I am trying to show that the series $$\sum _{n=1}^{\infty} \sin n$$ diverges but has bounded partial sums.   Plugging in some terms we see that,  $$\sum _{n=1}^{\infty} \sin n = \sin1 +\sin2 +\sin3+...+\sin n$$  My idea is to try and use $$e^{i\theta} = \cos\theta+i\sin\theta$$ $$e^{in}=\cos n+\sin n$$ $$\sin n = Im(e^{in})$$  But how can I use this to show that a finite geometric series won't converge to anything, therefore diverge, but is bounded?

Let $A_n=\sum\limits_{k=1}^n \sin k $ , show that there exists $M>0$ , $|A_n|<M $  for every $n$ .


I want to sort an list of string that sometimes contains numeric values  My list is like this:   Bedroom 1 Bedroom 2 Bedroom 10 Bathroom 1 Bathroom 2 Bathroom 10 1 Light 1 Paper   If I just use an orderby: roomList.OrderBy(x => x.Name) I get this list:   1 Light 1 Paper Bathroom 1 Bathroom 10 Bathroom 2 Bedroom 1 Bedroom 10 Bedroom 2   Is it possible to get the list like this instead ?   1 Light 1 Paper Bathroom 1 Bathroom 2 Bathroom 10 Bedroom 1 Bedroom 2 Bedroom 10   All list elements don't contain a number, and the list is about 1500 rows long  I have tryed to use this code, and it works fine on elements containing number, but not on just string elements:  public class SemiNumericComparer : IComparer<string>     {         public int Compare(string s1, string s2)         {             if (IsNumeric(s1) && IsNumeric(s2))             {                 if (Convert.ToInt32(s1) > Convert.ToInt32(s2)) return 1;                 if (Convert.ToInt32(s1) < Convert.ToInt32(s2)) return -1;                 if (Convert.ToInt32(s1) == Convert.ToInt32(s2)) return 0;             }              if (IsNumeric(s1) && !IsNumeric(s2))                 return -1;              if (!IsNumeric(s1) && IsNumeric(s2))                 return 1;              return string.Compare(s1, s2, true);         }          public static bool IsNumeric(object value)         {             try             {                 int i = Convert.ToInt32(value.ToString());                 return true;             }             catch (FormatException)             {                 return false;             }         }     }

Anyone have a good resource or provide a sample of a natural order sort in C# for an FileInfo array?  I am implementing the IComparer interface in my sorts.


Wizard 1 casts  which surrounds Wizard 2. Now both wizards have full cover against each other. For example, now they cannot cast fireball against each other, because "nothing can physically pass through the wall" per its rules.  But what about ? From description:     You tap into the nightmares of a creature you can see within range and create an illusory manifestation of its deepest fears, visible only to that creature   I think wall of force does not help against phantasmal killer because nothing is physically passing through the wall, but I wanted to confirm if that's how RAW works here.

The spell description of  is silent on the question of whether spell effects can pass through the wall.  The semi-relevant part of the description states:     Nothing can physically pass through the wall.  It is immune to all damage and can't be dispelled by dispel magic.  A disintegrate spell destroys the wall instantly, however.  The wall also extends into the Ethereal Plane, blocking ethereal travel through the wall.   How are folks ruling on the question of spells passing through the wall (in both directions)?  If the answer is that spells cannot pass through the wall, do you rule that it also blocks line of effect (so that you can't target a spell on the other side)?


What makes Sun’s corona so hot? I tried to google it but can’t find satisfactory answer.

How does the surface of the photosphere conduct thermal energy from the convective zone to the corona, while remaining at such a relatively low temperature itself?  It seems odd to me that the photosphere is wedged between the convective zone and the corona, both of which are millions of degrees in temperature, while the photosphere itself is observed to be much colder by comparison - approx. 5-10 thousand degrees.  Based on my understanding of convection, this would require thermal energy to jump from the convective zone directly to the corona, and somehow skip the photosphere surface material in-between.  Is there a different model of convection that explains this? Or is there a type of matter with thermal conductive properties that could accomplish this?  EDIT: Perhaps the convective zone is emitting heat as a different form of energy, such as electromagnetic - thereby allowing the outer layers to cool and sink in standard convection, but without directly heating up the surface of the photosphere.  Based on my understanding of the standard model of the sun, the following layers should be present:  Predicted:   The core A central area with pressures high enough to induce hot fusion of atomic nuclei The radiative zone A spinning ball of somewhat solid material surrounding the core, through which energy is conducted via radiation   Semi-observable:   The convective zone A layer of plasma surrounding the radiative zone, through which energy is conducted thermally via convection flows - millions of degrees in temperature This is the subject of some 2012 studies by NASA in coordination with various other reputable institutions, which observed that the sun's convection appears to be "anomalously weak"    Observable:   The surface of the photosphere The border between the convective zone and the corona - temperature in the ballpark of 5-10 thousand degrees The corona The outer plasma atmosphere, where flares take place - millions of degrees in temperature


Suddenly any webcam (integrated on USB) stopped working. For example my integrated camera (but any other USB connected camera produce the same) it works on my windows 10 partition, but it doesn't work anymore in Ubuntu 16.04. Here some commands that can be useful: Is listed in lsusb Bus 002 Device 002: ID 2109:0813 VIA Labs, Inc.  Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 003: ID 064e:930b Suyin Corp.  Bus 001 Device 005: ID 1bcf:0005 Sunplus Innovation Technology Inc. Optical Mouse Bus 001 Device 004: ID 0c45:7603 Microdia  Bus 001 Device 002: ID 2109:2813 VIA Labs, Inc.  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub  uname -a produces: Linux name 4.4.0-189-generic #219-Ubuntu SMP Tue Aug 11 12:26:50 UTC 2020 x86_64 x86_64 x86_64 GNU/Linux  dmesg | grep uvcvideo is: [   20.044256] uvcvideo: Found UVC 1.00 device HP Truevision HD (064e:930b) [   20.044265] Modules linked in: uvcvideo(OE+) videobuf2_vmalloc videobuf2_memops videobuf2_v4l2 videobuf2_core hp_wmi(+) v4l2_common sparse_keymap videodev(OE) media intel_rapl x86_pkg_temp_thermal intel_powerclamp coretemp arc4 rtl8188ee kvm_intel kvm snd_hda_codec_hdmi rtl_pci irqbypass rtlwifi mac80211 crct10dif_pclmul crc32_pclmul ghash_clmulni_intel snd_hda_codec_realtek cfg80211 snd_hda_codec_generic snd_hda_intel aesni_intel snd_hda_codec aes_x86_64 lrw gf128mul glue_helper snd_hda_core ablk_helper snd_hwdep cryptd joydev input_leds serio_raw snd_pcm snd_seq_midi snd_seq_midi_event snd_rawmidi snd_seq snd_seq_device intel_pch_thermal snd_timer lpc_ich shpchp hp_wireless mei_me mei snd soundcore processor_thermal_device int340x_thermal_zone intel_soc_dts_iosf int3400_thermal acpi_thermal_rel [   20.044334]  [<ffffffffc08bbb30>] uvc_probe+0x490/0x2aa0 [uvcvideo] [   20.044361]  [<ffffffffc08d2024>] uvc_init+0x24/0x1000 [uvcvideo] [   20.044412] usbcore: registered new interface driver uvcvideo  No program can detect the webcam, I tried with cheese "no device found" and also skype or chrome. In case you were wondering, I have no key to disable the webcam in my laptop (HP 15-ac194nl) and secure boot is disabled in BIOS (there no other options in BIOS reguarding the webcam). I already tried different reboots. Actually I don't know exactly when the problem appeared. Any hints?

The new kernel versions (4.4.0-186-generic and 4.4.0-187-generic) the ubuntu cannot recognizes my USB cameras (neither the original from the laptop or another USB webcam). If I start on the previous kernel version (4.4.0-185-generic), both work fine. Here is the result of "lsusb": ... Bus 001 Device 003: ID 04f2:b537 Chicony Electronics Co., Ltd  Bus 001 Device 009: ID 046d:0892 Logitech, Inc. OrbiCam  ... But they do not appear as /dev/video0 and /dev/video1, and cannot be detected by cheese, or zoom, or meet, and etc. Is there any additional driver required for those kernel versions, or it is really broken? Thank you


I've heard different type pf answers for this qs and not really sure which one to go for.

When speed is the path traveled in a given time and the path is constant, as it is for $c$, why can't light escape a black hole?  It may take a long time to happen but shouldn't there be some light escaping every so often?  I'm guessing that because time is infinite inside a black hole, that this would be one possible reason but wouldn't that mean that we would require infinite mass?  What is contradicting with measuring black holes in solar masses, what means they don't contain infinite mass.  So how can this be?


I want to get a space to the phrase "1\times 8 \mathrm{ matrix}", how can I get it inside the math environment?     \begin{align*} C_{D_{1\succ 2}, \mathrm{increasing}}   &=  \underbrace{\begin{pmatrix} 1   &   -1  &   1   &   -1  &   1   &   -1  &   1   &   -1  \\ \end{pmatrix}}_{1\times 8\mathrm{ matrix}}       \\ A_{D_{1\succ 2}, \mathrm{increasing}}   &=  \underbrace{\begin{pmatrix} 1   &   0   &   1   &   0   &   1   &   0   &   1   &   0   \\ 0   &   1   &   0   &   1   &   0   &   1   &   0   &   1   \\ 1   &   1   &   0   &   0   &   1   &   1   &   0   &   0   \\ 0   &   0   &   1   &   1   &   0   &   0   &   1   &   1   \\ 1   &   1   &   1   &   1   &   0   &   0   &   0   &   0   \\ 1   &   1   &   1   &   1   &   0   &   0   &   0   &   0   \\ 0   &   0   &   0   &   0   &   1   &   1   &   1   &   1   \\ \end{pmatrix}}_{7\times 8 \mathrm{ matrix}}. \end{align*}

I want to my statement to say u = g in Omega.  I tried coding $$u=g in \Omega$$, but this results in no spaces around the word 'in'.  How can I insert them?


was put on hold as "Primarily opinion-based" by user-voting on 2016-11-13 12:02:08. Yet, an answer was posted 55 minutes later on 2016-11-13 12:57:34.  How is that possible?

Question:   Answer:   The question was closed at 11:57:57 (according to the hover-over-"x-mins-ago" bar) and the answer was posted at 12:16:35. It's a fairly lengthy answer, so it's possible that it was started to be written before it was closed but I swear I've started to answer a question then I got a banner along the top saying "this question has been closed" and the answer was no longer post-able.


Occasionally, I will see a post that has  (or even ) rated content. The offensive flag can be applied to these posts. Should I wait for the community to declare it offensive and have the post removed, should I edit the post to remove the offensive content, or should I do both?

