$r$-separated sequence in Hilbert spaces

I'm trying (with no good results) to prove the follwing:  Prop. Let $B^1\subset H$ be the unit ball in the Hilbert space $H$. If $(x_n)_{n\in\mathbb{N}}\subset B^1$ is a $r$-separated sequence, i.e. $\vert\vert x_j-x_k\vert\vert\geq r$, for any $j\neq k$, then $r\leq \sqrt{2}$.  Can you help me to prove the reult above?


How to judge if a supervised machine learning model is overfitting or not?

Can anyone tell me how to judge if a supervised machine learning model is overfitting or not? If I don't have an external validation dataset, I want to know if I can use ROC of 10 fold cross validation to explain overfitting. If I have an external validation dataset, what should I do next?


In my node editor I have a small movie clip with a green screen. I keyframed it to get rid of the green screen and I am using a transparent background image. I have realized that most of the video formats don't support transparent backgrounds, so I am trying to just render it frame by frame. However, when I use a format that should support transparency, like png, the pictures just come out with a brown or black background. My goal is to overdrop the clip on another video I have. How do I export this clip with a transparent background? Thanks for any help!


Is it possible to make tables without markdown?

I wanted to edit  replace the bulleted list with a table. The answers to   that this isn't supported by markdown. I tried to make an HTML table, but I couldn't get that to work either.  Given that tables have no markdown support, are there any other ways to make tables on SE sites?


Should individual letters be preceded with "an"?

I was reading a comic book and I noticed that the author used "an A" and "an N" in a particular phrase (screenshot below). While I understand the usage of "An A" here (A being a vowel and what not) and "N" having a pronunciation which has a sound similar to "A".  Since most of English alphabets have pronunciations which start with a syllable similar to one of the vowels or semi-vowels; is it OK to prefix the letters using "An"?  For eg. An X, or An Y.        Zenescope's Grimm Fairy Tales - Werewolves: The Hunger, page #8 (Click to enlarge)


How to make mobs passive to you through commands in 1.16.4

I know you could do this with the scoreboard in 1.8 and with teams in 1.13+, but when I use the regular methods mobs are still hostile towards me. Any alternatives? Plugins work too.


Long question titles 'underflow' in timeline

When viewing the  on a narrow screen, the title divides itself both over and under the header line:


Interchangeability of order of partial derivatives

If $$f(x,y)=0$$ Then $$\frac{\partial(\partial f)}{\partial x\partial y}=\frac{\partial(\partial f)}{\partial y\partial x}$$  We use this fact to determine whether a differential equation is exact or not. Is there some way to prove this, rather than generalizing it with a bunch of examples? P.S. A proof completely based on derivatives is preferred because I just know the basics of partial derivatives


C++ 11x check: how to implement const-variants?

Pre C++ 11, I often needed to implement two very-alike variants of a method to deal with const and non-const usage scenarios of the class/struct:  struct my_struct_t{      ....      float_t& at( uint32_t row, uint32_t col)      {          return *(((float_t*)((uint8_t*)numbers+row*row_stride)) + col);      }       float_t const& at( uint32_t row, uint32_t col) const      {          return *(((float_t*)((uint8_t*)numbers+row*row_stride)) + col);      }  };   Has this changed in C++ 11?


On a typical keyboard, why is the 0 in the number row next to the 9 instead of the 1?  This seems like a question which should have a straight-forward answer, but the only one I could find is  which has two instances of entirely unsourced speculation as answers.  (0 as 10, and because 0 is rarely at the start of a number)  To complicate things, the  article adds that      0 and 1 were omitted to simplify the design and reduce the manufacturing and maintenance costs; they were chosen specifically because they were "redundant" and could be recreated using other keys. Typists who learned on these machines learned the habit of using the uppercase letter I (or lowercase letter L) for the digit one, and the uppercase O for the zero.   One might speculate that the 0 is placed where it is because of it's proximity to the O, but since the 1 was added down at the other end (nowhere near the I), it would have made just as much sense to put 0 down there too.  Almost every keyboard layout I've seen listed on wikipedia is this way, even the ones which don't use latin script at all. Only the Hungarian one (thanks, Gildas) puts 0 before the 1.  This may be due to inheriting from latin-alphabet keyboards, though.  Anyone have an explanation for this oddity?  Or specific sources backing up the yahoo theories?    Edit: Based on everyone's answers, I've done more research and come up with what I think is the logical explanation.  I don't have specific sources to cite, though, so I'm still open to an "official" answer, if anyone has one.


I am studying now Hypothesis Testing. I use for it book High-Yield Biostatistics, Epidemiology, and Public Health and videos of Brandon Foltz (recommending these videos for everyone, they are great!) from here  .  In High-Yield Biostatistics, Epidemiology, and Public Health author uses terms like Accept or Reject hypothesis. But Brandon Foltz in his video here  says:  As researchers we either reject the null hypothesis or fail to reject the null hypothesis; we do not accept the null.   So, which terminology is more right way to talk about hypothesis: Accept and Reject or Reject and Fail to reject ?


How does General Relativity explain the gravitational attraction between two distant bodies?

This is more like a conceptual question. Let's say we have two point masses $m_1$ and $m_2$ separated by the distance $r$. According to the Newton's law of universal gravitation, the objects will be accelerated with respect to each other by a force: $$\vec{F}=-G\tfrac{m_1m_2}{r^2}\hat{r}.$$  I was trying to visualize this problem from the General Relativity point of view - in terms of spacetime curvature and the objects following the geodesics.  So my question is: How would General Relativity explain this attraction between the two objects? I know that their mass will warpe the spacetime around them, but how does this curvature of spacetime explain the fact that they are getting closer together - esspecialy when $r$ is very large? Assuming that the object are perfect spheres and the mass distribution is uniform, isn't the spacetime curvature created by each object going to be isotropic?  I started by imagining that the objects will advance through time at 1 sec/sec in their proper frame, but because the spacetime is warped around them - the motion through time implies motion through space. How far off am I?  To put it more technically - How does the spacetime curvature in this particular case lead to geodesics that will eventually make the objects approach each other?


Prove that $\frac{1}{k+1} \le \ln(1+\frac{1}{k}) \le \frac{1}{k}$

I am trying to prove that $\frac{1}{k+1} \le\ln(1+\frac{1}{k}) \le \frac{1}{k}$. This showed up as a known fact in a proof for $(1+\frac{1}{k})^k = e$ as $k$ goes to infinity, so I would like to prove it without using that fact.  I tried to prove the first part of the inequality by using another known inequality (one which I am comfortable proving):  $1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k} >\ln(1+k)$  Let $a$ denote $1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k-2}$  $a+\frac{1}{k-1}+\frac{1}{k} >\ln(1+k)$  Scaling this down 1 term:  $a + \frac{1}{k-1} >\ln(k)$  Subtracting the second inequality from the first, we get:  $\frac{1}{k} >\ln(1+\frac{1}{k})$  However, this seems to contradict the statement I'm trying to prove. Could anyone help?


How to get access to the other drives in a dual boot system

I have a dual boot system (Windows 10 and Ubuntu 14.04 LTS) in my computer. I want to access the drive (which is available in Windows) in Ubuntu platform. How to do this. Please suggest a way.


If the Ratio test proves inconclusive does that imply the Root test will always be inconclusive as well (Alternating Series)

When determining the convergence of an alternating series does an inconclusive Ratio/Root test imply the other will be inconclusive as well? Is there a relationship between the results of these two tests? Or when solving problems involving infinite series should you use each test to see if there is an absolute convergence. Please comment any recommended resources to read further on this subject. ~Thanks


How to know a backup command failed or worked in a script

I have a command in a script to do a 'backup database [name] to [file]  and all the other parameters. Now, we have a problem where we run out of disk space, the script keeps on trucking, just issuing the message: BACKUP DATABASE is terminating abnormally. As if there is no problem... no exception is tossed, or anything... so the next command in the series, to do a restore of that database to another database... fails... and the script keeps on running... Why doesn't it throw an exception when there is a catastrophic failure like either of these? I've seen some suggestions that we should query log files to see if there was a database backup failure, but good grief, it should just DIE when you run the script. Do I need to catch the exception, and throw the exception with a higher severity (I'd assume that the other one is thrown with the max severity, but maybe someone thought that a complete failure of a backup is just minor?) I've seen other code / questions where people are doing a try/catch around the backup, but I have no interest in catching the exception, I want it to Abort right there, die, and report the error up the chain.. Instead, it just keeps going..


I see this when I go to delete from the Photos app      "Deleting will remove the photos and videos on your device and also   any backups in your account"   "Cancel"/"Delete everywhere"   is there a way to delete from my device without deleting the backup on my Google+ account Nexus 4 Android 4.4.4


Finding the area of a triangle if the distances from the centroid to the vertices are $3$, $4$, $5$

Let $G$ be the centroid of $\triangle ABC$, and let $AG=3$, $BG=4$, $CG=5$. Find the area of $\triangle ABC$.   So I calculated the lengths of the diagonals which is $9$, $12$, $15$, but now I don't know what to do next.


Does not break word into parts for a new paragraph

When I use \texttt{}, it does not break it into parts for new paragraph. Do you have any idea?


I've searched for this but no clear answers (especially on the latter). In what cases should you use a datetime or timestamp?


Gandalf a Maia (Spirit) was sent to Middle-Earth in human form to help the free peoples fight the evil of Sauron. Is the same reason for the Saruman sent to Middle-Earth ?


Today I installed Ubuntu along side windows 10. Everything seams fine apart from this wifi problem I'm having. The only way I can get an internet connection is through an Ethernet cable, because when I go to try and connect to a wifi network wirelessly the only thing I see is 'No Wifi adapter found'. I know that this is probably a driver problem, but I really don't know how to fix this. Any help is appreciated. Thanks in advance. EDIT: output of lspci -knn | grep Net -A3; rfkill list libkmod: ERROR ../libkmod/libkmod-config.c:656 kmod_config_parse: /etc/modprobe.d/iwlwifi.conf line 8: ignoring bad line starting with '“options' 04:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821CE 802.11ac PCIe Wireless Network Adapter [10ec:c821]     Subsystem: AzureWave RTL8821CE 802.11ac PCIe Wireless Network Adapter [1a3b:3041]     Kernel modules: wl, rtl8821ce 05:00.0 VGA compatible controller [0300]: Advanced Micro Devices, Inc. [AMD/ATI] Picasso [1002:15d8] (rev c2)     Subsystem: ASUSTeK Computer Inc. Picasso [1043:18f1] 0: hci0: Bluetooth     Soft blocked: no     Hard blocked: no


Will Windows 7 factory reset remove all my private data?

EDIT: this is NOT a duplicate of .  That question is about someone who's computer came with XP, mine came with Windows 7.   I intend to sell an old laptop that came with Windows 7 installed.  I don't have install disks.  If I follow the instructions here (for a factory reset):   Will this be sufficient to guarantee nobody can access any private data I have on the machine?    And will I have to worry about DRM stuff at all?  They mention it here:   If it is more complicated than just following the steps in the first link, what else do I need to do?


I have installed MATE on Ubuntu 14.04 and nm-applet doesn't run on startup despite being set as a startup application and being installed. When I log in, I am able to open up a terminal, type nm-applet, and then it works but not when I restart the computer.


