Transverse intersection is a well-defined operation on cobordism classes

Question: Let $M$ be a smooth manifold of dimension $n$, $\textsf{FC}_p (M)$ the set of all codimension $p$ framed cobordism classes of $M$. Just as a technical note, we are only considering compact submanifolds without boundary. I want to show that transverse intersection
\begin{equation*}
\pitchfork: \textsf{FC}_p (M) \times \textsf{FC}_q (M) \to \textsf{FC}_{p + q} (M)
\end{equation*}
is well-defined, i.e. for every $X \sim U$ codimension $p$ and $Y \sim V$ codimension $q$ framed submanifolds of $M$ satisfying $X \pitchfork Y$ and $U \pitchfork V$, we have $X \cap Y \sim U \cap V$.
My work so far: The natural first thing to try is let $Z, W \subseteq M \times [0, 1]$ be compact so  that $\partial Z = X \sqcup U$ and $\partial W = Y \sqcup V$, though even if we perturb our $Z$ and $W$ so that $Z \pitchfork W$, it is not necessarily true that $\partial (Z \cap W) = (X \cap Y) \sqcup (U \cap V)$. Consider for example two "bended" cylinders (e.g. two coffee cup handles) so that they do not intersect in the middle.
Another approach that I was thinking of was using the correspondence $\textsf{FC}_p (M) \cong [M, S^p]$ set of smooth maps $f: M \to S^p$ quotiented by homotopy. We know that every framed manifold is a Pontryagin manifold, e.g. $X = f^{-1} (a)$ for a regular value $a$. My thought was that we look at what transverse intersection looks like on the smooth maps. I would think it looks something like
\begin{equation*}
\pitchfork: (f, g) \mapsto f \times g.
\end{equation*}
Then if $X = f_1^{-1} (a)$, $Y = g_1^{-1} (b)$, $U = f_2^{-1} (c)$ and $V = g_2^{-1} (d)$, clearly we have a homotopy from $f_1 \times g_1$ to $f_2 \times g_2$ since $f_1 \sim f_2$ and $g_1 \sim g_2$, and moreover $X \cap Y = (f_1 \times g_1)^{-1} (a, b)$ and $U \cap V = (f_2 \times g_2)^{-1} (c, d)$.
The issue is of course $f \times g$ is a map into $S^p \times S^q$, not $S^{p + q}$, but this technicality can be looked over if we can find an injective smooth map $\phi: S^{p} \times S^q \to S^{p + q}$, in which case we just post compose the product maps with $\phi$.
Answer: The map $\phi$ you are looking for is not injective. It is the map which crushes $S^p \vee S^q$ to a point. The assumption that $f$ is transverse to the basepoint of $S^p$ and similarly for $g$ implies that $(f,g)$ intersects $S^p \vee S^q$ transversely.


How do you install samsung Kies to an alternative hard drive?

Question: I am trying to install Kies in order to get Ice cream sandwich for my galaxy note 1, my C drive is full and I would like to install on D drive which has plenty of space.
Comment: Kies should be able to be installed on any drive regardless of letter... so what's the issue?
Answer: Assuming your version of Kies doesn't let you specify a path, use mklink.
Creates a symbolic link.

MKLINK [[/D] | [/H] | [/J]] Link Target

    /D      Creates a directory symbolic link.  Default is a file
            symbolic link.
    /H      Creates a hard link instead of a symbolic link.
    /J      Creates a Directory Junction.
    Link    specifies the new symbolic link name.
    Target  specifies the path (relative or absolute) that the new link
            refers to.

So if the default install path was C:\Program Files\Kies and you want to install to D:\Kies, you would create the latter directory and then run mklink /D /J "C:\Program Files\Kies" "D:\Kies" before installing.


"as they may be", "as it may be" meaning and use cases

Question: "Belated as they may be", "expensive as they may be". Can someone please explain the structure of these sentence as to what exactly does "as they may be" mean and how it is used ?
Comment: It's used to grant a premise and then draw a conclusion in spite of assuming the premise. *As expensive **as health insurance may be**, it's still unwise to refuse to buy a policy*. That is, even if I grant that health insurance is expensive (and that may be true or false), it would still be unwise to remain uninsured.
Answer:

Belated as they may be

The above is not a complete sentence. Normally, such phrases are the middle of a complete sentence or the end of a complete sentence. For example:

Please accept my commiserations, belated as they may be.

The adjective "belated" is used to describe the nature of the subject such as the noun "commiseration" in the example above. The phrase "as they may be" is used to indicate that the "commiseration" is heart-felt, even though it is late in delivery.
Another example:

My offers to help, belated though they were, were gleefully accepted.

The example above is slightly different since the phrase "belated though they were" appears in the middle of the sentence. The meaning of the above example is that the offers to help were happily accepted even though they were late or delayed.
Further similar examples (hopefully self-explanatory):

Those few precious memories, treasured as they were, were tossed aside
  in a fit of rage.

In his sorrow, the Emperor stared at those glistening jewels in the
  palms of his hands. Then, as precious as they were, he let those
  precious stones fall into the sea.


What are the STOL features on the Pilatus PC-6 Porter?

Question: What's so special about the Pilatus PC-6 Porter that makes it a world-leading STOL aircraft? How do its features work?
Answer: Quite simple.  Big wings with decent flaps, lots of power.
11.2 lb/hp at gross.  Wing loading of 19 lb/sf.
Comes down to how slow can you fly, and how fast you can get to that speed.  Without exotic high lift devices, it's mostly about wing loading and power loading.  The Pilatus only has to accelerate to a little over 60 mph and there is power to get it there in around 600 feet.  So there you go.
It's STOL, but not what I would call "super STOL".  For that you'd need full span flaps and slats and or bigger wings and a higher power to weight.  Like a Helio Stallion.
The Porter isn't a unique super-plane and it doesn't have any fancy high lift secrets.  It still needs about an 800 ft runway.  It just has a good all around configuration for its job, easy to load, and is simple and rugged.  It's the simple and rugged + good-enough-for-most-short-strips short field performance that's made it successful.
Comment: Although it is done, use of ground beta mode - discing or even reversing props in flight- is a big no-no and is not something you could use to promote the airplane performance wise.  DeHavilland Canada pilots used to do that on Twin Otter demos but after some crashes in the 70s they were told to stop or else.  I'd be surprised at any operator that lets their pilots use less then flight idle until on the ground.
Comment: Don't forget the prop beta range which allows to reverse the prop in flight for very steep approaches.
Comment: Are there any other really good STOL planes?
Comment: Pretty much everything DeHavilland Canada designed between the Chipmunk and Dash 8, DHC 2 thru 7 https://en.wikipedia.org/wiki/De_Havilland_Canada.  The DHC5 Buffalo was 49000lbs and could operate from a football field.  The notable design feature for DHC products was full span double slotted flaps.  They dispensed with LE slats because you have to operate at crazy high pitch angles to exploit the STOL benefits of slats.  DH Canada was the US Army's go-to supplier of STOL utility airplanes up to the mid 60s.


Looking for a tiny GPS device (including battery) that transmits its current position via SMS at a pre-selected rate

Question: Is anyone aware of a tiny packaged GPS device (including battery, suitable for attachment to a pet collar) that can upload its current location via SMS at a predetermined rate? Ideally, the upload rate, phone number and enablement status should be programmable via bluetooth. Note that it should be able to SMS beyond bluetooth range, which should be only necessary for programming.
Comment: Have you searched "GPS pet collar" to determine if any off-the-shelf units meet your requirements?
Comment: Thanks for the 'just right Google search term', which is half the battle, Fred.  The only stuff that popped up with my searches were devices from Amazon and Ebay who source their goods from the Far East.  And there you find language like "Provides non-disturb function, can set a certain period of time mute, prevents the work and other important time to be disturbed. Control the shooting function of mobile phone through anti-loss device and take selfies by remote control.", ill-translated descriptions that hide the fact that SMS only works within bluetooth range, at least as far as I can tell.
Comment: I find that Walmart's 'chinese' can be just as bad.  It can be very difficult to determine exactly what the device can actually DO and what its limitations are from the chenglish.  So, the next challenge is trying to find an actual manufacturer with actual engineering data for the device in question, engineers being less ambiguous than salesmen.  Would anyone happen to know where to find any of THAT info for a typical 'GPS pet collar' with SMS and bluetooth capability?
Comment: Thus, still no actual answer to my actual question.
Comment: I did a different search, using "arduino sms gps tracker" and found a few prospects, but tiny doesn't apply for an instant. https://create.arduino.cc/projecthub/muchika/vehicle-tracking-system-based-on-gps-and-gsm-57b814 is a DIY project using five different boards, not including a battery. There's a link in the link referring to a UK product for off-the-shelf trackers, but I was not able to determine suitability for your objective.
Answer: In 2024, there appear to be a few such collars.  Heres one
Smart Dog Collar

Packed with innovation
LTE-M connectivity: the most innovative and power-efficient network for connected devices.
Smart geolocation using Bluetooth, Wifi Positioning System and GPS for optimal coverage and precision.
AI-based adjustments: the algorithms adapt to your dog for increased precision and personalized insights.
Smart Dog Collar has a built-in SIM card.