When flagging, there are two special case options: spam and rude or abusive.   What is spam, and when should I flag content as such? What is considered offensive, rude or abusive content? How does the spam flag differ from the rude or abusive flag? What is the effect of these special flags? When are these flags removed?


Please see the error of this program in the image  It is in java swing     blog: solvedprograms.blogspot.com  thanks  anuj    Please see the error of this program in the image  It is in java swing     blog: solvedprograms.blogspot.com  thanks  anuj   import java.applet.*; import javax.swing.*; import javax.swing.event.*; import java.awt.event.*; import java.awt.*; import java.io.*; import java.lang.*;  public class d1 implements ActionListener { JButton jb; JFrame jf;  d1() { button(); frame(); jf.setVisible(true);  }  public void button() { jb=new JButton("p2222222"); jf.add(jb,BorderLayout.EAST); jb.addActionListener(this); }   public void frame() { jf=new JFrame("p2 frame"); jf.setSize(500,500); } public void actionPerformed(ActionEvent ae) { if(ae.getActionCommand().equals(jb.getText())) {  } }  public static void main(String args[])throws IOException { SwingUtilities.invokeLater( new Runnable() {     public void run()     {     d1 a=new d1();     } }                  );   }  }

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 know one can logout from an individual SE site by clicking the logo in the SE bar and selecting "Log Out" next to the current site. However, is it possible to logout network-wide without logging out from each site individually?

Is a "log out from every SE site in the network" button technically feasible?  With so many SE sites popping up, it would be a very useful feature.  Edit: has this been implemented now, as @Ben suggests in his comment? I've lost track.


The rotation of the Earth about its axis makes it bulge at the equator and contract at the poles due to the centrifugal forces. How do we know, without any external references, that the Earth is spinning if there is nothing to compare it to? For example, imagine it was spinning in empty space with no other objects. Does it still bulge at the equator?   Particularly, what can we say theoretically about it?

What is the proof, without leaving the Earth, and involving only basic physics, that the earth rotates around its axis?  By basic physics I mean the physics that the early physicists must've used to deduce that it rotates, not relativity.


I was just reminded of this incident, and was wondering if somebody could explain how this could be possible!  In 2012, I took a flight to America and used my iPod Touch 4th Generation throughout the trip - whilst Airplane Mode was enabled during the flight, when touching down and after collecting everything and exiting the airport terminal, I then disabled this feature so that Wi-Fi was once again enabled. It's important to note that at this point, I hadn't connected or done a search for any nearby Wi-Fi networks, and when checking the time on the iPod itself the device was still showing my local time - and not the new time of the state that I had flown to.  Several hours later, when arriving at my hotel, I once again checked my iPod and to my surprise found that whilst I still hadn't connected to any Wi-Fi networks, the iPod had updated its time to match that of my new location. How would this have been possible if no network connectivity had taken place - is this a known feature? I haven't seen this since (and I've gone to America since this particular trip took place).

If there's no GPS in the iPod, how can it know (with such a good precision) my location?


I am travelling to the UK in the 3rd week of November on a business visit and intend to stay for more 10 days, along with my wife, when my business is over. I have my visa, but my wife's visa was refused.  I transferred around 1100 pounds into her accounts close to her visa appointment date, with an intent to enhance her financial strength. She has been working for the last 2 years and we submitted her salary slips, bank statements (last 6 months) and her latest ITR. Because of this fund transfer, we mentioned that she would be bearing 75% of the trip cost and the rest 25% would be borne by me. However, I didn't provide any cover letter or any of my salary slips or bank statements along with her application.  The rejection letter states two reasons primarily:        The most recent credit amount of GBP £1100 doesn't match with the salary credits reflected in the statement. Also, the documents and information that you have provided do not demonstrate the origin of the funds held in this account: therefore, bank statement does not satisfactorily demonstrate your income or whether these funds are under your personal control. Therefore, I am not satisfied that this bank statement is an accurate reflection of your personal and financial circumstances.   Moreover you state that you are married and that your husband intends to travel to the UK and will contribute towards the cost of your trip. However, the documents you have presented do not demonstrate any details about your husband, his whereabouts income or employment. I am therefore not satisfied you have accurately demonstrated your husband is able to meet the cost of your trip as claimed. This undermines your credibility and therefore I am not satisfied your intentions to visit the UK are as stated.         Given the above I am not satisfied that you are a genuine visitor and that you will leave the UK at the end of your visit. I am not satisfied that you are genuinely seeking entry for a purpose that is permitted by the visitor routes. I am not satisfied that you have sufficient funds to cover all reasonable costs in relation to your visit without working or accessing public funds. This includes the cost of the return or onward journey and cost of planned activities. Therefore your application is refused under paragraphs V4.2(a)(c)(e).   I wish to reapply, providing the following documents: cover letter signed by me confirming that I would bear all her expenses, my salary slips, bank statements, company's invitation letter, hotel details (with both of our names). Along with that, the funds I deposited in her account had been withdrawn by me and now I am thinking of mentioning that my intent was to share the money with her as a gift to let her bear the expense, and there was a mutual consent. Now, that money is under my control and I will take full responsibility of bearing the expenses.  Let me know if there is something else which I need to do or follow a different approach. The application was refused today and I wish to reapply early next week.

Many of the UK visa refusals we see here share a common pattern and the prevailing reasons refer to V 4.2 (a) and (c).    I do understand that, while the applicants may describe very different individual circumstances, there's a consistent pattern and, broadly, fall into specific categories:    Credibility (lifestyle, lack of ties, visit history, lies & omissions) Funding (insufficient funds, provenance of funds, funds parking) Sponsorship (family, friends, employer)   Question: What most commonly triggers a UK visa refusal where V 4.2 (a) and (c) are given as the grounds?  Secondarily: Given that there is a clear pattern, to what extent are these refusals predictable? Does sponsorship make a difference? Is there a set of personal circumstances, however abstract, where a refusal is all but guaranteed? For example, why do those we see here on TSE who sought entry for the PLAB or British Army appear to be refused with a common theme? Is there a uniform shortcoming or is it just discrimination?   PLAB: What is about applications for a visa, for the purpose of sitting the Professional and Linguistic Assessments Board (PLAB) exam, that seem to invite refusals. After all, the test is given so that international medical graduates can show that they qualify to practise medicine in the UK. The first part, PLAB 1, can be taken in centres outside of the UK. However, PLAB 2 can be taken only in the UK. Why can't you can't get a visa just to sit the exam, promising that you'll leave immediately after?    British Army: Since Commonwealth citizens are eligible to apply online to join, even those who don't reside in the UK, why is it so difficult to get a visa just to attend an interview to see whether you are suitable? Even with an invitation from the Army, such visa applications seem to be unsuccessful. Isn't a career in the British Army a valid reason?     Lastly:  After such a refusal, what approaches would increase the chance of a successful application?


I just wanted to flag a question for migration to math.stackexchange.com. But I could not find the option for migrating to the Math SE. It shows only the following   meta  Super User  Tex  DBA  Sharepoint   Do I need more reputation to perform the action? I have 660 on SO.

I think there should be more Stack Exchange networks available when flagging a question to be migrated. For example I'd think that the following question:    ...would be a better fit on unix.stackexchange.com instead of Stack Overflow. But without the option to mark it so, I feel hesitant to mark it.


How can I manually setup a passkey as "000000" (containing only zeros) to pair Bluetooth keyboard to iMac rather than the random keys generated by Mac. I'm currently using Mavericks & struggling to reconnect the keyboard as i'm unable to give the pass key other than 'zeros'.  In the link : , SingleShot has mentioned of a way to manually set the passkey to 'zeros'.

Keyboard: Apple Wireless Keyboard (model number MC184LL/B)  System: Macbook Pro Early 2011 running OS X 10.8  The keyboard gets detected and when I try to pair it, the system asks to enter some numbers through the keyboard.   However when I press the key (on the wireless keyboard) nothing happens, the only key that seems to work (i.e. to move to the next key in the code) is 0. I can also press enter to confirm but it always fails (since the only code I can enter is 0000...0).   I've also tried pairing from the bluetooth preference and changing the passcode option. However this won't work either.   Any ideas? The keyboard was paired with another MacBook Pro (I don't have access to it anymore). Is there any method to 'reset' the keyboard to factory settings?


Is there a big difference between general linear model and generalized linear model? I am quite confused a bit with the two.

My question relates mostly around the practical differences between General Linear Modeling (GLM) and Generalized Linear Modelling (GZLM). In my case it would be a few continuous variables as covariates and a few factors in an ANCOVA, versus GZLM. I want to examine the main effects of each variable, as well as one three-way interaction that I will outline in the model.  I can see this hypothesis being tested in an ANCOVA, or using GZLM. To some extent I understand the math processes and reasoning behind running a General Linear Model like an ANCOVA, and I somewhat understand that GZLMs allow for a link function connecting the linear model and the dependent variable (ok, I lied, maybe I don't really understand the math). What I really don't understand are the practical differences or reasons for running one analysis and not the other when the probability distribution used in the GZLM is normal (i.e., identity link function?). I get very different results when I run one over the other. Could I run either? My data is somewhat non-normal, but works to some extent both in the ANCOVA and the GZLM. In both cases my hypothesis is supported, but in the GZLM the p value is "better". My thought was that an ANCOVA is a linear model with a normally distributed dependent variable using an identity link function, which is exactly what I can input in a GZLM, but these are still different. Please shed some light on these questions for me, if you can!  Based on the first answer I have the additional question: If they are identical except for the significance test that it utilized (i.e., F test vs. Wald Chi Square), which would be most appropriate to use? ANCOVA is the "go-to method", but I am unsure why the F test would be preferable. Can someone shed some light on this question for me?


I am a newbie in statistics. I have collected data for a parameter Y at different time t. I would like to fit a function $ Y=A(1-e^{-t/B})$. I have to determine A and B. I am not able to use conventional methods.  P.S. The function is asymptotic to a line $Y=A$ or you can say that $Y$ will attain the value $A$ at time infinity.

I have the following data and would like to fit a negative exponential growth model to it:  Days <- c( 1,5,12,16,22,27,36,43) Emissions <- c( 936.76, 1458.68, 1787.23, 1840.04, 1928.97, 1963.63, 1965.37, 1985.71) plot(Days, Emissions) fit <- nls(Emissions ~ a* (1-exp(-b*Days)), start = list(a = 2000, b = 0.55)) curve((y = 1882 * (1 - exp(-0.5108*x))), from = 0, to =45, add = T, col = "green", lwd = 4)   The code is working and a fitting line is plotted. However, the fit is visually not ideal, and the residual sum of squares seems to be quite huge (147073).   How can we improve our fit? Does the data allow a better fit at all?  We could not find a solution to this challenge on the net. Any direct help or linkage to other websites/posts is greatly appreciated.


