Platform: OS X: Yosemite 10.10.4; MacbookPro 15" Retina (mid-2015). Fact: There is aging for battery in any case - using or not. But while using - there is difference of how to use. My questions - in order to minimize battery degradation:    How often should I totally discharge battery ? Is degradation rate is a matter of full cycles or it doesn't matter to what highest and lowest level I charge or discharge laptop ? Most (99%) of the time I am connected to power - which leads to 100% charge level always. But many sites say, like following link:  say, that better to keep battery 40% charged than 100%. How to achieve that (there is no ability, as far as I know, to manually limit charging battery level) ? Do you have empirical evidences to prove or disapprove this expectations ? I ask this since to replace battery in Macbook Pro is hard to be done - many screw types, many modules do disassembly, using glue to grasp components without moving inside. And therefore I prefer doing this rarest I can. How much time (how many years) it typically takes upon your experience to get to buttery degradation of 40% capacity compared to Day-1 of using your Macbook Pro ? After 2 minutes of laptop using - the internal temperature (CPU, RAM, Battery) gets to 85-90 degrees (Celsius) and stays so till I turn off (sleep) laptop - for 12 working hours every day. Is there something I can do about heat (both in general, and regarding battery especially)?   What else should I do or know to not be frustrated later ?

How do you maximize the cycle count of your battery?  There seems to be a debate between:   Leave plugged in 24/7 but do a full cycle once a month Charge to ~100%, drain to ~10%, repeat.   NOTE: Taking your   Which method is better and why? How much of a difference does it really make?  Here are some of the better sources I've found about battery behavior so far. Even still I feel they don't conclusively answer the question above. See my elaborations below:           Elaborating on Option 1  Now IF Apple engineers were smart and optimized for AC draw when plugged in to not use up your charge cycles, then it seem logical to assume that you are using effectively none of your 1000 charge cycles while plugged in. If that's the case, it would seem that the LiPo drop from holding at 100% would be vastly outweighed by the fact you're not using any charge cycles.  However, this is a purely speculative assumption and I could find no evidence to either confirm or deny.  If this is NOT true, and the AC adapter only goes to charging the battery, then there would be no difference. Your battery would drain to 99%, then back up to 100%, then back down to 99%, etc. Those micro-charge cycles would add up at the same rate as 100% -> 0% -> 100%, and you would get no gain. In this case the negative effect of holding LiPo batteries at 100% would outweigh everything else.  Elaborating on Option 2  There are lots of good reasons why Option 2 is the way it is:   Because of known LiPo chemistry issues, holding a 100% charge for a long time causes the battery to degrade Apple specifically recommends not to leave it plugged in all the time  Draining a battery all the way to zero all the time is bad for the cell (Which is why ~10% is used) Heat is a killer, and when plugged in AND charging, you get extra heat that causes damage.   There are a couple reasons why I'm challenging Option 2:   It seems silly that the most intuitive use case for thousands of people that use their macs as primary computers is wrong. If the hypothesis in option 1 is true, you're just burning unnecessarily through your finite charge cycles. It's a pain to have to remember to keep plugging in and plugging out and be worried about whether or not your device is plugged in.


I have shown that any group of order 35 is cyclic. I don't know what to do next.  EDIT: I am not asking how to show that any group of order 35 is cyclic, just trying to show that that implies its unique

Prove that every group of order $35$ is cyclic.    Now, the subgroups of this are ones whose orders divide the order of this group(by lagrange), these are of prime orders $7$ and $5$.  and I guess $\Bbb Z_7\times \Bbb Z_5$ is of order $35$ and since these are both cyclic, so is $\Bbb Z_{35}$.  But that doesn't prove anything about every subgroup of order $35$.  How do I do this.


I have Nikon D3500 with kit lens 18-55 VR and some other lenses af-p 10-20 among them.  As I renewed my interest for photography some time ago, I have some images at the LR scrutiny that were taken more than six months ago, when I was still refreshing my knowledge and making many mistakes.  Yet, I cannot realize how could I make some images look not so sharp when viewed on 100%.  I mean, image at 18mm focal, f/14 has hyperfocal distance slightly over 1m and with my habit to focus at least somewhat longer than hyperfocal, how could I miss it?  I know, depth of field is not a measure of ideal sharpness, yet, I don't Like many details on 100%.  Am I too demanding or there could be some problem with camera?   I'm simply wondering how to not take photo sharp enough with these settings. And shutter speed is 1/160, that shouldn't create a blur even with a bit shaky hands.  Am I missing something?!  ()  I have added one of typical pictures where buildings in the back lose definition.

I use a Canon EOS Rebel T3i (600D) with the kit lens. I have experimented a lot with different settings and modes, but I feel like I have wasted many good shots that could have looked amazing, if only they were a little bit sharper.  I use auto-focus on most of my pictures and make sure to choose the right focus point, but all of my photos are still a little bit out of focus. When I zoom in, I can see that the pixels are not very crisp or well-aligned.  I am not sure if this issue is caused by my equipment or skills.


Im having some trouble formatting my HTML code to UTF-8. I have HTML and PHP on the same page. I used notepad++ but alredy formated in general settings to save file in UTF-8 withot BOM. But still i get characters like "?".  Ive checked my headers and seems that it is UTF-8:   This is between my header tags:  <meta http-equiv="content-type" content="text/html; charset=utf-8">   Hope some of you could help me with this. If there is need for the HTML file just shout out.   I have been using Notepad++ as editor and some parts i have edited online on hosting editor(one.com) but that shouldt be a problem as the file is saved as UTF-8 and told to browser with meta tag that it should also read as UTF-8.  Thanks for the help :) - Asim

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


Show that the polynomial $X^4-10X+1$ is irreducible in $\mathbb{Z}[X]$ but reducible in $\mathbb{F}_p[X]$ for all prime $p$.  I could show the irreducibility in $\mathbb{Z}[X]$ but not sure how to proceed in case of $\mathbb{F}_p[X]$

How do we show that  $X^4-10X^2+1$ is reducible modulo every prime $p$?    I've managed to show it for all primes less than 10, for primes greater than 10 we have $X^4+(p-10)X^2+1$. Where do I go from here?


I have windows 10 enterprizes. i know that there is no way to stop windows 10 update. but we can only stop it from downloading updates by using registry and group policy. but it still takes too much of internet to check for updates on my computer i don`t want to update it because i use  WUD to update it. actually i want to delete these services so that neither windows update nor any other app can use internet through BITS. any way to delete it. i had tried soloutions to disable it but after some time they automaticaly start.

We've upgraded some machines to Windows 10 and realized there were some updates which updated as required. However, I realized there was no option available to stop the download similar to that on Windows 7 and 8.1. The only way I could stop the download was to stop the Windows Update service.  My question is does anyone know of a way to stop auto updates or is stopping the service is the only solution?


i am trying to make Java ucanaccess program and for some reasons i am not able to insert record to database and have appeared some error messages as following:  package lcp_v1;  import java.awt.BorderLayout; import java.awt.EventQueue; import javax.swing.JButton; import java.awt.event.ActionListener; import java.awt.event.ActionEvent; import java.sql.*;  public class DB2 extends JFrame implements ActionListener {      private JPanel contentPane;     private JTextField id_tt;     private JTextField name_tt;      Connection con;     Statement st;      /**      * Launch the application.      */     public static void main(String[] args) {          EventQueue.invokeLater(new Runnable() {             public void run() {                 try {                      DB2 frame = new DB2();                     frame.setVisible(true);                 } catch (Exception e) {                     e.printStackTrace();                 }             }         });     }      /**      * Create the frame.      */     public DB2() {         try {             setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);             setBounds(100, 100, 577, 550);             contentPane = new JPanel();             contentPane.setBorder(new EmptyBorder(5, 5, 5, 5));             setContentPane(contentPane);             contentPane.setLayout(null);              JLabel lblEmployeeId = new JLabel("employee id");             lblEmployeeId.setBounds(39, 53, 123, 23);             contentPane.add(lblEmployeeId);              id_tt = new JTextField("");             id_tt.setBounds(161, 50, 136, 29);             contentPane.add(id_tt);             id_tt.setColumns(10);              JLabel lblName = new JLabel("Name");             lblName.setBounds(39, 118, 71, 23);             contentPane.add(lblName);              name_tt = new JTextField("");             name_tt.setColumns(10);             name_tt.setBounds(161, 115, 136, 29);             contentPane.add(name_tt);              JButton insert = new JButton("Insert");             insert.setBounds(39, 388, 105, 30);             contentPane.add(insert);             insert.addActionListener(this);              Class.forName("net.ucanaccess.jdbc.UcanaccessDriver");             String dataSource = "jdbc:ucanaccess://D:/Database.accdb";             con = DriverManager.getConnection(dataSource, "", "");             Statement st = con.createStatement();          } catch (Exception e) {         }     }//end DB2 constructor            public void actionPerformed(ActionEvent ae) {          try {              String id = id_tt.getText();             String name = name_tt.getText();             String s1 = "INSERT INTO Table1 (ID, Name) VALUES (id,name)";             st.executeUpdate(s1);             id_tt.setText("");             name_tt.setText("");          } catch (SQLException e1) {             e1.printStackTrace();         }      } }                                                   please tell me what error did i make.thanks a lot

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


I found my laptop from 6 years ago that my partner installed your operating system on. I have no idea what the password is. I have attempted to change it in recovery but when I try to type in a new password it wont let my type anything. I can press enter but it continues to say; 'Authentication token manipulation error' and ' password unchanged'.  I am not amazingly tech savvy, i know how to find and fix alot of problems but this type of stuff... ive done everything I could think of.  Can anybody help me?

I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution?


(The questions are below the question heading)  I've seen this image posted:   I actually agree with it - that is not to say that $\mathbb{Q}$ isn't countable.    Reasoning The definition of bijection is a useful starting point, and it is easy to see that $\mathbb{Z}$ is countable. I shall denote this as $\mathbb{Z}\sim\mathbb{N}$ for simplicity.  I then take: $$f:\mathbb{Z}\times\mathbb{Z}\rightarrow\mathbb{Q}\text{ by }\ f:(a,b)\mapsto\left\{\begin{array}{lr}\frac{a}{b} & \text{if }b\ne 0\\ 1 & \text{otherwise}\end{array}\right.$$  There are other choices (like $\mathbb{Z}\times\mathbb{N} say) but this matters not. This mapping is surjective but not injective.   From this we know now: $|\mathbb{Q}|\le|\mathbb{N}|$     I got my set theory book out to check this, and it exhibits a similar map to mine and considers it proven that $\mathbb{Q}$ is countable, this is not enough as a function that maps numbers to even and odd has a finite range. It would prove that it is at most countable though? Can I use that?   I am not sure how to go from here, I was looking for a theorem along the lines of:       If $A\subseteq B$ then $|A|\le |B|$   We would then know that $|\mathbb{Q}|\le|\mathbb{N}|$ and $|\mathbb{Q}|\ge|\mathbb{N}|$  Questions   Can I do that with infinities? Are they ordered? Does $\le$ make sense? I know that exhibiting a bijection$\implies$ countability. As this is a definition it can be taken as $\iff$ (if we have a countable set, there must be a bijection with $\mathbb{N}$ - if there isn't it violates that it is countable). Thus for the statement in the image to be true we cannot have countability of $\mathbb{Q}$ ($^*$)     ($^*$) - damn, that shortens the point of this post.

