Math of eigenvalue problem in quantum mechanics

Question: I learned the eigenvalue problem in linear algebra before and I just find that the quantum mechanics happen to associate the Schrodinger equation with the eigenvalue problem. In linear algebra, we always gives the matrix of certain size (e.g. 4x4) so to find the eigenvalues is identical to solve the related secular equation. In quantum mechanics, in most case, it seems that the dimension of the matrix is not known or very large so to how to find the eigenvalue in those case? I just saw a problem in a book, if we know $A|a\rangle=a|a\rangle$ and $A|b\rangle=b|b\rangle$ for a Hermitian operator $A$. What's the eigenvalue of a Hamilton operator $H=|a\rangle\langle b| + |b\rangle\langle a|$. It is so confusing to me because if we don't know the matrix and elements, how can we write the secular equation and find the eigenvalues? Sorry I didn't take any class on quantum mechanics before, I learn it all my myself so I might be wrong in some statement above.
Comment: This is just a remark and not an answer to your questions, but I wanted to mention that in typical physical systems, the Hilbert space must be of infinite dimension. This apply more precisely when you have a pair of canonically conjugated variables, say a position operator $\hat q$ and momentum operator $\hat p$. By definition of 'canonically conjugated' they satisfy $[\hat q,\hat p] = i \text{Id}$ (up to a sign). If dimension is finite, then the trace of any operator is defined and taking the trace of this relation one arrives at a contradiction.
Answer: In principle, the operator $H$ is not a matrix. However, you can write down a matrix representation. For that, you need a basis, which should be complete (=very large matrix, probably infinitely large) - for many illustrating cases in quantum mechanics, it's not complete.
If your basis consists of $|a\rangle$ and $|b\rangle$, it's not complete, but you can still describe some effects nicely.
You gave the example $H=|a\rangle\langle b| + |b\rangle\langle a|$, which means that $H$ is (it's just another way to write it)
$$H=\begin{pmatrix}
0 & 1\\
1 & 0
\end{pmatrix},$$
and you can calculate its eigenvalues.
For a general 2x2 Hamiltonian matrix, the formula is
$$H=\sum_{i,j}c_{i,j}|i\rangle\langle j|=\begin{pmatrix}
c_{1,1} & c_{1,2}\\
c_{2,1} & c_{2,2}
\end{pmatrix}$$
$i$ and $j$ can take the value $a$ and $b$.
The matrix is a 2x2 matrix because the Hamiltonian only contains two vectors, $a$ and $b$.
How to expand a Hamiltonian operator into a matrix is explained nicely on Wikipedia (first four formulas of the section).
If it's already in the abstract form $H=|a\rangle\langle b| + |b\rangle\langle a|$, you can just read it off: The prefactor of $|a\rangle\langle a|$ ($=0$) is the top left entry, the prefactor of $|a\rangle\langle b|$ ($=1$) is the top left entry etc.
You don't need to know the explicit form of basis in which the matrix is written. Remember that the eigenvalues of a matrix are invariant to unitary transformations.
Comment: wow, it is so shocking to me that even we don't know the form or |a> and |b>, we can still write the matrix form of H? How do you do that? How can you extract the information from $H = |a\rangle \langle b| + |b \rangle \langle a|$ so to get the off-diagonal matrix element to be 1? And how do you know H is 2x2? Sorry, there is some terms I don't understand from your answer but I guess what you mean is we can choose vectors as a basis and we can also choose another matrices as basis. So in the last equation you show, you choose the matrix $|i\rangle \langle j|$ as the basis to expand H, right?
Comment: "How can you extract the information from $H=|a\rangle\langle b|+|b\rangle\langle a|$ so to get the off-diagonal matrix element to be 1?": What is the prefactor of $|b\rangle\langle a|$? Or, more precisely, what is $\langle b |H| a \rangle$ if $|a\rangle,|b\rangle$ are orthogonal?
Answer: You need to understand the difference between a linear transformation T and the matrix A which represents it. The entries of A depend on the specific basis you're working in. You should recall from linear algebra that to find the columns of A, you apply T to the basis vectors.
For example, in your problem, the Hamiltonian $\hat{H}$ plays the role of T, and $\{\vert a \rangle, \lvert b \rangle\}$ is your basis. If you apply $\lvert a \rangle$ to $\hat{H}$, you get
$$ \hat{H} \lvert a \rangle = \lvert a \rangle\langle b \vert a \rangle + \lvert b \rangle\langle a \vert a \rangle = \lvert b \rangle.$$
Note that this calculation is entirely independent of the representations of the vectors and the Hamiltonian.
Now relative to our chosen basis, it should be clear to you that the vector $\lvert a \rangle$ is represented by the ordered pair $\begin{pmatrix} 1 \\ 0\end{pmatrix}$ and $\lvert b \rangle$ is represented by the ordered pair $\begin{pmatrix} 0 \\ 1\end{pmatrix}$. In terms of matrices and the ordered pairs, the relation $\hat{H}\lvert a \rangle = \lvert b \rangle$ would be written
$$A\begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \end{pmatrix},$$ so the first column of A is $\begin{pmatrix} 0 \\ 1 \end{pmatrix}$. You can find the second column of A by applying $\lvert b \rangle$ to $\hat{H}$. Then once you have the matrix, you can find the eigenvalues and eigenvectors the usual way.
Comment: I was going to post something like this but Conrad got there first. To the OP user1285419 : the eigenvalue problem can be defined for any linear operator. For example, $\frac{d^2y}{dx^2} = ky$, the simple harmonic equation, is an eigenvalue problem! (look up Sturm-Liouville). The solutions to that ODE, $y$, are the eigenfunctions of the linear operator $\frac{d^2}{dx^2}$. Does $\frac{d^2}{dx^2}$ have a matrix representation? Yes - for example, choosing a basis $\{1, x, x^2, \cdots \}$, one can write an infinite dimensional matrix for it. but the important thing is that you don't have to!
Answer: The stuff about the operator $A$ is just so that you'll know that $|a\rangle$ and $|b\rangle$ are orthogonal (if we assume $a \neq b$). This follows from the properties of Hermitian operators (just evaluate $\langle a | A | b\rangle$ two different ways).
Since $|a\rangle$ and $|b\rangle$ are orthogonal, they are a good choice for a basis, and we can write the matrix of $H$ in this basis. It is the operator that switches $|a\rangle$ and $|b\rangle$ (this is fairly easy to see without the matrix, but you asked for the matrix). The square of this operator is the identity, so its eigenvalues are $\pm 1$.
Comment: Thanks Mark. I am not totally understand this thought I know it is right (I read the similar statement from a book). My question is even we don't know the explicit form of |a> and |b>, can we still know that the eigenvalues of H? Also, you gave that the eigenvalues are +/-1, so what's the corresponding eigenvector? I try to have H apply on |a> or |b> but it doesn't give me the |a> or |b> back so I know they are not the eigenvectors. It seems that |a>+|b> could be the eigenvectors but I don't know why (just guessing)
Comment: What do you mean by "the explicit form of |a> and |b>"? They are vectors in a vector space. We know that they are orthogonal. What else do you want from them? The eigenvectors are |a> + |b> and |a> - |b>.
Answer: Eigenvalue problems are much more general than what you see in matrices. For example, you can look for solutions to the eigenvalue problem
$ \frac{d }{d x} y = \lambda y$
solve for $\lambda$. The solution is, of course, $y = e^{\lambda x}$ and $\lambda$ can be a continuum. If you impose some other boundary conditions, you may end up with a discrete spectrum of $\lambda$.
If you insist on a matrix representation, you can use orthogonal functions as your "basis vectors" and their orthogonality relations to define an inner product. Read up about the quantum harmonic oscillator, and Hermite polynomials are an orthogonal basis to expand the solution in that also happen to solve the differential equation exactly.
Answer: This matrix has only 2 states $ |a> $ and $ |b> $
then ti will gbe a 2x2 matrix
with elements
$ a1,1 = <a|a><b|a>+<a|b><a|a> $
$ a1,2=a2,1 = <a|a><b|b>+<a|b><a|b> $
$a2,2 = <b|a><b|b>+ <b|b><a|b> $
From this matrix you can evaluate the eigenvalues


QGIS world imagery does not repeat itself

Question: Is it possible to make raster imagery from a service like OSM repeat itself like google maps does? I want to create a map of the world that shows Australia at the center, but the imagery stops at new zealand? It doesnt repeat the imagery from the other side of the dateline. I imagine this is just a tick box somewhere, any ideas. (i know i could do this manually by exporting and joining, but i am more curious if this is possible in qgis in a more dynamic way)
Comment: Im using Open layers plugin to bring in imagery..and qgis 2.16
Comment: Thats interesting. Have you set the CRS as EPSG:3857? Also what version of QGIS are you using? I'm in 2.16.1 and layers from the openlayers plugin draw continuously when I load them in a fresh project.
Answer: Openlayers use EPSG: 3857 which is WGS 84 / Pseudo Mercator. OpenLayers plugin does not display only Google map layer without any other vector/raster layer. In order to display the map correctly you need to add one vector layer at least, then you can turn off that layer, and make sure the CRS used to display Google map layer is EPSG: 3857 which is WGS 84 / Pseudo Mercator in the lower left window of QGIS, as you can see below:

The result in the map composer is as follows:

Google map uses continuous tiles by default, but in case of OSM, it is not, and open layers cannot provide an option to adjust the tiles to repeat itself again.
Another option is that you can use QuickMapServices Plugin. Although it does not provide an option for the tiles to repeat again, but you can change the project as a workaround to something like EPSG: 53003 'Sphere_Miller_Cylindrical', but there is gap between the tiles when it is start to repeat itself, as you can see below:


What can be saftly deleted in data/data

Question: What can be saftly deleted in data/data.  I have almost no space left on a few devices.  I don't want to delete account info.
Answer: Remove apps via Settings > Apps > Your app > Uninstall. It is safer and you will be able to know easily the app(s) that you want to uninstall (you won't need to know the package name).
Start by removing apps you don't use. If there are system apps (i.e Google play music, duo, Hangouts, etc), you can remove their updates then disable them.
If there are apps you want to remove and keep their data in case you reinstall later, use Titanium backup or Helium to backup the apps and their data then remove them.
Comment: The apps are easy to remove, but data/data is taking 75% the space.

