Are there theories about the end of the universe where time ends?

Question: We always tend to think that future will come no matter how far in the future that is. But according to some theories, time started at the big bang and the term "before the big bang" doesn't make any sense just like going to north does not make any sense when you are at the north pole. But there is also the south pole where going to further south makes no sense. So are there theories which implies that there is a future point where time ends and going into further future doesn't make any sense ? And if there are theories like these, what are those theories?
I know that there is a theory according to which after a finite amount of time the expansion rate becomes infinite and it creates a singularity everywhere and space together with time just rips apart and time ends.
So I want to know about other theories.
Comment: I have voted to close this question because "are there theories like this?" either 1) Has a simple "yes or no" answer, or 2) will attract various answers that include different theories, thus giving rise to a question without a single accepted answer, which is against the SE Q&A model (i.e. IMO this is a list question). Perhaps you could edit the question to ask about a specific concept in such a theory you are confused about?
Comment: I edited the question so that it becomes much more specific about the question I am trying to ask. Can you please review the edit.
Answer: A description in which spacetime comes back to a situation like the south pole in your question is the possibility in general relativity called "Big Crunch". We don't think the universe will do this (the matter density is not high enough) but you asked if there were models which allowed that sort of thing. The Big Crunch is in some respects like spacetime curving round on itself like the south pole of a sphere, so that there is no longer any direction called "south". However, it does not necessarily follow that the question "what comes after?" loses its meaning in a Big Crunch. Rather, in the conditions of the crunch, when the scale factor of spacetime has become small and the density large, our understanding of physics runs out and we do not know how to predict or even describe what the conditions are. So we just don't know if the concept of "future" ceases to have validity. Maybe it does, maybe it does not.
More generally, the human race does not have the data to answer a question like "will future always exist?". I suspect we do not have the intellectual capacity either. We can propose theoretical models, but all will reach a regime where there is no longer good reason for confidence that they still apply.
Currently the model believed by many is that matter will first get captured into black holes and then these will evaporate and then everything just fades into an expanding dust, expanding forever and doing nothing. But who knows? This model might be profoundly wrong. You can also find speculations about new bursts of "life" (that is, new patches of spacetime and matter undergoing a fresh big-bang-like behaviour) going on and on forever. Or perhaps the universe as we know it is in a state called "false vacuum" and the whole thing can get transformed by something like a phase transition. Or perhaps another type of transformation can happen.
Part of the aim of this answer is to reduce the level of confidence that readers place in whatever was the latest description they read which pronounced with confidence on questions concerning an ultimate future.
Comment: @MauroGiliberti Thanks. I see what you mean and will modify my answer a bit.
Comment: I think you misunderstood OP's question. It asks: "Are there other theories like this?" and that's a perfectly good question and doesn't need a reduction of confidence.
Answer: From your question, I reckon you don't want a too-in-depth answer. Please correct me if you want some equations to make sense of what I write.

This is a diagram widely used in cosmology. Roughly, you can see $\Omega_M$ as the matter density, and $\Omega_\Lambda$ as the Dark Energy density. There are various theories that try to explain what the universe might look like in the future.
The theory you were talking about (I presume) is what is commonly know as "Big Rip", and is represented by the dashed line on top. The universe never slows down its expansion, and eventually every particle will become a separate system unable to interact with every other one. In some sense, you can say that "there is no future", but please try not to use these kinds of expression while talking physics, as they can be really opinion-based.
The other probably interesting theory for your question is the dash-dot line at the bottom: it describes a "Big Crunch" and while this currently doesn't seem to have a lot of interest, it surely did when physicists were trying to figure out various models. If the matter density $\Omega_M$ is big, greater than one, the universe should slow down and eventually start contracting back until everything becomes really close. In some sense, this can also be seen as a "no-future scenario".
Lastly, you could just dive into a (non-rotating) black hole. You should reach its center in a finite amount of time and (while probably dying) you can't do anything else, ever, from there. So, again, no-future scenario.
Comment: @MauroGilberti See for example the Wikipedia article https://en.wikipedia.org/wiki/Big_Rip - it is explicit that "the structure [of spacetime] is 'ripped apart'". Yes, matter does decay into elementary particles, but that is just the heat death - the Big Rip does not end there.
Comment: What you describe as the Big Rip is more correctly regarded as the "heat death" of the Universe. In the Big Rip proper, that upper line eventually hits a sharp endpoint where the forces driving it rip apart the fabric of spacetime itself.
Comment: @GuyInchbald I beg to disagree. In the Big Rip scenario, "A steady increase in the Hubble constant to infinity would result in all material objects in the universe, starting with galaxies and eventually (in a finite time) all forms, no matter how small, disintegrating into unbound elementary particles".
Answer: There are many theories about the nature of Time. Whether the Universe is "open" with Time indefinitely long or "closed" with a finite Time ending in a Big Crunch is a matter of ongoing debate, although the standard model of cosmology has no mechanism for ending Time.
Some cosmologists propose a "Big Rip", in which the expansion of the Universe gets out of control and it destroys itself, like a balloon being over-inflated. Space and Time are the fabric of the balloon, so it is actually they which explode into nothing.
Some cosmologists propose a cyclical "Big Bounce", in which the Universe rebounds from the Big Crunch in a new Big Bang, endlessly.
These models are all based on the idea of Time as a single dimension conforming to particular solutions, or families of solutions, of Einstein's equations of General Relativity. But maybe Time itself is more complicated than that.
Stephen Hawking proposed a mathematical model of a complex Time which leads to a closed Universe where one dimension slides around the poles like just keeping going and suddenly you find yourself heading back towards the equator, so this dimension of time is finite but unbounded. Meanwhile the time which we perceive may still be open-ended.
Roger Penrose, in some ways Hawking's heir, has proposed a cyclic cosmology in with the Universe is constantly expanding but our measuring yardsticks for space and time get periodically reset so it looks like a bounce but isn't really.
If the Multiverse is a reality, does each Universe have its own independent flow of time or do they all tick in sync?
Many other fringe ideas have been investigated.
The big problem is finding experimental evidence to distinguish between these possibilities. It is a vastly difficult task. Some has been gathered, but it all remains either inconclusive or controversial.
Comment: It seems a bit odd to refer to Sir Roger [Penrose](https://en.wikipedia.org/wiki/Roger_Penrose) as Hawking's heir. They were colleagues, and did some important work together on black holes, etc. But Penrose was born about a decade before Hawking (and was awarded his PhD about 8 years before Hawking. FWIW, I heard about Penrose in the early 70s, via Scientific American, but I didn't know about Hawking until the 80s.
Comment: @PM2Ring I agree. "Survivor" might be more appropriate than heir, but I'd suggest that in the UK at least, Penrose seems to be inheriting the mantle of popular figurehead.
Answer: When you ask about a "theory" it  is important that you not confuse it with a "speculation". The following is a very good definition for "theory".
From https://en.wikipedia.org/wiki/Theory
In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it.
The following is an acceptable definition of "speculation".
From https://en.wikipedia.org/wiki/Speculation_(disambiguation)
Speculation is the process of thinking about possibilities, or a particular conclusion arrived at from such thought.
There was a time (about a century ago) when the theory called General Relativity was born with (at the time) some ideas about how some of the possibilities might be supported by observation. One of these ideas (theories) was (at the time) a finite universe that expanded and reached a maximum size and then contracted. At the present time, there is now a lot of observed data that tells us that this possibility just cannot happen, and no ideas about how new observations will likely occur to support this idea.
On the other hand, a principle of science is that nothing is ever known with absolute certainty (except maybe mathematics). Therefore one might speculate that some time in the future some idea for a theory will come along with a conceptual possibility of observing evidence that will support the idea of a universe reaching a maximum size and then contracting. I would guess that most professional cosmologists would not expect this possibility to have any significant chance of ever happening.


Touchscreen/xinput-calibrator

Question: I have been trying to install xinput-calibrator but when I type: sudo apt-get install xinput-calibrator, it returns with: Unable to locate package xinput-calibrator.
I have tried through the software center with no luck as well. I am fairly new to this, what should I do now?
Answer: In order to use xinput-calibrator, you must first add the ppa.
Open up a terminal by pressing and holding CTRL + ALT + T.  At which point you will enter
sudo add-apt-repository ppa:tias/xinput-calibrator-ppa
sudo apt-get update
At which point you can now sudo apt-get install xinput-calibrator.

Touchscreen/xinput-calibrator


Turn out all the lights and call on the Lord

Question: A man I knew, born in 1921, used to enter a room at festive gatherings and say "Turn out all the lights and call on the Lord." Do you know the origin of that phrase, or do you think it was just an idiosyncrasy of his?
Comment: He could have heard a certain James Brown song, and be misquoting for his own amusement: "Cut off the lights/And call the law" (Funky Drummer, 1970)
Comment: Literally the only place this appears on a Google search is your post here, so I think it was his alone.
Comment: @jimm101 or maybe the other people didn't post it on the internet? Especially considering the internet wasn't around for a long time.
Comment: Sounds like an idiotsyncrazy to me.
Comment: @JJJ True, but the Internet is littered with lots of things that predate it.
Answer: Turn out all the lights and call on the Lord appears to be as you said, idiosyncratic.  His own 'turn of words'. I can find no registry listing for the same, nor anything close.  I suspect his intention was meant 'to focus on said deity'!


How do I connect a Juno LED light to a switch when the light receives power first?

Question: I'm trying to connect a new LED light to a new single pole switch. I have a 14/2 main power feed coming in to the LED light first then a 14/3 wire going from LED light to switch. I feel like I have it wired correctly but the light does not turn on. Is it not possible to wire LED lights this way?
Comment: Yes, it is.  You made it easy by running 14/3 to the switch. Just mark the black or brown wire on the LED with red tape to redefine it as a red.  then you will have a situation where all the color codes just happen to match up.
Answer: Harper's comment is, as usual, a correct summary of the solution. Here (copied from part of another question) is the full diagram:

Light fixture junction box:

All whites (neutral) together
All grounds (green or bare) together
Blacks from 2-wire & 3-wire cable together (hot)
Mark light fixture black wire (may be labeled "hot" or "switched hot", but it should be the only wire or screw other than white/neutral and ground) with red tape.
Reds from light fixture and 3-wire cable together (switched hot)

Switch junction box:

All grounds (green or bare) together
Black to "hot" screw on switch
Red to "switched hot" screw on switch

If switch does NOT use neutral:

Cap white (neutral) with a wire nut

Note that with a simple (not smart, not dimmable, not timer, etc.) switch there is no functional difference between the hot & switched-hot connections, but if there is a clear indication on the switch (or in the switch instructions), follow the directions.
If switch USES neutral (e.g., smart switch)

White to neutral screw on switch.