I remember my professor in college challenging me with this question, which I failed to answer satisfactorily: I know there exists a bijection between the rational numbers and the natural numbers, but can anyone produce an explicit formula for such a bijection?


I didnt understand how to apply general relativity to Earth. If there is no such a thing as gravity but spacetime bending. Can someone just show, send something to read how gravity works in Earth according to general relativity? Why people don't fall from earth? I think that the idea is there is no difference between gravity and accelerating up. But what about southern hemisphere?

It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration. Do we also say along with it, that the object flying past in reality exeriences NO attraction force towards the massive object? Is it just following the spacetime geodesic curve while experiencing NO attractive force?  Now come to the other issue: Supposing two objects are at rest relative to each other, ie they are not following any spacetime geodesic. Then why will they experience gravitational attraction towards each other? E.g. why will an apple fall to earth? Why won't it sit there in its original position high above the earth? How does the curvature of spacetime cause it to experience an attraction force towards the earth, and why would we need to exert a force in reverse direction to prevent it from falling? How does the curvature of spacetime cause this?  When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve. So we cannot just say that it fell to earth because its geodesic curve passed through the earth. Why did the spacetime curvature cause it to start moving in the first place?


How can I prove that a system $\{t^k\}_{k=0}^{\infty}$ is not a Schauder basis for C([0,1]) I tried to come up with a function that on the one hand is equal to 1 when t->1, and on the other hand given series $\sum_0^{\infty}{\alpha_k t^k}$ doesn’t converge. And that will contradict a definition of a Schauder basis

why the monomials are not a Schauder basis for $C[0,1]$?  $p_n(x)=x^n$ such that $(p_n)$ does not form a Schauder basis for $C[0,1]$  span$\lbrace p_n : n\ge 0\rbrace$ is dense in $C[0,1]$ by Weierstrass approxmation theorem, but I cannot figure out why they are not a Schauder basis.  Could you please explain


I have a XML file(MyXML.xml) like this :  <?xml version="1.0" encoding="UTF-8"?> <S:Envelope xmlns:S="http://schemas.xmlsoap.org/soap/envelope/">     <S:Body>         <ns3:GetAllInfoFromRest xmlns:ns2="http://com.lanuk.cfe/b2_7/service/objects" xmlns:ns3="http://com.lanuk.cfe/b2_7/service/operations">             1111,GH43567,Hamburger,GET,278598655,\n000001,                    ,Kunal,Bhyuo,Ramond,856 K. 98 Rd,                                        ,                                        ,Tripura,AGT,INDIA,856987,                    ,S,S,S,8956,\666666         </ns3:GetAllInfoFromRest>     </S:Body> </S:Envelope>   Now i need to strip out the SOAP content and all the tag attributes from this xml and get only the string response 1111,GH43567,Hamburger,GET,278598655,\n000001,                    ,Kunal,Bhyuo,Ramond,856 K. 98 Rd,                                        ,                                        ,Tripura,AGT,INDIA,856987,                    ,S,S,S,8956,\666666.  How can i do it with awk or  sed ?  I tried it in this  way :  $ xgawk -lxml 'XMLATTR["xmlns:ns3"]=="http://com.lanuk.cfe/b2_7/service/operations"{print $2}' MyXML.xml   But obviously I am making some mistake  due to which it is not working.  Can some one suggest any other way around this ?

The Unix environment has some excellent tools for parsing text in various forms. However, of late, the data is not in the traditional (historical) formats (CSV, TSV, record-based or some other delimiter-based) it used to be before. Data these days is exchanged in structured formats like XML/JSON.  I know there are some good tools like sed, awk and Perl which can chew down nearly any form of data out there. However, to work with this sort of structured data, often one has to write a complete program, and, given the little time available to extract information, one has to sit down and figure out the whole logic of what one wants to query and put it down programmatically. Sometimes this is not OK – basically because the information extracted from those files acts as inputs for further work; also because of the time it takes to search for the appropriate solution and code it up. A command line tool is needed with sufficient switches to find, query and dump data.  I'm looking for tools that take a XML/JSON or other forms of structured data and dump it into other formats like csv, etc., so that from there one could use other commands to get any information out of it.  Are there any command line utilities you know of which do this kind of a job? Are there already awk/Perl scripts available to this?


Whenever I transfer large files, or large amounts of files, over USB to or from an external drive, the whole computer slows down to a crawl during the transfer. I'm using Ubuntu 14.04, but I've had this problem before in earlier versions. Why does this happen? I want to be able to file a bug report to stop this from happening.  Cheers, Reid

Yesterday I was copying a single, 8 GB file to a USB with a slow, 7 MB/s write speed, while my RAM is 3 GB. While copying the system froze, to the point where I couldn't even move the cursor.  I managed to log into the text console, and ran iotop, it showed that a process named kswapd0 was taking 99.99% of IO.  Are there workarounds so copying a large file doesn't make my system unusable?


Consider two conducting sheets separated by a dielectric and wound like in the picture below. Suppose the area of one of the unrolled sheets is $A$, the distance between the sheets is $d$ and the the dielectric $\epsilon_r$ fills the total space between the plates.  What is the capacitance of this system? If it was unrolled it would be $C = \epsilon_0 \epsilon_r A/d$. I think in wound configuration the capacitance should be larger by a factor 2 since then every plate "sees" each other twice (expect of boundary effects).  I feel that this argument is very vague and I am looking for a way to see this clearer in more detail.

If you have two parallel plates of opposite charge with a dielectric in between, then Capacitance $$ C = \dfrac{A \epsilon_{0}}{d} K$$ Where $ K $ is the dielectric constant. This is used to calculate the capacitance of a capacitor. However, a real capacitor is actually two of those plates rolled up many times. Wouldn't the electric field $ \vec{E} $ be different? So why is the equation for the capacitance still valid?


I have encountered the statement says that the statistics $${{X_1-\overline{X}} \over {S}},$$ where $X_i$ are i.i.d normal, is ancillary (where $S$ is the sample variance square root). I know that $(X_1-\overline{X})$ is normal, but I have no idea what the distribution is when divided by $S$. It looks might be $t$ distribution, but since the nominator and denominator are not independent, this may not be true. Does anyone have any idea? Thanks in advance!

Suppose $X_1, X_2,...,X_n$ be i.i.d from $N(\mu,\sigma^2)$ with unknown $\mu \in \mathcal R$ and $\sigma^2>0$  Let $Z=\frac{X_1-\bar{X}}{S},$ S is the standard deviation here.  It is can be shown that  $Z$ has the Lebesgue p.d.f.  $$f(z)=\frac{\sqrt{n} \Gamma\left(\frac{n-1}{2}\right)}{\sqrt{\pi}(n-1)\Gamma\left(\frac{n-2}{2}\right)}\left[1-\frac{nz^2}{(n-1)^2}\right]^{n/2-2}I_{(0,(n-1)/\sqrt{n})}(|Z|)$$  My question is then how to get this pdf?  The question is from  in example 3.3.4  to find the UMVUE of $P(X_1 \le c)$. I can understand the logic and procedures to find the UMVUE but don't know how to get the pdf.  I think this question also relate to this    Thank you very much for help or point to any related references will be also appropriated.


From Willard's General Topology:  Let $\tau_1$ and $\tau_2$ be Hausdorff topologies on the same set $X$. Let $\tau_3 = \tau_1 \cap \tau_2$. If $(X, \tau_3)$ is Hausdorff, then the diagonal is closed in $(X, \tau_1) \times (X, \tau_2)$.  I know that since $\tau_1, \tau_2,$ and $\tau_3$ are all Hausdorff, that the diagonal $\Delta = \{(x,x) : x \in X\}$ is closed in each of the following product topologies $(X, \tau_1) \times (X, \tau_1)$, $(X, \tau_2) \times (X, \tau_2)$, and $(X, \tau_3) \times (X, \tau_3)$. Without thinking much about the question, it seems intuitive that yes, $\Delta$ will also be closed in $(X, \tau_1) \times (X, \tau_2)$. I've tried to proceed by contradiction below, but I can't figure out how to finish it off. I would appreciate any help finishing it off. I tried to proceed by contradiction: Supposing that $\Delta$ is not closed in $(X, \tau_1) \times (X, \tau_2)$, then $\exists y \in X, y \neq x$, such that $(x,y) \in \overline{\Delta}$ (the closure of $\Delta$ in $\tau_1 \times \tau_2$). Then $\forall U \times V$ basic nbhoods of $(x,y)$, we must have that $(U\times V) \cap \Delta \neq \emptyset$. So $\exists z \in X$, such that $(z,z) \in U \times V$. Also, since $U \times V$ is a basic nbhood of $(x,y)$ in $(X, \tau_1) \times (X, \tau_2)$, then $U$ is a basic nbhood of $x$ in $(X, \tau_1)$ and $V$ is a basic nbhood of $y$ in $(X, \tau_2)$. But then, since $(z,z) \in U \times V$, we must have $z \in U$ and $z \in V$. So $U, V$ are not disjoint. But $U$ was an arbitrary basic nbhood of $x$ in $(X, \tau_1)$ and $V$ was an arbitrary basic nbhood of $y$ in $(X, \tau_2)$, so there cannot exist any open disjoint sets $A \in \tau_1$, $B \in \tau_2$ such that $x \in A$ and $y \in B$... I'm guessing this contradicts the Hausdorff-ness of $(X, \tau_3)$, but I'm having trouble putting it together. Thanks.

Let $X$ be a topological space. The diagonal of $X \times X$ is the subset $$D = \{(x,x)\in X\times X\mid x \in X\}.$$   Show that $X$ is Hausdorff if and only if $D$ is closed in $X \times X$.   First, I tried to show that $X \times X \setminus D$ is open using the fact that $X \times X$ is Hausdorff (because $X$ is Hausdorff), but I couldn't find an open set that contains a point outside $D$ and is disjoint to it...


It only seems the blinking line on desktop and Ubuntu software is not opening  i just updated using terminal then it is not opening

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


Is anybody able to recommend the best way to sound proof my wall which is adjoined to the bathroom.  I'm gutting out my bathroom and having it refitted which new shower, bath and etc and relocating the shower to the corner of the adjoining wall of the bedroom and exterior rear wall.  I want to minimise the sound that the shower,pipes etc would make.     What is the best product to use? Will the sound proof be resistant to water?