Can't enable the proprietary drivers for Broadcom BCM43142 wireless after installing Ubuntu 14.10? Offline package required?

I have installed the new Ubuntu 14.10 on my Dell Inspiron 3521.  I was able to use my wifi in the Boot Live Stage and during the Installation phase by enabling the BroadCom BCM 43142 proprietary drivers.  But after installation I can't enable the proprietary drivers.  I can see the drivers listed there and when I select the option to use them and click Apply, the progress bar starts going ahead but stops in process and the 'Do not use them' option gets reselected.  I have searched some questions here according to which I must connect my laptop with an ethernet cable to get my wifi drivers working.  But I don't have any ethernet cable at present with me. I can only use the wifi on my second laptop.  Is there any other way to get the drivers working or Is there any offline installer like a .deb file for the drivers?  If anyone knows, please help!  I've reinstalled ubuntu thrice but the problem remains same.


Identify the plane defined by $|z-2i| = 2|z+3|$

I tried:  $$|z-2i| = 2|z+3| \Leftrightarrow \\ |x+yi-2i|=2|x+yi+2|\Leftrightarrow \\ \sqrt{x^2+(y-2)^2}=\sqrt{4((x+2)^2+y^2)} \Leftrightarrow \\ \sqrt{x^2+y^2-4y+4} = \sqrt{4x^2+24x+36+4y^2} \Leftrightarrow \\ x^2+y^2-4y+4 = 4x^2+24x+36+4y^2 \Leftrightarrow \\ y^2-4y-4y^2=4x^2+24x+36+x^2 \Leftrightarrow \\ -3y^2-4y=5x^2+24x+26 \Leftrightarrow \\ ???$$  What do I do next?


Downloading shapefile from geoserver after applying CQL filter?

I have managed to download a zipped shapefile from geoserver but now I want to be able to download part of the layer in a shapefile. This is what I did in order to download the whole layer as shapefile:  http://localhost:8080/geoserver/wfs?format_options=charset%3AUTF-8&typename=something%3layer_1&outputFormat=SHAPE-ZIP&version=1.0.0&service=WFS&request=GetFeature   I have also managed to apply a single CQL filter based on the answer of   How can I apply multiple CQL filters in the same URL? I read  that I need to encode the 'and' string in the CQL part of the URL. Is there an example illustrating this?


Is there a preferred format for numbers on Stack Exchange?

In the US and UK, numbers have a comma separating the thousands and a period separating the decimal portion.     The median round-trip time is 1,256,532.65 milliseconds.   In much of the EU, as well as Canada (both French- and English-speaking), numbers have a space separating the thousands and a comma separating the decimal portion.     The median round-trip time is 1 256 532,65 milliseconds.   In much of South America, numbers have a period separating the thousands and a comma separating the decimal portion.     The median round-trip time is 1.256.532,65 milliseconds.   India (specifically Hindi-speaking India) uses a format much like the US and UK, except (if I understand correctly) after the least-significant thousands grouping, additional groupings are by the hundreds. (I must admit, whenever I encounter this format, I tend to assume a digit got omitted unless I know the author's culture.)     The median round-trip time is 12,56,532.65 milliseconds.   In most cultures, the localized number format is used only when communicating in the native tongue (transitioning to the US/UK style when communicating in English). However, this is not universally true.  Of note: Canada is the only country I could find whose official language is English and whose number formatting conventions do NOT align with the US/UK convention. Edit: I've been informed in the comments that the US/UK system is the norm in Canada.  There may be other culture-specific Arabic-numeral number separator formats as well. These are the ones that I found in my research.  These numbering systems can usually be interpreted without knowing the author's culture, but sometimes there are ambiguities (such as the number "one and one one thousandth" vs "one thousand and one", both of which could be written as either "1,001" or "1.001", depending on culture). Sometimes these ambiguities can be deciphered from context within the rest of the answer/question, but sometimes not.  Is there a preferred format for numbers when writing question/answer content on English-language Stack Exchange sites, or is it okay to use whichever format is native to us?  Edit:  @Rene has dug up a couple relevant links in the comments, I will summarize their relevance here.    This discusses a preference between US and UK spellings of words like "favorite/favourite". The answer says that, for tags, the US spelling should be used. For body text, there is no official preference. For question titles, the most commonly used spelling should be used to increase search engine visibility.    This discusses editing questions to conform to a specific culture's number formatting. The answer says that one should not edit to conform to cultural standards unless there is an official preference, but stops short of saying whether there is such a preference for numbers.    I initially thought my question was a duplicate of this one, but this one discusses how numbers are displayed by the Stack Overflow software (in places like vote counts) rather than what formats are okay to use when writing question/answer content. The consensus on that question is that Stack Overflow should use US/UK number formatting, unless otherwise localized.


Continually getting "you do not have enough application memory" despite plenty free

A few times recently my MacMini running 10.14.6 gets into a loop of giving this error every few minutes to seconds. This is despite having 1.5-3GB application memory free, according to the Memory Clean 3 app. Even using it to clean the memory doesn't help. Eventually it just grinds to a halt and rebooting is the only answer.  Anyone else seen this, or can suggest a remedy short of rebooting?


Given $n$ different univariate non-normal sample sets calculate for a new sample, $x$, which it most likely belongs to

Say you have $n$ different, non-normal, potentially overlapping data sets of samples. Maybe their densities look something like:    and you are given a new sample $x$, how would you decide to which of these sample sets it would most likely belong?  I would assume it is possible to do a (kernel) density estimation of each of the sample sets, interpolate them to functions $p_n$, and then calculate $p_n(x)$ for each, selecting the one with the highest probability.   However both the decision rule and the method seem, well, off. Can anybody help me in getting a better intuition of this problem?  EDIT Say the data comes from a continuous scoring system, like a depression scale, and I have annotated data for many different subjects. So I can get the density plots for "severe", "mildly" and "non-depressed" subjects. Now I have a new sample and wish to know (based on the score) which the person most likely belongs to.


Removing PHP 7.2, and installing PHP 5.6

I'm a new Linux user, and I'm using a web server with a software that requires PHP 5.6, creating an incompatibility issue that I have been trying to solve for at least two days now. I read up a bunch of threads here on it, but none of them really solved the issue. The Linux version I'm at is 18.04.   So, what I tried so far:   To uninstall PHP 7.2 using sudo apt-get purge php7.0-common To disable the proxy using sudo a2dismod proxy_fcgi proxy (it returns that the proxy is already disabled) To install PHP 5.6 using sudo add-apt-repository ppa:ondrej/php or sudo add-apt-repository ppa:ondrej/apache2, it installs it After using sudo apt-get update, and using this sudo apt-get install php7.0 php5.6 php5.6-mysql php-gettext php5.6-mbstring php-xdebug libapache2-mod-php5.6 libapache2-mod-php7.0, I get the error:   I used  suggested on the comments, and the php5-compat helped, now at least when I try to unmount/mount (or whatever it's called) I don't get a "php5.6 module doesn't exist" anymore, and now if I do sudo apt-cache search php5.6 --names-only I get the list of packages for the first time.     Since I got that part done now, I'll consider it as done and see with the Oxwall people about their requirements. Thanks a bunch.


Hand-to-hand strategy for taking down the mothership

I've been attempting to take ships by killing all their crew hand-to-hand, and was going to attempt the mothership in a similar way but I noticed they had what seemed like, a million doodz.  After barely scraping by the first stage, I got quickly polished off by a Rebel bomber.  I was wondering, if I kill a few of their guys, do they replenish between boss stages?


Is the matrix $A^*A$ and $AA^*$ hermitian?

As the title says. Is the matrices $A^*A$ and $AA^*$ hermitian (symmetric if $A$ is real)?


Eyes And Teeth Going Haywire With Rigify Rig And MakeHuman Model

hope all is going well for you!  I'm having an issue where the eyes and teeth of a MakeHuman model do not quite work properly with a Rigify rig.   Simply put, I have no idea how to fix this. If anyone can provide some insight concerning this, I would greatly appreciate it. Also if anyone needs to poke around in the blend file itself,  is a link.  If any other details are needed, just let me know!  Thanks, and take care. =-)


Task is real simple to understand: I need an example of two fields, E and F, such that their additive parts are isomorphic, and their multiplicative parts are also isomorphic, but fields themselves are not isomorphic.  What I was thinking are two things: First, if E and F would be finite, they would be vector fields over the same field, of the same dimension, and thus linear algebra tells us this is isomorphic. So, counterexample has to be among infinite fields.  Now, I got stuck there. Counterexample cannot be C and R, so we have to search among $Q(\alpha_1,...., \alpha_n)$, but then it seems that we have vector fields of dimension n over field Q, which are again isomorphic.  Now, you see, I must be wrong, because professor who asked this is a real pro in algebra, and he would not allow any mistake. This is just curiosity, because he asked just to think about this, this is no homework for mark or anything. Thanks for any help!


For a natural number $n$ say that $d(n)$ is the sum of the digits of $n$ (in base $10$). Then what is the value of $$d(d(d(4444^{4444}))) ?$$  I have been trying with modular arithmetic, but can't do it.


Why is one's place of birth even mentioned in a passport?

I was discussing this with someone and we couldn't agree on anything... why is it so vital to have one's place of birth on a passport?  Are officials trying to judge whether you were involved in "terrorist" activities in the past since you were born in country that has problems?  For instance, my friend came to Canada as soon as she was born; she has never been back to her place of birth...if the governments want to "track" you it would be not useful in this case since her whole life has been in Canada.  What is the official purpose of being made to state your place of birth on your passport?  And, if you choose not to...you will be hassled apparently...anybody know?  Edit: I have read the response to the "similar" question but it doesn't state whether one has a choice to exclude their birth place worldwide & what are the consequences if they do...?


Can light continue without a light source?

If you have 2 mirrors over for each other placed exactly so they face each other perfectly, and then use a laser light pen as the source into one of the mirrors so it bounces to the other mirror and back again:   Would the laser light line continue to exist between the 2 mirrors if the source of the laser stopped? If so, how long could the laser light continue to be between the mirrors without a source? Would it just continue existing between the mirrors using itself as the source or is this not possible for light?   Note: It doesn't have to be only 2 mirrors. It could be any amount of mirrors if that would change the outcome.


Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists

A function $f$ is defined in $R$, and $f'(0)$ exist. Let $f(x+y)=f(x)f(y)$ then prove that $f'$ exists for all $x$ in $R$.  I think I have to use two fact: $f'(0)$ exists $f(x+y)=f(x)f(y)$ How to combine these two things to prove that statement?


I installed an application that screwed my PATH variable. Now I cannot run anything from the command prompt. Is there any way I can restore PATH variable?


Disable activities hot corner in Ubuntu GNOME 17.04?

How do I disable the activities overview screen from popping up when I hit the top-left corner of my screen in Ubuntu GNOME 17.04?


How can I check which partition contains Ubuntu intstallation, using Gparted while in live USB of Ubuntu?

I have Windows 10 and Ubuntu 16.04 installed on my machine.  Now I want to check from live USB using Gparted or the df command which partition contains my Ubuntu 16.04 installation.   I am getting a / value output under mounted on, aufs as coordinate parameters and i am not sure which partition aufs refers to.   (Click image to enlarge)


Is there a way to edit the new object menu in blender 2.83.5?

