thing really changing might be a $-$ sign popping out due to the chain rule.   How can I more rigorously express that $f(z)$ is analytic iff $\overline{f(\bar{z})}$ using this? Many thanks.


See . PHP syntax highlight is clueless about namespaces:    First letter of a class name in a root namespace should not be black. Could this be updated? I know namespaces aren't most popular feature of PHP, but they are quite important one.

I noticed that sometimes my code gets highlighted in different colors when rendered.   What is syntax highlighting? How does it work? Why isn't my code being highlighted correctly? How do I report a bug or request a new language? How do I use syntax highlighting? What languages are currently available on Stack Exchange?


I am using an early 2011 MacBook Pro with the Mavericks OS. I've researched a similar issue on an  but As far as I know, being in Single User mode won't help my situation.   One of my external drives with all my photos stopped working - it does not mount, even though I see it in Disk Utility. Using DU I tried to verify and repair the disk and got this message:  'Invalid B-tree node size'  Following the advice in this :  I tried to list my drives with the Terminal command  df -hl  The specificied disk was not in the list When I tried the suggested tail command  tail -f /var/log/fsck_hfs.log  I saw the name of the disk as   /dev/rdisk3s2: ** The volume   could not be verified completely.   Following that, I used this command (also suggested in the above link)  sudo fsck_hfs -r -d /dev/disk3s2  Instead of the expected proper outcome, what I received was an error message in Terminal as below:  inancs-MacBook-Pro:~ INCA$ sudo fsck_hfs -r -d /dev/disk3s2 Password: journal_replay(/dev/disk3s2) returned 0 ** /dev/rdisk3s2     Using cacheBlockSize=32K cacheTotalBlock=65536 cacheSize=2097152K.    Executing fsck_hfs (version hfs-226.1.1). ** Checking Journaled HFS Plus volume.    Invalid B-tree node size (3, 0) ** The volume   could not be verified completely.     volume check failed with error 7      volume type is pure HFS+      primary MDB is at block 0 0x00      alternate MDB is at block 0 0x00      primary VHB is at block 2 0x02      alternate VHB is at block 1464477326 0x574a268e      sector size = 512 0x200      VolumeObject flags = 0x07      total sectors for volume = 1464477328 0x574a2690      total sectors for embedded volume = 0 0x00      CheckHFS returned -1317, fsmodified = 0   What are my options? I have Data Rescue but not Disk Warrior (low on budget these days). Is there a possibility to fix the drive?  If not, and if I can rescue my data and put it on a different disk, is it safe to format the current drive and re-add my photos or should i stay away from this disk?

Earlier today my 2009 iMac emitted I/O errors trying to copy files. So I ran disk utility, verify disk to see if anything was amiss. It was. But as it's my startup disk I couldn't repair it, so I tried safe mode. Safe mode worked the very first time, but when I rebooted it shows the progress bar filling up, before halting. Every time I turn it on now, the same progress bar then crash happens. Booting in verbose mode reveals fsck is failing with signal 8.  Using single-user mode, as that's as far as I'm aware the only way I can get any access to the system, I've been running fsck_hfs. However, it always fails. Below is the output from fsck_hfs -d /dev/disk0s2.  ** /dev/rdisk0s2         Using cacheBlockSize=32K cacheTotalBlock=65536 cacheSize=2097152K. ** Root file system    Executing fsck_hfs (version diskdev_cmds-491.6~3). ** Verifying volume when it is mounted with write access. ** Checking Journaled HFT Plus volume. ** Checking extents overflow file. ** Checking catalog file.    Missing thread record (id = 9931104)    Missing thread record (id = 16434146)    Missing thread record (id = 19370458) disk0s2: I/O error hfs_swap_BTNode: offsets 10 and 11 out of order (0x0000, 0x0000)    Invalid node structure (4, 115897) ** The volume Macintosh HD could not be verified completely.         volume check failed with error 7         volume type is pure HFS+         primary MDB is at block 0 0x00         alternate MDB is at block 0 0x00         primary VHB is at block 2 0x02         alternate VHB is at block 1952491198 0x74622d5e         sector size = 512 0x200         VolumeObject flags = 0x07         total sectors for volume = 1952591200 0x74622d60         total sectors for embedded volume = 0 0x00   I absolutely need to be able to boot to use it as an external monitor.