I have a question about installing desktop system (e.g. Ubuntu) on a smart-phone. I know, there are few topics, but there are emulators etc..  Is it possible to install regular Ubuntu (doesn't matter which GUI) on rooted android phone?  If yes, please tell me how please.

With the announcement of the Ubuntu Phone OS I'd like to know what phone (and tablet) models are supported at this time.  Note from foss & Oli: We are making this the master question for all future "Will this work on <insert random tablet/phone/device here>?!" questions


Let $H$ be a Hilbert space. For $T\in\mathcal{B}(H)$, define the numerical radius of $T$ as $\omega(T):=\displaystyle{\sup_{\|x\|=1}|\langle Tx,x\rangle|}$. I am trying to prove that $\|T\|\leq2\omega(T)$ but I just don't see it. My text simply says that this is "easy" and all the literature online simply refer to this estimate as "well-known".   I know that, for self-adjoint operators, it is $\|T\|=\omega(T)$ and it can be proven elementary. I thought that maybe writing $T=X+iY$ with $X,Y$ self-adjoint could help, but then I couldn't estimate the numerical radii of $X,Y$ related to $\omega(T)$.

It is a standard result that for a bounded self-adjoint operator $T$ on a complex Hilbert space $H$, we have $\|T\|=\sup_{\|x\|=1}|\langle Tx,x\rangle|:=M(T)$, where $M(T)$ is called the  of $T$. It seems that for any bounded operator on $H$, we have $||T||\leq 2M$. Why is that so?


I have some C# code that I have compiled into a .dll to use as a resource for other programs.  How do I import that into my Java project for use and then how do you reference the code in the dll. I am using Eclispe for Java.

Does anyone have a good solution for integrating some C# code into a java application?   The code is small, so I could re-write in java, but I would rather reuse the code if possible. Don't repeat yourself, etc.   Also, I know I can expose the C# as a web service or whatever, but it has some security/encryption stuff in there, so I would rather keep it tightly integrated if possible.    Edit: It's going to be on a server-based app, so "downloading" another runtime is irrelevant.


I've include some graph in my document but the graphs are goign everywhere, 2 pages later, or they just go at end, or they can go 2 subsection under it.  Can you help me  Here is my code:  Thank you  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{tikz} \usepackage{SIunits} \usepackage{pgfplots} \usepackage{xcolor}  \begin{document}   \begin{figure}[h] \centering \caption{Chute de la tension première expérience} \label{fig:Chute Tension 1} \begin{tikzpicture} \begin{axis}[% no markers, xmin=0, xmax=200, ymin=12.3, ymax=12.7, ylabel = $U$, xlabel = {$Temps (secondes)$}, ] \draw[<->,thin] (axis cs:60, 12.621) -- node [right]{$\Delta U$} (axis cs:60, 12.380); \draw[dashed] (axis cs:60, 12.621) -- (axis cs:20, 12.621); \addplot [color=blue] table [x=Temps, y=U1, col sep=comma] {test2.csv}; \end{axis} \end{tikzpicture} \end{figure} \begin{figure} \centering \caption{Augmentation de l'intensité première expérience} \label{fig:Augmentation Intensite 1} \begin{tikzpicture} \begin{axis}[% no markers, xmin=0, xmax=200, ymin=0, ymax=7, ylabel = $I$, xlabel = {$Temps (secondes)$}, ] \addplot [color=red] table [x=Temps, y=I1, col sep=comma] {test2.csv}; \draw[<->,thin] (axis cs:40, 1.1308) -- node [right]{$\Delta I$} (axis cs:40, 6.0160);  \draw[dashed] (axis cs:25, 1.1308) -- (axis cs:40, 1.1308); \end{axis} \end{tikzpicture} \end{figure} \end{document}

I have a little problem with the placement of my picture. I want to insert it at the end of the introduction chapter but its place is not where I want.   I think the problem become from the:  \begin{figure} ... \end{figure}   Because when I insert the picture without using \begin{figure}... the picture is at the end of the chapter as I want.   Look the picture below.


I'm looking for a formula to calculate the product of all proper divisors of a number number $n$. Any idea?      Thanks, Chan

how to prove:   $$ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$$   $\prod_{d|n} d$ is product of all of distinct positive divisor of $n$,  $\tau (n)$ is number (count)of all of positive divisor of $n$


I'm new to Ubuntu and I try to drag a file directly from a fold to the desktop in order to copy the file as one can do in Windows. But it doesn't work. I know how to do it in terminal, and I have disabled experiment view and is able to drag files between folders to copy them. I'm justing wondering why I can't drag and copy it to the desktop? Is it not supported in Ubuntu?

In Ubuntu 20.04, on the desktop, there is a number of actions I wish I could do, such as, by order of importance :  use keyboard shortcuts such as select all, copy / paste. use drag & drop with icons deactivate the "mouse over" highlight, and restrict the clicking area to only the icon, not the surrounding square  To put it simply, I'd like to have the exact same features as offered by the desktop of Ubuntu 18.04 (probably related to a specific version of GNOME, and not Ubuntu itself). Am I missing something obvious here? I actually see no reason why those actions are removed or deactivated on the desktop, since they all work in any Nautilus window.


Prove that $\dfrac32\leq \dfrac{a}{b+c}+\dfrac{b}{a+c}+\dfrac{c}{a+b} < 2.$ where $a$ ,$b$ ,$c$ are sides of Triangle   I tried using sine rule which makes up the the expression $\sum \dfrac{\sin{A}}{\sin{B}+\sin{C}}$. Now i dont how to find the range of $\sum \dfrac{\sin{A}}{\sin{B}+\sin{C}}$. Any ideas(hint) or solution would be really appreciated.

If $a,b,c$ are sides of a triangle, prove that ${3\over2 }\le {{a\over b+c}} + {{b\over c+a}}+{{c\over a+b}} \lt 2$ .


Gentlemen,  We are in a bit of a debate here. An old one, php framework or no framework. We ran some tests and core php clearly takes the lead in handing requests per second and better memory consumption.   We are building an enterprise level micro services based app. So the question is, when it comes to operating costs of server, how big the difference could be if we use a framework which can handle 1k requests per second, vs no framework which can handle 7k requests.  Framework in question is laravel  Our server is centos, apache, mysql on GCP

This is a  about  Related:      I have a question regarding capacity planning. Can the Server Fault community please help with the following:   What kind of server do I need to handle some number of users? How many users can a server with some specifications handle? Will some server configuration be fast enough for my use case? I'm building a social networking site: what kind of hardware do I need? How much bandwidth do I need for some project? How much bandwidth will some number of users use in some application?


I'm building a references generator and I need to keep track of the generated references. To achieve this, I'm currently using Javascript to store a cookie containing the raw data, then a PHP page embedded on the result page takes the cookie and logs it into an HTML page, however, some characters appears like this : �. I really don't know which way to go to solve this (base64 encoding, unicode encoded characters...)  Here's the link to the website :   [It's in french]  I can't give you the link to the HTML page for obvious confidentiality reasons, however I'll provide a screenshot :

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.


I'm still getting used to Linux, having come from Windows.  I was receiving an error that "compiz" had crashed a few times so I figured I'd uninstall it.  sudo apt-get remove compiz sudo apt-get install compiz   I logged out then back in, after that, the GUI was totally gone and I have no idea how to get it back or what I need to do to restore the GUI to what it was before I killed poor Compiz.  GUI was pretty much unmodified after a fresh install of 14.04  How can I fix it? I'm not even sure how to get to a terminal or anything. The login screen looks normal, but after logging in, it's a totally bare desktop with my backround and a few icons.  No Dash, toolbar, etc.  Hot Keys don't seem to work either (Super = Dash doesn't work, etc); although I did accidently open "Disk" UI.  Not sure how.  Please Help! Right now I'm working off my W7 dualboot.

I accidentally removed all the packages starting with the name jpeg with:  sudo apt-get remove jpeg*   This screwed up a lot of things, removed Unity, Firefox, Flash player etc.  I somehow managed to recover the desktop and unity but then a lot of things are still buggy. For example .rpm files and .tag.gz just won't open up at all.  What I want is a way to fix everything that's amiss. Something that is the equivalent of a 'repair installation' with a windows disc.  Any tips, anyone?


I created some pdf files in Visio which includes some figures as well as text. I need to import those PDF files in Latex, what I want is to match the syntax and font of text in PDF files with syntax and font in latex. Is that possible ? and how can I proceed?   Waiting for helpful replies.

Visio can export many different image formats but only .emf and .pdf as vector graphics. Tex can only handle .eps and .pdf vector graphics and therefor .pdf is the file format to go.  But there is the problem. All PDF exports allways have a big white margin around them and can't be imported in Tex like this.  How to export a Visio graphic properly to use it in Tex?


I am aware of proof of divisibility of binomial coefficients of a prime $p$.  I've seen it is easy to show that when $0<k<p$ $$\binom{p}{k}\equiv 0 \mod p$$  Can there be anything stronger.  Suppose I have an integer $n=pq$.  Can we prove that  $p|\binom{pq}{k}$.  I feel like this is an impossibility since, looking at a case like $n=15$, $3|\binom{15}{4}$, but $3\not|\binom{15}{3}$.  $5|\binom{15}{3}$ but $5\not|\binom{15}{5}$.  Yet there ARE binomial coefficients where that 15 divide evenly.    Is there a way to determine which coefficients will successfully be divided by $n$ and which will be divisible by $p$ or $q$?  And are there stronger divisibility laws for powers of a prime?

If $p$ and $q$ are primes,  which binomial coefficients $\binom{pq}{n}$, $1 \le n < pq$,  are divisible by $pq$?  In particular, if $p$ and $q$ are distinct odd primes, and $n$ is even, does $pq \mid \binom{pq}{n}$?  This question is inspired by my answer here:   According to Kummer's theorem (), "the largest power of $p$ dividing $\binom{m+n}{m}$ equals $p^c$,  where $c$ is the number of carries when $m$ and $n$ are added in base $p$."  If $m+n = pq$, $m = pq-n$. So, if there is at least one carry when $n$ and $pq-n$ are added in base $p$, then $p \mid \binom{pq}{n}$. So, we want to know for which $n$ there is at least one carry in base $p$ and base $q$.  An obvious generalization is to ask, if $p, q, \ldots, r$ are primes,  which of the binomial coefficients $\binom{pq\cdots r}{n}$ are divisible by $pq\cdots r$. But I don't even know how to do this for two primes.  Note: The answers to this question may be useful:


I am following some basic tutorials of smoke simulations. And I always can't find the settings tab "smoke" under the smoke domain settings. I jumped through some tutorials to see if I am just using another blender version (2.92) but I always have the same problem. Also, the smoke sim looks a behaves different. It feels like they have different preset settings, but the most looks the same. I am also using mantaflow as everyone else. I am very new to smoke sims but have a good understanding of blender. I hope someone can explain. Thank you in advance Here is a picture of the smoke sim of my desktop: ´ And here is an example of a tutorial file:

I am trying to make an explosion with Blender Mantaflow, but I do not see the following in the Properties view in the Physics Properties:  Color Mapping Smoke   I am using Blender 2.91. Can you help me solve the problem?