I've been enjoying the new features and stability of blender 2.83.5, however I discovered an issue. Normally when you create a new object in your scene a menu appears to offer options on the object. I am getting this menu however it is entirely grayed out and uneditable. If anyone knows something about the new version having either a bug or new way of working I'd be very appreciative of any info.


When I do a search on Wolfram|Alpha, I get that $x≥0$, except I thought that this isn't exactly the case. Because it is defined for all real numbers greater than zero, but there are infinitely many negative numbers for which the function is also defined. So why can't we extend the domain to numbers less than zero? It isn't continuous, I understand, but I suppose this is linked to the domain of the Dirichlet function?


Should I expect better results from more expensive variable ND filters?

To be able to make videos, I purchased inexpensive ($25) Bower FN72 and FN58 filters. While I haven't expected anything great from inexpensive filters, the result was below my expectations, so I purchased a more expensive ($135) 77mm Hoya Variable Neutral Density ND3-ND400 filter.  I'm disappointed by the more expensive one as well (see the comparison below).  What I need is:   A sharp image, Smaller color shift, Reduced , Less ghosts.   Is it worth spending $300 on a filter, or the results will be similar?  Here is what I get with Bower and Hoya filters:  1. Sharpness and color shifting  This is a cropped part of a photo shot with the sharpest lens I have (AF-S NIKKOR 50mm f/1.8G). Hoya performs well, but it could be better; Bower is terrible. Both Hoya and Bower shift colors toward yellow (white balance is set to a constant value across shots).  Open the images in a new tab to see a slightly larger version; all images contain EXIF.    Fig 1. With no filter, the image is sharp    Fig 2. Hoya filter slightly affects the sharpness of the image    Fig 3. Bower filter adds severe blur  2. Cross effect  This is a comparison of cross effect at 18mm. Both Hoya and Bower perform really bad at maximum and maximum-adjacent density.  No larger versions available; all images contain EXIF.    Fig 4. Original image    Fig 5. Cross effect when using Hoya filter    Fig 6. Cross effect when using Bower filter  3. Ghosts    Fig 7. Without filters, the Nikkor 50mm f/1.8G produces a ghost    Fig 8. Hoya filter creates an additional ghost    Fig 9. Bower filter creates not one, but two ghosts  For Bower, notice two ghosts in the bottom left corner, as well as a ghost near the light source itself.  Comparison                   Hoya                         Bower ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Sharpness           Slight blur                  Severe blur Color shift         Important shift to yellow    Important shift to yellow Cross effect        Severe                       Severe Ghosts              Clearly visible ghost        Severe ghosting Vignetting          Unknown¹                     Not noticeable Uneven darkening    Noticeable in some cases     Noticeable in some cases   While the five times more expensive Hoya gives sharper images and less ghosting, the images are still blurry and ghosting still present. Moreover, the more expensive filter has no benefit in terms of colors shift and .    ¹ Since I only have 77mm filter and my lenses are Ø58mm and Ø72mm, it is impossible to determine the level of vignetting.


Show that $\lim_{n\to\infty} 2n(a^{1/(2n)}-1)=\log(a)$

Show that  $$\lim_{n\to\infty} 2n(a^{1/(2n)}-1)=\log(a)$$  is true for $a > 0$.  I am really stuck on this task.


I am trying to change the color of my plots in pgfplots but the argument color in addplot is not recognized. Here is my picture:    and here is my code:    \begin{figure*}[t]   \centering   \hspace{-5em}\begin{subfigure}[t]{0.6\columnwidth}   \captionsetup{justification=centering}   \begin{tikzpicture}   \begin{axis}[    axis y line=none,    y=0.3cm,    x=1cm,    xtick={15,15.5,16,...,18},    restrict y to domain=1:5,    axis lines=left,    enlarge x limits=upper,    cycle list name=exotic,    scatter/classes={    o={mark=*}    },    scatter,    scatter src=explicit symbolic,    every axis plot post/.style={mark=*,thick},    xlabel=Time,    x label style={at={(axis description cs:0.95,-0.1)},anchor=south},    xticklabels={,,},    legend style={       draw=none,       at={(-0.1,-1)},       anchor=south east   },   legend image post style={mark=none}   ] \addplot table [y expr=1,meta index=1, header=false] { 17.5 c 18 c };\addlegendentry{$g_{\alpha}$} \addplot table [y expr=1,meta index=1, header=false] { 15 c 16.5 c };\addlegendentry{$\backhtxt g_{\alpha}$} \addplot table [y expr=2,meta index=1, header=false] { 16.5 c 16 c };\addlegendentry{$\zonep{\delta-\varepsilon}g_{\alpha}$} \addplot table [y expr=3,meta index=1, header=false] { 16.4 c 15.9 c };\addlegendentry{$\zonep{\delta-2\varepsilon}g_{\alpha}$} \addplot table [y expr=4,meta index=1, header=false] { 16.3 c 15.8 c };\addlegendentry{$\zonep{\delta-3\varepsilon}g_{\alpha}$}   \end{axis}  \end{tikzpicture}   \caption{Example of an interaction guard $g_{\alpha}$ and its planning intervals} \end{subfigure}\hspace{15em} \begin{subfigure}[t]{0.6\columnwidth}   \captionsetup{justification=centering}   \begin{tikzpicture}   \begin{axis}[    axis y line=none,    y=0.3cm,    x=1cm,      xtick={15,15.5,16,...,18},    restrict y to domain=1:5,    axis lines=left,    enlarge x limits=upper,    scatter/classes={    o={mark=*,fill=white}    },    scatter,    cycle list name=exotic,    scatter src=explicit symbolic,    every axis plot post/.style={mark=*,thick},    xlabel=Time,    x label style={at={(axis description cs:0.95,-0.1)},anchor=south},    xticklabels={,,},    legend style={       draw=none,       at={(2,-1)},       anchor=south east   },   legend image post style={mark=none}   ] \addplot table [y expr=1,meta index=1, header=false] { 17.5 c 18 c };\addlegendentry{$g_{\alpha}$} \addplot table [y expr=1,meta index=1, header=false] { 15 c 16.5 c };\addlegendentry{$\backhtxt g_{\alpha}$} \addplot table [y expr=2,meta index=1, header=false] { 16.5 c 16 c };\addlegendentry{$\zonep{\delta-d}g_{\alpha}$} \addplot table [y expr=3,meta index=1, header=false] { 16 c 15.5 c };\addlegendentry{$\zonep{\delta-2d}g_{\alpha}$} \addplot table [y expr=4,meta index=1, header=false] { 15.5 c 15 c };\addlegendentry{$\zonep{\delta-3d}g_{\alpha}$}   \end{axis}  \end{tikzpicture}   \caption{Discretized planning intervals for $g_{\alpha}$} \end{subfigure} \caption{Discretizing Planning Horizons for Interaction} \label{fig:disc} \end{figure*}   When I remove the cycle list name from the axis parameters, I got an automatic coloring of my lines, and when I try to force the color by adding for example \addplot table [color=red,...] the color is not taken into account.  Any idea on what causes this?


Improve unbiased estimator of $\theta$ with sample from $U(-\theta,\theta)$ using Rao-Blackwell theorem

Let $X_1,X_2,\dots, X_n$ be rvs with pdf: $$f(x\mid \theta)=\frac{1}{2\theta}I(-\theta<x<\theta)$$  I know that $Y=\max|X_{i}|$ is a sufficient statistics for $\theta$ and I found an unbiased estimator $\hat\theta$ of $\theta$,  $\hat\theta = c_n(X_{(n)}-X_{(1)})$, where $X_{(n)}$ is the largest sample,  $X_{(1)}$ is the smallest sample and $c_n = (n+1)/(2n-2)$ is a constant which makes $\hat\theta$ unbiased estimator of $\theta$!  So, by Rao-Blackwell theorem, I should calculate conditional expectation $E(\hat\theta | Y)$ to improve  $\hat\theta$!!  I tried to calculate this by using that  $$\max|X_i| = \max(X_{(n)},-X_{(1)})$$  However, since $X_{(n)},-X_{(1)}$ are not independent, I am having a trouble with calculating this conditional expectation!


Consider a Cyclic Quadrilateral ABCD. The diagonals AC and BD meet at the point P, and DA and CB produced meet at Q. The midpoint of AB is E. Show that if PQ is perpendicular to AC, then PE is perpendicular to BC.


Understanding C# proper uses of 'using' keyword

Considering the follow code can someone explain to me why and why not to use 'using'? I've read about the rule of thumb with IDisposable but why is IDisposable the determining factor?  private string GetWMIProperty(string property) { string value = string.Empty; SelectQuery selectQuery = new SelectQuery("Win32_OperatingSystem"); using (ManagementObjectSearcher searcher = new ManagementObjectSearcher(selectQuery)) {    foreach (ManagementObject mo in searcher.Get())    {      value = mo[property].ToString();   } } return value; }


Control your smartphone using your laptop

I have a sony xperia z and the screen recently smashed.  Touch screen capability has also gone.  As such I can't even unlock the phone.  Does anyone know of an app or a method for connecting it to my laptop and gaining full control of the phone through the laptop?  I need to unlock it and access an app that's installed.  I've been through the folders on it using the laptop but need access to the app itself to get the data I need.


Factoring product of two primes from solutions of congruence

The algorithm purposed to play a fair game of heads or tails over the phone given  claims that knowing the four solutions to  $$ x^2 \equiv a^2 \pmod n$$ would allow us to factor $n$ where $n$ is a product of two unknown primes $p,q$ and $\gcd(a, n) = 1$. However, I am not seeing why this would be true. Can someone please explain?


Why are mutants hated, but superheros venerated?

Please correct me if I have misconceptions, I have mostly only seen the movies (I've read a few comics, mostly of the superhero side. Would like to get more into that.).  The marvel universe is home to both mutants from X-men,  as well as various superheros like the Fantastic 4 and the Avengers. Some people are both (Though for licensing reasons it may be along time before it is said in those words in a movie).  It seems like the difference between a Mutant and a Superhero (/Super-villain) is almost entirely arbitrary (with some exceptions for equiptment base heroes (eg iron man) and aliens (eg Thor), etc). It seems like just looking at most Supers/Mutants it would be hard to tell one from the other. It being largely a matter of origin story.  However Mutants seem to be immediately assumed to be problematic/bad by the general populous (or at least a large amount of it), Where as superhero/villains are judged on their actions. (and indeed often get away with a huge amount of collateral damage.)   Is it just that the different franchise focus on different aspects of the story, but without that focus they are in fact treated the same? Ie Supers are actually just as contentious as mutants, but the contention is not part of the main story, where as X-men has strong themes of acceptance.


This is a subsection in my statistics homework. It goes back to calculus II and summations, and it's been a long time since I've studied it so I'm rusty.  I'm looking to solve the summation of $c\left(\frac{2}{3}\right)^x$ where $c$ is a constant to where I can solve for $c$.  I understand that we say that this summation is: $$c\left[\frac{2}{3}+\left(\frac{2}{3}\right)^2 +\left(\frac{2}{3}\right)^3 +\cdots\right]$$ But the book then says that this then equals to:  $$c\dfrac{\dfrac{2}{3}}{1-\dfrac{2}{3}}$$  Any help?  Also I know my coding ability is little to none so if you'd like to edit my question to make it look more presentable feel free to.  Thanks all.