It does a lot more than position tracking, such as health tracking, virtual fences etc.
Note, I am not associated with it.


iPhone 4S CDMA updating and activating

Question: I live in Iran and I want to buy a CDMA iPhone 4S.I know that I won't be able to use CDMA network and I have no problem with that.Basically I want to have an iPhone but use it as an iPod because I can only afford the money of a CDMA iPhone.GSM models are much more expensive and I have two other cell phone so I have no problem with not having a network in my iPhone.
Now, I have few questions:
If a CDMA iPhone is updated but not in range of the CDMA network,will it be deactivated ? I mean when I update a running and usable CDMA iPhone 4S which has no network,will it become deactivated after the update ? If it becomes deactivated,is there any way to make it activated and usable without being in the CDMA network range ?
I searched for iOS 8 update for iPhone 4S CDMA but I only found "Iphone 4S" title, not iPhone 4s CDMA, check this link : http://www.iphonehacks.com/download-iphone-ios-firmware
All other GSM and CDMA iPhones and iPads have their own dedicated update but there is only iPhone 4S title,no GSM,and no CDMA.
Does this mean that for iPhone 4S there is only one update that works on both GSM and CDMA versions ?
Comment: I can't answer this question, but I would seriously advise against getting a CDMA iPhone when an iPod Touch can be bought for very little brand new.
Answer: Every iPhone requires a network ID (whether this is a SIM card or eePROM chip or whatever is irrelevant). Essentially, so long as the phone thinks there is a possibility of it getting a network connection, you're fine.

iPhone 4S CDMA updating and activating


Delooping the quotient space $SU/SU(n)$

Question: Let $SU$ denote the infinite unitary group. Does the quotient space $SU/SU(n)$ admit a delooping $X$? One could also ask that this space $X$ sit in a fiber sequence $BSU(n)\to BSU\to X$, but this is not strictly part of the question. Note that $SU/SU(n)$ is not a topological group, because $SU(n)$ is not normal in $SU$ --- but this doesn't prohibit $SU/SU(n)$ from admitting a delooping. Perhaps a geometric construction of a H-space structure can be given by viewing the space as a Stiefel manifold. Note that $SU$ is an infinite loop space by Bott periodicity.
Answer: I'll work with mod $2$ cohomology.  Note that $H^*(BSU(2))$ is polynomial on $c_2$ (in degree $4$) and $H^*(BSU)$ is polynomial on $c_k$ for $k\geq 2$.  Here $c_k$ has degree $2k$ and so $H^6(BSU)=\{0,c_3\}$.  If $X$ exists then it seems we should have $H^*(X)$ polynomial on generators in degrees $6,8,10,\dotsc$.  In particular, $H^6(X)$ should be generated by $c_3$ and $H^{10}(X)$ should be generated by a single element that is $c_5$ modulo decomposables.  However, $H^*(X)$ should also be closed under the action of the Steenrod algebra so it should contain $\text{Sq}^4(c_3)$, which is $c_2c_3$ by a calculation with symmetric polynomials.  This is inconsistent, so $X$ cannot exist.  I would guess that this line of argument can be improved to show that $SU/SU(2)$ does not deloop, but I have not tried to work out the details.
Comment: Thanks. I guess the equation $\mathrm{Sq}^4(c_m) = c_2 c_m$ shows more generally that there's no delooping of $SU/SU(n)$ with a map from $BSU$ whose homotopy fiber is $BSU(n)$.
Comment: Is the story similar for $U/U(n)$?

Delooping the quotient space $SU/SU(n)$


Object Oriented design for PHP application

Question: For our school project, we are tasked to define a design document describing the architecture of a PHP application.
We are free te decide what to include in the document.
Our professor suggested, lots of (UML) diagrams.
He also asked us to consider class diagrams, but with care, as PHP is not fully object oriented.
My question: Is a Domain Driven Object Oriented Design feasible for a PHP application? What to consider when doing OO in PHP? What are the pro's and con's? Any helpful resources on OO in PHP and PHP best-practices?
Answer: IMHO it's pretty difficult to describe the architecture of any application without knowing what the application is supposed to do. All applications (PHP or otherwise) of any complexity look different.
Secondly, PHP5 gives you classes/objects and the usual plethora of OO gubbings - so to describe it as 'not fully object orientated' is misleading I think. If you mean you can take a procedural approach with out being restricted to objects then yes, but if you wanted everything to be an object then that's your choice.
Is DDD feasible for PHP? Yes, of course. A particular approach to architecture is not usually dependent on technology. Best practices, pros/cons of OO design apply to most languages - PHP leaves you pretty free to decide how to structure your code.
You may find this Best Practices talk from the PHP site useful ;)
Answer: PHP can nowadays be described as fully object oriented by choice. It offers everything you need but you are not forced to write OO code.
There are two books which helped me a lot in understanding the OO principles in relation to PHP:

PHP in Action (Manning)
Zend Study Guide for PHP5 (Zend)
Answer: Most OO languages currently in use are not fully object-oriented.  Every language has idiosyncrasies and gotchas.
So I'd say PHP is OO enough for most simple projects.  I worked on the Zend Framework which is designed as an OO class library, with design patterns and such.
One suggestion for PHP is that you should pay attention to its SPL component, which gives you interfaces for many basic classes.
I think it's pretty weak if your teacher said, "put anything you want into the design document, UML diagrams are pretty."  Design documentation is an important but woefully undervalued part of software engineering.  Your teacher should be showing you examples or templates for good design doc.
Answer: OO is first and foremost a design methodoligy.
As such it is possable to come up with an OO design which can be implmented
in procedural langauges. I have seen this done for both C and COBOL projects.
And it has convinced me that nearly all the advantages of OO are to do with design and NOT language implmentation.
So yes you can come up with an OO design with lots of UML (Class diagrams, use cases, swim lanes etc.) and you can implement it in php (using classes or not).
Anyway php is effectively a superset of OO so if you restrict youself to classes
and functions inside classes ( == methods) you have an OO implementation.
The only thing lacking will be interface definitions but it makes very little
sense to define interfaces in a language with such (un)limited type checking.


Skype version says it is older than it is

Question: OS: Ubuntu 12.04
Problem: When I try to login to Skype, it says ¨cannot connect to server¨ - i understand that Skype no longer connects to server when the Skype version is less than 4.3, so my problem is as follows:

Skype Version
When I ask terminal for Skype version, it says the Skype version I have is 4.3
But when I open the Skype application (the only one available) it says it is version 4.0
I have removed and reinstalled it but it just produces the same problem.
How do I solve this problem?
- Thanks!
Answer: Solution: Problem solved after installing software updates and then reinstalling Skype v4.3
Comment: There is no link here, could you please update it?
Comment: There isn´t meant to be a link. I was just explaining how I solved it in case others had the same problem. No need to rate it down!
Comment: Not me, you could explain more in detail about what you did. I think this would be helpful to other users.


Where did my downloaded music on sd card go?

Question: I downloaded all of my amazon music to my SD card to switch to a new device. So I take the SD card with all of the downloaded music put it in my new phone then sign into my Amazon music account and it says I have no fricken music downloaded. I seriously need a solution to this problem before I go ballistic because after waiting for all my stupid music to download just for it to not show up on the new phone I am frickin livid. Keep in mind it shows up in offline music on my sd card on the old device. I NEED TO KNOW
Comment: downloaded songs are stored in internal storage in encrypted form
Answer: I'm not very experienced with Amazon Music, but on other sources, when you download music to an SD card, it stays on the SD card. So most likely, your music will not appear in Amazon Music because Amazon Music doesn't know to look in your SD card for the music. If you use a file explorer, you should be able to find your music on the SD card.
If your phone doesn't come preinstalled with a file browser, ASTRO File Browser works pretty well for me. There are a lot of file browser apps out there.
There might also be an option on Amazon Music to import or show music on the device/SD card.
Comment: Amazon music hides its downloaded files. I cant find them even when trying to view them in the folders.


randomised cron command

Question: I'd like to write a cron command so that a job would execute once at some random time during the week - is this possible without having the crontab modify itself? I've considered writing a function that, based on a random number generator, may or may not execute the task - but I'd like the command to definitely execute and there to be no second in the week that was more likely than any other second...
Answer: One quick solution is to write a cron script that is called once a week
and delays itself for a random time (not longer than the week) before doing the real job,  for example by using the following command (works for bash and zsh)
sleep $(($RANDOM/32768.*60*24*7))m

Answer: Use a combination of cron and at.  Your crontabbed script will contain something similar to:
TIME=$(($RANDOM/32768.*60*24*7))m
at -f /usr/local/bin/scriptfile $TIME

In /usr/local/bin/scriptfile have the commands you want to run.
Answer: A quick (and dirty, and BAD, see comments below) solution to that problem would be creating a bash script which would run everyday as a cron and designed as follow:
That shell script would have a 1/7 chance to run your command each day and would update the timestamp of a file each time it successfully runs (use 'touch' for that).
You would just have to check that the file is >7 days old to decide if you run the script beforehand ('find' can do the job here).
There must be a better way but I'm too tired to see it ^^
update: As Joe pointed this script has a big flaw in that it can (and will eventually) not run at all some weeks. Thus you should not use it but I'll leave it as a counter-example.
Comment: I think this might mess with the probabilities... also there's a small chance that the script doesn't run at all in the week :(
Answer: lacqui is correct, but his explanation is a bit short.
cron:
0 15 * * 1 /home/myhome/cron/schedulerandomjob.bash

/home/myhome/cron/schedulerandomjob.bash:
#!/bin/bash
TIME="now + $(( RANDOM % (60*24*7) )) minutes "
at -f /path/to/your/script $TIME

cron runs once a week, scheduling an 'at' job which randomly occurs during the week.  (nb. There's a corner-case here to watch for... it might be possible for the job to occur at the end of the week and the beginning of the week, which might cause two simultaneous executions.  If it is important, subtract a few minutes from the modulo to be sure.
Answer: I put together a small script called weekrand (looked online somewhere for advice, forgot where it was) that does just that:
#!/bin/bash

FLOOR=1
RANGE=10080 # number of minutes per week

number=0   #initialize
while [ "$number" -le $FLOOR ]
do
  number=$RANDOM
  let "number %= $RANGE"  # Scales $number down within $RANGE.
done

sleep ${number}m
$@

So basically weekrand {some command} {parameters} will randomly execute {some command} with {parameters} between 0 and 10080 minutes, i.e. within a week.
An example crontab line using it:
 0  0    1   *   *      nice -n 10 /usr/local/bin/weekrand /root/jobs/weekly_job

randomised cron command


What about Photosynthesis which uses oxygen?