What can be saftly deleted in data/data


What do Sunni Muslims recite during Zil Hijjah Month after prayers

Question: What do Sunni Muslim recite after prayers during 9th and onwards of Zil Hijjah Month?
Answer: If you mean the takbir after the fard prayers then one can start with it after the fajr prayer of the day of 'arafah (9th dhil Hijja) end it ends with the sunset of the last day of tashreeq (13th dhil hijja) for a person not wearing ihram (doing hajj) for the one who wears ihram it beginns after dohr prayer of the day of 'id al adha (10th dhil hijja).
Scholars and fiqh schools have differences in this for example according to maliki sources takbir is done after 15 fard prayers (so they start takbir after dohr prayer of the day of 'id and end after fajr prayer of the last days of tashreeq according to ar-Rissala متن الرسالة from abu Zayd al-Qayrawani ابن أبي زيد القيرواني)! Some scholars say doing it in congregation is bida'h.
You could find some details here or in Arabic here
And Allah knows best!


What do horizontal (H) and vertical (V) polarization mean for satellite radar?

Question: I'm reading about synthetic aperture radar (SAR), and one of the basic concepts is that the transmitted and received signals can have "horizontal" (H) or "vertical" (V) polarization, but I can't find anywhere what that means in terms of the real-life physical direction.  If the radar were on top of a building and transmitting a wave parallel to the surface of the earth, then I can understand that horizontal and vertical would mean relative to the surface of the earth.  But if the radar is on a satellite, then the direction of propagation of the wave is more like perpendicular to the surface of the earth, so both of the polarizations would be nearly horizontal in that sense (and in the case where the radar is looking directly downward (zero "incidence angle"), both polarizations would be exactly horizontal relative to the surface of the earth).  So what do horizontal and vertical refer to in this context?  Is vertical the direction that's in the plane containing the direction of the satellite's movement and the direction of the wave (and is perpendicular to the direction of the wave), and horizontal the direction that's perpendicular to that plane?
Answer: I think you have the gist of it. From Iain H. Woodhouse's text "Introduction to Microwave Remote Sensing" (a great resource on SAR and RADAR):

For convenience, in remote sensing the horizontal axis, x, is defined to be parallel to the surface of the Earth when we are taking oblique (off-nadir) measurements. The vertical axis, y, is then defined as being perpendicular to this so that the x-y plane is defined at the instrument, not the ground (i.e. it need not be vertical with respect to the Earth's surface). When viewing towards the nadir, the choice is completely arbitrary since there would be no distinction between the horizontal and vertical at the ground surface. In such a case the instrument designers would choose the axes based on the instrument configuration. If the field of view is large enough (or if it is a scanning instrument) so that part of the data is effectively oblique, then the surface in this direction can be taken as the horizontal axis. Otherwise, the horizontal is taken as parallel to the motion of the platform.
Comment: Thanks, I think that makes sense.  Just to be totally clear, I drew a picture: http://oi63.tinypic.com/2qake2f.jpg
The green direction is vertical, and the purple direction (directly out of the page) is horizontal?
Comment: Actually, I think my picture is slightly wrong because I was imagining the radar beam being in the plane of the satellite's movement but actually it's perpendicular.  So I think in my picture, I would change the "satellite's path" arrow to be pointing directly out of the page, but otherwise it accurately represents my current understanding.  I also found this helpful image/description: https://earth.esa.int/handbooks/asar/CNTR5-5.html#eph.asar.gloss.geo:GEOMETRY , and I think the "E" direction in that image represents "horizontal"?


Alternative to xsel or xclip *without* X11 installed?

Question: xclip/xsel need X11.
When I use putty from a Windows box to linux (without X11 installed), is there an alternative to xsel or xclip?
I would like to pipe the complete shell command output to the clipboard which I then paste on the Windows box to an application. I would like not to have to install all the X11 dependencies xsel and xclip need on those linux servers.
Answer: The clipboard itself is a feature of X11, so you will not be able to use it without having any X11 server instance running anywhere. More about that below.
However, xclip/xsel don't have the X11 server as dependency, they only need some client libraries installed. You should install xsel though if you want to have as few packages as possible, as it has significantly less dependencies than xclip (compare the output of apt depends --recurse --important xsel and apt depends --recurse --important xclip).
Back to the X11 server. You said you don't want to install a full graphical X11 server stack on your headless Ubuntu server, which is not necessary. That requires you to have an X11 server running on your local client instead though, if you want to use its features like the clipboard.
On a Linux desktop client this is no problem, as you already have X11 running there usually, but on Windows you don't. Luckily there seems to be a small X11 server version for Windows too, called Xming.
Once you have that running and configured, you should be able to forward your local X11 session via SSH (using PuTTY) to your headless server. There you can then use e.g. xsel to interact with it and access your local clipboard.
More details about how to set up Xming, PuTTY and the SSH server for X11 forwarding can be found in these posts:

How to use PuTTY to get X11 connections over ssh from Windows to Ubuntu
xclip on headless server
How to use X11 forwarding with PuTTY (on Super User)
Comment: `screen` and `tmux` have copy-paste buffers: [Does non-X Linux have a clipboard?](https://unix.stackexchange.com/q/414303/246819)
Comment: I actually only want to mimic the windows/cmd feature provided by clip.exe on any linux server I access with ssh.
c:\> dir | clip
would put the output of dir into the copy buffer and I could use it anywhere to paste. usually I am using ubuntu and terminator, thus xclip/xsel work fine. But whn I am abroad, I access servers via ssh from a Windows box.
Comment: Yeah, well, the difference is that clip.exe locally on Windows or xsel/xclip locally on an Ubuntu desktop are command-line clients that interact with their respective local GUI/input stack which provides the shared clipboard functionality on that system. Each alone works well, but they are not directly compatible with each other. X11 supports quite easy forwarding via ssh, which PuTTY can make use of, so if you have an X11 server and client on one end of the ssh connection each, you can access a remote clipboard. No magic involved. But remotely *and* cross-platform isn't that easy.
Comment: @dessert I did not know that. From how I understand it though, those "buffers" are not really a system-wide or sharable or remotely accessible clipboard-equivalent, but just a local feature of that respective application, so I'm not sure if these would help to transfer data from a pipe on the server to the client clipboard, as described in the question. I'd guess not, unless you could explain that in a separate answer?
Answer: script logs the whole dialogue
The compiled program script is a program in the package bsdutils in the repository 'main' in Ubuntu. It saves the whole dialogue in a text screen, terminal window or remote connection. You can run script in your server.
The default name of the log file is typescript in the directory where you start script, but you can select another name if you start script with a parameter (alias argument)
script my-script.log

Demo example
Start script and run some commands:
sudodus@bionic64 ~/test $ LANG=C script my-script.log
Script started, file is my-script.log
sudodus@bionic64 ~/test $ echo 'Hello World'
Hello World
sudodus@bionic64 ~/test $ pwd
/home/sudodus/test
sudodus@bionic64 ~/test $ ls
my-script.log
sudodus@bionic64 ~/test $ exit
exit
Script done, file is my-script.log

Check the log file:
sudodus@bionic64 ~/test $ cat my-script.log
Script started on 2019-01-21 19:50:22+0100
sudodus@bionic64 ~/test $ echo 'Hello World'
Hello World
sudodus@bionic64 ~/test $ pwd
/home/sudodus/test
sudodus@bionic64 ~/test $ ls
my-script.log
sudodus@bionic64 ~/test $ exit
exit

Script done on 2019-01-21 19:50:52+0100
sudodus@bionic64 ~/test $

Answer: If using a modified PuTTY is an option to you, you might want to look at this patch to PuTTY, which adds custom escape sequences to copy to and paste from Windows clipboard. It also ships a small winclip shell script that can be used to access the Windows clipboard from the target Linux/Unix host.
The patch is for PuTTY 0.53b (over ten years old), there's a rebase to PuTTY 0.60 here but that's still an old version. You might need some work to adapt it to latest PuTTY (0.70 at time of this writing) but it might just apply without any changes since PuTTY codebase has been mostly stable at this point. So perhaps this might be useful to you.
The patch is unlikely to be accepted to official PuTTY, since the escape sequences are custom and not really part of any standards, so unlikely to be officially supported by PuTTY in its official distribution.
Answer: PuTTY on Windows side allows copying on-screen text via set of shortcuts. If the output of command is too large, consider using nc on Ubuntu server and ncat on Windows client ( available from nmap.org ).
On Ubuntu, execute
$ command > output.txt
# port 1234 is just an example, you can use your own port of choice
$ nc -N -l 1234 < output.txt

On Windows , use ncat:
PS C:\Users\Admin> & 'C:\Program Files (x86)\Nmap\ncat.exe' <ip of the server> 1234 --output foo.txt

The output saved on server will be transferred into foo.txt on the client.


Conceptual proof relating linear fractional transformations to matrices

Question: Define a map from $2 \times 2$ invertible matrices to linear fractional transformations $$ f:\left( \begin{array}{ccc}
a & b  \\
c & d \\\end{array} \right) \mapsto \frac{az + b}{cz + d}.$$  It is well known that $f(AB) = f(A) \circ f(B)$.  This is easy to prove:  just simplify both sides of the equation.  But is there a more conceptual proof that does not involve this computation?  Is there a generalization to $3 \times3$ matrices, etc.?
Comment: Yes.  See [here](https://en.wikipedia.org/wiki/Riemann_sphere#As_the_complex_projective_line) for a description of homogeneous coordinates on the Riemann sphere.  The natural generalization is the action of any [projective linear group](https://en.wikipedia.org/wiki/Projective_linear_group) on the corresponding [projective space](https://en.wikipedia.org/wiki/Projective_space).
Comment: Ah, I see.  Thanks for the links!
Answer: The complex general linear group ${\rm GL}_2(\Bbb C)$ acts on $\Bbb C^2$. Since matrices act linearly, there is an induced action on complex projective space (the collection of one-dimensional subspaces).
This space ${\Bbb P}^1(\Bbb C)$ can be defined by putting an equivalence relation on the set of nonzero points $(z,w)$ of $\Bbb C^2$, where $(\lambda z,\lambda w)\sim(z,w)$ for all $\lambda\in\Bbb C^\times$: then the equivalence classes will be the one-dimensional subspaces of $\Bbb C^2$ (not counting the origin, since all subspaces contain $0$). All points can be represented as either a tuple $(z,1)$ with $z\in\Bbb C$ arbitrary or as $(1,0)$. If we think of $(z,w)$ as the ratio $z/w$ on the so-called Riemann sphere $\widehat{\Bbb C}$, the point $(z,1)$ represents $z\in\Bbb C$ while $(1,0)$ represents $\infty$, according to the convention $1/0=\infty$.
In summary, the action of ${\rm GL}_2(\Bbb C)$ on $\Bbb C^2$ induces an action on ${\Bbb P}^1(\Bbb C)$ which can be transported to an action on the Riemann sphere $\widehat{\Bbb C}=\Bbb C\cup\{\infty\}$. Writing out the action explicitly yields these linear fractional transformations, also called Mobius transformations: $[\begin{smallmatrix}a&b\\c&d\end{smallmatrix}]z=\frac{az+b}{cz+d}$.
If a group $G$ acts on a space and $H$ is the subgroup of elements acting as the identity map, then we can descend to an action of $G/H$ on the space. Since the subgroup of multiplication-by-scalars in the general linear group maps each line to itself in ${\Bbb P}^1(\Bbb C)$, after collapsing superfluous redundancy we "really" have an action of ${\rm PSL}_2(\Bbb C)$ on ${\Bbb P}^1(\Bbb C)$.
More generally, an action of ${\rm GL}_n(\Bbb C)$ descends to an action of ${\rm PGL}_n(\Bbb C)$ on ${\Bbb P}^{n-1}(\Bbb C)$.
Comment: Hmm, I don't think I saw this the first time around.  Nice answer - not too late for a +1 and accept!