I'm trying to figure out the best, least intrusive way of sound proofing the walls of a bathroom. The bathroom shares a wall with my bedroom, and my 3 yea old's bedroom. The main problem is the sound of water running (plus every bump on the counter and everything) echos loud and clear through the wall into my sons room.  I found  and it seems like a good choice. Another option is adding another layer fo drywall with something like  between them. But all the walls and ceilings in the house are textured. So replacing just one or two walls in a room is just not possible.   This is the layout of the two rooms. I've added red box around the wall with the most noise.   Is there anything else I'm missing here that I could do to dampen the noise short of tearing the bathroom apart?


I am currently applying to graduate school in mathematics. In the last year of undergraduate study I have read many papers and books by experienced mathematicians, and with the help of my honours advisor, I have a list of potential PhD supervisors at universities in the USA and Europe.  I am wondering if it is good form to email mathematicians (or more generally any faculty) at graduate schools you are applying to, just to assert your general interests and/or goals to work with them.  I'm definitely not planning on spamming hundreds of mathematicians with a generic email, but there are a handful who I think I can say a few words to.  Is this type of think considered annoying? Does it help the application process in anyway? Does anyone else do this?

In his answer of , aeismail says     If the program in question is in the US, for instance, you should probably never contact the professor directly until after you've been admitted into the program in question. Since admissions decisions are handled centrally, it's just a waste of time.   Now I'm surprised with this, and I think I'm not the only one. For many times, not only in this site, but also in real-life examples in my university, I have seen that my friends get accepted through contacting professors beforehand, and those professors are helpful and willing to get you through the adcom. Recall it back, they don't go to US, but I don't think US should be an exception.  Why is it an exception? Why do the "admissions decisions are handled centrally", unlike other universities in the world, where the weight of the professors is heavier? Isn't that sorting the applications by score not good as checking their ability directly through interview? And who is the most suitable interviewer, if not the one who will advise you in the future?


If we keep differentiating $\sin x$ we eventually arrive back at $\sin x$:  $$ \begin{align} y &= \sin x \\ \frac{dy}{dx} &= \cos x \\ \frac{d^2y}{dx^2} &= -\sin x \\ \frac{d^3y}{dx^3} &= -\cos x \\ \frac{d^4y}{dx^4} &= \sin x \end{align} $$  It has to be differentiated 4 times before it gets back to itself  I was wondering, what function has the longest chain of derivatives before it gets back to itself?

Consider (non-trivial) functions that are their own nth derivatives.  For instance  $\frac{\mathrm{d}}{\mathrm{d}x} e^x = e^x$  $\frac{\mathrm{d}^2}{\mathrm{d}x^2} e^{-x} = e^{-x}$  $\frac{\mathrm{d}^3}{\mathrm{d}x^3} e^{\frac{-x}{2}}\sin(\frac{\sqrt{3}x}{2}) = e^{\frac{-x}{2}}\sin(\frac{\sqrt{3}x}{2})$  $\frac{\mathrm{d}^4}{\mathrm{d}x^4} \sin x = \sin x$  $\cdots$  Let $f_n(x)$ be the function that is it's own nth derivative.  I believe (but I'm not sure) for nonnegative integer $n$, this function can be written as the following infinite polynomial:  $f_n(x) = 1 + \cos(\frac{2\pi}{n})x + \cos(\frac{4\pi}{n})\frac{x^2}{2!} + \cos(\frac{6\pi}{n})\frac{x^3}{3!} + \cdots + \cos(\frac{2t\pi}{n})\frac{x^t}{t!} + \cdots$  Is there some sense in which this function can be extended to real n using fractional derivatives?  Would it then be possible to graph $z(n, x) = f_n(x)$, and would this function be smooth and continuous on both $n$ and $x$ axes?  Or would it have many discontinuities?


Probably duplicate ,      If $x$ and $y$ are non- negative real numbers and $x+y=2$ then prove that $x³y³(x³+y³) \leq 2$   I tried it by AM GM inequality but not getting.

If $x,y$ are positive reals such that $x+y = 2$ show that $x^3y^3(x^3+y^3) \leq 2$.   I thought about working backwards on this one. We can try to prove that $x^3y^3(x^3+y^3) \leq 2$ is true by first realizing that $x^3+y^3 = (x+y)(x^2-xy+y^2)$ and substituting in for $x+y = 2$. We then get $x^3y^3(x^2-xy+y^2) \leq 1$. How do I prove this is true?


Evaluate   $$ \lim_{n\to+\infty}\frac{1}{n}\sum_{k=1}^n\Big[\frac{2n}{k}\Big]-2\Big[\frac{n}{k}\Big], $$   where $[x]$ means the largest integer that no more than $x$.   Let $\Delta=\Big[\frac{2n}{k}\Big]-2\Big[\frac{n}{k}\Big]$, I found that  $$ \Delta= \begin{cases} 1,&\mbox{$\Big[\frac{2n}{k}\Big]$ is odd.}\\ 0, &\mbox{$\Big[\frac{2n}{k}\Big]$ is even}.\end{cases}   $$  By trying several cases for small number, I found that the cases $\Delta=1$ are quite rarely.

Problem: Evaluate $$ L=\displaystyle \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^{n} \left(  \left\lfloor \frac{2n}{k} \right\rfloor -2\left\lfloor \frac{n}{k}\right \rfloor \right).$$  Please help me with this one.  I tried using the sandwich theorem by first constructing the following  $$ 2 \geq \left\lfloor \frac{2n}{k} \right\rfloor -2\left\lfloor \frac{n}{k} \right\rfloor \geq -1 $$ and then summing over. But the limit of the two bounds are different so sandwich theorem doesn't help!. Is it possible to construct sharper bounds?  Also I observed that if we ignore question of continuity, etc. then we can write,  $L= \displaystyle \int ^{1}_{0}\left\lfloor \frac{2}{x} \right\rfloor -2\left\lfloor \frac{1}{x} \right\rfloor dx$  Now I am able to compute the above integral. But is the above process correct? If then how can make it rigorous? Or if any other approach is possible, please tell.


I have been building out an app and to save important time information I have been using System.currentTimeMillis() to get the timestamps in ms.  All my algorithms use this ms data and dates are saved with this ms data.  Also duration of cache is determined and object dates are formatted from this millisecond timestamp. I am unsure if this is a good practice though.  Is it better to use Calendar.getinstace() I have gathered that currentTimeMillis() could be a bad practice as it can lead to inconsistencies in the time data but I don't understand why this is.

In Java, what are the performance and resource implications of using  System.currentTimeMillis()    vs.   new Date()    vs.   Calendar.getInstance().getTime()   As I understand it, System.currentTimeMillis() is the most efficient. However, in most applications, that long value would need to be converted to a Date or some similar object to do anything meaningful to humans.


I have an old pc and it works perfectly with ubuntu 14.04 in newer versions it does not work that well, so I want to know exactly what is the downside and if I can continue to use ubuntu 14.04 , I'm a student and I only use it to programming and basic browser use like social media and youtube.

ESM is available for 12.04, which enables Advantage customers to keep receiving kernel updates and updates for many user space packages. In our case it's very important to know if we'll be able tot use Ubuntu 14.04 safely after April '19, because it is not possible to upgrade our application and migrate it to say, 16.04.


How do I change from user to superuser (root)? What command do I use in the Terminal to switch to root? I have tried --help but I get lost with all the listed help. I'm looking for a recent download/install so I can use it.

When I'm doing something that requires root be typed in dozens of times in a row, I prefer to switch my session to a root session. In the various tutorials and instructions I have used on the Internet, I see sudo su, sudo su -, sudo -i and sudo /bin/bash being used to open a root session, but I'm not clear on the difference between these and when or if that difference matters.  Can someone clear this up for me?


I have 2 structures of the same type and want to compare them. The size of the structure is 420 bytes and I want to skip over the first 2 bytes when I do the comparison since I know these will never match. I am using memcmp as follows:  ` typedef struct foo    // total of 420 bytes {   char c1,c2 ;   int x ;   struct temp y ;   ...  // lot of other members   ...   ... } ; foo f1, f2 ;  memset (&f1, 0xff, sizeof(foo) ) ; memset (&f2,0xff, sizeof(foo) ) ;  update_foo(&f1) ; // function which updates the structure by reading value from flash memory  // Now compare 2 structures starting with value x if ( memcmp(&f1.x, &f2.x, sizeof(foo)-2 ) == 0 )   // Do something else   // Do something else`   The result of comparison gives me random values. I assume that when I pass "&f1.x" and "&f2.x" I am skipping the first two bytes and the comparison will be for the remaining 418 bytes. Is this assumption correct?

How do you compare two instances of structs for equality in standard C?


It is given that $$pdf(x)=\lambda_1 e^{-\lambda_1 x}$$ for $x\geq0$ and elsewhere it is zero. Next, It is given that $$pdf(y)=\lambda_2 e^{-\lambda_2 y}$$ for $y\geq0$ and elsewhere it is zero. Assume that $x$ and $y$ are i.i.d.I need to find the pdf of $Z=X/Y$. Can someone give me hints or redirect me to some source. I has been a while since I have dealt transformation of random variables.

Let $X$ and $Y$ be independent exponential variables with rates $\alpha$ and $\beta$, respectively. Find the CDF of $X/Y$.  I tried out the problem, and wanted to check to see if my answer of: $\frac{\alpha}{ \beta/t + \alpha}$ is correct, where $t$ is the time, which we need in our final answer since we need a cdf.  Can someone verify if this is correct?


Long story short:  bash --version | head -n 1; [[ "abc" =~ "^a" ]] && echo Match || echo No match   Results on host 1:  GNU bash, version 3.2.25(1)-release (i686-redhat-linux-gnu) Match   Results on host 2:  GNU bash, version 4.1.2(1)-release (i386-redhat-linux-gnu) No match   What environment directives and/or configuration options should I check in order to produce consistent results?  For completion, please be advised they don't always fail to match all regular expressions. Slightly altering the regular expression (removing the "beginning of string" caret constraint) does produce consistent results:  bash --version | head -n 1; [[ "abc" =~ "a" ]] && echo Match || echo No match   Results on host 1:  GNU bash, version 3.2.25(1)-release (i686-redhat-linux-gnu) Match   Results on host 2:  GNU bash, version 4.1.2(1)-release (i386-redhat-linux-gnu) Match

The following code  number=1 if [[ $number =~ [0-9] ]] then   echo matched fi   works. If I try to use quotes in the regex, however, it stops:  number=1 if [[ $number =~ "[0-9]" ]] then   echo matched fi   I tried "\[0-9\]", too. What am I missing?  Funnily enough,  suggests this should work.  Bash version 3.2.39.


I am looking to see if I can solve an issue with installing different graphics card drivers.  I am using 18.04 with a Radeon HD6450 (quite old hardware) I can see drivers for these but they are for older versions of Ubuntu.  Will they cause an issue if I try and install on a later version than specified? Thanks

I have 14.04.5/16.04 or newer and an AMD GPU. I'm not getting the performance I want, and some programs say they need things like OpenCL.  I've heard about fglrx, but if I try to install it on my machine, it breaks and I have no GUI.  Is there anything I can do to get my AMD card working to its full potential?


is there any way to secure your whole code ? or some important files. which is not changeable to other even it is deployed to other servers like client's server.  or we can create any DLL file(which is not changeable) which can be run by Apache server and authenticate the requirements.