Posting a comment results in a blank page in iOS app

When submitting a comment on any post, the page will become blank and stay that way. Occasionally it may reload the post, but in order to see the comment you have to go to the previous page and then back into the post.  Example:         App Version: 1.6.6.2 Device: iPhone10,3 OS Version: iOS Version 12.1.2 (Build 16C101)


When Peterson says 'fixed-lens digital cameras have greater DoF', is he assuming a smaller sensor?

I'm reading  and ran across some discussion of apertures in fixed-lens digital cameras as compared to SLRs (page 54 in the 3rd edition). The author says that fixed-length digital cameras give much larger depth of field than SLRs, and gives some examples, but never explicitly says why the depth of field is so much greater. For example, he says that f/5.6 on a fixed-lens digital is equivalent to f/22 on a digital SLR. It's not clear to me what "equivalent" means here, but I'm pretty sure he's talking about depth of field (DOF).  I think this discussion is just saying that fixed-lens digital cameras have smaller sensors (), but I'm not sure. Can anyone help clarify or explain what the author is talking about here?


How to get package list from one PC and install that on another PC?

I want to install to PC2 all the packages, that were installed by apt install on PC1. That is for Debian, but i think that since Debian and Ubuntu share same package system - the solution would be same. How to do that?


I found a lot of dialogue choices requiring high Perception and I started the game with just 10 plus 1 for being an elf. With a magical helm and tower rest bonus I can temporarily boost it to 13, but is it possible to raise it permanently?


Getting a unique parameter off of client's device

I need to create complete random numbers using a seed in JavaScript. I'm not using the built-in Math.random(), but rather something else that can take a seed and generate a random number based on that.  This solution is supposed to serve a situation in which two users log in at the same time to a website (it happens A LOT, and I'm getting a lot of users with identical IDs because of it). Math.random() isn't working for me, and I can't use timestamps because these also don't provide an accurate number (they're not being sampled every MS). I also don't want to use any ajax call in order to get an IP or something similar.  Is there anything anyone can think of that's either unique, or might be rare enough to use to create a good seed?  **EDIT: ** This is NOT a duplicate of , because that one is still using Math.random(). I can't use that function anywhere in my code. I sometime have thousands of hits at more-or-less the exact same moment, and that's what screws up the random. It's also the reason why I need to find some attribute I can use as a seed.


After updating to Windows 7 SP1 I updated with every new update that came out, but there were problems with the last two:    UPDATE: In the updates history I have found a lot of updates failed:    What can be done? Can I manually update?  P.S. I was offered a fix for this: Windows6.1-KB947821-v12-x64. Should I install?


How to pack all linked data inside the current .blend file

I'm working on an animated short. I am trying to send my final results to a render farm because I don't have the processing power to render it on my computer. Each shot is in a separate linked .blend file, and the render service cannot see the linked data.  Note : All paths are relative and File->External Data->Pack All Into .blend doesn't do it  Is there a way to send a linked file as its own isolated .blend, with its own path data?


Displaying all ‘.sh’ files with size more than 5kb

I want to list all the files with .sh extension and size greater than 5kb with the same directory. what I know is how to list all files with a specific size by:  find . -size +5k -exec ls -l {} \+   and how to list all the files with specific extension by:  ls *.sh   what do I need to know is how to do both simultaneously?


I need to show that F test is equal to T test squared, when the T test is for 2 independent groups and assuming variances are equal.  I know that $F=\frac{MSB}{MSW}=\frac{SSB/k-1}{SSW/N-K}$ and I know that $T=\frac{X-Y}{S_p \sqrt{\frac{1}{n}+\frac{1}{m}}}$,   so $T^2=\frac{(X-Y)^2}{S_p^2 ({\frac{1}{n}+\frac{1}{m}})}$  I've seen this proof in Regression but here we're not using MSE and MSR, so i'm not sure how to connect between the two.


Accounting Software for Ubuntu other than GnuCash?

I have performed numerous searches looking for accounting software for Linux (I am running Ubuntu) and haven't found any good solutions.  Maybe I am glossing over something?  I have been using GnuCash for years after dropping Moneydance.  I don't remember exactly why I stopped using it, probably for reasons similar to my wanting to get away from GnuCash. Plus, it isn't open-source and I didn't want to buy a product that I hadn't been satisfied with in the first place.  The problems I have with GnuCash are the constant errors I have in reconciliation.  Every statement is a wrestling match of importing data, matching data, transactions not being imported, account totals changing after a reconciliation, math errors and on and on.  Plus, I have tried to find support but there is little to be had; I have tried to get on the mailing list a couple of times with no success.  I am a sole proprietor of a business and own property so I have multiple accounts to handle.  I need accounting software mostly for year-end P&L statements for income tax preparation for my accountant.  If you have any suggestions, I'd love to hear about them.  GnuCash has pretty much worn me out, so I need to find something else.


How to derive Maxwell's equations from the electromagnetic Lagrangian?

In Heaviside-Lorentz units the Maxwell's equations are:  $$\nabla \cdot \vec{E} = \rho $$  $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + \frac{\partial \vec{B}}{\partial t} = 0 $$ $$ \nabla \cdot \vec{B} = 0$$  From EM Lagrangian density: $$\mathcal{L} = \frac{-1}{4} F^{\mu \nu}F_{\mu\nu} - J^\mu A_\mu$$   I can derive the first two equations from the variation of the action integral: $S[A] = \int \mathcal{L} \, d^4x$. Is it possible to derive the last two equations from it?


How do I stop Excel from converting value 0503E000 to 5.03E+02 automatically?

Excel converting value 0503E000 to 5.03E+02 in any cell automatically in CSV I tried to convert it to text number and general but after i save it and reopen it again it goes back to 5.03E+02  How do I stop this from happening?


Do students use Floo powder to come to school?

In The Cursed Child, we see that Harry and Co. use Floo powder to come to Hogwarts and talk to McGonagall about Albus and Scorpius. This means that Floo Powder can be used to come in and out of Hogwarts. Even if The Cursed Child is not counted as one of the 'mainstream' books, in OOTP, we see that Sirius is able to use Floo Powder to talk to Harry. From the above lines, it is quite evident that students may be able to use Floo Powder to come to, or get out of Hogwarts. Is there any mention in the books of students using Floo Powder to come to school?


Is there a hash function h(M + t1) = c1 that relates to h(M + t2) = c2 in a way that can be verified without knowing M?

Is there a hash function h(M + t1) = c1 that relates to h(M + t2) = c2 in a way that, knowing t1, t2, c1, c2, and with no knowledge of M, it can be verified whether both use the same M?


Well, I have a Galaxy Ace with 2.3.3, build XWKPY and Samsung Kies doesn't show an update to 2.3.4 yet.  I'm thinking of manually updating it through Odin and I need to know if I can just download any Gingerbread 2.3.4 update file or is there anything else that I need to be worried about?


Is there a site where I could ask for SE data-mining scripts?

I have basically no programming experience, and I essentially want someone to write a data script for me to use the SE data-mining ... thingy.  Is there a site where I can ask kind-hearted (or easy-reputation seeking) individuals to write a script for me?


How to Install a Managed Package into a scratch org

I have tried to install using force:deploy as well as force:install. When I try to install using the METADATAPACKAGEVERSIONID I get,  ERROR running force:package:install:get:  Encountered errors installing  the package!,<empty> ERROR running force:package:install:get:  <empty>.   I am trying to install a base package so I can push the extension package into the scratch org for development. Any help?


Using C#/WIA version 2.0 on Vista to Scan

I want to implement a paperless filing system and was looking to use WIA with C# for the image acquisition. There are quite a few sample projects on CodeProject, etc. However, after downloading every one of them that I can find, I have run into a problem.  In each and every one of them, the reference to WIALib is broken. When I go to add "Microsoft Windows Image Acquisition" as a reference, the only version available on my development workstation (also the machine that will run this) is 2.0.  Unfortunately, every one of these sample projects appear to have been coded against 1.x. The reference goes in as "WIA" instead of "WIALib". I took a shot, just changing the namespace import, but clearly the API is drastically different.  Is there any information on either implementing v2.0 or on upgrading one of these existing sample projects out there?


Auto-deleting an answer when it gets so many downvotes or so many flags

I am asking the current question because of . I've never ever seen an answer with so many downvotes. We are waiting for some mod to remove it, and people keep voting it down. They should, but why not delete it automatically?  It will be better for SE users not to see this garbage on the site. Auto-deleting something so it's not done manually will be better for the mods. It will be better for the poster himself; receiving more downvotes will increase his chance of at least being banned from answering on Chess.SE.


Why my markers move when I resize my map on Leaflet?

I have already get an eye on Google and seen that the solution should be the iconAnchor property.   I have set it to the same values that my iconSize. But it fails. When I resize my map the icon change their location with the map resizing.  How can I ensure my marker remain responsively on the same location?  Here my marker' code:  var placeholder1 = L.icon({       iconUrl: "https://image.flaticon.com/icons/svg/484/484167.svg",       iconSize:     [47, 47], // size of the icon       iconAnchor:   [47, 47], // point of the icon which will correspond to marker's location       popupAnchor:  [-25, -50], // point from which the popup should open relative to the iconAnchor       tooltipAnchor:[30, -2]     });      var placeholder2 = L.icon({       iconUrl: "https://image.flaticon.com/icons/svg/484/484167.svg",        iconSize:     [47, 47], // size of the icon        iconAnchor:   [47, 47],        popupAnchor:  [-25, -50], // point from which the popup should open relative to the iconAnchor       tooltipAnchor:[10, -2]     });      var placeholder3 = L.icon({       iconUrl: "https://image.flaticon.com/icons/svg/484/484167.svg",        iconSize:     [47, 47], // size of the icon        iconAnchor:   [47, 47], // point of the icon which will correspond to marker's location        popupAnchor:  [-25, -50], // point from which the popup should open relative to the iconAnchor       tooltipAnchor:[0, 0]     });      var placeholder4 = L.icon({       iconUrl: "https://image.flaticon.com/icons/svg/484/484167.svg",        iconSize:     [47, 47], // size of the icon        iconAnchor:   [47, 47], // point of the icon which will correspond to marker's location        popupAnchor:  [-25, -50], // point from which the popup should open relative to the iconAnchor       tooltipAnchor:[-30, 130]     });   var marker1 = L.marker(location ,{icon: placeholder1}).addTo(this.map);  var marker2 = L.marker(location ,{icon: placeholder2}).addTo(this.map);  var marker3 = L.marker(location ,{icon: placeholder3}).addTo(this.map);  var marker4 = L.marker(location ,{icon: placeholder4}).addTo(this.map);


Can I remove the first original OS (Windows 10) from Ubuntu 16.10 dual boot?

My Windows 10 was really slow, I was really frustrated so I decided to dual boot Ubuntu. I only put 100 Gigs on it because I wasn't sure if it was a great idea (I have 400gb in total). But it was a love at first test, so I wanna get rid (uninstall) of Windows 10 and put all the 400gb on Ubuntu. The question is, how do i go about doing that? thanks in advance.