Hadoop Name Node HA Hive failures

Question: I have two namenodes in HA environment. And Hive configured to point to HA namespace. But intermediatly my Hive fails pointing to passive namenode giving below error even tough my active namenode is still in service. Kindly help me dig where the issues is. Even Zkfc logs dosent show any failover happening when Hive fails.
Couldn't set up IO streams; Host Details : local host is: "my node/10.10.11.6"; destination host is: "passive node":8020;
Answer: To prevent hive server from opening too many connections with namenode, we need to set ipc.client.connection.maxidletime to the default value of 10 seconds. By default, PHD will set this parameter to 1 hour in the core-site.xml which can cause out of memory errors on HiveServer2.
<property>
  <name>ipc.client.connection.maxidletime</name>
  <value>10000</value>
</property>
Refer Below…
https://issues.apache.org/jira/browse/HIVE-6866
https://discuss.pivotal.io/hc/en-us/articles/201646766-How-to-Configure-HiveServer2-and-use-a-Beeline-Client-on-a-Pivotal-HD-Cluster

Hadoop Name Node HA Hive failures


How can I /fill water?

Question: I have a huge amount of area that i need to fill relative to the player's place. I tried typing /fill ~-80 69 ~-80 ~80 69 ~80 water which basically fills a 160x160 hole 1 block deep relative to the player's coordinates, but that didn't work because it said There is no such item id with name minecraft:water
Comment: That works fine for me (and is supposed to so), are you using latest stable version of vanilla minecraft?
Comment: @QbsidianH20 I am using 1.8.2 prerelease 6. I guess they might have taken the feature out?
Comment: Taht's weird, I'm using same version too. Are you on singleplayer/multiplayer/realms?
Comment: @QbsidianH20 single player
Comment: I can't reproduce the problem here, in either latest stable or latest snapshot.  Are you sure you typed the command correctly?
Answer: Try /fill ~-80 69 ~-80 ~80 69 ~80 minecraft:flowing_water.
Answer: I had a similar problem, so I wrote a mod to do it (and other things) for me.
Grab a copy of the Builder's Helper mod from http://www.minecraftforge.net/forum/index.php/topic,26612.0.html .  This needs Forge and minecraft 1.7.10 or 1.8.
This comes with a 'blueprint' called 'water-table'.  Give yourself the builder's wand item, use /wand set water-table, then right-click the wand in front of the hole you want to fill.  It will fill up with water to the level you clicked.  It will not remove any existing blocks from the world.
There is a similar plan to evaporate existing water, plans to build houses, glass dones, and so on, as well as copy existing structures.

How can I /fill water?


upgrading a factory contract

Question: What is the most efficient/optimal way to upgrade a factory contract? Let's say I have a factory contract which can generate 3 different child contracts, how can it be upgraded to be able to generate 5 different child contracts in the future instead of 3?
Answer: You'll have to deploy a new factory, and update every reference from the old factory to the new one. Whether that's doable, depends on your situation.
If you have a main contract which contains a reference (address) of the factory, you'll have to update that address.
Comment: Thanks henk, how can I update every reference? could you give an example of updating a reference

upgrading a factory contract


Specific lay-out for every content-type

Question: Is it possible to change the layout for a content type through CSS? How do I do it?
Answer: Based on the comment of the OP (Niels) I changed my answer:
Each content type page will have a different class (node-type-CONTENTTYPE) associated to the BODY element of your HTML.

So you can add to your CSS file:
body.node-type-mycontenttype1 img { border-color: red; }
body.node-type-mycontenttype2 img { border-color: yellow; }

Original answer:
Wich version of Drupal do you use?
For Drupal 7:
You can use a different template for each node of different content type by creating a template:
/site/all/themes/YOUR THEME/templates/node--CONTENTYPE.tpl.php
You can read on Template Suggestions to know which template you can create.
For the CSS, I suggest you to put everything in your main CSS file and not use a different CSS for each content type.
Comment: Thank you, I only want to change some text-layout and not the whole theme. For example some Borders around images, text-align,...
Comment: I changed my answer.
Answer: Also for different page layout (not only node layout) for different node types you have to add template suggestions to your theme, then you can style in with CSS.
For Drupal 6
add this code  to template.php
<?php
function themeName_preprocess_page(&$vars, $hook) {
  if (isset($vars['node'])) {
   $vars['template_files'][] = 'page-'. str_replace('_', '-', $vars['node']->type);
  }
}
?>

Then make different files for any content type you have and layout them as you wish

page-blog.tpl.php for blog content type
page-news.tpl.php for news content type ... etc.

Similar for Drupal 7
<?php
function themeName_preprocess_page(&$vars, $hook) {
  if (isset($vars['node'])) {
   $vars['theme_hook_suggestions'][] = 'page__'. str_replace('_', '--', $vars['node']->type);
  }
}
?>

Then make different files for any content type you have:

page--blog.tpl.php for blog content type
page--news.tpl.php for news content type ... etc.
Comment: We were writing at the same time.
Based on your comments, ignore my answer.
Just Follow FR6 Instructions
Comment: Thank you for the answers guy. I was trying to fix this but I'm not able to do it and i Don't know what I do wrong.
I'm just a beginner but I want to learn more.
I located this CSS file ((drupalfolder)/modules/system/system.theme.css) and i wrote this in it:

body.packages field-item even p
{
 font-weight:bold;
}

I don't know what i'm doing wrong. Maybe this could help you guys. http://nielsjansen.be/drupal
Comment: Hi! Consider using Context Module. You'll be able to add classes based on node type, taxonomy term, path....Here is great video podcast http://mustardseedmedia.com/podcast/episode38

Specific lay-out for every content-type


bitcoin adresss in my email from 2014

Question: i did a search in my email for "bitcoin" and i came up with a bitcoin address sent from me to me looking like this "bitcoin:1AQhW**************" is that bitcoin money and if so how do i get it ?
Answer: That's just a bitcoin address, it may not have any bitcoins sent to it, and even if it does, you can't spend them unless you find the private key too. Check the balance of that address here https://blockchain.info

bitcoin adresss in my email from 2014


Why are there hexagonal holes in my donut?

Question: I'm currently making a donut using blender gurus tutorial. I have no idea why, but there are holes in my icing. Does anyone know what could be causing it? Thanks for any help.
Comment: There's also this Q&A of the same problem. You can try his solution as well: https://blender.stackexchange.com/questions/151044/why-are-there-holes-in-the-icing
Answer: I ran into the exact same problem when trying to follow the tutorials. It seems like Andrew unhides some vertices in the icing at one point but forgot to show it.
If you press Alt + H before applying the modifiers, it should work.
Comment: Thanks, this solved the problem.
Answer: If you already edited the donut, and then press Alt + H , and you can't go back, you can do this.
Go to Sculpting, press Grab (the yellow circle one) and press Shift while clicking and holding on the holes until it's gone.


calculate EVI for numerous tiles

Question: I am trying to calculate EVI from MODIS data in Arc. I know how to run one raster group of 3 bands but don't know how to tell it to move on to the next group of 3 bands in that directory. Here is the formula EVI = 2.5 * (NIR-Red)/(NIR+6*Red-7.5*Blue+1). So ideally I would like it to run a directory of many tiles with their bands in order from 1-3.
Answer: The following assumes you have ArcGIS 10.2 and the Spatial Analyst extension. If you have the Spatial Analyst extension available to you, I'm pretty sure the ArcPy.sa Raster Object can be used to apply the *EVI = 2.5 * (NIR-Red)/(NIR+6*Red-7.5*Blue+1)* formula across all MODIS rasters in your directory. I'm thinking we need these steps:

Get a list of all of the MODIS raster datasets in the directory (the trickery shown below with the paths here is a poor hack, there is probably a better way)
For each MODIS raster identify NIR, BLUE, and RED bands. Create a Raster Object for each.
Use math expressions on the Raster Objects to get the EVI output raster

The code may look something like:
<code>import arcpy
from arcpy import env
arcpy.CheckOutExtension("Spatial")
from arcpy.sa import *

env.workspace = "The\\Modis\\Rasters\\Directory"

RasterList = arcpy.ListRasters()

counter = 1
for Rasteroo in RasterList:
    RedBand = arcpy.Raster(env.workspace + "\\" + Rasteroo + "\\" + "Band_1") # here,    we can create raster objects from single bands in a raster dataset
    BlueBand = arcpy.Raster(env.workspace + "\\" + Rasteroo + "\\" + "Band_2")
    NIRBand = arcpy.Raster(env.workspace + "\\" + Rasteroo + "\\" + "Band_3")

    EVI_Raster = 2.5 * (NIRBand - RedBand)/(NIRBand + (6 * RedBand) - (7.5 * BlueBand) + 1) # Is this math correct to your EVI formula?

    EVI_Raster.save(env.workspace + "\\" +  "EVI_Raster_" + str(counter))

    counter +=1
</code>
Best Luck with this.
Comment: After I enter:RedBand = arcpy.Raster(env.workspace + "\\" + Rasteroo + "\\" + "Band1")
BlueBand = arcpy.Raster(env.workspace + "\\" + Rasteroo + "\\" + "Band2") I get the following error:   RuntimeError: ERROR 000732: Input Raster: Dataset Z:\E\MRT\MRT_download_Win\Out_2\float\mcd43b4.a2011353.h08v04.005.2012007011256.nadir_reflectance_band1.tif.flt\band1 does not exist or is not supported
In the error I can see it finds the raster but then tries to add a folder extension from the raster name as band1. Instead I want it to pick the raster with the extension of band1.
Answer: Just use model builder.
Step 1 iterate your rasters.