I get the following error while installing Cinnamon using sudo apt-get install cinnamon:      Reading package lists... Done  Building dependency tree        Reading state information... Done  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:   cinnamon : Depends: gir1.2-muffin-3.0 but it is not going to be installed              Depends: libgjs0-libmozjs185-1.0 but it is not installable              Depends: libgjs0c (>= 1.34.0) but 1.32.0-1ubuntu1 is to be installed              Depends: libgnome-desktop-3-4 (>= 3.2.0) but it is not installable              Depends: libmuffin0 (>= 1.1.1) but it is not going to be installed              Recommends: gnome-themes-standard but it is not going to be installed              Recommends: gnome-session-fallback but it is not going to be installed              Recommends: nemo but it is not going to be installed  E: Unable to correct problems, you have held broken packages.   I tried everything on this:    but I am still unable to install it. Please help.

After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.


I know this question has been asked many times, but I need a specific part of it. When we get to the limit part, I had it written like this: $\lim_{n \to +\infty} a_{n+1} = \sqrt{2+\lim_{n \to +\infty} a_n}$ What is the reason I am allowed to put the limit under the square root? Why am I just allowed to put it there? I know it's true, but I am not sure why. I need to justify that in order to receive credit. My instructor said it is a "special word." I have no idea what the word is.

Suppose $f$ is a continuous function at $x = c$ in $[a,b]$.  Prove that for any sequence ${x_n}$ in $[a,b]$ converting to $c$, the sequence $\{f(x_n)\}$ converges to $f(c)$.  That is, $$ \lim_{n\to\infty}f(x_n)= f\left(\lim_{n\to\infty}x_n\right)$$    This proof seems simple but there are a few things that I need to know first. If $\{x_n\}$ converges to $c$, is it sufficient to substitute $c$ in for $\lim_{n\to\infty}x_n$?  Also needing some guidance on the structure of this proof.  Thanks!


Assuming I have a new character that chooses starting equipment instead of rolling for gold and buying items. Can I exchange some of the gold I got from the background for additional gear from the "Adventuring Gear" Table?

So if I'm correct, when you chose your starter gear and wealth you can either choose to roll some dice depending on your class and buy everything from that or you can choose the starter gear from your class and add the background items (including some gold). Here are my 2 questions:   If I choose the gear from my class, do I have to take all the equipment from only one of the (a) or (b) choices, or can I freely mix-and-match choices from the two sets? Can you spend the extra gold you get from your background on extra equipment (e.g. some soap and some fishing equipment) or do you have to start with that gold in its pouch?   The reason I ask is that I have recently created a level 1 wood elf druid and I mixed-and-matched the gear from the class, so that I chose a shortbow as a "(b) simple weapon" for the first point and a "(a) Scimitar" at the second point. My DM wasn't so happy about this, as he can't understand why I'm mixing (a) and (b).  He also wasn't so happy with me spending my 10gp from my outlander background. I decided that my druid wouldn't lay so much worth in 10gp compared to a bunch of stuff I got for that (e.g. some soap and some fishing equipment and some other useful things) and he seems to think that I'm supposed to just start with the gold instead.


I have an iPad 3, running iOS7. Following some articles I read, alleging to degraded performance undr iOS8, I decided to not upgrade (if anyone can contribute any experience to the contrary - I'd be thanklful).  Recently, when I connected the iPad to my laptop to transfer some files, the iOS8 upgrade file was downloaded off the internet and onto my iPad. I now have a permanent notification asking me to upgrade, not to mention a 3.3GB file stuck on my iPad.  How do I get rid of it? Is there a way to delete it on the device, or do I need to do it through iTunes?

I've downloaded the new iOS 8 update on my iPhone 5 but am getting second thoughts about actually installing it.  Is there a way for me to delete that download or am I at the point of no return?