Change account type from terminal in ubuntu 18.04

How can I do by command line in terminal that an administrator should become standard (normal)?


I got a paged loop that pulls in 4 posts per page from custom post type. It works great, with the only downside that the pagination wont go over the page/20 everything after that is 404, and the posts_nav_link won't show the next arrow at all. Like the pages just aren't there.  In total there are 119 published posts in the custom post type. If I change posts_per_page to, say 6, then I get access to more of the posts from the end, but it also stops at the page/20.  On the production site the pagination stops at 21, I guess because the live database has more entries.  I got the "Blog pages show at most" setting set to 6.  Here's the loop I'm using:  <?php $paged = get_query_var('paged') ? get_query_var('paged') : 1; $args  = array(     'posts_per_page' => 4,     'orderby'        => 'modified',     'post_type'      => "projekte",     'paged'          => $paged ); $custom_query = new WP_Query($args); $c = 0; while($custom_query->have_posts()) :     $custom_query->the_post();     ?>     <article>...</article>     <?php endwhile; wp_reset_postdata(); // reset the query ?>   I've gone through the functions.php a million times looking for a some limiting get_pre_posts filter but there's nothing I can see.  I also got an error log setup and nothing is returned there, I've tested it that it works.  Any suggestions?


WoeUSB Installation failed! Exit Code 256. Trying to install Windows 10 on USB from a laptop running 14.04

I am trying to build a new computer and run Windows 10 on it. I've run into a snag, and can't get the ISO on a USB flash drive using my Ubuntu 14.04 laptop. When trying to download the ISO onto 16GB USB flash drive I get the following error message:   Installation failed! Exit code: 256 Log: WoeUSB v@@WOEUSB_VERSION@@ ============================== Mounting source filesystem... Error: File "/media/woeusb_source_1544835295_14348/sources/install.wim" in source image has exceed the FAT32 Filesystem 4GiB Single File Size Limitation and cannot be installed.  You must specify a different --target-filesystem. Refer: https://github.com/slacka/WoeUSB/wiki/Limitations#fat32-filesystem-4gib-single-file-size-limitation for more info. Unmounting and removing "/media/woeusb_source_1544835295_14348"... You may now safely detach the target device   It says the USB is formatted to FAT32 but I have installed GParted and formatted it to NTFS. I've actually formatted it several different ways trying to following other users on here, and I keep getting various error codes when using WoeUSB.


Small features don't draw when zoomed out using Geoserver WMS

I am using Leaflet to access polygon layers through Geoserver WMS. When I zoom out the smallest polygons will disappear and not draw. They would essentially be a dot if they did draw. Is there a way for the dot to be drawn? This makes it confusing to the user as it can be their impression that there are no polygons in certain areas unless they zoom in.  Alternately, is there a way to display things say in larger hexagons with aggregated data when zoomed out and then to have it seamlessly change to the smaller polygons as soon as someone zooms in?


Is there any reason to use string over String in c# (IDE0001)

I just upgraded to VS 2015 and its complaining about me using the capital String  version of string, saying it can be simplified.  I tried googling for IDE0001 and clicking the link but neither gave me any good info on why this is a thing. CS0168 appears to be unrelated as well ()  Is there any reason to use the lower case version over the upper case version?


I tried to change the only the shapefile datasource encoding through properties and also  but it doesn't change it.   Without saving the QGIS project can't I directly change the shapefile datasource encoding?  I also tried this code, it shows change encoding but as I open the shapefile again it show the same old system encoding:  for layer in QgsMapLayerRegistry.instance().mapLayers().values():     layer.setProviderEncoding(u'UTF-8')     layer.dataProvider().setEncoding(u'UTF-8')     print layer.name(), layer.dataProvider().encoding()     (I am not saving QGIS project, just accessing and saving shapefile directly. When I save the project and do this task then it work correctly)


Review article in an area already published few years ago

I want to write a review article in a particular narrow area of interest as part of my Doctoral research. But there is already a review article on that area published 2 years ago. So can I write a review paper on that area ?


After Ubuntu install, computer boots directly to windows7, no dualboot

I have a laptop, where Windows 7 is pre-installed. I installed Ubuntu 16.04 with a USB-stick, using this guide  with windows7 alongside.  After the installation, it restarts, but it boots directly to windows7, no dual-boot.  Using the USB-stick again, I chose Try Ubuntu and I tried to use Boot-Repair. The recommend fix didnt work. This message shows up      The current session is in Legacy mode. Please reboot the computer, and   use this software in an EFI session. This will enable this feature.   For example, use a live-USB of Boot-Repair-Disk-64bit   (www.sourceforge.net/p/boot-repair-cd), after making sure your BIOS is   set up to boot USB in EFI mode.   Here is the from Boot-Repair generated pastebin   I dont know what to do next. Can someone please help me_


add one object to another object in javascript

I have 2 objects, and I need to add one object to the other object.  var loc = {   leftArray: [],   topArray: [],   bottomArray: [],   rightArray: [] }  var obj = {   id: "ce",   icon: "logo/image.png",   name: "CE",   type: "type2",   version: 3.4 }   var obj = {   id: "ce",   icon: "logo/image.png",   name: "CE",   type: "type2",   version: 3.4,   leftArray: [],   topArray: [],   bottomArray: [],   rightArray: [] }   Is there any simple way to do this?


"Maximum common divisor" for entire functions

I have found this exercise.  Let $f, g$ be entire functions.  a) Show that there exists entire $f_{1}, g_{1}$ and $h$ such that $f=hf_{1}$, $g = hg_{1}$ and $f_{1}$ and $g_{1}$ have no common zeros.  b) For $f$, $g$, and $h$ as above, show that there exists entire functions $A$ and $B$ such that $Af+Bg = h$.  Any idea ? How to manage the case ord($f$) = $\infty$ and ord($g$) = $\infty$ ?


but I don't understand how:  $$a^n - b^n = (a-b)(a^{n-1} + ba^{n-2} +\cdots + b^{n-1})$$  follows from  $$x^{n-1} + x^{n-2} +\cdots + x + 1 = \frac{x^n - 1}{x-1}$$  Could someone explain to me how the summation of the the geometric series explains the factorization?


How do I remove the last  tag in a foreach loop in Codeigniter?

Sorry for posting like this but I am learning I want all the results to have a hr or any html based line except the last one I put a line break but it won't look  good help me foreach ($newsqry->result() as $n) {     $nr=$n->numrows();     $nlink = array_keys($routesAll, "news/index/" . $n->n_id);     ?>

                             <a class="post-imgn" href="<?=site_url($nlink)?>">                                 <img  class=""src="<?=base_url("assets/uploads/news/thmb/$n->img")?>"alt="<?=character_limiter($n->title,'50')?>">

              <?php     $t = $n->tags;     $s = explode(',', $t);     foreach ($s as $a) {         ?>                             <a class="tags" href="<?=site_url("news/view?tag=".strtolower(str_replace(' ','-',$a)))?>"><?=ucwords($a)?>                         <?php } ?>

                                     <a href="<?=site_url($nlink)?>"><?=character_limiter($n->title,'100')?>"

<a href="<?=site_url("news/view?author=".strtolower(str_replace(' ','-',$n->author)))?>"><?=$n->author?>

 <?=date("h:i A",strtotime($n->time))?> <?=date("F-d-y",strtotime($n->date))?>

<?=character_limiter(strip_tags($n->desc),'190')?>

                         <?php if($nr<1){echo "
";}else{ echo "
End of Page
";}?>                 <?php } ?>


I use dual monitor setup with diffrent screen layouts. So I have a "Default_l" screen layout and a "Default_r" screen layout. Is there a way to automate the change of the screen layout: When I change one screen layout for example from "Default_l" to "Compositing_l" the other screen layout also changes from Default_r to "Compositing_r"?


What is the correct English name of these lines?

Hello.  I'm looking for the English name of these two lines in a two dimensional plane:   they go through the origin they make angles of 45° and 135° with the $x$-axis, dividing the plane in two parts    From my native language, they would translate to "first bissector" and "second bissector" or "first diagonal" and "second diagonal", but I could not find any reference to such names.


set closedDate to past for cases in unit tests

I have a requirement that uses filters based on closedDate for cases.  When unit testing this logic I will need to create cases with a closeDate in the past but since it is not a writeable field I haven't got very far. I have some options like creating a custom date field to capture the closeddate and use this in the unit tests or using test.loaddata which lets you write on audit fields(I haven't tried it with ClosedDate yet). Has anyone come up with an efficient way of doing this? maybe looking at something like the test.setCreatedDate function but can't find anything similar for closeddate  Thanks!


Instead of changing permissions to /var/www, installing nautilus permission related extensions or having to execute gksu i want to know an easy to do way of changing /var/www to another place like /home/cyrex/www for example. This way I save on doing all the permission related problems.


Intuitively, why is the median special in this case of minimizing the sum?

I'm not a smart guy, but I recently reading a book about programming where it said that: $|a_1 - x|^c + |a_2 - x|^c + ... + |a_n - x|^c$, in the case of $c$ = 1, the median minimizes the sum.   The example used was [1,2,9,2,6], so we have: $|1−2| +|2−2| +|9−2| +|2−2| +|6−2| = 12$  Although it is true that if you make $x$ any bigger, you could make the sum smaller by reducing it, and vice versa also holds true.  The big question is why? Is this some mysterious mathematical property that laymen cannot understand? Or is there some intuitive explanation. For context I have completed first year of a math degree and understand the basics of proof and number theory (really really basic stuff though).


Is it possible to add multiple materials to a text object?

I know that for a mesh you can go into edit mode and select vertices and assign a specific material to them quite easily. I want to know if it is possible to do this with a Text object (which has no vertices).


I still remember during my English class, my English teacher taught us that we should always put ourself at last when referring to a group of people.      Eg. Ali, Ahmad and me instead of me,Ali and Ahmad.   Why would the first sentences sounds grammatical but the second is not ?


Why do people buy stocks that pay no dividend?

Before recently, Apple Inc. did not give dividend to shareholders.  This makes me curious why people buy Apple Inc. stocks; while it might be due to the expectation of selling stocks at a higher price, this can only be possible if other people are thinking the same, thereby increasing demand. But the stocks themselves do not pay interests - so Apple's amazing revenue/profit records would not matter....


Proving two free modules are isomorphic iff they have the same rank

Technically the question was  prove that if $R^m$ $\cong$ $R^n$, then m=n.  My proof was basically considering the case m>n, then consider an isomorphism $\phi$, then the image of the basis of $R^m$ under $\phi$ must still be linearly independent, but $R^n$ has a rank of n which is less than m, which will make the images of the basis of $R^m$ linearly dependent, contradiction.  My professor's comment of my solution was "long answer but you've shown nothing".  I do not understand what exactly is he looking for or the "proper" solution. Can anyone help explain?  edit: R is commutative


Delphi: Paradox DB Field Name Issue (Spaces in field name)

I have a paradox table from a legacy system I need to run a single query on.  The field names have spaces in them - i.e. "Street 1".  When I try and formulate a query in delphi for only the "Street 1" field, I get an error - Invalid use of keyword. Token: 1, Line Number: 1  Delphi V7 - object pascal, standard Tquery object name query1.