Question: So for a project I'm working on I need plants which make the air around them toxic to Earth life. A way I had thought of to make this was to make the plants photynthesize with oxygen and release a gas toxic to most non-extremophiles.
Would plants that use oxygen instead of carbon dioxide to photosynthesize be possible?
Comment: I am wondering if when you say "photosynthesize" you mean something quite different from standard photosynthesis.  What do you mean by photosynthesis as you use it here?
Comment: Is there a reason you want to use oxygen photosynthesis to make things toxic? Needing protection against herbivorous predators is perhaps a simpler reason to spew toxic gases around ^^.
Comment: It will not be a local effect, most gasses mixes into the atmosphere too fast.  also plants already use oxygen for respiration.
Answer: Oxygen, said in layman term, is high up in the ladder of free energy for chemicals, while oxides are lower. Because of this oxidation is a spontaneous reaction while the opposite isn't.
Using oxygen as photosynthesis start material would mean finding something with oxygen in it which has an even higher free energy and is still a gas.
As far as I know there is nothing like this. If you want a toxic gas released by plants, just go with CO2 released during respiration: since also plants breathe, they also release it.
Additionally, early photosynthetic organism did precisely create an atmosphere which was toxic for the other living beings, because the oxygen they released forced the anaerobic organism out of their way.
Comment: Fluorine is. Chlorine has a similar oxidation potential to oxygen so could conceivably be made this way.
Comment: @SeanOConnor you can't make chlorine or fluorine out of oxygen, since they are all different chemical species
Comment: You'd need to oxidise fluoride or chloride that the plant had absorbed via its roots.
Comment: Ozone, maybe? It would spontaneously break down very quickly and mix readily into the atmosphere, but it is very hazardous to terrestrial life even in very low concentrations.
Answer: You could try fluorine...
There are very few gases with higher oxidation potential than oxygen. Fluorine is one. It's lethal if at all concentrated.
Your plant would need lots of fluoride in the soil, so would have to grow near fluoride containing rocks, like fluorite ('ite' not 'ide').
Chlorine is also an option; take common salt and oxidise it to chlorine gas.
But why?
Photosynthesis is special because it takes a low energy gas (CO2) and releases a higher energy gas (O2). Most really toxic gases aren't higher in energy than O2. You can probably get whatever you want using normal photosynthesis.
For example, you could A) make something nasty out of carbon dioxide (e.g. carbon monoxide), or B) make toxins without photosynthesis the way many plants do, except gaseous (e.g. sarin, hydrogen cyanide), only using normal CO2 -> O2 photosynthesis indirectly to power it. This option is how plants make 99% of the most lethal poisons that they do make.
An outside option is nitrogen
There's lots of nasty nitrogen containing compounds that could be made if a plant could use it as an input for photosynthesis.
E.g.
Nitrogen + water -> ammonia + oxygen (toxic, corrosive and maybe explosive).
Nitrogen + CO2 -> cyanide + oxygen.


Change Font Size on Blog (Twenty Twelve)

Question: I have a Twenty Twelve child theme. I love the fonts on the site. I am willing to live with the normal font size that Twenty Twelve has on pages like the home page. However, on pages like the blog, I want to have a nice big font that is easy to read (see the size on Medium.com).
The questions is how do I increase the font size on the blog posts only, and not the rest of the site.
Thanks in advance,
Shaan
Answer: Try to add those styles with the CSS class .single or .single-post. Because it's a child theme you'll probably need to use !important
Comment: Thanks, I'll try that. I feel that I might make the font size increase site wide (I know how to do that), but I would have to see. Thanks again.


Converting census data to block groups with regard to their area

Question: I have population data for census blocks and want to convert them to block groups. I know that block groups has an extra digits, but how it will be possible to break down census data between blocks weighted by their area!I have little experience with qgis and have to use it for this purpose.
Answer: The code for the 2010 Census Block contains information from higher level geographies. For instance, "060599800001002" the GEOID for some hotels/motels near Disneyland also contains information on the state (06 > California) the county (06 > 059 Orange County) the Census Tract (980000) and the Census Block Group within the tract (1). So, having information on Census Blocks you will be able to identify their Census Block Groups (060599800001).


What was the purpose behind Daphne collecting data on the wizards?

Question: In the Fairy Tail anime, what was the purpose behind Daphne collecting data on the wizards? Was it just to keep them busy fighting the Lizardmen while she destroyed Magnolia, or was she planning on using the data in some other way?
Answer: I believe that she was collecting data on wizards so she can find a dragon slayer worthy of her invention (the fake non-working dragon, i'd like to call it) to make it work and show the people back in her village that dragons are real and that she was not lying when she told them that she saw one.
And for the lizard men, I believe that she used them to distract the Fairy Tail wizards and focus on putting Natsu in her invention using Gray, so it can work. And I believe that she did not want to destroy Magnolia and do some evil stuff. She just wanted to prove that dragons are real.


Combining Textures with baking

Question: i am trying to combine tiled textures of edited peach castle from Mario 64.
H read i need to bake it, so i tried built in bake, but some parts become black.
I also tried principled bake addon, but it exports only 1 texture somewhy.
Am I making mistake somewhere ? or is there some another possible way ?
here is download of my blend file.
here is how the texture tiles look like:
Answer: hello is so easy just follow this steps:
1- add a mix node for your images you want to mix, and plug it to principled shader.
2- set the render sampling to 1 , and tile size to the size of your image.
3- set the bake option to diffuse, and uncheck direct and indirect, and choose a margin size (i recommend 1024px= 4px, 2048 px = 8 px, 4096px = 16px).
4- and then bake your image it should take a few seconds...also if your textures/materials are not in the same uv map it wont bake properly...

Combining Textures with baking


Semidirect Products of the form $(\mathbb{Z}_p \times \mathbb{Z}_p)\rtimes_{\phi}\operatorname{GL}(2,p)$

Question: What are the different (non-isomorphic) semidirect products $(\mathbb{Z}_p \times \mathbb{Z}_p)\rtimes_{\phi}\operatorname{GL}(2,p)$, when $\phi \colon \operatorname{GL}(2,p)\rightarrow\operatorname{Aut}(\mathbb{Z}_p \times \mathbb{Z}_p)$ is injective homomorphism? ($p$ is any prime).
Comment: Ehr... $GL(2,p)$ *is* the automorphism group of $\mathbb{Z}_p\times\mathbb{Z}_p$, so the only $\phi$s are the automorphisms of $GL(2,p)$ itself. All those are isomorphic, you are just looking at the holomorph of $\mathbb{Z}_p\times\mathbb{Z}_p$.
Comment: @Arturo: But I could not convince that two different injective homomorphisms from $GL(2,p)$ to $Aut(Z_p\times Z_p)$ will give isomorphic semidirect products; the well known result is that if $H$ is cyclic, then any two monomorphisms $\psi_1, \psi_2\colon H\rightarrow Aut(N)$, s.t. $\psi_1(H)$ and $\psi_1(H)$ are conjugate, will give isomorphic semidirect products of $N$ by $H$; but in this example $H=GL(2,p)$ is not cyclic, I could not apply the criteria stated.
Comment: @user9332: You don't need that. You are trying to compare $K\rtimes_{\phi}H$ and $K\rtimes_{\phi\circ\psi}H$ where $\psi\in\mathrm{Aut}(H)$. These two semidirect products are always isomorphic, no matter what $\phi$ is.
Comment: @user9332: Note: an "injective homomorphism from $GL(2,p)$ to $\mathrm{Aut}(\mathbb{Z}_p\times\mathbb{Z}_p)$ Is just an automorphism of $\mathrm{Aut}(\mathbb{Z}_p\times\mathbb{Z}_p)$. The two groups are isomorphic and finite, so an injective homomorphism is just an automorphism. Perhaps this is what is tying you up in knots?
Answer: The automorphism group of $\mathbb{Z}_p\times\mathbb{Z}_p$ is isomorphic to $\mathrm{GL}(2,p)$ (view $\mathbb{Z}_p\times\mathbb{Z}_p$ as a two-dimensional vector space over $\mathbb{F}_p$, the field of $p$ elements). So your $\phi$ is just an automorphism of $\mathrm{Aut}(\mathbb{Z}_p\times\mathbb{Z}_p)$.
If $\phi$ is the identity, then you have the holomorph of $\mathbb{Z}_p\times\mathbb{Z}_p$, where the holomorph of $G$ is $\mathrm{Hol}(G) = G\rtimes \mathrm{Aut}(G)$, with the obvious action.
And so the question comes down to the following: if $K\rtimes_{\phi} H$ is a semidirect product, and $\psi\colon H\to H$ is an automorphism, is $K\rtimes_{\phi\circ\psi}H$ isomorphic to $K\rtimes_\phi H$?
The answer is yes. Define $F\colon K\rtimes_{\phi}H\to K\rtimes_{\phi\circ \psi}H$ by $F(h,k) = (\psi^{-1}(h),k)$. This is trivially a bijection, so we just need to show that it is a group homomorphism.
If $(h,k),(y,x)\in K\rtimes_{\phi}H$, we have:
$$\begin{align*}
(h,k)(y,x) &= (hy, k^{\phi(y)}x).\\
F\bigl( (h,k)(y,x)\bigr) &= (\psi^{-1}(hy),k^{\phi(y)}x).\\
F(h,k)F(y,x) &= (\psi^{-1}(h),k)(\psi^{-1}(y),x)\\
&= \bigl( \psi^{-1}(h)\psi^{-1}(y), k^{\phi\circ\psi(\psi^{-1}(y))}x\bigr)\\
&= \bigl(\psi^{-1}(hy), k^{\phi(y)}x\bigr)\\
&= F\bigl( (h,k)(y,x)\bigr).
\end{align*}$$
So $F$ is a group homomorphism, hence an isomorphism.
Applying this to the particular case you have, there is exactly one such semidirect product, isomorphic to the holomorph of $\mathbb{Z}_p\times\mathbb{Z}_p$.


I need to set up a sftp server, that could use different keys, and use different directories for the same login, depending on the ip used

Question: I got a problem, that I cannot solve myself. I tried to google it, but no satiscactory solution that i could find.
I have a server that is available with let's say 3 different IP addresses (A,B,C), and a user login lets say "user".
I need to setup an sftp server that:
when connected with IP A, the SFTP server will announce itself with Key A, when connected with B, announces itself with key B, and so on.
But that is not the end, of the problem, I want to set it up, so when a client tries to connect to "user" with IP A, it would use directory A for accessing user files, when connected with IP B it would use direcotry B, and when connected with IP C, then it would use directory C.
I thought of proftpd with sftp mod on, but I got stuck on how to configure directories, that would be accessed with login "user".
for eg.
if client tries to access file:
user@A:file.dat
real pathname would be directoryA/file.dat
if client tries to access:
user@B:file.dat
the real pathname would be directoryB/file.dat
and so on...
Now the question is, how to set it up?
Comment: multiple instances of sshd bound to the three ips would probably do this.  If you are using keys to connect, I notice you can specify environment variables within authorized_keys, and may be able to affect the home directory of the connecting user.
Comment: yes, that I considered,but I will have more than 3 ips, and unfortunately I will have to configure more and more with time. Running multiple instances of ssh would be kind of problematic... And yes, I will have a key authorization...
Comment: Do they have to use the same private key with all ip addresses? user@A, user@B, user@C it should be the same private key?
Answer: Your proftpd.conf for this would, I think, look something like this:
<IfModule mod_sftp.c>
  # Virtual host configuration for server A
  <VirtualHost a.a.a.a>
    Port 22
    SFTPEngine on
    SFTPHostKey /path/to/key/A

    # Restrict members of group A to this directory
    DefaultRoot /path/to/directoryA groupA
  </VirtualHost>

  # Virtual host configuration for server B
  <VirtualHost b.b.b.b>
    Port 22
    SFTPEngine on
    SFTPHostKey /path/to/key/B

    # Restrict members of group A to this directory
    DefaultRoot /path/to/directoryB groupB
  </VirtualHost>

  # Virtual host configuration for server C
  <VirtualHost c.c.c.c>
    Port 22
    SFTPEngine on
    SFTPHostKey /path/to/key/C

    # Restrict members of group C to this directory
    DefaultRoot /path/to/directoryC groupC
  </VirtualHost>
</IfModule>

The key part of making the above work is to use the optional group parameter of the DefaultRoot directive (for more info, I recommend the Chroot howto).
The user name "user" would be configured slightly different for each of your virtual hosts.  For server A, "user" would be a member of group A.  For server B, "user" would be a member of group B.  And for server C, "user" is a member of group C.  If you did not want to use chroot restrictions for any reason, you could use the DefaultChdir directive instead; this simply places the authenticated client at the requested directory at the start of their session, once they've authenticated.
Hope this helps!
Answer: You could try Sysax Server. It is not free but gets the job done.