First of all, I'm not looking for miracle... I know how PHP works and that there's not really way to hide my code from the clients without using encryption. But that comes with the cost of an extension to be installed on the running server.  I'm looking for something different though... I'm not looking to encrypt my code or even obfuscate it. There are many PHP scripts without encrypted/obfuscated code but they are commercial applications. For instance, vBulletin and/or IP.Board forum applications.  I just want to know what approach do these guys use for their applications...  I'm also open to any other suggestions.  Please note that I'm a single person and not working for a company. My product is also very specific, it won't sell that much. I just want you guys to know that I can't afford to consult a legal professional either to sue someone or prepare a commercial license. I'm just looking for a simple way to protect my simple product, if it's indeed possible, somehow...


I am experiencing this weird bug where if a figure touches the top or bottom of a page, is the page numbering reset to zero on that page.  I haven't been able to make a minimal example showing the effect as it seems to be very situational. But I have attached a picture of the resulting pages at the bottom of this post. (Don't mind the blurred out text.)  What could cause this weird behaviour, is it a bug or intended? If it is a bug, where can I report it? And what can I do about it? (Besides changing picture sizes and moving text around by hand.)    Edit: I have made the smallest version of the file I can and attached it here: The picture used is also attached. The first page is indexed as page number 0, when it should be 1.  Notice that I use a non-standard header, footer and margin size. I don't think this should influence that the bug can appear.  The highlight of the text in the second section is necessary to show the bug, I am not sure why.   \documentclass[a4paper, 12pt]{article}  \usepackage{float} \usepackage[margin=2cm, includefoot, footskip=30pt, includehead, headsep=20pt]{geometry} \usepackage{graphicx} \usepackage{soul}  \begin{document} \section{Lorem ipsum dolor sit amet}  \subsection{Lorem ipsum dolor sit amet} Lorem ipsum dolor sit amet, consectetur adipiscing elit. In sollicitudin pulvinar sapien in tempus. \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\  \begin{figure}[h]     \centering     \includegraphics[width=.8\textwidth]{tree.png}     \caption{Lorem ipsum dolor sit amet, consectetur adipiscing elit. In sollicitudin pulvinar sapien in tempus.}     \label{fig_areasOfWork} \end{figure}  \section{Next section} Lorem ipsum dolor \hl{ Lorem ipsum dolor sit amet, consectetur adipiscing elit. In sollicitudin pulvinar sapien in tempus.  Etiam non orci ut dolor efficitur sodales. Mauris egestas sapien nunc, in facilisis mauris elementum ac.} \end{document}

I recently ran into a curious bug when using the soul package. I managed to boil it down to the following example. The problem is that the page numbers get messed up. In the example below, they should be 1, 2 and 3. In fact, they are 1, 0 , and 1, in that order. It appears (in some cases) that adding blank lines inside a \hl environment sometimes causes this problem, and removing the blank lines fixes the problem. As one can check, removing the blank line inside the \hl{} fixes the problem in the example below. It is also possible to fix the problem in other ways.  Anyway, now that I have discovered this, I can work around the problem in my paper. However, I'm curious as to what is causing this, so I thought I might as well post the question. I didn't try asking the creator ofsoul, which I think is probably unmaintained. The last update was a long time ago. This is with Debian squeeze, using TeX Live 2009 and soul.sty version 2.4.  I'm using the LaTex function dummytext below to generate dummy data courtesy of the kind folks on this site, see  The specific solution I'm using is by .  \documentclass[10pt]{article} \usepackage{soul} \usepackage{pgffor} \usepackage{setspace} \doublespacing \newcommand\dummytext[3]{%     \foreach \n in {1,...,#3} {%         \foreach \k in {1,...,#2} {%             #1%         }%         \\     }% } \pagestyle{myheadings} \begin{document} \dummytext{HelloWorld}{5}{52}  \dummytext{HelloWorld}{5}{17} \hl{  x } \end{document}


Why is $$L=\lim_{x\to 0} (1+x)^{1/x}=e$$  I understand that if we take log on both sides and solve we get $L=e$ but if we inspect right hand limit, then base is slightly greater than $1$ and exponent approaches $+\infty$, hence overall value must approach $+ \infty$ . If we inspect Left hand Limit, then base is slightly less than $1$ and exponent approaches $-\infty$, hence overall expression should again approach $+\infty$. Then why is limit approaching towards $e$.

From : In calculus and other branches of mathematical analysis, an indeterminate form is an algebraic expression obtained in the context of limits. Limits involving algebraic operations are often performed by replacing subexpressions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is known as an indeterminate form.    The indeterminate forms include $0^{0},\frac{0}{0},(\infty - \infty),1^{\infty}, \ \text{etc}\cdots$   My question is can anyone give me a nice explanation of why $1^{\infty}$ is considered to be an indeterminate form? Because, i don't see any justification of this fact. I am still perplexed.


I am using a script that emails me a particular status report. The script sends me the contents of several files. I am using echo to provide a heading in the email that is used to differentiate between parts of the files. I need to make the heading bold and underlined. However, when I do this using tput bold and tput sgr0, or \033[1m the email sends an attachment instead of just populating the body of the email with the data I want. For instance, in the script I have tried placing these variables at the top and wrapping the variables around the text I want bolded:  bold=${tput bold} normal=${tput sgr0}  echo -e "${bold}Bolded text${normal}"   I have also tried:  echo -e "\033[1mBolded text:\033[0m"   But like I mentioned when I use these methods I get a .bin attachment instead of the data in the body of the email. If I stop trying to bold the headings it works as expected, except my heading does not stand out. I am wondering if this is not compatible when combined with mailx. Is there a way to make this work when emailing? Here is my complete echo command with mailx:  { echo -e "\n" "\033[1mBolded Text:\033[0m" "\n" "\n"  "More text:"; cat     /script; } | mailx -r "user" -s "email subject " someone@somewhere.com

mail -s "subject" xxxxx@gmail.com <test.html works, but only for plain text email.  What is the correct way to send HTML email using the Linux command mail?


The problem I was given is as follows:    Let $(X,\mathcal{A},\mu)$ be a measure space.  Let $\{A_i\}$ be a strictly increasing sequence of inclusions on $\mathcal{A}$, i.e.,          $$ A_1 \subset A_2 \subset \cdots \subset A_i \subset A_{i+1} \subset \cdots $$         Prove that          $$ \mu\left(\bigcup_{i=1}^\infty A_i\right) = \lim_{N\rightarrow\infty}\mu(A_N) $$ My attempt at a proof:         $$\mu\left(\bigcup_{i=1}^\infty A_i\right) =  \mu\left(\lim_{N\rightarrow\infty}\bigcup_{i=1}^N A_i\right) = \lim_{N\rightarrow\infty}\mu\left(\bigcup_{i=1}^N A_i\right) = \lim_{N\rightarrow\infty}\mu(A_N) \qquad \blacksquare$$  This seems too good to be true -- is the second equality justifiable?

Show that if $A_1\subseteq A_2\subseteq A_3\subseteq\cdots$ is an increasing sequence of measurable sets (so $A_j\subseteq A_{j+1}$ for every positive integer $j$), then we have $$m\left(\bigcup_{j=1}^\infty A_j\right)=\lim_{j\to\infty}m(A_j)$$  Here is my proof: According to the $\sigma$-algebra property, $\bigcup_{j=1}^{\infty}A_j$ is a measurable set, so it makes sense to talk about $m(\bigcup_{j=1}^{\infty}A_j)$. Firstly, I prove that $\lim_{j\to\infty}m(A_j)\leq m(\bigcup_{j=1}^{\infty}A_j)$. This is because for any given positive integer $N$, $A_N\subseteq \bigcup_{j=1}^{\infty}A_i$, according to monotonicity, we have $m(A_N)\leq m(\bigcup_{j=1}^{\infty}A_i)$. Take the limit,we will have $\lim_{j\to\infty}m(A_j)\leq m(\bigcup_{j=1}^{\infty}A_j)$. Secondly, I prove that $m(\bigcup_{j=1}^{\infty}A_j)\leq \lim_{j\to\infty}m(A_j)$. For any given positive integer $N$, $\bigcup_{j=1}^N A_j = A_N$. According to monotonicity,we have $m\left(\bigcup_{j=1}^N A_j\right)=m(A_N)\leq \lim_{j\to\infty}m(A_j)$. Take the limit, we will have $m\left(\bigcup_{j=1}^\infty A_j\right) \leq \lim_{j\to\infty} m(A_j)$. Combine the above two arguments, we will see that $$m\left(\bigcup_{j=1}^\infty A_j\right)=\lim_{j\to\infty} m(A_j)$$$\Box$  The above is my proof, unlike many books, my proof does not use the property of countable additivity. So I doubt my proof is correct. Who can point out where are my mistakes?


In C++11, to find out whether a class has a member function size, you could define the following test helper:  template <typename T> struct has_size_fn {     typedef char (& yes)[1];     typedef char (& no)[2];      template <typename C> static yes check(decltype(&C::size));     template <typename> static no check(...);      static bool const value = sizeof(check<T>(0)) == sizeof(yes); };   Is there a similar trick for doing this in C++98 without relying on compiler extensions such as typeof?

Is it possible to write a template that changes behavior depending on if a certain member function is defined on a class?  Here's a simple example of what I would want to write:  template<class T> std::string optionalToString(T* obj) {     if (FUNCTION_EXISTS(T->toString))         return obj->toString();     else         return "toString not defined"; }   So, if class T has toString() defined, then it uses it; otherwise, it doesn't. The magical part that I don't know how to do is the "FUNCTION_EXISTS" part.


Since I recently started to use c++ STL library, so i found that there are so many methods to iterate through a vector some of which are-: vector<int> V for(int i=0; i<V.size(); ++i) //using index based method  for(auto it=V.begin(); it != V.end(); ++it) //using iterator based method  for(const auto& x : V) //using range based loop  So my question is which one is the most efficient method to use and when to use rest of the methods?

Take the following two lines of code:  for (int i = 0; i < some_vector.size(); i++) {     //do stuff }   And this:  for (some_iterator = some_vector.begin(); some_iterator != some_vector.end();     some_iterator++) {     //do stuff }   I'm told that the second way is preferred. Why exactly is this?


I watched the crossover between Supergirl and The Flash and as probably all of you also did, noticed a device we hadn't really seen before on Barry's chest.  I can only assume it has something to do with the blueprints he got from Wells but we haven't seen that thing before.  Was The Flash in Supergirl a future version of The Flash or is it just because both series don't run simultaneously?  And the main question is what that device does for him? Anyone who knows this through any other sources? Comics, etc..