I have just a normal bezier curve. And i have sub divide once. I want to extrude the sub divide vertex. Like the branch. But when i extrude the handle is remove and when i extruded from the handle it is extruded good way. I just want to make the branch type.

I want to extrude a curve in two directions.    Or join both curves into one, is it possible? I've tried copying it and then join segments, but I don't see Remove Doubles option while working with curves.


A bookshelf has $15$ books. in how many ways can $4$ books be removed such that no two adjacent books are chosen?    I started to solve the question by saying that the first book can be selected in $15$ ways, the second one can be selected in $13$ ways,the third one in 11 ways and the fourth one in $9$ ways. Total number of ways:$15\times13\times11\times9=19305$. However the correct answer must be $495$. Can you explain why my counting technique is false and provide me with hints about the correct one? Thanks you for your help

I am a newbie in combinatorics and still don't have enough tools to handle this kind of problems.  Assuming I have a set of integers: $ \{1,2,3,4,\dots,n\} $  In how many ways, can I choose $k$ numbers out of those $n$, such that none of them are consecutive?  For instance, for the following set $ \{1,2,3,4,5\} $  For $ k=3 $ I have only 1 option: $\{1,3,5\}$  My purpose is first of all to understand the way you would think about this  problem, not necessarily the solution itself (I have the final answer for it).  Thanks.


Please read till the end, before you answer.  I'll start off with the examples to get to the point.   Drop a block from 1 meter and it will have speed v when it reaches the ground, with total work done on it w.   Drop it from 2 meters and it won't have twice the speed, since it has less time to gain speed. Surprisingly,  2w work is done to it.   Another example. I know it's weird but it's important  A 1 Ton block of lead in space is at rest. A human is standing beside the lead block. The human is going to use  chemical potential energy 2000 J to do work on the lead block and move it and displace it  2000 meters,  using a force of 1 N on the block,  Neglecting the force he uses to move himself to be able to push the block. How much time has he spent doing force?   Since force 1 N is done to on a 1 ton(1000 kg) block,  and acceleration is force over mass,  the acceleration is 1/1000. using the distance traveled by  acceleration formula,  the time needed is 2000 seconds. He has increased the momentum of the object from 0 to 2 thousand.   In another scenario,  A human used 2000 J chemical potential energy using force 1 N on a 1 ton block of lead, but this time it was moving with a speed 50 m/s. The amount of time he would need to move it would of be less than 20 seconds, because of the block's speed.  The increase in  momentum of the object must be less than 20. Surprisingly, In both scenarios  the human used chemical potential energy 2000 J, which is absurd, because the one in the first scenario must have used more energy.   Tl;Dr 2 humans consume the same amount of joules but the first uses so much "effort" and the second guy uses no effort but in the end,  same joules consumed.   This is what I'm trying to say. The amount of work you have done is affected significantly by the initial speed  of the object.   What consumes more food(energy) , adding 2, 000 momentum to an object or 20?  Physics tries to tell me they use the same energy?I don't understand how in each  of the scenarios the human  consumed the same amount of Joules  even though he clearly would be so much more tired after pushing the block at rest than the moving block . This absurdity is slowly driving me insane.  Where did I mess up?

Consider a rocket in deep space with no external forces. Using the formula for linear kinetic energy $$\text{KE} = mv^2/2$$ we find that adding $100\ \text{m/s}$ while initially travelling at $1000\ \text{m/s}$ will add a great deal more energy to the ship than adding $100 \ \text{m/s}$ while initially at rest: $$(1100^2 - 1000^2) \frac{m}{2} \gg (100^2) \frac{m}{2}.$$ In both cases, the $\Delta v$ is the same, and is dependent on the mass of fuel used, hence the same mass and number of molecules is used in the combustion process to obtain this $\Delta v$. So I'd wager the same quantity of chemical energy is converted to kinetic energy, yet I'm left with this seemingly unexplained $200,000\ \text{J/kg}$ more energy, and I'm clueless as to where it could have come from.


Stack Overflow has a “” tag for questions about the programming language Logo, and a “” tag for questions about logos (e.g. getting them to display correctly on web pages).  Yesterday I looked at how many questions used each tag:   logo: ~80 graphical-logo: ~85   However, around 50 of the questions tagged “logo” (almost all of which were in the most recent 50) were referring to graphical logos, rather than the programming language. I went through and corrected them (it was a slow afternoon at work), leaving:   logo: 30 graphical logo: 135   It seems that, at least recently, when users type “logo” into the tag field, they’re almost always talking about graphical logos, not Logo the language, but don’t realise that graphical-logo is the appropriate tag.  I know this isn’t by any means a big problem, but I was wondering whether renaming the tags (from “logo” to “logo-language”, and “graphical-logo” to “logo”), or possibly doing some sort of special-case thing in the tag autocomplete, might result in fewer mis-tagged logo/Logo questions.  Previously suggested here:

On Stack Overflow, the logo tag is used to refer to the  and also to refer to . The latter is also used in Meta Stack Overflow.  Is the latter tag a legitimate one? If so, should we move questions referring to the former to the tag logo-language? How do I move the questions?


I am rendering a still scene of a house. it is quite a large mesh, the issue I have is that only half of it is showing up in the camera view and the render.    If you look at the screen shots you might see what you mean, it looks like half the mesh is being swallowed. I've been searching for answers and can't find. It's driving me mad. Thanks

I'm having an odd issue - When I try to zoom in on a detail using my MMB, the "camera" in the 3D view seems to be cutting off the exterior surface of my object and showing me the inside instead. I'd expect this behavior, but only when I was much more zoomed in.  If I zoom out a bit (one click on the scroll wheel) then I can see the exterior as I intend.  Is there any way to adjust this behavior?  Thanks!


I was trying to create a github.io site which have a URL box where we can enter any URL and as an output, I need the IP address of the URL entered by the user. I tried several methods but none of them worked. I tried to get solutions from so many similar questions in stackoverflow but all of them are returning the users IP address instead of the IP address of the URL the user entered.   Is there a way to create this in Only Javascript (+HTML) ?

I would like to use client-side Javascript to perform a DNS lookup (hostname to IP address) as seen from the client's computer. Is that possible?


I just made a reboot because I have got some upgrades and need to reboot. After reboot, Ubuntu 20.04 the fonts of the top bar and filenames on the desktop are very big. Even the symbols for network and other things are big, so it may bee a scaling problem. Can't find anything in Settings or Tweaks (that I installed after the problem) that may explain this issue. My desktop after upgrade and reboot:

So I was configuring VS code on my Notebook when suddenly I noticed that my interface font got really small on my desktop, terminal and files. I use Gnome Tweaks Tool to increase my scaling factor to 1,15 , but, even though it was active, the font stayed tiny. The solution I found was moving my scaling factor, which instantly fixed my font issue, however, every time I restart my Notebook the font gets tiny again and I have to repeat the process. I tried reseting my font configuration using this command, but had no success. gsettings reset org.gnome.desktop.interface text-scaling-factor  I also tried using the command dconf reset -f /  Finally, I tried using dconf-editor, but still had no success altering the font rendering DPI or changing the scaling factor. All of the steps I mentioned fixed my fonts temporarily, but the issue still persists when I restart my Notebook I am out of ideas and even considered getting a fresh Ubuntu install by now... My video card: NVIDIA GeForce GTX 1050 GPU


Let $G$ be a simple group of order $168=2^3 \cdot 3 \cdot 7$. By simplicity we get that $n_7=8$. Let $G$ act on the set of $7$-Sylow P subgroups (of which there are 8).  This induces an injective homomorphism $\psi:G \to S_8$, and by the first isomorphism theorem $G/\ker(\psi) = G \cong \psi(G)$ How do I show that $\psi(x)$ is necessarily even to complete this proof?

I am trying to solve this problem:  Let $G$ be a finite and simple group, and let $p$ be a prime number such that $p$ divides $|G|$. If $n_p(G)=n$ for $n>1$ (n_p denotes the number of p-Sylows) then $G$ is isomorphic to a subgroup of $\mathbb A_n$.  What I thought of was the following:  I consider the action of $G$ on $X$={H subgroup of G, H p-Sylow} by conjugation. Then there is a morphism $$\psi:G \to S(X)$$ $$g \to gSg^{-1} \space \forall S \in X,$$  where $S(X)$ is the set of all bijective functions $f:X \to X$. First of all, I would like to affirm $S(X) \cong \mathbb S_n$, but I don't know if this is true. Second, note that  $Ker(\psi) \neq G$ because if not $n_p=1$ and $Ker(\psi)$ can't be a proper subgroup because if that was the case $Ker(\psi) \lhd G$, then we have $Ker(\psi)=\{e\}$.  By the first isomorphism theorem, $G \cong G/Ker(\psi) \cong Im(\psi)$. Now, if I could show that $Im(\psi)$ is isomorphic to a subgroup of $\mathbb A_n$, then I would be done.  I would appreciate any hints or suggestions.


I just thought about the safety of my php script and read a lot about sql injections.Now I have a question to save me from it.Is it right when my script doesnt accept characters like ' , ; or " ? Or I just catch this from my Android app ? So I just see the problem in these caracters. Am I right ? Or is there sth I dont see ? If not what would be the easiest way to safe it ?

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


How do I refill a fire extinguisher in NYC. I went to the fire department and they do not refill them. I bought a new one but if the old one can be refilled, I would use it as a backup.

My fire extinguisher is out of charge and I want to either refill it or buy a new one.  Is it better/cheaper to refill it or just buy a new one?  (Can I even refill this fire extinguisher?)     EDIT:


While studying the Riemann - Stieltjes integral, I read this exercise in my book:  "Let $f:[a, b]\to \mathbb{R}$ be a bounded function. Denoted $L(P, f)$ the lower Darboux sum and $|P|$ the mesh of the partition $P$. Prove that for every $\epsilon>0$, there exists $\delta>0$ such that for every partition $P$ with $|P|<\delta$, we have: $\underline{\int_{a}^{b}}f(x)dx-L(P, f)<\epsilon$."  I have a solution for this exercise, but my question is: Can we generalize this problem for Stieltjes integral, with $\underline{\int_{a}^{b}}f(x)d\alpha$ instead of $\underline{\int_{a}^{b}}f(x)dx$?  Particularly, can we have this theorem?  Let $f:[a, b]\to \mathbb{R}$ be a bounded function and $\alpha$ is a monotonic function on $[a, b]$ . Denoted $L(P, f, \alpha)$ the lower Darboux sum and $|P|$ the mesh of the partition $P$. Prove that for every $\epsilon>0$, there exists $\delta>0$ such that $\underline{\int_{a}^{b}}f(x)d\alpha-L(P, f, \alpha)<\epsilon$ for every partition $P$ with $|P|<\delta$?