Select the folder or Geodatabase of all your rasters on the left.
Step 2. would be (many options here but I would use map algebra) put your math into the Single Map Algebra Function. Remember to specify the bands.
Then use this for the output name EVI%Name%
This will result in one output file in your output geodatabase or folder named EVIinputname with the EVI result. You can do hundreds overnight.
HINT -- if your inputs are Integer and you want decimals in the output (I think this will be the case, it almost always is) they just add a FLOAT command between the Iterator and the Raster Calculator (I process EVI often...). Otherwise you get zero for everyone.
Comment: What I don't understand with the model builder method is how I distinguish the bands in the raster calculator. When you link the arrow from the raster (or converted float) it only gives you one choice of raster but the EVI equation has all three bands. In the directory all the tiles are labeled with their tile and band number.

calculate EVI for numerous tiles


How common is it for academics to write fiction?

Question: I have submitted a few papers to academic journals. I love writing non-fiction articles and long form "literary" non-fiction. I also would love to write at least one novel. None of my fiction is anything that I would not want a relative to read. None of my fiction is embarrassing. My question is how common is it for academics to write fiction? I use a pen name when I write anything that is not meant for more formal situations like academic journals. Is it common? Is it frowned upon?
Comment: I don't have numbers, but yes, it is common and not frowned upon. Good fiction requires intelligence and imagination. Who better than an academic? Some popular writers were academics in the past and remain in the vicinity of their former employment to enjoy the benefits of living in a community of intellectuals. A pen name is probably a good compromise for a working academic so as not to confuse people about your priorities.  There are a few books (Moo - Jane Smiley) that made people uncomfortable as they recognized themselves in the characters. But brilliant satire of academia.
Comment: What exactly do you think professors in the English (or your local language) department do?
Answer: I am an academic and a professional writer. In my particular field of writing (interactive fiction), a large chunk of writers are academics, so it's definitelt possible.
Most employers are not concerned about outside activities as long as they don't interfere with your responsibilities. However, writing commercially requires a large enough time commitment that it will be very hard to conduct research at the same time. The most prolific and successful academic/writers I've seen either stopped writing or stopped being a research academic. A few are able to find a position where there writing is valued as academic research (such as Nick Montfort).
If research is an expectation for your position, then your best bet would be to take a more teaching-focused job or to work only a small amount of time each day and marketing your writing after you finish it in your own.
Comment: And even geeks and scientists can do it.


Subspace of $\Bbb R^2$ with fundamental group $\Bbb Z \oplus \Bbb Z$?

Question: Does there exist a subspace of $\Bbb R^2$ with fundamental group $\Bbb Z \oplus \Bbb Z$?
Comment: In general a connected subspace of $\mathbb{R}^2$ doesn't need to behave like that. The Hawaiian earring has a very big (and I think nonfree) fundamental group for example: https://en.wikipedia.org/wiki/Hawaiian_earring
Comment: I don't think so. I think that connected subspace of $\mathbb R^2$ should retract on something like $U \backslash D$ where $D$ is a disjoint union of disks and $U$ is open and connected. Thus the fundamental group of subspace should be something like free group on $|D|$ generators. But I have no rigorous proof of what I am saying.
Comment: Yeah intuitively that's what seems....
Answer: No. I prove in this answer that $H_2(X;\Bbb Z)$ surjects onto $H_2(K(\pi_1 X, 1);\Bbb Z)$. (Actually, the coefficients can be whatever you want.) If you want to do this for gross $X$ this is still true but you need to use CW approximation. Further, for $X$ compact, it follows immediately from (Cech) Alexander duality that $H_2(X) =0$. If you further assume that $X$ is locally contractible, you can drop the Cech parenthetical; in this case, the techniques used in the proof can all be found in a first-year course on algebraic topology (even though they require heavier machinery than the fundamental group alone).
Unfortunately without these assumptions this gets more difficult. It is apparently a theorem of Zaslow that the higher homology of any subset of the plane vanishes identically. For $\pi_1 X = \Bbb Z^2$, $K(\Bbb Z^2,1) = T^2$, so we see that the second homology of any space with $\Bbb Z^2$ fundamental group is nontrivial.
In fact, being a subset of the plane places severe restrictions on the fundamental group; see here. In particular, any finitely generated subgroup is free. I consider this much harder than the first paragraph, but that's probably partly because I only know how to prove what's in the first paragraph.
Comment: I would be interested in a proof specific to the case of $\Bbb Z^2$, perhaps that doesn't require much machinery. I'm skeptical it exists, though.


I would like another Mod to consider if my answer should be deleted https://hermeneutics.stackexchange.com/a/74668/33268

Question: I believe that @curiousdannii is bias against me and has been for some time.  I would simply ask that another Mod considers the above link.  I believe I have answered all the factors in the Q in a very comprehensive way.  Covering all points requested by the person who asked the Q.  @curiousdannii doesn't like the answer.
Answer: Thanks for coming to Meta with this rather than continuing too far into the comments section. Just FYI I didn't get your tag on your Answer as I had not previously interacted with the Answer - however Moderators do get a notification for new Meta posts, so this is where it came up for me.
First off, it's worth saying that as I have written an Answer to this Question myself, that in itself is a potential bias and usually a good reason for any Moderator not to critique other Answers too strongly. However, I would agree with the OP and curiousdannii that your answer does not attempt to answer the given Question about 1 Corinthians 12, and so the post notice appears valid.
In my opinion, the criticisms are valid and unrelated to your conclusions (several non-Trinitarian answers have been received positively by the community), but are rather on the basis that your answer follows just about every approach except exegesis - gathering together various verses and arguments and using them to interpret 1 Corinthians, rather than beginning with the text, examining it carefully and letting it interpret itself.
For example, you speak very strongly against any personification of the Holy Spirit, all whilst answering a question about the passage which at face value seems to have the strongest personification of the "Holy Spirit" found in the New Testament.
I probably wouldn't go as far as to delete the answer given how hard you have evidently worked on it, but would strongly suggest that you ought to check the balance of your content, to ensure that the lion's share of your argument arises from exegesis of the text rather than other texts by different authors.
Comment: @anothertheory - essentially, Answers on BH.SE aren't supposed to flow "this is my conclusion -> here are some arguments/passages to justify it", but rather should always begin "this is what the text says -> this is what it means in context -> this is what I conclude based on the textual evidence." This is what we mean by the term "exegesis".
Comment: Many thanks Steve - to answer the Q as Dottard appeared to want (see his initially comments to me, all aspects needed to be covered. ie. HS-as you say it is taken as 1 of the strongest passages - if my A is ***neither***, I have to explain why.  Which takes a lot of explaining, I cant see how you can A all points without such an exercise of the Text.  My second point every Q I have ever looked at has always has much weaker A yet they do not get deleted.  its only being deleted because its me - Albeit I know that my answers are controversial & not liked or agreed.
Comment: Having said the above - I am sorry for taking up your precious time, which is appreciate and accept your judgment as Honest and when I get some time next week I will Edit.
Comment: Don't worry, post notices are never intended as threats - it's more to serve as user guidance that content needs work. People are trying to help you write better content, by flagging where content is in need of improvement.
Comment: Many thanks, appreciated
Answer: Comments relating to the question show that the opinion of the Moderator is not 'bias' but is shared by other users :

I did not ask for a rebuttal of the trinity. I asked about what this passage meant. So this does not answer the question. [User 1 - the OP]

Putting together a kaleidoscope of verses to support your conclusion does not answer the question. [User 2]

The crux of the question was not an invitation to write a refutation of a particular doctrine. The heart of the question was quite specific :

If, for the sake of this question we accept that this triplet is NOT discussing the Trinity (as some have asserted), is it effectively saying that the Holy Spirit is "Lord" and "God"?

And I would also agree that the answer under discussion was not a valid answer to the question which had been asked, since the opening argument of the answer stated :

A cogent case cannot be made to support the trinity or Holy Spirit as "Spirit", "Lord" and "God" . . . .

. . .   which then confused the answer as only one of those things (and not the other) had been the purpose of the question.
The answer appears to be down-voted but is still (at the time of my writing) open for editing.
Comment: I have read your edited answer and I find that it confuses the question and the doctrine you are trying to refute. It is, at best, unclear (at least to myself). Granted the question is a kind of double negative which requires thinking about. But anyone taking on the task should realise the complexity of the question and needs to be in empathy with its purpose. (In my view.) The answer is still (at this moment) open for further editing, I would note.
Comment: sorry - the comments you used where before my last 'edit'                                                      I did not ask for a rebuttal of the trinity. I asked about what this passage meant. So this does not answer the question. If it does not represent the ***trinity then would you agree that the triplet represent three names for the Holy Spirit as "Spirit", "Lord" and "God"/ If not what does it mean? Or is it "an odd passage that should be excised*** from the NT? –
Dottard  - I answered that it means ***neither*** and explained why.
Comment: - that does answer the question - and its ***odd*** and why - to come to my conclusion i provided a comprehensive answre to explain Lord/spirit/HS/God - Dottard did not come back after my last Edit to say I had not answered.
Comment: due to the complexity - a number of aspects had to be covered - I have broken it down as heading - the readers i believe do understand & ***it does answer the Q*** - What you are saying is that it is ***far from perfect*** is that the staring point?  Also there are vast number of answers in all the questions that are more lacking than this but don't get deleted.   I have had no issues with anyone else but @curiousdannii continuously targets me. Nothing would have been said is someone else.  Dottard seems to believe it has been answered albeit he would not agree with the answer.
Comment: Maybe you have hit the nail on the head. Due to the length and complexity of your answer - the question was quite brief - it is (perhaps) difficult to follow. I have noticed that the questions and answers which attract most attention, on Stack Exchange generally and on both SE-C and SE-BH particularly, are brief, succint and non-controversial (I mean by that that they do not attempt to resolve a division, something which is highly unlikely on a website of this nature).
Comment: The Q was brief but a lot of points, as you will see from Dottards initial comments as to he felt needed to be covered.  The point being the Q has been answered.  I note the very high quality / knowledgeable audience who would appreciate a comprehensive answer (albeit may not agree).  Again if that was someone else, no one would have threatened to delete it.   All I want is a honest judgment - should it be deleted compared to what is not deleted on other Q?
Comment: I think I have done all I can here and I shall leave the matter to others to comment upon.
Comment: Appreciated - I just want another Mod to make a decision - if honestly believes compared to what is left alone -  the my A needs edit / delete so be it - I'm arguing principal - (I can put everything I have in a different way or on another Q that's not the point)
Comment: I'd like give some feedback to moderators who delete answers for not properly addressing the question. It seems to me the site would be better served by moderators downvoting and commenting on such answers, with suggestions for improvement... rather than deleting them. A deletion hits hard especially if the post involved serious effort. IMO deletions should be reserved for answers of very poor quality or which violate decorum rather than not hitting the mark intended by the OP. An answer such as that given by @anothertheory should be left to readers to judge, not expunged.
Answer: I believe the answer in its current form is stronger than the original answer; I also believe further editing could make it stronger still.

