If $F(x + iy) = \frac{Q}{2\pi}\ln (x + iy)$, how to prove that $\phi(x,y) = \frac{Q}{2\pi}\ln (\sqrt{x^2 + y^2})$?

Question: The potential flow theory states that
$$
F(z) = \phi + i\psi
$$
where $z = x + iy$
In case of a source/sink, we have
$$
F(z) = \frac{Q}{2\pi}\ln z\tag{1}
$$
$$
\phi(x,y) = \frac{Q}{2\pi}\ln (\sqrt{x^2 + y^2}) \quad \text{or}\quad \phi(r,\theta) = \frac{Q}{2\pi}\ln(r)\tag{2}
$$
$$
\psi(x,y) = \frac{Q}{2\pi}\arctan{\frac{y}{x}} \quad \text{or}\quad \phi(r,\theta) = \frac{Q}{2\pi}\theta\tag{3}
$$
how do we go from (1) to (2) and from (1) to (3)?
Answer: This is a matter of the definition of the complex logarithm. If $z = r e^{i \theta}$ for $\theta \in (-\pi, \pi],$ the principal value of the complex logarithm of $z$ is defined as
\begin{equation*}
\mathrm{Log}(z)= \mathrm{ln}(r) + i\theta.
\end{equation*}
So given $z = x + iy,$
\begin{equation}
F(z) = \frac{Q}{2\pi}(\mathrm{ln}(r) + i \theta),
\end{equation}
where $r = |z| = \sqrt{x^2 + y^2}$ and $\theta = \mathrm{Arg}(z)$. Comparing to
\begin{equation}
F(z) = \phi + i \psi
\end{equation}
and equating the real and imaginary parts gives $(2)$ and $(3)$.
Note also that the formula $\mathrm{Arg}{(x + iy)} = \mathrm{arctan}{\frac{y}{x}}$ is only valid for $x > 0$. A more general formula makes use of the $\mathrm{atan2}$ function.
Comment: many thanks @Zac. For the sake of interest, what is the atan2 function. Could you provide a insighful link?
Comment: The Wikipedia page [here](https://en.m.wikipedia.org/wiki/Atan2) on the $\mathrm{atan2}$ function gives a reasonable explanation. A problem with using the $\mathrm{arctan}$ formula is that the range of $\mathrm{arctan}$ is $(- \pi/2, \pi/2)$, so it will never give a correct argument for a complex number whose real component is less than zero (for example $-1 + i$.) The $\mathrm{atan2}$ function fixes this by adding or subtracting $\pi$ as appropriate. Often things will still work out if we stick with the $\mathrm{arctan}$ formula, but it can be good to know about its shortcomings!


Tools for helping to learn openings by heart

Question: Is there any tool that can help us learn openings by heart? I tried to use Fritz but without success.
Answer: Two well-known programs that are meant specifically to aid in the memorization of opening variations are

Chess Position Trainer
Chess Openings Wizard (formerly Bookup)

Both programs are designed to recognize and handle transpositions seamlessly, and they allow a player to drill all the positions that are part of any repertoires that he or she inputs.
Answer: Chessable is famous for learning chess openings by the MoveTrainer space repetition. Check out MoveTrainer at https://www.chessable.com/movetrainer.
Answer: Personally I use Chessable. It makes you play through all the variations when you review a course, and there are a bunch of free courses on there that are excellent for getting started with an opening.
The Short & Sweet series is pretty good. Sam Shankland, Anish Giri, and a bunch of other masters have some good S&S courses that are 20-30 lines or so, as they are just a demo version of the massive "Lifetime Repertoires" series. They're great for club players.
There are also free courses published by community members that are more extensive. I used the "Ruy Lopez: Masterclass Edition" course to learn a new opening that I now enjoy immensely.
If those aren't enough for you, you can find some pretty low-priced courses on more or less anything you want. Lifetime Repertoires courses are expensive and have huge numbers of lines, but there are smaller ones you can get for a lower price. For example, I am an owner of "Rafael Leitao's Najdorf Sicilian" which was around $5 and has 150 lines or so.


Car Battery Voltage

Question: Why is the voltage of a car battery rated for say 12V around 14V when the car is running? Is it because of the alternator?
Comment: Yes. All batteries have a nominal voltage, but their actual voltage during use will be higher or lower.
Comment: A car battery that has an unloaded (nothing connected) voltage of 12 V isn't fully charged. A fully charged battery will have a voltage of around 13.8 V.
Answer: All batteries vary in voltage base on charge state and on loading.
A 12V lead acid battery is 12V nominally. This means that 12V is a about middle of the range of the battery. A fully discharge 12V lead acid is around 11V, fully charged it's about 14 to 15V.
Lithium Ion batteries are the same: 3.6V nominally but really they vary from 2.9V to 4.2V (there is variation in this depending on the precise cell; I've seen some Samsung ones got down to 2.5V for example). This is why you sometimes see prodcuts which are "42V" having the same power as a 36V battery pack, they've just used the maximum voltage to make their product seem better. This is legal in the EU and USA, though the ethics of it are questionable.
As for the second part of your question: the car goes up to 14V because the battery is being charged up, yes from the alternator (or other power source). To push power into the battery, you need a higher voltage than the current battery state. As a general rule you have a current limited voltage source, which charges the battery. Back to Li-Ion cells again (as that's what I've has most experience of) we use 4.4V per cell to work out the charging voltage (which is why if you look at chargers they are always higher voltage than the battery they are charging). For a car it is similar, often 15.2V is chosen as the charging voltage to balance safety (lowest voltage possible) and charging time (highest power possible). You're only seeing 14V for a combination of reasons: the car may keep the voltage lower to save over charging the battery pack and the current limit has taken effect, so the voltage as dropped.
Comment: Some charging profiles go up to 15.2V, and yes I am sure, have the car and the workshop manual.
Answer: You are absolutely right, it is because of the alternator. When the car is running the alternator is set to generate around 14 volts which not only charge the battery but also supply all electrical requirements of the car. The battery is only used to start the car or for lighting some bulbs and other accessories when the car is not running and the alternator is therefore not generating any power. Once the car has started, thereafter even if we remove the battery the car would keep running till the engine is switched off intentionally or due to any other reason. For starting the car again it would need a battery. When one is driving a car and the alternator fails due to some reason the car would keep running till such time the battery is able to supply power. However, since all the power requirements of the car in such a case are met by the battery, it would get discharged quickly. Therefore, it is necessary to get the alternator repaired at the earliest.
when the alternator fails, the battery warning lamp would light in the display panel indicating that the battery is not getting charged.

Car Battery Voltage


Open liberty and Hibernate

Question: Can I use Hibernate as JPA implementation in open-liberty? If such integration exists, I would presume that it comes with distributed caching and JTA?
Answer: Yes, in OpenLiberty we have the jpaContainer-2.1 feature, which provides only the JPA container integration code, and allows the user to plug in their own JPA 2.1 compliant implementation (i.e. EclipseLink or Hibernate).
Specifically for Hibernate, the jpaContainer-2.1 feature will integrate Hibernate with Liberty's transaction manager. See LibertyJtaPlatform
You can find full documentation here, including config examples:
Deploying a JPA application to Liberty
The basic config you will need in server.xml is the following:
<featureManager>
   <feature>jpaContainer-2.1</feature>
   <feature>bells-1.0</feature>
      ...
</featureManager>

<bell libraryRef="hibernate"/>

<library id="hibernate">
    <fileset dir="${server.config.dir}/hibernate/" includes="*.jar"/>
</library>

<application location="myApp.war">
   <classloader commonLibraryRef="hibernate"/>
</application>

Comment: Thanks Andy, the only thing I am still unclear about is the configuration of Hibernate's second level cache. Typically this is is done with Infinispan, or in case of Payara - nazelcast. How is this done in OpenLiberty?
Comment: @HristoStoyanov I have not configured Hibernate's session factory cache before, but if I had to guess... you will need to provide your own implementation (for instance Ehcache) since I don't think youll find one in OpenLiberty. Then add it to the shared library in your server config and set the persistence properties Hibernate needs.
Comment: Thanks Will,I figured that I had to do something like that
Comment: Will configurations be the same if I'm using jpaContainer-2.2?