While studying the Riemann - Stieltjes integral, I read this exercise in my book:  "Let $f:[a, b]\to \mathbb{R}$ be a bounded function. Denoted $L(P, f)$ the lower Darboux sum and $|P|$ the mesh of the partition $P$. Prove that for every $\epsilon>0$, there exists $\delta>0$ such that for every partition $P$ with $|P|<\delta$, we have: $\underline{\int_{a}^{b}}f(x)dx-L(P, f)<\epsilon$."  My question is: Can we generalize this problem for Stieltjes integral, with $\underline{\int_{a}^{b}}f(x)d\alpha$ instead of $\underline{\int_{a}^{b}}f(x)dx$?  Particularly, can we have this theorem?  Let $f:[a, b]\to \mathbb{R}$ be a bounded function and $\alpha$ is a monotonic function on $[a, b]$ . Denoted $L(P, f, \alpha)$ the lower Darboux sum and $|P|$ the mesh of the partition $P$. Prove that for every $\epsilon>0$, there exists $\delta>0$ such that $\underline{\int_{a}^{b}}f(x)d\alpha-L(P, f, \alpha)<\epsilon$ for every partition $P$ with $|P|<\delta$?  I don't know how the mesh of the partition relate to the function $\alpha$.


I want to understand the relationship of the so common $SU(N)$ and $SO(N)$ groups in physics with the symplectic group which I think is the double cover of the first and the Spin groups $Spin(N)$.  Is there a good reference, mainly for physicists.

I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.  Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated?


I stumbled upon something that for the time being looks really weird to me. Maybe i have been looking at it for too long and too up-close, so i am counting on your fresh pair of eyes and, of course, expertise.  I have a list that i want to update, namely ply_info. The update consists of getting an element from the list (the one pointed by sign_reversal_index), duplicating it and adjusting the values of the original and copy-cat entries. This final bit is the weird one and takes place at the two last lines of code.  ply_info = [[0.3], [0.13], [0.13], [0.3], [0.13], [0.13], [0.3], [0.3], [0.3], [0.3], [0.3], [0.3], [0.3], [0.3], [0.3], [0.3], [0.3]] t_ply = [0.3, 0.13, 0.13, 0.3, 0.13, 0.13, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3]  height_list = [0] for i in range(len(t_ply)):     height_list.append(height_list[i] + t_ply[i])  mid_plane_z = sum(t_ply) / 2  if mid_plane_z not in height_list:     print("...No ply boundary lies on mid plane.\n   ...Splitting the one that crosses it.\n")     height_list.append(mid_plane_z)     height_list = sorted(height_list)     sign_reversal_index = height_list.index(mid_plane_z)     ply_to_duplicate = ply_info[sign_reversal_index-1]     ply_info.insert(sign_reversal_index-1, ply_to_duplicate)     ply_info[sign_reversal_index-1][0] = height_list[sign_reversal_index] - height_list[sign_reversal_index-1]     ply_info[sign_reversal_index][0] = height_list[sign_reversal_index+1] - height_list[sign_reversal_index]   I debugged the thing and it looks like the two entries are somehow linked and updating the one, updates the other too. Both values get updated twice, once in the second to last and once in the last line of code. Can anybody please explain why something like that is happening and how it relates to the creation of the copy? what would be the way to go about\around this?  the correct output would be:  [[0.3], [0.13], [0.13], [0.3], [0.13], [0.13], [0.3], [0.3], [0.3], [0.19], [0.11], [0.3], [0.3], [0.3], [0.3], [0.3], [0.3], [0.3]]   notice the ...,[0.19], [0.11],...   Instead I am getting ...,[0.11], [0.11],...

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


Let $S=\{1,2,\ldots,n\}$ and $\mathcal{F}=\{A_1,A_2,\ldots,A_k\}\subseteq\mathcal{P}(S)$ such that $|A_i\cap A_j|\geq r$ for all $1\leq i<j\leq k$, where $r\in\mathbb{N}_+$ and $1\leq r\leq n$. Find the maximum of $k$.   The special cases $r=n-1,n$ are trivial, where $\max k=2^{n-r}$. The case $r=1$ is easy. We pair each $A\subseteq S$ with $S\setminus A$. There are $2^{n-1}$ such pairs and the answer again is $\max k=2^{n-r}$ by the pigeonhole principle. However, $k\leq 2^{n-r}$ does not hold for all $r$. An example is $n=6$, $r=2$ and $\mathcal{F}$ consists of all subsets of $S$ of cardinality $\geq4$, in which case $k=22>2^4$. Is it possible to find the maximum for the general case and how do I proceed?

What is the maximum size of a family of subsets of $[n]:=\{1,2,3,\dots,n\}$ say $\mathcal{A}$ such that $\mid A\cap B\mid \ge k$ where   $A,B\in \mathcal{A}$ and $1\le k\le n-1$?      This not . In Erdos-ko-rado theorem, we place an extra restriction that subsets of $\mathcal{A}$ have to be of same size.  My idea:      There are $2^{n-k}$ subsets of $\{k+1,k+2,\dots ,n\}$. Append $\{1,2,\dots ,k\}$ to each of these sets. Hence, $2^{n-k}$ is a lower bound. Is it possibly the maximum we are seeking?   With some change:     2 Let $C$ be the set of subsets of $[n]$ such that size of each subset does not exceed $r$. What is the maximum size of a family of subsets from $C$ (say $\mathcal{B}$) such that $\mid A\cap B\mid \ge k$ where   $A,B\in \mathcal{B}$ and $1\le k\le r$?


How to calculate the integral $\displaystyle\int \dfrac{a\tan^2{x}+b}{a^2\tan^2{x}+b^2} dx$?  It seems like a $\arctan$ of what else... but I can not work it out.  I have previously asked how to calculate the definite integral between $0$ and $\pi$ , but the answers there only use complex analysis, so they are of no help for the indefinite integral.

Evaluate the integral $$\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx.$$   I have no idea.   $$\int_0^{\pi}\dfrac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx=\int_0^{\pi/2}\dfrac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx=\int_0^{\pi/2}\dfrac{a^n\tan^2x+b^n}{a^{2n}\tan^2x+b^{2n}}dx$$  I try the substitution $\tan{x}=t$, but it doesn’t work.


In relation with this example: , I have to pass the current font size to the environment, but I prefer it takes it by itself?   To make it clear, I would like to store the selectfont parameters and reuse them later.  There is an obvious bracket solution, but the OP of the related question doesn't want to use brackets.  \documentclass{article} \pagestyle{empty}  \begin{document}  \begin{itemize}  \item Bla  \item{\small Small is small}   \item Bla is not small, but the OP of the related question doesn't want to use brackets.  \end{itemize}  \end{document}   I then try to make a switch system inside the \item macro and for this I have to know what are the fontsize parameters, to store and restore them.  \documentclass{article} \pagestyle{empty} \usepackage{paralist,xparse}  \newcommand{\Com}[1][\hspace{1cm}]{\item[#1\aftergroup\footnotesize]}  \NewDocumentEnvironment{Itemize}     {O{}    % item caracter ex $\bullet$     D<>{\normalsize}}{%     \begin{list}{#2#1\aftergroup#2}{%         \setlength{\labelwidth}{0em} % adapt as you want         \setlength{\leftmargin}{0pt}         \setlength{\itemindent}{5pt}%     }}{%     \end{list}}   \begin{document}  \large  \begin{Itemize}[$\bullet$]<\large> \item One \item Two \Com This is my comment \item Three \Com This is my comment \end{Itemize}  Back to current font size !  \end{document}

In the preamble I have:  \documentclass[a4paper,11pt]{article} \usepackage{fontspec} \setmainfont{Arial}   What can be inferred about the real font pt size for the following?  \tiny, \scriptsize, \footnotesize, \small, \normalsize, \large, \Large, \LARGE, \huge, \Huge


I'm looking at a sentence on the side of a box of Imperfect Produce (TM.)  It reads:  "1 in 5 fruits and veggies grown in the U.S. don't meet the strict cosmetic standards of grocery stores, often causing them to go to waste."  My issue is with the verb "don't."  I would have used "doesn't."  Is there any sense in which "don't" can be correct here?  I can see getting confused here, since "fruits", "veggies", "standards", and "stores" are all plural and floating about.  But still, "1" is the subject.  I thought perhaps that the construction "1 in 5" was somehow collectively plural, since they don't really mean just one plant, but 1 fifth of all the plants, so it's really a lot of veggies they're talking about.  I don't think so, but this is my question:  Can this construction be correct?  I note that later in the sentence "them" appears, so at least in the author's head, he's talking about lots of plants.  FYI, Imperfect Produce gathers up these ugly plants and will deliver them to my door at a cost less than the sexy plants available at the HEB.  So I have a number of these boxes sitting around my house, displaying the offending sentence.

Take the examples:   "One in ten children are dyslexic."  "One in ten children is dyslexic." "One in ten children has dyslexia." "One in ten children have dyslexia."   The "one" is singular so 2 and 3 should be correct. But the "one in ten" is a fraction" so 1 and 4 should be correct. And yet I think I usually say 1 and 3. Which is/are correct?!


I'm a Filipino working in Canada as a temporary foreign worker. I'm going back to Philippines this coming Dec and my flight have to stop over in Korea for 16 hours.  I would like to see my husband who is currently in Korea.  Can I go out from the airport to see my husband without a Korean visa?

I'm a Filipino immigrant from USA about to visit home in December.  I have a 14-hour lay over in Seoul,  South Korea.  Do I need a visa to leave the airport to do a little sightseeing?


I am trying to kill for example a dragon head (as a "dropped item") only not all items with /kill so I want to know how to specify what type of item I want to kill without using /scoreboard

I want to kill a specific item using a command block. If this is possible, how do I do this. Can you kill 2 specific items using a single command block. If yes, how?  I tried killing a gold ingot but it didn't work. Here is the screenshot.


In this diagram, can the op-amp be used as the error detector? Can it compare the load position to the input position at CX and produce an error signal?

I have some questions regarding this system that is supposed to take in an input signal and move the load according to this signal. The current load position is feedback to the CT, which compares the current position to the desired position and produces an error signal that is amplified by the amplifier. I understand the processes involving the CT being connected with the CX and comparing it to produce an error signal but am unsure about other things. CX is a control transmitter and CT is a control transformer 1.What type of feedback inductive position sensor component is used and how does it work? Or is the CT THE feedback component  How exactly does the amplifier amplify the error signal that makes the load move to the correct position. Quite unclear about this  Any help is appreciated thanks


The following bash script prints out c, but I'm not sure why. a=b b=c echo ${!a}  I believe that !a will be converted to the last command which began with a, so in this case that would be a=b. This should mean that the last command is equivalent to the following. echo ${a=b}  However, that prints b, not c. Is anyone able to explain why this is the case?