Where do electrons jump to when they jump to next shell in emission spectrum? Why are there no emission lines for jumps btwn orbitals, same shell?

Question: In the emission spectrum, do electrons that jump up to the next shell go to any orbital in that shell? Or if the electron is originally in say the p orbital, does it jump to the next p orbital in the next shell??
Also wouldn't there be more colors on the emission spectrum if energy is emitted when electrons fall down from an excited orbital down to lower orbital in the same shell? Why does it seem like there are only colors for change in shell and not orbital within a shell?
Comment: See also [wikipedia: Selection rule](https://en.wikipedia.org/wiki/Selection_rule).
Answer: Yes there are emission lines for jumps between the orbitals for multi electron lines as seen in the form of doublets( two closely spaced lines) and triplets( three closely spaced lines).
Infact this is one of the reason why Bohr's model failed. Doublets and triplets appear in the spectra of some atoms as very close pairs of lines. Bohr's model cannot say why some energy levels should be very close together. These closely spaced lines corresponds to transition from one orbital to other.


In what way is a Craft Port different from a conventional RS-232 Port

Question: In what way is a Craft Port different from a conventional RS-232 Port? It seems to be similar. Are there any interface or other important differences? Does craft port imply a higher level protocol on top of RS-232 as well?
Answer: Quick search reveals that it may be essentially a marketing term for Analog Devices series of RS-232 transceivers meant for low-power portable applications.  This web page seems to corroborate: http://forum.wordreference.com/showthread.php?t=1944943
Here is a datasheet for one of their CraftPort devices: http://www.analog.com/static/imported-files/data_sheets/ADM101E.pdf
So in short, it doesn't seem to be a protocol, but instead the name of the transceiver line.  Shouldn't be any different from regular RS-232.  I guess people like the sound of the name and use it on their products.
Ah, one edit:  It seems that the output voltage levels are +/4.2V and it allows full +/-15V input.  Some 'RS-232' transceivers don't like the full +/-15V range and only produce 0-5V output.  This is a step above those in terms of compatibility with the true RS-232 standard, which is not often completely met nowadays in terms of input/output voltages.
Comment: Some devices draw power from the hardware handshaking pins defined in RS232 (DTR, RTS, etc.). Using less then 5 volts, even though allowed by the RS232 standard, may not be enough to power them. We had an issue with serial mouse that would work reliably on a new system and had to use RS 232 transceiver to make it work.
Comment: There aren't even connections for the serial handshaking lines on the transceiver so it wouldn't be an issue for it, but the system surrounding it.  I can't believe someone actually used them for something.  I've never hooked up a serial port with more than Tx, Rx and GND.
Answer: From this Expert sexchange question (scroll to bottom):

A craft interface is a direct connection to a device, usually, as you have read, through an RS232 port using an RJ45 type connector or a DB9 or DB25 connector. This interface provides access to a command line for the purpose of configuring the device or diagnosing problems, or for whatever reason the "user traffic" interfaces are inaccessible. In any event, the craft interface provides access to diagnostic and configuration functions.

It sounds like you provided the proper answer, where "Craft" is just a protocol that sits on top of lower level links--RS-232 perhaps being the most common.  Perhaps analogous to AT commands.
Comment: craft port is the telco name for a serial console.  Not well known outside of legacy telco industry.
Answer: A craft interface is a command line interface for directly configuring a network device - typically an ip router or switch.  The connection is often over an rs232 or similar serial port on the physical device itself but can also be via telnet, ssh or various other methods.
Typically these interfaces are complex and hard to use for those not familiar with them. Each is specific to the manufacturer, device type and often the particular device. They can have hundreds of complex commands and multiple contextual modes with many inconsistencies in the way different commands and modes work.
For this reason the word "craft" is often thought to come from the idea that when you're faced with the cli prompt you "Can't Remember A F...n Thing."


How to compute $(\int f(x) \, dx)^p$ with fractional number $p$?

Question: It is well-known that one can say $(\int f(x) \, dx)^p = \int \prod_{i=1}^p f(x_i) \, dx_i$ if $p$ isa natural number. But what is if $p$ is a fractional ore even a real number? Is it possible to set $\int f(x) \, dx = h \sum_k f(hk)$ for infinitesimal number $h$ and then use the multinomial Theorem when computing $h^p (\sum_k f(hk))^p$? How I compute $(\int f(x) \, dx)^p$ for General number $p$?
Comment: Is there a reason, why you specify $\int f dx^p$ instead of simply $a^p$ for some number $a$? Or do you mean integrating $p$ times? In that case, you might want to check out [Fractional Calculus](http://en.wikipedia.org/wiki/Fractional_calculus)
Comment: Because I want to know whether there exist an equation $(\int f(x)dx)^p=\int \prod_{i=1}^j' f(x_i) dx_i$ for a generalized product $\prod'$ or similar.
Answer: It sounds like you are interested in fractional calculus. The wikipedia article linked will give you some information but I also have a lengthy answer here on math stackexchange that might give you some leads: Fractional Calculus.


GIT folder not seen

Question: I have subccessfully installed git and was able to create a master and push the files to a remote repository. However,  I do not see the '.git' folder in my master. Is that a problem? Do I have to redo anything?
Answer: When a folder has a dot in front of it on most systems it is hidden.
On Unix systems, you can type ls -a to see all files in the directory.
On Windows, dir /a.
Answer: It's a hidden folder. At the base of your git repo, ls -a will show you the folder.

GIT folder not seen


How to choose scales for improvisation based on chords used in a progression?

Question: When playing a tune that has both, minor and major chords, what scale would be safe to use for soloing? It seems that a Minor Pentatonic would work for the minor chords, but not that well for the major ones
Comment: If you play a Blues you can take take the  minor scale above both tone genders because the minor 3rd and 7th are part of the blue note scale.
Answer: If I understood you correctly, you're trying to play notes from a scale that's always rooted on the root note of whatever chord there is at that moment. And that's why for example if your chords are C - Dm - G - Am, a minor pentatonic scale seems to work nicely on the Am and Dm, but feels a bit funky on the C major and G major chords. If this is what you're doing, there's something quite important you're missing, and that's the concept of key.
Songs are usually in a key, for example C major. Not the C major chord, but the key of C major. (Unfortunately music is full of words loaded with multiple different meanings depending on the context.) Being in the key of C major means two things:

(1) C is a very special note in this song. It's the so-called tonic, which is a home note, a place of rest, the central perspective where you stand and look at everything. All the notes and chords happening in the song live in a C centric universe.
(2) Other notes in the song come mostly from the C major scale: C, D, E, F, G, A, B. (Many songs do have notes that aren't from the key's base scale, and those notes slightly change the harmonic feeling.)

If your song is in C (which is another way of saying "in the key of C major"), it might have a chord progression like: C - Am - Dm - F - G - Dm - G - C. During the whole chord progression, your ear only expects to hear notes from the C major scale, and the most expected ending note for a melody would be the C note. All of the notes of all of the chords are from the same scale:

C : notes C, E, G
Am : notes A, C, E
Dm : notes D, F, A
F : notes F, A, C
G : notes G, B, D

For soloing on a song like that, you select the C major scale for "safe" notes: C, D, E, F, G, A, B. If you don't know what you're doing and want to be even more safe, leave out the F and B notes (which I highlighted in the chord listing above), which might disagree with the backing chord changes here and there. This leaves you with C, D, E, G, A. These should be quite "safe" to play even completely chaotically.
So, find out what key your song is. Where is the tonic, the home note? When you know that, then you can assess your scale choices, and begin to reason about why and when something works or doesn't work. If you don't know the key, i.e. which note is the tonic, then you're floating around in space eyes closed and don't know which way is up, down, left, right - you're disoriented. You need a reference point to reason about the notes, and the musical key is your reference point.
(If I misunderstood what you're doing, then this whole answer is pointless.)
Comment: That is exactly the kind of answer I was looking for.Thank you
Answer: It would help if you provided an example.  In any Key there are a combination of major and minor chords.  Specifically the folling list of 7th chords are in each Major key,
IMaj7, ii-7, iii-7, IVMaj7, V7, vi-7, vii-7(b5)
So, in principle if you see anything from this combination would could just stay on the I major scale and be fine.  For example, in the changes I, vi, IV, V which is in many Rock ballads and similar to Rhythm changes, you could stay on the I major scale all the way.  There is no need to modulate and use the minor scale over the vi chord, etc.  If, on the other hand you see I, vii-7(b5), III7, vi-7 then because of the insertion of the Major chord on the iii you really have modulated to the vi and you will hear it that way.
There is a chord stream for the harmonic and melodic minor scales similar to what I posted above for the major scale.  I wouldn't pick a scale for each chord but rather use the patterns to determine the key changes if any and stick to the key.
Answer: Here is an online tool where you can enter a sequence of chords, and see what scales and modes are a best fit for those chords:
http://www.micrologus.com/tools/online_harmonic_analyzer
Below the form for entering the chords you'll also find an explanation of how are the scales and modes chosen to fit the different chords.
For disclosure, I programmed that online tool a few years ago, so if you find any mistakes, I'm the one to blame... :)
Comment: If the OP's problem is being unaware of such a fundamental concept as _key_, then I wouldn't suggesting using any automagical scale-finding tools. :)
Comment: This is a great tool! I especially like the way the adjacent chord tones are laid out graphically so you can easily see common and neighboring tones. +1
Answer: The minor pent. has been used for decades by guitarists to solo over both major and minor chords.
It's the mainstay for three chord wonders, 12 bars et al.
Let's take a key. A major, when there are simply three chords - A D and E, then A pent. works over most of the song. In fact, a lot of guitarists would make it work over all the song.
One could also use A maj. pent. again for most or all (being judicious) of the song.
The question asks 'what scale?' So in key A major, which may well have the chords A, Bm C♯m D E F♯m, then it makes sense to use the major scale diatonic to those - A.
Or have I missed the point of the question?
Comment: You got the question right, so, let's say the chord progression is in the key of A  and it goes A Bm E, soloing with the A major scale would be ok?
Comment: Yes. If you consider *modes*, they work in a very similar way. A is Ionian in this case, and the mode uses all the A scale notes. If instead you go from B to B, using the same notes, it's B Dorian. C# to C# is C# Phrygian, and go from E to E, it's E Mixolydian. All the same set of notes, but different 'centres', or 'home' notes. Those are never going to be the *only* notes to use, but they are the safe ones. My students are aware that any note (of all 12), can be used in any key, anywhere - if they know what they're doing!