Open liberty and Hibernate


What improvisational techniques were employed by Thelonious Monk and Charlie Parker that defined bebop?

Question: I'm looking specifically for the principles of improvisation as demonstrated by Charlie Parker and Thelonious Monk, the fathers of bebop.  I realize my opinion may be controversial but I see Dizzy Gillespie as the foremost promoter of bebop, not one of the inventors, a view I share with Monk.
Answer: Charlie Parker's improvisational technique was largely based on formulas (or riffs) that he would transpose to fit chord progressions.  He would have to do this in order to play as fast and as fluently as he did, even when he was high and this is in no way a criticism of his creativity--he did invent an entire musical language using his riffs as words.  A statistical analysis of Parker's formulas can be found in Toward a cognitive analysis of creativity: Improvisation in jazz by Weisberg et. al. and a musical analysis by close reading of the Charlie Parker Omnibook.
Thelonious Monk's contribution was along multiple reinforcing lines.  First there were his reharmonizations, which included chords, tone clusters and even microtones--his use of minor seconds was his way of trying to play the note in the crack between the keys.  There was his strong rhythm combined with an amazing use of space. And then there was his innovative use of the blues scale to create angular melodies with repeating melodic fragments.  To hear just how different his musical sensibilities were, listen to his version of "Tea for Two."

A detailed analysis of Monk's improvisation style can be found in The Musical Language of Thelonious Monk by Eddie S Meadows
Answer: A really really important principle that bebop players used was that they improvised on top of the melody and not the harmony.
Another important thing was they didn't think of the harmony as a whole, but they thought out every single chord change.
Let's take Parker's  Moose the Mooch for instance:

Bb / C- F7 /Bb /C- F7 etc

When Charlie Parker improvised on top of those chord changes, he didn't think "I'm in Bb major, so I can solo on top of that". At the first bar he thought the notes of the chord Bb, as well as the notes of the melody. On the first two beats of the second bar, he thought the notes of the chord C- as well as the notes of the melody etc.
Comment: But if you listen to Charlie Parker, and look at books that have been collected of his riffs you see that he uses the same riffs over and over again over particular harmonic changes, although he does a lot of chord substitutions. Monk, on the other hand, appears to improvise as you say.
Answer: Some characteristics of Monk's playing are his use of fragments of the song's theme. Often he would repeat a phrase or a part of a phrase, as if breaking it down into smaller parts, interrupting it with some of his other signature figures such as a whole tone descending scale.
I'm less familiar with Charlie Parker, but maybe you could find out something interesting by having a look at the harmonic content of the solo and how it relates to the underlying chords. You might also try to analyse the melodic profile [*] once you have the solos transcribed and see if that leads to any insights.
[*] For some ideas, see Friedmann (1985): A methodology for the discussion of contour, Journal of Music Theory, 29:2.
Answer: Read the book Jazz and Justice, specifically chapter 4 "Hot House".  Everything the other answers mention is true to some extent but in this era there is a tendency to "formularize" jazz and that is not what the originators did. Both Parker and Monk are discussed in this text and there was a common motive to their approach.  Specifically to "play something others could not easily steal".  The ferocious speed and intricacy of Parker and being melodically and rhythmically "out" for Monk were an evolution driven by other musicians (mainly white) stealing tunes fro black musicians.  Now we analytically dissect Jazz as if it is completely divorced from these roots and that waters it down.
Improvisation is variation on a theme and that has been a method for 1000s of years.  Most musical traditions are improvisational by nature so I'd say you will see and hear a lot of this at play in Jazz and bop.


Terraria - How To Find Plantera Bulb Easiest Way

Question: I am on hard mode and I have been exploring underground jungle for 3 days.
I cant find any Bulbs, and I think I am prepared to kill it now.
How do I find the Plantera Bulb in the easiest way?
Comment: Have you defeated any of the mechanical bosses?
Answer: From the wiki:

Plantera's Bulbs emit moderate light and appear in the minimap in
  areas the player has already explored. They spawn one at a time after
  a delay of about half a day between them, and unless destroyed,
  several will eventually be present (10-15 in a small world's
  naturally-generated Underground Jungle). If destroyed, they respawn
  after the same delay (though not necessarily in the same spot),
  allowing the player to summon Plantera an infinite number of times.
Answer: While I cannot find the link now, there used to be a guide on the wiki for farming Plantera's Bulb, and following it helped me on later runs. The idea is basically to make a second area of underground jungle somewhere well away from the normal jungle, and give it large areas of flat jungle grass. The design that I saw was a large room with a stack of one tile thick mud and jungle grass platforms. The platforms also had actuators behind them so that you could quickly turn the room into an open area for actually fighting Plantera.
The explanation in the article, although I cannot vouch for its veracity, was that one bulb spawns per time period, per isolated jungle region. So if you made a reasonably sized jungle region then you could find it more easily.
You should also note that the bulb requires a flat patch of jungle grass at least two tiles wide.
In my experience this patch must also be empty, but I have no other sources to back up that assertion. So you may need to periodically remove bushes and tall grass. This can also help with getting it to spawn in regular jungle areas. They tend to get overgrown and need to be
You should also note that Plantera's bulb does not spawn until after you have defeated all three mechanical bosses. Your question does not indicate that you have done so.


What is the difference between "kinematics" and "dynamics"?

Question: I have noticed that authors in the literature sometimes divide characteristics of some phenomenon into "kinematics" and "dynamics".
I first encountered this in Jackson's E&M book, where, in section 7.3 of the third edition, he writes, on the reflection and refraction of waves at a plane interface:

Kinematic properties:
  (a) Angle of reflection equals angle of incidence
  (b) Snell's law
Dynamic properties
  (a) Intensities of reflected and refracted radiation
  (b) Phase changes and polarization

But this is by no means the only example.  A quick Google search reveals "dynamic and kinematic viscosity," "kinematic and dynamic performance,"  "fully dynamic and kinematic voronoi diagrams," "kinematic and reduced-dynamic precise orbit determination," and many other occurrences of this distinction.
What is the real distinction between kinematics and dynamics?
Comment: kinematics: study of how things move
Dynamics: the study of why things move
Answer: In classical mechanics "kinematics" generally refers to the study of properties of motion-- position, velocity, acceleration, etc.-- without any consideration of why those quantities have the values they do. "Dynamics" means a study of the rules governing the interactions of these particles, which allow you to determine why the quantities have the values they do.
Thus, for example, problems involving motion with constant acceleration ("A car starts from rest and accelerates at 4m/s/s. How long does it take to cover 100m?") are classified as kinematics, while problems involving forces ("A 100g mass is attached to a spring with a spring constant of 10 N/m and hangs vertically from a support. How much does the spring stretch?") are classified as "dynamics."
That's kind of an operational definition, at least.
Comment: To try to make this a little sharper, I would say "kinematics" is about things that are determined by conservation laws: kinematics tells you that momentum and energy have to balance, for instance. "Dynamics" is any detail that depends on the interactions and not just on conserved quantities, and would tell you for instance the detailed cross-section of a scattering process as a function of the kinematically possible configurations.
Comment: @Matt: That's not a standard definition however.
Answer:
Statics: Study of forces in equilibrium without consideration of changes over time.
Kinematics: Study of motions (position, velocity, acceleration) and all possible configurations of a system subject to constraints.
Kineto-statics: Study of forces in equilibrium, with the addition of motion related forces (like inertia forces via D'Alembert's principe) one instant at the time. Results from one time frame do not affect the results on the next time frame.
Dynamics: Full consideration of time varying phenomena in the interaction between motions, forces and material properties. Typically there is an time-integration process where results from one time frame effect the results on the next time frame.