I have the following lines in my .cfg bash script file  DDF_SOURCE="siebel_DATA_DATE_FORMAT" DATA_DATE_FORMAT=${!DDF_SOURCE}   how is ${!DDF_SOURCE} evaluated? It would be !siebel_DATA_DATE_FORMAT, which doesn't make sense to me.


Open the Tags page and select a specific tag(ex: Android) View the list of questions and open a question for more details. After answering the question press back button. I expect to go back to question list but Stack Exchange Android app is taking me to list of Tags.  This is very inconvenient. Every time either I have to press back key once more or select the tag and again move to the place where I was previously.

This looks a little bit like a variation on  but specific to the tags view.  Reproduction (app version 1.0.71):   Select any site (say Meta) from the sidebar Switch to the tags view using the top bar Choose a tag, any tag ( is nice)   optionaly refine your search with more terms  Go to any question found, go back   you end on the unfiltered tags view  Go back again   lucky you, your search is here


"Let $T$ be a projection operator on a finite dimensional inner product space $V$ such that $\|T(x)\| \leq \|x\|$ for all $x \in V$. Prove that $T$ is an orthogonal projection."  If I try to prove this by way of contradiction, what is the particular element in $V$ that I can take such that the given inequality doesn't hold? Any other way of solving this problem is also welcome.

Seems like I , I think I am missing something important.     Let $V$ be an $n$ dimensional inner product space ($n \geq 1$), and $T\colon\mathbf{V}\to\mathbf{V}$ be a linear transformation such that:         $T^2 = T$   $||T(a)|| \leq ||a||$ for every vector $a$ in $\mathbf{V}$;         Prove that a subspace $U \subseteq V$ exist, such that $T$ is the orthogonal projection on $U$.   Now, I know these things:   The fact hat $T^2 = T$ guarantees that $T$ is indeed a projection, so I need to prove that T is an orthogonal projection (I guess this is where $||T(a)|| \leq ||a||$ kicks in). To do this I can prove that:   For every $v$ in $ImT^{\perp}$, $T(v) = 0$ Alternatively, I can prove that for every $v$ in $ImT$ and $u$ in $KerT$, $(v,u)=0$. $T$ is  (according to Wikipedia) The matrix $A = [T]_{E}$ when $E$ is an orthonormal basis, is hermitian (this is equivalent to the previous point). What else?    I've been thinking about it for quite some time now, and I'm pretty sure there is something big I'm missing, again. I just don't know how to use the data to prove any of these things.  Thanks!


I picked up a virus a few hours ago, and have identified one of its files. I know the exact minute that the virus was installed, and would like to search my entire hard drive for files modified in that minute. Is there a utility that can do this? Windows search only searches documents.  I am using Windows 8.

OS: Windows 7 64-bit  Here's a hypothetical problem: there's a folder with multiple sub-folders (which themselves may have sub-folders and so on). A program creates/modifies files in any of these folders say at time t=YYYYMMDDHHMM. Is there are simple command to search for all the files created/modified after time t?


I want to make a search in a datagrid with the text "Modele" but it takes only the upper case or lower case according to the text to search. i want that it show me the "Modele" regardless of upper or lower case.  This is what i try:    private void textBox_model_TextChanged(object sender, EventArgs e) {      string searchValue = textBox_model.Text;      for (int u = 0; u < dataGridView_Articles.RowCount; u++)     {         if (dataGridView_Articles.Rows[u].Cells[5].Value.ToString().Contains(searchValue))         {             dataGridView_Articles.Rows[u].Visible = true;         }         else         {             dataGridView_Articles.Rows[u].Visible = false;         }     }             }

Is there a way to make the following return true?  string title = "ASTRINGTOTEST"; title.Contains("string");   There doesn't seem to be an overload that allows me to set the case sensitivity.. Currently I UPPERCASE them both, but that's just silly (by which I am referring to the  issues that come with up- and down casing).  UPDATE This question is ancient and since then I have realized I asked for a simple answer for a really vast and difficult topic if you care to investigate it fully. For most cases, in mono-lingual, English code bases  answer will suffice. I'm suspecting because most people coming here fall in this category this is the most popular answer.  answer however brings up the inherent problem that we can't compare text case insensitive until we know both texts are the same culture and we know  what that culture is. This is maybe a less popular answer, but I think it is more correct and that's why I marked it as such.


This story is probably from an anthology.  It involves a kid or teenager who is secretly developing a black hole in his room. Eventually things get out of hand.   I believe this was written in English.

When I was in elementary school, I remember borrowing a science fiction short story collection from the library. It had a number of great stories in it, but I've never been able to find it as an adult.   This was in the early nineties but I think the book was published in the early eighties. I remember the name "Ben Bova" on the cover, so I assume he wrote one or more of the stories. I also remember one of the tales was about a boy who bought a make-your-own-star kit, which allowed people to construct a miniature star in a glass jar. He did as instructed at first, but eventually got bored and started feeding bricks and things into it. Catastrophe ensued.  Anyone know the name of the story, the author, or the collection?


I'm trying to find the name of a book I read about 15 years ago. The cover had a picture of a girl standing in front of a bunch of rockets.  The story was about a girl who finds out that a computer that was surgically implanted in her head is a prototype that allows for her brain to be broken into multiple personalities.   The company or government (I don't remember which) is trying to capture her again but she escapes and gets help from a hacker who helps her unlock her true potential.

I'm looking for a story about a youthful (late teens?) female protagonist who begins the story by making an emergency escape from an orbital habitat. The protagonist is actually host to multiple disassociated (as many as seven?) identities, of whom she is initially unaware. They are capable of holding council internally, however.      Some of the identities/personalities are more sexual than others, leading to intercourse that only some of the personalities actively consented to.   Another spoiler-free notable story piece is a race of aliens who mark their 'naturally present' personalities/identities with a glyph or character on their bodies before venturing into public spaces.  FTL in this story must be performed by a non-human pilot, while the remainder of the occupants are either put to sleep or in suspended animation (I don't recall), due to eldritch somethings in the great beyond that will drive human pilots mad.      The driving action in the story is the protagonist's flight from corrupt human government groups that brutally experimented on her as a child to deliberately induce disassociated identities in an attempt to yield a viable human FTL pilot. The experiments were in fact successful, and the climactic scene involves the protagonist, now reconciled to her multiple personhood, piloting allies through an FTL jump.   I believe it was written in either in the late nineties or early aughts.


Image texture distorted in compositor by UV Map node koks like lowres on output. For distortion is used render of UV pass. Screen bellow explanes situation better. Did I missed something in setup?    Example-blendfile is linked for short time. Or is it possible to upload zip file too?

I have a problem. I am going to make a minecraft animation in blender. But when I put a minecraft texture on a 3d cube that is 16x16x16 it is very low resolution is there a way to get the texture in a better resolution or is there a way to make blender make the texture better?  I hope you have an answer. Thanks in advance


Here's my situation: I have a "Project" content type. I want to be able to add employees to a project based on their role with a select or multi-select drop down widget with unlimited number of values. So I can add multiple people with different roles.  I would like to be able to choose a Role first - say a "designer" - and then have the drop down for the entity reference only show just the roles for designers.  Project   --> choose Role "designer"   --> choose designer "John Doe"   Add next person   --> choose Role "??"   --> choose person "??"   What are possible ways to do this?

there is two content types "country" and "state". content type "state" has entity reference field for "country".  there is another content type called "shop" which has two entity reference field for "country" and "state".   when i creating "shop" it display all the "state" .  but i want something like when user select one country, the corresponding states to the country should display.  how to do that help needed .


I have a monitor that has a defect (red star) in a lower section, is it possible to contain the screen to the section above this defect?    I have tried setting the overscan_bottom in /boot/config.txt, but it seems to shrink the the page horizontally (in addition to the intended direction, vertically) trying to preserve the aspect ratio of the resolution, is my guess.  I believe the monitor is 1920x1080, I don't mind going down to a lower resolution because it's for an arcade game emulator.  I am using HDMI output  The OS is Raspbian.

I'm running a Laptop with Arch Linux, X.org and i3. Due to a broken LCD panel, I would like to disable/ignore the left ~228 Pixels of the screen until I have time to get it repaired.  So far, I've tried using a non-standard resolution and then adding an offset, but had no success. Is there any simple solution for this?


Using TeXWorks and TeXLive, usually errors display the relevant text, and I can go find the problem.  Of course, it would be nice if there were a button I could click to go there, but it's not crippling.  However, I now have a large document, and suddenly, I get the following error, with no clue about where in the document it is failing:  (c:/bin/texlive/2013/texmf-dist/tex/latex/hyperref/hyperref.sty (c:/bin/texlive/2013/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty (c:/bin/texlive/2013/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty)) (c:/bin/texlive/2013/texmf-dist/tex/latex/oberdiek/auxhook.sty) (c:/bin/texlive/2013/texmf-dist/tex/latex/hyperref/pd1enc.def) (c:/bin/texlive/2013/texmf-dist/tex/latex/latexconfig/hyperref.cfg) (c:/bin/texlive/2013/texmf-dist/tex/latex/url/url.sty))  Package hyperref Message: Driver (autodetected): hpdftex.  (c:/bin/texlive/2013/texmf-dist/tex/latex/hyperref/hpdftex.def (c:/bin/texlive/2013/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty)) (c:/bin/texlive/2013/texmf-dist/tex/latex/geometry/geometry.sty) (c:/bin/texlive/2013/texmf-dist/tex/latex/listings/lstlang1.sty)  (./QuickFlippedLessons2.aux ! Undefined control sequence. l.75 \@writefil  ?    I don't have a previous version saved, so finding this could be an extremely tedious process of deleting sections until I find the relevant one.  Is there anything I can do?

Im having this weird error that says:  Underfined Control Sequence. 1.60 \@writefi   I can press [s] on the command line and the message is ignored, and the code still runs ...  What can be causing this error?


I have 2 random variables, all independant, discrete and uniform  I want to compute standard deviation for Z = X - Y  Here is the R code:  #create X and Y X = rep(0:1, c(733-41,41)) Y = rep(0:1, c(742-60,60))  #create Z as Y - X Z = c() for (i in X) {Z = c(Z,c(Y-i))}   Means are equal:  mean(Z) [1] 0.02492802 mean(Y) - mean(X) [1] 0.02492802   Then I count standard deviation and variance of Z using the formula:  sd(Y) + sd(X) [1] 0.5027599 var(Y) + var(X) [1] 0.1273021   Ann then, using sd() and var() functions:  sd(Z) [1] 0.3565528 var(Z) [1] 0.1271299   Where is my mistake and why sd(Y) + sd(X) != sd(Z) and var(Z) != var(Y) + var(X)?  Thanks!

