Why is non-relativistic quantum mechanics used in nuclear physics?

Question: I am a little bit surprised to see people doing nuclear physics use the Schrödinger equation. I expected the Dirac equation. The energy scale of nuclear physics is on the order of MeV, right? Why is the non-relativistic quantum mechanics relevant for such high energies?
Comment: The rest mass of nucleons is about 940 MeV. This makes the binding energy of nucleons small compared to the rest mass leading some (but not all) to use nonrelativistic methods.
Comment: I know this is not directly relevant to the specific equations you are talking about, but the Schrödinger equation sweeps a lot of nuance under the rug with the Hamiltonian. It is completely compatible with the mathematics to pick a Hamiltonian with relativistic mechanics. The basic wave equation is compatible with special relativity.
Answer: When you have MeV-scale energies but GeV-scale particles, you can get a lot of mileage from working in the non-relativistic limit.
Comment: And to clarify, "GeV-scale particles" refers to the masses of the particles times $c^2$.
Answer: The force which drives apart atomic fission products is their electrostatic repulsion. Their departure speed is determined by their mass and that force. While the resulting speed of the fragments is high (translating into a very high temperature of the resulting fireball), it is still not high enough to require any relativistic corrections.
Answer: Nuclear physics is done in a non-relativistic limit, but it is not mere quantum mechanics, since the main forces are strong and weak interactions (more first than second) rather than the electromagnetic forces exclusively treated in the QM. In simpler terms: one can get a lot of mileage by replacing Coulomb potential with the Yukava one.
The reasonf or this are the energy scales, as it has already been pointed out by @rob: the products of nuclear reactions move at sub-relativistic velocities and the transformation of particles, which are the domain of the HEP, are not needed to be taken into account.
I recommend the introductory chapter of Fundamentals in nuclear physics by Besdevant for the excellent discussion of this approximations.
Comment: You can get a lot of mileage from an even simpler potential: treating the nucleus as a finite square well. A famous example is Gamow's alpha-tunneling decay rate estimates. There are dozens of other examples in the theory of thermal (and colder) neutrons interacting with matter.
Comment: @rob Yes, this is correct.
Answer: There is a nice answer by rob, I would just add a few interesting notes. Your question is an interesting one, because nuclear reactions are extremely fast, and there are neutrinos involved, which do travel at relativistic speeds. However, when we say that we do not need relativity in the calculations, what we mean is that nucleons (neutrons or protons) and fragments travel at slower speeds.
Now I have found basically official information only for two cases that we consider:

slower or thermal nucleons, that travel at speeds around 600 km/s

Let us compare this to a characteristic proton-proton collision rate, npσvth, where n ≈ 6 × 1025 cm−3 is the central number density of protons and vth = (3kBTc/mp)1/2 ≈ 600 km s−1
is their thermal velocity

https://www.astro.princeton.edu/~burrows/classes/403/nucl.masses.fusion.pdf

faster nucleons that travel at speeds around 20000 km/s, so less then 10% of the speed of light

Nuclear fission produces neutrons with a mean energy of 2 MeV (200 TJ/kg, i.e. 20,000 km/s), which qualifies as "fast". However the range of neutrons from fission follows a Maxwell–Boltzmann distribution from 0 to about 14 MeV in the center of momentum frame of the disintegration, and the mode of the energy is only 0.75 MeV, meaning that fewer than half of fission neutrons qualify as "fast" even by the 1 MeV criterion.[5]

https://en.wikipedia.org/wiki/Neutron_temperature#Fast
So the ultimate answer to your question is that even these fast nucleons travel only at speeds less then 10% of the speed of light and thus do not require relativistic calculations.
Comment: So, in principle, one would still need the Dirac or Majorana equations to describe emitted neutrinos?
Answer: Lets take the Energy to be 1000Mev (1Gev). Then the rest mass of proton is 940 Mev.(Not exactly)
You will apply relativity when Total Energy >> Rest Mass Energy.
In nuclear physics, we don't deal with relativistic particles, the calculations I deed is just to convert energy scale to velocity scale so as to make it more apparent that relativity is not needed.
Lets take 1000 Mev as the kinetic energy.$$m_0c^2(\frac{1}{\sqrt{1-\beta^2}})= 1000\ Mev$$
put $m_0c^2=940Mev$
$$(\frac{1}{\sqrt{1-\beta^2}})=1.06382$$
$$\frac{1}{1-\beta^2}=1.13173$$
$$1-\frac{v^2}{c^2}=0.8836$$
$$\frac{v^2}{c^2}=0.1164$$
$$v=0.36c$$
again, These calculations are just an analogy. when you are taking energy in GeV the Relativistic effect starts rising up. While in nuclear physics, The order  of energy is few Mev. So relativistic effects are negligible(Not here) in nuclear problems we are dealing with
Comment: You write "you will apply relativity when total energy $\gg$ rest energy." This suggests, incorrectly, that you can *ignore* relativity in the [semi-relativistic case](https://physics.stackexchange.com/q/610521/44126). I start keeping track of relativistic issues when the *kinetic* energy is more than about 1% of the mass; your example here is above my cutoff.


Elliptical radial gradient overlay in Photoshop CS5

Question: I've found that you can change the aspect ratio of a radial gradient in Illustrator to create an elliptical gradient, how do you achieve the same effect in Photoshop please?
Answer: Create the radial gradient on its own layer, whether directly or through the use of a gradient effect, then convert the layer to a Smart Object using Filter > Convert for Smart Filters or Convert to Smart Object from the Layers Panel flyout.
You now have a gradient that you can resize and transform using the Edit > Free Transform as needed. Because it is a Smart Object, the transform is non-destructive, so you can adjust it later if the composition requires it.
If your transformed elliptical gradient needs to fill the whole canvas, make it larger than needed in a separate document, then drag it into your working canvas to give you the most flexibility.
Comment: I think I took this approach but the long way round (I actually saved my gradient to a file and imported back, forgive me I'm new!) When I convert my layer to a smart object it seems just as destructive? For instance, I loose the layer effects that create the gradient, so I can't go back and alter the colour.
Comment: Once the gradient is captured as a Smart Object, you can go back into it at any time (just double click the icon in the Layers Panel) and change colors or anything else you want. But the gradient must be IN the Smart Object, not applied to the Smart Object after the fact.
Comment: AH! So that's how smart objects work, thanks very much. In that case your approach definitely gives the most malleable end result.
Answer: The Gradient Tool in Photoshop produces a raster effect (i.e. just pixels applied onto a layer). You can transform the pixels to change the aspect ratio. Here's an example:

Create a new empty layer.
Use the Gradient Tool to create a Radial gradient that fits fully in the canvas
Press Ctrl+T (Windows) or Cmd+T (Mac) to get the transform controls
Use the transform controls to resize the gradient horizontally or vertically

This is destructive, unlike in Illustrator, which means once you change the aspect ratio, you are changing the pixels forever (assuming you don't undo).
Comment: and Depending on the Gradient style.. **Brush Tool** and **Soft Round Brush** with the help of **Free Transform** will give the same effect..
Answer: I found this, and I think it's best option since I don't think you can have automated elliptical gradients. Taken from: http://www.clearps.com/photoshop-forum/index.php/t/16625/
There are many, many ways to do this but here's what I'd probably do:
1) Create a new layer and place it under your photo layer.
2) Fill it with white.
3) Select the eliptical area you'd like "highlighted" or rather, not faded at all with your marquee tool.
4) Select "QuickMask" (or hit Q) and you'll notice a colored mask now around your selection.
5) Go to Filters>Blur>Gaussian Blur and adjust the slider to the level of blur you think would work. Click OK.
6) Switch out of QuickMask mode (hit Q again). You will see your "marching ant" selection again (which might be a bit smaller now, but that's ok).
7) Making sure you're on your photo's layer (and not the white one you created in step 1), hit the Layer Mask button at the bottom of your layers palette. This will mask out the image that wasn't in your blurred selection.
Since you are new, don't forget to accept the best answers for your questions.


How to transform an Oracle SQL into a Stored Procedure that should iterate through some tables fetching a certain data field?

Question: I need to transform an Oracle SQL statement into a Stored Procedure therefore users with less privileges can access certain data field:
SELECT
    info_field, data_field
FROM
    table_one
WHERE
    some_id = '<id>' -- I need this <id> to be the procedure's parameter
UNION ALL

SELECT
    info_field, data_field
FROM
    table_two
WHERE
    some_id = '<id>'
UNION ALL

SELECT
    info_field, data_field
FROM
    table_three
WHERE
    some_id = '<id>'
UNION ALL

...

Given that I'm no SP expert I've been unable to figure out a good solution to loop through all the involved tables (12 aprox.).
Any ideas would be helpful. Thanks much!
Answer: If you just want to restrict users' access you could create a view and grant them select on the view but not the tables:
CREATE VIEW info_and_data AS
    SELECT info_field, data_field
    FROM   table_one
    UNION ALL
    SELECT info_field, data_field
    FROM   table_two
    UNION ALL
    SELECT info_field, data_field
    FROM   table_three
    ...

The users could then type:
SELECT info_field, data_field
FROM   info_and_data
WHERE  some_id = <id>

Answer: There are other ways to achieve your goal besides my suggestions below, but I would warn against splitting up data that really belongs in one table just to implement a data access policy that may change in the future.
The simplest solution to limit which table columns a user sees is through views on those tables. Use different views that show or hide specific columns and grant access to those views to different users/roles.
If you don't know in advance which combination of columns a user may be allowed to see, then you could use dynamic sql: You assemble the SQL statment in the stored procedure based on the access privileges of your user (look up from some other table you create to hold this info), meaning that you only include the proper columns in the SELECT portion of your statement. See this document from Orace
for more info.
If you are using Oracle 10g, then you may find this Oracle article interesting. It introduces the topic of the Virtual Private Database, or VPD for short, where you can hide certain rows, or columns or even individual column values depending on who is accessing a table.
Comment: Thanks a lot! Actually I've been convinced by you guys that views are the best approach to solve this problem.
Answer: Is the expectation that, among all these tables, only one will have a match for a given ID?
If no:  You need to explain what you want to do when there are multiple matches.
If yes:  You simply do the same SQL query, selecting the result into a variable that you then return.
It would look something like this:
PROCEDURE get_fields( the_id  NUMBER,
                      info_field_out  OUT  table_one.info_field%TYPE,
                      data_field_out  OUT  table_one.data_field%TYPE
                    )
  IS
  BEGIN
    SELECT info_field, data_field
      INTO info_field_out, data_field_out
      FROM (
        ... put your full SQL query here, using 'the_id' as the value to match against ..
      );

  EXCEPTION

    WHEN no_data_found THEN
      -- What do you want to do here?  Set the outputs to NULL?  Raise an error?