As far as the source if kinematic and dynamic viscocity, I am not sure, and I have wondered this myself. Maybe it stems from the test methods used to measure each property.
Comment: And these stem from **Mechanics:** The study of interactions between bodies and forces that produce motion.
Comment: It seems indeed natural to explain _statics_ when discussing _dynamics._
Answer: Since everybody already gave nice replies to this question, I'll give a more pragmatic answer:
Don't worry about it. It is an arbitrary distinction made by humans. Nature doesn't care if some phenomenon can be described/explained purely from kinematic considerations or not. It's not a fundamental distinction.
On the other hand, it is a useful distinction. I'm sure you know the distinction somehow implicitly when you solve problems.
Let me give an example in mechanics: you swing a pendulum in a vertical plane, you swing sufficiently fast so that the trajectory is a circle. What is the tension in the pendulum when it passes in the lowest point of the circle. The tension is a dynamical quantity, because it is a force. Now, when you solve the problem, you don't write down the full equation of Newton and solve them. You use the kinematic information you have about the trajectory: it's a circle, in the lowest part of the trajectory there is no tangential acceleration, so the acceleration is directed radially inwards and is $v^2/r$. From this you can find the tension by using purely kinematic considerations and never solving $\vec{F}=m\vec{a}$ as a differential equation.
I guess you understood that in physics we do this all the time. If we didn't, many problems would be impossible to tackle without resorting to extensive computer simulations all the time. In most problems we consider, we already have some idea of the kinematics, which permits to reduce the space of acceptable solutions. Sometimes so drastically (but that is only for the simplest problems) that we can solve them by purely kinematic considerations.
Comment: In your example, how do you know the velocity at the bottom without making a dynamical calculation?
Answer: You should think of it in terms of programming a computer to simulate the physical system. Kinematics is the data structure you need to simulate the general situation, what variables with what range of values. Dynamics is the actual algorithm that simulates the motion.
Answer: Another pragmatic definition: If you only need SI units derived from the meter and the second (length, time, velocity, acceleration, …), it's kinematics. If you also need SI units involving the kilogram (mass, energy, momentum, force, …), it's dynamics.
Answer: Kinematics is about the range of movement or change a system can undergo, or the state space in which it acts. Dynamics is about the movement it undergoes according to the laws of motion.
For example the kinematics of a rigid body in space describes its possible coordinate positions and orientations and the range of velocities and angular velocities etc. The dynamics describes how these would change under the influence of a given system of forces.
This means that conservation of energy and other quantities is dynamical because it only holds when the equations of motion are in effect.
Although kinematics and dynamics are most used in classical mechanics you can extend the idea to quantum mechanics where the kinematics are described by the phase space and operators, while the dynamics is the evolution under the influence of a given Hamiltonian.
It is traditional to regard the distinction between kinematics and dynamics as absolutely clear cut, but possibly the most important thing to understand about them is that this is not always the case. As a simple example consider the case of a particle that can move along a fixed track. You could regard the constraint that keeps it on the track as kinematical and only its actual motion along the track would be part of the dynamics, but we know that at a deeper level the particle is held on the track by dynamical forces.
Another example might be conservation of charge. If you consider the Dirac equation for a charged particle in the presence of an electromagnetic field, you find that charge is conserved only under the influence of the equations of motion. If you quantise the system the charge is given by the sum of the quantised charges on the positrons and electrons which can only be created and destroyed in pairs. It is possible to view this as a kinematic constraint with the dynmaics only accounting for the motion of the particles.
Perhaps the best example is in electrodynamics where a vector potential describes the field kinematics with the electric and magnetic fields being given by suitable derivatives. In this case the Maxwell equation that tell us that the magnetic field has zero divergence is kinematical because it follows without use of the equations of motion, but the divergence of the electric field is equal to the electric current according to the equations of motion. So some of Maxwell's equations are kinematic and some are dynamic. In a deeper theory these fields may be derived from a system which exhibits electromagnetic duality where magnetic monopoles act as sources for the magnetic field. In that case the kinematic and dynamic parts of the Maxwell equation are interchanged under the duality so we are forced to realize that the original distinction between kinematic and dynamic was an illusion.
In the final analysis the evolution of the universe does not make the same distinction between kinematic and dynamic that physicists do and it is important to appreciate that at a deeper level kinematics may turn out to be dynamics or vice-versa. So any attempt to define the difference is to some extent arbitrary and may not stand the test of time.
Answer: This is how I understand it. There is a series of definitions used in physics, and one used in engineering mostly. I'll describe the one used in physics first:
In mechanics, we describe the motion of bodies, and the causes that effect them. This includes the special case where the "motion" is no motion, i.e. bodies are stationary.
The description of the motion itself is called kinematics. This just sets up the relevant degrees of freedom, represented as variables in a relevant mathematical form.
The description of the causes, and how these causes effect the motion is called dynamics. These causes are often divided into forces and torques. This description relates the variables describing the motion above, to forces, which should depend on those variables themselves. This means that in dynamics we often have closed equations that we can solve in full generality.