I know that the variance of the difference of two independent variables is the sum of variances, and I can prove it. I want to know where the covariance goes in the other case.


I'm running Ubuntu Server  Distributor ID: Ubuntu   Description: Ubuntu 14.04.2 LTS   Release: 14.04   Codename: trusty     And when I run apt-get update is get the following errors  Err http://ppa.launchpad.net trusty/main amd64 Packages   404 Not Found   W: Failed to fetch http://ppa.launchpad.net/inizan-yannick/mono/ubuntu/dists/trusty/main/binary-amd64/Packages 404 Not found   E: Some index files failed to download. They have been ignored, or old ones used instead.     What can I do to resolve this, so I can once again run updates for my server, sorry if this is a simple answer, but I'm new to Linux package management. Thanks

PPA seems to be constantly offline. Whenever I use sudo apt-get update, this error is shown:  W: Failed to fetch http://ppa.launchpad.net/ 404  Not Found   How do I fix these errors?


Question :  Let $f$ be real valued function on $R^3$ satisfying (for a fixed $\alpha \in \mathbb R$) $f(rx) = r^{\alpha}f(x)$ for any $r>0$ and $x \in \mathbb R^3$. Then which of the following statements are true.   If $f(x) = f(y)$ whenever $||x|| = ||y|| = \beta$ for a $\beta >0$, then $f(x) = \beta ||x||^{\alpha}$ If $f(x) = f(y)$ whenever $||x|| = ||y|| = 1$ for a $\beta >0$, then $f(x) = ||x||^{\alpha}$ If $f(x) = f(y)$ whenever $||x|| = ||y|| = \beta$ for a $\beta >0$, then $f(x) = c||x||^{\alpha}$ for a some constant c. If $f(x) = f(y)$ whenever $||x|| = ||y|| $ , then $f$ must be constant function.   Please help me to see this question more clearly and help me to answer this.

$f:\mathbb{R}^3\to\mathbb{R}, f(rx)=r^{\alpha}f(x)$ for some $\alpha>0$, $\forall x\in\mathbb{R}$, for any $r\in\mathbb{R}$, could any one tell me which of the following is true?  $1.$ If $f(x)=f(y)$ whenever $||x||=||y||=\beta>0$, then $f(x)=\beta ||x||^{\alpha}$  $2.$ If $f(x)=f(y)$ whenever $||x||=||y||=1$, then $f(x)= ||x||^{\alpha}$  $3.$ If $f(x)=f(y)$ whenever $||x||=||y||=1$, then $f(x)=c||x||^{\alpha}$ for some constant $c$  $4.$ If $f(x)=f(y)$ whenever $||x||=||y||$, then $f(x)$ must be a constant function. Thank you.


I want to develop some skills in statistical inference for a career in data science or machine learning. I purchased the book "All of Statistics" which is a good book, but there are not answer keys online, which makes it difficult to check whether or not I am doing things correctly. Can anyone suggest books that are similar, but have exercise answers available.

Can anyone recommend some books that are considered to be standard references for classical (frequentist) statistics? IE, fairly comprehensive, and also, been around for a while so that typos and mistakes in formulas had a chance to be checked and corrected


Here's the problem: I carry around two devices, but at different power requirements - one at 20V/3.5A and the other at 12V/3.5A. I'd like to only carry around one power brick and just carry an adapter cord.  I've looked around everywhere for universal power supplies, but the only one I found that included both 12V and 20V was at 5A. I don't want to risk damaging my batttery at the higher amps.  So now I'm looking to an engineering solution. I have a basic understanding of electrical engineering, but I'm having a little trouble here figuring out what I'll need.  From my research, I believe I can use a 20V/3.5A power supply and a 12V step down voltage regulator. The problem is I can't find any voltage regulators at the correct amps - either too low at like 600 mA or way to high at 20A. Does anyone know where or how I can find the part I'll need?   I assume, using the pinout diagram, I can essentially just run the power from the 20V power supply thru the voltage regulator and come out with 12V. Am I missing anything?  And if anyone has a better solution, I'm all ears (or eyes).

Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.


How do I calculate the affects of alcohol on someone that's been drinking as far as combat, using skills, and just the aftermath of a hangover?

If a character is drunk, what are the penalties associated to it? Are there any benefits to it? I do remember a special prestige class for monks about it, but I don't remember anything specific in the core rulebook.


Can you help me with this?  $$\int_{-\infty}^{+\infty} e^{-x^2}\cos x \, dx$$

Prove that :  $$ \frac{\sqrt{\pi}}{2} e^{-\frac{a^2}{4} } =\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$$    the only thing I can think of is differentiating the RHS and trying to get :  $$ -2 f'(a) =a f(a) $$ But I couldn't do it.  Can anyone show me how to do this ?


The two most popular types of loss functions are  1) squared error: $L(y,f(x))=(y-f(x))^2$ --> best estimate is the $E(Y|x) $ 2) absolute error: $L(y,f(x))=|y-f(x)|$ --> best estimate is the $median(Y|x)$  I have two questions.  1) Why do people use the squared error method? The absolute error method makes much more intuitive sense. You get the difference between the actual and the estimate. Plain and simple. If you square the difference, then won't you get "warped" values depending on the size of the difference?  2) This also got me thinking about what is "expected value." Expected value is defined as the mean. However, the best estimate under the absolute error loss function is the median. So is the "expected value" the median? I would very much appreciate it if someone can help me clarify my thinking. Thanks.

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute value of the difference instead and get the expected value (mean) of those, and wouldn't that also show the variation of the data? The number is going to be different from square method (the absolute-value method will be smaller), but it should still show the spread of data. Anybody know why we take this square approach as a standard?  The definition of standard deviation:  $\sigma = \sqrt{E\left[\left(X - \mu\right)^2\right]}.$   Can't we just take the absolute value instead and still be a good measurement?  $\sigma = E\left[|X - \mu|\right]$


Graphics card nvidia gtx 1660 from and processor amd athlon 4x 845. On Windows I watched videos in YouTube at 8k on the linux even 4k does run slowly. I also played the game world of tanks on ultra settings on Windows. After switching to Linux, I was forced to switch to medium settings driver to Linux using 460 Prior to that, I put the previous ones starting from 440.The performance has not changed very low than windows10. How to increase the performance of the graphics card?

I just ordered the Nvidia GTX card. I have a dilemma, though. Should I keep using the driver which is available in "additional drivers" in Ubuntu, or should I install the driver from the Nvidia site?  So which driver is the best for me?


How do I upgrade from Ubuntu 12.10 to Ubuntu 13.04? I have tried nothing yet,however this is trying my patients, I have been here for over an hour trying to ask a simple question and this  is my LAST ATTEMPT!!!

What are the different ways I can use to upgrade Ubuntu from one release to another?


The equation of a parabola with vertex at the origin is given by $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ with the contraints, $B^2-4AC=0$ and $F=0$.  There exists a parametrization as follows: $$r(t)=\left(\begin{array}{cc}at^2+bt\\ct^2+dt\end{array}\right)$$ I believe this is true because Geogebra will show me the numeric parametrization going either direction.  That is, I can put in any $A,B,C,D,E$ or I can put in $a,b,c,d$ and the program will show me the other set. I just have to play by the constraint rules above.  How do I find variables $a,\;b,\;c$  and $d$?  What I have tried?   Brute force. Use a CAS and substitute $x=at^2+bt$ into the general conic form and solve for $y$.  From the mess of terms, I collected the ones where $B^2-4AC$ could be factored away thus reducing the complexity.  What remains is $$r(t)=\left(\begin{array}{cc}at^2+bt\\\frac{-B(at^2+bt)-E\pm\sqrt{(2BE-4CD)(at^2+bt)+E^2}}{2C}  \end{array}\right)$$ This is a parametrization and it will half-graph but it isn't in the correct form. The $y$ term didn't become $ct^2+dt$. I did notice in passing that the root term is somehow related to the eigenvectors.  It was elusive.   Discovery using numerical examples showed me something. In the desired parametrization let the parabola's focal point be $(f_x,f_y),$, then $a=f_x$ and $b=2f_y$ and $c=f_y$ and $d=2f_x$. I can get the focal point by rotating the graph to the vertical with $\lambda x^2+E_1y=0$ (eigenval/vec rotation method) and using $x^2=4py$ to get p and then rotating back again.     I know that "discovery" is sort of an answer to my question, but I really want to know how to derive $a,b,c,d$ rather than my didactic method for finding them.

It is well known that a parametric form of the parabola $y^2=4ax$ is $(at^2, 2at)$.      What are possible parametric forms of the general parabola   $$(Ax+Cy)^2+Dx+Ey+F=0$$   ?


Today, while browsing for a question, I encountered this wild Pokemon. I saw it in his profile and I do not know how the user created that.    So my question is, how can I make something like that? If you can provide the necessary steps to take, that would be appreciated.

I want to include a tag or kind of business card on my homepage where a link to my account, my current reputation and my current badges are show. Could be something like the user card under a question or answer:        Is there an API for this or is it allowed to parse it from the Stack Overflow website?


I can't install anything on my Ubuntu. It gives me the following error. I tried all the things I found on different websites but it still doesn't work.  The following packages have unmet dependencies:  libpcap0.8-dev: Depends: libpcap0.8 (= 1.5.3-2) but 1.4.0-2 is installed sqlite3: Depends: libreadline6 (>= 6.0) but 6.3-4ubuntu2 is installed          Depends: libsqlite3-0 (= 3.8.2-1ubuntu2.1) but 3.8.2-1ubuntu2 is installed

Occasionally, when I'm installing stuff, I get an error like the following:  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  package1 : Depends: package2 (>= 1.8) but 1.7.5-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.   How can I resolve this?


I am trying to use 'date' to get the time in a different time zone, and failing. All the methods I've found on google involve changing the time zone on the system, but that is not what I want.  Is there a single command that will return current time in a time zone different from my own?

I have a server running with the timezone set to UTC. It seemed like that was generally a good practice (please correct me if I'm wrong).  Anyhow, one of the servers I connect to, in order to scp files, is running on EDT and stores files that I need to copy in the format /path/to/filename/data20120913  I looked at trying to rsync files using something like find's -mtime -1 flag for files modified in the last day, but I didn't have any luck.  I don't mind just using scp to copy the current day's file, but as of right now there is a 4-hour window where running date +%Y%m%d will give a different day on each server and that bugs me a little.  Looking through man date I see that I can have the time output as UTC, but I don't see a way to have it output as another timezone like EDT  I suppose I could also use something like the GNU date extension date -d 20100909 +%s to get the date in seconds from the epoch, apply a manual 4 * 60 * 60 second calculation, and see about rendering that as a date - but then when daylight time kicks in it will still be an hour off.  Is there a simpler way to output the date in a YYYYMMDD format for EDT on a server that is set to UTC ?