What is the mathematical relationship between MOSFET switching frequency (motor speed control) and motor speed in rpm?

Question: What is the mathematical relationship between the switching frequency of MOSFET in a three phase motor controller (induction motor and BLDC motor) and the speed in rpm of the motor shaft?
Comment: In a BLDC motor drive, there are two switching frequencies: the commutation frequency, and in most drive methods, a higher frequency switching with the goal of effectively applying less than the full supply voltage to the windings. There is also a third possibility: some BLDC motors with an integrated controller receive a speed or torque input through a PWM signal. Which are you asking about?
Answer: There isn't one really.
The switching frequency of the MOSFETs is a function of the inductance and resistance of the motor and is used to control current ripple (and therefore torque ripple).
The speed of the motor shaft is a function of how fast you change which of the three phases are being powered.
That being said, there are limits. For instance the switching losses incurred from a high switching frequency will limit the amount of power available to the motor and therefore limit the speed with which you can commutate the motor.


A Hadamard product representation for Keiper's $\tau$-function?

Question: In this paper J.B. Keiper defined the following function:
$$\tau_k = \sum_{j=1}^k (-1)^j\,{k-1 \choose j-1} \sigma_{j+1} \qquad k \ge 1, k \in \mathbb{N} \tag{1}$$
where $\displaystyle\sigma_r = \sum_{\rho}\frac{1}{\rho^r}$, with $\rho$ a non-trivial zero of $\zeta(s)$ and taken in pairs $\rho, 1- \rho$.
Keiper also notes that $\tau_k = \lambda_{k+1} + \lambda_{k-1} -2\lambda_k$ where $\lambda_k$ is Li's constant ($=k\lambda_k^{Keiper})$. These $\lambda_k$ can be expressed in terms of the (paired) non-trivial zeros:
$$\lambda_k = \sum_{\rho,1-\rho} \left(1-\left(\frac{\rho}{\rho-1}\right)^k+1-\left(\frac{\rho-1}{\rho}\right)^k \right)$$
and from this it follows that $\lambda_{-k} = \lambda_{k}$ and $\tau_{-k} = \tau_{k}$.
Numerical evidence suggests this could be continued further into this entire function:
$$\tau_s = \sum_{j=1}^\infty\, (-1)^j\, {s-1 \choose j-1} \sigma_{j+1} \qquad s \in \mathbb{C} \tag{2} $$
Below is a plot to illustrate its behaviour. The RH implies the oscillations must stay (at integer values) within the two bounds and vice versa:

With $\tau_s$ being an entire function, it should have a Hadamard product factorisation into its zeros. After computing the first few of them, I found only a single complex zero $z=55.309... + 12.826...i$ (i.e. inducing a party of 4 complex zeros in total). All other zeros appear to be real and come in pairs $(\mu_{n},\mu_{-n})$, with $\mu_{1..24}$ shown below:

All the typical $e^{(.)}$-factors in the Hadamard product nicely cancel out and what remains is:
$$\tau_s = \tau_0\left(1-\frac{s^2}{z^2}\right)\left(1-\frac{s^2}{\overline{z^2}}\right)\prod_n\left(1-\frac{s^2}{\mu_n^2}\right)\left(1-\frac{s^2}{\overline{\mu_n^2}}\right) \tag{3}$$
where $\tau_0 = \sigma_1 = 1 + \dfrac{\gamma-\log(\pi)}{2}-\log(2)$. Numerical results look pretty good already at 24 real zeros.
Q: Is there anything more to learn from the existence of such a canonical Hadamard product? Could it say anything about the oscillating behaviour of $\tau_s$ or the distribution of its zeros?
Note 1:
$\tau_s$ could also be expressed in terms of $\rho$'s:
$$\tau_s = \sum_{\rho,1-\rho} \left(\frac{\left(\frac{\rho}{\rho-1}\right)^s}{\rho^2}+\frac{\left(\frac{\rho-1}{\rho}\right)^s}{(1-\rho)^2)}\right)\qquad s\in \mathbb{C}, \Re(s) \ge 0$$
$$\tau_s = \sum_{\rho,1-\rho} \left(\frac{\left(\frac{\rho}{\rho-1}\right)^s}{(1-\rho)^2}+\frac{\left(\frac{\rho-1}{\rho}\right)^s}{\rho^2}\right)\qquad s\in \mathbb{C}, \Re(s) \le 0 $$
Note 2:
Also found that $\tau_s$ could be split into a smooth first term and an oscillating second term:
$$\tau_s=\sum_{k=1}^{\infty} \left( {s+k-1\choose k-1}\cdot \frac{\zeta(k+1)}{(-2)^{k+1}}- {-s+k-1\choose k-1} \sigma_{k+1}^*\right)$$
with $\sigma_k^*$ defined here. The first term is asymptotic to $\dfrac{1-2^{-s}}{2s}$ for $\Re(s) \gt 0$.
Note 3:
It seems also possible to expand the domain of $\lambda_k$:
$$\lambda_s = \sum_{j=1}^{\infty} \, (-1)^{j+1}\, {s \choose j} \sigma_{j} \qquad s \in \mathbb{C} \tag{4}$$
and of $\lambda_k - \lambda_{k+1}$:
$$\lambda_s - \lambda_{s+1} = \sum_{j=1}^\infty\,{s + j - 1 \choose s} \sigma_{j} \qquad s \in \mathbb{C} \tag{5} $$
However, their Hadamard products turn out to be less elegantly compared to the one for $\tau_s$. Product (4) seems to have only complex zeros (which makes sense, since the positivity of $\lambda_k$ for all $k$ also implies the RH, hence no real zeros are expected to be found). Product (5) also appears to have a single real zero at $s=-\frac12$ and complex zeros otherwise.
Answer: $$\frac{\xi'(s)}{\xi(s)}=\sum_\rho \frac1{s-\rho}+\frac1{\rho} = -\sum_{j\ge 1} s^j\rho^{-j-1}$$ the Taylor series is valid for $|s|<|1/2+14.13i|$
Thus the coefficients  have exponential decay which implies that
$$ \sum_{j=0}^\infty\, (-1)^j\, {z-1 \choose j} \sigma_{j+2}$$ is entire.
Comment: Thanks! A proof like this is obviously much better than my numerical assessment.


Replacing pressure switch for my water pump

Question: I have to drain the pressure tank when I replace the pressure switch. When I do this can I install a shut off valve just below the pressure switch? This would allow me to change it in future years and avoid draining the tank.
Answer: Here is the down side.  The pressure switch, generally speaking has a very long life, many, many years.  So they have to be renewed relatively seldom.  And if you put an isolation valve between the switch and the main water line and it accidentally get turned off you really mess things up and cost yourself $1000's.  Better to have to drain the tank down.


How to change the color of the modes names (--INSERT--, --REPLACE--, --VISUAL--, etc)

Question: What is the color scheme property for the mode indicator (that says --INSERT--, --REPLACE--, --VISUAL--, etc) that appears at the bottom of the screen?
I would like to change this because the color scheme I am using has set the defaults to be too low contrast to be useful for an at-a-glance reference for the current mode.
Here's an image for reference of what I am talking about (circled with an arrow pointing to it):
Comment: does this help : http://vim.wikia.com/wiki/Change_statusline_color_to_show_insert_or_normal_mode ?
Comment: Somewhat, I now know that the property I am looking for is not `StatusLine` or `StatusLineNC`., which changes the line that says `~/Folder/file.txt` in my example image.
Comment: This is not a late nineties forum. Check the most helpful answer and mark the question as answered.
Answer: With a half hour of experimentation, I was able to figure out the answer to my own problem. The properly that I wanted to change the value of in my .vim color scheme was the "ModeMsg" property. I also edited the "MoreMsg" property because it had the same value and would have caused similar problems later.
My mode message and more message now are high enough contrast that they can be viewed easily.
Comment: You should report that issue to the maintainer of that colorscheme.


Does playing with a "default" weapon set-up in MW3 unlock weapon proficiencies?

Question: If you have the weapon in the default weapon class is it able to earn proficiencies?
OR earn points towards the same weapon if you've earned it in rank?
Comment: It's difficult to determine what you're asking here - are you asking "If you are using any of the non-custom default classes, do you still earn progress toward weapon proficiencies?"  What exactly do you mean by "earn points towards the same weapon if you've earned it in rank?"
Comment: If you use the default non-custom weapon for MW3 and you also have same weapon unlocked, does the non-custom default class version of the weapon still earn the proficiencies for the weapon type...
Answer: Playing with weapons before unlocking them does not help leveling up. after they are unlocked, it does regardless of how you pick them up


Terminal object in the category of embeddings

Question: Let ${\bf CPO}$ be the category of $\omega$-complete partial orders and $\omega$-continuous functions. Let ${\bf CPO}^{E}$ be the category of embeddings of ${\bf CPO}$. Does ${\bf CPO}^{E}$ have a terminal object?
Comment: I don't know what you mean by "embedding" but as long as 1) the unique map $\{\bot,\top\}\to\{\bot\}$ is not an embedding, and 2) any map $f:\{\bot,\top\}\to X$ such that $f(\top)\neq\bot$ is an embedding, then the answer is "no", and these seem to me to be pretty reasonable requirements.
Comment: Copying from Tennent's book: "If $D$ and $E$ are domains, a continuous function $f: D\rightarrow E$ is an embedding just if there is a continuous partial function $g:E \rightarrow D$ (termed a projection) such that: (1) $g \cdot f = id_D$, and (2) $f \cdot g \sqsubseteq id_E$". So, I think, your second condition is not always satisfied.
Comment: Ok, so these are "open" embeddings.  The answer is still no, because they are monomorphisms, and the only way for terminal arrows to be monos is that the category is posetal, which is not the case of $\mathbf{CPO}^E$.  I'll write up an answer.
Answer: The answer is no.
Let me first rewrite the definition given in the comments: an arrow $f:D\to E$ of $\mathbf{CPO}$ is an embedding if there exists $g:E\to D$ such that $g\circ f=\mathrm{id}_D$ and $f\circ g\sqsubseteq\mathrm{id}_E$, where $\sqsubseteq$ denotes the pointwise order.
Observe that, being right-invertible, embeddings are monic, so the arrows of $\mathbf{CPO}^E$ are all monic.  Now, for any category $\mathcal C$ with a terminal object, if all terminal arrows are monic, then $\mathcal C$ is posetal (there is at most one arrow between any two objects): let $1$ be the terminal object, let $f,g:A\to B$ be two parallel arrows and let $t:B\to 1$ be the unique terminal arrow from $B$; we have $t\circ f=t\circ g$ (because $1$ is terminal), so $f=g$ because $t$ is a monomorphism.
Now, it is immediate to see that $\mathbf{CPO}^E$ is not posetal: let $\mathrm{Unit}$ be the cpo $\{\bot,\top\}$ and let $\mathrm{Bool}$ be the cpo $\{\bot,0,1\}$ with $0$ and $1$ incomparable; there are two distinct embeddings $\mathrm{Unit}\to\mathrm{Bool}$.  Therefore, $\mathbf{CPO}^E$ cannot have a terminal object.