    WHEN too_many_rows THEN
      -- Is this an invalid condition?

  END;

Comment: Thanks much for the reply! I think I actually need to have multiple results so in this case it seems the best solution would be a View instead. What do you think?
Comment: If a view will accomplish what you need, then that is the simpler solution.  If not, you can adjust the technique I showed to fetch and return multiple rows.


Can someone tell me how to wire the MX mechanical keys to an Arduino?

Question: I am thinking of making a custom keyboard for a VJing software. I couldn't find momentary switches of size greater than 15mm, so I am thinking of buying these MX keys (they have 3 pins.) I could'nt find a wiring diagram online. So will you be able to help me out with the wiring diagram (I will connect them to an Arduino Uno R3.)

Comment: A switch is a switch, doesn't matter the size they come in. There are plenty of tutorials for that on the web. Just imagine the tact switch on the tutorial as any other switch.
Comment: Ohh thank you!! I am a beginner btw. But it has 3 pins and most of the tacts have 4. So i got confused.
Comment: You can measure the resistance between pins with the button pressed, and not pressed, to determine the functions of the pins.
Answer: Cherry Switches come in 3 pin and 5 pin varieties. In both cases there are only 2 electrical pins, as these are just momentary switches. The other pins are plastic and for mounting stability. They dictate whether they will be mounted on a PCB or not (5 pin is for PCB).
Answer: You need something called a datasheet. That will have all (or most) of the information necessary for a knowledgeable designer to use the parts.
In this case, you know what the part is: a switch
You know the model series: MX
You should know the manufacturer: Cherry Americas LLC (owned by a German conglomerate and probably manufacturing the switches in Zuhai China, near Macau).
So google that and you should come up with this datasheet. A similar one is here  Unfortunately I don't see any with an odd number of contact pins, unless you count the plastic locating pin in the center.
Anyway, all the information you need should be there for whatever type of switch you are looking to purchase. Unless you want the kind with a matrix diode or LED incorporated, in which case contact the manufacturer to find out the polarity of the diode(s).
Answer: If you find a switch with more than 2 pins, you can use a multimeter in continuity mode to find the right pins. The pins you want are connected and disconnected when the switch is pressed and released.
Continuity mode on a multimeter is a mode where the meter beeps if the 2 probes are connected together.
Once you've got the switch figured out, search "how to connect switch to arduino" and you will find hundreds of tutorials to walk you through it. I won't get into that because it's already been said 1000 times.


Can I do an Oman visa change/run on a tourist visa?

Question: We have 3-month tourist visit visa to the UAE which expiring soon. Is it possible to exit via Oman and apply for another visa from there? They say it's a visa change or run. How is the process done? Also, we not from one of those countries that can get a UAE visa upon entry at the airport or border post. Below is example of the visa type.
Comment: Do you want a visa change (from tourist to residence) or to obtain a new tourist visa? Does this example show your nationality (Indian) and, if yes, don't you also need a visa to enter Oman (not eligible for e-visa or visa on arrival)?
Comment: @Dorothy I think the image was given as an example of the visa type, and is not the OP's as he says in the question.
Comment: @mkennedy although OP isn't able to enter visa free or get one on arrival. It occurred to me that would make a run to Oman difficult is OP can't enter w/o visa. So far, I've found this, that tourists who do not live in the UAE are only granted access to Oman if they have passports from EU countries, the US or Australia.
Answer: There is a difference between visa change and visa run since, in 2016, the government announced that:

visit visa-holders no longer need to leave the country to amend the status of their visa to a residency permit, the Ministry of Interior revealed...

Such changes can be done through an Emirates ID Authority e-form typing service
To make a UAE-Oman visa run, tourists in the UAE must hold passports from the specific countries listed below. For other nationalities, the alternative is a visa flight, which can be arranged through any travel agency or through FlyDubai.
You walk off the plane, into the departure terminal and straight back on again, without actually entering the destination country, even though you've left the UAE.
Among the many companies that offer visa service, the First Gate Business Service web site has the details.

Following nationalities can utilize this facility for Tourist Visa renewal, Employment Visa Status Change, Family Visa Status Change.
• UK
  • Ireland
  • USA
  • New Zealand
  • Australia
  • Canada
  • France
  • Italy
  • Germany
  • Netherlands
  • Singapore
  • Malaysia
  • South Korea
  • Hong Kong SAR
  • Belgium
  • Luxembourg
  • Switzerland
  • Austria
  • Sweden
  • Norway
  • Denmark
  • Portugal
  • Greece
  • Finland
  • Spain
  • Monaco
  • Iceland
  • Liechtenstein
  • Japan
  • Brunei
  • Poland
  • Hungary
  • Romania
  • Bulgaria
  • Lithuania
  • Estonia
  • Latvia
  • Czech Republic
  • Slovakia
  • Slovenia
  • Croatia
  • Malta
  • Cyprus
• UAE Immigration will put exit stamp at UAE border. Exit Fee Dh35. Then pass through Oman check point and they will charge Dh50 for in-out stamp.
• Return through UAE border and you will get Entry stamp after eye scan. From the date of entry you have 60 days time to complete Medical, Emirates ID and Visa Stamping.
• Other nationalities can change visa by air. Visa change package is available from Fly Dubai. Approximate charge Dh650. Contact any travel agency for available packages. You must have valid UAE visa in hand to use this facility.
• [Y]ou can change status without exit on payment of Dh510 (typing charge extra). Type status change form from typing centre, sign the sponsor and submit it at Immigration counter. If a company is your sponsor, you can submit status change application through eDNRD online. read more
• Visa Change is allowed for Tourist and Visit visa holder to Employment/ Residence/ Investor by paying Dh680+510 (typing charge extra). No need to exit UAE.
Immigration Helpline: 800 5111


Allowed help in thesis

Question: If you write a thesis, is it legal to ask somebody if things you did are correct in the thesis? When it's my own work and this person says, everything correct, there shouldn't be any problem, right? When does plagiarism start?
Comment: What kind of "thesis"? Original research, or a learning exercise? Are you working with an advisor?
Comment: This isn't a "legal" issue anywhere that I can name. It has ethical, but not legal, implications.
Answer: From a publication point of view:
In general, this is nothing else than peer review and totally fine.
As long as the other person only tells you "all good", or "this here doesn't look good, maybe rewrite it so that X is more clear", that is no problem at all. If the other person writes the whole new version for you, that is obviously not good. Either way, this wouldn't be plagiarism in this case. Plagiarism means copying from a different paper/book/source without properly mentioning it. What this would be is someone else writing (part of) your publication without getting mentioned. That is at least as bad as plagiarism, but it is something else.
Depending on the level of help you got, consider mentioning the other person in the acknowledgements.
From a university point of view:
A thesis isn't completely the same as a paper, so here, other rules might apply. At some universities, you have to sign that you didn't use any sources or help apart from the ones clearly mentioned and cited. Thus, rules might be stricter here. While I would not worry about, say, a math major getting feedback on their English grammar by someone who has no idea about math, as soon as the one reviewing your work is from the same field and/or also gives feedback regarding content, this is something that should be cleared with your advisor first.
Answer: Certainly where we are it would be seen as very poor practice for your supervisor not to have read and commented on your thesis, and in certain circumstances might be considered negligence on the part of the supervisor.
Answer: My answer will complement that of user Dirk, but partly counter it. Yes, you need to follow the stated rules of your university. But ....
In most larger universities, students get a lot of help on their theses, not just from their advisor, and not just on their writing style. In both of the graduate (R1) institutions at which I studied I was part of a (mathematics) research group in which ideas were freely shared. The groups held weekly seminars for discussion and sharing. We would make suggestions to one another and get advice from the faculty members of the group. No one ever suggested that I wasn't sole author of my dissertation or the paper that resulted from it. My advisor was acknowledged, of course.
So, I doubt that the sort of "help" you got would be considered wrong, though the formal rules apply. You didn't ask for, or get, corrections to your work if your statements are accurate.
I think such research seminars are a marvelous thing. The insights that led to my dissertation were mine, though I suspect that my advisor had them in parallel also. The "help" from the seminar didn't lessen the quality or value of the research experience. In fact, it is how real researchers in the real world actually work. It would be foolish to lock yourself up in an office until you produce a paper with no outside consultation. Research activity would stop.
And plagiarism is only using someone else's work without attribution. I don't see it as having any bearing here. And, as I said in a comment, neither is it a legal issue.
Note, for the record, that my Erdős Number is 2. We value collaboration in mathematics and related fields.

Allowed help in thesis


Processing performance: Singlepart vs Multipart Polygon

Question: I have a single-part polygon containing thousands of features which I converted/dissolved into a multipart polygon. Which is faster to process  (i.e. when I clip them using a simple rectangular polygon)? Is there any basis or explanation for that?
Answer: Clipping, intersection etc are performed two steps:

Identify which features should be processed
Process each feature found in the previous step.

For step #1, the bounding box of each feature is typically used first, ideally stored in a spatial index. If using a layer with a single giant (multi)polygon, then the feature will be typically returned. If using a layer with many small (single)polygons, only the features truly intersecting will be found.
For step #2, the number of vertices in each feature to be process matters a lot. If a single giant (multi)polygon is to be processed, the computation becomes very complex and slow. If many small features were to be processed, the clipping/intersection becomes very fast.
Overall, it is faster to process many small polygons rather than bigger ones.
Comment: +1 You might note that there is a law of diminishing returns involved -- once *all* the polygons are tiny, making more of them may slow things down again.


How to coat gummies with beeswax/carnauba wax and coconut oil/palm oil?

Question: I tried coating my gummies with beeswax but it was a failure. First, I melted beeswax and tried to pour it in a spray bottle but it hardened so fast. Also, I tried coating them by just putting them in the beeswax but the gummies dissolved with the wax because of the heat. I tried to coat them with a mix of olive oil and wax (2/3+1/3) but it wasn't perfect, there were some little pieces of wax on the gummies.
Answer: From what I understand, the way waxy coatings are applied is actually by adding your candies and powdered wax to a tumbler.
Claire from "Bon Appetit" tried to accomplish it by abusing a salad spinner to make gourmet jelly beans and M&Ms. Ann Reardon from "How to Cook That" used a children's toy rock tumbler to apply a cocoa butter coating to some jelly beans.
Claire's video
Ann Reardon's video
Comment: Would you describe the difference please? As far as I knew the only difference was textural? I hear the words interchangeably really.
Comment: thank you but jelly coating is different from gummy coating.


Worst technical knowledge gap you've seen?