If I were asked to vote on deleting the answer, I would vote "no, do not delete". The answer passed the "low quality posts" check from 2 experienced editors, and the community has given it a net +12 reputation points (2 upvotes, 4 downvotes)
If I were the question-asker, I would not select this answer (but of course I'm clearly biased because I wrote an answer to this question too)

--
Editing
It appears to me that this post does offer an answer to the question, but that ~75% of the post is not a direct answer to the question--rather, the bulk of the post is what most writers would include in a footnote. Such "footnote" material is relevant in that it makes the case for the validity of the exegetical landscape in which the answer resides.
After being advised that I tend to write answers that are too long (and sometimes I still do =) ), I took to adding an appendix to posts where background information (supporting my answer but not really answering the question) could be provided. This sometimes produces a short answer and a long appendix building the worldview for the answer. This wasn't my idea--I copied if from Dottard--who graciously hasn't come after me for use of his intellectual property =).
My 2 cents on the answer - a lot of the content is relevant "footnote" material but is not, strictly speaking, an answer to the original question.
--
Bias
Of course this site has a pro-Trinitarian bias, most of the regular contributors on the site hold Trinitarian views.
The site also has a pro-Biblical inerrancy bias, because most of the regular contributors adhere to Biblical inerrancy. The site has a bias in favor of traditional authorship attribution (for the same reason), and somewhat less-pronounced but still present biases in favor of Markan Primacy and in opposition to Catholicism.
There are probably other biases of which I am unaware--and it's a lot harder to recognize the bias when I'm in the majority and those biases exist in a personal blind-spot  (I am in the majority on some views and in the minority on others, and I've caught myself in the past using votes to overwhelm a minority view--I have since tried, imperfectly, not to do that).
So what do we, as biased humans, do about it? I don't claim to have a silver bullet here, but at the very least, if I know I have a blind-spot, it's probably wise to do the same thing I do in a car--pause for a moment to look at my blind-spot before cutting somebody off.
--
This answer is useful
We probably all forget from time-to-time (I know I have), that a +1 to an answer on the main site does not mean "I agree with you" and a downvote does not mean "this is heresy". We're voting on whether a post is useful.
I really, really, really doubt at Judgement Day God is going to ask any of us if we upvoted a post on SE that included something that turned out to be false, heretical, or painted an incomplete picture. But He might ask us how we handled this verse:

Inasmuch as ye have done it unto one of the least of these my
brethren, ye have done it unto me. (Matt. 25:40b)

Appendix
Some will take exception to my claim that the site has a pro-Trinitarian bias (or a bias on some other topic). I'll offer 2 data-points to corroborate my claim:

I have, to date, written 264 answers on this site. My answer to the question we're discussing here is the first time  I have written a post on this site explicitly disagreeing with the Nicene Creed and received a net score of +4 or more. I honestly expected my post to get down-voted to Hades, and was pleasantly surprised. Kudos to site members who were willing to vote for an argument they disagreed with
There is a user (you know who you are, but I have no interest in publicly shaming anyone) who anonymously downvotes nearly every post I make within a certain specific tag. I respectfully suggest that this approach entirely misses the point of this site.
Comment: @HoldToTheRod - thank you very much for the above very decent of you to have taken your valuable time to write that, much appreciated.  specially when I have very controversial views.  I note the tip 'footnotes' which make sense.  Kind regards
Comment: Okay, I didn't look closely at the post you linked to.
Comment: "Kudos to site members who were willing to vote for an argument they disagreed with" It's a good sign, but you shouldn't necessarily assume the upvotes came from people who disagree with you. There are lots of active non-trinitarians on this site.
Comment: @curiousdannii since none of the other active non-trinitarians on the site agree with me (with respect to the Godhead generally, and probably with respect to the description I gave in the post specifically), I'm reasonably confident the votes came from people who disagree with me
Comment: And, of course, one of the people who upvoted my post specifically identified himself in the comments
Answer: Other moderator here...
I would choose whether to delete based on what you want other users to see.
I agree with the comments from the OP and other moderators, that you don't address the question, which is about how to understand the passage. You make a theological case concerning the Trinity. While the Question uses the word "Trinity", that does not mean that a proof text concerning Trinitarian beliefs is fitting. An answer should have some kind of explanation of that Bible passage specifically.
Your well-worked answer would be more fitting to answer Questions for and against the doctrine of the Trinity on Christianity.SE. Perhaps your answer here answers a Question already asked on Christianity.SE, in which case you might delete the answer on BH.SE and post it where it is fitting on C.SE. But, I would remind you to be cautious: you thought you were answering a Question here when your answer didn't address the Question; don't make that same mistake on Christianity.SE.
The central issue is to know what a Question is asking and whether an Answer addresses that. All the best!
Comment: Not perfect A - but see worse on many Q not deleted.  A was amended after Dottard comm specifically to address the com feb 23 20:20, which clarifies the Q.  The Q really is, does it confirm - i) HS = spirit/Lord/God - if not ii) only possibility Trinity if not iii) is this an odd passage.  If the answer is NO to i & ii - you need to explain why.  If my answer is NO - its an odd passage, that is not understandable and why - difficulty to explain what it means.   Really what is being said is i have to agree to i) or ii) otherwise I cannot answer the Q.  My A explains why its neither
Comment: It's not about one's theology, but about explaining and using Bible study methods to examine the Bible verses.
Comment: yes to many Q - but this Q was asked in such a way that it needed certain aspect covered.    specially when my conclusion is that it is a 'odd' passage - Ans needs to explain the conclusion otherwise not complete.  In any event I will amend when I get some time - as it will take a bit of time
Comment: Theology is allowed, but it's not the main content and Bible study how to understand the Bible passage is required. That should serve as a good compass. All the best!


Mean Sunrise Time

Question:
How did the author arrive to these numbers? How did he take the $\tan(\log(14 \deg 26 \text{ minutes}))$? I tried many times but I am not reaching to his numbers.
Comment: how did he arrive to 18deg 51 minutes
Comment: Please do use links to link the sources you have questions about. Preferentially don't use screenshots to talk about texts and equations, copy&paste or type them. MathJax displays them better than the source you screenshoted. Images do not work with screen readers. Also that's an example, so this is likely explained above?
Comment: The question is about math and interpreting equations from an (old?) book. Perhaps Math S.E. would be better. For example, is it really the tangent of a log? Is that log base 10? How can the sine of any number be 9.509? The math makes no sense.
Comment: @planetmaker, due to the obvious non-standard notation, I think a screenshot is the best way to show this.  Any attempt to use standard math notation would certainly miss important notation.
Comment: Those are common base 10 logarithms. You do the trig function, then take the logarithm, eg $\log(\tan(14°26'))$. Also, he's adding $10$ to the log if the result is negative. But why do you want to use logarithms for these calculations? That method was standard many years ago, before electronic calculators. Are you just trying to check his calculations?
Comment: Thanks......The book is from 1920 and it is explaing planetary hour table
Comment: But how would you do it in the modern method you are referring to?
Answer: The author is doing the following: $\log_{10} \tan(14^o 26') = -0.58943$ and then adding 10 to get to 9.41057. I didn't know about that practice, but it's akin to shifting the decimal point. Anyway, it is compensated for by the 'inverse sine log' ('sine ,,' two lines below).
Next line, $\log_{10} \tan(51^o 28') = 0.09888$ so that fits. (The operations are just in a different order than listed; first the tangent, then the logarithm.)
From the subsequent line, 9.50945, you're expected to take that value minus 10 (-0.49067), then the inverse of the base-10 logarithm ($10^x$), so 0.32309, then the arcsine, which gives 18°51'.
The entire calculation seems to be a variation of the sunrise equation reproduced below; the logarithms change multiplication into addition, and the sine and cosine are just a shift/flip (which happens in the next lines).
$$\cos \omega _{\circ }=-\tan \phi \times \tan \delta$$
A proof that they're equivalent is left as an exercise for the reader.
If it seems weird to you, don't worry. I feel exactly the same. Please keep in mind that people used lookup tables rather than calculators for that kind of calculations at that time, so it shouldn't be such a surprise back then as it is now ...
Comment: @GregMiller see the 3rd paragraph?
Comment: From the OP: how did he arrive to 18deg 51 minutes?
Comment: Those of us who went to high school before the era of cheap calculators (~1975) spent a significant amount of time doing calculations using log tables and slide rules.

Mean Sunrise Time


Relation between voltage drop across incremental resistance and VD of diode

Question: In small signal analysis of diode (silicon) we take voltage drop across diode (VD ) is 0.7 volt. using other data we calculate current through diode " I " and then incremental resistance \$r_d = \frac{nV_t}{I}\$ . As it is a resistance there must be a voltage drop across it which is \$nV_t\$ (constant for a certain temperature).
What is the significance of this voltage drop ?
Does it add up with 0.7 voltage drop ?
Is there any other noticeable effect of this voltage drop ?
Answer:
In small signal analysis of diode (silicon) we take voltage drop
  across diode (VD ) is 0.7 volt.

That's not quite correct.  In small signal analysis, one linearizes about the operating point so, in fact, no assumption is made about the DC operating voltage - one should in fact solve for the operating point.

What is the significance of this voltage drop ? Does it add up with
  0.7 voltage drop ?