Why there is no timer for upvoting?

Question: As far as I know, you can't upvote two comments in less than 5 seconds. Why don't we have such a system for up/down-voting questions? For example once you vote you can't vote again for 10 or 15 seconds later. Doesn't that reduce serial voting?
Comment: I don't think people vote enough as-is, so I'm hesitant to put up any more barriers...
Comment: I often read a question, then the answers, and subsequently, having read them all, I decide whether to upvote the question, and which answers get my vote. It would be a pain to have this method impaired by some rate limiting.
Answer: A main reason, AFAIK, for this delay for comment voting is rather 'technical'. By which I mean it is (also) there to prevent somebody automatically attacking the site with extreme numbers of votes. Note for example that you also cannot fetch comments too quickly in succession.  This is irrelevant for the other voting as there there is a global limitation on your votes and thus this local one is not necessary to prevent such an attack.
To prevent too much voting on comments is perhaps also a consideration, but I think a secondary one.
When people talk about problems with serial voting I think most mean the problem of one user voting many posts of some particular other user. To do this, typically, there is some inevitable small delay, like, visit post, vote, go back to userpage, visit another post, vote. So that might be done more quickly than in 15 seconds but than perhaps not even this is clear.
In addition, there is an argument to be made that it is actually better not to have some weak measures against serial voting (like such a delay) because as they are trivial to get around people will do yet then the serial voting gets harder to distinguish from legit voting.
Comment: What? Serial voting is so easy to do within seconds. Just go to the user page, open some 10 posts, then just vote-close tab-vote-close tab-... until you're through.
Comment: Okay, if you *prepare* for having the votes in as rapid succession as possible you will certainly manage to make it in less than 10 seconds, or even 5. And if you do not do the opening in advance (*which costs some time too*) you might from beginning to end even be about as (admittedly perhaps a bit more)  efficient in the way I described it. But I would still maintain that serial upvoting ineveitabbly has slightly more delay to it than upvoting all comments in a long comment thread. Besides this not having been my point anyway.
Comment: That one sentence did not come out as intended. I meant to admit that the procedure described by Asaf Karagila is more efficient than the one I described though IMO from beginning to end only slightly so.

Why there is no timer for upvoting?


How to darken an image using the Imager plugin

Question: I'd like to 'darken' an image using the Imager plugin. How would I go about doing this?
I'll explain the exact effect I'm after in Photoshop terms: I have an image on one layer, then I create a new layer above it and fill it with black. I then change the opacity of the black layer to 40%. This is the end result that I'm trying to achieve with the Imager plugin (ImageMagick is available too).
I realise I could add a div with a black background over the images and change the opacity of this div, but I think it would be nicer if I could do this with the Imager plugin instead if this is possible.
This is the closest I've managed to get so far, but it doesn't quite match what I'm seeing in Photoshop:
<code>{% set image = block.image.first() %}
{% set transformedImage = craft.imager.transformImage(image, {
  width: 1500,
  height: 700,
  effects: {
    vignette: ['none', 'black', 3],
    modulate: [100, 80, 100],
    gamma: 0.7 }
}) %}
</code>
Thanks in advance for any help with this.
Comment: Do you have some kind of blend mode on the black layer, or is it just a normal semi-transparent layer on top of the image?
Comment: Hi André, it was just a normal semi-transparent layer on top of the image. No blend modes were used. I then reduced the opacity of this black layer to 40% and this is the result I was trying to reproduce.
Answer: Seems like you might be better using colorBlend?
<code>{% set image = block.image.first() %}
{% set transformedImage = craft.imager.transformImage(image, {
  width: 1500,
  height: 700,
  effects: {
    colorBlend: ['rgb(0, 0, 0)', 0.4] }
  }
}) %}
</code>
Comment: Hi Seth, thanks for the suggestion. I've just tried this, but it didn't seem to make the image darker, unfortunately. It just seemed to desaturate the image a bit.


I need a one-line description for a Christian horror novel I'm writing

Question: I need a one-liner description for the book I'm writing. There are three main characters, a brother and sister and a young man.  My book is a Christian horror novel. The sister must keep her surrogate family together as she tries to forget her family of origin. Her half-brother searches for his biological mother and wants a woman he can truly trust. At first, the demon-possessed man wants to get rid of the evil spirit but, he changes his mind and starts collaborating with the demon to destroy the siblings. Example of a One line description: The Day of the Jackal, by Frederick Forsyth, "a thriller about a professional assassin hired by French terrorists to kill Charles de Gaulle."
Comment: We can't do this for you. But, we can point you to websites about writing log lines. There are plenty of blogs out there. Google is your friend. My crack at it: "a Christian horror about a demon destroying an already broken family..."  <- See? It's not what you want. You need to find it yourself.
Comment: I'm voting to close this question because it appears to be about what to write rather than how to write. If _Tiny Bookworm_ wants to create a new questions asking how to come up with a one-line description, that would be awesome!
Answer: Hell has come for the [Surname]'s!
It's short, sweet, but edgy enough to grab a millennial's attention.


Was there ever a situation where members of two warring militaries were on leave in the same neutral location?

Question: Or not necessarily on leave, but in some capacity where they were present in numbers but not allowed to fight?
Comment: Yes, don't know about the famous football match between the Huns & English at christmas in WW1? 2014 marked the 100th anniversery of this event. Check the wikipedia article on this:  https://en.wikipedia.org/wiki/Christmas_truce
Comment: Does meeting in a third country for peace negotiations or mediations count?
Answer: Germans and British combatants frequently visited Ireland which was neutral in WWII. German submarine crews would frequent pubs in Dublin as did RAF pilots and crews of British Navy vessels. Sometimes there would be knowing encounters of Germans and British; sometimes unknowing encounters; sometimes just vague suspicions that the bunch of square-heads sitting at the bar were German submariners. This wasn't the proper venue for violence so visiting belligerents either avoided each other or talked shop with each other. Under Article 17 of the Hague Convention belligerent vessels or aircraft requiring repairs or with sick, wounded or dead crewmen on board could stay in neutral ports for a period of 72 hours. After that time internment of ship and crew would occur. To avoid internment,  belligerent ships and aircraft had to leave the neutral country after the prescribed time had elapsed.
Ireland has a long history of allowing aircraft of belligerent nations to overfly Irish territory or to refuel at Shannon. The prerequisites were: no weapons, no armaments on board, no explosives. Allied pilots frequently landed in Ireland or crash-landed, refueled or hospitalized and were then escorted to the border with Northern Ireland. Crews of German aircraft had to prove they were not on a 'combative mission' which was a hard test for them, but not impossible. I should note here that ROI neutrality was never a statutory matter of law. It was a policy of the government then in power. So internment or no internment was decided on an ad hoc basis.
Comment: Some actual data, please? Neutral countries are forced to avoid being used as a military base by belligerants (Switzerland shot down both German and Allied planes), and given Ireland officers pro-Allied stance, `a German submarine crew might hide somewhere in an inlet and the crew goes ashore` is difficult to believe (other issue are submarines delivering/receiving spies/commandos, but those usually try to not get identified).
Comment: That's exactly the kind of thing I was looking for, but I can't find sources for german soldiers/sailors/airmen in Dublin. I did manage to find something similar http://www.express.co.uk/expressyourself/255828/The-Cushiest-PoW-camp , is this what you were referring to?
Comment: I  refer to fraternization between Germans and British servicemen--not POWs. Entry into Ireland was often surreptitious to avoid internment. But Irish rules of neutrality were flexible, especially in rural coastal areas. A German submarine crew might hide somewhere in an inlet and the crew goes ashore. Ireland was less neutral when it came to British servicemen and many were not interned. In truth, I have read of only one incident of a British officer and a German officer meeting in a pub and discreetly avoiding military topics--but the circumstances were not that unusual to the bartender.
Comment: @user3847 What these sorts of discussions seem to overlook is that although Ireland was technically neutral, thousands of the Republic's citizens served in the British armed forces during the war (many of them winning the highest decorations for bravery - such as the Military Cross, and even a few the Victoria Cross). Nobody should get the idea that German U-boat crews were all over Dublin. They would fairly quickly have been popped off had they been, and perhaps Mr de Valera with them.
Comment: It would be a mistake to conclude that every belligerent vessel or aircraft entering a neutral country is automatically interned and the crews consigned to an internment camp. Even the crew of the Graf Spee had a pleasant shore leave before being forced to leave Uruguay.


SEBI RULE For Closed Company / Share not traded

Question: I have Invested good amount in SUPREME TEX (BSE: 531934).. This company is not traded from last two month. What is the SEBI rule to for refund ?
Answer: SEBI doesn't refund money for shares. It regulates the exchange.
The company has lost value and SEBI has stopped trading on exchange.
Given that it's book value is negative, I doubt if you can find any offline buyer's


No file transfer window?

Question: New to the forum and to elementary OS, trying it out and enjoying it very much for the moment, thanks to the devs!
I'm transferring a big folder from an external hard disk to the pc and I find it quite strange not to have a files transfer window popping up and showing me the transfer speed, the amount of time elapsed and so on.
Is it a deliberate decision not to have this window or is it just my fresh installation who's somehow missing it? Or is it an optional feature maybe?
Cheers,
Edoardo
Answer: You should see a progress bar in the icon in the dock? There are some known bugs in the progress window at the moment e.g. see https://github.com/elementary/files/issues/1275 and https://github.com/elementary/files/issues/1050.
I find that after some file transfers, the operation is  not properly cleaned up (e.g. the progress bar in the plank icon may continue to show) which may affect subsequent operations.  Hopefully it will be fixed in the not too distant future.
Comment: Hi Jeremy and thanks for your answer.I see it's a known issue then. I experience the exact same problems as those described in your first link. I do see a progress bar in the dock icon (actually the only proof that the transfer is ongoing), but that too eventually gets stuck in strange ways. Hope it gets fixed soon!