Question: What's the worst technical misunderstanding you've ever seen?  Worst abuse of a good system due to lack of knowledge?
Answer: I didn't know I could write my own functions (php)
When I was teaching myself to program years ago I wrote an entire php web application without a single function.  All code reuse was done by calling include(...) on other .php scripts.  The book I was learning from never introduced the concept of user defined functions.  (The day I learned about functions was a very good day.)
Comment: holy crap! are you serious :D
Comment: Seen a similar thing before at a job I consulted on very briefly (bought in by the product owners - but had to work with a different company that developed the web app).
This dev company had the mistaken belief that calling a function was too expensive in PHP so their code tended to look like what you're saying.
While there were a couple of method calls and includes, a regex to validate an email address in a couple of places shouldn't be encaplusate in a method - but copy paste it wherever you need it - eventually gave up trying to convince them that method call overhead is not important
Comment: The app i currently have to maintain must have been from you. Ok, it has a wrapper around the mysql functions but thats it. I've seen a single SQL Query repeated 12 times in _one_ file.
Comment: Don't worry... my code has long since died and been replaced.  I've learned my lessons! (and I worked alone at the time and had no one to teach me better practices) :)
Comment: well you should consider yourself successful. I don't think it is easy to achieve that :)
Answer: Polymorphism.
Didn't really understand it's power at first. Resulted into bloated, and over complicated routines. Boy, try not to remember those days...
Comment: I can see what you mean. At first I was mostly seeing Object Orientation as way to keep functions and data together. Like how C++ let you declare functions inside a struct. I was aware of the virtual keyword but I didn't really see the usefulness. Smalltalk implementation of the if control structure with polymorphic #ifTrue: and #ifFalse was a real eye-opener.
Answer: The worst i've ever done was storing comma seperated ids in a database. I did not fully understand joins so it was the easiest thing i could do but the queries where horrible
(WHERE foo_ids LIKE "%,$id,%" OR foo_ids LIKE "$id,%" OR foo_ids LIKE "%,$id").
The worst thing i regularly see are classes that just work like namespaces with all methods public static (PHP).
EDIT:
I just remembered the time when a school mate tried to create an XML file for a database table
Table:
teacher_id | name
         1 | foo
         2 | bar
  ...      |   ...

His XML:
<teachers>
  <id1>foo</id1>
  <id2>bar</id2>
   ....
</teachers>

Answer: Database joins in PHP code
When teaching myself SQL with PHP, I was using SQL like a permanent flat-file type store with complex filtering capabilities (WHERE).  I did not understand that you could "join" tables together.  All join operations were implemented in a PHP function after all the data was pulled into memory.  If I knew more back then I might have called it a nested loops join function!  (That will teach you to de-normalize your data very fast!)
I'm sorry database gods!
Answer: Some Java - "developer" (lol) trying to write a piece of software in C#, not knowing that this is a modern language with a "foreach" - statement.
Result:
Software had iterations using... iterators. Ugly, 90s style, typical of Java.
Made me hate Java even more. :-(
Comment: But Java has a foreach statement (`for (e : iterator) {}`), so the developer was just generally ignorant.
Comment: Except theres a time and place for iterators depending on the operations being performed in the loop. The big example is when you need to remove something from the collection that you're iterating over.
Comment: @Freiheit

If you are doing that THIS way, you are doing it wrong. IEnumerables are to be considered immutable, if you need to mutate them, you are supposed to create a modified copy. Everything else is premature optimization.
Comment: Slight correction to my previous comment: that shouldn't be "iterator" but "collection"/"object being iterated over".
Comment: @Turing complete - not in Java: right from the early days, it's explicitly supported non-immutable Enumerators. I consider this an intelligent improvement on early C based enumeration that was more interested in what was easy to implement than in what real-world programs actually needed.
Comment: @Adam

If a program needs a mutable enumeration, the developer isn't a good one. Functional programming will tell you why. :-)
Answer: A colleage and I worked as consultants on a medium software project. He'd been working for a year on similar projects, so he was billed to the client as an "expert" on the platform.
Soon I discovered that my colleage didn't fully understood the fine points of file I/O on the language we were using, consequently leaving lots of subtle bugs. The funny thing is, all his previous projects had the same subtle bugs but the clients learned to use the system in ways that didn't trigger them.
Answer: Back when I was a beginner, I wrote some code in PHP without understanding pointers, objects, or even tuples/structs.  I just built all my data structures using PHP's ridiculously flexible, dynamically typed arrays.  It's actually pretty surprising how much you can accomplish that way, but I feel bad for anyone (including myself a few months later) that ever needed to modify that code.
Answer: That I had to call ToString() on every variable when concatenating strings, even if the variables were strings.
Examples:
Enum.GetName(...).ToString()
myDate.ToShortDateString().ToString()

...


Office word 2010 history/activity

Question: I was curious if Word 2010 for Mac has a activity/history viewer for what there has been written/deleted in the document, like Google Docs has?
So far I have not found anything, not even on the web (Googled it).
Answer: If I understand your question correctly, I think you're talking about tracked changes.
You can access this via MS Word's Tools menu: Tools > Track Changes > Highlight Changes...
Comment: This has been available in [Word since at least 2004](http://www.peachpit.com/articles/article.aspx?p=412916&seqNum=6)

Office word 2010 history/activity


Image Resizer is the default image preview application, but it should be Photo Viewer

Question: Under System Settings > Applications I have Photo Viewer set as the default image viewer. However, when I click on an image using Files, it opens with Image Resizer. I need to right click to open an image with Photo Viewer.
Answer: In order to fix this, right mouse click on an image file, select Open with and choose from the menu there Other application, no matter that your favorite application is on the list above. On the next popup screen choose your fav application and set the checkbox Set as default if it isn't set already and confirm with Select.
note: If your favorite application is not in the list, probably you can find it using the "View All Applications button" there.
From now on, all files with this file extension will be open with the application you just choosed for. Image files can be a lot of different file extension formats and the settings you describe using the screenshot on your question cannot fit for all of them (installing a new program can steal the right for automatic open of some, for example), so this is the way you can change the default program for any file extension(not only images), following the steps above. Again, the steps I have described will not work for all image files automatically, but for all files with the  current extension you've set up. If you want to change it for another ones also, you have to repeat the steps above.


How can I do Databinding in c#?

Question: I have the following class

public class Car
{
   public Name {get; set;}
}

and I want to bind this programmatically to a text box.
How do I do that?
Shooting in the dark:

...
Car car = new Car();
TextEdit editBox = new TextEdit();
editBox.DataBinding.Add("Name", car, "Car - Name");
...

I get the following error

"Cannot bind to the propery 'Name' on the target control.

What am I doing wrong and how should I be doing this? I am finding the databinding concept a bit difficult to grasp coming from web-development.
Answer: You want
editBox.DataBindings.Add("Text", car, "Name");

The first parameter is the name of the property on the control that you want to be databound, the second is the data source, the third parameter is the property on the data source that you want to bind to.
Answer: Without looking at the syntax, I'm pretty sure it's:
editBox.DataBinding.Add("Text", car, "Name");

Answer: editBox.DataBinding.Add("Text", car, "Name");

First arg is the name of the control property, the second is the object to bind, and the last, the name of the object property you want to use as the data source.
Answer: You are quite close the data bindings line would be
editBox.DataBinding.Add("Text", car, "Name");

This first parameter is the property of your editbox object that will be data bound.  The second parameter is the data source you are binding to and the last parameter is the property on the data source that you want to bind to.
Bear in mind that the data binding is one way so if you change the edit box then the car object gets updated but if you change the car name directly the edit box is not updated.
Answer: Try:
editBox.DataBinding.Add( "Text", car", "Name" );

Answer: I believe that
editBox.DataBindings.Add(new Binding("Text", car, "Name"));
should do the trick.  Didn't try it out, but I think that's the idea.
Answer: Using C# 4.6 syntax:
editBox.DataBinding.Add(nameof(editBox.Text), car, nameof(car.Name));

if car is null, then the above code will fail in a more conspicuous way than using literal string to represent the datamember of car
Answer: You're trying to bind to the "Name" of the TextEdit control.  The name is used for accessing the control programmatically, and cannot be bound against.  You should be binding against the Text of the control.
Comment: plus won for explaining why everyone is using .Text.
Answer: The following is generic class that can be used as a property and implements INotifyPropertyChanged used by bound controls to capture changes in the property value.
public class NotifyValue<datatype> : INotifyPropertyChanged
{
    public event PropertyChangedEventHandler PropertyChanged = delegate { };

    datatype _value;
    public datatype Value
    {
        get
        {
            return _value;
        }
        set
        {
            _value = value;
            PropertyChanged.Invoke(this, new PropertyChangedEventArgs("Value"));
        }
    }

}

It can be declared like this:
public NotifyValue<int> myInteger = new NotifyValue<int>();

and assigned to a textbox like this
Textbox1.DataBindings.Add(
    "Text",
    this,
    "myInteger.Value",
    false,
    DataSourceUpdateMode.OnPropertyChanged
);

..where "Text" is the property of the textbox, 'this' is current Form instance.
A class does not have to inherit the INotifyPropertyChanged class. Once you declare an event of type System.ComponentModel.PropertyChangedEventHandler the class change event will be subscribed to by the controls databinder
Answer: it's
 this.editBox.DataBindings.Add(new Binding("Text", car, "Name"));

How can I do Databinding in c#?


How does the taste of Bird Eye Chillies differ at different stages of maturity (green vs red)?

Question: What's the difference in taste between green and red Bird's Eye Chillies?
Comment: Great first question. Welcome to the site.
Answer: This is pretty much the same throughout the pepper family. The green chilis have "green" flavors - underripe, metallic, grassy. The ripe, red chilis develop more rounded, fruity flavors. You can just think of the difference between green and red bell peppers as a basic guide.


When do I use non-, ir-/i-, dis-, a-, or un-?

Question: Between using the prefixes non-, ir-, i-, and dis-, a-, or un-, meaning "not (root word) to do something", when is the best time to use each?
Comment: Consult a dictionary.  Or do you mean: how should you invent your own words?
Comment: @GEdgar -- well, I'm not trying to invent a word, but a particular word I looked up had multiple prefixes, ended with the same meaning.
Answer: You use each prefix with the words that can take that prefix. I'm sorry, but that is the whole of the answer.
There are tendencies which might help (for example, in- and its variants il- and ir- are only used with words of Latin origin, a- with words of Greek origin, and un- mostly with words of Germanic origin. But even if you know the origins of words, these rules are not reliable.
Comment: Germans seem to experience particular difficulty in choosing the right ones. I had a colleague whom I swear used to toss a coin, and would talk about things being *unpossible*, and *inofficial*. In other respects he would speak faultless English.