Another division of the areas of classical mechanics, used mostly in engineering leaves the definition of kinematics the same, but what we referred to as dynamics above is called kinetics.
Dynamics then refers to mechanics applied to proper motion only (i.e. not including stationary case). In other words, dynamics is the kinematics and kinetics of proper motion.
Mechanics applied to the stationary case is referred to as statics. In other words, statics is the kinematics and kinetics of static equilibrium.
Answer: Kinematics: what Galileo worked on with his numerous experiments measuring displacement, velocity and acceleration of balls rolling down inclined plans.
Dynamics: what Newton worked on when he formulated his three laws.
Answer: The difference is: consideration of forces.
In many cases, forces themselves are related to location (lookup entries potential, potential energy, hamiltonian) so dynamics would allow you to predict system's behavior from given initial state.
Answer: I'd say that kinematics has to do with the space of all possible configurations of a system at one time, for example what restrictions are placed on those by conservation laws. Dynamics has to do with how configurations change as a function of time. As always, the way the term is actually used may depend on the person.
Answer: Primarily, the distinction between kinematics and dynamics is one of causation. What do we mean by this? The etymology of the word kinematics is the Greek kinēma, which means motion. On the other hand, dynamics draws its origin from dunamis, meaning power (though we are better off thinking of it as a power in potentia, as in the ability to do something).
So? Well, we all know another word that is based of the Greek kinēma -- cinema. If we were to represent the trajectory of a particle as a function, as a computer simulation or as a movie, we would be providing a description of the particle's motion without explaining what caused it to move that way. But as physicists, we should not be merely content with painting a picture of a system's motion. That is the job for the artists.
In order to explain why our system of interest exhibits the motion that we observe, we identify forces and potentials that may have been responsible for triggering the motion. In classical mechanics, once we have identified the forces and the initial conditions of the system (the dynamics), we can then solve a differential equation to obtain a solution parameterized in time (the kinematics).
The study of dynamical systems is, after all, a branch of mathematics. I hope this helps. Moreover, I hope that you appreciate that the distinction is not at all arbitrary, as some people have been led to think.
Answer: In mechanical systems, I would say the difference is whether the forces involved are due to static or quasi-static situations in which the forces are due to weight/gravity, springs, etc. If the forces result from accelerations then we have a dynamic system, whereas the former would be a kinematic system.
In the transmission of light example of the original questioner, I don't understand the distinction that is being made. All of the phenomena are related to the interaction of particles and light which to my way of thinking is a dynamic system. But that's at a lower level.
Comment: I disagree. Kinematics is, by etymology, the study of motion; restricting it to static situations is bizarre. I have yet to see either of those terms used in the literature in the senses you state, though maybe you can provide references.
Comment: I'm also not sure how the second paragraph is at all an answer. In any case, the distinction drawn by Jackson makes perfect sense to me: Snell's law is required simply to have a wave on one side match up with a wave on the other side with matching phases along the boundary at all times even when their speeds are different; transmission and reflection coefficients, and their interaction with polarization, on the other hand, require the application of Maxwell's equations in their boundary form to know how the system will respond.
Answer: Mechanics can be broadly classified into following branches:
1.Statics- Deals with study of material objects at rest OR deals with the study of motion of objects under the effects of forces in equilibrium.Here time factor does not play any role.
2.Kinematics- Deals with study of motion of material objects without taking into account the factors which causes motion( i.e. nature of force,nature of body).Here time factor plays an essential role.
3.Dynamics- Deals with study of motion of objects taking into account the factors which cause motion.Dynamics is based on concept of force.Here,time factor plays an essential role.
Answer: I think in general, one might interpret a distinction between kinematical and dynamical models as loosely referring to phenomenological descriptions (kinematical) versus. descriptions obtained from first principles (dynamical)
Comment: -1 : I disagree. Kinematic has to do with motions and paths but not with forces and masses. A kinematic description might tell you what are all the possible configurations, but a dynamic description will narrow it down to what is likely to happen in a time sequence.


Can you displace vehicles with explosions?

Question: Do vehicles get moved by plasma cannons, grenades, or any other blasts? I'm only looking for explosions made by guns.
Answer: All vehicles can be moved (and potentially destroyed) by any type of explosion: weapons (such as rockets), grenades, tanks, etc.
I should note that there can be a fine line between moving a vehicle from an explosion and destroying it, but I'm not exactly sure what your question is.
Comment: @MyTreeko78255 You can thank me by accepting my answer.


$\sqrt{n} = \Omega(3^{\log{}n})$ is not true? Why?

Question: Had this question on an algorithm exam. Can any one explain why
$\sqrt{n} = \Omega(3^{\log n})$
is false?
Comment: It really depends on the base of the logarithm.
Answer: We'll start with some arithmetic, and assume the base of the logarithm to be $x$. First, remember the log law:
$$
\log_{a}(b) = \frac{\log_{c}(b)}{\log_{c}(a)}
$$
So
$$
\begin{array}{rl}
3^{\log_{x}(n)} &= 3^{\frac{\log_{3}(n)}{\log_{3}(x)}}\\
&=(3^{\log_{3}(n)})^{1/\log_{3}(x)}
&=n^{1/\log_{3}(x)}
\end{array}
$$
Whether $n^{\frac{1}{2}}$ is in big-omega of this then depends on what $x$ is.
If we make the right and proper computer science assumption that the base 2 logarithm is the only logarithm (that was a joke of course), then $1/\log_{3}(x)=1/\log_{3}(2)\approx 1.6$, which is certainly bigger than $1/2$.
You'd need $x\geq 9$ for the statement to be true.
Comment: The problem actually states log base is 2. I forgot to add it. Thank you


SH process is using 50% of CPU, why is that?

Question: I have CRON running every 30 seconds, but that would fall under the crond process correct? Why is sh command sucking up 50% of my CPU when no one is running a Shell Script?
Comment: Best of my knowledge, you can't run a cron job at any smaller granularity than 1 minute.   Are you doing something special?  *how many* of the cron jobs are running?  Maybe it got loose and many are consuming your cpu? (all named similarly so you might not notice only the PID changing)
Answer: Cron will run the command specified in the command field using sh -c. You can specify another shell by setting SHELL in the crontab file.
EDIT:
Just to clarify, the sh -c command will be ran as a subprocess of cron, which may spawn other subprocesses depending on the command given.
Answer: crond runs as root on every system I'm familiar with:
1016 % ps -ef | grep crond
root       342     1  0 12:37 ?        00:00:00 /usr/sbin/crond

That's on a fairly current Arch installation, but an elderly Slackware says the same thing.  If you as some non-root user puts together a crontab file, crond will run the commands as your non-root user ID.  The root ownership has been a cause of several major security problems over the years.
As far as using 50% of a CPU, running something heavyweight every 30 seconds could easily consume 50% of a CPU.  Lots of "globbing" could do that, I'd think, as could doing a lot of sh-builtin string pattern matching or arithmetic.
Comment: Or it could be consuming 100% of a single core on a dual-core machine...


How can I install my script into the user's $HOME/.bin (or $HOME/bin) directory and make sure that is in their PATH?

Question: Edit: places where I said $HOME/.bin I should have written $HOME/bin or any equivalent is fine.
So I have a bash script which I am distributing as a client for my API.  Current version installs like this curl -s http://api.blah.com/install | sudo sh.  I may try to deal with six different package management systems so that they can just apt-get or brew install at some point, but for now I am going with the one-liner since I want this solution to work for multiple systems.  However, apparently there are quite a few users on systems like cygwin or even Macs who don't have sudo at all or don't have it set up.
My install script just downloads the API client script and puts it in /usr/bin and makes it executable.  But I am thinking based on the issues with sudo and the fact that this doesn't really need to be installed globally, I would like to just install it into the user's $HOME/.bin folder (create that if it doesn't exist) and then make sure that $HOME/bin or $HOME/.bin is in their PATH.
This is my current install script:
#!/bin/bash
BASE="https://api.blah.com"

if ! hash curl 2>/dev/null; then
  echo "Please install curl. On Ubuntu/Mint/Debian, command is sudo apt-get install curl"
  echo "Trying to install curl.."
  sudo apt-get install curl
  if ! hash curl 2>/dev/null; then
    echo "Yeah couldn't install curl.  Please install it."
    exit 1
  else
    echo "curl installed. Continuing."
  fi
fi

sudo bash -c "curl -s $BASE/mycmd > /usr/bin/mycmd"
sudo chmod uga+x /usr/bin/mycmd

Three reasons I am asking this question rather than just starting to hack on a solution right away: 1) I think that this is a common requirement or desire (installing something non-globally without requiring privileges) and so the answer to this question will probably be useful to someone else.  2) since this is supposed to work on the majority of systems, I believe there are going to be a few wrinkles, perhaps ones that I am not aware of since I don't use all types of systems regularly, just Ubuntu.  3) I believe that at least a few users out there may have already solved this problem.
Regarding 2), first wrinkle that occurs to me is that many users are now in zsh.  So if I add or modify a line in ~/.bashrc that updates the PATH to include $HOME/.bin, that won't work for those systems.
So to restate the question, what code should I use to download and install my script into the user's $HOME/.bin or ($HOME/bin) directory and make sure that is in their PATH, with the requirement (or at least strong desire) that this will work on almost everyone's system (if they have something like a Unix prompt)?
Also, one more meta statement about this question.. I am shortening it.. if you object completely to the approach, please just don't answer, rather than giving me a lecture.  For example I am aware that some people don't like one-line installs.  If you have minor changes to the approach however, please do answer.
Thanks very much!
Answer: If you can access the user's $PATH variable, try installing your script in a (the?) directory owned and executable by the $USER.