No file transfer window?


Azure enable HTTPS on naked custom domain for an end point

Question: I am hosting a static website using the following Azure Resources:

Azure Storage Account
Azure CDN
CDN End Points
DNS Zone

and my domain is purchased from GoDaddy.
The implementation is very straightforward:

I deploy my static website to the storage account and all is fine I got my primary and secondary URLs which are both working fine
In my CDN profile, I have created an endpoint pointing to my storage account URL and as a result, a new endpoint resource was created testing endpoint hostname works perfectly
My DNS Zone is based on my GoDaddy purchased domains I already added the @ record of the type "A" and the www record of the type "A" as well also Azure automatically created 2 additional Cname Records for CDN verify purpose
back to the endpoint that I created in the CDN I add 2 custom domains for my web site which are "example.com" & "www.example.com" both URLs work fine now and open the site hosted in the Storage account but it's happening over HTTP, not HTTPS
I click on the www.example.com custom domain in the endpoint overview blade and from the new blade I select on for custom domain HTTPS and choose CDN managed and click on save after some time for verification it works fine and www.example.com is working over HTTPS
repeating the same step 5 for the naked custom domain in the endpoint is not working as when I click on save it is throwing an error

We couldn't find a DNS record for custom domain that points to endpoint. To map a domain to this endpoint, create a CNAME record with your DNS provider for custom domain that points to endpoint.

My ultimate goal is to be able to open both www.example.com and example.com over HTTPS, if I can fix this error or perhaps follow an alternative implementation there is no problem with that, or if it's possible to redirect without a redirection server from the naked domain to the www it would be fine as well I am open to any solution.
I tried adding a cname with naked domain value to my DNS zone but I am learning that it's not possible as I have to provide a prefix to the .example.com when creating a cname in the Azure DNS zone.
Comment: I have a similar issue. Any workaround? Thanks!
Answer: You can go to your DNS settings and add a new A record with blank name. You will have to select Alias type and pick your CDN resource.
Then after you can go back to your CDN and add the custom domain.
https://azure.microsoft.com/en-us/blog/announcing-alias-records-for-azure-dns/


What does the title "The Fault in Our Stars" signify?

Question: I just saw The Fault in Our Stars and was quite confused with the title in relation to the plot of the movie. Can anyone help me to understand the co-relation between the plot and the title?
Answer: It is from a line from the play Julius Caesar, by Shakespeare:

Cassius:
  The fault, dear Brutus, is not in our stars,
   But in
  ourselves, that we are underlings.
Julius Caesar (I, ii, 140-141)

To quote from the eNotes interpretation of the play:

...Cassius continues by reminding
  Brutus that Caesar is just a man, not a god, and that they are equal
  men to Caesar. They were all born equally free, and so why would they
  suddenly have to bow to another man? On another level this phrase has
  been interpreted to mean that fate is not what drives men to their
  decisions and actions, but rather the human condition.

In other words, we're to blame for the badness in our lives. We have driven it, through our own actions.
However, the film is based on a book by John Green, who appears to be arguing something different.
Rather than the fault being in ourselves, that the bad stuff is because of us and our choices in life, Green's title suggests the fault is in our stars - that the bad things happen through no fault of our own. That we have little control over our own eventual fate.
The whole novel (and movie) follows this logic and shows the characters leading their lives to the fullest, despite the fault in their stars.
Comment: This distinction is more clear when you recognize that that while Cassius says the fault "is **not** in our stars", John Green omits the "not".
Comment: It's also relevant to note that, elsewhere in Shakespeare's body of work, Romeo and Juliet are referred to as the "star-crossed lovers".  Stars represent fate, and you'd want them to align, to smile on you, or at the very least leave you alone.  When the stars/fates have faults or are crossed, it's easy to predict an unhappy ending.
Answer: It means not everything or everyone is perfect . But what highlights or shines like a star in anyone or anything is those little imperfections . And we or anything are the result of those imperfections which came through situations rather than what we could have avoided.


Center–align arabic text

Question: Is it acceptable to center–align Arabic text and if so, is there anything I should take care of in this regard?
Answer: I don't know Arabic but I don't see why it wouldn't be acceptable. it is just read from right to left but you can still center-align it.
example:

Center–align arabic text


Java heap keeps on shrinking! What is happening in this graph of heap size?

Question: This is a screen shot of a JVM (win64, 6u17) running ActiveMQ, after every garbage collection the heap size is reducing.  As the heap size reduces garbage collection gets more frequent and the heap reduces more quickly.  Eventually the VM locks up as it's spending all it's time in GC.
-Xms is the default and -Xmx is 2048mb.
What is happening!!? How can I avoid this?
http://imagebin.org/92614
Shrinking heap http://imagebin.org/index.php?mode=image&id=92614
n.b originally posted on serverfault.com, moved to stackoverflow.com as requested
Comment: please include images in your question, rather than providing links (which no longer work)
Answer: Google found me the following, from the IBM JVM FAQ (how's that for an NLA):

When does the Java heap shrink?
Heap shrinkage occurs when GC determines that there is a lot of free heap storage, and releasing some heap memory is beneficial for system performance. Heap shrinkage occurs after GC, but when all the threads are still suspended.

The Sun JVM does something similar.  Below is an excerpt from an Oracle Technology Network article entitled Ergonomics in the 5.0 Java Virtual Machine.

The heap will grow or shrink to a size that will support the chosen throughput goal. Some oscillations in the size of the heap during initialization and during a change in the application's behavior can be expected.
...
It is typical that the size of the heap will oscillate as the garbage collector tries to satisfy competing goals. This is true even if the application has reached a steady state. The pressure to achieve a throughput goal (which may require a larger heap) competes with the goals for a maximum pause time and a minimum footprint (which both may require a small heap).

I suggest you have a look at the rest of that document; it may have more information relevant to your problem.
Answer: There is a JVM argument that controls when the heap is resized.
-XX:MaxHeapFreeRatio
The default value for this is 70. The free ratio is the amount of space not allocated on the heap over the total heap size. If the percentage of free space rises above the default of 70% the jvm will reduce the size of the heap to allow the OS to use the memory.
If the heap is shrinking too often you can increase the value of -XX:MaxHeapFreeRatio. If it is set to 100, i.e., -XX:MaxHeapFreeRatio=100 presumably it will never shrink.
Answer: Just a guess:
It looks like the system is pretty much idle. There might be some caching going on, and stuff drops out of the cache and gets gc'd. Or since it is a queuing system, maybe it has some messages, in the queue, which slowly get delivered and gc'd afterwards.
The increased frequence of gc-runs might be due to ever decreasing load on the system.
As to how to avoid it. Why do you want to avoid it? It seems like your CPU load is zero. So you are free to let the gc do whatever it wants
Comment: I think that "Eventually the VM locks up" (if true and as the OP stated) would be something to want to avoid.


Are flared elbows better for upper chest?

Question: I was told that the positioning of the clavicular head meant that the muscle was activated best when the arms are flared, almost 90° to the body. I'm just wodnering if this is true?
Answer: If EMG activation is an outcome you care about, maybe.
The full text is paywalled (thanks Elsevier), but figure 4 of "Force direction and arm position affect contribution of clavicular and sternal parts of pectoralis major muscle during muscle strength testing" indicates that the highest ratio EMG amplitude between the clavicular and sternal heads of the pectoralis major occur when the arms are in the transverse plane and you're doing incline or decline bench press. However, this study observed greater clavicular head activation with the arms at 45 degrees to the transverse plane when doing a flat bench press. So to directly answer the question, "maybe?".
But is EMG activation really something you care about? No research to date has reliably indicated a strong relationship between EMG activations and the outcomes most people actually care about, hypertrophy and strength.
Comment: You're right, I have no interest in EMG results. I'm just interested in whether it has an significant affect on hypertrophy and strength increase in the upper cheat.
Comment: I will have to dig around, I ***thought*** I saw something a while ago that suggested the best angle was around 60-70 degrees (Counting next to the body as zero and at right angles to body as 90), but I have no idea where I read that.]
Comment: @JohnP Even then, we ought avoid the mistake of allowing group-level averages dictate individual practice. We can use study results like this to generate hypotheses for our own training, but from there we ought be individualizing our training to what works for us.
Comment: @ThomasMarkov - Correct and true. Read, educate yourself and figure out what applies for your own training. Good point.
Comment: @Ethan it seems to be a less important detail compared to pressing angle, for example.


Unable to edit subpages with Full Control permissions

Question: I am the owner of a site in which I have created sub-pages. I receive an error message with my correct user ID when I try to Edit the pages. I verified, multiple times, I have Full Control permission. I tried using the Designer and Style Resource Readers groups without success. Why is this happening and how can if be fixed?
Comment: Make sure that the pages are not checked out for editing by someone else.
Comment: Yes- I have ensured the page is checked-in and published. Thank you.
Answer: If the pages reference, even one item from somewhere where you don't have rights you will get access denied.
Run browser tools and start a network trace when you access the page.  You should see all the requests being made for the page and resources.  Review those and you should be able to see which element is being requested (and from where) that you can not load.
If it is the page library itself - try the following

Attempt to access the list settings page.  It's difficult via the browser as you need the GUID, but opening it up in SharePoint designer should work.
If inheritance is broken - then change that to inherit site permissions.  If it is not - then break it, remove permissions, and then inherit from the site again.
You may need to have your account removed from the site collection and re-added - before that however I would....

Get more information from the server logs.  the ULS logs will have a request for all SharePoint resources as well as any access denied messages and why.  Your admins should be able to query and extract all request for your user account.
Answer: I had same issue. I simply had to provide global read access to the master page library. Site actions > site settings > Master Page and page layouts > Library tab > Permissions. Add All authenticated users to READ ONLY.
Comment: Interesting... I am also unable to view/edit the Master Page settings. I receive the same Access Denied error.


Is there a difference between x++ and ++x in java?