No, to see the significance, let's review small-signal analysis.  First write the total diode voltage as the sum of a constant and a time varying component:
$$v_D = V_D + v_d $$
where \$v_D\$ is the total voltage,\$V_D\$ is the DC (time average) voltage, and \$v_d\$ is the AC voltage.
Next we assume that the total voltage is at all times not very different from the time average which allows us to do small signal analysis in the first place.
The following is the justification for this approach.
The ideal diode equation is (assuming significant forward diode current)
$$i_D = I_S e^{\frac{v_D}{nV_T}}$$
Setting \$v_D = V_D + v_d\$ in the above yields
$$ i_D= I_S e^{\frac{V_D + v_d}{nV_T}} = I_S e^{\frac{V_D}{nV_T}}e^{\frac{v_d}{nV_T}} = I_De^{\frac{v_d}{nV_T}}$$
where \$I_D\$ is the DC diode current.
Expanding the exponential in a Taylor series yields
$$i_D = I_D (1 + \frac{v_d}{nV_T} + \frac{1}{2}(\frac{v_d}{nV_T})^2 + ... )$$
Now, here's the crucial move.  If we assume \$v_d\$ is small enough, we can ignore the 2nd order and higher terms in the expansion yielding
$$i_D \approx  I_D (1 + \frac{v_d}{nV_T}) = I_D + \frac{I_D}{nV_T}v_d = I_D + \frac{v_d}{r_d} = I_D + i_d$$
where
$$r_d = \frac{nV_T}{I_D}$$
Thus, assuming \$v_d\$ is small enough, this linear model gives good agreement and allows us to find the total diode current by superposition of the DC current and the small-signal current.

As it is a resistance there must be a voltage drop across it which is
  nVt

It isn't a resistance.  As shown above, \$r_d\$ is the ratio of the small-signal voltage \$v_d\$ to the small signal current \$i_d\$ which means
\$r_d\$ is the inverse slope of the diode IV curve at the operating point; it is the dynamic resistance at the operating point.
Answer: The problem is that you are mixing two models.
The first one is known as the ideal diode in series with voltage source, and that's your \$V_\gamma=0.7V\$. Remember that \$V_\gamma\$ has no physical meaning, it is just chosen so that the average diode characteristics looks a bit like the ideal one.
The second one is the Shockley model, that is more precise and allow you to compute things like the small signal resistance \$r_d\$.
Is there a mid point? Actually, yes, it's called piecewise linear model. What you basically do is fit the exponential with two or three segments to simplify calculations and avoid the huge errors you might encounter with the first model.
Comment: Well, let's say that using \$V_\gamma\$ is just convenient. You can either solve the circuit using the Shockley model or say "ok let's assume this voltage drop", that is a *lot* easier. The trick is that \$V_\gamma\$ is correct enough in most of the cases, for most of the diodes, so you are speeding up your calculations without affecting precision. \$V_\gamma\$ belongs to all the diode models in some ways, it's just an agreement.
Comment: But in my book many circuit is analysed by using Vγ=0.7V to find the current I and then use this I to find rd.Is't it using two model for one circuit?
Answer: The voltage-plus-ideal-diode model is a large-signal model. It's perfectly valid to use the large signal model to find the operating point, then use the small signal model. For example, if you were asked to find the AC voltage here:

simulate this circuit – Schematic created using CircuitLab
The DC current through D1 is about 4.3V/10K or 430uA. Say n = 1.836 for the 1N4148
So, \$r_d\$ = 111 ohms. The output voltage (assuming the capacitors do not affect the AC voltage) is going to be \$V_{OUT} = \frac {r_d \cdot 100mV}{(r_d + 10K)}\$ (ignoring R1) or approximately \$V_{OUT} = \frac {r_d \cdot 100mV}{10K}\$
We'd expect output voltage of 1.11mV, and indeed when we simulate it in PSPICE, the result is 1.06mV, with an average diode current of about 443uA, accounting for the slightly lower than expected output voltage.


Is (the) article necessary in "All the light we cannot see"?

Question: There is a book called "All the Light We Cannot See".
Would be possible to remove the article in this sentence?
Is "All light we cannot see" still grammatically correct? If so, would it change the meaning of the sentence in some way?
Comment: This is not a sentence.  A sentence is something that has at least a subject and a main verb.  This looks like just a title or a phrase.
Answer: I feel that removing the article makes the title make less sense.  In "all the light", the definite article the means some specific light - in this case, the specific light that we cannot see.
If it were "All light we cannot see" it could be referring to light as a general phenomenon, but it also sounds like it's saying that we cannot see any light, which is a very different meaning!
Answer: Removing the article makes no significant change in the meaning. Including the article may be considered more ornate or poetic.
One may also add "of"; "all of the light we cannot see" without changing the meaning.
Answer: It would be correct and understood in context, but it is less elegant and precise. There is a subtle shift in meaning, but it also has poorer prosody, which is an important consideration for a title.
In its published form, the phrase is composed of an alternating pattern of stressed and unstressed syllables.
This is probably best analysed as four iambs with a dropped initial unstressed syllable, given the terminating quality of the final syllable): "... ALL the LIGHT we CAN-not SEE". If the last word had onstead been "picture", it would probably be analysed as trochees, (think "Hiawatha" or The Kalevala), the contrast of which I think puts us firmly in iambic territory.
Dropping the article creates an awkward pattern of stress which may be acceptable in prose but best avoided in poetry, lyrics, titles, etc. Starting an entire work on an otherwise-unaccounted-for spondee is generally to start on the wrong foot.
In this case, that spondee would be particularly disastrous, as it would lead to a tendency to read "all" as unstressed, and so guide us into the error of analysing the phrase's meaning as "All light, we cannot see", perhaps suggesting weightlessness causes blindness.
In terms of the semantic shift (which I assert is less important in this context) the addition of the article would invoke an implicit contrast with the other kind of light, the light which we can see. Without the article, there is no implicit contrast.
In the context of the book, the light being referred to is the invisible parts of the electromagnetic spectrum (radio waves, radar, and so on). This is not what first comes to mind when we use the word "light" so it's essential to have the article. Imagine if someone had written "But what about ..." or "Consider..." before "all the light ...". This is the meaning which seems to have been intended.


Can customer community license user be added in Account Teams

Question: I cannot locate my customer community user in the account team, hence unable to assign the user to the team. Can we not add community users to Account team? Is there any work around?
Answer: You cannot add Customer Community Users in Account Teams. You can only add Internal Users or Partner Community Users to Account Teams. While this is not clearly documented anywhere, a good way to verify this is by attempting to add one in the Account Team.
In LEX, if you try searching for a Customer Community User while adding Users in Account Team, you won't get the User returned in the search result. If you switch to Classic, and try to add a User in the Account Team, you will see the option of only Internal and Partner User (sample screenshot below).
Answer: You can add Customer Community Plus Users license users in Account Teams with Apex code. You are not able to add it from UI.
Adding users from the Apex code will automatically create a record in the AccountShare table.
<code>AccountTeamMember accountM = new AccountTeamMember();
accountM.AccountId = <AccountId>;
accountM.UserId = <UserId>;
accountM.TeamMemberRole = 'Sales Manager';
accountM.CaseAccessLevel = 'Edit';
accountM.ContactAccessLevel = 'Edit';
accountM.OpportunityAccessLevel = 'Edit';

try {
    insert accountM;
    System.debug('successful added');
} catch (DmlException e) {
    // Handle potential errors, such as sharing rule conflicts or duplicate team members
    System.debug('Error adding Account Team Member: ' + e.getMessage());
}
</code>
I have tried this in my developer environment, and it works fine.
You can not add Customer Community Users license users from Apex. You will get this error if you try to add:
Error: 20:11:06:025 USER_DEBUG [14]|DEBUG|: Insert failed. First exception on row 0; first error: OP_WITH_INVALID_USER_TYPE_EXCEPTION, Operation not valid for this user type: []


How can I set environment variables when I ssh login to my Unix box by passing custom arguments?

Question: I want to pass some parameters as part of my ssh connection that I can use to set custom variables for my login to do certain things or run certain scripts. How do you do this running Putty on Windows machine, connecting via SSH to a CentOS machine?
Answer: On the CentOS machine, create a file in your home directory named .bashrc and set your environmental variables in there.  For example, the contents of the file can be:
export VARIABLE=foo

Here's some discussion of this: http://tldp.org/LDP/Bash-Beginners-Guide/html/sect_03_01.html

You can also use the SendEnv and AcceptEnv options.  This will allow environmental variables on the client to be passed to the server.
You will also need to change the server's sshd_config file to specify which environmental variables are accepted by the server.  I'm not sure what you'll need to do with PuTTY to issue the SendEnv option, but that should get you started.
Comment: Yeah I know how to do that, but how can I pass variables over as part of my connection?
Comment: Edited to include the SendEnv and AcceptEnv suggestion.
Answer: You can enter environment variables in the PuTTY configuration under Connection -> Data.

But this works only under certain conditions. Quote from the
documentation:

The Telnet protocol provides a means for the client to pass environment variables to the server. [...]
Version 2 of the SSH protocol also provides a similar mechanism, which is easier to implement without security flaws. Newer SSH-2 servers are more likely to support it than older ones.
This configuration data is not used in the SSH-1, rlogin or raw protocols.

Additionally, this has to be allowed on the server side. For the OpenSSH server the configuration directive is named AcceptEnv. On an Ubuntu server it looks like this by default:
AcceptEnv LANG LC_*

This allows you to define the variable LANG and all variables starting with LC_ in PuTTY, so you can always get the output in your preferred locale.
If you want to set additional variables you have to add them to the list on all servers you want to connect to. On older (SSH1 only) hosts it won't work at all.
Comment: AcceptEnv is located by default in: `/etc/ssh/sshd_config`

Don't forget to restart the ssh service (`service ssh restart`) to apply the changes afterwards.
Answer: For those, that cannot modify sshd config for various reasons and/or have +2000 servers (and no access to mass-configuration tools or can't/don't want to change settings for other users), here's a solution I came up with:

In PuTTY load the desired session, go to Connection > SSH. In the "Data to send to the server" section, in "Remote command" field use:
env [OPTION]... [-] [NAME=VALUE]... [COMMAND [ARG]...] bash

Example:
env -u PS1 PS1="[\u@\h]\\$ " bash

I unset the variable first, because it didn't work otherwise.
Comment: You can add variables via the Data tab as @Gerald Schneider shows in his answer.
Comment: Not in my scenario. I've tried all obvious options in PuTTY first, before coming up with this hack. Please read carefully first 7 words of my answer. Gerald's answer also mentions this: **this has to be allowed on the server side**.
Comment: @yahol Your solution somehow deprived me from having a terminal, `vim` now says : `Vim: Warning: Output is not to a terminal`
Comment: @SebMa what's the string you're using in "Remote command" in putty?
Comment: @yahol My command was `env debug=1 bash` and `tty` shows nothing
Comment: this works, @SebMa try `sh` or `/bin/bash` instead of `bash`. Or whatever your shell is there.
Answer: You could can modify PermitUserEnvironment in sshd.conf to allow processing of ~/.ssh/environment or "environment=" options on keys in ~/.ssh/authorized_keys.
The format of these two files differs. ~/.ssh/environment is lines of VARIABLBE=VALUE where in ~/.ssh/authorized_keys the environment option is environment="VARAIBLE=VALUE"
Comment: Ok I found where to change PermitUserEnv but how do I pass params?