What is the physical interpretation of the Wick rotation?

Question: What is the physical interpretation of the Wick rotation?
How is it that we can just propose there's a new time coordinate tau? Are physicists saying time is modeled by an imaginary number? Isn't that at odds with the clocks we use everyday?
Comment: There is no physical interpretation of Wick rotation.  It is only a mathematically justified step (coming from complex analysis) to obtain a result.
Comment: Also potentially relevant: https://physics.stackexchange.com/questions/538350/what-is-physical-meaning
Answer: There's a couple of different points of view on what exactly it means.
Wick Rotation and diffusion
Even in the Schrodinger equation, Wick rotation has an interesting viewpoint. Namely, that Wick rotating the Schrodinger equation gives us the diffusion equation! More explicitly, the Schrodinger equation (say, with no potential) is given as
$$i\partial_t \psi + \nabla^2\psi = 0$$
Wick rotation of $t = i\tau$ gives
$$\partial_t \psi - \nabla^2\psi = 0$$
which is precisely the diffusion equation. So quantum propagation in real time is, roughly-speaking, diffusion in imaginary time!
Boltzmann statistics and the Hamiltonian
Remember from statistical mechanics that the partition function of a system at inverse temperature $\beta = 1/{k_B T}$ is given by
$$Z(\beta) = \Sigma_i e^{-\beta E_i}$$.
It turns out that this thermal quantity can be defined in terms of the Hamiltonian, namely that
$$Z(\beta) = Tr(e^{-\beta H})$$
where $\rho(\beta) = e^{\beta H}$ is the matrix known as the density matrix of the Hamiltonian. This density matrix is actually all we need to provide a complete description of the thermal properties of a quantum system.
Also note that $\rho(\beta)$ is closely tied together the time-evolution operator $U(t) = e^{iHt}$ by setting $\beta = -it$. This is closely tied together with what we said about diffusion earlier. Remember that a thermal system is an equilibrium notion about letting a system relax given some energy constraints. But the abstract mathematical standpoint is telling us that letting a system thermalize to an inverse temperature $\beta$ is the same thing as letting it evolve in imaginary time for a time $\beta$. But from before, we can see that evolving in imaginary time is the same as letting the system diffuse for a time $\beta$.
In particular, we can also say something about the ground state of the quantum system from this viewpoint. Mathematically speaking, if there is a unique ground state $|\psi>_{ground}$ at energy zero, then it can be obtained (in an unnormalized form) from any initial state $|\psi>_{0}$  with nonzero overlap from the ground state:
$$|\psi>_{ground} = \lim_{\beta \rightarrow \infty} e^{-\beta H} |\psi>_{0} $$
(which is a simple exercise that one should do.) So, from this viewpoint, the ground state of a system is obtained by letting the system evolve for an infinite amount of imaginary time from any starting point, or by letting it "diffuse" for an infinite amount of time.
Note that I've necessarily been a bit hand-wavy here. No one truly knows what the precise connection between diffusion and real-time evolution is apart from the mathematics, but presumably, it will be more clear once we understand what quantum mechanics truly is.
From a computational standpoint
Wick rotation just transforms a path integral into something that actually converges. To understand this point, it suffices to just look at a simple one dimensional integral
$$I(\alpha) := \int_{-\infty}^\infty e^{i \alpha x^2} dx$$
For $\alpha$ being a purely a real number, this integral does not converge, since the integrand has norm 1 at all $x$. But, if we shift $\alpha \rightarrow \alpha + i \epsilon$ for some small number $\epsilon$, then we the imaginary part forces the integrand to go to zero exponentially as $x\rightarrow \infty$, and will converge to $I(\alpha) = \sqrt{\frac{\pi}{-i \alpha}}$. From here, we see that we can evaluate the non-convergent integral $I(\alpha)$ by simply making $\alpha$ into a slighly imaginary number, which allows us to define the integral for $\alpha$ purely real.
The reason that this is important for quantum field theory is that the path integral
$$\int D\phi e^{iS[\phi]}$$
is an infinite dimensional integral. Moreover, a prototypical example of such an action looks like
$$S[\phi] = \int d^4x \phi(x)(-\partial_t^2 + \partial_x^2 + m^2)\phi(x)$$
The comparison point between this infinite dimensional integral and the finite dimensional one is that they are both quadratic matrices with imaginary eigenvalues all with real part bigger than zero. (The spectrum of the operator $(-\partial_t^2 + \partial_x^2 + m^2)$ turns out to satisfy this property.) So, evaluating the path integral in this case will give us an infinite number of nonconvergent integrals! Luckily, making the transformation $t = -i\tau$ will make the integral in terms of $\tau$ a convergent integral for real $\tau$ the lesson learned from the 1D case will allow us to evaluate it for a small imaginary.
The reason this silly-looking substitution works is because QFT's are holomorphic. This is typically an axiom of QFT's and means that any observable $<{O(x_1)...O(x_n)}>$ is a holomorphic function of the $x_i$. So, making time imaginary and continuing back to real time allows us to actually define finite quantities in the first place. An important caveat of this is that there are generically poles in these correlation functions, so we actually have to be careful in how we analytically continue.
Comment: I think the more precise statement is that they'll be holomorphic in the upper-half plane of the coordinates $x_i$. Physically, this is because (once properly normalized) the Hamiltonian $H$ has all its energies above zero (which is pretty much an assumption of what "physically plausible" means). This implies the time-evolution $e^{i H t}$ is holomorphic in the upper-half plane.

Some guiding examples would be reviewing the pole structure of the Feynman propagator for a free theory and seeing how Wick rotation avoids the poles there.
Comment: There are some applications of these ideas to axiomatic QFT and operator algebras, which are introduced very nicely in Witten's lectures, where I learned of the above comment (https://arxiv.org/abs/1803.04993). Here, holomorphicity plays a crucial role in results like the "Reeh-Schlieder Theorem" which shows surprisingly that the entire Hilbert space of certain QFT's can be generated entirely from operators concentrated in a small region of space. Although, holomorphicity is still an assumption here.
Comment: C.f. section 5.4 of the Witten article. Or the book "Introduction To Black Holes, Information And The String Theory Revolution, An: The Holographic Universe" talks about this in an accessible way.
Comment: Could you tell me more knowledge on the axiom of QFT's to indicate any observable $\langle O(x_1) \cdots O(x_n) \rangle$ is a holomorphic function of $x_i$ ?

Is one of the Wightman axioms linked to this conclusion?
Comment: Thank you for your info.