Error loading Qt libraries with Wing and PyQt

Question: I've been trying to get PyQt4 to work on my OSx machine (10.8.5) for some time - I've loaded it on my windows machine with no problem by using an installer.
I have sip 4.8.5, Python 2.7 Qt 4.8.5 loaded on my machine using homebrew.
When I try to debug the following file in WING, I get the following error:
Code from Zetcode as a test
import sys
import QtGui

def main():

    app = QtGui.QApplication(sys.argv)

    w = QtGui.QWidget()
    w.resize(250, 150)
    w.move(300, 300)
    w.setWindowTitle('Simple')
    w.show()

    sys.exit(app.exec_())

if __name__ == '__main__':
    main()

Exception:
ImportError: dlopen(/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/PyQt4/_qt.so, 2):
Library not loaded: QtDesigner.framework/Versions/4/QtDesigner
Referenced from: /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/PyQt4/_qt.so
Reason: image not found

Why is the Qt library not loading? What do I need to do to get the library to load?
Thanks,
-j
Answer: I don't personally use homebrew, but I'm pretty sure it installs stuff in /usr/local. From the error message it looks like it is accessing /Library/Frameworks/Python.framework. I also don't use WingIDE, but it looks like it is using a different python install than you want it to. I'm sure there is a way to specify which python it uses.
Answer: You probably need to set the Python Executable in Project Properties (from the Project menu) to /usr/local/bin/python -- or whatever the value of sys.executable is in the Python that has PyQt4 installed into it.
Note that in Wing 101 this is done in the Configure Python dialog instead, which is accessed from the Edit menu.


Installing package with service account

Question: I need to install a software called nominatim on ubuntu. Following the install instruction,  I created a service account user with a specified home directory at /srv/nominatim. I know service account normally don't have home dir, but this one specifies a -m options.
My problem is, since i'm logged in as user A, and am not suppose to run installation as root(no sudo), i keep getting access denied problem when running trying to create things for this "nominatim" user under its own home directory /srv/nominatim. I can't really do a su because there is no password for service account.
what's the best practice to install?
I'm thinking of

installing everything under my own home directory and move it to "/srv/nominatim" folder and then chown them later
create a password for this "nominatim" user and then remove it later. will this even work ?
Answer: Switch to the nominatim user using sudo and run the installation as that user:
sudo -u nominatim -i

Installing package with service account


How did all of the weird creatures end up in class 2A?

Question: Class 2A in Negima has many different creatures, such as a robot and a vampire. In fact, many of the students in class seem to be non-human or at least weird. Was there a reason given for them all being in the same class? Were they all purposely put in the same class or was it a coincidence?
Answer: Most likely, it's purposely because the entire academy was run by mages, and they would know about most if not all of these cases. There also is the fact that a 10 year old genius mage was given that class specifically.
It will, though, remain in the realm of speculation as no such thing has been mentioned in the manga series.


relationship between C-command and Binding

Question: What is the relationship between C-command, binding and Co-reference? Does it mean that C-command is the precondition of binding? Can somebody help me get clearer about these three terms?
Answer: In its most basic incarnation, binding is a combination of c-commanding and coreference.
In other words, in a sentence like Sam talked to herself, Sam c-commands herself and is co-referential to it (the two phrases refer to the same person). Therefore Sam binds herself.
But in Sam talked to him they don't co-reference, and in Alex talked to Sam, and James talked to her too they don't c-command. So in these sentences, Sam does not bind her.
Notably, in the first sentence we see a reflexive herself, and in the other two we see a non-reflexive her. Which brings us to the whole point of "binding": we can say reflexives must be bound, and non-reflexive personal pronouns can't be.
Answer: There are a few concepts being conflated here.  C-Command is a tree-geometric relationship that describes two nodes relation to each other.  @Draconis is correct in the sense that C-Command (specifically asymmetric c-command) is necessary but not sufficient condition for binding.  The examples s/he offers however are incorrect (In all cases the subject is c-commanding the predicate), the issue becomes one of how that tree geometric structure is processed semantically (see Heim and Kratzer 1998).  Binding is related to scope (which is defined by c-command) where a quantifier (in the Lambda-calc sense) binds a variable--in the cases above the DP subject is quantifier that is binding a pronoun (a variable).  Whether that can be a reflexive binding or not is governed by Chomsky's Principle A B or C respectively.
The last comment Draconis makes: " Notably, in the first sentence we see a reflexive herself, and in the other two we see a non-reflexive her. Which brings us to the whole point of "binding": we can say reflexives must be bound, and non-reflexive personal pronouns can't be." Is not really true either. Binding is more than pronoun reference, it is also crucial in sentences with traces (eg What did you eat t? and other A-bar movement scenarios).  S/he seems to be confusing coreferentiality (or co-indexing) with reflexivity constraints (eg Mary gave sally her favorite toy) where her can be referential to either Mary or Sally.  Ellipsis phenomena seem to illustrate this as well:
Bill washed his car and John did too
There are two readings here (strict/sloppy in in the literature)
(i) John washed John's car and Bill washed Bill's car
(ii) John washed John's car and Bill washed Johns car too
Another example you may want to consider are islands/crossover effects:
Take:
(iii) John wonders whether Bill ate his food.
Wh-movement here across a CP boundary still creates a c-command relationship but binding is blocked:
*(iv) Who does John wonder whether t ate his food?
Comment: The person who poses such a question is not going to understand the answer provided here, for the answer is too advanced. It appears to have been added to show off rather than to be helpful and increase understanding.
Comment: The answer is directed more at Draconis than at Buffoon. It is an esoteric message that most people in this forum are not going to understand. Name dropping occurs, i.e. Heim & Kratzer; concept dropping occurs, e.g. lambda calculus, Principles A, B, C, trace, A-bar, co-referentiality vs. co-indexation. Buffoon is certainly not going to understand all that, nor are most people in this forum. Young academics who are trying to impress their peers write such answers. Experienced academics pen answers that are accessible to a broader audience.
Comment: If someone is asking about 'binding' and 'c-command' then they know a trace is, at least have heard of Principle A, B, and C, and since the word 'co-reference' was in the question, they probably know that too. As far as including a citation, that is not name dropping. Also, the idea that most people in the "Linguistics" forum don't know anything about Linguistics is on its face absurd.  I look forward to reading your citation-free and concept-free answer or any substantive concern you may raise.  You can start by answering any of the 5 issues raised above or just answer Buffons question.
Comment: Just to clarify—in my example of not c-commanding, I'm saying that in "Alex talked to __Sam__, and James talked to __her__ too", Sam can't c-command her (because it's deeper under the &P or whichever analysis of conjunctions you prefer). In "Mary gave Sally __her__ favorite toy", surely that's the possessive "her" (which doesn't become reflexive), not the objective "her" (which does)? Cf "Sam talked to __her__ reflection", not "*herself reflection".
Comment: Apart from that, I agree; binding definitely affects more than pronoun reference, but my understanding is that pronoun reference is where the notion arose, and then it got extended to other phenomena that can be said to co-reference (like traces).
Comment: Couple things: (1) the question is NOT specific to anaphors but the upvoted answer is, (2) these posts are read by others (not just the one writing the question), (3) the upvoted answer is wrong with respect to reflexive binding (4) it is important to note that c-command/chain-coindexing are syntactic and coreferentiality is semantic and (5) it seems pretty dismissive/disrespectful to just suggest that the person writing the question is incapable of understanding the answer


How to change the text after username@ in Ubuntu

Question: I just installed Ubuntu and opened an admin panel where I saw that I accidentally allowed the system to use my laptop's name. Can anyone suggest how would I remove it?
Answer: This is the 'hostname'. Check this question for how to change it: How do I change the hostname without a restart?
If you want to have a completely different prompt, not in the form of user@hostname, check out the answer here: change prompt of terminal, permanently | how
Comment: Happy to help. If you could mark my answer as correct, that would be great :)
Answer: That's actually the standard Ubuntu Bash prompt which shows your hostname, you can change your hostname if what bothers you is that it's so long otherwise you can just remove it.
Start by reading what your prompt is actually set to look like using echo ${PS1}. You should get a rather unreadable string that contains @\h at some point. Removing that part will remove the hostname from the prompt.
Simply export your new settings with export PS1="your_new_string".
If you want to make that change persistent, add it to your .bashrc.


How to bend cylinders in 3DS Max

Question: Im new to 3DS Max and trying to recreate this object:

I found that "bend" does something similar to this but I need to only bend the edges of the cylinder, if anyone can direct me I would be grateful.
Answer: Most of us probably do not have 3DS Max and even fewer can do anything useful with it. I am not an exception. 3DS Max has numerous common geometry definition methods. Beyond them it even can simulate physics and make realistic material deformations (seen only demos) so an advanced 3DS Max user may well let a hammer hit a straight round tube to make its ends flat.
In case you are not interested in simulating hammering, but want an easy to make lookalike try for ex. this:

2 circles and a rounded rectangle are blended to get a surface. This is a common method to generate solid pieces and shells which have smoothly changing cross-section profiles. Here those profile samples are placed on a straight line, but generally programs allow also one to insert a curved sweep rail. The method is in some programs called lofting and it's blending or sweeping in others. One must also define does he want a filled solid or a surface. This example has a zero thickness surface.
Making realistic looking joints to other truss structure parts is another problem. It was not asked here.

How to bend cylinders in 3DS Max


Can I download older versions of apps?

Question: I've got a 1st Generation iPod with iOS 3.1, and I'm frustrated because I most apps don't run on such an old iOS, but I can't put a new iOS on. Is there eny way to get old versions of all those apps?
Comment: It is not possible to do it legally, but you may be able to do it with jailbreak stuff
Answer: I'm afraid not. You can keep running old versions of apps, but you can not download them. For example, Check the Weather was recently updated to require iOS 6. If you have an iOS 5 device you can no longer purchase it on the device, but I can keep running the version I have as long as I don't delete it.
I understand and share your frustration.
Answer: It's worth pointing out that whilst you can't get old apps for iOS3.x Apple do now offer the option to download the last compatible version of an app on devices running ios4.2.1+ and later. There are some catches in that you need to already have installed the app under your user ID but these are discussed in the Reddit comments and explained in this article - basically you can install the app on another device and then you'll get the option to download the older compatible version on the old device.
FYI each app file is specific to a particular user ID so you can't just copy an app from someone/where else, though if you've got a copy of an older version of the app you can use that.

Can I download older versions of apps?


How do I take a question offline?