Is it unprofessional to order food after an interview?

Question: I'm applying for a restaurant that also is my go to breakfast spot. The interview is early in the morning and I was thinking of knocking out 2 birds with one stone and ordering a bite to eat after the interview is over but I don't know if that could be seen as unprofessional or make me look bad in some way.
Comment: If that is concern, why dont you just get it some other place for one day?
Comment: It's worth, and I mean really worth, to be absolutely sure you want to apply there, work there or be rejected, if you plan to keep going there for breakfast.
Comment: Seems like it would count in your favor.  You aren't applying for some random job, you are applying at a place that you really like.
Answer: If you've been going there for a while then it seems perfectly normal to eat there afterwards - as long as it doesn't look like you're spending an excessive amount of money or leaving an unusually large tip as a slightly indirect kind of "bribe".
But it's worth considering that if the interview goes badly, it might be a bit awkward...
Answer: If you have to ask, you already know the answer. Avoid it. Get an early breakfast or late one or carry a breakfast energy bar. There are several other alternatives to avoid eating breakfast at the same place without spending additional time or money.
Answer: I would say that is not problem. The main reason is that you wrote that "that also is my go to breakfast spot". Most workers at that restaurant already know that you are a regular customer. They like the fact that you enjoy their food, and appreciate your interest in their restaurant. Maybe, even the manager already knows that you like the food/restaurant.
I don't see why you have to go somewhere else for breakfast on the interview day while you already eat breakfast regularly at that restaurant.
It is just another day, and another breakfast at your favorite spot (regardless of the outcome of the interview). If you don't get a job at that restaurant, you will eventually get another job somewhere else. It's no big deal either way.

Another way to think of this is: Would that restaurant rather lose 1 customer on the day of his interview ? While losing 1 order is not a big deal for a restaurant, they would rather not losing any customer any day.


Generating different number of random points for features using iteration with tool parameter values in feature attribute table using ArcPy

Question: I want to generate a certain number of random points in N number of zip codes. The number of points to be generated for each individual zip code is stored the attribute of the feature class of all state zip codes, field type = Long. There is also a field with a unique ID for each zip code. This unique ID is a 5 character string.
This is the Python script I wrote to accomplish the task. The code throws multiple errors.
import arcpy # Import ArcPy site-package and os modules

fc = r'C:\ArcData\2018Cases\ZCTA_Cases.shp' # Path to input feature class

fields = ['id2','Num'] # Fields to be searched. id2 is zip code. Num is the number of points to be generated in the zip code

p = r'C:\ArcData\2018Cases\\ZCTAScript_Results' # Output Path

scur = arcpy.da.SearchCursor(fc,fields) # Create a searchcursor object, which consists of rows of data. Each row will be a tuple of (id2,Numcase)

for row in scur: # Iterate scur
    query = ' "id2" = row[0]' # Query used to select current zip
    selection = arcpy.SelectLayerByAttribute_management(fc, 'NEW_SELECTION', query) # Selection of current zip
    arcpy.CreateRandomPoints_management(p, row[0], selection,'', row[1]) #Create random points for each
    # row in scur using id2 as output name and Num as number of points

del scur # Delete the cursor to release schema locks

This code is based off of code posted by a previous user in response to a previous question that I asked on this issue that was placed on HOLD. The code the user provided did not throw errors but it did not produce the desired result; it generated random points in the full feature class (all zip codes in the state) extent not in the extent of a given individual zip code. Here is that code:
import arcpy

fc = r'path/to/feature/class' #path to input feature class
fields = ["ID","PointNum"] #the fields you want to search
p = r'output/path' #output folder or gdb

scur = arcpy.da.SearchCursor(fc,fields) #create a searchcursor object,
#which consists of rows of data.  each row will be a tuple of (ID,PointNum).  there will be N rows.

for row in scur: #iterate scur
    arcpy.CreateRandomPoints_management(p, row[0], fc, '#', row[1]) #create random points for each
    #row in scur using ID as output name and PointNum as number of points

del scur #delete the cursor to release schema locks

My code tries to resolve the issue by selecting the individual zip code that is being read by the search cursor and setting the constraining extent of the random point tool to that zip code. I cannot figure out how to write the code to accomplish the desired task.
Comment: You mention that your code throws errors. Could you please [edit] your post to include the errors you are receiving?
Answer: arcpy.CreateRandomPoints_management has an input parameter number_of_points_or_field. Input the field name containing your point count for this parameter.
Example:
arcpy.CreateRandomPoints_management (r"OutPath", "OutName", "PolygonFeatureClass", "", "NumberField")

Results:


Lengthening in-flight evaporation time of water droplet in air

Question: How one can increase the in-flight evaporation time of sprayed water droplets in air without changing the thermodynamic conditions of the ambient air ( i.e. RH, T ). For instance mixing water with some chemical additives (non-toxic) that does not change the property of water so much.
Answer: I guess your question is how to increase evaporation amount because the time is the droplet traveling time.
To increase evaporation amount without changing air condition, followings can be considered.

reduce droplet size: the evaporation rate is proportion to $\frac {1}{D^2}$, where D is droplet diameter.
increase droplet speed: this can increase convection heat transfer so to keep the droplets' temperature up. Otherwise evaporation can cool down the droplet and thus reduces its temperature.

same as above, high speed can also displace vapor so to reduce partial pressure, which is also good for evaporation.
if you want to add something to water to increase its evaporation rate.


Using "aligned" environment with optional argument in LyX

Question: I would like to align the bullet point to the first line of equations in an "aligned" environment, rather than the default of a middle vertical alignment (see image). I know this can be achieved by adding the [t] optional argument to \begin{aligned}, but there seems no easy way to do this in LyX. How can I make this work without typing everything in raw latex code (ERT)?
Comment: @egreg I do use tex editor for collaborative projects, but would prefer to keep LyX for stuff where I don't need to share the code as I still find the instant math/table display indispensable.

@scottkosty It should be `\begin{aligned}[t]`; I have updated the question to make this clear.
Comment: @egreg Is it a general advice or do you have a non-LyX solution? In the second case, I think the OP could use ERT.
Comment: Welcome to TeX.SX! Did you consider not using LyX?
Comment: Optional argument to `\begin{itemize}` or to `\item`? If the second, you can go to Insert > Custom Item.
Comment: There is a way to do it with latex code (that is, using `\begin{aligned}[t]` as I mentioned) - the problem is really that my equations are quite a lot more complicated than `3y+4=22` and it will be a mess when viewed in the LyX editor if I type everything in ERT. I just need LyX to put in that `[t]` at the appropriate place.
Answer: solution 1 (recommended):

Place the cursor in the aligned environment.
Go to Edit > rows & columns > top.

Or see the shortcut listed in when you do the menu, which with the default cua bind is: Alt + M, W T.
The shortcut works with "T" for top, "B" for bottom, or "M" for middle.
Note that the LyX display and PDF output both change:

solution 2 (hackish, not recommended, but more general):
Alternatively, you can open the .lyx file in a text editor and add the [t]. This is not recommended because you should only use LyX to edit .lyx files. But in the case of math, sometimes it works. If you follow this approach, you should always open the resulting .lyx file from the terminal (if on Linux, just type lyx file.lyx) to see if there are any parsing errors that show up (these are not reported in the GUI).
Here is the resulting .lyx file, in 2.2.x format:
#LyX 2.3 created this file. For more info see http://www.lyx.org/
\lyxformat 508
\begin_document
\begin_header
\save_transient_properties true
\origin unavailable
\textclass article
\use_default_options true
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding auto
\fontencoding global
\font_roman "default" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\graphics default
\default_output_format default
\output_sync 1
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 1
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header

\begin_body

\begin_layout Itemize
\begin_inset Formula $5x+6=10$
\end_inset

\end_layout

\begin_layout Itemize
\begin_inset Formula $\begin{aligned}[t]3y+4 & =22\\
3y & =18\\
y & =6
\end{aligned}
$
\end_inset

\end_layout

\end_body
\end_document

Comment: Thanks! It's easy to overlook options in the Windows toolbar. With this, I find that it is worth bringing out the Table toolbar at the bottom (View > Toolbars > Table (auto)) to avoid going through the menu search.
Comment: As an alternative to editing the .lyx file externally, you can copy the part of the math expression from the LyX window to an external editor, do the edit there and then paste it back into the LyX math environment. This will be parsed automatically, without risk of breaking the whole file or need to reopening LyX.


! LaTeX Error: Unknown float option `d'

Question: I have two tables in an article written by somebody else which compiles fine with TeXLive 2013, but after an upgrade to the 2015 version xelatex hangs at them. Pressing enter the file still compiles and looks fine on first view, just I'm wondering what the d option is/was, if I can just delete it, or if I would be missing something. The table environment starts \begin{table}[htdp]. If I get it right, h means to place it where it has been defined, t means the top of the page, p means that it should have a page of its own (which the second table, 15 rows long, doesn't have), but so far I didn't find a d option of floats.
Comment: I do not know it. Maybe something custom. The only parameter which is missing here is `b` for bottom. Just delete all of them and see, where it floats. You may adapt that behaviour later on.
Answer: there isn't any float option d.  however, until the version of latex on tex live 2015, unknown options were simply ignored.
effective with tex live 2015, options are checked and unknown ones are flagged as errors.
Comment: Where did you learn this? ;-)
Comment: @egreg -- it was in (i think) frank's discussion.  *somebody* mentioned it this afternoon.