I see the eqn (2.7) in Wittern's paper, the holomorphic function refers to $g(u)$ with respect a temporal variable $u$. It's not a holomorphic function about variables $x_i$ ,is my understanding right?
Comment: Yes seems that *time evolution* being holomorphic is the more precise statement. I guess being 'holomorphic' doesn't really make sense for the $x_i$ themselves. Although, people use holomorphicity even in curved spacetimes when it comes to analytically continuing a time coordinate to turn the metric from Minkowski to Euclidean signature. For example, studying QFT in an analytically continued accelerating coordinate system in flat space is a key ingredient in the 'Unruh Effect' where accelerating observers see the vacuum as having a finite temperature.
Answer: Besides the nice answer by Joe, I would like to mention a noncommutative-geometry-inspired approach -- which is more 'geometric' in nature than 'physical' and attempts to arrive at an interpretation of the Wick rotation. Disclaimer: Now, one could, in principle, argue that 'geometry is physics' as in the sense of Einstein: 'geometry is gravity'. So take how 'physical' it is, at all, with a pinch of salt, as per your taste.
Noncommutative geometry à la Connes is defined by a spectral triple, which could be twisted by algebra automorphisms [1], [2]. Although the motivation for the twist was mathematical: to construct spectral triples for type III algebras [3], it quickly found applications in quantum groups, C*-dynamical systems, Standard Model and its extensions, cf. [4] and references therein.
The twisted noncommutative Standard model was intended for electroweak vacuum stability and fixing Higgs mass. Later twisting was found to naturally yield a Krein space (of Lorentzian spinors) and hinted at a tight link with Wick rotation [5]. In a recent paper, twisting Euclidean spectral triples and evaluating fermionic action induced on them by the twist has led to the derivation of Weyl and Dirac equations in Lorentzian signature [6].
In this setting, Wick rotation is something that naturally appears, at least at the action level, as a consequence of twisting Euclidean spectral triples. One might even go ahead and say that the transition to a Lorentzian geometry from a Euclidean one, in this sense, is a result of a (spontaneous?) symmetry-breaking: from a non-twisted geometry to a twisted one.


How is EMF still induced in an incomplete/open circuit?

Question: I understand that current can't flow through a coil if it is not complete, but surely this means that if a magnet is dropped through the coil, no EMF would be induced either, since work is done when a second field is induced to do work on the magnet opposing its motion, and no second field is induced without current, so what's doing the work here?
Answer: EMF is induced inside metal line even in an open circuit.
At the same time, $-\nabla(\phi)$ (the electric field caused by electric scalar potential) is generated, and it cancels EMF so that the total electric field becomes zero. As a result electric current along metal line vanishes.
Answer: Some transient current can flow in the open coil as there is some (small) capacitance.
Answer: In simpler terms to the above comment. In open circuits, whether it be induced EMF or a battery,  an initial potential difference is across the ends of the wire.  As a result, electrons move against field lines.  This causes charge to build up on the ends of of wire, until the electric field produced by this build up of charge cancel with the initial potential difference


Is my wife eligible for an HSA?

Question: I had an HSA with a previous job but I no longer work there and am no longer contributing to it.  I still have the account and there is still money in it.  My wife recently got a new job as well and has been told that if her spouse has an HSA then she is not eligible for one.  So...  since I still have the account, is it considered an "active HSA" that would make my wife inneligible?  Again, I haven't contributed to it nor has any employer for over six months.
Comment: By for over six months, do you mean since last year?
Comment: The last contribution I made was in October of 2014.
Comment: Is your wife covered by a health plan at her employer?
Comment: @Ben Miller She isn't yet, something about a 90 day window before she can enroll or something like that.
Comment: @GeoJohn But the plan is to have her covered by her employer, correct? Do you know if it is an HDHP?
Comment: @Ben Miller Yes, she is planning on taking an HDHP  with her employer.
Answer: Your spouse is eligible for an HSA even if you have one as long as she is covered by a qualified high-deductible plan. In the case that you both had HSAs you would be limited in how much you contribute each year, but both can have accounts.
In 2015, you could each contribute $3350 to your separate HSA plans. If you have a combined plan, and even if you switched mid year, you could contribute $6650 during that year total to the two HSAs. That can be divided any way you want as long as the total does not exceed that maximum for the year. You can contribute an extra $1000 if you are over 55 years old.
(I should probably also mention that you can still make contributions for the 2015 year until April 15, 2016, because it's relevant to most who would read this. Also you can only contribute a percentage of that limit matching the percentage of months that you are covered, but if you are covered for the last month of the year, you can contribute the full amount as long as you are covered for the ENTIRE following year.)

Is my wife eligible for an HSA?


Is there an ideal decomposition that counts the number of monomial generators?

Question: Consider the ideal $I\subseteq S[x,y,z]$ where $S$ is some field of characteristic 0 (probably any field will do) and $I=\langle x^9-y^4z^4,y^9-x^5z^4,z^8-x^4y^5,x^6\rangle$.  Notice that because the lone monomial in $I$ also divides half of one of the binomials, we have that $I=\langle y^9-x^5z^4,z^8-x^4y^5,x^6,y^4z^4\rangle$.  What I am looking for is some sort of computational tool that will catch that division and tell me about the existence of this 'simpler' generating set.  I was thinking that I'd have to use some sort of Groebner bases trick, but if the term order (in this case) decreed that $y^4z^4 > x^9$, then I can't imagine that the division would get noticed.  So, in general, what I am looking for is an invariant on an ideal that says "if you write this ideal using as many monomials as possible whilst maintaining a finite minimal generating set, you have such and such many monomials".  Any ideas out there?  Thanks.
Answer: This is not a general answer, but it is the answer I ended up using to solve my particular problem.  I was interested in knowing if I had an ideal with binomial and monomial generators, if any of the binomials could be replaced by monomials.  I just computed the universal Groebner basis, and if my binomial still remained in that basis, it was essential to the first generating set.  It seems like this trick should work for more general cases than binomials, though.


Analog multiplier using log and antilog amplifier

Question:
What should I add here to make it work? The output should be 3 * 5 = 15V.
Comment: by adding the same identical question 4 times, you somehow broke your question. Please repair it, we can't see anything. Also, whatever this is, you need to **explain** what you've tried and where you're stuck, and ask a precise question.
Comment: What models are you using for D1 and D2? What do you expect those models to produce at the intermediate log voltages? What do you expect those intermediate voltages to produce at the output, given the model for D3 that you're using? This looks like a 'back of a napkin' sketch of how you might think about starting a mulitplier. However, you have some offset voltages to take into account, you need to understand the effect of those offsets.
Answer:
what i should add here to make it work .... the output should be 35
=15v*

It looks like you have got U5's inputs swapped around so it's acting as an inverting comparator and not a linear circuit with positive gain: -

You should also ensure that the op-amps have enough power supply headroom to be able to generate +15 volts on their output. Maybe retest but using smaller voltages that give a product that is less than 10 volts.

I also think that your output stage needs some refinement to make it a unity gain buffer. For instance, I believe that the 100 kΩ resistor (R7) should connect to 0 volts and the node between D3 and R7 should be the output that feeds the unity gain buffer.