Question: I want to contact a person who was helping me - how?
I could not find way to email or message the person. They were helpful. Our question was getting too long for work on the main page seciton.
Comment: If your question is running too long, consider that it's possibly too broad. Mostly this may mean that a question should  be multiple questions or that the question is not specific enough. Try to specify questions to the single obstacle which is blocking you from progressing. Skip code & comments that are not related to the issue and stay focused. When you have multiple issues, ask multiple questions.

Try to always ask the right question.  Many ask for help on their code and requirements while they should be asking where to find the documentation or how to use a specific salesforce feature.
Comment: Another reason to keep your questions online is so others can find the question and answer and it may help them as well. When you go one on one, then nobody else benefits.
Answer: If your questions goes too long, you get the option to continue over chat.
Comment: How do I continue over chat?

How do I take a question offline?


Cauchy problem for quasi-linear pde $u_t+uu_x=1$

Question: I am solving following Cauchy IVP: $$u_t+uu_x=1,$$ $x$ is real,$t>0$, and initial condition is $$u(t^2/4,t)=t/2$$ and found contradictory results:-Parametrizing the given initial curve as follows $x=s^2/4$, $t=s$, $u=s/2$. Characteristic equations are $dx/u=dt/1=du/1$, solving these and using initial conditions, I got solution as $x=u^2/2+s^2/8$, $t=u+s/2$, eliminating $s$ I got $2u^2-2tu+t^2-2x=0$ giving $2u=t+\sqrt{4x-t^2}$, $2u=t-\sqrt{4x-t^2}$. My question is that inspite of conditions of non-existence being satisfied,viz, $P/x'(s)=Q/t'(s)$ not equal to $R/u'(s)$ at the initial data, non-unique solution exists.How to resolve this situation?
Comment: Please use Latex for symbols and equations.
Answer: I agree with your result. This is confirmed below.
$$u_t+uu_x=1$$
Chapit-Lagrange system of ODEs : $\frac{dt}{1}=\frac{dx}{u}=\frac{du}{1}=ds$
A first characteristic equation comes from $\frac{dt}{1}=\frac{du}{1}$ :
$$t-u=c_1$$
A second characteristic equation comes from $\frac{dx}{u}=\frac{du}{1}$ :
$$2x-u^2=c_2$$
The general solution of the PDE on the form of an implicit equation $c_2=F(c_1)$ is :
$$2x-u^2=F(t-u)$$
where $F$ is an arbitrary function, to be determined according to initial condition.
CONDITION : $u(\frac{t^2}{4},t)=\frac{t}{2}$
$$2(\frac{t^2}{4})-(\frac{t}{2})^2=F\left(t-\frac{t}{2}\right)$$
$$\frac{t^2}{4}=F\left(\frac{t}{2}\right)$$
The function $F$ is determined : $\quad F(X)=X^2$ .
This shows that $F$ exists and is unique.
We put this function into the above general solution :
$$2x-u^2=(t-u)^2$$
$$2u^2-2tu+t^2-2x=0$$
This is the solution of the PDE fitting to the specified condition.
This solution exists and is unique since $F$ exists and is unique.
We can write it on the form :
$$u=\frac{t}{2}\pm\sqrt{x-\frac14 t^2}$$
Writing on this form doesn't mean that we now have two solutions. We still have only one solution, the same as before.
This is like the equation of a circle $x^2+y^2=R^2$ written on the form $y=\pm\sqrt{R^2-x^2}$. There is still one circle made of two demi-circles.
On a purely mathematical viewpoint the result is : A solution exists and is unique.
But the conclusion can be different if the PDE is a mathematical model for a physical problem. The use of the variable noted $t$ makes think to "time". If so, we are going outside the pur mathematics to go into physics. In that case some implicit conditions can appear, for example that the terms be real (no complex root for example). Or other constraints such as the time always increasing, or requirement about stability, for examples.
Without knowing the context of the problem (What the PDE is supposed to model, etc) one cannot discuss the existence of solution, in other words if the above mathematical solution is a convenient answer to the question.
Comment: To JJacquelin,I disagree with you.Here is a counter example:-consider following IVP-.  (t+2ux)u_x-(x+2ut)u_t=(x^2-t^2)/2 with Cauchy data x-t=0,u=0.Solving as usual,we get   (x-t)^2=4(u+1/2)^2-1 , from which we obtain 2u=-1+√{(x-t)^2+1},2u=-1-√{(x-t)^2+1}, but only 2u=-1+√{(x-t)^2+1} satisfies initial data.Hence according to you only solution should be combined form solution (x-t)^2=4(u+1/2)^2-1.Any way ,it is half story.You have not answered the existence part.Pleas reread my comments and original question.
Comment: The example that you cite is not comparable to your problem. In the cited example, only one branch of the whole function satisfies the condition. In your case the two branches satisfies the condition. So, there is a unique solution  $2u^2 −2ut+t^2 −2x=0$ which is the whole function (artificially cut in two branches by the solving for $u$ ).
Comment: My answer is very simple. The solution $2u^2 −2ut+t^2 −2x=0$ satisfies the PDE $u_t +uu_x =1$ and satisfies the condition $u(t^2/4,t)=t/2$ . One can check it directly. The unicity of this solution is proved by the method used in my answer. I have nothing to add. Good luck for the kind of answer that you expect.
Comment: U may certainly.But existence part of my question remains unanswered.
Answer: Using the method of characteristics, one writes

$\frac{\text d t}{\text d s}=1$. Letting $t(0) = t_0$ gives $t = s + t_0$.
$\frac{\text d u}{\text d s}=1$. Letting $u(0) = \frac{1}{2} t_0$ gives $u = s + \frac{1}{2} t_0$.
$\frac{\text d x}{\text d s}=u$. Letting $x(0) = \frac{1}{4} {t_0}^2$ gives $x = \frac{1}{2}s^2 + \frac{1}{2} t_0 s + \frac{1}{4} {t_0}^2$.

The parameter $s$ is eliminated by injecting $s = t-t_0$ in the expression $x(s)$ of the characteristic curves. The latter becomes $x = \frac{1}{4}\big( t^2 + (t-t_0)^2\big)$, which is inverted as $t_0 = t \pm \sqrt{4x - t^2}$.
If we inject the equation of the characteristic curves in the expression of $t_0$, we get
$t_0 = t \pm |t-t_0|$.
Therefore, the top sign ($+$) corresponds to times $t\leq t_0$, while the bottom sign ($-$) corresponds to times $t\geq t_0$.
The curves in the $x$-$t$ plane are shown below for several values of $t_0$ (the blue line marks the boundary where the data is imposed).

For example, let us consider the point $(x,t) = \big({5}/{32}, -{1}/{4}\big)$ of the $x$-$t$ plane. From the expression of $t_0$, we find the value $t_0 = {1}/{2}$ which satisfies $t<t_0$, and the value $t_0 = -1$ which satisfies $t>t_0$. Hence, two characteristic curves are passing through this point. The first one carries the value $u = t - t_0/2 = -1/2$. The second one carries the value $u = t - t_0/2 = 1/4$. Both solutions
$$ u(x,t) = \tfrac{1}{2} \big( t \mp \sqrt{4x - t^2} \big) ,\qquad 4x - t^2\geq 0 $$
exist simultaneously. The classical solution deduced from the characteristics is bi-valued everywhere in the region $4x - t^2 > 0$. The problem is not well-posed in the sense of existence and uniqueness.
Answer: Follow the method in http://en.wikipedia.org/wiki/Method_of_characteristics#Example:
$\dfrac{dt}{ds}=1$ , letting $t(0)=0$ , we have $t=s$
$\dfrac{du}{ds}=1$ , letting $u(0)=u_0$ , we have $u=s+u_0=t+u_0$
$\dfrac{dx}{ds}=u=s+u_0$ , letting $x(0)=f(u_0)$ , we have $x=\dfrac{s^2}{2}+u_0s+f(u_0)=\dfrac{t^2}{2}+(u-t)t+f(u-t)=ut-\dfrac{t^2}{2}+f(u-t)$ , i.e. $u=t+F\left(x-ut+\dfrac{t^2}{2}\right)$
$u\left(\dfrac{t^2}{4},t\right)=\dfrac{t}{2}$ :
$\dfrac{t}{2}=t+F\left(\dfrac{t^2}{4}\right)$
$F\left(\dfrac{t^2}{4}\right)=-\dfrac{t}{2}$
$F(t)=\mp\sqrt t$
$\therefore u=t\mp\sqrt{x-ut+\dfrac{t^2}{2}}$
$(u-t)^2=x-ut+\dfrac{t^2}{2}$
$u^2-2ut+t^2=x-ut+\dfrac{t^2}{2}$
$u^2-ut=x-\dfrac{t^2}{2}$
$u^2-ut+\dfrac{t^2}{4}=x-\dfrac{t^2}{4}$
$\left(u-\dfrac{t}{2}\right)^2=x-\dfrac{t^2}{4}$
$u=\dfrac{t}{2}\pm\sqrt{x-\dfrac{t^2}{4}}$
Comment: That solution I have already given.I am unable to understand how to resolve contradictory non-existence of solution and existence of solution  (moreover two solutions).
Comment: I mean that when the problem is viewed as existence problem then we get contradictory answers.Existence test (given in my solution) shows that solution should not exist but routine solving comes up with two solutions.My question is how to explain this happening.


modifying local environment in python

Question: I need to inject same variables into settings.py for multiple django apps.hence i wrote a module which takes in output of local() and modifies. This works but is it the right way to do things?
def enable_theme(theme_name, container):
"""
Enable the settings for a custom theme, whose files should be stored
in ENV_ROOT/themes/THEME_NAME (e.g., edx_all/themes/stanford).