! LaTeX Error: Unknown float option `d'


No hot water in faucet where return line for recirculating pump is installed

Question: Just had a recirculating pump installed. I have only a trickle of hot water at the single handle control faucet where the return line is attached when I turn off the cold water supply. What could be the cause? Is the faucet bad or do we need some kind of valve? Cold water mixes at the faucet and sends cold down the return line no matter if pump is on or not.
Comment: "A trickle of hot water"; does this mean that a) you open the faucet all the way to hot and you only get a trickle, or b) you get a small burst of hot and then you get cold, or c) you only get hot if you open the faucet to a trickle; any more and it becomes cold?
Comment: Open the faucet and I only get a trickle of hot. No burst of pressure. I turned the supply to the cold off so only hot going to the faucet.
Comment: I thought about your question and am amending my answer. When the cold supply is on the faucet gets hot for a count of three then goes cold and stays that way no matter how long you run it and the water going down the return line turns cold as well. With the cold supply off everything is hot but you only get a little water out of the faucet. Seems like all the hot water is going down the return line and not into the faucet.
Answer: "A trickle of hot with the cold turned off" is utterly normal for any modern fixture with a built-in anti-scald valve arrangement, which responds to low cold water pressure by blocking hot water flow.
If cold water is flowing from the faucet to the hot water circulating loop, it sounds like you need a check valve, or if you have one it's backwards, in the wrong location, or not working.
Comment: The only place cold water could mix with the hot at this faucet is at the faucet itself. Does that mean the faucet is malfunctioning? Is the "t" junction for the return line (installed at this faucet) malfunctioning? I can't seem to get the plumber who installed it to come and troubleshoot. I appreciate any help.


Is it a bug or a task when something doesn't work, yet, in development process

Question: We usually have this dilemma in our team.  Sometimes, in order to implement a task or a story we find out that the system must be in a specific state.  For example, a specific system configuration has to be made beforehand.
The task / story can be completed and it is working as specified on it with the proper configuration in place.  Note that the configuration is not directly related with the task.
Next, we have to create a new ... ??? ... something for the process of generating that configuration file.  This is where the problems appear.  Some say that it is a bug others say it is a task or an extra feature.
So, where is the limit between bugs and tasks in the development phase?  Should we even consider something a bug if all the tasks are working as stated in their definitions?  Can a thing be considered a bug because one compares it to the current (unstable) state of the system?
Short example:

A feature requires configuring a communication service for a specific
operation.
In the process of the implementation the team discovers that the service requires the hostnames of the pears to be resolvable to an IP address.
The team adds the hostnames to the DNS server (or hosts files) and continues implementing the required feature.
After the initial feature is working, a question is risen. Should the sysadmin configure the DNS or hosts file or should our application do it automatically?

An automatic solution is possible. So a decision is made to implement it.

... here start the discussions ... is this a bug or an extra feature / task?

PS: I know that I mixed feature / task / story in the question.  It is intentional.  I am interested in separating bugs from the rest.  Doesn't matter what the rest means in a particular case.
Answer: I would call this a task. If I understand you correctly, it is meant to enable a new feature, so it is not a bug fix - otherwise everything should be called a bug.
If the change made by this makes a meaningful difference to end users (independent of the main feature it is meant to support / enable), you may consider calling it a (sub)feature.
All in all, no need to agonize too much on terminology, the main point is to get it done :-)
Comment: so why not call everything a bug?
Comment: @jk., I think there is a clear difference between bugs and features, which is meaningful and useful for both customers and developers. Calling everything a bug may demoralize developers in the long run (who likes to work on a product full of bugs?), and turn away customers (who would buy a product full of bugs?), while I can't see any benefit of it.
Comment: @jk  I like that. Bug 000001: The system doesn't exist.
Answer: Don't get hung up on what to call it -- does it really matter? It's something that needs to be done, so write a story so that the work gets done. If you are an agile team you have the power to call it whatever you want. Come to a consensus as a team then start worrying about more important things.
Answer: I would say that from the moment something doesn't work to spec, or is simply broken, it is a bug.  Anything else is a task/feature/story, in other words: something extra you add to the program.
You could also introduce the concept of a 'change': not really fixing something that is broken, not something new you add, but changing how something works (usually as the result of a change in requirements).  But that's three types of 'todos', so a change would also be a task.
Answer: I'm actually with @pleinolijf and @Péter Török on this: it's only a bug if the software isn't working according to the spec. A specification error that wasn't caught in the design or initial development phase may warrant a spec change and subsequent code changes, but generally speaking, is not a bug.
Generally speaking, a "task" is actually the most generic type of issue in most trackers, and is useful when there is no other fitting type of issue. Anything else (change request, bug, requirement, feature request, gizmo banana, ...) is actually a specialization of the "task" issue type. This means that if there is a more appropriate type of issue available, you should think twice about using "task". Bugs should also be reasonably limited in scope, but of course sometimes it's hard to tell what the scope of a particular issue will be before having dived into it.
Hence, generalizing, the question really becomes "does the lack of a feature constitute a bug?". The feature in this case is the ability to set up, in an automated or user-friendly manner, the prerequisites for specific functionality which in turn is laid out in the spec. Since the base functionality is already there and works properly (according to the requirements laid out in the spec) without the change that is being discussed and without requiring workarounds during use, assuming the spec didn't call for an easy set-up process specifically, I would argue that everything that is currently in the software works the way it is supposed to. Hence, not a "bug".
What you are talking about is the addition of new functionality (automated set-up of prerequisites), which in general terms has a pretty high bar for being considered a bug in my book.
About the only way I could consider something like this to be a bug is if the specification states that there must be no manual set-up required. Otherwise, it's a specification omission, which calls for the spec to be updated with the newly discovered desired functionality and for it to be developed along the same lines that the original functionality was (the lack of which probably wasn't considered a bug).
Answer: During the development process, something is only a bug if the programmer has ticked it off the TODO list and thinks that it works. Not if the program doesn't match the spec yet.
When the specs change (i.e. a new rule "Program should do X"), that doesn't mean the program suddenly has a new bug ("doesn't do X yet").
Answer: Your question hits a lot of people very squarely where they live, in a place that can be pretty painful.  Bug is not a very precise technical term, but it certainly has a lot of emotional baggage.
Where you work, do people consider features to be planned improvements, and bug fixes to be unplanned improvements?  When a developer created code with bugs under the crunch of an all too short schedule, is he or she called back to be accountable for work that might not have been as thorough as needed?  As the expert on the code, do people give kudos for a rapid and responsive solution?  Do habitual under estimators have consequences after taking credit for features and for being fast, even though finding and fixing their bugs was very frustrating for testers and customers, and very time consuming for developers working on maintenance?
Of course they don't.  The more bugs we have, the less pride of workmanship we have, the less accomplished our team.  If you are working on features, you must be trusted and skilled.  If on bugs, not so much.  Features get a thank you and a party when they are done.  Bugs get the silent treatment or a retrospective that discusses how late the release was because we had so many bugs.  Maybe where you work the retrospective talks about how the features unfolded into additional unanticipated functional and systems requirements that were not part of the estimate but were resolved with overtime and heroic efforts from team members?
Making a feature is a task.  Fixing a bug is a task.  What we call bugs are often defects that relate to features we said were done, or missing parts that are due to incomplete understanding of functional or system requirements (or in Agile, user stories or use cases that are incomplete or missing alternative flows).
If our customer visible code is constantly constructed in advance of the underlying support, this is a design or project management problem.  We have TDD and unit testing, so ideally, we can be pretty thorough in our testing and pretty selective about exactly when we expose features through the UI to testers, customers, or product management.
Projects often use rapid UI prototyping to show a user interface that has no code behind it.  It does not do development any favors if product management believes that 80% of the work is done when that demo is shown, but the project continues to run for a long time.  Weigh carefully how far you let your prototypes run ahead of your field ready product.
Agile aims to break the contract mentality and makes collaboration using prototypes more palatable.  The relationship and communication between developers and stakeholders needs a high degree of give and take.  It helps to methodically manage requirements using a burn down list or other way to limit scope and shorten the time line that is subject to estimation.
Part of our problem is how we track progress.  If we have features described by percentage complete, we essentially take credit for something before it is accomplished.  Estimates percentage complete are extremely unreliable.  If we need to show progress, we should break things down to the level where we can say something that is considered important in our project that stands alone as a cohesive object that provides functionality is completely done.  Instead of partially complete milestones, only use fully complete inch-pebbles.
For the work that you describe, if it brings more pride and motivation into the team, I definitely vote for calling it a task and not a bug.
Answer: What is the difference between a "bug" and a "task/new feature"?
I define a "bug" as something you have to fix/implement for free (the software provider has to pay the costs).
A "task/new feature" is something the customer has to pay for.
With this definition a customer might see every "issue" as a bug because he will get it fixed for free. The software provider on the other hand wants to get paid for his development.
Your example

Should the sysadmin configure the DNS or hosts file or should our application do it automatically?
  An automatic solution is possible. So a decision is made to implement it.

is a classical feature creep.
For a fixed price project the solution for this dilemma is a contract that defines which features are included in the product and which are not.
Every contract-feature that is missing is a bug.


Item and ability visit on the same person

Question: Do roles like stalkers and harlots see two separate visits if a player visits the same player with an item and their ability at the same time?
Answer: Stalkers and Harlots identify where people go, not what they do
If a stalker follows a person that makes two visits to the same target, they would only see one target, and thus only receive report of that single target. Their target only went to a single house (that was not their own) that night.
Similarly, if a person visits themselves as one of the two targets, the stalker will only solely identify the third party as the visited target.
The harlot can identify a self-visit. But, like with the stalker, multiple visits by the same individual are not seen separately. The harlot only observes who visited a place, not how many times or how many observed individuals.
A good reason for this: loops
If this were not the case, in large games it may be possible to do strange things in the game by generating very large reports by (ab)using the fibonacci sequence.
If a pair of harlots starts observing a multi-using person, and then a series of stalkers starts observing eachother, you would get 2, then 2, then 4, then 6, 10, etc. multiples of the same player in the report with each additional stalker/harlot. That would quickly get very unwieldy. (And very confusing).
Comment: has this changed? you used to be able to "hide" visits by using multiple items and stalkers/harlots would see you visit the same person twice, was a good way to hide a shift.
Comment: If that's true, that would be a bit of a bug: the stalker's description is that they follow you around and find out who you visit. If you could mask one visit with another that'd make no sense. The harlot checks who visited someone, so should only see one of the two?
Comment: I haven't played since March/April so this may have changed, it used to be that each action (night action and items) was treated as a seperate visits. So with enough items a stalker could see you visit someone 2 or 3 times, same with harlot. So. You could have multiple visits to multiple players, and so if you shifted it wouldn't be blatantly obvious from the visits


How free is BSD / CC-BY usage?