I am a bit confused with the The Flash/Supergirl crossover. I always thought Supergirl was Earth-1, but The Flash rescued her and implied that she was Earth-2. If she is Earth-2 and The Flash has rescued her by accidentally crossing over to Earth-2, what is that thing on his chest? The tachyon accelerator Dr. Well was talking about in the Flash Back episode of The Flash? I thought the purpose of that device was making him faster? How did he change his frequency enough to change Earths?


Given f and g defined in $ [0,1] $ continuous and increasing in that interval. Show that: $\int_{0}^{1}f\left(x\right)dx\ .\ \int_{0}^{1}g\left(x\right)dx\ \le\ \int_{0}^{1}f\left(x\right)g\left(x\right)dx$ I've looked everywhere about the properties of integrals but I haven't found this one. Why?

Given two monotonically increasing continuous functions $f,g$ prove that  $$(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx,\; b>a$$  what I have tried:  Let $$h(x) = (x-a)\int^x_a f(t)g(t) dt - \int^x_a f(t)dt\int^x_a g(t)dt $$ and trying to figure out that $h'>0$ using MVT to reform $h'(x)$ as   $$h'(x) = (x-a)(-f(x)g(\xi_1) - g(x)f(\xi_2) + f(x)g(x) + f(\xi_3)g(\xi_3))$$ where $\xi_{1,2,3} \in (a,x)$ (That method does not seem to work)


When one orders an "almond milk latte," can "almond milk" be considered an adjective?

I read this recently in :     At the end of the summit, the French and European officials had   claimed a points victory over the Germans by getting them to agree   more firmly to a target date of January 1st next year to entrust the   European Central Bank (ECB) with the ultimate authority to supervise   the euro zone’s 6,000-odd banks.   "Points" is a plural, and I suppose it doesn't function as a noun in this sentence since it's following the article "a", so is it an adjective adorning "victory"?


I do not know if this correct. So I ask.  Given a number $n\geq 2$, can we find a Galois extension of $\mathbb Q$ such that the group has order $n$? Similarly, given $n\in \mathbb N$ can we find a totally imaginary number field that is a Galois extension of $\mathbb Q$ and for which the order of its Galois group is $2n$?

An old qual problem asks us to     Show that for every positive integer $n$, there exists a cyclic extension of $\mathbb{Q}$ of degree $n$ which is contained in $\mathbb{R}$.   A first thought might be towards Kummer theory: we could adjoin an $n^\text{th}$ root of, say, a prime number.  But when $n>2$, $\mathbb{Q}$ lacks the full cohort of roots of unity that would make this work.  If $n$ is a power of $2$ we can get what we want by adjoining ($\mathbb{Q}$-linearly independent) square roots to $\mathbb{Q}$, and I think some  things can be done in other degrees ( at least $n=3$ and $n=5$)  but a more general $n$ has me stumped.  Could I get a nudge in the right direction on this problem?


My husband has lost all his calendar entries after upgrading to iOS 7 on his iPhone earlier today. He deleted 3 football calendars from his iPhone as they were duplicated.  Everything was fine.  Now everything is gone, including on iCloud.  He has no back up elsewhere.  Any ideas?

Calendar on iPhone 4s does not work with iOS 7. It stopped working 2 days ago. It won't open on the phone. iCloud is working fine and so is iCal on my MacPro.  How do I get it to work again?


I need to run perfomance testing for a simple java class which does some simple file read and write. I am new to perfomance testing and all the tools I am seeing are for web application. Which tool should I use.  My program has four methords doing same purpose and written in different logic I want to find which of the methord is more efficient

How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related:


Running df -h gives me the following:  Filesystem                       Size  Used Avail Use% Mounted on /dev/mapper/centos-root           50G   49G  1.3G  98% / devtmpfs                         7.8G     0  7.8G   0% /dev tmpfs                            7.8G     0  7.8G   0% /dev/shm tmpfs                            7.8G  769M  7.1G  10% /run tmpfs                            7.8G     0  7.8G   0% /sys/fs/cgroup /dev/mapper/centos-home           78G  182M   78G   1% /home /dev/sda1                        497M  338M  160M  68% /boot tmpfs                            1.6G     0  1.6G   0% /run/user/0   I want to allocate more spare to /dev/mapper/centos-root, by reducing the allocation for /dev/mapper/centos-home  How would I remove 50GB from home and give it to root?    Further Info  Running mount tells me the following:  /dev/mapper/centos-home on /home type xfs (rw,relatime,seclabel,attr2,inode64,noquota)   Does this mean it's the XFS filesystem? When I run resize2fs I get the following error:  resize2fs: Bad magic number in super-block while trying to open /dev/centos/home Couldn't find valid filesystem superblock.

I'd like to resize an existing LVM partition and add the space to another LVM partition.  [root@dckapstaging ~]# df -h Filesystem                           Size  Used Avail Use% Mounted on /dev/mapper/vg_dckapstaging-lv_root   50G   50G     0 100% / tmpfs                                3.9G     0  3.9G   0% /dev/shm /dev/sda1                            485M   91M  369M  20% /boot /dev/mapper/vg_dckapstaging-lv_home  215G   93G  111G  46% /home   I want /dev/mapper/vg_dckapstaging-lv_root to be extended to another 15 GB from /dev/mapper/vg_dckapstaging-lv_home; how can I do it?


Show that if  $\gcd(a,b)=d\Rightarrow\gcd(a^2,b^2)=d^2\ $    $\gcd(a,b)=d\Rightarrow\ d\mid a,b\Rightarrow\ \ d^2\mid a^2,b^2\Rightarrow\ d^2\mid\gcd(a^2,b^2)$. But to complete  the proof we must show that: $\gcd(a^2,b^2)\mid d^2$ How can I achieve this?

The problem's quite clear. Prove that $$\gcd(a^2, b^2) = \gcd(a, b)^2$$  This is easy to understand intuitively and using the Fundamental Theorem of Arithmetic would be easy but I want to prove it by using the Divisibility axioms and the GCD. I have attempted it and am mentioning my results.  Here $d = \gcd(a, b)$.   $$d | ax + by \implies d^2 | a^2x^2 + 2axby + b^2y^2 \implies d^2 | a^2x^2 + b^2y^2 \implies \gcd(a^2, b^2) | d^2$$  I feel that this is not necessary. Please help.  Also, the proof can be generalized to $$\gcd(a^n, b^n) = \gcd(a, b)^n$$  Any help would be appreciated.


If I press Escape by mistake while working, it exits full screen mode.  I could use Ctrl+Cmd+F if I want to exit full screen mode. How can I prevent Escape key in full screen mode?

I use Safari in Full Screen mode on OS X Mavericks all the time.  I also use the escape key in web pages fairly frequently for various things (depends on the webpage).  One unfortunate side effect of these two facts is that I will occasionally turn off Full Screen mode inadvertently by hitting the escape key on a page that doesn't intercept the escape key.  Is there a way to disable the "Escape turns off full screen mode" behavior in Safari?


I have: Passengers:[{id:falling_block,Block:command_block,Time:1,TileEntityData:{Command:"setblock ~4 ~-5 ~ command_block 1 replace {Command:"fill ~-2 ~-1 ~-2 ~4 ~3 ~2 minecraft:air"}"} (there is more code but that isn't relevant). Anyway, when I run the command block it says there is an error:     [09:59:24] Data tag parsing failed: Expected '}' but got 'f' at: ...command_block 1 replace {Command:"f<--[HERE]    Please help :V

I need help with a specific command that I am using in a new game that I am creating inside of Minecraft. The command is:  /give @p sign 1 0 {BlockEntityTag:{Text1:"{"text":" [MF2]","color":"gold","clickEvent": {"action":"run_command","value":"tellraw @a [""{"text":"[MF2]  ","color":"gold"},{"selector":"@p","color":"dark_aqua"},{"text":" is now an admin of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"},display: {Name:"Custom Sign"}}   If I take out the /tellraw command then the command works fine, but I need the command in there to announce to the game that a new admin has joined.  With the tellraw command, the error message is the following:  Data tag parsing failed: Unexpected token 't' at: text":" [MF2]","color":"gold","clickEvent":{"action":"run_command","value":"tellraw @a [""{"text":"[MF2] ","color":"gold"}, {"selector":"@p","color":"dark_aqua"},{"text":" is now an admin  of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"   If anyone knows how to fix this, please let me know.


A boolean ring is a commutative ring where $x^{2} = x$ for every $x$.  Why in such a ring a finitely generated ideal is principal ?

The classical book on commutative algebra Introduction to Commutative Algebra, by Atiyah and Macdonald, has the following as exercise I.11.       A ring is Boolean if $x^2=x$ for any $x$ of $A$. In a Boolean ring $A$, show that     i) $2x=0$ for all $x\in A$;    ii) Every prime ideal of $A$ is maximal, and its residue field consists of two elements;   iii) Every finitely generated ideal of $A$ is principal.     I can but solve the first two of them; for the last one, I cannot even perceive the situation here, for it will not, generally speaking, be a Dedekind domain, whereof my knowledge is somewhat more. I have hitherto tried to find one element for each ideal of two generators which can stand the stead of them, and then proceed by induction. But even the first step fails to produce any result. Thanks for any hints and inspirations in advance.


Even though there are several other questions with answers in this blog, I found the answers to my following question very useful. I want to render animations of a shiny type of steel, for example, the goal is having a rendering like this, but with a white background!  It seems the lighting, environment and HDRI are important, but I could not make it work! The result of my rendering is this picture:  Can you please have a look at this file and give any hints about any changes that I should do?  Thanks, Kind regards

When I apply a glossy shader to the material of my text, the text becomes just black. Why?    I have lamp and everything, but the problem persists. The text is red before I add the glossy shader.  I'm using Cycles render.   Thanks!


I did something like this.  var person = function (){   this.print = function ()   {     console.log('person');   } }  console.log(person.prototype);   This logs Object{}, but if I do:  person.prototype.print = function () {     console.log('person'); }  console.log(person.prototype);   Now it prints the entire object and its proto

I'm not that into dynamic programming languages but I've written my fair share of JavaScript code. I never really got my head around this prototype-based programming, does any one know how this works? var obj = new Object(); obj.prototype.test = function() { alert('Hello?'); }; var obj2 = new obj(); obj2.test();  I remember a lot discussion I had with people a while back (I'm not exactly sure what I'm doing) but as I understand it, there's no concept of a class. It's just an object, and instances of those objects are clones of the original, right? But what is the exact purpose of this ".prototype" property in JavaScript? How does it relate to instantiating objects? Update: correct way var obj = new Object(); // not a functional object obj.prototype.test = function() { alert('Hello?'); }; // this is wrong!  function MyObject() {} // a first class functional object MyObject.prototype.test = function() { alert('OK'); } // OK  Also these  really helped a lot.