The question is to show that for any $x,y \in\Re^n$  $||x+y||\cdot||x-y||\le||x||^2+||y||^2$  with equality if and only if $\langle x,y \rangle= 0.$  I have that $||x+y||^2=||x||^2+2 \langle x,y \rangle+||y||^2$ , which helps me prove equality but I'm lost on how to show this and show that the inequality part.


I have a big data file of size 8 MB. Now while my page is downloading it from the server, I would like to present a status update on how much is downloaded, e.g. 56% is downloaded. The data file in itself is a .js file!  I would like to do it from my javascript. I was thinking of the below option.  1) First measure network speed. 2) Then do a linear interpolation as I know the size of the file.  But measuring netspeed in JS is not very reliable given connection timing, caching, rendering etc etc.  Is there any direct approach, where I can straightway get the size of the partially downloaded file and calculate how much is downloaded so far.  Thanks for your help!

Is it possible to get the progress of an XMLHttpRequest (bytes uploaded, bytes downloaded)?   This would be useful to show a progress bar when the user is uploading a large file. The standard API doesn't seem to support it, but maybe there's some non-standard extension in any of the browsers out there? It seems like a pretty obvious feature to have after all, since the client knows how many bytes were uploaded/downloaded.  note: I'm aware of the "poll the server for progress" alternative (it's what I'm doing right now). the main problem with this (other than the complicated server-side code) is that typically, while uploading a big file, the user's connection is completely hosed, because most ISPs offer poor upstream. So making extra requests is not as responsive as I'd hoped. I was hoping there'd be a way (maybe non-standard) to get this information, which the browser has at all times.


Pure Virtual Class, AbstractThing.hpp:  #ifdef ABSTRACT_INTERFACE_FOR_THING #define ABSTRACT_INTERFACE_FOR_THING  namespace A { namespace B  {  template <class T> class AbstractThing { public:   virtual ~AbstractThing() = 0;   virtual T    GetStatus() = 0;  };  } } #endif   Header File, Thing.hpp:   #ifdef _THING_H #define _THING_H  #include "AbstractThing.hpp" namespace A  {    namespace B  { template <class T> class Thing : public AbstractThing<T> { public:   Thing();     ~Thing();   T  GetStatus();  };  } }  #endif   Source file, Thing.cpp,  #include "Thing.hpp"  namespace A { namespace B { template <class T> Thing<T>::Thing() {}  template <class T> Thing<T>::~Thing() {}  template <class T> T Thing<T>::GetStatus() { ... } } }   I keep running into this issue where compiler the complains about the class name (Thing) not being a type.  However, it is declared in the header file.  From reading other posts, it seems like this issue is generally caused by failing to pre-declare a function or class.  However, I don't see why my code does not accomplish this.  I thought that it might be a namespace issue because GetStatus() will compile if I remove the namespace access (Thing::), but removing the namespaces did not help.

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I am looking for a book that I read in the 80s where magic is used to help with tasks and science is forbidden. What I recall is that the protagonist (I think a boy) has to move a something heavy like a rock or tree stump but doesn't have magic, or it hasn't manifested yet, but he gets the idea to use a stick as a lever, at which point he gets into some sort of trouble for using what he later learns is called science. A bit later in the story I think he finds a section in the library that he's never seen before, which contains books on the "forbidden" (science). Possibly in a post-apocalyptic world where science is forbidden because people remember it leading to catastrophe.

I have a vague recollection of a book I devoured while in college; it was from the late 80's or early 90's. I remember that there were two 'classes' of mages, the ones who could harvest magical energy from the environment and supply that power to the other 'class' of mages.  The main character learned that he could reverse the flow and sap the other mage of his/her power. I also seem to remember that there was a lot of technological warfare and travel to the planets moon(s)?


It is never too late to change the direction your life is headed in.

Like many others, I commonly find myself ending a sentence with a preposition.  Yes, it makes me cringe.  I usually rewrite the sentence, but sometimes (in emails) I just live with it.  To, with... you know who you are.  Should I keep fighting myself on this one, or is it okay in some circumstances?