The THEME_NAME setting should be configured separately since it can't
be set here (this function closes too early). An idiom for doing this
is:

   THEME_NAME = "stanford"
   enable_theme(THEME_NAME)
"""
    container["THEME_NAME"] = theme_name
    container['MITX_FEATURES']['USE_CUSTOM_THEME'] = True
    # Calculate the location of the theme's files
    theme_root = container['THEME_ROOT'] / "themes" / theme_name
    # Include the theme's templates in the template search paths
    container['TEMPLATE_DIRS'].append(theme_root / 'templates')
    container['THEME_SASS_DIRECTORY'] = theme_root / 'static/saas'
    container['MAKO_TEMPLATES']['main'].append(theme_root / 'templates')
    # Namespace the theme's static files to 'themes/<theme_name>' to
    # avoid collisions with default edX static files
    container['STATICFILES_DIRS'].append((u'themes/%s' % theme_name,
                                   theme_root / 'static'))
    container['FAVICON_PATH'] = 'themes/%s/images/favicon.ico' % theme_name

#Test case
from theming_utils.template_customizer import enable_theme
THEME_NAME = "sokratik"
PIPELINE = False
MITX_FEATURES['USE_DJANGO_PIPELINE'] = False
DEBUG = True
TEMPLATE_DEBUG = True
enable_theme(THEME_NAME, locals())

Comment: The code you posted doesn't use `local()`. Also, you need to format your code so that it shows up correctly.
Answer: You're not trying to modify a local environment, you're trying to modify the module's dictionary, which you can access by calling globals().
Note: the dictionary returned by locals() isn't meant to be modified.
Comment: that explains a bit of stuff, in case I am actually using globals, is it fine to modify globals in this way??
Comment: It's okay to modify a module's dictionary, I don't know whether or not it's the right way to handle themes in Django.

modifying local environment in python


Redirect call to another iPhone

Question: Can an iPhone redirect a call to another iPhone? For example, if I receive a call on my iPhone from one party, can I tranfer that call to let's say a coworker that uses an iPhone?
Answer: If you go to Settings/Phone/Call Forwarding/ Turn on Call Forwarding then enter the number you want to forward your call to. Note this occurs as soon as the call is received, and you cannot answer first.
Call conferencing would work too. You should look up your specific carriers method to accomplish this. Conference in the third-party, then hang up.
Comment: Could you conference in the third-party, then hang up?
Comment: I would think yes.

Redirect call to another iPhone


WP All Import - Using Xpath to set a select value

Question: I'm working on setting up an import using WP All Import, the idea is to update/add/remove posts within a custom post type which contain ACF fields.
The CSV we are importing contains a column called "Feed ID" which holds data like Apple12343, Banana98799, Carrot2198379, Onion1287361 and so on.
What I want to achieve is to populate an ACF select box value that has options like 'Fruit' and 'Vegetable', depending on the Feed ID value, using XPath. So essentially I need some sort of function that will take the first part of the feed ID (letters only), then assign the select box value based on that. Is this doable?
Answer: Looks like you can use the Variable Repeater Mode (CSV) to import your data:

If your repeating data is stored in a single column in your CSV file, and is separated by a separator character, use this option.

Then create a custom PHP function that would break up each value into the title and ID (Apple => 12343, etc.) and call your function from the text box:
[custom_function({feed_id[1]})]

As for the last part of actually creating a select box from titles and IDs - I don't know how to do that. Hopefully someone can build on this answer. Also please share if you figured it out.


Software that can automatically login to a website, perform tasks and take screenshots?

Question: Does anyone know of software that can be configured to automatically login to a website, perform tasks, and take screenshots at regular intervals? Preferably Mac-compatible.
Answer: Sounds like FakeApp is what you're looking for.
Answer: You can try Sikuli.
Here's a video of it in action, it's actually a really neat tool.
Answer: iMacros can probably do what you need.  We use it in a commercial environment and it is very effective.
Comment: I've been checking out iMacros - I think that I can make it work if I used it in conjunction with a screen capture program
Answer: Since "performing tasks" can mean so many different things, there most likely isn't a program out there, that would fully satisfy your needs. There are programs automatically logging you in (LastPass is a good example), there are programs taking screenshots, but if you want a all-in-one solution you probably need to let somebody write that software for you (or do it yourself).
Answer: If you're willing to script it,watir might do everything you need. Not sure if it does real screen shots or just captures of the HTML though.
Answer: I use AutoHotkey to do this.
This is an example of a script that logs into a website.
http://www.autohotkey.com/forum/viewtopic.php?t=20195


Applying quantum mechanical logic on simple pendulums

Question: I'm in an introductory quantum mechanics course and we just covered Heisenberg's uncertainty principle. One thing that came to mind is are we allowed to estimate the minimum energy of anything, say a pendulum? If I have a mass and a rigid rod of some fixed length, then I know $\omega$. Can I estimate it's 'lowest' possible energy by using: $$E=\dfrac{\Delta p^2}{2m}+\dfrac{1}{2}m\omega^2\Delta x^2$$ where $$\Delta x\Delta p=\dfrac{\hbar}{2}$$
I did this and I got a really small number (which makes sense I guess). But in classical mechanics, we have two equilibrium points (one pointing directly downwards and one standing perfectly upwards). Since I always have a minimum energy, does this mean the unstable equilibrium solution is impossible (in quantum mechanics)? Am I thinking in the right way? If so can I estimate how long it will take for the unstable equilibrium to fall back to the stable point?
Comment: Your expression for the energy is only valid near the minimum.  The unstable position will not produce oscillations in classical or quantum mechanics.
Comment: Related: https://physics.stackexchange.com/q/459403
Answer: There are two things one should say about this:

The unstable equilibrium is already practically impossible in classical mechanics. Or have you ever seen a pendulum standing in upright position and staying there?
Unstable equilibrium solutions should be taken as some kind of mathematical curiosity, but they will not occur in the physical world, since the tiniest perturbation by the environment or whatever will destroy them. So if quantum mechanics now would tell you that it may not occur, well, this would not be any surprise at all. The effects that would make a pendulum fall down from the unstable point are thus surely not quantum mechanical but come from very classical effects like the air molecules hitting the pendulum etc.
(A different thing is if you build a pendulum out of, say, only a couple of atoms, in that case you might be right and it might be quantum effects driving it away from there.)
The Heisenberg uncertainty relation is about the variance of measured quantities. Not more, not less. (If you ascribe an ontological status to it depends on your interpretation.) It should not be overused.
It is true that you can see the following: The value of $h$ is so small that is has no effect in situations where classical physics is valid.


I have a smart contract in Ethereum. Is there a way to migrate it over to Cardano?

Question: I have a smart contract for an NFT in Ethereum and I'd like to put it in the Cardano eco system as well. How can I do that? Is there any 'smart contract bridge' through which I can port it over?
Comment: Since I don't know your Smart Contract I am sorry if I am stating the obvious: you know you don't need a smart contract for minting NFT on Cardano, right?
Comment: Yes. My requirement is that - I need to deploy an NFT collection which will be generated programmatically. I guess my thoughts were to somehow connect it to the Cardano eco system such that the public can view what's in it to be transparent. My assumption was that such a capability would require programmability over a zero code solution.
Answer: You can either rewrite your smart contract in Plutus (haskell) or you can wait for the ERC20 Converter. I haven't heard much about it lately, but the latest status update (October) shows there is progress towards a public testnet deployment:

The team is making continued progress towards public testnet deployment as they parallel track some additional mainnet optimizations. DevOps has completed the first round of testing on an internal environment and is now addressing some fixes prior to redeployment. Once the fixes are confirmed, SingularityNET will do additional testing prior to determining a confirmed release date.

Hope that helps a bit.
Comment: Just a couple of weeks ago there was an announcement about IOHK and Bondly partnering up to create a bridge for Ethereum based NFTs to move them over to Cardano.

https://bondlyfinance.medium.com/io-global-and-bondly-announce-development-of-bridge-from-ethereum-to-cardano-networks-3a829e56b5e9
Comment: A query on the second part of the suggestion: NFTs are minted using the ERC721 protocol right? So does an ERC20 converter help in moving NFT issued on the Ethereum network to Cardano eco system? TBH I doubt it.
My main goal to do this is to save gas fees and eventually sell it off via CNFT platform. Re-minting all of it again seems tedious atm.


How much should I charge for creating a WordPress plugin?

Question: How much should I (working as a freelancer) charge for creating a custom WordPress plugin?
Comment: I think you'd need to provide some more specific information such as what is involved, is it a simple plugin? will it be a product that someone will sell? Etc.
Comment: It is neither too complex nor too straight forward from my perspective. There is very bleak chance that someone would sell it as it will be very custom made.  It will involve creating a simple database table, and creating few options for the client to fill in, and some interface in the main web page.
Comment: It is better practice to lock the cool utilities in addons and give the plugin free with limited features and extendablity, I think it is more profitable.
Comment: The question is very subjective and cannot have a straight answer.
Answer: The short version:
Figure out how much it costs you to eat, go to movies, pay utilities, pay taxes, etc., each month.  Divide that by the number of working hours in a month.  Congratulations, that's your minimum hourly rate.
Get the specs in writing, as detailed as possible.  Then figure out how long it will take you to develop, test, and implement the plugin as per the specs.  Multiply the number of hours the project will take you times the money you need to live.  That's how much you need to charge for your project.  At minimum.
Get the specs in writing, and don't deviate from them unless your time suddenly is no longer valuable to you or you decide you don't need to eat.  Put in writing that deviations from the specs (feature creep) will cost $X per hour additional, where $X is your hourly rate.
Keep in mind that if you're freelancing for a living, you will not have work 100% of the time, so your hourly rate will need to encompass the amount of time it takes you to find more work and close a sale.  So if you're doing this for a living, go back to the first paragraph and add in the average amount of time it will take you to find work and close a contract, then add that to your hourly rate.  That's why many freelancers and contractors will charge less for regular clients or for retainers; they can afford to because they don't have to spend extra time finding the work and negotiating the fees.
Also note that there are other people who will charge less than you.  If you enjoy your current standard of living, do not compete on price, compete on quality and reputation.  So let other people charge less, and make sure your work is good and that you meet deadlines.