Question: I looked at blendswap.com where there are models that I want to make walk along a wall in this level.
AFAIK I can take this file and sell it or did I misunderstand licensing?
Answer: Th CC-BY 3.0 terms are pretty clear in this regard:

You are free:

to Share — to copy, distribute and transmit the work

to Remix — to adapt the work

to make commercial use of the work

Under the following conditions:

Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).

So yes, you can sell the CC-BY work from someone else, unmodified or modified. You just have to credit the author. And you don't have to release your work under the same license (the CC license which requires that is CC-BY-SA).
The BSD licenses (there are multiple of them) also allow you to use the work, even commecially and even under a different license. The difference is in the attribution clause. All BSD licenses demand that you give credit by including the original copyright notice. The 4-clause license (which is rarely used nowadays) also demands that you give credit in any advertising material:

All advertising materials mentioning features or use of this software must display the following acknowledgement: This product includes software developed by [organization].

But beyond that, you have to be careful with giving any more credit than that, because the 4-clause and 3-clause BSD-licenses forbid you from using the names of the original authors to promote your product:

Neither the name of the [organization] nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

The 2-clause BSD license doesn't contain this term. It only requires that the original copyright notice with the license terms stays intact.
Note that it is OK to state that the BSD license terms only apply to those parts which were made by the original authors, not to your modifications. Many proprietary software companies do that.
Comment: This was very helpful, but I got a little lost while reading it. Are you supposed to, or not supposed to, write the creators name when mentioning credits for the created assets? In regards to: "you have to be careful with giving any more credit than that."
Comment: @Lemony-Andrew *"Neither the name of the [organization] nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission."* - you must not give credit in a way which looks as if the original authors endorse your product. By the way, when you have more questions about open source software, you might want to commit to the proposal for the new site [Open Source Stackexchange](http://area51.stackexchange.com/proposals/82234/open-source?referrer=LYVOhcyWjB2btmuqLjy44w2).

How free is BSD / CC-BY usage?


How to understand the relationship between complex baseband equivalent model and block-fading channel model?

Question: Considering a bandpass communication system, where $y(t)=x(t)*h(t)+n(t)$ ($x(t)$ is the transmitted bandpass symbol, $h(t)$ is the channel impulse response, $n(t)$ is the AWGN, and "$*$" means convolution). I can write its baseband equivalent model as $v(t)=u(t)*h_l(t)+n_l(t)$, where $v(t),u(t),h_l(t),n_l(t)$ are the complex baseband counterparts. But for block-fading channel (i.e., the channel gain remains constant over many symbols), there is also a representation $y=hx+n$, where $x,y,h,n$ are all complex-valued. I am confused about how I can intuitively or rigorously deduce $y=hx+n$ from $v(t)=u(t)*h_l(t)+n_l(t)$. In other words, are there any correspondence between the signal, channel, and noise terms between these two representations? Moreover, is $x$ in the block-fading representation the same as "constellation point" of a transmitted symbol in essence? They both seem to be complex-valued, but I am confused about their relationship. Thank you.
Answer: $y=hx+n$ describes a memoryless channel, i.e., a channel with unlimited bandwidth. With such a channel, an output value $y$ is dependent on the current input symbol $x$ only.
On the other hand, $v(t)=u(t)∗h_l(t)+n_l(t)$ describes a more  general case where the channel may have memory, i.e., the channel with limited bandwidth. With such a channel, the output value of $v$ is also dependent on previous and/or future symbols, in addition to the current symbol. For  example, a channel with inter-symbol-interference (ISI).
For a memoryless channel, $h_l(t)$ in the second expression is a $\delta (t)$ function with a scaling. In such case, the expression $v(t)=u(t)∗h_l(t)+n_l(t)$  degenerates to $y=hx+n$, and both expressions are the same.


Delegating responsibilities for business page on Facebook

Question: Suppose I have a Facebook page for a business or organization, and I want to delegate posting responsibilities to an employee. As far as I can tell, the only way to do this is to give that employee full admin status, which seems to allow removal of other admins and even permanent deletion of the page. How can I delegate responsibilities to an employee without opening up this sort of risk?
Answer: Most major CMS applications have a plugin that allows for posting items to FB accounts. Assuming you also have an actual site for your business and it's running on top of some system, this might be something to look into. You'd just create a section, content type, or whatever's appropriate to your particular CMS, limit access to it, and post from there instead.
Comment: +1 as,.. this may be the same thing I'm saying but I'm not sure, either way it seems similarly effective.
Answer: I've found one solution, but it's suboptimal - Facebook provides "mobile" posting via a randomly-assigned email address. This address can be given to anybody you trust to post, without giving them any other permissions to modify the page, and it can be changed at any time if it's compromised.
I'd still like to know if there's a better solution...
Answer: Develop a backend for your Facebook page using the Facebook API.
Answer: You can give all users the ability to post content on your page, but those users won't be able to delete your site.
Unfortunately, there is not a way to give posting ability to only some users without making those users "Admin".
This has of course upset quite a few people. See this thread for more information:
http://www.facebook.com/permalink.php?story_fbid=130416483643948&id=10381469571
Comment: I disagree about levels of damage. If a rogue employee made destructive and offensive posts, you could simply remove them and apologize to your fans. Sure it would be some damage, but you could take actions to minimize it - and most importantly, you'd have access to your fans to reach them and apologize. If a rogue employee could remove you as an admin and/or delete the page, though, they'd destroy your channel of damage control and apology.
Comment: Also, one should consider not just malicious/rogue employees, but also well-meaning employees who get infected with viruses. A nasty targeted virus could take control of business pages (adding a malicious admin and removing all other admins) and attempt to extort the original owner to regain control (possibly even threatening to post offensive content if payment is not made).
Comment: If someone *really* wants to hurt your business, I'm sure they can think of plenty of ways to do that that don't involve Facebook. I think trust is important. On another note, why don't you just open up the page to updates from all users? The more interactive your page is, the more likely you are to build a community. Maybe make a feature request to Facebook? I'm sure you aren't the only one who would not trust their staff enough to want such a feature.
Comment: You could create a special "Shared account", with a strong password, that is "Admin", then you'll be less likely to be hacked. At any rate, there is unfortunately no way I know of to do what you're trying to do. Perhaps see if Facebook has a feature request or feedback channel and ask for another level of permissions for power users.
Comment: FWIW, creating a special "shared account" is a violation of the Facebook ToS...


Zohar / Facial features

Question: Shalom all.
I once read/heard that the Zohar says that when Jews move to a certain location, then those Jewish people's facial features change to look like the people that they live among.
Does any one have a reference to the topic that I am talking about?
Thank you
Comment: The Maharitz Chiyus on Shabbos 31a with the story of Hillel and the questioner who asked why different countries have different physical features, says that Hillel's response was that each country affects the features of the children born there in different ways and that he meant to answer this exact question of how if everyone comes from Adam Harishon there are so many different variations.
Comment: Related https://judaism.stackexchange.com/q/432/759
Comment: just look at ashkenazi jews versus sefardi jews.
Answer: Is it this? Anyhow searching the terms here might help you find it.
https://www.sefaria.org/Zohar.1.90b.8?vhe=New_Torat_Emet_Zohar&lang=bi
אָמַר רַבִּי חִיָּיא תָּא חֲזֵי, כַּמָּה אִנּוּן רַבְרְבִין עוֹבָדוֹי דְּקוּדְשָׁא בְּרִיךְ הוּא, דְּהָא אוּמְנוּתָא וְצִיּוּרָא דְּבַּר נָשׁ אִיהוּ כְּגַוְונָא דְעָלְמָא, וּבְכָל יוֹמָא וְיוֹמָא קוּדְשָׁא בְּרִיךְ הוּא בָּרֵי עָלְמָא מְזַוִּוג זִוּוּגִין כָּל חַד וְחַד כְּדְקָא חָזֵי לֵיהּ, וְהוּא צִיֵּיר דִּיוּקְנֵיהוֹן עַד לָא יֵיתוּן לְעָלְמָא.

R' Chiyya said: Come and see how mighty are the Holy Blessed One's works! For behold the artistry and form of a man is like (the world/the people around him). And every day the Holy Blessed One creates the world (anew) and pairs matches and unions, each one (resulting from which?) in the way that you see it - but yet He made the form of their faces/semblances even before they came in the world!
Answer: The rambam in the introduction to avot called shmeonah prokim le HaRambam talks about this.
Comment: Shemonah Prakim is fairly big. Do you have a more exact reference/link to the relevant section/can quote where he refers to this?

Zohar / Facial features


Symbolic convex analysis toolkit for Maple

Question: I'm looking for the SCAT (Symbolic convex analysis toolkit) for Maple written by Hamilton and Borwein.
I have seen some references in the specialized literature than mention some urls. However, the links are dead.
References

Borwein, J.M. & Hamilton, C.H.: Symbolic Fenchel Conjugation.  Math. Program. (2009) 116: 17. doi:10.1007/s10107-007-0134-4
Hamilton, C.H.: Symbolic convex analysis. Masters thesis, Simon Fraser University, (2005)
Answer: A working link is provided in this site: http://vaopt.math.uni-goettingen.de/software.php


Can a black hole collapse in itself?

Question: As we know that the black hole is a lump of highly dense matter, and that's the reason for it's so strong gravitational force. Bat let us assume that it has sucked up a huge amount of mass and it's gravitational force has become of very high strength. Than what will happen. Will the black hole collapse in itself like a dying sun an give birth to another worst nightmare for the cosmologist or anything else will happen.
Comment: Meanwhile someone with actual knowledge of general relativity and/or cosmology writes an answer, as a comment I may add that you can't collapse what already collapsed
Comment: Your question presumes that a black hole has some structure/size, so that it could in principle collapse. That it NOT correct.
Comment: We don't _know_ that a black hole is a "lump" of highly dense "matter."  We know that it has mass, and we know that all of its mass is within Swartzchild radius.  General Relativity tells us that all of the mass must move toward a single point.  But is GR True under such extreme conditions?  We don't know, and nobody's yet performed an experiment that can answer that question.
Answer: According to general relativity, the matter in a black hole is already collapsed down to a volume of exactly zero.  It is not meaningful to talk about further collapse.
Comment: @Akash: are you talking about the central singularity or the horizon that grows around the central singularity?  If it's the singularity, then it is definitely an object that is of a dimension smaller than the enveloping space, and therefore, has zero volume.  For instance, a spinning Kerr black hole has collapsed to form a ring-shaped object of zero thickness.  We don't expect general relativity to be exactly right here, and that it will be corrected by quantum gravity.  But if you believe relativity literally, the object has COMPLETELY collapsed.
Comment: A spinning black hole probably doesn't have a ring-shaped singularity (despite the fact that this is a solution of Einstein's equations), as that produces all sorts of paradoxes (including closed time-like curves, otherwise known as time travel). It may spontaneously break symmetry to become several point-shaped singularities orbiting around a center. But nobody really knows for sure.
Comment: How can general relativity theory say it have collapsed to a zero volume. It have mass and it also occupy some volume in space. it have a shape, and even a radius?
Comment: @PeterShor: sure, but it's all speculation regardless, and the Kerr singularity is the best model we have.  The CTCs are all confined to the interior of the inner horizon anyway.  But yeah, until you have quantum gravity to resolve the issue, no one knows.  You could also probably resolve the CTC issue with a gluing condition, too.
Comment: @Dimensionless, According to GR, It is physically impossible for anything that is inside the Swarzchild radius of a non-rotating black hole to _not_ move toward the singularity if it is not already there.  The singularity is an infinitessimal point, so either the density at that point goes to infinity, or else GR diverges from reality under those conditions.  So far, nobody's been able to perform an experiment to tell us which is the actual case.
Answer: A black-hole is the most dense, most collapsed object or state of matter in the universe.  To our knowledge, nothing really changes as a black-hole increases in mass except that it gets bigger, and its gravity stronger.  Its properties are, for most intents and purposes, scale invariant1.