How to insert cell text from one cell into an ImportRange Function

Question:
Hello! so I have an issue where I am trying to do is have multiple functions in C, D, and E where a link is required. Instead of copying and pasting the link inside all the functions in specific locations several times, I am hoping to have to only insert it once in Column B, and then having that link insert itself into specific locations per that row. Is there any way to do that, an app or function that I can use to make this faster?
Answer: <code>=IMPORTRANGE(INDIRECT("A4"), "Sheet1!A1:B2")</code>


How to fully disable auto-fill-mode in Aquamacs 3.3?

Question: After upgrading Aquamacs to version 3.3, many modes turned on auto-fill-mode. I've followed the answers from questions such as "How can I disable auto-fill mode in emacs?" to disable it, but without complete success. Specifically, I:

set line-wrapping option to "Wrap" (Options→Line Wrapping→Wrap)
turned off "Auto-Detect Line Wrap in Text Files"
set line-wrapping options as default (Options→Line Wrapping→Adopt as Default)
saved options
added lines to .emacs to disable mode globally:
(auto-fill-mode -1)
(remove-hook 'text-mode-hook 'auto-detect-wrap)

added (auto-fill-mode nil) to hooks for specific modes (e.g. html-mode, nxhtml-mode, xhtml-mode).
set text mode hook in customizations.el to disable auto-fill-mode:
'(text-mode-hook
  '((lambda nil (auto-fill-mode nil))
    smart-spacing-mode))

Despite these changes, auto-fill-mode is enabled for some newly opened files (e.g. txt, html, svg) in Aquamacs (the system emacs also enables auto-fill-mode when entering html-mode, but not text-mode). I've grepped for auto-fill in the load path directories that exist but haven't found anything that appears to be enabling it:

~/Library/Application Support/Aquamacs Emacs/
~/Library/Application Support/Emacs/
~/Library/Preferences/Aquamacs/
/Applications/Aquamacs.app/Contents/Resources/lisp
/Library/Application Support/Aquamacs Emacs
/usr/share/emacs/site-lisp

Where else might auto-fill-mode be enabled? How can I fully disable auto-fill-mode?
Answer: Add this to  ~/Library/Preferences/Aquamacs Emacs/Preferences.el:
(remove-hook 'text-mode-hook 'auto-detect-wrap)

Comment: Did you read the question?


RP sd card WLAN

Question: I have a Raspberry Pi 3 with Jessie and I forgot to bring a keyboard and mouse. I am at a new location and I need to connect my Pi to the WiFi here. I do not have an Ethernet cable.
I can access the SD card from a Windows computer.
Any ideas?
Answer:
First, you need to add a file called ssh (with no file extension) to the /boot/ directory on your SD card so that it will enable the SSH access. The content of the file doesn't matter.
Create a file name onetimewifi.txt and save it to SD card /boot/ directory, the content of onetimewifi.txt looks like this:
ctrl_interface=DIR=/var/run/wpa_supplicant GROUP=netdev
update_config=1

network={
    ssid="wifi_ssid"
    psk="wifi_password"

Boot your Raspberry Pi, and find out your raspberry pi IP address from your router (raspberry pi MAC address always started as b8:28:xx:xx:xx:xx. If you don't have access to router, try run linux command on your terminal arp -a.
Login to your raspberry pi using ssh command from putty (terminal application) ssh firstname.lastname@example.com (replace 192.168.0.100 with your own raspberry pi IP address you found out in step 3).
Once login, run sudo mv /boot/onetimewifi.txt /etc/wpa_supplicant/wpa_supplicant/wpa_supplicant.conf.
Answer: This is similar to hcheung's response above, but a little simpler.
As of about a year ago, Raspbian will automatically move any wpa_supplicant.conf file it finds in the boot partition (which contains the files that the CPU reads on boot up) to the correct folder for everything to work.
So connect the SD card to your computer and create a file called wpa_supplicant.conf in the drive it shows up as.
Note that if you do this from Notepad, when you save it you'll want to find the drop-down menu that says Text files (*.txt) and select the option All files (*.*) instead, otherwise it won't work correctly.
Put this in that file:
ctrl_interface=DIR=/var/run/wpa_supplicant GROUP=netdev
update_config=1

network={
    ssid="<your wifi network name>"
    psk="<your wifi network password>"
}

It should connect when you plug it in. If not, try rebooting (if you have no way to access a command line, you should be able to just pull the plug to shut it down, though avoid that if possible). If it still doesn't work, hcheung's solution is your best bet.

RP sd card WLAN


finding ADSP-BF518 JTAG connection on the board

Question: I have a PCB board with ADSP-BF518, I want to use its jtag pins. (It is not an evaluation board) there are some VIAs on the board that comes from its jtag pins. but by using Continuity Test I couldn't find any header that was connected to these VIAs. Is there any special points here that make me couldn't find headers of VIAs? or Is it possible these VIAs don't connect to any header?
Comment: A photo of the board might elicit (better) answers.
Comment: sorry I can not send an image from the whole of the board. just can take a photo of its vias. if it can help you. there is no buffer near them also.
Answer:
sorry I can not send an image from the whole of the board

As you "can not" do that (not allowed?) then you will have to do more investigation on your own.

there are some VIAs on the board that comes from its jtag pins

I have not used Blackfin MCUs. Assuming that these JTAG pins are dedicated to that function, and are not multi-purpose and switched to other functionality (e.g. GPIO) then having PCB tracks (with Vias) to those JTAG pins, means those tracks lead somewhere. You will need to reverse-engineer the board and discover where those tracks go.

Is there any special points here that make me couldn't find headers of VIAs? or Is it possible these VIAs don't connect to any header?

Yes, it is possible that the JTAG signals don't go to a header.
Assuming that the JTAG signals are used only for programming during manufacturing (and that might be an incorrect assumption) then the connections to those JTAG signals don't need to be made via a header. In fact it can be easier (quicker) for programming, if they don't use a header.
Instead the JTAG connections could be made using automated "bed of nails" or "flying probes" or other techniques. This could explain why you can't find a JTAG header - there doesn't have to be one! Instead there could be test points for the JTAG signals spread around the PCB, for example, for temporary connections during manufacturing.
As an example, I had to reverse-engineer a board recently to do exactly this - breakout the JTAG signals to a standard header, using Vias as the connection points for the signals, since there was no JTAG header provided on the board for the main MCU which I wanted to re-program.
A sensible "next step" for you, would be to follow the JTAG signals on the PCB, without expecting there to be a header where all the JTAG signals are connected.
Comment: Thanks for your great guidance @SamGibson.
it's better to say I'm not allowed.
JTAG pins of ADSPBF518 are not multi-purpose just there is a notation in its data sheet about Instruction Register that can select to be in test mode or "bypass".
I will search for "flying probs" thanks for this keyword.
about follow the JTAG signals, I have done Continuity Test on all signals, headers, VIAs on the board, but could not find any connectivity between them and JTAG VIAs.
Comment: finally, I found that these Vias don't connect to any header and maybe they were used for programming during manufacturing


Can I programmatically output the same map with different shp files?

Question: I have 39 different .shp files of the same locations but different data values and I need to output a map for each of them.  Is there a way to build a map template and then run a process that will loop through each .shp file and output a map, either .pdf or .png, of the map template with the individual .shp files?
Answer: you can achieve this with the atlas function of QGIS. Let's say you have different themes with names 1..n. Then you have to make an additional pointtheme to control the atlas, e.g. called 'control'. Just put one point for each theme on the same coordinates into the control layer (copy and paste the same point from 1..n). Then put all the names of your 39 themes into the control layer into an attribute column.

Then make an ATLAS with your maplayout and set the controllayer to your layer 'control'

At least use the data defined override to control the visiblity of the layers through our control layer. Just put the column name (in this example it is called ID, together with the atlasfeature into the expression builder:
Comment: I have not dealt with themes at all up to this point.  It seems to me that I still have the tedious task of creating a theme for each individual file and then copying that file into a control theme.  From there, it does appear that the mapping will be much easier but it still requires me to deal with each file individually to get set up for the atlas map production.  Is that correct?
Comment: yes this is correct more or less, you have to deal with the themes names, but this process can be automated with a python script: collecting all theme names and putting one record for each into a point control theme.
Comment: can you give me an example of what a point control theme file looks like so that I can generate it?
Comment: Hi, you can download a a project from my dropbox account: https://www.dropbox.com/s/g21hamaibdcziwq/control.zip?dl=0 there is also a layout included, where you can see the expression. The only thing is, how to include more themes in the expression. The help is a bit unclear in that... may be someone can help with that issue....best regards Stefan
Answer: Update: I figured out a good way to do this using the Basemap package in Python. I wrote up a tutorial that walks through how to plot several .shp files on different maps all with the same extent. It is posted at https://mapping-with-python.herokuapp.com/index.html
The essential components are to open a map object
map = Basemap2(llcrnrlon= LongLeft,llcrnrlat= LatBottom,urcrnrlon=LongRight,urcrnrlat=LatTop, projection='tmerc', lat_0 = midLat, lon_0 = midLong, epsg=3857)
and then to read in the .shp file you want to map
map.readshapefile(file[:-4], 'Param')


何より meaning in a sentence

Question: From jisho, it seems like 何より means best, more important than anything, above all else, etc. The meaning doesn't change much from that. I have heard ご無事で何よりです. If I use the meaning in jisho, it will sounds like "most importantly, you are save/ healthy". From the conversation though, this translation doesn't seem too cohesive so to say. In other words, it doesn't fit very well. I judge from my own guts that the more accurate translation of that phrase is really "it is good to hear that you are save (more then anything)". I realised that there it still means "more than anything" but there is also an added nuance that is (probably) more important and that is "it is good to hear". Am I right on this or is what I am saying utter gibberish that is meant for the garbage
Answer: As you have correctly suspected, this type of 何よりだ is a common and polite set phrase used simply like "(I'm) very glad to hear/see (that)". You have to remember this usage as a fixed pattern. It can still mean "more important than anything", depending on the context. Compare the following two sentences:

子供には親の健康が何よりです。
For children, the health of the parents is more important than anything.
お母様は健康なようで、何よりです。
I'm glad to hear your mother is healthy.