Question: Is there a difference between ++x and x++ in java?
Answer: ++x is called preincrement while x++ is called postincrement.
int x = 5, y = 5;

System.out.println(++x); // outputs 6
System.out.println(x); // outputs 6

System.out.println(y++); // outputs 5
System.out.println(y); // outputs 6

Answer: yes
++x increments the value of x and then returns x
x++ returns the value of x and then increments
example:
x=0;
a=++x;
b=x++;

after the code is run both a and b will be 1 but x will be 2.
Answer: These are known as postfix and prefix operators. Both will add 1 to the variable but there is a difference in the result of the statement.
int x = 0;
int y = 0;
y = ++x;            // result: x=1, y=1

int x = 0;
int y = 0;
y = x++;            // result: x=1, y=0

Comment: Shouldn't it be `suffix`?
Answer: In Java there is a difference between x++ and ++x
++x is a prefix form:
It increments the variables expression then uses the new value in the expression.
For example if used in code:
int x = 3;

int y = ++x;
//Using ++x in the above is a two step operation.
//The first operation is to increment x, so x = 1 + 3 = 4
//The second operation is y = x so y = 4

System.out.println(y); //It will print out '4'
System.out.println(x); //It will print out '4'

x++ is a postfix form:
The variables value is first used in the expression and then it is incremented after the operation.
For example if used in code:
int x = 3;

int y = x++;
//Using x++ in the above is a two step operation.
//The first operation is y = x so y = 3
//The second operation is to increment x, so x = 1 + 3 = 4

System.out.println(y); //It will print out '3'
System.out.println(x); //It will print out '4'

Hope this is clear. Running and playing with the above code should help your understanding.
Answer: Yes,
int x=5;
System.out.println(++x);

will print 6 and
int x=5;
System.out.println(x++);

will print 5.
Comment: This "answer" just tells you a test case output, and I consider that outputs are not answers. On the contrary, normally the (unexpected) result of some code execution leads as to the question. Hence my down vote.
Answer: I landed here from one of its recent dup's, and though this question is more than answered, I couldn't help decompiling the code and adding "yet another answer" :-)
To be accurate (and probably, a bit pedantic),
int y = 2;
y = y++;

is compiled into:
int y = 2;
int tmp = y;
y = y+1;
y = tmp;

If you javac this Y.java class:
public class Y {
    public static void main(String []args) {
        int y = 2;
        y = y++;
    }
}

and javap -c Y, you get the following jvm code (I have allowed me to comment the main method with the help of the Java Virtual Machine Specification):
public class Y extends java.lang.Object{
public Y();
  Code:
   0:   aload_0
   1:   invokespecial  #1; //Method java/lang/Object."<init>":()V
   4:   return

public static void main(java.lang.String[]);
  Code:
   0:   iconst_2 // Push int constant `2` onto the operand stack.

   1:   istore_1 // Pop the value on top of the operand stack (`2`) and set the
                 // value of the local variable at index `1` (`y`) to this value.

   2:   iload_1  // Push the value (`2`) of the local variable at index `1` (`y`)
                 // onto the operand stack

   3:   iinc  1, 1 // Sign-extend the constant value `1` to an int, and increment
                   // by this amount the local variable at index `1` (`y`)

   6:   istore_1 // Pop the value on top of the operand stack (`2`) and set the
                 // value of the local variable at index `1` (`y`) to this value.
   7:   return

}

Thus, we finally have:
0,1: y=2
2: tmp=y
3: y=y+1
6: y=tmp

Answer: When considering what the computer actually does...
++x: load x from memory, increment, use, store back to memory.
x++: load x from memory, use, increment, store back to memory.
Consider:
    a = 0
    x = f(a++)
    y = f(++a)
where function f(p) returns p + 1
x will be 1 (or 2)
y will be 2 (or 1)
And therein lies the problem.  Did the author of the compiler pass the parameter after retrieval, after use, or after storage.
Generally, just use x = x + 1.  It's way simpler.
Answer: Yes.
public class IncrementTest extends TestCase {

    public void testPreIncrement() throws Exception {
        int i = 0;
        int j = i++;
        assertEquals(0, j);
        assertEquals(1, i);
    }

    public void testPostIncrement() throws Exception {
        int i = 0;
        int j = ++i;
        assertEquals(1, j);
        assertEquals(1, i);
    }
}

Answer: Yes, using ++X, X+1 will be used in the expression. Using X++, X will be used in the expression and X will only be increased after the expression has been evaluated.
So if X = 9, using ++X, the value 10 will be used, else, the value 9.
Answer: If it's like many other languages you may want to have a simple try:
i = 0;
if (0 == i++) // if true, increment happened after equality check
if (2 == ++i) // if true, increment happened before equality check

If the above doesn't happen like that, they may be equivalent
Answer: Yes, the value returned is the value after and before the incrementation, respectively.
class Foo {
    public static void main(String args[]) {
        int x = 1;
        int a = x++;
        System.out.println("a is now " + a);
        x = 1;
        a = ++x;
        System.out.println("a is now " + a);
    }
}

$ java Foo
a is now 1
a is now 2

Answer: OK, I landed here because I recently came across the same issue when checking the classic stack implementation. Just a reminder that this is used in the array based implementation of Stack, which is a bit faster than the linked-list one.
Code below, check the push and pop func.
public class FixedCapacityStackOfStrings
{
  private String[] s;
  private int N=0;

  public FixedCapacityStackOfStrings(int capacity)
  { s = new String[capacity];}

  public boolean isEmpty()
  { return N == 0;}

  public void push(String item)
  { s[N++] = item; }

  public String pop()
  {
    String item = s[--N];
    s[N] = null;
    return item;
  }
}

Answer: Yes, there is a difference, incase of x++(postincrement), value of x will be used in the expression and x will be incremented by 1 after the expression has been evaluated, on the other hand ++x(preincrement), x+1 will be used in the expression.
Take an example:
public static void main(String args[])
{
    int i , j , k = 0;
    j = k++; // Value of j is 0
    i = ++j; // Value of i becomes 1
    k = i++; // Value of k is 1
    System.out.println(k);
}

Answer: The Question is already answered, but allow me to add from my side too.
First of all ++ means increment by one and -- means decrement by one.
Now x++ means Increment x after this line and ++x means Increment x before this line.
Check this Example
class Example {
public static void main (String args[]) {
      int x=17,a,b;
      a=x++;
      b=++x;
      System.out.println("x=" + x +"a=" +a);
      System.out.println("x=" + x + "b=" +b);
      a = x--;
      b = --x;
      System.out.println("x=" + x + "a=" +a);
      System.out.println("x=" + x + "b=" +b);
      }
}

It will give the following output:
x=19 a=17
x=19 b=19
x=18 a=19
x=17 b=17

Comment: This response would be even better if accompanied by a few words of explanation.
Answer: public static void main(String[] args) {

int a = 1;
int b = a++; // this means b = whatever value a has but, I want to
increment a by 1

System.out.println("a is --> " + a);    //2
System.out.println("b is --> " + b);    //1
a = 1;
b = ++a;  // this means b = a+1

System.out.println("now a is still  --> " + a);    //2
System.out.println("but b is --> " + b);           //2

}

Answer: With i++, it's called postincrement, and the value is used in whatever context then incremented; ++i is preincrement increments the value first and then uses it in context.
If you're not using it in any context, it doesn't matter what you use, but postincrement is used by convention.
Answer: There is a huge difference.
As most of the answers have already pointed out the theory, I would like to point out an easy example:
int x = 1;
//would print 1 as first statement will x = x and then x will increase
int x = x++;
System.out.println(x);

Now let's see ++x:
int x = 1;
//would print 2 as first statement will increment x and then x will be stored
int x = ++x;
System.out.println(x);

Answer: Try to look at it this way:
from left to right do what you encounter first. If you see the x first, then that value is going to be used in evaluating the currently processing expression, if you see the increment (++) first, then add one to the current value of the variable and continue with the evaluation of the expression. Simple


Do the different skills on the skill tree add to each other?

Question: In the bounty hunter: powertech skill tree, the skill puncture lets rail shot ignore up to 60% of your opponents armour and the skill superheated rail let you ignore 30% of your oppenents armour.  So does the combination of these two skills mean that you are ignoring 90% of your opponents armour with each shot? or does the game calculate the values some other way?
Comment: How far down the trees are each of these skills?  They may have intentionally made it so that you cannot have both skills at once.
Comment: one is a first level the other is five tiers up the other tree.
Answer: I would have thought the answer was 72% (1-(1-.6)*(1-.3)), but all the sources I find seem to suggest that 90% is the correct reduction.
Citations: 1,2,3


Controlling Arduino through python

Question: How to set the registers of Arduino through python code to vary the sampling rate of Arduino?
Can we control Arduino through python?
Comment: what runs the python script?
Answer: If you mean can you run a python script on a "PC" and send messages to an Arduino then yes but you would need to write code that ran on the Arduino to receive messages from the "PC" and turn those into actions on the Arduino.
If you mean can you run a python script on an Arduino directly, well yes you can there are python implementations for Arduinos, but if you go down this route you need to remember you only have a small amount of memory and you are going off piste where there will be little or no help.
Honestly I would learn how to program the arduino in C++ and stick to that.
Comment: welcome back Code Gorilla. you could mention Firmata
Comment: Thank you very much :)  That was the one I had a quick look at, but I didn't investigate it in any detail so I didn't want to hint it might be any good.

Controlling Arduino through python


Is it important to show order receipt every time?

Question: Can anybody tell me how important is to show the order receipt every time, whenever the order is placed. Is there any other way to cut off this step? We are handling large enterprise applications where in users buy & provision services using this application.
Answer: YES
Giving order receipt is a MUST for any transaction, more so for an enterprise application. In fact, you can be in legal trouble if the customer is not given his order receipt. For enterprise applications, it's also used by employees/users to reimburse the amount from the company if they paid it from their pocket. Some companies mail the receipts instead of showing it to you after completing the transaction. In my opinion, both should be done -- Show the receipt after payment and also mail a copy to the user.
Comment: Most welcome :)
Answer: No process is complete without an acknowledgment at the completion.
In this case, the customer performs a transaction involving money. It is mandatory that an acknowledgement in the form of a receipt is shown to the user. Also it will save your customers some anxiety trying to figure out if their order was successfully processed. Besides, the receipt is a good place to show reference information to track down purchase.
Hope this helps.