Use the Laurent series of $e^{1/z}$ on the punctured plane $\mathbb{C} - \{0\}$ to compute $1/\pi \int_0^\pi e^{\cos\theta}\cos(\sin\theta-n\theta) d\theta$ for $n=0,1,2,...$   I have been trying to attempt this question from my complex analysis book and I am not sure where to even begin. All I know is that the Laurent series of $e^{1/z}$ is $f(z)=\sum_{n=0}^{\infty} \frac{1}{n!}\frac{1}{z^n}$, for all $|z|>0$.   I have no idea how this relates the the integral though because there is no $e^{1/z}$ only a $e^{\cos\theta}$ in the integral. I thought maybe I have to put the $\cos\theta$ values into Taylor form but I'm not sure if that's correct.  Any help is greatly appreciated! Thanks :)

I'm taking a complex analysis course and doing some practice computing residues & evaluating integrals. I pulled out an old book called     On page 196-197, there are some interesting integrals to evaluate. I'm at 5.4.3.10.: I was able to do question 1, but was stumped at how to even begin with question 2:     Evaluate the integral   $$\int_0^{2 \pi} e^{\cos x} \cos (nx - \sin x) \,dx ,$$   where $n$ is an natural number.   The answer is simply $\frac{2 \pi}{n}$. Any hints?


When using the Stack Exchange Android app, it is not possible to search for a specific word or topic across all the sites (you have to pick a site first then search for the problem).  But It's possible to search for a specific question or word in Stack Exchange in Google, by typing the question and adding "Stack Exchange" at the end of it, and  also got "search all sites" option: (using Google custom search)        Can such functionality please be added to the android app as well? It's hard to know where I can find an answer for some questions or words.

Is it possible to search for a question across all Stack Exchange sites in the Android app?   Right now I can search in only one specific site at a time.   If not, can you add that feature?


Is the former like there were a few days where a single shooting star appeared? And is the latter like there were a few days where one or more than one shooting stars appeared?

I never saw anyone work as hard as he did, many a time I saw him on the weekends working to his highest standards to give the best research he could give.   From the context, I understand many a time equals many times. My question is when we can use this structure. Can we, for example, say many a person in place of many people?  A link explaining this structure will be appreciated.


I am new to to Ubuntu. My laptop is connected to the WiFi but I am not being able to access internet. However the same WiFi is working on my mobile. If any other information is reqd than I can provide the same.

I'm having serious problems installing the Broadcom drivers for Ubuntu. It worked perfectly on my previous version, but now, it is impossible.   What are the steps to install Broadcom wireless drivers for a BCM43xx card?  I'm a user with no advance knowledge in Linux, so I would need clear explanations on how to make, compile, etc.    lspci -vnn | grep Network showed:   Broadcom Corporation BCM4322 802.11a/b/g/n Wireless LAN Controller [14e4:432b]      iwconfig showed:  lo        no wireless extensions. eth0      no wireless extensions.   NOTE: Answer below is updated every time new information is added and confirmed working.


With C/C++ macros it's quite easy to generated long constructs automatically. For example, if I want a huge set of methods to not ever throw exceptions (a must for COM-exposed methods) I can do something like this:  #define BEGIN_COM_METHOD\     try{  #define END_COM_METHOD\     return S_OK;\     } catch( exception& ) {\         // set IErrorInfo here\         return E_FAIL;\     }   to make such macros manageable one can use "\" character to make the macro definition multiline and more readable.  The problem is sometimes code with such constructs will not compile - something will not expand as expected and invalid code will be present to the compiler. Compiler usually have "generate preprocessed file" option to show the developer the preprocessing result. But in the preprocessed file the macro is expanded into one line and the result is barely readable.  Is it possible to make the preprocessor to keep the linebreaks present in the macro definition?

How do I write a cpp macro which expands to include newlines?


I have a couple of big text files and in the file UNIQS.txt I have a list of strings to grep from another file. The code I use is  grep -f UNIQS.txt EEP_VSL.uniqs.sam > UNIQ_templates.sam   which does nothing - the file generated is empty. But when I do  grep -F -f UNIQS.txt EEP_VSL.uniqs.sam > UNIQ_templates.sam   it works correctly. This confuses me because I didn't think grep would interpret the entries in UNIQS.txt as regexp patterns without quotes and slashes and so on being in the file (which there aren't). Is it the case in general that if you are getting the patterns from a file then it will automatically think that they are regexp patterns?  Edit: In the UNIQS.txt file, there are newline separated strings of the form  HWI-ST365:215:D0GH0ACXX:2:1101:10034:186783   (called template names) and the file EEP_VSL... tab separated columns, with about 14 columns and the first column is the template name, so basically I want to extract the line corresponding to each template in the file.


Just out of curiosity I tried making a new operation to see its properties. It is like a variation of addition that works like this: a ¨ b = a + b - 1 For example, I found that it has the commutative property and that a ¨ b ¨ c ¨ d ... = a + b + c + d + ... - [number of operations done] Then I tried to make the equivalent of the multiplication in terms of this operation. The same way as a*b is a+a+a+a...(b times), a " b = a ¨ a ¨ a ... (b times) From here I find that a " b = ab - b - 1 What I can't figure out is whether this formula can also be applied for negative numbers or zero. By the way, I found that it doesn't have the commutative property. Since it is a negative number I don't know what it would mean to repeat the first operation a negative number of times. I know that for example 5*(-3) equals -15 because it is the same as doing - 3 - 3 - 3 ... (five times), but since my operation does not have a commutative property I don't know how to look at this problem. I realise this question might be silly but I hope someone can help me. Thank you in advance.

here says a new operation addition and new operation multiplication  x ⊕ y = x + y − 1, x ⊗ y = x + y − xy on set Z,where the operations on the right hand side are ordinary addition and multiplication of integers. Prove that the set Z equipped with these two new operations ⊕, ⊗ is a ring. Does it have a multiplicative identity?  I tried to use the addition cancellation but I do not understand why or I got the wrong understanding for this question.   I assume the there is y and y' are 2 solution for equation  x ⊕ y = x + y − 1, therefore:   x ⊕ y = x + y − 1  x ⊕ y' = x + y − 1 and I get  x ⊕ y =  x ⊕ y' after the cancellation, then I get y=y', and it means the addictive is unique. So, can I say that the set Z equipped with new addiction x ⊕ y = x + y − 1? or I just go into a wrong way for solve this problem?  ask in advance, thank you


I'm trying to center this image vertically inside a div. As you can see I've accomplished that, however, it's still pushed slightly towards the bottom of the div. I can't find any reasons why this would be and I've even tried a different image.   HTML:

   My CSS:  html, body {     margin: 0;     background: #F7B267; } .site-header {     background: #eee;     color: #555;     height: 3.125em;     line-height: 3.125em;     margin-bottom: 1rem; } .logo {     max-height: 75%;     vertical-align: middle;   }   Result:

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...


I'm getting a rather unhelpful NullPointerException from my junit test of my Azure Functions test service with SpringCloud.  I am a complete novice at this, so I apologize if this seems obvious.  The stack trace:  java.lang.NullPointerException    at org.springframework.cloud.function.adapter.azure.AzureSpringBootRequestHandler.doResolveName(AzureSpringBootRequestHandler.java:86)  at org.springframework.cloud.function.context.AbstractSpringFunctionAdapterInitializer.initFunctionConsumerOrSupplierFromCatalog(AbstractSpringFunctionAdapterInitializer.java:387)  at org.springframework.cloud.function.context.AbstractSpringFunctionAdapterInitializer.initialize(AbstractSpringFunctionAdapterInitializer.java:124)  at org.springframework.cloud.function.adapter.azure.AzureSpringBootRequestHandler.handleRequest(AzureSpringBootRequestHandler.java:58)  at test.TestCloud.start(TestCloud.java:42)   I thought maybe that the NPE was caused by me passing null into the 2nd parameter of handleRequest, but this is what the example I looked at was doing.  I've tried with both the commented line or the line below it, using the concrete extension I made or the generic version.  Both behaved the same, and control never gets to the execute method.  The example uses the generic class, but the specific implementation seemed to make more sense to me (otherwise I don't see how the connection gets made).      @Test     public void start() throws Exception { //        AzureSpringBootRequestHandler<String, String> handler = new AzureSpringBootRequestHandler<String, String>(CloudFunctionApplication.class);         AzureReverseAdapter handler = new AzureReverseAdapter(CloudFunctionApplication.class);         String result = handler.handleRequest("Hello World", null);         handler.close();         Assert.assertEquals(result, "dlroW olleH");     }   The test class has just one function in it right now, and it is below.   @FunctionName("reverseString") public String execute(@HttpTrigger(name = "request", methods = {HttpMethod.GET, HttpMethod.POST}, authLevel = AuthorizationLevel.ANONYMOUS) HttpRequestMessage<Optional<String>> request, ExecutionContext context) {      context.getLogger().info("Input: " + request.getBody().get());     return handleRequest(request.getBody().get(), context); }   The CloudFunctionApplication class has a method that look like below.  Oddly, and I don't know how, but control DOES get to this function.  I thought the execute method was supposed to act as a redirect but it seems to find reserveString anyway.  I guess because it is the only @FunctionName?    This is the method.  The breakpoint on the return(value) -> { line get hit by the breakpoint, but then the exception happens before the internal gets called.   @Bean public Function<String, String> reverseString() {     return (value) -> {         return new StringBuilder(value).reverse().toString();     }; }   UPDATE: The linked question absolutely is NOT a duplicate of this question. Yes, all NullPointerExceptions are because something was null when you tried to dereference it. That link was a generic treatment of that.  This was a specific question about why I was getting that from a 3rd party library.  So they are absolutely NOT the same.  However, I have found the issue as suggested in the comments.  It was that I was passing null in as the 2nd parameter.  This seemed allowed because of the example I was working on which did the same.  My solution was to mock fabricate an ExecutionContext object that returned basic values.  Unfortunately, I can't record that as the answer because someone thinks I was just asking what a NullPointerException was and marked the question as a dupe.  So for anyone else who hits the same issue, that was my answer.

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


I have recently proven that given $f:X\rightarrow Y, f$ continuous, X connected, then Y is connected. I wonder if the converse is true if we consider open mapping. In other words, Given X and Y connected set, if $\exists f:X\rightarrow Y$ s.t.  $f(U)$ is open in Y $\forall$ open set $U\subset X$, then can we prove that f is continuous?

What is an example of an open map $(0,1) \to \mathbb{R}$ which is not continuous? Is it even possible for one to exist? What about in higher dimensions? The simplest example I've been able to think of is the map $e^{1/z}$ from $\mathbb{C}$ to $\mathbb{C}$ (filled in to be $0$ at $0$). There must be a simpler example, using the usual Euclidean topology, right?


I installed the java jre via my package manager and get this version:  $ java -version java version "1.8.0_66" Java(TM) SE Runtime Environment (build 1.8.0_66-b17) Java HotSpot(TM) 64-Bit Server VM (build 25.66-b17, mixed mode)   But the current Java Update is 71, so I downloaded it from the  , but I don't know how to install the download and what exact file I should download. How do I do that? I use Ubuntu 14

I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7?