Not able to install Ubuntu on new system

Question: I have here a system with

Asrock Z77 Extrem 4
Intel 3570K
Nvidia GTX 570
OCZ Vertex 2 SSD

I burned the newest Ubuntu 12.10 x64 Image and started to boot from the cd.
The menu is there, but after selecting installation there is just a black screen.
Is this because Im using a Z77 chipset? Maybe I just have to change the boot option, but I have no idea how and what to edit there. Some help? Thank you
Edit: Somebody gave me openSuse 12.2 just to see what is happening, and with the newest suse Im able to go through the install menue and start the installation. Whatever, unfortunately I would like to use ubuntu :) So the question is still there: why and how to run it.
Answer: I figured out the problem. It was because of the sata connector on the mainboard.
The mainboard got 4x SATA3 connectors. But these are not equal. If we look into the manual (http://www.asrock.com/mb/Intel/Z77%20Extreme4/?cat=Manual) there we can see:

2 x SATA3 6.0 Gb/s connectors by Intel® Z77, support RAID (RAID 0,
  RAID 1, RAID 5, RAID 10, Intel Rapid Storage and Intel Smart Response
  Technology), NCQ, AHCI and Hot Plug functions
2 x SATA3 6.0 Gb/s connectors by ASMedia ASM1061, support NCQ, AHCI
  and "Hot Plug" functions (SATA3_A1 connector is shared with eSATA3
  port)

I was using two devices on ASMedia ASM1061 and I think Ubuntu dont have any drivers for the ASMedia SATA connector. So after I connected everything to the Intel connector -> no more crashes or black screen during the installation. This is interesting. Wondering why Ubuntu is not able to ignore the devices on the ASMedia connector. Even if I would connect a HDD to the ASMedia that I wont use for the installation for Ubuntu -> crash.
Whatever, I hope this can help for people with the same problem with newer asrock boards. You just should not use the the two connectors

SATA3 Connectors (SATA3_A0_A1, Gray)
Answer: In my experience it's not limited to the ASRock motherboards but to (at least) that ASM1061 chipset.
I've recently installed a SY-PEX40039 PCIe SATA card (ASM1061 chipset.)
Moving the disk from the add-on PCIe controller to the onboard AMD SB950 of my M5A97 EVO mobo, it boots fine.
I stumbled on this post:

Can I prevent an IDENTIFY PACKET DEVICE command to a specific device at boot?

It states that the culprit is the DVD drive... So I tested this... disconnected my DVD drive, leaving only the hard drive containing the Ubuntu install and it boots fine (fast too! :)
My problem is solved. I just have to move that drive to an onboard one and vice-versa with a hard disk on the onboard ports.


Spin Orbit ($LS$) interaction energy

Question: Well, I am currently using a pretty old book by H.E White "Atomic Spectra", and he defined spin orbit interaction energy as the product of the resultant frequency and the projection of spin angular momentum on the orbital angular momentum. My question is why? On what basis did he defined the spin orbit interaction energy as such.
Comment: I don't know the answer to that, Roshan. But there's a bit about this on [hyperphysics](http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydfin.html), which I think is good for delivering understanding.
Answer: There's a semiclassical way of deriving the Hamiltonian term corresponding to the spin orbit interaction in an atom, but I don't know if this is what you're looking for (the correct way would be using the relativistic correction included in Dirac's equation), anyhow:
Consider the classical picture of an atom orbiting the nucleus, now in the electron's frame the nucleus of course appears to be rotating the electron, this orbiting leads to a magnetic field equal to
\begin{align}
\mathbf{B} = \frac{E\times \mathbf{v}}{c^2} \tag{1}
\end{align}
which you can obtain by doing the Lorentz transformations of the fields in SR (I showed you this derivation recently here). Now the $E$ field felt by the electron can be written as the gradient of its potential energy, $\mathbf{E} = -\nabla V(\mathbf{r})$ or in polar coordinates: $-\frac{\mathbf{r}}{r}\frac{dV(\mathbf{r})}{dr}: (*)$ The spin orbit term results from the interaction of this $\mathbf{B}$ field with the electron's spin:
\begin{align}
H = -(1/2) \mathbf{m}\cdot \mathbf{B} \tag{2}
\end{align}
Now by substituting $(*)$ in $(1)$ you end up with a $\mathbf{r}\times \mathbf{v}$ term which you can express as the orbital anglular momentum $\mathbf{L},$ and the magnetic moment $\mathbf{m}$ in $(2)$ is equal to:
$$
\mathbf{m} = \frac{ge\hbar}{2m_e}\mathbf{S}
$$
with $g$ the Landé factor and the factor $1/2$ the Thomas factor. Inserting everything back into $(2)$ we obtain:
\begin{equation}
H = \frac{e\hbar^2}{2m_e c^2 r}\frac{dV(\mathbf{r})}{dr}\mathbf{S}\cdot \mathbf{L} \tag{3}
\end{equation}
In case your model is hydrogen-like then you can substitute the $1/r\frac{dV}{dr}$ term in $(3)$ by its corresponding Coulomb potential. If you plan to look at a more recent book covering such topics, Stephen Blundell's book comes recommended.

Spin Orbit ($LS$) interaction energy


How to neutralize candied glacé strawberry and kiwi

Question: I have 200 gm of candied glacé  strawberry and 200 gm of candied glacé kiwi. I cannot eat it, as it has too much sugar for me. Is there a way to neutralize the candied strawberry and kiwi?
Comment: ...don't eat them?
Answer: Glacé, or candied fruit, is basically fruit preserved with sugar.  So, yes, it can be very sweet.  Even for sugar lovers, it is hard to eat much.  I would suggest using it in cake or cookies.  Italians have a tradition of such cakes and cookies that call for the addition of chopped candied fruit.  I am sure other cultures do as well. I would suggest using them as an ingredient, rather than attempting to somehow remove or reduce the sugar content.
Answer: Strawberries and kiwi generally pair well with lemon or other citrus.
If the problem is just 'too sweet' and not truly a health concern (eg, diabetic), you might consider making a lemon tart (holding back some of the sugar), and topping it with the fruit.
... then sharing it with friends so you don't eat it all yourself.


App Recommendation for automatically stitching screenshots together on iOS

Question: As per this marvellous screenshot on another question, is there an App available (preferably an iOS app, but a Mac OS X one might do) that will take a series of screenshots that are produced by taking snaps of various sections of a scrolling App or Webpage display, and automatically create a conjoined single image file.  The example below was done in Photoshop, but the effect is what I would like to achieve.
Answer: AutoStich Panorama
...has been my choice for the iPhone. You still need to take the pictures manually fist. You can choose all the pictures which you want to stich from your camera roll.

up to 18 megapixels are supported for stitched panoramas
camera images in any order or arrangement (vertical, horizontal, mixed).
option to stich using high res images for better result
Comment: Does this support simple stitching without using perspective to match the images?
Comment: @jtbandes The perspective is chosen automatically. I've not used this tool to stich screenshots.
Answer: You can try using an app like Photosynth, which creates stitched images from a set of images. Unlike some apps that only stitch panorama left to right, this allows for both up-down and left-right, which makes it a good choice for your purpose.

Using the latest in computer vision techniques, you can not only make a panorama from left to right, but also up and down, enabling you to capture a full "sphere".
Answer: Autostitch
It's a panorama app, but you can choose images from the camera roll to include in your panorama. The developers webpage says

AutoStitch now brings the latest in image recognition technology to
  your iPhone. Stitch images in any order or arrangement, using photos
  taken from your iPhones camera. Just select a set of images from the
  camera roll or photo albums, and AutoStitch does the rest. For more
  details, see our webpage, or go directly to the app store
Answer: I currently use StitchIt! which is available in the iOS App Store.
Stitched screen shot here:


What are the real-world applications of real analysis?

Question: I've read the wikipedia article on mathematical analysis and this, but I can't exactly find an answer. Is real analysis just some pure math, or does it really have something to with physical applications? Feel free to send me any references that might answer my question, thanks!
Comment: The name "real analysis" has not anything to do with "real applications". It hints that we're doing analysis using the real numbers.
Comment: Any way I can somewhat refine my question?
Comment: Can you be a bit more specific about the definition of 'real analysis' and 'real world'?
Answer: Engineers and physicists need to solve differential equations. Most differential equations are impossible to solve symbolically.  Instead, one obtains a numerical solution by either approximation methods or infinite series.  Analysis was invented to understand the circumstances under which these methods produce correct answers.  For example, when does the formal power series solution of a differential equation converge to the actual solution?
Answer: Each time someone does a derivative, integrates something, or solves a differential equation she is doing real analysis. Our modern world (starting with the most down-to-earth apliances and even furniture) would be totally impossible without it.
Answer: Real analysis stems from the concept of the real numbers.where each numbers on the real number line are understood as pattitions with infinite enumerations.it tries to analyse the relationship between partitions.its application can be clearly seen in the computer world,engineering,etc.