First book on algebraic topology

Question: Is there a good book on introduction to Algebraic Topology which is self-contained and does not assume any background in topology, only standard calculus and linear algebra courses?
Comment: Here's a non-recommendation for a first book on algebraic topology:  Edwin Spanier's *Algebraic Topology*.  I know, I *tried* to read Spanier first!  Cheers!
Comment: Since I haven't studied the book in details, I'll leave this just as a comment, but [A First Course in Algebraic Topology, by Czes Kosniowski](http://www.amazon.com/A-First-Course-Algebraic-Topology/dp/0521298644) covers the minimum needed in point-set topology in the first few chapters. Maybe it is worth looking.
Comment: @RobertLewis: +1. As much as I loved algebraic topology, I hated that book.
Comment: @anomaly:  yeah, what a bear!  but it's ***all*** there.  I think it's better as a reference for people who already know most of that stuff, although I still have fond memories of the sections on the Lefschetz fixed point theorem!
Comment: If you can read german check "Algebraische Topologie - Eine Einführung" by R. Stocker, H. Zieschang, it's really good.
Answer: Warning : the following books are not algebraic topology books in the classical sens, but anyway it's impossible to get in AT without any background in topology : these two books will give you the necessary background and go after in the beginning of algebraic topology.
"Introduction to Topological Manifolds" by Lee is very readable and starts from scratch. It covers classic topology (4 chapters), one chapter on CW complex and classic topics in algebraic topology (fundamental group, covering space and groups) with emphasis on surfaces (with classification of compacts surface) with finally last chapters about homology and cohomology.
Another reference is the book of Munkres, Topology, which covers with lot (and lot) of details general topology, and also fundamental group and covering space.
For both, no background is needed (There is an appendix in Lee about group theory, and a chapter consacred to Set theory in Munkres !). For more advanced topics in algebraic topology (homology theory for example, or differentiable topology) I think calculus in $\mathbb R^n$, general topology and abstract algebra are highly recommended.
Comment: I agree too, but first the OP ask a book of introduction to algebraic topology. I don't really think Spanier is really suitable for an introduction. Secondly, he asked no background in general topology, and obviously it's needed for doing algebraic topology, so why not a book which covers both ? In Lee there is only 4 chapters but almost all is used after. I think it would be ridiculous to recommand a normal book on algebraic topology. If he wants learn more, he can still ask again.
Comment: I liked munkres too. Very readable.
Comment: Clearly I did not read carefully (eg at all) what was asked; I now agree with your recommendations. I've deleted my first comment. (Might I suggest a statement, though, that these aren't really algebraic topology books?)
Comment: I edited my post !
Answer: The canonical reference is probably Hatcher's "Algebraic Topology," which in addition to being a very well-written text also has the advantage of being available online for free in its entirety. It stays in the category of CW-complexes for the most part, and there's a self-contained appendix describing enough of its topology to get you through the book. The only drawback I'd mentioned of it is that the more advanced topics (e.g., obstruction theory) covered in the appendices to its individual chapters often assume a bit more background or general sophistication than the rest of the book. It's not really a problem, and it's definitely not a reason to decide against the book, but you will probably notice a sharp difficulty spike if you go through those sections in order.
On the other hand, there's unfortunately no way of getting around the prerequisites in point-set topology. You'll find it easier after the first half of Hatcher, when things get more algebraic, but you should at least be comfortable with basic concepts like connectedness, compactness, metric spaces, various extensions lifting properties, etc. For that, I think Munkres' Topology is the canonical reference, but I can't recommend it to anyone; it's pedantic, tedious, and dull. I can't remember exactly what Lee's Introduction to Topological Manifolds, which N.H. mentioned above, covers in basic topology; still, it's a good book, and I'd recommend reading it regardless of whether you plan on continuing in algebraic topology.
Comment: See this mathoverflow discussion http://mathoverflow.net/questions/40945/compelling-evidence-that-two-basepoints-are-better-than-one for some of the issues behind my own book "Topology and Groupoids", (T&G), issues ignored by almost all other texts. T&G gives good motivation, assumes only some knowledge of analysis, has lots of figures, and exercises, does not do homology, introduces category theory, and includes topics such as orbit groupoids not even ventured into by other texts. It allows paths as maps $[0,r] \to X$, not just $r=1$.
Comment: I ought to give the url http://pages.bangor.ac.uk/~mas010/topgpds.html, which has a link to a £5 e-version. For more on groupoids, see the free download http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html, ad how to fit this with homology theory see http://pages.bangor.ac.uk/~mas010/nonab-a-t.html, with a free pdf, and which discusses history, intuitions,  and motivation.
Comment: @N.H. With this approach, the paths with composition form a category, with associativity, etc. Also it is more intuitive:  if you think of a path as a journey, we are used to journeys of different length, and their composition.   This avoids some proofs students find tricky, and technical, and which do not really convey much. Of course you have at some stage to discuss reparametrization, and the definition of equivalence of paths.
Comment: @RonnieBrown : I'm curious, what is the main interest of allowed path as map $[0,r] \to X$ ?
Comment: @RonnieBrown: Neat, thanks for the link! I'm not familiar with the text (I've used Hatcher when presenting introductory algebraic topology in the past), but I like the approach.
Comment: @RonnieBrown thanks for the explanations, looks very natural presented in this way.
Answer: The question about the first topology textbook has been asked and answered several times but what about specifically undergraduate textbook? Munkres has a good reputation but it's too dry in my opinion for a good undergraduate textbook. Kosniowski, mentioned above, is a very good choice with illustrations on almost every page. The only problem I have with it (and Munkres, and Basic Topology by Armstrong) is that its first topic in algebraic topology is the fundamental group. I prefer homology. The advantages are: (1) you can start with no point-set topology, (2) homology studies topological features of all dimensions instead of just one (cuts, tunnels, voids, etc.), and (3) you can connect homology back to calculus. For a short introduction to homology (with some point-set topology) I recommend  Topology of Surfaces by Kinsey and for a longer one my own Topology Illustrated.

First book on algebraic topology


Messaging platform with public-private key pairs as identifier

Question: Is there any platform available for Ethereum address 0x1d53.. to message 0xcc23..., and so on? It seems like there would be a lot of demand for something like that, which suggests it exists. Off-chain, I guess. I need it for the pairs in Pseudonym Pairs (source code) to agree on a random video channel over something like https://gotalk.to or https://meet.jit.si.
Comment: worst case scenario I'll do it on-chain initially but, doesn't need majority consensus so would be better to have some sort of email-like platform, where messages are stored entirely public for anyone to download, but, only those with the private key could decrypt them. kind of seems like that would already exist.
Answer: Ethmail.cc is ordinary email + secp256k1 public-private key accounts, email format <code>[ETH address]@ethmail.cc</code>. Then there is BitMessage, closer to what I was thinking of, stores encrypted messages publicly but only owner of private key can decrypt a message, https://bitmessage.org/bitmessage.pdf. Ethmessenger.co was built after 6 months of research by Ethereum Foundation Advisors. Status.im almost supports key-to-key messages, the account is controlled by Ethereum accounts, but adds a different identifier than the public key. dChat supports ENS domain names, and is like Status.im controlled by Ethereum accounts, but, does not support key-to-key messaging.


How do you make mortise and tenon joints using power tools?

Question: There is already a question about making mortise and tenon joints using hand tools. It would be nice to also catalog the various ways of making mortise and tenon joints using power tools. Wherever a jig is required for safety or quality of fit, please also include a photo or link to the type of jig mentioned.
Comment: @jmathew that would be great if you could post your comment as an answer and include a brief discussion on how a pantorouter is easier than the other methods.
Comment: Mattias Wendal's panto router seems the easiest way. But it's a complicated jig that can do much more than mortise and tenon. http://woodgears.ca/pantorouter/
Comment: I'm tempted to vote to close this for being opinion based. There are lots and lots of ways to make mortise and tenon joints with power tools, and method that works is correct, so there's no basis for accepting a single answer unless it's exhaustive. It's an old question, so I'll leave it be, but I don't think a new question of this form would survive today.
Comment: I'd agree in general, @Caleb, however, this makes a nice canonical answer for anyone who comes along later asking.
Answer: Copying my answer from the 'by hand' question.
The mortise as the other have mentioned can be done with a hammer and chisel, and drilling consecutive holes to the correct depth will help speed the process up.
If you have a drill press that will make the job easier and you can be very accurate on how deep you drill all the holes.  If you are using power drill, you might want a collar for the drill bit for depth.
Here's an article for step by step directions with pictures for the mortise.

If you have a little extra money to spend you can buy and actual mortising machine, it drills square holes. It has a drill bit with 4 chisels surrounding it.

Cutting the tenon.  There are many different ways to do this.
Of course there is the handsaw, routers etc.  You can also use a table saw.
The table saw can be used several different ways, the easiest would be if you have a Dado blade so you can run the pieces flat across the saw table.
You can do it without the dado as well, just make a bunch of cuts and then clean them up with a chisel.  At the very least you can cut the shoulders of the tenon on the table saw, giving you an nice square cut to work with.
There are also tenoning jigs for the table saw which you cut the face of the tenon with one pass, so a full tenon would be 4 passes.  Kind of like this:
Comment: @rob No problem, I'll get around to editing the other one, or maybe delete it to more closely match the question
Comment: I swear, I didn't even see any other answers when I went to update mine. Now I feel like a cheater linking to the same shop-build tenoning jig... :(
Answer: Long mortises and tenons, like the following, are probably best created with a hand router and a table saw.

Mortise
For the mortise, you will need

A jig or brace to ensure a straight path for your router.

A straight router bit with a flat blade on the top will provide the necessary cut. However, a spiral-fluted bit will make the cut easier.
Obviously, make sure the diameter is less than or equal to the width of your mortise. If it's less then you'll have to adjust your jig or set up a second one corresponding to each edge.

from rockler.com

The router will leave rounded edges to the mortise. In order to square them up, you'll have to use a hand tool like a chisel.

Image from acornhouseworkshop.com
Tenon
As mentioned in other answers, a matching long tenon can be made with a table saw, a dado blade, and a tenoning jig.
Comment: Alternatively with a routed mortise, you could round the corners of your tenon with a file or chisel instead of chiseling the mortise corners square.
Answer: To make the mortise, you can get a dedicated mortising machine:
Image courtesy of Harbor Freight
You can also get a mortising attachment for your drill press:
Image courtesy of LowesNote: Some people feel that these attachments require too much force be applied to the quill and handle of your drill press. I've used my attachment on a bench-top drill press a few times and don't recall any excessive amounts of pressure. If you're making a lot of mortises, you'll probably want to invest in a dedicated mortising machine anyway.
Either machine uses a mortising chisel to cut a square hole:
Image courtesy of Lee Valley
The tenons can be cut on a table saw using a tenoning jig. Here is a commercially available one:
Image courtesy of woodgears.ca
And here is a shop built version:
Image courtesy Wood Magazine. Image links to the instructions to build it.No particular endorsement, that's the first shop-built one Google coughed up
Comment: I think you should add a disclaimer on the drill press mortising attachment. Anyone I've talked to has said those attachments require you to exert a tremendous amount of force on the quill and handle, and that those parts aren't necessarily designed to stand up to that kind of force.
Comment: It's only been... 3.5 years since that comment, @rob. I've got the Delta mortising attachment for my Delta bench-top drill press. I've used it a few times and don't recall having to exert what I felt was an excessive amount of force on it. That's a reasonable warning, though - they may not all be made the same.
Answer: Another alternative is to make and use a horizontal mortising machine.  It's much easier than you might think.
I use mine to make loose tenon mortise and tenon joints.  It's a joy to use.  There were 18 mortise and tenon joints per chair in my dining room table set project.  That's 108 joints.  That's far too many conventional mortise and tenon joints to be practical. So I built this:

The vertical face closest to you holds the sliding fence with the router.
Here is the sliding fence that carries the router:

This is based on a youTube video at https://www.youtube.com/watch?v=knk4vWXI5ZQ0
Notes:
1) The video uses sliding dove tails.  I couldn't get them to slide smoothly so I used drawer slides.  Because drawer slides are very loose, I added four machine screws in each table and adjusted them to ride on steel bars as shown above (just visible on the far left under the handle).  This holds everything level and tight.
2) The router is a cheap Chinese router from a well known tool chain store.
3) I added a foot switch from the same source.  It's very convenient.
4) My first version flexed too much.  I built this version from 3/4" MDF and added a third bolt which runs in the same slot as the primary height adjustment bolt.
5) How to not lose all 5 fingers on one hand at once:  DON'T FORGET TO DISCONNECT THE FOOT SWITCH before adjusting the height of the bit.
"Shop Improvements" from Taunton Press page 163 shows a simpler but less capable alternative.
Comment: If you could add some photos or a video of this, that would be extremely helpful.
Answer: I commented on one of the answers and mentioned Mattias Wandel's pantorouter.  Somebody else said I should add it as an answer, so here it is.
Wandel's pantograph is a more complex take on a typical router pantograph, only horizontal and with plunge so you can do multiple passes and variable depth.
First, Wandel's website (which has lots of fun woodworking projects, btw):
http://woodgears.ca/pantorouter/
Wandel actually started with this simpler (but still pretty nifty) slot mortiser:
https://www.youtube.com/watch?v=sw0FDdIWds4
What I like about both this mortiser and the pantograph, compared to the many other slot mortiser designs I've seen, is that they make it much easier to make larger mortises.  I mess around with viking-style furniture based on the Oseberg bed ( http://www.currentmiddleages.org/tents/osbergbed.PDF ) which requires a lot of mortise & tenon joints that are much, much larger than most of the stuff I can find on M&T.
However, Wandel's slot mortiser only does simple rectangular holes.  The pantorouter can do complex shapes, just like any pantograph, and you can use it to do both mortises and tenons.
Oh, note also that Wandel's pantograph has a 2-1 size ratio, i.e. you cut the pattern twice as big as the actual result.  This is nice because it shrinks any errors in your pattern.
Here's one of Wandel's videos that I found to be the most effective demonstration of the pantorouter.  I added a time parameter to jump to 4:12 where he cuts a tenon and then a matching mortise.  Watch it from the start if you want more detail:
https://www.youtube.com/watch?v=Apovqke6KYQ&t=4m12s
And here's a video where he explains how the pantorouter design works:
https://www.youtube.com/watch?v=8wZ1v4PIsYI&t=40s
He has lots of other videos that go into building it, etc, like this one:
https://www.youtube.com/watch?v=J_72hOY2vPg
One of Wandel's fans started producing (with his permission) pantorouters made from metal.  Last I looked they were $1200 and had to be shipped from Japan, but that was a few years ago.  A quick google just turned up this video Wandel did, explaining how to assemble it:
https://www.youtube.com/watch?v=vy7STrsqzU4
I've always wanted to build one of these, but then again this doesn't look like a trivial project at my skill level.  I mean, the reason I want to build one is that I'm not that good at woodworking :-).  And I'm more interested in the result (building stuff I can use) than in the process.  Don't get me wrong, I'd like to be highly skilled at this stuff, but clearly spending the actual time and energy required to get there has not yet made it to the top of my priority list :-).


Is the sharp dollar (#$) sign the same as load-file-name in Emacs?

Question: I see Emacs use #$ in autoload files, but I don't known if there are any difference between #$ and load-file-name. When I use them in a file, they looks like the same and when I print them by M-: they are both nil. So I did some test but only get more confused. Does #$ behave more like __FILE__ in Python?
Answer: Ask Emacs.
M-x elisp-index-search RET #$ RET

Internally, the dynamic loading of documentation strings is
  accomplished by writing compiled files with a special Lisp reader
  construct, '#@COUNT'.  This construct skips the next COUNT characters.
  It also uses the '#$' construct, which stands for "the name of this
  file, as a string".  Do not use these constructs in Lisp source files;
  they are not designed to be clear to humans reading the file.
Comment: Note that you can do that kind of search when inside an info document by using `C-s`, entering the term and hitting `C-s` repeatedly.


Display custom link in static blocks

Question: I have a few links(containing image and title) to some of my store's pages, this can be a filtered search page, or a category page or any other URL.
I want to manage these link from an static block in a way that admin doesn't have to deal with html coding.
For example, I want them to enter something like this:
{{image_url="/images/blahblah.jpg" href="http://mystore.com/accessories.html?price=-100" title="Accessories under $100"}}
And I want to render each item like below:

Accessories under $100

               Show all products

Any suggestions on how this can be done is highly appreciated.
Answer: You can add like normal image tag used in HTML.

Display custom link in static blocks


How does one discern a calling to the vocation of religious life?

Question: Approaching this from a Catholic perspective, I'd like to ask believers how they came to know that they were called to join the religious life (as a brother or nun), as opposed to the other vocations (priesthood, marriage, single life etc). Rephrasing the same question, what should a believer look for when discerning whether they are called to the vocation of religious life?
Answer: Here are some resources:

Vocation to the Religious State by St. Alphonsus de Liguori
Vocations Explained: Matrimony, Virginity, the Religious State and the Priesthood by A Vincentian Father.
Vocations by Rev. William Doyle, S.J.
Religious Vocation: An Unnecessary Mystery by Fr. Richard Butler, O.P.

See also Pope Pius XII's apostolic constitution Sede Sapientiæ on vocations to the religious life says (part II.) that two necessary conditions must be met when discerning a vocation: that one is called by God and called by the Church.
Answer: I can't answer directly from a Catholic point of view, but the identification of a calling to the priesthood in the Anglican church probably has some similarities. I also know people who have been called to religious communities.
The key thing is that the identification of such a calling is done by the community. Thus you don't show up at a theological college (or presumably a monastry) and ask to be admitted. Instead it is done by approaching your own parish priest, who will also talk to other people who know you, and probably instruct you to do the same. At later stages a Bishop will be involve, and also a group of people who have special skills in discerning such callings.
Discernment of the calling has usually taken many years. There have been retreats and visits to religious communities, and discussion and prayer with the people in those communities, as well as other people.
Comment: I'm not qualified to say whether this corresponds to the Catholic point of view, but it strikes me as being full of wisdom. (And somewhat like the difference between 'falling in love' and an arranged marriage :))
Answer: Why? This will be the question asked most often. "Why do you want to be a...?" And related: "What can you do as an ordained person that you cannot do as a lay person?"
The theology of 'calling' is pretty low in my Diocese (Episcopal). That is to say, it's less of a calling and more of an offering. An offering of where one is and what gifts one has and how God can make use of what you bring.
Here's this.

The saying is trustworthy: If anyone aspires to the office of
  overseer, he desires a noble task. Therefore an overseer must be above
  reproach, the husband of one wife, sober-minded, self-controlled,
  respectable, hospitable, able to teach, not a drunkard, not violent
  but gentle, not quarrelsome, not a lover of money. He must manage his
  own household well, with all dignity keeping his children submissive,
  for if someone does not know how to manage his own household, how will
  he care for God's church? (1 Timothy 3:1-13)
Comment: The call to a 'religious life' isn't the same as a call to leadership, or to ordination.
Comment: A) This question ask for a Catholic response, not an Episcopal one B) you seem to have not interpretted the 'religous life' label the way Catholics do and answered from a Protestant idea of the term. I don'n see how this answers the question that was asked.
Comment: I agree @Caleb, though the answer was still useful, mentioning at least one component that is necessary in the discernment process, thanks Stephen.
Comment: @W1M0 You're welcome. I thought the anglo-catholic tradition of the Episcopal Church might tangentially apply in some regard. We're not as Protestant as Caleb thinks.


Where does Euler write the definition $\gamma=\sum^\infty_{k=1}\left(\frac1k-\ln\left(1+\frac1k\right)\right)$ of the Euler-Mascheroni Constant?

Question: I am writing a research paper on the Euler-Mascheroni Constant when I mentioned this sum: $$\gamma=\sum^\infty_{k=1}\left(\frac{1}{k}-\ln\left(1+\frac{1}{k}\right)\right)$$ which was derived by Euler. I saw this in wikipedia but it doesn't reference Euler's paper. Do you know where Euler writes this identity?
Comment: possibly [here](https://scholarlycommons.pacific.edu/cgi/viewcontent.cgi?article=1042&context=euler-works) (top of p.157), but of course it doesn't use that notation. Someone who reads latin can confirm.
Comment: For future questions of this kind, consider [History of Math and Science Stack Exchange](https://hsm.stackexchange.com/)
Comment: This follows directly from the limit definition of $\gamma$ as $$\sum_{k=1}^n\ln\left(1+\frac1k\right)=\sum_{k=1}^n[\ln(k+1)-\ln k]=\ln(n+1)=\ln n+o(1)$$
Answer: As Matthew Towers already identified in a comment to the question, the relevant publication is:
Leonh. Euler, "De Progressionibus Harmonicis Observationes."
Commentarii Academiae Scientiarum Imperialis Petropolitanae, Tomus VII ad Annos MDCCXXXIV & MDCCXXXV. Petropolis, Typis Academiae 1740, pp. 150-161. (Leonh. Euler, "Observations on Harmonic Progressions", Notices of the Imperial Academy of Sciences of St. Petersburg, Vol. 7 for the years 1734 and 1735. St. Petersburg, Printer of the Academy 1740). A scan of the original publication can be found at the Bavarian State Library. The relevant portion is in §11, at the top of page 157:

Quae series, cum sint convergentes, si proxime sum-
mentur prodibit $1+\frac{1}{2}+\frac{1}{3} ---\frac{1}{i} = l(i + 1) + 0,577218$
Si summa dicatur $s$, foret, ut supra fecimus, $ds = \frac {di}{i+1}$,
ideoque $s=l(i+1)+C$. Huius igitur quantitatis con-
stantis $c$ valorem deteximus, quippe est $C=0,577218$.

Note that Euler uses $l$ in his publications to denote the natural logarithm. My translation, with changes for modern typography:

These series, since they are converging, when they are summed up
approximately, will result in $1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{i} = \ln (i+1) + 0.577218$. If the sum is called $s$, it would be, as we did above, $ds = \frac {di}{i+1}$, and therefore $s=\ln(i+1)+C$. We therefore discovered the value of this constant quantity $c$, which is $C=0.577218$.

In general, when one searches for the first occurrence of a particular identity in the scientific record, one should expect that the historical notation used is quite different from modern notational conventions and preferences, and that it can therefore be quite challenging to identify such first occurrences, especially if one goes back several centuries.