So, let me explain my setup a bit.  I have a MacBook Pro (Early 2011) which I dual booted (Windows 10 and Mac OS). Then I decided I also needed Ubuntu, which I installed on an external disk.  And here's where things turned messy.  When the mac boots up, after pressing the Option button, I can see two options:   One to load Mac OS (which works fine) "EFI Boot"   Selecting "EFI Boot" brings up GRUB, with the following options:   Ubuntu Windows 10 (at /dev/sda1)   If I select Ubuntu it works fine. If I select Windows 10, after a while, it throws me the message File /efi/microsoft/boot/bootmgfw.efi not found  I've read a few posts on the subject, and many suggested running grub-update from Ubuntu.  However, the weird thing is, grub-update seems to recognize Windows. It just doesn't work when selected from the boot menu.  Generating grub configuration file ... Found linux image: /boot/vmlinuz-4.13.0-21-generic Found initrd image: /boot/initrd.img-4.13.0-21-generic Found Windows Boot Manager on /dev/sda1@/efi/Microsoft/Boot/bootmgfw.efi done   What's going on? Any ideas?

I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this?


What is the gcd of any two consecutive odd integers

Ok i feel like this is an easy question that I'm making more complicated than it needs to be  $$ \begin{align} 2n+1 &= (2n-1) + 2\\ (2n-1) &= 2(n-1)+1 \end{align} $$  so is it $1$ ?


I had link a html type text to jqueryui datepicker. I only want user select date via the calendar not typping in, any function can do this?

How do I use the jQuery Datepicker with a textbox input:  $("#my_txtbox").datepicker({   // options });   that doesn't allow the user to input random text in the textbox. I want the Datepicker to pop up when the textbox gains focus or the user clicks on it, but I want the textbox to ignore any user input using the keyboard (copy & paste, or any other). I want to fill the textbox exclusively from the Datepicker calendar.  Is this possible?  jQuery 1.2.6 Datepicker 1.5.2


I am using xmodmap to remap the capslock key to escape for my Linux system running X.   I am now working directly on a headless Ubuntu 14.04 LTS server that does not run X. Is there any easy way to get the same behavior in the system terminal as well, when directly logged in to the machine and typing on a USB keyboard?

Because I now and then need to use scandinavian letters despite using US Dvorak as my layout, I would like to use Caps Lock as a compose key. (I don't need Caps Lock at all, I'm not a forum troll)  How would one accomplish this?  Using Linux Mint 17 with xfce, if that makes a difference.  For the record, I am the only user of this PC, and would prefer to have this be the system default, mainly in xorg, but also in tty if that's not too much drudgery.


This question is almost the same as      with one difference. I'm using the GNOME Shell desktop in Ubuntu 14.04 and therefore, the solution given in the linked Q&A does not work.  Does someone know, how I can turn off the unresponsive warning and the graying out of the window?     The main problem is that Mathematica even in version 10.3 does something weird, when you have dynamic content and you move a slider for more than a few seconds. Somehow the desktop environment thinks that the window does not work anymore (although it does) and shows this warning in the middle of your work.   The most unfortunate thing is that when you press Esc, like I do in my IDE when I want a dialog to disappear, the whole program is killed and all unsaved work is lost.

I have Ubuntu 14.04 with Gnome-Shell running and use Mathematica 10.2. Whenever I open a mathematica file and select some lines in it, I get a message from the system that mathematica is not responding. You may choose to wait a short while for it to continue or force the application to quit entirely. This problem is also described at . However, it is stated there, that they cannot do anything about it. Now there is a statement at the  that one only has to change one line in the delete.c file from mutter, to deactivate the whole message. This hack would be a sufficient solution for me.   The question now is, how do I implement the proposed change in the file? I cannot find a delete.c file on my computer. Do I have to compile mutter myself?  diff --git a/src/core/delete.c b/src/core/delete.c index 141cd49..d8a126e 100644 --- a/src/core/delete.c +++ b/src/core/delete.c @@ -98,6 +98,8 @@ show_delete_dialog (MetaWindow *window,                "Got delete ping timeout for %s\n",                window->desc);  +  return; +    if (window->dialog_pid >= 0)      {        present_existing_delete_dialog (window, timestamp);


Why is this thing true  $$\{\{\varnothing\}\}\subset\{\varnothing,\{\varnothing\}\}$$  I'm trying to underestand, but I need an explanation.

Note: Actually there's no error in the book and the manual. I actually misread it. The answer is of a different question : True or False: {0} ⊂ {0}  This question is from Discrete Math Book by Rosen.     {{∅}} ⊂ {∅,{∅}}   Answer in the manual is:     This  is false. For one set  to  be  a  proper  subset  of  another,  the  two sets  cannot  be  equal.   How is {{∅}} is equal to the set {∅,{∅}} ? I know the two sets have different cardinal numbers. So they cannot be equal.


I'm trying to use \mathscr in my documents, but it just doesn't show up. I'm using MacTeX, with pdfTeX and XeTeX version 3.1415926 and TeXShop version 3.26. As an MWE, I can use:    %!TEX TS-program = xelatex   %!TEX encoding = UTF-8 Unicode   \documentclass[a4paper]{report}   \usepackage{mathrsfs}   \begin{document}   $\mathscr{abcdefghijklmnopqrstuvwxyz}$   \end{document}     the first two lines being TeXShop's way to be told to use XeLaTeX (though using pdfTeX changes nothing) and to save the document in UTF-8 Unicode encoding. How do I get the \mathscr to appear?

Recently I switched from pdflatex to xelatex to be able to use OpenType fonts. I like to use variables highlighted using \mathcal for specific variables, while I used to use \mathscr-typeset variables for matrices. But when I compile with XeLaTeX they look exaclty the same.  Old code  \documentclass{standalone} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        New code  \documentclass{standalone} \usepackage{unicode-math} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Broken code  I tried to get back the glyphs from mathrsfs, but it failed this way.  \documentclass{standalone} \usepackage{unicode-math} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Question: How can I get back the behaviour? In principle I'd like to have the old \mathcal letters from the pdflatex-version of Computer/Latin Modern.    Alternate solutions (Addendum 2016/05/11)


Find all holomorphic functions $f: \mathbb{C} \rightarrow \mathbb{C}$ such that, for all $x,y\ \epsilon \ \mathbb{R} $ , $Re(f(x+iy)) := 2xy$   So I figured out thus far that $\frac{\partial u}{\partial x}:= 2y$ and $\frac{\partial u}{\partial y}:= 2x$ with $u(x,y):= 2xy$. Now by the Cauchy-Rieman equations I can see that  $\frac{\partial v}{\partial y}:= 2y\ $ and $\frac{\partial v}{\partial x}:= -2x\ $ for some $v(x,y)$.  However I seem to be stuck finding $v(x,y)$. Can anybody help me out here, would be very happy.

Find all holomorphic functions $f:\mathbb C\to\mathbb C$ such that for all $x,y\in\mathbb R$ $\Re(f(x+iy))=2xy$  So $f$ must be complex differentiable, which is equivalent to that Cauchy-Riemann equations must be satisfied Let $f(x+iy)=P(x,y)+iQ(x,y)$ (Here $P(x,y)=2xy$) then $\frac{\partial P}{\partial x}=2y=\frac{\partial Q}{\partial y}$ $\implies Q(x,y)=y^2+Q(x)$ the second equation is: $\frac{\partial P}{\partial y}=2x=-\frac{\partial Q}{\partial x}$ $\implies Q(x)=-y^2$ Hence $Q(x,y)=x^2-y^2\implies f(x+iy)=2xy+i(x^2-y^2)$ Can you verify my steps, and holomorphic means differentiability in the complex sense right ?


I installed it but all my files have been lost. I had Windows 7 before that.  How do I remove Ubuntu from my computer? How do I recover my files?

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


I've set a global variable in functions.php like so:  $cat_args = array('cat1', 'cat2', 'cat3');   and tried to use it in a template file:  global $cat_args; if is_cat($args): //do stuff endif;   The conditional returned false. If I echo $cat_args I get an array. Is there an extra step to passing it to the conditional / is what I'm trying to do possible? Thanks!

I want to be able to echo the URL of the featured image of a post and after looking some on the web I found the following which works fine when I put it in a loop in my front page template.   <?php $thumbSmall = wp_get_attachment_image_src( get_post_thumbnail_id($post->ID), 'small' ); $urlSmall = $thumbSmall['0']; ?>  <?php echo $urlSmall; ?>   However, want to use variable $urlSmall in other places than in the front page template, and this is where my limited coding skills let me down. I tried to just copy paste  wp_get_attachment_image_src( get_post_thumbnail_id($post->ID), 'small' ); $urlSmall = $thumbSmall['0'];   into my functions.php but that did not work. I need these variables to be globally recognized. What do I do here? write some kind of function?


I'd like to use Blender cycles to generate an image which can be used as a world background image. An example is this kind of image is from    How can a blender scene be rendered like this?

I would like to turn a specific blender scene into an animated sky box I can use in other animations.   is the top google search result for "blender sky box", but it's for an old version of blender, and some of the buttons it references no longer exist.  There are several tutorials on how to set the sky box if you already have an image, but I have yet to find a modern HOWTO that lays out how to create the sky box image from a scene.  How do I accomplish this?  Keep in mind I want it to be animated, so I'll need to bake a hundred frames or so.


My setup is:  1, Bounce umbrella 2, Shoot Thru Umbrella 3, camera :)  Lighting:    The result:   I think there are too many shadows. Is there any way to avoid shadows with this setup?

My friend asked me to create a photo like this:    I noticed that its shadowless and my first question is whether it was setup to be shadowless, or was it made shadowless in post? How many lights are involved here? I think there's one for the background, and one above the product pointing something like 30 degrees down, and then some reflectors to the side. Just guessing.   I did some Googling and came across . How could that be shadowless? Looks like the product is a few feet above the ground, which is a white seamless background, and the camera and all the lighting are all pointing down. How could there be no shadow on the ground?  Thanks!


It would be great if there was a way that we could associate our accounts with Twitter and when viewing questions and answers, could "tweet" it automagically.  I know that there have been times that my question was not very straight forward and someone from twitterville actually came in and answered it for me...  This would essentially be a one way form of communication, maybe a button in each post that would allow you to tweet the post's link with a brief text input (obviously keeping the entire post to under 140 characters)  EDIT you can argue that SO is not a social networking site, but that does not imply that there is no value or utility to be had there by some form of integration.

Sometimes, especially with niche or otherwise tricky questions, I'd like to increase posts' visibility as much as possible. One approach I've taken for this is posting a link to the question as a facebook status update.  I think it would be great if that functionality were integrated directly with the question/answer posting form similar to the way I can currently share projects I follow/commit to on Area 51.