Im writing a paper on norms, we use two bars \|\cdot\| for vector norms and triple bars for matrix norms. The problem is that if I use |||\cdot||| the distances between the bars is different and that bothers me (using \|| is just horrible). I wanted to make a new command but i cant make the distance between the bars small enough to look like the vector norm. This is what I tried:  \newcommand{\norm}[1]{|\hspace{0.05mm}|\hspace{0.05mm}|\hspace{0.05mm}#1\hspace{0.05mm}|\hspace{0.05mm}|\hspace{0.05mm}}   I don't know how to make the distance smaller, maybe there's another command for smaller distances that I'm not familiarized with.   Thanks in advanced :)

I would like to create a norm-like operator with 3 verticals bars instead of two. It has to look like $|||\cdot|||$. I would like to know how to decrease the spacing between the vertical bars such that it has the same spacing as the $\lVert .. \rVert$ command.  There is a command available in the stmaryrd package called \biginterleave, but this command has to much spacing between the vertical bars, especially in display math mode.  Is there some work-around to adjust the spacing between to vertical bars?


This is the way we are currently converting a UTF-16 to UTF-8 on Ubuntu 18.04.  The input is a const wchar_t* (UTF-16) and the output is a const char* (UTF-8):  const char* to_string(const wchar_t* input)  {     std::wstring w(input);     std::string s(w.begin(), w.end());     return strdup(s.c_str()); }   However, it doesn't seem to be working because I'm still seeing non UTF-8 encoded characters in my string. Example:     Adobe® Flash® Player   Is there a problem with the to_string function above?

Is it possible to convert UTF8 string in a std::string to std::wstring and vice versa in a platform independent manner? In a Windows application I would use MultiByteToWideChar and WideCharToMultiByte. However, the code is compiled for multiple OSes and I'm limited to standard C++ library.


As a retired school teacher, and to become a professor at a university. Is it okay to get into a PhD program at the age of 65 and complete it to become a professor? Or is it too late and I can’t get employed at a university?

I am 33. I live in the US. I am a neither a US citizen, nor a green card holder. I have worked in various jobs as a research assistant (physics, biology, economics) usually involving programming, mathematics or statistics.  As a newly minted undergraduate, I didn't really have much confidence in myself and I completely ruled out graduate school as pointless.  I didn't think of myself as smart enough.  I drifted into working in labs, because those are some of the easiest ones for which one can get a work permit in the US as a non-American.  Having worked in academia for a while now, I've had a chance to leap into various fields and help build solutions to complex problems.  I think I have literally gone as far as I can go researching in academia with no higher degree.  I work at one of the top universities in the world.  (If you looked at US News rankings or the Academic Ranking of World Universities, it's in the top 5.)  Lately, I've been thinking about applying for graduate school.  I do have a few papers in various fields.  I'm thinking of a PhD in either pure mathematics, applied mathematics, statistics or computer science.   I see two big minuses to applying to graduate school:   Most people applying are more than a decade younger than I am.  (Alas, more than a few gray hairs have made an appearance in recent years.) Perhaps my achievements would look good for someone younger, but partially my achievements are the result of a long career rather than any special brilliance. So, I wonder how my record will be perceived.  I did take GRE and I scored 800 quantitative, 800 verbal and a 5 on the essay.  (I would most likely have to do a GRE subject test depending on what field I ultimately decided.)   Please advise on how accomplished, but older candidates, are viewed in the graduate school application process.


Why does adding more neutrons to an atom unstabilise it? Won’t adding more neutrons increase the strong force and thus knit the nucleus more tightly? Or is it because it’s being added in a particular place, the force is polarising part of the nucleus so it splits?

If you take any large nucleus and add protons to it, the electrostatic repulsion between them will make the nucleus more unstable, because the electrostatic force between them is more repulsive at a greater distance than the strong force is attractive  So how come if you add more neutrons, which don't have a charge and so there is no electrostatic force, the nucleus still becomes more unstable?  Also why aren't there groups of neutrons bound together, so purely neutron nuclei (because they are neutral, I'm guessing they couldn't form atoms, because of the electrons needed for an atom)