How to send an access database

Question: I'm having trouble trying to find a way to send a ms access application to someone I have built one for. They say you cannot open it from OneDrive or problems occur. But is the person able to copy it from OneDrive to there desktop? Email works but has a 25 mb limit. How can I simply send an accdb file?
Comment: I see no reason why a file can not be opened from a Onedrive location. I assume that the person has MS Access installed. You must be more specific about the problems that occur.
Comment: I can open an Access .accdb from OneDrive. With OneDrive installed on Windows 11 the Desktop is synchronised so there would be no need to copy a file between the two. I assume your user is remote so you need to sit beside them and see exactly what is happening.
Comment: [What have you tried?](https://stackoverflow.com/help/how-to-ask)
Answer: I'm presuming that your Access app do not have split database (front-end/back-end). Your Access app users have to download the App to their desktop and launch the App from their desktop.
If for any reason you need to allow your app user to launch and use the Access app from Onedrive. They need to have their own Onedrive account and you need to grant them permissions to run App on top of your Onedrive. Managing of user access on Onedrive can be quite confusing therefore to put it simply download and run the app on desktop.
Whether you are sharing the ACCDE or ACCDB, either way it should work if downloaded and running from the desktop. But if you have forms designed and VBA developed then ACCDE should be shared rather than ACCDB because you won't want the app users to mess around with the VBA/forms.
Answer: If the purpose is just sending the file then you can use OneDrive or Google drive would work fine. You would have to provide them link of the file by using get link or share link option. Even you can use wetransfer that will transfer the file through a link to the email.
As cbk said, you may share accde instead of accdb plus a split database. I alway distribute frontend in the form of .exe file to the end users and backend as a zipped file. You can use SSE Setup maker to make .exe of access file (if your project is free, SSE is free to use, for commercial projects you have to buy a licence). SSE takes care of many things like installing prerequisites (runtime and other), add trusted locations and more. Just my two cents.
Best Regards

How to send an access database


Simulating two wires touching

Question: I found this motor from an old piece of equipment. When a button is pressed, the battery powered motor turns on. When I took apart the button, its functionality was to make two metal plates touch each other, creating a current flow. I'm wondering if I can hook up these wires to my Pi's GPIO pins and program a script that will fake the wires being connected. Is this possible?
Answer: No! You can use a relay.
I suggest you do some research before connecting anything to your Pi and learn a bit about circuitry.
There are hundreds of books and tutorials.
Answer: A relay is your best choice, as it will connect the wires, and will require only one line. The script will have to power the relay to activate the motor. Connect the relay to the button's signal, and it will simulate the button when you close the relay.
Comment: What specs should I look for when trying to find a compatible relay?
Comment: @user Try [this](https://www.amazon.com/4-Channel-Optic-Isolated-Trigger-Arduino-Raspberry/dp/B00WJXJ27I)

Simulating two wires touching


Application Server <-> Database Firewall

Question: What threats can a firewall between an application server and a database server mitigate that would not otherwise be mitigated when both the database server and application server are behind the same firewall?
Comment: Breaking into your application server and then launching attacks against the database server or the rest of the LAN by running hostile software on the application server.

Also, vice versa, assuming SQL Injection compromises the database server rather than the application server directly.

Essentially, a firewall between the two restricts the communications, and thus the vectors by which they can be compromised.
Answer: The risk is simple: an attacker that gets control over one of those servers would likely be able to compromise the second server. From database to application or the other way around.
If you setup a firewall device between those two, there are two possibilities:

Network (standard) firewall: you won't be able to do much from that kind of device, apart of limiting connections from application server to the database server (i.e. deny connections from DB to application server).
Web Application Firewall (WAF) or any other layer 7 technology: you would be able to prevent and/or detect attacks from one server to another and to restrict trafic as with the previous solution.

So basically the answer is really that you should be using some firewalling / filtering technology between your application and your database servers. A host-based solution can be considered too, in addition to a network device or as the main solution.


User Interface for creating Oracle SQL Loader control file

Question: Is there a good user interface for authoring Oracle SQL Loader control files? PL/SQL Developer includes a "Text Importer" feature (that reminds one of the Excel import wizard) to import text files into tables, but uses a proprietary format instead of the SQL Loader format. Something like this for the SQL Loader format would be quite helpful.
Answer: TOAD has an interface to do SQL*Loads, it can generate the control files too...
http://www.toadsoft.com/get2know9/#Loader
Answer: The TOAD answer is probably the best at present. However, in trying out the TOAD SQL Loader wizard, I was disappointed at the level of usability. It assumed that I had a pre-existing table to load the data into. I was looking for something that would let me first

locate columns in the fixed-width input file, then
analyze the columns for candidate names and data types, then
generate a table and control file for loading the data

Since I couldn't find anything that would adequately meet my needs, I created a utility for the purpose. The utility is somewhat custom to my specific needs (fixed-width file format, headers on top, dashed divider separating headers from data, white space between columns) and only supports the SQL Loader features that I required. If I have opportunity to flesh it out to something more universally usable, I'd be happy to post it for the community.


Can I stack two l293d h-bridge IC's to drive more current?

Question: I need more current but I do not want to change my pcb board so can I piggy back two L293D pin for pin? I am driving dc motors and I am not seeing any gross failures but I am very close to the max ratting and so I wanted just a bit more headroom.
Comment: I would ask the vendor's FAE.
Comment: I am just a hobbiest so I am not sure how I would get a hold of one or if they would even bother to answer my questions.
Answer: That's not generally recommended.  If you know the devices are from the same batch (i.e. are more closely matched) and you can ensure that they are thermally coupled (hard to do since they are in packages) then it's not recommended.
It would safer to get another similar device that has lower Rds(on).
Comment: Looked at the datasheet and it's a bipolar device, which is not good news as they can have thermal run away.  However, since it's marginal now, any current that is diverted into a parallel circuit should increase your margin as LONG as the mounting of the 2nd package doesn't compromise the the total thermal system.  If this is a one off thing then experiment.  If a production unit, I'd not recommend it.
Comment: So are you saying that one could turn on before the other one? And even if it did would it really do damage?
Comment: Turning on is the least of your worries, it's about current hogging.  You don't say what the device is, so I'll assume a MOSFET of IGFET.  One device will take a majority of the load and as it heats up it will pull more.
Comment: Oh, okay. I see where you are going. So where will it end up (stable state), will it be that one is taking 75% of the total current or are you saying that it would end up that one would end up taking >95% of the current. I have not tried to run the numbers in a long time but from a gut feel it seems like they might differ slightly but that one would not end up taking a large majority of the current.
Comment: Obviously you're at the limit of one driver otherwise you'd not be thinking of doing this.  BUt you've not said how badly or marginally you're presently failing.  Maybe all you need is a heat sink.
Comment: I am not failing yet but I am getting towards the hairy edge and I just want a bit more for margin of error. I would prefer not to add a heat sink as I am tight on space as it is but I might be able to come up with something creative...
Answer: I've definitely seen this done with exactly this chip, so it  can work. As rawbrawb indicates, though, it's a hack - it might work, but it might cause problems due to mismatched components. Your worst case scenario: you burn out both of them from excessive current. Since they're cheap parts, it might be worth a try anyway, depending on your constraints.
Answer: If you have through hole chips, it could be feasible to increase the amount of power on your board in a safer way than soldering two chips on top of each others.
As explained in the datasheet, the safe way to double the power of l293 chips is to use 1 chip per motor. To do that, you have to connect channel 1 to channel 4 and channel 2 to channel 3.
In other word, if you want to connect two chips, you'll have to solder them above the board next to each others. One chip for the left side and one chip for the right side.
The tricky part is to have both pin enable, vcc connected correctly as they are not parallel to each others.
I'd flip the chip on the side like this:

simulate this circuit – Schematic created using CircuitLab
The advantage of this method against piggy backing two chips is that if one chip fails, then the second motor will still work. And you only have to replace one chip.
One way that would look less like a hack would be to have a new PCB that you can stack on top of the l293d socket.


Can we extract public key from signature created by RSA?

Question: I know it's possible with ECDSA. How bout RSA?
Answer:
Can we extract public key from signature created by RSA

I assume the question is: we have both the message and the RSA signature; can we find an RSA public key that could have been used to sign that message?
The answer is no, it is infeasible.
On the other hand, if we have two signatures (to two different messages), and those messages, and if the RSA padding method was deterministic (e.g. RSASSA-PKCS1-v1_5), and the public exponent is not too large (e.g. 65537, which is common), and we can guess the hash function, then it becomes feasible.
The RSA verification relation is $\text{Pad}(M)^e \equiv S \pmod N$ (where $M$ is the message that was signed, $\text{Pad}$ is the deterministic function that hashes and pads the message, $S$ is the signature and $N$ is the modulus); here, we know everything except for $N$ (since $e$ is assumed small, we can iterate through the possibilities).
We can rewrite this as $\text{Pad}(M)^e - S = kN$ (for some integer $k$).
While the left hand side is computable, it is also huge; it would be infeasible to find the factor $N$.
On the other hand, given two such distinct message $M_1, M_2$ and two signatures $S_1, S_2$, we have:
$$\gcd( \text{Pad}(M_1)^e - S_1, \text{Pad}(M_2)^e - S_2 ) = kN$$
where (in this case) $k$ is likely to be small; we can compute the left hand size (for $e = 65537$, it's a bit of work, but still feasible), and once we hae that, it is easy enough to scrap off the small factor $k$ to recover $N$.
Answer: So far as I know, this is impossible unless the signature data structure includes more information than is necessary. You may want to ask on crypto.stackexchange.com to get a higher-confidence answer, though. Security.SE is about threats, attacks, and mitigations in general, but crypto.SE is where people who like to get into the mathematical details behind various ciphers (among other things) hang out.
It is conventional, when creating or sending signed data, to include your public key (potentially in an X.509 certificate) so that the recipient knows who signed it and can verify the signature. Of course, unless the public key is signed by a trusted third party (such as a certificate authority or somebody you trust in OpenPGP's web-of-trust model), or you already know what public key or at least public key fingerprint (hash) to expect, merely sending along a public key with a signature doesn't prove anything about who signed the message.


Can I see a list of gyms I left a pokemon at?