Can a Ranger select two humanoid races as their favored enemies at 6th and 14th levels?

In D&D 5e, the Ranger can choose at first level to have a Favored Enemy of a single broad type (i.e. fiends, giants, aberrations, etc.) or of two different specific humanoids (such as orcs and gnolls). They gain additional Favored Enemies at 6th and 14th level.  At each of those levels, could they opt to pick two humanoid races? Or would the choice be between one type and one specific humanoid?  Relevant text:     Choose a type of favored enemy: aberrations, beasts, celestials,   constructs, dragons, elementals, fey, fiends, giants, monstrosities,   oozes, plants, or undead. Alternatively, you can select two races of   humanoid (such as gnolls and orcs) as favored enemies.   And:     You choose one additional favored enemy, as well as an associated   language, at 6th and 14th level.   (Both quotes from PHB, pg 91.)  Specifically, I'm wondering whether "one additional favored enemy" means one absolutely, or whether the "Alternatively..." sentence means that two humanoid races can be substituted for one type whenever you select a favored enemy.


this is my setup: public class MyEnums {     [Flags]     public enum MyGroups     {         None = 0,         Test1 = 1,         Test2 = 2     } }   [AttributeUsage(AttributeTargets.Class | AttributeTargets.Method, AllowMultiple = true, Inherited = true)] public sealed class MyAttribute : AuthorizeAttribute {     private readonly MyGroups _allowedGroups;      public MyAttribute(MyGroups allowedGroups)     {         _allowedGroups = allowedGroups;     }      ... }   [MyAttribute(MyGroups.Test1 | MyGroups.Test2)] public class MyController : Controller {     ... }  I specifically do not understand what is happening in the [MyAttribute(MyGroups.Test1 | MyGroups.Test2)] part on the controller side. Am I instantiating multiple attributes (?)" [MyAttribute(MyGroups.Test1)] [MyAttribute(MyGroups.Test2)]  Thanks in advance!


Do we calculate the power with Chinese theorem?

For a natural numbr $n$ we know that $n=3k_1+1$, $n=4k_2+1$ and $n=5k_3+4$, for natural numbers $k_1, k_, k_3$. Calculate $5^n\pmod {13}$ . For that, do we apply the Chinese Theorem?


I'm loading an image from a file, and I want to know how to validate the image before it is fully read from the file.  string filePath = "image.jpg"; Image newImage = Image.FromFile(filePath);   The problem occurs when image.jpg isn't really a jpg.  For example, if I create an empty text file and rename it to image.jpg, an OutOfMemory Exception  will be thrown when image.jpg is loaded.  I'm looking for a function that will validate an image given a stream or a file path of the image.  Example function prototype  bool IsValidImage(string fileName); bool IsValidImage(Stream imageStream);


What does the little number following "closed" signify in flag history?

I'm not quite sure what to search for on this, but I noticed a little number on one (and only one, so I couldn't pinpoint a trend) of my flags in my flag history.   The text appears as follows:     title of question [closed] (1)   the flag was marked as helpful, the question was subsequently closed, yet a little (1) remains. I tried to see what that question had that the other questions did not, but moderator shut-down, specific tags, number of votes didn't matter. My only guess would be number of answers to the question? But I have no evidence for that. Does anyone know for certain?


How do I copy a property from an active object to selected objects?

I have been using the Copy Attributes add-on to copy some properties from active object to selected objects. This add-on is not enabled by default and must be explicitly enabled. But its a very useful workflow enhancing tool.    There is a limitation though. Not all properties can be copied and even those that can be copied are copied in groups (Its hard-coded in to the add-on).  My question is if there is a built-in feature or any another other way to copy any property from the active object to the selected objects?


How to make the optional title of a theorem bold with amsthm?

I use the code mentioned in :  \begin{theorem}[The title] Some statement \end{theorem}   However with amsthm the optional title -- above: "The title" -- is neither bold nor italic, but (ordinary) roman. I prefer to work with amsthm, so how can I solve the problem?    Update: After applying the code  \newtheoremstyle{mystyle}%                % Name   {}%                                     % Space above   {}%                                     % Space below   {\itshape}%                                     % Body font   {}%                                     % Indent amount   {\bfseries}%                            % Theorem head font   {.}%                                    % Punctuation after theorem head   { }%                                    % Space after theorem head, ' ', or \newline   {}%                                     % Theorem head spec (can be left empty, meaning `normal')  \theoremstyle{mystyle} \newtheorem{theorem}{Theorem}  \begin{document}  \begin{theorem}[abcd]\label{firstlabel}% 111 \end{theorem}   The output looks like this:    The content in the bracket is still not bold. How can I change it?  It can be solved by  \begin{theorem}[\bfseries abcd]\label{firstlabel}% 111 \end{theorem}   although I'd like to have it set universally.


Blender live-action footage and Grease Pencil animation

I have a bit of live-action footage that I would like to incorporate into a scene done with Grease Pencil to. Think of a newscaster talking about something and the live-action video is in a smaller window on the screen. Where the newscaster and set are done in Grease Pencil and the video they're talking about is live-action. I've brought the live-action footage into the video sequencer and I will be editing the live-action footage with pauses. The live-action footage will not fill the screen. it will only take up about 25% of one part of the screen.  Is there a way to see the video from the video sequencer in the Grease Pencil view? It would be helpful to be able to see the video sequencer video while working on the character in Grease Pencil.  If not, is there a workflow that would help with this?   Thanks, Jim


How can I syntax highlight the output from the exec() function in PHP?

I'm fetching output from the  and I would like to have some syntax highlighting in the results.  Raw output  Current output is raw:  * [35mmanu[m/etc/init.d/mast: line 105: /var/log/mast/mast-all.log: Permission denied    Text such as [35m are color .  Goal  I want to do it in HTML, I already have a colored shell script.


With sufficient randomness, is XOR an acceptable mechanism for encrypting?

I have heard criticism of various cryptosystems saying that "at their heart, they were just XOR."  Is this just ignorance, or is there something inherently wrong with XOR based ciphers?


Whom or Who in this sentence: These men, all of WHOM or WHO were well-known, well-respected statesmen, were viewed by their peers

Here's the full sentence: "These men, all of who were well-known, well-respected statesmen, were viewed by their peers and common people alike as great thinkers in their day.  I just can't really see where it would fall into: subject? predicate? object? What would it be?


To get password that is used to protect sheet

Is there any possibility to get the password that is used to protect sheet? I have a protected a sheet with password by the code. Now I need to retrieve that password with the help of the code? How do we retrieve that in apache-poi.  sheet.getCTWorksheet().getSheetProtection().getPassword(); This is giving me some "[B@da4eab14" value. How to convert that to string?  Do we have any other way to get the password?


Does $\det(I+A) = 1 + \mbox{tr}(A)$ hold if $A$ is a rank-$1$ complex matrix?

If $A$ is a complex $n \times n$ matrix of rank $1$, then $$\det(I+A) = 1 + \mbox{tr}(A)$$   How to approach this problem?  Rank-$1$ matrices have special . Also, thinking about the determinant of a matrix as the product of its eigenvalues and the trace of the matrix as the sum of its eigenvalues,   $$\prod_{k=1}^{n}(1+\lambda_{k}) = 1  +\sum_{k=1}^{n} \lambda_{k}$$  I could not proceed.


Why angular velocity is a vector quantity?

Angular displacement isn't a vector quantity (according to some websites) then how angular velocity can be a vector? shouldn't it be a scalar?


Why does a person sees water in the desert even then when no water is present there at that time? How does this happens?


Each of the 25 cells in a five-by-five grid of squares is filled with a 0, 1, or 2 in such a way that the numbers written in neighboring cells differ from the number in that cell by 1. Two cells are considered neighbors if they share a side. How many different arrangements are possible?


Where does this formula for sagging of a beam come from?

In one of my physics textbooks there is a chapter on the elasticity of materials which contains pretty basic outline about Young's modulus, stress-strain, elastic potential energy and related stuff. There is only one thing stated in the book which I didn't understand, which is this:   Consider an elastic beam rigidly supported at both its ends in a horizontal fashion, which is loaded with a weight $W$ at the centre. It's length is $l$, breadth is $b$, depth is $d$ and the Young's modulus is $Y$. Then the beam sags by an amount $\delta$ which is given by: $$\delta={Wl^3 \over 4bd^3Y}$$  The book says that it can be derived easily with basic concepts of elasticity and some calculus. What I tried was:  Try to calculate longitudinal strain by approximating the bent beam as a circular arc. Integrate the shear stress along the beam and approximate the shear modulus $G\approx {Y \over 3}$ Equate the work $(W\delta)$ done on the beam due to the load to the elastic potential energy.  Despite many efforts, I could not arrive at the result. Can anyone please help me in proving this result?


Is it possible to have longtable and tabulary together in a table for autofit and Auto continuation of table in next page  Below is my code   \documentclass{article} \usepackage{longtable,tabulary,capt-of,dcolumn} \usepackage{booktabs} \usepackage{showframe}   \makeatletter  \def\ltabulary{% \def\endfirsthead{\\}% \def\endhead{\\}% \def\endfoot{\\}% \def\endlastfoot{\\}% \def\tabulary{%   \def\TY@final{% \def\endfirsthead{\LT@end@hd@ft\LT@firsthead}% \def\endhead{\LT@end@hd@ft\LT@head}% \def\endfoot{\LT@end@hd@ft\LT@foot}% \def\endlastfoot{\LT@end@hd@ft\LT@lastfoot}% \longtable}%   \let\endTY@final\endlongtable   \TY@tabular}% \dimen@\columnwidth \advance\dimen@-\LTleft \advance\dimen@-\LTright \tabulary\dimen@}  \def\endltabulary{\endtabulary}  \makeatother  \begin{document}   \begin{table} \captionof{table}{Sample Table 1 }\label{table_specrot} \begin{ltabulary}{LLD..{1.3}} x&y&1.1\\ x&y&1.244\\ x&y&1.3\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&y&1.2\\ x&yaaaa&1.2\\ \end{ltabulary} \end{table}  \end{document}


What is the best way to test normality for a very large sample size 15000?

Also do I need to test the normality for the categorical data?  Thanks


YA/kids' book featuring a kid and an alien whose preferred pronoun is "it" rather than "he" or "she"

There's a book I read in the late '90s that I'm trying to remember. Definitely in it The scene I remember very vividly is one of the aliens telling the point of view character (a kid, I think) that it would be ruder to call it "he" or "she" than to call it "it". Probably in it I think the aliens are very small and shrink the POV character to their size to be able to be on their tiny spaceship, but honestly I'm not certain that's the same book. I think the shrinking may be accidental? And maybe the aliens can't un-shrink him? Maybe in it? At the same time I read that book I also read a book that involved someone being taught to use a rocket belt. I don't know if that was the same book though.


Human beings have evolved from their ancestors to their modern forms adapting many changes in structure and I would assume that every change has a significance.  So, what is the cause of our hair turning white at old age? Was it meant for frightening away predators at old age when our body is weak? Or what is it actually?


Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$

Prove or give a counterexample:  $$(A ∪ B = A ∪ C) \land (A ∩ B = A ∩ C) \implies B = C.$$  I think this is true, but I am not sure how to show it. I don't know if there are any manipulations with unions and intersections that allows me to move things around. Thanks in advance for any hints.