When a linear regression model yields correlated errors it is claimed that the standard error of the estimators is under estimated. Can anyone give a proof of this fact? This is stated on page 94 of Introduction to Statistical Learning by James, Witten, Hastie, and Tibshirani

It  that OLS residuals autocorrelation is not always an issue, depending on the problem at hand. But why residuals autocorrelation would  the coefficient standard errors? From the :      While it does not bias the OLS coefficient estimates, the standard   errors tend to be underestimated (and the t-scores overestimated) when   the autocorrelations of the errors at low lags are positive.


How to draw centerlines of Oriented Minimum Bounding Box in the orientation closest to overall orientation of all polygons collectively in the layer in QGIS? I have a shapefile of Oriented Minimum Bounding Box rectangles (accessible from the following link: ) produced by using Oriented Minimum Bounding Box Tool in QGIS and as Input Layer: a shapefile of irregular polygons (accessible from the following link: )  Figure 1: Shapefile of Oriented Minimum Bounding Box  Figure 2: Shapefile of Irregular Polygons I constructed centerlines using the centroid of the polygons (in this case rectangles) and angle values in the attribute table of Oriented Minimum Bounding Box using the following expression:  The overall orientation of all polygons collectively as illustrated in the Rose Diagram below from the Line Direction Tool QGIS plugin:  approximates to 30 degrees.  I am seeking to draw the centerlines of each polygon in the overall orientation of all polygons in the layer collectively. That is, the deciding factor whether the centerline will be drawn either across the shortest segment or the longest segment of each polygon, will be the angle of the resulting centerline. For example, let assume that the overall orientation of polygons collectively is 30 degrees. Angle of Centerline of polygon across shortest segment is 40 degrees, Angle of Centerline of polygon across longest segment is 130 degrees, The centerline of polygon with angle 40 degrees is drawn. 40 degrees being closer to 30 degrees, which is the overall angle of all polygons collectively. This rule is applied for each centerline in each polygon in the layer when drawn.

How can I calculate dominant angle of a polygon in QGIS without main_angle function? I have a shapefile of Oriented Minimum Bounding Box rectangles (accessible from the following link: ) produced by using as Input Layer a shapefile of irregular polygons (accessible from the following link: )  Figure 1: Shapefile of Oriented Minimum Bounding Box  Figure 2: Shapefile of Irregular Polygons I need to find the main_angle of every polygon in the Oriented Minimum Bounding Box layer. I used the main_angle function available in QGIS 3.16 onwards. main_angle function returns the main angle of a geometry. However, when I constructed centerlines using the centroid of the polygons (in this case rectangles) and main_angle values computed using the main_angle function in QGIS with the following expression:  intersection ( extend (     make_line (         centroid ($geometry),          project (             centroid ($geometry),              25000,              radians("main_angle")         )     ),     25000,     0 ), $geometry  ) Main_angle of the polygons computed with main_angle function is not at all times the angle of longest collection of segments as in the image below encircled below:  What expression can be used such that main_angle is always the angle of longest segment of the Oriented Minimum Bounding Box in a project whereby main angle of every Oriented Minimum Bounding Box is the determining factor of accuracy of end results. I found this comment from the following link:  You need an expression dependent on the height and width data:  The end result I am seeking is the overall orientation of all ploygons collectively as illustrated in the image below from the Line Direction Tool QGIS plugin. By unfortunately provides no values.  I used XLSTAT to use Principal Component Analysis but did not achieve conculsive results. Computed results and report is accessible from following link:


If I'm writing 100% ANSI C but compiling in .cpp files will the compiler automatically "optimize" malloc and free calls to new and delete? Does that even make sense given their differences? I didn't think this is how it worked but a friend of mine said this is what happens.

I see in C++ there are multiple ways to allocate and free data and I understand that when you call malloc you should call free and when you use the new operator you should pair with delete and it is a mistake to mix the two (e.g. Calling free() on something that was created with the new operator), but I'm not clear on when I should use malloc/ free and when I should use new/ delete in my real world programs.  If you're a C++ expert, please let me know any rules of thumb or conventions you follow in this regard.


I use Ubuntu 13.10.  I don't like to put my password at each time.  How to attain the logging without password entry ?

Whenever Ubuntu boots up, a dialogue pops up asking me to unlock my default keyring. Is there some way this can unlock automatically through PAM or some other magical way?


I want the inner while loop to be broken when the input data is 5, but if the input is other than 5, the loop will be executed again. In this code, the input value of each number I enter is printed as X = 1: x = 1 while True:     def state():         x = input("Enter Your number:")      while True:         print(x)         if x==5:             print('x=5')             break         state()   In this code, I tried to solve the problem but it didn't work too. condition = True x = 1 while True:     def state():         x = input("Enter Your number:")      while condition:         print(x)         if x==5:             print('x=5')             condition = False         state()   Is there anyone to help me?

Given the following code (that doesn't work):  while True:     #snip: print out current state     while True:         ok = get_input("Is this ok? (y/n)")         if ok.lower() == "y": break 2 #this doesn't work :(         if ok.lower() == "n": break     #do more processing with menus and stuff   Is there a way to make this work? Or do I have do one check to break out of the input loop, then another, more limited, check in the outside loop to break out all together if the user is satisfied?


Problem: For integer $n>2$, show that $(n!)^2 > n^n$   My attempt: I tried using induction. For $n=3$, the given condition is satisfied. Let us suppose $k!^2>k^k$ for some $k\geq3$.  Then, $(k+1)!^2 =k!^2(k+1)^2> k^k(k+1)^2$  Thus if I can somehow show that $k^k(k+1)^2\geq(k+1)^{k+1}$,  i.e., $k^k\geq(k+1)^{k-1}$,  I am done.  Any hints/suggestions are welcome. Any non-inductive proofs are also allowed

Show that if $n>2$, then $(n!)^2>n^n$.     My work: I tried to apply induction. So, at the induction step, I need to prove, $n^n>(n+1)^{n-1}$ Here, I tried to use induction again without any luck. I also took log of both sides, but I did not get anything. Please help!


I've seen this question asked before but the answers either didn't quite seem to address the question, or were very old so I'd like to see if there's any way to do this today.  I have a mid-2011 iMac that does support Target Display Mode, but since I want to connect it to a Windows (7 Home) PC I understand TDM to be irrelevant and it won't work.  So, is there in fact any way at all to physically connect my iMac and use it as the display for my Windows PC?  A software solution won't do since this PC is almost exclusively for gaming and decent performance is required.  My video card is a GeForce 1050ti and has DVI and HDMI options on it.  I know this is a long shot but... is it possible at all?

Recently (less than one year ago) i bought an iMac 21,5". Now i would like to use it as secondary monitor for my laptop. (My laptop runs Windows 7).  Is it possible? (I found conflicting opinions on the web, even on the Apple forum).  What type of cable do I need? (I will appreciate also a link to the product on some online store: amazon, ebay etc.)  Thank you in advance.  UPDATE:  I tried air display... i'm not satisfied at all...  typical scenario: browser window on the main Windows laptop, dev tools/firebug on the secondary iMac screen. The mouse goes fast between the 2 screens (GOOD), but when i changed the selected tab nothing happens. I had to drag the dev tools window to the main screen to get an update of the selected tab.  My test is ended here.  I'm still waiting for other answers.   I will prefer an answer that suggest me what kind of cable i've to buy, and where i can find it on the web.


When I manually 'check for updates' , it gets stuck on 'checking for updates'  I read that I should install KB3112336 manually, but the standalone installer also gets stuck on 'searching for updates on this computer'  And above all both take 17% CPU (100% of a single virtual core)  I'm pretty much losing fate in Windows  help me please

I am attempting to install two hotfixes manually from Microsoft - one addresses the svchost.exe extreme memory usage problem, and the other addresses the slow Windows Update problem.  This system is a freshly installed Windows 7, and I have the two MSU updates saved locally to my desktop, but it is never actually finding such updates, and therefore never actually installs the two fixes.  Is there a way to force Windows Update Standalone Installer to just install the single update and not look for all the updates?


In The Dark Knight a city-wide surveillance system resembling sonar is portrayed. What is the in-universe explanation of how Gotham's phone's speakers and microphones are able to be used to generate and interpret the waves used to operate Batman's surveillance system?

In Nolan's Dark Knight, Batman (or rather Lucius Fox) develops a technology which allows using a phone as a mini-radar (I didn't quite catch if it was using EM like radar or sound like sonar, but given this is Batman I wouldn't be shocked if it was sonar).   Was this technology detailed anywhere as being hardware based or software based? If it was stated as hardware based, how exactly did Batman manage to equip pretty much everyone in the entire city with a new phone containing that hardware in the short time period that the movie takes place in? If it was software based, how did he download the software to both emit and receive the signals onto EVERYONE's phone without the cell companies objecting[1]?    I am looking for answers from canon (movie, script, DVD, delete scenes); creative team interviews; or if there are specific DC comics that Nolan based the movie on, I'm ok with answer from those specific comics if it matches up to the movies.  [1] If it was software, I would accept an answer listing the (canon) fact that Wayne was a major cell carrier in Gotham  h/t: Based on a comment on another post.


I've been trying to solve this problem, I realized the following: For example, for $3|6$ we have: $$F_6=F_5+F_4=(F_4+F_3)+F_4=2F_4 + F_3$$ I realized that doing this, for $m,n$ and $m|n$ we will always get an expression such as: $$F_n=xF_m+yF_{m+1}$$ The value of $x$ doesn't seems to matter. But if $y=F_m$ which I strongly suspect it is, then we are done because: $$F_n=F_m(x+F_{m+1})$$ Until now, I've been unable to show that $y=F_m$ or find another way to prove this. I've been stuck for a while, can you help?

Given the Fibonacci sequence $(F_1, F_2,F_3, ...)$ how do I prove that if $m|n$ then $F_m|F_n$? Can this be proven with mathematical induction?


This function is not sum correctly. sum=1    aj=121 sum=12   aj=12 sum=121          aj=1 This is not show in the alert.   // declaring the recursive function /////////////////////////////////////////////////// function isPal(aj, n) {   var sum = 0;   //alert("aj=" + aj);   if (Math.trunc(aj) != 0) {      sum = sum * 10 + aj % 10;      alert("sum=" + sum + " aj= " + aj + " n=" + n);     isPal(aj / 10, n); // recursive call same as while(n!=0) using loop   } else if (sum == n)     return 1;   else     return 0; } //////////////////////////////////////////////////// var palindrome; n = parseInt(prompt("Enter a number to check for Palindrome", "121")); palindrome = isPal(n, n); alert("palindrome = " + palindrome); if (palindrome == 1)   alert(n + " is palindrome\n"); else   alert(n + " is not palindrome\n");

How do I check if a number is a palindrome?  Any language. Any algorithm. (except the algorithm of making the number a string and then reversing the string).