Question: I captured a gym today just before the servers went down. I am wondering if I lost my progress. Is there a way to see if I own a gym or not?
Comment: @DanmakuGrazer latter - gyms where I left pokemom
Comment: Do you mean gyms owned by your team or gyms where you've left Pokémon?
Answer: If you keep personal track of which Pokemon you left where, then yes. The game shows a colored icon above one of your Pokemon if it's at a gym, but not which gym it is. You could also monitor which Pokemon you have at 1hp. Additionally, the icon in the top-right of the Shop (which you use to claim rewards for holding gyms) tells you the number of gyms you control.
Comment: Not necessarily blue, but your team color.
Answer: A good little trick is rename your pokemon with the gyms location.
Change:
"Ponyta" to "Town Hall"
"Rhydon" to "College University"
"Rattata" to "University Cafe"
This way when a gym you own is taken down, you know which one it is.
Comment: Heh, nice idea man. Will do that once I get back to a place with Gyms... or pokemons for that matter :(
Answer: As of today, there is finally a way to see what gyms you have Pokémon occupying!
If you go to your trainer profile after visiting gyms, there will be a list of gym badges you've earned. There is an indicator next to the gyms that currently have one of your Pokémon occupying it:

If you tap on this gym badge, it will show what Pokémon you have defending that gym as well as how long that Pokémon has been defending the gym for.
Comment: Just FYI: If you want to keep your location secret (I assume so as you blacked out the name of city), I'd recommend blacking out all pokestop names as they can be used to determine your location too.
Comment: @Avery I was being lazy.
Answer: You can see in your Pokemon screen which of your pokemon are assigned to a gym. They will have the gym symbol over the image of the pokemon.
That's the best you'll get as there's currently no way to see occupied gyms.
Answer: Searching for "defender" in your Pokemon search will show a list of all defending Pokemon, which effectively shows which gyms you've left Pokemon at.


Transit visa in Australia

Question: I'm flying to Vietnam from Vanuatu and I have a stop in Sydney, Australia. The luggage are not directly sent to Vietnam so I have to take them out in Australia and send them again. In that case, does it require for a transit visa ? Btw I'm only staying for 3 hours.
Comment: What country issued your passport?
Comment: I have a Vanuatu passport
Answer: Timatic, the database which airlines use to verify passengers' travel documents, states in part:

Visa required, except for Nationals of Vanuatu transiting
  through Cairns (CNS) or Sydney (SYD) with a confirmed onward
  ticket for a flight to a third country within 8 hours on the
  same calendar day. They must stay in the international transit
  area of the airport and have documents required for the next
  destination.

If you are able to stay in the international area, then you won't need a visa. However, you said that you have to recheck your luggage. In this case you have to go through immigration in order to get your luggage, so you do need a visa.
You also should consider that for separate tickets, three hours is probably too short a connection. You are likely to miss check-in your connecting flight depending on how much time you spend waiting in immigration. You have to have your baggage checked in to the connecting flight an hour before departure, and that might not be possible.

Transit visa in Australia


Negative interest rate on bond yield

Question: In Black-Scholes model $r$ is defined as risk-free interest rate. What I have understood is that risk-free comes from the yields on sale of government bonds. What does that mean if the interest rate(fed fund rate) are negative? Does the yield on government bonds then also go negative? I understand the price of the bond will go up, but is that yield correlated with the fed fund rate?
Answer: The yield on government bonds is not necessarily equal to fed fund rate. Fed fund rate is a rate at which other banks can borrow from Fed.
This being said the funds rate affects interest rates on all debts since if the banks can borrow more cheaply from Fed they can also offer better terms to their own creditors. Bonds compete on markets for loanable funds so if the interest rate on loans go down  the bond yield will also be lower.
If we are talking about risk free bond then it's yield will be quite close to the funds rate but not necessarily equal. Also, yes the bond yield can be negative.
Answer: Usually, no one uses government bond yields in Black Scholes, at least not professionals. You can have a look at this answer for some details.
In terms of the model, there is no difference if rates are positive or negative. You simply plug in the value (and all other parameters in the model) and get the option price. In fact, rates have been negative in many countries (e.g. EUR) for a very long time until recently.
Below is a screenshot from Bloomberg's OVME:

Negative interest rate on bond yield


Is there a way to get Project from View unwrap to work with modifiers without applying them?

Question: I have an object with an armature modifier (although this would apply to any modifier that deforms the mesh). I want to Project from View unwrap to get a UV map for one pose, then change the pose and Project from View again for another UV map. This doesn't seem to be possible because Project form View apparently only works with the base unmodified mesh. I tried using the on cage and edit mode options on the armature modifier, but it still uses the base mesh.
Answer: I found a solution if anyone sees/needs this, you can make duplicates of the object, pose them, apply the armature modifier, then do a Project from View unwrap for both of them. Then use Transfer UV Maps(Ctrl + L) to transfer them back to the original mesh.
(https://docs.blender.org/manual/en/2.80/editors/uv/layout_management.html)
Answer:
Create a pose.

"Duplicate" the Armature Modifier from the down arrow menu over in the Modifier Tab (in older versions, it's a "Copy" button).

Save your pose as a "Shape Key" with Armature > Save as Shape Key (in the duplicate Armature Modifier).

Activate the "Shape Key".

Unwrap your mesh.


As quick as we can?

Question: Is it acceptable to say "We'll get back to you as quick as we can"? Is "quick" a flat adverb in this case?
Answer: The article Flat Adverbs Are Flat-Out Useful suggests that "quick" is a flat adverb.
Just as an example, "come quick" and "come quickly" are both grammatically correct.
Consider the similar sentence: "We'll get back to you as soon as we can." Here, "soon" is taking the place of "quick" with all most the exact same meaning ("fast" works as well).
Consider an alternative sentence: "We'll do it as quick as we can." and a sentence with similar structure but different meaning: "We'll do it as quietly as we can." Here the word "quiet" is almost never presented as a flat adverb (maybe never?) and so you need the -ly.
Answer: It's interesting to note that AHDEL lists the adverbial usage as synonymous with quickly, and with no caveats.
Collins lists the adverbial usage as being in an informal register.
I'd certainly choose 'quickly' for Michael's delightfully highbrow example, but would use either variant in OP's example.
Comment: Flat adverbs are much more acceptable in American English, although this does vary regionally. This probably accounts for the difference between AHDEL and Collins.
Answer: I'd say it was acceptable, since it's a common usage. It's not quite correct, however. "Quickly" is the proper adverb.
Comment: Your second link states '_Quickly_ is the adverb form of _quick_. Many dictionaries, however, describe _quick_ as a very informal use of _quickly_.' However, of the five reputable online dictionaries I've checked in, three have no label and two label the usage merely 'informal'.

As quick as we can?


What type of printing technique is this called?

Question: Apologies for the poor quality images
Comment: What aspect of it are you asking about? The colour, paper, texture, folding, etc?
Comment: Welcome to Graphic Design SE. Are you sure that you are interested in the printing technique, i.e., the method used to put the images and text on the medium? If yes, you probably need to provide more information such as what medium is used (paper, metal, …) and it would be very helpful to have closeups.
Answer: It looks to me like a single colour offset litho print, using one "special" ink (ie the turquoise/blue) instead of the normal Cyan / Magenta / Yellow / Black.
Answer: Hard to say. Could be any number of processes:

one color offset (as Digital Lightcraft mentions) likely using a spot color (Pantone)
one color screenprint (unlikely but if it's a limited run poster, maybe)
color laser
low-fi one color duplicator (such as a Risograph)
Comment: Its unlikely to be a screenprint as the sharpness is too good (and text too small), nor is it likely to be laser as the reflectivity of the printed areas doesn't look right for that.


Index was outside the bounds of the array

Question:
I get an "Index was outside the bounds of the array" error with the below code. It occurs after the music stops and I try to click another song. How do I solve this issue?
private void button1_Click(object sender, EventArgs e)
{
    if (openFileDialog1.ShowDialog() == System.Windows.Forms.DialogResult.OK)
    {
        files = openFileDialog1.SafeFileNames;
        paths = openFileDialog1.FileNames;
        for (int i = 0; i < files.Length; i++)
        {
            listBox1.Items.Add(files[i]);
        }
    }
}

private void listBox1_SelectedIndexChanged(object sender, EventArgs e)
{
    axWindowsMediaPlayer1.URL = paths[listBox1.SelectedIndex];
}

Comment: the selected index will be -1 if item is not found. Is your out of bound -1 ?
Comment: Why don't you use `listBox1.DataSource = files` and be done with it.
Answer:
You are not clearing old items from your ListBox when new files are selected. Use the Clear method to remove the old items before adding the new ones.
The error you are describing occurs because you have more items in your ListBox than you do in your paths variable.
This would be your new code:
private void button1_Click(object sender, EventArgs e)
{
    if (openFileDialog1.ShowDialog() == System.Windows.Forms.DialogResult.OK)
    {
        files = openFileDialog1.SafeFileNames;
        paths = openFileDialog1.FileNames;
        listBox1.Items.Clear(); // added this line
        for (int i = 0; i < files.Length; i++)
        {
            listBox1.Items.Add(files[i]);
        }
    }
}

Answer: You need to use the DisplayMember and ValueMember of the listbox, and bind to a collection of Tuple<string,string>.
    private void listBox1_SelectedIndexChanged(object sender, EventArgs e)
    {
        string path=listBox1.SelectedValue as string;
        // return the path of the item
    }

    private void button1_Click(object sender, EventArgs e)
    {
        if (openFileDialog1.ShowDialog()==DialogResult.OK)
        {
            var files=openFileDialog1.FileNames;
            var paths=openFileDialog1.SafeFileNames;
            var items=new List<Tuple<string, string>>();
            if (paths.Length!=files.Length) throw new IndexOutOfRangeException();
            for (int i=0; i<files.Length; i++)
            {
                items.Add(
                    new Tuple<string, string>(files[i],paths[i])
                    );
            }

            listBox1.DataSource=items;
            listBox1.DisplayMember="Item1";
            listBox1.ValueMember="Item2";
        }

    }

Answer: Try
axWindowsMediaPlayer1.URL = paths[listBox1.FocusedItem.Index];

instead
I am not sure but it seems you focused the item before you play right?.  If so then Try the above code. Also Spooky above made a good point . His suggestion might work as well.
Try clearing the list view before adding a new file.
listBox1.Items.Clear();


How do I move a list to the top of the page in Google Sites?

Question: I have created a page using the built-in List template in Google Sites. However, the list appears after all the other text. How can I move the list to the top of the page?
Answer: The only way I've found to do this is as follows:

Copy the contents of the list onto your computer's clipboard. You need to do this first, as the list isn't stored in the revision history, and will be permanently deleted!
Change the template used for the page to Web Page.
Edit the page (press the 'e' key to edit it)
Paste the list from your computer's clipboard into the page, where you want it to be.
Go to the row containing the words "sort", and from the Table menu in Google Sites, select Delete Row.
Save the page.

It now won't be a "proper List" as before unfortunately, so you won't be able to add items directly from the page - you'll have to go in and edit the page in order to add items to the list.