1: Hawking Radiation is, in a way, an exception to this, but not astrophysically relevant.
Comment: @Akash I didn't say its something *'greatly collapsed'*, I said it is **the most** collapsed.  It **can not** collapse further.
Comment: @Learningisamess The gravity and radius both scale linearly with mass, is basically what I meant.  There are no characteristic scales at which the properties change---for example, there is no special mass limit, or radius limit, etc.
Comment: You are right it is something which collapsed really to a great extent. But what if it does collapse further the pressure and temp at it center will be like hell in a hell. Those conditions could give rise to pretty interesting event's that we don't know till the date.
Comment: Hum, I'm puzzled by your statement " Its properties are, for all intents and purposes, scale invariant". A Schwarzschild black hole for example as a radius, a mass, so is not properly scale invariant (not to my definition at least), which properties are you thinking about?
Answer: The collapsing of the black hole is impossible. It is like trying to burn ashes. Ashes are already burnt. Similarly, the black hole is already collapsed. The black hole can evaporate and get bigger, but not collapse.
Answer: Well a black hole actually has 5 tons of mass or in other words a stellar hole if it collapsed into itself it would cause a hypernova
Because according to the law of consevation of mass that mass cannot be created or destroyed but it can be rearranged in space therefor no mass can be .000000000000000000
Because that would mean a mass has been removed but most black holes have more than 10 times the mass of the sun my source is http://amazing-space.stsci.edu/resources/explorations/blackholes/lesson/whatisit/stellar.html
Comment: How do you know that " a black hole actually has 5 tons of mass"?
Comment: If I'm not mistaken, the smallest observed black hole is $\sim10^{27}\text{ tons}$, which is well more than the *five* you're claiming. Also, do you have any relevant papers on "a stellar hole collapsing into itself" and hypernovae?
Comment: I am only in the eigth grade but even so black holes can have different masses it all depends of the schwartzchild radius
Answer: Black holes can evaporate. Black holes formed beneath the Chandrasekhar limit will evaporate quickly.
Comment: What does this have to do with anything?
Comment: You have a very strange definition of "quickly".
Comment: To decay "quickly" by the Hawkings process an black hole would have to have a mass around that of a smallish asteroid. One with a more than a solar mass would not be in any danger of going away any time soon, and in any case that process would not be described as "collapse".
Comment: I think the answer means to say something to the effect of: the black hole will not collapse (into itself). Instead, all its energy eventually goes out due to "evaporation".

Can a black hole collapse in itself?


non-Noetherian r-Noetherian ring with Noetherian total quotient ring

Question: A commutative ring is said to be r-Noetherian if every regular ideal is finitely generated, where an ideal is said to be regular if it contains a non-zerodivisor.  Does there exist a non-Noetherian r-Noetherian commutative ring whose total quotient ring is Noetherian?
EDIT: A commutative ring is Dedekind if every regular ideal is invertible. (A domain is Dedekind if and only if it is a Dedekind domain.)  Does there exist a non-Noetherian Dedekind ring whose total quotient ring is Noetherian?
The motivation for this question is that conditions like r-Noetherian and Dedekind control only the regular ideals of a ring and one can try to use the total quotient ring to control the non-regular ideals.  By this philosophy one would hope that an r-Noetherian ring is Noetherian if its total quotient ring is Noetherian.  But there is no obvious proof of this, leading to the desire for a counterexample.
Answer: I believe I have answered my question in the positive.  Let $R = \mathbb{Z}+\varepsilon\mathbb{Q}[\varepsilon]$, where $\mathbb{Q}[\varepsilon]$ denotes the ring of dual numbers over $\mathbb{Q}$.  Then $R$ is the integral closure of $\mathbb{Z}$ in the total quotient ring $\mathbb{Q}[\varepsilon]$ of $R$, so in particular $R$ is integrally closed.  Every regular ideal of $R$ is principal, and every finitely generated ideal of $R$ is principal, $R$ is non-Noetherian, and yet the total quotient ring $\mathbb{Q}[\varepsilon]$ of $R$ is Noetherian.


Can I clip on all objects at once using Inkscape?

Question: I have created a poster using several objects throughout several layers. I would like to export the final document with a small, white padding. Can I use Inkscape's clipping functionality to create a rectangle that is slightly smaller than the page and then make everything outside of that rectangle transparent, such that a margin appears?
Answer: You don't need to use clipping for this.  In Inkscape a page is fully transparent by default, unless you put an opaque object on the page.   So, you can use this to your advantage.

Draw a white rectangle smaller than the page, and move it to the bottom of the stack using the Lower Selection to Bottom icon in the control bar along the top, or alternatively use the keyboard shortcut End. This will ensure all other content is on top.

When you export, under Export area choose the Page button, then hit Export. The result will be a white rectangle within a larger transparent page.
Answer: Yes, that is possible, but you will lose the layer structure if you use clipping, because the clip will force all objects into the same group in the same layer.
If you want to keep the structure, you can instead add a white frame on top of your drawing. For this, I would use snapping to snap a white rectangle to the page corners while drawing it, then I would duplicate that rectangle, and in the width/height fields subtract 2*margin, so you get a smaller version of that. Center it on the page and subtract that from the larger white rectangle. Put the frame on its own layer, that you can hide and show as needed.


Bolzano-Weierstrass Theorem and Pareto Efficient Allocation

Question: Wikipedia says 'The Bolzano–Weierstrass theorem allows one to prove that if the set of allocations is compact and non-empty, then the system has a Pareto-efficient allocation.'
However, I couldn't find a compelling simple proof for this theorem anywhere. Could someone provide a proof for the theorem in a simple fashion that is understandable for Undergrad students in Economics who have done a course in Analysis?
Comment: In order to understand any of the proofs you have to grasp either the concept of "nested intervals" ( https://en.wikipedia.org/wiki/Nested_intervals ) or the concept of a subsequence. If you get those the proof is straight foreward. Anyway these arent complicated. They are taught in intro to analysis in all undergrad programs in math.
Comment: Perhaps insofar as Bolzano-Weierstrass theorem is [used to prove the extreme value theorem](https://en.wikipedia.org/wiki/Extreme_value_theorem#Proof_of_the_extreme_value_theorem), which in turn can be invoked to easily establish the existence of Pareto optimality. See also: https://www.quora.com/How-is-the-Bolzano-Weierstrass-theorem-used-in-general-equilibrium-theory/answer/Amit-Goyal-135
Answer: What one needs are two facts:

Scalarization/Sufficiency for Pareto Optimality
Suppose the economy has finitely many agents $u_i$, $i = 1, \cdots, I$, with feasible allocations given by some $X \subset \mathbb{R}^I$. If
$x = (x_1, \cdots, x_I) \in X$ solves the problem
$$
\max_{x \in X} \sum_{i=1}^I \lambda_i u_i(x_i),
$$
where $\lambda_i > 0$ for all $i$, then $x$ is Pareto optimal. This maximization problem is called the social planner's problem with social weights $\lambda_i$.
(The converse is not true. In other words, not all Pareto allocations arise as such, not even when $u_i$'s are concave.)
Continuous functions map compact sets to compact sets. (The Bolzano–Weierstrass gives a characterization of compactness on $\mathbb{R}^n$---closed and bounded.)

So if the preferences are continuous and feasible set $X$ is compact, existence of Pareto optimal allocation follows immediately. Choose any social weights $\lambda_i > 0$. A solution of the resulting social planner's problem is a Pareto optimal allocation.


What do sunchokes look like when they're sprouting?

Question: What does a sunchoke look like right after it begins to sprout?
Answer: The sunchoke, also frequently called Jerusalem artichoke, is a species called H. Tuberosus, in the Helianthus genus of Asteraceae, which is a large plant family that includes sunflowers and daisies. Even though it grows from a tuber root rather than a seed, the plant when it emerges looks very much like any other flower in that group.
The Ohio Perennial and Biennial Weed Guide shows an excellent progression of the stages of the plant, beginning with the answer to your question.

The first leaves to emerge (cotyledons) have a united base in the shape of a short tube. Young leaves are elliptic, dull green, and covered with short stiff hairs.

This is a picture of a newly sprouted plant.

This picture is of a group of young seedlings, in the stage right after the first appearance of leaves.
Comment: Are those fuzzy like mullein leaves (I've heard mullein leaves are soft like felt)?
Comment: They look like pineapple sage in the last picture. :) @blackthumb You don't want to rub those leaves, probably. I hear sunchoke leaves can give you a rash or make you itch (like sunflower leaves can).
Answer: Although they're currently normally grown from tubers, they can be grown from seed, according to Joseph Lofthouse, who has a blog with Mother Earth News, and is known for breeding landraces in northern Utah for many kinds of plants. He sells the seeds, too. However, you need to have two genetically distinct plants, if you want them to produce fertile seeds (and you may need to bag the blossoms after pollination to keep birds from eating too many of them). Commercial tubers may or may not have cytoplasmic male sterility (so, if you want to grow seeds, you may need to actually buy seeds instead of tubers to start with, at least for the pollinating plant). Kansas Native Plants sells true seeds, too.
Here's a link that shows pictures of seedlings with cotyledons. (It is also a source for some of the other information in this answer.) The cotyledons in the picture look a lot like those of sunflowers, but the first true leaves in the picture, at least, look like somewhat pointy green tongues (complete with tastebuds) with a bit of fur on the sides, without much of a line down the middle (and flatter than tongues, of course).