The Avenger's side implies everyone joining the battle against Thanos, from the mystic art warriors to Valkyrie.  Of course, this doesn't include,      Tony Stark who has died after the battle.

During the final battle in Avengers: Endgame, apart from the obvious death of      Tony Stark,    were there any other known protagonist casualties such as Asgardians, Sorcerers, Wakandans etc.


Can somebody explain for what activities users get the Generalist badge, because I didn't understand its short description.

Formerly List of all badges with full descriptions.  What are badge name's requirements? Why didn't I get badge name ? Which badges can I earn multiple times?    Jump to:                    Note: Some badges are awarded based on score. The term score means the total number of upvotes minus the total number of downvotes.  Any badge with a *** next to it is one of 20 badges that count towards the  displayed on a moderator candidate in an election. The candidate score is a total of 40 points: the first 20 are awarded based on the user's rep divided by 1000 and rounded down; the second 20 represents the total number of unique badges earned of the 20 that count. Note that if the same badge is earned multiple times, it will only count once towards the candidate score.  Any badge with a "(retired)" next to it is no longer awarded, but is retained by users who previously earned them. See  for more info on what it means for a badge to be retired.       Visit the  of the  on any site to see a complete list of badges that you can filter by earned, unearned, or type.


I was working on the system all day on Friday and had it logged out for the weekend. This morning when I try to boot Ubuntu, I'm taken to a screen consisting of the default desktop purple-orange and nothing else. I can right click and use the standard options available, but nothing else. I have tried every possible keyboard shortcut for the terminal (other answers say to run ccsm) but I can't get a terminal to appear.   Is there another way to get the terminal to show up so I can attempt to fix this? Any other workarounds?

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


I have a table which roughly looks like this   uuid uuid,  id id,  data text, last_updated timestamp   Each row has an associated unique uuid. However, the key of interest is the id (indexed). Whenever we do an update, it happens that a row with the same id is inserted, the timestamp is the moment of putting it in the database, and it gets its own uuid. I would like to retrieve several of these rows in one query, but retrieving only the latest version.   So far I have   SELECT * FROM table WHERE id IN (16638051, 14727883)  GROUP BY id, uuid;   (ids are examples). However, I'm curious how to efficiently retrieve only the rows with the latest timestamp in that query?  Or would doing a single row at a time and retrieving it as a transaction be better?  UPDATE  This seems to do the trick (from ).  SELECT * FROM (    SELECT DISTINCT ON (id) *    FROM   table    WHERE  id IN (14727883, 16638051)     ORDER  BY id, last_updated DESC NULLS LAST    ) sub ORDER BY last_updated DESC NULLS LAST   However, I wonder if a materialized view wouldn't be easier. It's a read heavy & low write database with a couple million rows, with the updates only happening daily.

I'm sure its a simple question and I suppose it was asked many times, but I just can't figure it out from other answers, sorry.  I use recent versions of PostgreSQL and MySQL. I have 2 tables:  CREATE TABLE authors (     id INT,     name VARCHAR )  CREATE TABLE posts (     id INT,     author_id INT,     text VARCHAR,     date DATE )   I need to select one most recent post for each author. Thanks!  UPDATE  Thanks, both links provide answers to my question with some exception. All the following queries give the same result (which one is the most efficient btw?) The issue is when there is more than one post from the same author with the same date. Then the returned result set contains all such posts. How should I modify these queries to return exactly one post per author?  SELECT p1.* FROM posts p1 LEFT JOIN posts p2 ON p1.author_id = p2.author_id AND p1.date < p2.date WHERE p2.author_id IS NULL ORDER BY p1.author_id;  SELECT p1.*  FROM posts p1 INNER JOIN (   SELECT author_id, MAX(date) AS max_date   FROM posts   GROUP BY author_id) p2   ON p1.author_id = p2.author_id AND p1.date = p2.max_date ORDER BY p1.author_id;  SELECT * FROM posts p1 WHERE date = (SELECT MAX(p2.date)               FROM posts p2               WHERE p1.author_id = p2.author_id) ORDER BY author_id;  SELECT * FROM (     SELECT author_id, MAX(date) date     FROM posts GROUP BY author_id ) p1 INNER JOIN posts p2 USING (author_id, date) ORDER BY author_id;


Whenever I try to read about what are Hooks in Drupal, and how to manipulate forms or content with them, the text seem not to deal with the UI at all, but mostly with coding... Maybe I did not encounter the right reading material about UI-Hook relationship?  Can someone please detail in simple words and  a simple example?   What are Hooks? Do you use them via UI or only through Coding?  Do I need to know PHP to use a module such as Hook form-alter?

I am intermediate in PHP. To polish my skills I start learning Drupal 7. While learning Drupal architecture concepts, the terms hooks and bootstrapping puzzled me a lot. I read the "Pro Drupal development" book, and some documentation on drupal.org, but it is so advanced for me to learn how hooks work in Drupal to display the web page.  Can anyone tell me what hooks are in simple words?


I would like to know how do I reconstruct the data using only the first principal component of the PCA?

Principal component analysis (PCA) can be used for dimensionality reduction. After such dimensionality reduction is performed, how can one approximately reconstruct the original variables/features from a small number of principal components?  Alternatively, how can one remove or discard several principal components from the data?  In other words, how to reverse PCA?    Given that PCA is closely related to singular value decomposition (SVD), the same question can be asked as follows: how to reverse SVD?


For reasons beyond me, I can no longer access the following question:     What can I do?

I asked and answered a question on an SE site without registering. I was accessing my unregistered account through my browser, which kept me logged in. However, someone reset my cookies and now I've lost my account.   Is there anyway to regain it, or should I give it up for lost?


Problem Let $R$ be a ring of continuous functions from $\mathbb{R}$ to $\mathbb{R}$. Show that $A = \{f \in R \mid f(0)=0\}$ is a maximal ideal of $R$.  If $f,g \in A$, then $f-g(0) = f(0)-g(0) = 0$ . So $f-g$ is in $A$. Also $f(0) h(0) = 0$ for all $h \in R$. So $A$ is an ideal. Attempt to show $A$ is maximal If  $R/A$ is a field then $A$ is maximal. Let $f \notin A$. Then $f(0) \neq 0$. Let $g(x)=0$. Then $f-g \in A$. So $f+A = g+A$. $1/g$ is the inverse of $g$. So $f$ has unity (not sure about this). Is this correct?

Well, the problem I'm trying to solve is this:      Let $A$ be the ring of all continuous functions from $\mathbb{R} \to \mathbb{R}$. Show that $M = \{f \in A: f(0)=0\}$ is a maximal ideal of $A$.   I tried to show that if $J$ is an ideal of A that properly contains M, so $J = A$: we know that there is a function $g \in J$ with $g(0) \neq 0$. So, we have that $$J \supseteq \langle g, M\rangle=\{ag+f;a \in A, f\in M\}$$   I tried to show that 1 $\in$ $\langle g,M\rangle$. However I'd have to find some function $h(x)\in A$ such that $h(x)(ag+f) = 1$, but this function $h$ has to be different from 0 for all x $\in \mathbb{R}$, so I don't know how to find this function.  My second idea to solve this problem was prove that the quocient $A/M$ is a field. We have that $$A/M = \{h(x) + M; h(x) \in A\},$$ but again I have the problem to show that all elements of $A/M$ are units.  If someone could help, I would be really grateful (:


Question  How (quantitatively speaking) does temperature influences rate of turnover of transcription factors?  Which protein?  As I am not looking for any accurate number I am talking about an "average" transcription factor. I leave to you the choice of answering this question with some very accurate example (Transcription factor GTF II A for example) or with some broad observation on how temperature influences protein turnover.  The organism I'd like to model is a typical unicellular eukaryote such as a yeast for example that lives at "standard" range of temperature (between 5°C and 35°C roughly speaking).  Of course, I am not interested in considering a transcription factor that is directly involved in some response to a change in environmental temperature. I am interested in transcription factors which are involved in developmental pathways that have nothing to do with reaction of the body to temperature.  I am looking for a referenced answer $\ddot \smile$

For computer modeling purposes, I am looking for some referenced quantitative measurements of the effect(s) of temperature on biochemical reactions.  Question  In particular, my question is:  How does temperature influence the rate of protein degradation?  Reducing the scope of my question  My question might be too broad in the sense that there might have too much variance in how different proteins respond to temperature in order to draw in general tendency. If this is so, someone willing to answer may reduce the question to transcription factor, to  or even to .    I am NOT looking for..  I am not looking for a theoretical explanation of how temperature influences this process (I have basic understanding of the importance of the activation energy as displayed on a Maxwell-Boltzman distribution and of the Michaelis-Menten equation).  I am looking for..  I am looking for a function that I can plug in my algorithms to incorporate the influence of various temperatures on the process I want to simulate. I want to simulate the average gene network from an average standard eukaryote. For other purpose, I chose parameter values coming from the yeast. A index such as the  would be very useful as well.  Similar already-answered question  Similar questions have been asked and answered  and


I dont' want it done automatically, I just want to get a bunch of screenshots from the phone to the Mac (OS X El Capitan). I plug in the phone but only iTunes starts up and I can't find any photos in it.

I would like to import my photos off my camera without using the OS X Photos app and locate my photos direct in the Finder so I can store them in folders, edit them in Photoshop etc. (i.e. do whatever I like with my files without getting involved with the Photos app)  This app automatically recognises my camera and offers to import but I can't work out how to import them to a folder or seperate hardrive where I can sort through the files.  Does anyone know how to import to a folder? or even access the individual files in finder if photos has to be used for import?   …or is there a free import software I can use to avoid "photos " completely  (Theres no camera software available for Yosemite from the company that made my camera)


I can get the not equal to sign, but can't seem to find the not equivalent sign!

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


I'm trying to connect 32 I²C "root of trust" NXP A71CH devices.    I'm trying to multiplex 32 devices for that chip.   I'm looking for a very fast way of multiplexing those 32 devices, an idea or schematic or a design.  The only solution that I found is to use an FPGA.  Is there a clever solution with just normal embedded microcontrollers ?  One chip costs 50ms, If I want to do 1000 signing, it would cost 1000*50ms. What I want to achieve is to have 1000signing with just 50ms cost. Is there a way of that without using FPGAs ?! Only with discrete components

I'm trying to connect 32 I²C "root of trust"  devices.    I'm thinking about a good way that does that, I mean what kind of communication should I use? A digital multiplexer that selects a device? but based on what? switching on the VDD source? but that needs reinitialization of the device and that takes time.


For some reason i can not understand,a TypeError occures when using min and max functions..  Here is the code: import random from typing import List, Any, Union  list1 = []  for i in range(0,200):     x = random.randint(1,50)     list1.append(x)  list2 = [ j for j in range(0,51)]  list1.append(list2) print(list1)  del list1[99:130]  print(len(list1))  print(min(list1))   And this is the error:TypeError: '<' not supported between instances of 'list' and 'int'  Thank you :)

What's the difference between the list methods append() and extend()?