Why is the auto-replace for on-site question-links with the respective question-title only enabled in posts but not in comments?

When you paste an url in a question or answer (i.e. a post), its link text is automatically replaced with the title of linked-to question, like so:   However, this is not done for comments. When you paste a link to a relevant question (perhaps even only the url) into the comment box, it will be displayed verbatim. This is especially tiresome for recurring c++-faq question-link comments. These questions have usually fairly well-curated titles that say enough on their own, but I have to Copy-Paste both the url and the title and manually [Ctrl-V](Ctrl-V) them.  What is the reason for this? Or am I using the interface wrong?


Electrics fields in Electromagnetic waves

It might sound naive but the question is:  In an Electromagnetic wave in  a vacuum the electric and magnetic fields are vibrating but what are the source and drain of these fields?  An electric field must start from a charge and end or be in a circular fashion due to varying magnetic field and in a similarly way, magnetic fields must form a closed loop.  Please explain  this idea?  if magnetic fields are to be in closed loop always then the oscillating fields of a em waves must be too.  So what is the shape of fields in general near a em wave?


If the set $B={\{e_1,...e_n\}}$ is a basis of a finite dimensional vector space $V$ then the set $D=\{\epsilon_1,...,\epsilon_n\}$ where $\epsilon^i(e_j)=\delta_j^i$ is a basis for the dual space $V^*$    If $B'={\{e'_1,...e'_n\}}$ is a different basis for $V$ and then we get a different basis for the dual space $D'=\{\epsilon'_1,...,\epsilon'_n\}$  I am trying to work out how to relate the change of basis matrix from $B$ to $B'$ to the change of basis matrix from $D$ to $D'$  That is, there is to be a matrix $M$ such that $e'_i=M_{ij} e_j$ and a matrix $N$ such that $\epsilon'_i= N_{ij} \epsilon_j$ but I feel like there should be a close relationship between the two things because $\epsilon_i$ depends on $e_i$.  Can anyone help me with this?  (Also, this is my first question so I apologise if I have made errors here and there!)


Countable Union of sets of the same cardinality

Let $A_n$ be a sequence of sets having the same cardinality $k$ (possibly uncountable, and may not be equal to the cardinality of the continuum). Also assume they are disjoint. How could I show that $\cup_n A_n$ has cardinality $k$?


sed remove all lines starting with x or X, but the lines start with spaces

I have to remove lines from a text starting with x or X, but the lines start with spaces. So far I have this: sed plik.txt -e "/^[xX]/d"  I have tried many combinations from other questions but nothing works. Here's the text:    Sed testing Testing             xTest test           test test test xxx XXX        X test test      End of text


$ \triangle $ is symmetric difference. I want to proof that $A \triangle (B \triangle C) = (A \triangle B) \triangle C $ It seems like join's rule. I tried to assume that $ x \in Left $ and then move to $ (...) $ so $ x \in Right $ but when I use definition of $ \triangle $ I get something like that: $x \in A \land x \in B \land x \in C \land x \notin A \notin x \in B \notin x \in C \land (...) $ what does not have sense...  I have seen  but there is well explained algebraic way but I am trying to do this with normal set theory (By this I mean something as I presented on the begining).


I currently own a Canon 60D, and I am perfectly happy with the camera. It is going to be years until I move to a better (most likely full-frame) body.   My main, walk-around lens is the . I am also very happy with this lens, although I also know its shortcomings, like the variable aperture (3.5-5.6).   But this morning, as a "what if" exercise, I started thinking about upgrading this lens.   Since my 60D is a crop sensor body, the closest and cheapest upgrade I can do is the   EF-S USM IS. It has a constant aperture of 2.8, and people say that it produces the best picture quality of all EF-S lenses. The upgrade would probably cost me $300-$500, depending on the price I sell my 15-85 at, and whether I want a used or new 17-55.   But 'upgrading' from an EF-S lens to another EF-S lens is not really upgrading, is it? It is more like switching between two similar quality products. Is it worth it?   A TRUE upgrade would be to get an L lens. So, assuming that price is no object (one can only dream :(), what L lens would you recommend to replace my 15-85?   EDIT: What I would look for in the ideal replacement lens.  Thanks for all the answers so far. One conclusion I came to after reading them is that there is no point for me to invest in L glass if I care about wide angle on my crop sensor body. And I do.   I like my 15-85 because it offers me the flexibility of being able to capture moments like a few snapshots in a restaurant with friends, or my 2 years old daughter who won't sit in one place for long - definitely not long enough for me to switch lenses.   I could give up the 2mm difference on the wide end of the spectrum, if the 17-55 offered me much higher IQ than the 15-85 does.   Hence the followup question - Please let me know if you upgraded from 15-85 to 17-55 and if that was a right decision.. I know it is all personal - and that is what I am asking about - what was your experience with such upgrade if you did it?


If I understand correctly, 105 should be written     one hundred five   as in     The building has one hundred five stories.   But is it     A one-hundred-five-story building   or     A one hundred five-story building   or something else?  Note: I'm familiar with the rules stated in the , but the answer there doesn't necessarily apply because numbers greater than 20 and less than 100 are hyphenated regardless. My confusion arises when combining the rule that 105 is not hyphenated on its own, but compound adjectives should be hyphenated. Note also that the links in the suggested duplicate are dead, so I rely only on the text of the answer.


public static void Main() {     Stream s1 = this.GetType().Assembly.GetManifestResourceStream("WindowsApplication1.sudhir.jpg");     Stream s2 = this.GetType().Assembly.GetManifestResourceStream("WindowsApplication1.sunil.jpg");     Bitmap img1 = new Bitmap(s1);     Bitmap img2 = new Bitmap(s2);      if (img1.Size != img2.Size)     {         Console.Error.WriteLine("Images are of different sizes");         return;     }      float diff = 0;      for (int y = 0; y < img1.Height; y++)     {         for (int x = 0; x < img1.Width; x++)         {             diff += (float)Math.Abs(img1.GetPixel(x, y).R - img2.GetPixel(x, y).R) / 255;             diff += (float)Math.Abs(img1.GetPixel(x, y).G - img2.GetPixel(x, y).G) / 255;             diff += (float)Math.Abs(img1.GetPixel(x, y).B - img2.GetPixel(x, y).B) / 255;         }     }      Console.WriteLine("diff: {0} %", 100 * diff / (img1.Width * img1.Height * 3));   Here I'm trying to match the two images and finding their difference but I'm getting this error      Keyword 'this' is not valid in a static property, static method, or static field initializer.   What's wrong and how can I fix this?


Is it standard Javascript behaviour for new variables to reference objects rather than copy them?

I am currently learning about objects in javascript.  I have encountered behaviour I didn't expect and I want to confirm if I am seeing what I should be seeing or if I have made a mistake somewhere.  var a = 1; var b = a; b++; console.log(a); // 1 (As expected) console.log(b); // 2  var a = 'string'; var b = a; b += 'ier'; console.log(a); // string (As expected) console.log(b); // stringier  var a = {}; var b = a; b['testValue'] = 'test'; console.log(a); // {testValue = 'test'} (Wait... what?!) console.log(b); // {testValue = 'test'}     Added:  I've just tried the same experiment with an array and I see the array is exhibiting the same behaviour as the object (perhaps to be expected, given that arrays are objects in Javascript)  var a = []; var b = a; b[0] = 'test'; console.log(a); // ['test'] (Hmmm... again!) console.log(b); // ['test']     Why are the object and the array behaving differently from the number and the string?  Why is var b only referencing var a rather than duplicating it?


Let us say I extract all tweets containing a certain hashtag (main subject of the tweet) and bin them by the hour i.e. count the number of tweets that occurred during a certain hour. I will then be obtaining a time series for this particular hashtag. I have recently come across the  which decomposes a given timeline into its seasonal, trend and error components and R provides a simple function stl to achieve this.  I am trying to understand if using this in my context (timeline of tweet counts) is appropriate. What I would like to examine is whether two given hashtags have a similar timeline and I was wondering what I can understand by using time series decomposition. Any suggestions?


SubSonic 3.0.0.3 | SimpleRepository | DB DataType - Class DataType mapping

I am beginning to make friends with SubSonic 3.0.0.3 - SimpleRepository. Since you/I have to create every object class, so I made a simple code below, just to save some time.  My only question is, does my mapping are correct (DB DataType to .Net DataType)?  Here's the simple code:  public string CreateClassEntity(string ConnectionSring, string TableName)         {            SqlDatabase db = new SqlDatabase(ConnectionSring);              string sqlCommand = "SELECT TOP 1 * FROM " + TableName + "";             DbCommand dbCommand = db.GetSqlStringCommand(sqlCommand);              DataSet subsonicDataSet = db.ExecuteDataSet(dbCommand);              DataTable subsonicDataTable = subsonicDataSet.Tables[0].Clone();             string classEntity = "public class " + TableName + " \n{";             foreach(DataColumn column in subsonicDataTable.Columns)             {                 classEntity += "\n\tpublic ";                 classEntity += column.DataType.ToString().Replace("System.", string.Empty) + " ";                 classEntity += column.ColumnName + " ";                  classEntity += "{ get; set; }";             }             classEntity += "\n}";              return classEntity;         }   Sample target Table (SQL 2008):  CREATE TABLE [kiss].[Users](     [ID] [int] IDENTITY(1,1) NOT NULL,     [UserName] [nvarchar](20) NOT NULL,     [UserPassword] [varbinary](128) NULL,     [UserTypeID] [tinyint] NOT NULL,     [ByPassAccessRestrictionsFlag] [bit] NOT NULL,     [IsEnforcePasswordPolicy] [bit] NOT NULL,     [PasswordExpirationDate] [datetime] NULL,     [IsPwdChangeNextLogin] [bit] NOT NULL,     [ShowLatestNewsFlag] [bit] NOT NULL,     [SortRowNumber] [int] NOT NULL,     [CreatedDate] [datetime] NOT NULL,     [CreatedBy] [nvarchar](20) NOT NULL,     [UpdatedDate] [datetime] NOT NULL,     [UpdatedBy] [nvarchar](20) NOT NULL,     [DeletedDate] [int] NULL,     [EntityTypeID] [int] NOT NULL     )   Sample Class Output:  public class Users  {     public Int32 ID { get; set; }     public String UserName { get; set; }     public Byte[] UserPassword { get; set; }     public Byte UserTypeID { get; set; }     public Boolean ByPassAccessRestrictionsFlag { get; set; }     public Boolean IsEnforcePasswordPolicy { get; set; }     public DateTime PasswordExpirationDate { get; set; }     public Boolean IsPwdChangeNextLogin { get; set; }     public Boolean ShowLatestNewsFlag { get; set; }     public Int32 SortRowNumber { get; set; }     public DateTime CreatedDate { get; set; }     public String CreatedBy { get; set; }     public DateTime UpdatedDate { get; set; }     public String UpdatedBy { get; set; }     public Int32 DeletedDate { get; set; }     public Int32 EntityTypeID { get; set; } }


Booting Debian into Virtualbox or other Virtualization Software

On my laptop, I have Windows 10 on first disk drive and Debian 10 on second disk drive with dual-boot functionality. However, is it possible to boot Debian 10 installation from Windows 10 through some kind of virtualization software, while Windows 10 is running?