Surjectivity of Invariants

Question: Suppose $V, W, U$ are $Z_p$ module over a field $F$ of characteristic $p$ and $V=W \oplus U$. Is there a degree preserving surjective map from $F[V]^{Z_p}$ to $F[W]^{Z_p}$ ? In non-modular case the Reynold's operator does the job but in this case I don't have any clue.
Answer: That holds more generally: If $k$ is any commutative ring with unit, $G$ any group and if $U,W$ are $k$-free $kG$-modules, $V = U \oplus W$, then there is a $k$-linear surjection $k[V]^G \to k[W]^G$:
Let $r: V \to W$ be the projection. Then $k[V]=k[W] \otimes k[U]$ and $r$ induces a $k$-algebra hom. $r: k[V] \mapsto k[W]$. Aussume for the moment we know that $r$ is compatible with the $G$ action, i.e. $r ( g \cdot v) = g \cdot r(v)$. Then $r$ preserves the invariants: $r: k[V]^G \to k[W]^G$.
Moreover, $r$ is surjective on the invariants. For, let $w \in k[W]^G$ and put $v := w \otimes 1$. Then $g \cdot v = (g\cdot w)\otimes (g\cdot 1) = w \otimes 1 = v$, i.e.
$v \in k[V]^G$ and $r(v) = w$.
Now let's show that $r$ is compatible with the $G$-action. Note that we have an $k$-algebra homomorphism $\epsilon: k[U] \to k$ that satisfies $\epsilon(g \cdot u) = \epsilon(u)$: If $\lbrace x_1,...,x_n\rbrace$ is a $k$-basis of $U$ then $\epsilon$ is just the augmentation $k[x_1,...,x_n] \to k$.
Now $r$ is given by $r(w \otimes u) = \epsilon(u) \cdot w$ and we obtain $$r(g (w \otimes u)) = r(g w \otimes g u) = \epsilon(g  u) (g  w) =\epsilon(u) (gw) = g  (\epsilon(u)w) = g\; r(w \otimes u).$$
BTW: To my understanding, the Reynold's operator yields $k[V]^H \to k[V]^G$ for $H \le G$ and adresses another problem than yours.
Comment: Added: $r$ is degree-preserving. For let $u,w$ be monomials such that $r(u \otimes w) \neq 0$. Then $\deg u = 0$ and $\deg r(u \otimes w) = \deg(u \cdot w) = \deg w = \deg w + \deg u = \deg(w \otimes u)$.
Comment: @Ralph Your argument shows, still more generally, that if $U$ is a submodule of $V$ with quotient module $V/U \cong W$ then there is a  $k$-algebra homomorphism $k[V] \rightarrow k[W]$ that preserves degrees and invariants. Is there any characterization of when the induced map $k[V]^G \rightarrow k[W]^G$ is surjective? (One small typo: the Reynolds averaging operator sends $k[V]^H$ to $k[V]^G$ for $H \le G$.)
Comment: I don't know, if there is such a characterization ($W$ $k$-free is sufficient, probably also $W$ $k$-projective). And thanks for pointing out the correct order of the Reynolds operator.

Surjectivity of Invariants


What's the difficulty of using elliptic curves to design homomorphic encryption protocols?

Question: I have recently been very interested in elliptic curves because they are a powerful tool in crypto, ECC, pairing, etc. However, it seems that elliptic curves are not popular in homomorphic encryption. I understand that lattice-based crypto is currently the only way to construct FHE, like LWE. Elliptic curves can only be used to construct PHE; for example, BGN. After doing some research as a freshman in HE, I found that there is not much effort in trying to use EC to construct FE. So, I'm just wondering why. Is it because elliptic curves have some issues in their structure, making it hard to construct HE? Or is it because lattice-based construction is a hot topic, so researchers prefer it over EC?
Comment: For FHE you need two operations: addition and multiplication (or equivalently "xor" and "and"). What's your suggestion for a second operation for two elements of a elliptic curves?
Comment: If I trust my instinct about [what](https://doi.org/10.1109/ICCS45141.2019.9065871) searching for recent articles mentioning Fully Homomorphic ECC [returns](https://doi.org/10.1007/s10586-018-2723-9), indeed nobody has figured it out. Note: I didn't read much past the abstracts (beyond the obligatory color graphs), and advise against it.
Comment: @j.p. I understand that point adding is the rule of the elliptic curve group, and we can not multiple points directly cause it seems meaningless. However, that's not the only way, in BGN scheme, multiplication can be done by pairing, but only once. So I think the problem is that we just have not found THE right solution yet.
Comment: @HilderVitorLimaPereira  In fact I really don't know and that's why I ask the question here. I read some papers recently and get the conclusion that constructing such a scheme with EC is definitely not easy, someone has to dive into the mathmatical background of EC. I can't grab the key problem and that's why I ask for some help or direction. Thanks for your reply.
Comment: I am not an expert, but I think that you can get "FHE for quadratic functions" from elliptic curves (see [this](https://link.springer.com/chapter/10.1007%2F978-3-540-30576-7_18)). I think the difficulty for getting higher than degree 2 is related to the difficulty of getting multilinear maps of degree greater than 2, of which there has been a decent amount of research within the last decade due to applications to constructing indistinguishability obfuscation. That being said, someone who works in pairings-based crypto should probably verify this understanding.
Answer: From my point of view, Homomorphism is a inherent attribute of certain lattice-based scheme.Researchers try every means of solution to enhance the attribute,but not all primitives have this attribute.


QGIS Raster Merge - Change in the band values problem

Question: I have two raster files and I want to merge them in QGIS. The first raster has values between 0 to 8627 and the second one has 0 to 9118. However, when I do it with the Merge tool (in GDAL/raster miscellaneous) new raster's values are between 0 to 9,260. Somehow, it is rescaled or some raster values are combined. When I checked the map, only one raster is rescaled but the other one stayed as original.
Do you have any suggestions?
Comment: If you are just looking at the min/max values in layer legends in the QGIS Layers tab, your original max values (8627 and 9118) are likely estimated, not actual max.
Comment: I dont change any parameters actually. I have added an image to the question about parameters.
Comment: Oh yes, I change them via

Symbology>Min Max Values Settings>Accuracy>Actual(slower)

So there was no problem, just the max min values were poorly estimated.
Answer: By default, QGIS shows estimated min and max values in the layer legend (faster). To see the actual values, in the raster layer properties, symbology tab, change "Accuracy" from "Estimate (faster)" to "Actual (slower)".


How do I bend a scanned .stl object with several complex features

Question:
I'm trying to make a cylinder out of this textured slab. One side is flat while the other side is textured with an intricate pattern.There are several triangles and vertices. I would like to temporarily simplify it while i curve the object into a cylinder and then return it to its full detail.
I have tried doing a loop cut, but i can't select a whole face, and it all keeps failing/crashing. Please advise.
Comment: the triangle topology will not help you to "bend" the object you need regular subdivisions that can conform to a cilyndrical shape. For such a simple object, create a new quad based mesh,  and re-apply the texture to it. Then use a curve modifer or a simple deform modifier in bend mode.
Comment: HI, welcome. I don't understand, perhaps, an .stl has no textures in itself, it's usually an highly subdivided shape so, what you mean by "textured slab", and by "trying to make a cylinder" out of it ? are you wishing to curve that flat panel as if it was rolled around a cylinder, around it? You would get a sort of cylinder with a cilindric hole inside... ?
Answer: Ok, not having your exact object, and having not well understood your question I should probably avoid inserting an answer here, but I wish to show an easy way you could "roll up" that plane to a "cylindrical" shape, since it could give you some ideas on how to proceed. Then maybe you can suggest if some variant could be better.
Note, I simulated a flat rectangular object with irregular vertices (I randomized them): I know it's not as your object, which seem far less easy to be deformed than mine, but if you could arrange your object, subdividing it a lot perhaps, the following could fit your case too. Maybe.
Here it goes:

Here is my "simulation" of your flat rectangular object, with its red twin I leave there for comparison

in the same "object center" I add a "curve circle", from top view

obtaining this

Then I select the grey rectangular object and insert a curve modifier, targeting the bezier circle just inserted before

...and I get this horrible shape! But don't worry, it's just the circle, too little. We're going to fix it.

Now, I zoomed a bit to show you better, but I selected (see the upper right outliner area) the bezier circle

Then I enter the edit mode with TAB and select all control points

Then I scale it outwards, perhaps too much in the picture below, but at least now I can see where my curved surface ends are, which should probably stick together

...and I can make then stick together just by scaling a bit less (some snapping to grid could help while scaling)

Exiting edit mode, this is what I get.

As said above your object could not follow the curve so easily, and it could need to be subdivided, maybe with subsurf modifier applied in advance. Or, you could give us hints on how exactly you need it to be.
You could share your object, also, preferably using this dedicated hosting service and then pasting in your question the provided link:
http://blend-exchange.giantcowfilms.com/


How to force the user to draw on certain elements if there are images in the layout

Question:
Well, I ran into the problem of distinguishability of content in a mobile application. In fact, there are a huge number of pictures on the page (movie poster, preview of the film as a picture). A lot of information is actually important, so it is made very contrast. And everything would be fine if it were not for the presence of pictures, which can be either unsaturated or very saturated, which is why I fear that everything can confuse the user. Although the main action (view from last place) is always at the bottom right in the form of a Floating Action Button (Which is actually not the best thing to do, but I just don't really know, what could be better and the same time consistent).
Comment: So what are you trying to draw their attention towards?
Comment: @NicolasHung Well, the most important thing is to let user find the "Play" button to continue watch serial/film or whatever it is. But at the same time, someone needs to just choose an episode. So, I don't really know what to rely on better. No, of course, often the user decides to continue to watch the show from the place where he finished, but, on the other hand, it can be played differently.For example, you can make it so that the user can do the same at the very beginning when the application is turned on.
Comment: @NicolasHung However, I don't know how good this step is, because sometimes I myself first look at all the episodes, and then choose the right one. For example, if I already watched the movie.
Answer: You can do something like this:
The first scenario allows the user to easily find the continue playing button in the banner, while also indicating your progress in each episode via a progress bar.
The second scenario is when someone as finished watching the series. Therefore all progress bars are full.
As for image overload, I don't see it as an issue. Make sure not having autoplaying videos, only static images. It's just like browsing any e-commerce product listing or Netflix app.
Also, the screenshot provided looks like longer than a phone screen, so it might also be contributing to the content overload concern.
Comment: Well, that was... pretty easy! Thanks a lot, I think I've got this!