Other examples:

それは何より。
Glad to hear that.
理解していただければ何よりです。
I would greatly appreciate if you understand this.
Comment: Thanks. Makes sense. So what's the difference really in saying 聞いてよかった and 何よりです
Answer: 何より = Above all else, or sure most importantly
より means more than, though it crops up in places where the translation to English seems odd to our ears.
This in one good example of where simply knowing the language from a text may not assist. Why? Because if you really want to speak a language (in this case Japanese) then you must approach the concepts that you are trying to convey in the manner that the native speakers would.
So try to listen and use the phrases you hear others using, making sure you correctly understand their meaning. 何より、諦めずに、勉強を頑張ってください!

何より meaning in a sentence


Differences Between the Central Limit Theorem and Consistency

Question: I have recently finished studying the central limit theorem and the idea of consistency. I am still a little fuzzy about them, so I was wondering what are some key similarities and differences of the two. Can they be used together?
Comment: It is the law of large numbers that is more directly related to consistency (at least for sample averages converging to expected values) than the CLT is.
Answer: Consistency is a property of an estimator.
The central limit theorem is, well, a theorem: it relates to the asymptotic property of the sample average under certain conditions, and that they tend to a normal distribution with variance equal to the inverse of the information matrix at a rate of root-n.
Not all estimators are sample averages. And if they're lucky enough to have an asymptotic distributions, it may not be normal.
For instance, you can estimate the upper bound of a uniform (0, $\theta$) distribution by $X_{(n)}$, the sample maximum. This is a biased estimator, but it is consistent because the bias goes to 0 in large samples. The bias can be corrected by a factor of $n/(n-1)$ and this estimator has an asymptotically exponential distribution due to Huzurbazar.
Answer: Here is my attempt to explain the similarities and differences between the CLT and consistency from a statistical point of view using a particular example. My main focus here is intuition and I completely understand that this example is not flawless but I hope this is still useful.
Suppose that $X_1,\ldots,X_n$ are iid random variables such that $\operatorname EX_1=\mu$ and $\operatorname{Var}X_1=1$. Our goal is to learn the value of $\mu$ (which is unobservable) using the observations $X_1,\ldots,X_n$.
The natural estimator of $\mu$ is the sample mean given by
$$
\bar X_n=\frac1n\sum_{k=1}^nX_k
$$
for $n\ge1$. Of course, we need to investigate how good this estimator is. For example, are we be able to obtain more and more accurate information when the sample size increases? The answer is yes and that is what consistency tells us. For all $\varepsilon>0$, we have that
$$
P(|\bar X_n-\mu|>\varepsilon)\to0
$$
as $n\to\infty$. In simple terms, if we choose any accuracy level $\varepsilon>0$, the probability that the value of the estimator is further away from $\mu$ than the accuracy level $\varepsilon>0$ gets smaller and smaller when the sample size increases. However, we are not able to saying anything beyond that.
If we want to know more, we can investigate the error that we make by estimating $\mu$ further. Using the CLT, we have that
$$
\sqrt n(\bar X_n-\mu)\to N(0,1)
$$
as $n\to\infty$. Observe that the CLT implies consistency (see here). This tells us that not only the error goes to $0$ in probability as $n\to\infty$ but also gives us some approximate information about the distribution of the error. For large values of $n$,
$$
P(|\bar X_n-\mu|> z_{\alpha/2}/\sqrt n)\approx\alpha,
$$
where $z_{\alpha/2}$ is the $\alpha/2$-level quantile of the standard normal distribution.
Intuitively, we can think that we are interested in the same thing: the accuracy of $\bar X_n$. This is what is similar between consistency and the CLT. The difference between consistency and the CLT is the information that we obtain. If we only have consistency, we know that the probability to observe a large error gets smaller and smaller when the sample size increases. If we have the CLT, in addition to having consistency, we are able to obtain approximate information about the distribution of the error.
I hope this is useful.


sending a method on nodejs with admin account

Question: I want to send a method from the owner's account to which I have the private key.

I tried adding the private key int he red rectangle but when I run it I get this error:
Answer: You're calling the send() method incorrectly. Please read the web3js official documentation in order to send a transaction to a smart contract and execute its method.
Seems like you want to sign a transaction using a hardcoded signer private key, rather than requesting a signature through a crypto wallet. In this case, follow this answer.
Comment: I'm trying to send a method. The issue is when doing that `code` send({from:address}).then((err,result)=>

I receive an error saying that the acount is unknow. And I should call this from the owner's account which should be hooked to the server. Any ideas?


Can I play Starcraft II with a friend if I have the free version?

Question: I have the free version of StarCraft II (the one from Battle.net).
Can I play StarCraft II with a friend — us against AI?
How? His computer will be in the same network (IP) as mine.
Comment: Hi Gravity, what have you tried so far and where did it go wrong?
Comment: @Joachim - I haven't tried yet. I don't want to try to do something if that thing is impossible. This is why I asked if it is possible in the first place :)
Comment: I think I have seen at some point in the past a menu that said "invite a friend".
Answer: When both of you only have the free edition, you can:

play co-op with free (Raynor, Artanis and Kerrigan) commanders
play arcade contents (they are inherently free)
play elimination; elimination is now free
play Wings of Liberty (Terran) campaign

As long as your friend has LotV, you can play co-op with LotV (Swann, Vorazun, Karax, Zagara) commanders as long as you are in the same party with your friends. (FYI this does not require you to be in the same network with the friend; Battle.net provides the means to make a party with a remote friend)
Regardless of what the party member has, you can't:

play campaigns not purchased (Heart of the Swarm-Zerg, Legacy of the Void-Protoss and Epilogue, Nova Covert Ops-Terran espionage)
play with premium co-op commanders not listed above (they can be leveled up to level 5, but they are rather thought of as "starter editions")
Comment: https://us.battle.net/support/en/article/27568
Also now apparently Full access to custom games, including all races, AI difficulties, and maps.
Unranked multiplayer, with access to Ranked granted after the first 10 wins of the day in Unranked or Versus A.I.
Answer: Yes, you can play with your friends who bought the game ages ago.
The base game itself became free some years ago. Since then, it's like you bought the game "Starcraft II: Wings of Liberty".

Upon account creation, StarCraft II includes the following:

The complete Wings of Liberty campaign
Full use of Raynor, Kerrigan, and Artanis Co-Op Commanders, with all others available for free up to level five
Full access to custom games, including all races, AI difficulties, and maps
Unranked multiplayer, with access to Ranked granted after the first 10 wins of the day in Unranked or Versus A.I

Once you reach level 10 with a Commander, level 15 with a race, or
make any purchase, you can also access public chat channels, and join
or create Clans and Groups. Making any purchase also grants the
ability to publish custom maps.

See also this blizzard post from 2 years ago.
As described, this includes custom games and unranked/ranked(after 10 unranked) games. It doesn't matter if your friend is in the same LAN or anywhere else as SC2 does not support local-only multiplayer. You need a internet connection to join/make games.
Also, as far as I know you can play content from the expansions (Heart of the swarm and Legacy of the void) if your friend owns them [citation needed].
Comment: No, no one needs to purchase the game. You cannot purchase SC2:WOL anymore, it's completely free. If you want to play content of the expansions, one of you need to purchase it. If you want to play SC2:WOL, you are free to go.
Comment: So, this is not very clear: you say that at least one of us needs to have the game purchased.


Is it practical for HF skywave propagation to be utilized for space exploration robot telecommand when outside of microwave/mm wave range?

Question: Is it practical for HF skywave propagation to be utilized for space exploration robot telecommand when outside of microwave/mm wave range?  Currently it appears that only the C band and UHF is used in general (on Mars).  After all, some other planets (incl. Mars) do have an ionosphere, which can potentially be utilized for low-throughput intra-planetary communications, just like it has been traditionally done here on Earth.
Comment: What is outside of microwave/mm wave range? Wavelengths below 1 mm?
Comment: @Uwe Any line-of-sight propagation mode (f > 30 MHz/lambda < 10 m) is obviously limited by the radio horizon, unless there exist terrestrial repeaters, communications satellites, natural reflective objects (e.g., moons), etc.
Answer: Assuming that you have a "good enough" ionosphere it is possible to use HF for telecommand, however microwaves will be more efficient.
HF has quite long wavelengths (meters, tens of meters). Antenna for such frequency is a fraction of the wavelength (eg. quarter or half wave), ie. an efficient antenna will be physically large compared to a microwave antenna (there are ways to make smaller HF antennas at the cost of efficiency). Large = heavy.
HF antennas have very poor bandwidth compared to microwave antennas. Again wideband antennas are even larger. Small bandwidth = small throughput.
Next issue - gain. It is much easier to focus microwaves than HF. Every dB of antenna gain can be spent on smaller transmit power (ie. power efficiency). HF directional antennas are large. Large = heavy and difficult to turn around.
I did not mention yet the atmospheric effects, noise floor, thunderstorms, space weather etc. (they affect microwaves less than HF).
You may try to get around the above limitations by more signal processing, but nevertheless the end result will not be compact, nor fast, nor power-efficient. That is why terrestrial HF today is mostly limited to specialized communication (ships, aircraft - and only on specific routes),  some broadcasting, amateur radio and high-frequency trading.
Comment: It is not the antenna that have a very poor modulation bandwidth, it is the frequency itself. The bandwidth is also small when the frequency is used over a cable without an antenna.
Comment: @uhoh Well that's the whole point...imagine a base on the surface of Mars engaged in telecommand via HF skywave (utilizing the Martian ionosphere) to rover(s) under moderate AI control far away, but on the surface of Mars, beyond the radio horizon.
Comment: @RuslanNabioullin whoa I completely misread the question, my mistake! Yes I was thinking of 1. robotic satellites, not robotic surface vehicles, and 2.only Earth's ionosphere. This is a really, really interesting question btw! [QRP](https://en.wikipedia.org/wiki/QRP_operation) on Mars! There is no or negligible lightning artificial sources of RF noise. Time to go read up on the Martian ionosphere!