Commenting out large blocks in the preamble when in draft mode

I would like something to enable me to comment out large blocks of my preamble when I've specified that my document is a draft.  The comment environment provided by the verbatim package works well for commenting out a large block of my preamble. The problem I am having is that I'm not sure how to make the comment enviroment active only when the draft option is specified in \documentclass[draft]{article}.  How do I make the inclusion/activation of this comment environment conditional upon the specification of the draft option? If that is not possible, is there some work around, perhaps through the creation of new booleans and something like \ifbool?


How to find the best route through multiple points?

I am using postgreSQL, postGIS and pgrouting. Now I am really confused on how am I going to find the shortest path between multiple points.   I know how to find it between two points through dijkstra but I am confused how to accomplish the same result with more than two points.   I have done some research and found this:    But still I did not understand if its the right way and how to install it.


Best way to See if String in Hashset contains elements from another hashset? C#

I  have a hashset of strings that contain lognames called pidLogsLines. From this hashset I want to filter out logs that only contain strings from another hashset called pidList and put these logs inside a new hashset called filesWithPid. I am doing this with two loops: var filesWithPid = new HashSet<string>(StringComparer.OrdinalIgnoreCase); foreach(var logname in pidLogsLines) {     foreach(var pid in pidList)     {         if (logname.Contains(pid))         {             filesWithPid.Add(logname);         }     }  }  Is this the optimal way to do it? I am new to C# so I am not aware of any elaborate faster ways to do it


Consider a transformation between the coordinates given by $x^{a}$ to another system given by coordinates $x^{'a}$. So a transformation of the type: $x^{a} \rightarrow x^{'a}$.   With that I can construct the Jacobian matrix:  $\bigg[ \frac{\partial x^{'a}}{\partial x^{b}} \bigg]$  The determinant of this matrix is called the Jacobian determinant, hereafter J. I want to prove that:  $dx^{'1}dx^{'2}...dx^{'N} = Jdx^{1}dx^{2}...dx^{N}$  where primed system is cartesian and the unprimed one is a general set of coordinates. How can I do that?  I remembered that in transformation of coordinate is valid to write (using the summation convention) that:  $dx^{'a} = \frac{\partial x^{'a}}{\partial x^{b}}dx^{b}$   And tried to apply that to proof that I need, but, I was not abble to go anywhere because of lot of terms shows up.  Actually, in the case we considerer just 2 dimensions I ended up with something like that:  $dx^{'1}dx^{'2} =  \bigg( \frac{\partial x^{'1}}{\partial x^{1}} \frac{\partial x^{'2}}{\partial x^{1}} \bigg)(dx^{1})^{2}+ \bigg( \frac{\partial x^{'1}}{\partial x^{2}} \frac{\partial x^{'2}}{\partial x^{2}} \bigg)(dx^{2})^{2} + \bigg[\bigg( \frac{\partial x^{'1}}{\partial x^{1}} \frac{\partial x^{'2}}{\partial x^{2}} \bigg) + \bigg( \frac{\partial x^{'1}}{\partial x^{2}} \frac{\partial x^{'2}}{\partial x^{1}} \bigg)\bigg]dx^{1}dx^{2} $  As is possible to see, the last two therms inside the brackets are almost the Jacobian determinant. So my question is: what is wrong in this approach?   with a different ideia of the proof. But why should I use that instead of the mine? And also: how could I generalize the ideia of this article for N-dimensions?


Sometimes I erroneously copy & enter file name into terminal, for example, instead of youtube-dl <some-link> I trying to execute <some-link> Just for now I wrote the script f like case "$1"     ...     '*youtu.be*': youtube-dl "$1" ;;     '*.html': links "$1" ;;     ...     else xdg-open "$1" ;; esac  Is there any ability in the bash to replace <input> by <command> <input> depending on <input>?


The difference between "Closed" and "On Hold"

I keep on seeing questions either "put on hold" or "closed" by the same thing, like for instance here a question has been "put on hold" for being off-topic:    And here is a question which has been "closed" for being off-topic:    So what is the difference then between a question being "closed" and "put on hold"?


upgrading the Ubuntu this error occurs:  $ sudo apt-get upgrade error Malformed line 1 in source list /etc/apt/sources.list (type) E: The list of sources could not be read   Line 1 in source list is this:  123#deb cdrom:[Ubuntu 16.04.3 LTS _Xenial Xerus_ - Release amd64 (20170801)]/ xenial main restricted


Aditive functor characterization. Aditive iff right/left exact.

I need to prove this:  Let F be a functor between abelian categories. F is aditive iff is right exact or left exact.  I think that for <-- I'll need to use the characterization:  F between aditive categories is an aditive functor iff F preserves products (or coproducts).  So I'll need to prove that if F is right exact, then it preserves coproducts and if F is left exact, it preserves products, and then I could use this result, but I'm not sure about it.  Any help or idea to both sides of the proof is welcome, thanks in advance!


Limits Problem : $\lim_{n \to \infty}[(1+\frac{1}{n})(1+\frac{2}{n})\cdots(1+\frac{n}{n})]^{\frac{1}{n}}$ is equal to..

Problem:   How to find the following limit :   $$\lim_{n \to \infty}[(1+\frac{1}{n})(1+\frac{2}{n})\cdots(1+\frac{n}{n})]^{\frac{1}{n}}$$ is equal to   (a) $\frac{4}{e}$  (b) $\frac{3}{e}$   (c) $\frac{1}{e}$   (d) $e$    Please suggest how to proceed in this problem thanks...


Proof that the Casimir invariant of a representation commutes with everything

We have some representation $\rho:L\longrightarrow End(V)$ of a $d$-dimensional complex Lie algebra $L$. Let $\{X_1,...,X_d\}$ be any basis of $L$, and let $\{\xi_1,...,\xi_d\}$ be another basis such that $\kappa_\rho(X_i,\xi_j):=tr(\rho(X_i)\circ\rho(\xi_j))=\delta_{ij}$ where $\kappa_\rho$ is the Killing form. Define the Casimir invariant by $$\Omega_{\rho}:=\sum\limits_{i=1}^{d}\rho(X_i)\circ\rho(\xi_i).$$ I want to prove that $\forall a\in L:$ $$[\Omega_{\rho},\rho(a)]=0.$$ By taking [] to be the commutator and thinking of $\circ$ as a multiplication (matrix multiplication? I think this is justified because a basis has been chosen for $L$), I've reached $$[\Omega_{\rho},\rho(a)]=\sum\limits_{i=1}^{d}\rho(X_i)\rho(\xi_i)\rho(a)-\rho(a)\rho(X_i)\rho(\xi_i)=...$$ $$...=\sum\limits_{i=1}^{d}\rho(X_i)[\rho(\xi_i),\rho(a)]- [\rho(a),\rho(X_i)]\rho(\xi_i)$$ but I don't know where to go from here. Any push in the right direction would be much appreciated.


Show that $F(x) = f(\|x\|)$ is differentiable on $\mathbb{R}^n$.

Let an even function $f:\mathbb{R}\to\mathbb{R}$ which is even and differentiable. We define $F:\mathbb{R}^n\to\mathbb{R}$  as $F(x) = f(\|x\|)$. Show that $F(x)$ is differentiable on $\mathbb{R}^n$.   My Work:    Let $x_0\in\mathbb{R}^n$.   If $x_0\ne 0$ then the partial derivatives of the norm are well-defined and: $$ \frac{\partial \|.\|}{\partial x_i} = \frac{x_i}{\|x\|}$$ $\frac{x_i}{\|x\|}$ continuous and since $f$ is differentiable it's partial derivatives are continuous. So we can conclude that $\frac{\partial F}{\partial x_i}$ is continuous and therefore $F$ is differentiable. If $x_0=0$ then the $\|x_0\| = 0$ and since $f$ is even $f(0)=0$ and it must be an extremum point. Therefore, $F'(0)=0$.   I'd like to get a critique of my work. Am I being right/rigorous?  Thanks.


To prove $x+\frac{1}{x}\geq2$ where $x$ is a positive real number. This is what i try: $$\text{We need to prove } \hspace{1cm} x+\frac{1}{x}-2\geq 0$$ now,$$\frac{x^2-2x+1}{x}=(x-2)+\frac{1}{x}$$ its enough to show that $$\frac{1}{x}\geq(x-2)\hspace{0.5cm} \text{ when } \hspace{0.2cm}0<x\leq 2$$ we can easily show it using the graph.  but my question is can we do it algebraically or using calculus to prove it without any reference to the graphs.


Where can I ask interview related questions?

Interview, asking for offer etc. I wonder if Stack Exchange has a sote for this kind of question?   Sample question:     Do company usually do not reveal their benefit package until you sign the accepting offer letter?


What do you call snow that has collected between a car body and the tire?

Snowy areas commonly see snow collect between a car body and tire. There is some strange satisfaction in kicking that snow off of the car and I've been in many conversations about miscellaneous details of this particular type of snow collection. Photographic example:    But is there a word I can use to refer to this clump? I am looking for a word similar to "icicle" or "stalactite" but a bit more specific.


I know this is a series of an arithmetic and geometric progression product which looks like  $$\sum\limits_{n=0}^{\infty} (2n+1) \left(\frac{1}{2}\right)^n$$  but I don't know how to calculate the sum. Any help would be appreciated!


How to run multiple commands with psexec?

I need to run a command to uninstall forefront on some of our workstations and am having a bit of trouble formatting the command.  Here's what needs to happen (in multiple commands)  xcopy \\serverpath\Installer.exe C:\Windows Install.exe /u /s Del C:\Windows\Install.exe  I'm using psexec with a computer list but keep running into errors. This is what my command looks like as of right now.   psexec @ComputerList.txt -u domain\administrator cmd /c (xcopy "\\NetworkPath\Forefront Software\Install.exe" "C:\Windows" && Install.exe /u /s && del C:\Windows\Install.exe)   I think the spaces in the path name and quotes are messing things up...  EDIT:  Tried running it with a script with no luck. It looks like scepinstall.exe just hangs on the remote machine. I also tried using the exe that can be found in C:\Windows\ccmsetup\  Thanks for the help


Combinatorics proof involving Fibonacci numbers

I've found an interesting problem in my Combinatorics class notes but I am unsure how to start or even where to start. The question is:  Prove that $\sum_{j=1}^nf_j^2$ = $f_n$$f_{n+1}$, where $f_j$ are Fibonacci numbers.  Would anyone mind giving me a hint or at least giving me a start?


Can I get the chronology of books written for LaTeX  For example I have gone through D._Knuth-The_TeXbook.pdf  But most of the examples will not compile in the modern Win Cmptr running MikTex like \line \topinsert etc   What book comes next in the series after the aforementioned TeXbook?


I can find primary decomposition of ideal generated by two elements . For example ideal $\langle xy, y^2\rangle=\langle x, y^2\rangle  \cap \langle y\rangle $  But I face problem when I tried to find primary decomposition of the ideal $\langle x^3, x^2y, yz, xz^2\rangle $  in $K[x, y, z]$ . Can someone help me how can I find primary decomposition of ideal which is generated by 4 elements?   Thanks.