NirCmd won't run on Windows XP

Question: I am using the NirCmd Command Line utility. It works fine on Windows 10, but I am trying to use it on Windows XP SP3. It says that it is not a Win32 compatible program. The website claims that it works on Windows XP - 10. I have turned off my antivirus and firewall and it still won't run. Is there anything I can do to get it to run on Win XP?
Comment: Got a 64-bit version of Windows XP? Why are you using XP anyway, it's pretty old, and long unsupported
Comment: I think its 32-bit... I am only using it because of its compact size. It is an MSI U123 Notebook.
Comment: Well, for now, is there _any_ way for me to run NirCmd on WinXP? The website says I should be able to.
Answer: You have accidentally downloaded the 64-bit version of NirCmd. This generally results in a not a Win32 Application error.
Use the 32-bit version available for download here:
http://www.nirsoft.net/utils/nircmd.zip
P.S. Don't listen to people who try to scare you into upgrading. You are safe to stay with Windows XP if you have a decent firewall and avoid malicious sites while browsing the web.

NirCmd won't run on Windows XP


What`s wrong with this Eevee Lighting Setup?

Question: I have run into some issues with the EEVEE render engine. I want to render a smartphone but the areas around the camera Lens show some weird lighting problems as you can see in the first picture.
The area near the seams is lit up, but in reality, it should be darker near the seam. I have tried to solve the problem with a boolean operation in case it is a topologic issue. I have also enabled ambient occlusion and tweaked the light and shadow settings but it does not help.
I have never really worked with EEVEE.
Comment: Hi! It would be really helpful if you could share the file     https://blend-exchange.com/
Answer: Solved: There are more Lighting-Settings in each Lightsource. Tweak this in Combination with the Shadow Cube Size and Cascade Size in the Render Settings is the solution.
This video describes:
Video Tutorial i`ve used


Tabs with status

Question: I have this kind of Tabs in my design, however I have to integrate count of the items (which I did with just a circle and number inside), and I need Status like thing since one of those tabs (in my case it's restoraunt menu) has to be active. Now tricky thing is that I tried making it like my primary color when it's active (when you're on selected tab) but problem is how can I leave that tab Active as Status when I leave to the next tab (which is inactive) ?
Comment: I'm having trouble understanding your problem. The "status" you're talking about is just the tab's active state, shown when the user is currently viewing that tab, correct? When the user clicks into a new tab, that active state will transfer to the other tab? You said "*how can I leave that tab Active as Status when I leave to the next tab*"... are you trying to keep the previous tab showing an active state even after the user leaves it?
Comment: I understand the question, but you should add a mockup to build the answer from it. You are talking about primary color, active tab, inactive tab, status colors, etc. leaving too many items to the imagination.
Comment: Okay well, these are the menus. In POS system user can set menu which will be active (NOT on here on tabs). And when he sets it one of them here in tabs becomes active and when I say active I mean activated. However since I can switch let's say some other tab which is not active like on the case below on the picture, my solution was to leave the tab that Activated to be in color but without the bottom line/stroke. However managers don't like this solution they want some other indicator that menu is active

https://i.imgur.com/JUiT9U7.png
Answer: If you take a look at the Material 3 Design System and see the different types of states a tab can have, you'll find that there are the following you can use to create the status required:

Enabled
Hover
Focus
Pressed

That means you can use the Enabled for all the tabs that are active, and then for each of the hover, focus or pressed behaviour you can use a variation of the main colour palette to indicate different states or statuses as required.

Tabs with status


Eisav Harasha having good kibbud av vaem?

Question: Is there a way to make sense of Eisav Harasha knowing he did 5 big aveiros in one day (including murder) and wanting to kill his brother Yackov,  and also exhibiting very good kibbud av vaem?  How do we explain this fellow?
Comment: Plenty of people are that way. Evil in many ways  but not in all I once had a neighbor who was rumored to be a mafia hit man, he kept a car that he didn't use in my parents garage which was presumably a getaway car, one day he just disappeared… In all my dealings with him he was a nice guy, he used to attend block meetings about safety and fighting crime.
Comment: Maybe the same way many Nazis spoke politely as they massacred Jews...
Comment: Esau was his father's favorite. Esau paid him back by being very good to him.
Comment: @MauriceMizrahi I think it's the other way around: Esav was his favorite because he was honored his father so greatly.
Comment: Genesis 25:28 says otherwise.
Answer: At the Bottom of page 179 of the Juggler and The King, Rav Aahron Feldman explains the Gra, where he basically asks how can someone evil (Eisav) do a Mitzvah so well.
He answers that it was in his best interests (selfish) do so as this will cause his children to take care of him in his old age the same way he cared for his father.
He adds there may be an even subtler self interest where to get the maximum pleasure out of this world there needs to be law and order and honoring the past generations fostors a respect for tradition which helps create social stability. Thus he could get the most pleasure out of this world.


Why not always use https when including a js file?

Question: For what reasons do sites provide logic to switch between http/https protocols for JavaScript include files?  Why not always use https?
Answer: HTTPS means :

You need a server configured properly
You need a certificate on your server

And, to not get a warning in the browser, you need a certificate signed by some trusted authority
And this costs a bit of money

A small bit of performance impact

The server has to crypt the data
The client has to de-crypt it

I would bet HTTPS means less caching

Maybe on the client side ?
And, most probably, on proxies ?

If you don't need HTTPS... Well, why use it ?
Comment: can someone confirm/refute the less caching client side with https?
Comment: There's no caching issue that I can imagine.  I don't know why the client would decide not to cache.  And if you're going through a proxy, that proxy *is* the SSL endpoint, so there's no reason it wouldn't cache.
Comment: Also, the first two points are moot.  The whole point of switching assets over to HTTPS is to keep the page fully secure when the page itself is served over HTTPS.  The server and certificate configuration should already be taken care of if you have this problem.  The only issue I can imagine is performance.
Comment: Really not a fan of this answer. Regarding points 1 & 2: you're writing these from the points of view of someone serving a JS tag. If you're serving a JS tag, then you _need_ to provide HTTPS support, so these arguments are moot. Regarding point 3: It's actually a huge performance impact :) The TLS handshake takes a relatively long time, but if you're loading the JS async, then you should be fine. Point 4: Clients will cache all the same, but edges cannot cache since they cannot see the headers. Regarding 5th point: because developers are lazy and information leaks in URLs and cookies ;)
Answer: There's less overhead if you just use http to serve the javascript include files. However, if you are running a site over https then you'll want to load everything over https, including the javascript include files.
Answer: Because you can get the page both with and without SSL.
If you mix secure and unsecure requests in a page, the user will get a warning, so when the page is requested using https, it will have to requests the scripts using https also. This is usually done automatically when you request scripts from the same site with a relative URL, but if you have to use a complete URL to request a script from a different domain, the protocol has to be set dynamically.
Comment: This isn't true. You only get warnings if you load a page from HTTPS and then that page loads content over HTTP. If you load a page over HTTP, and the page loads content over HTTPS, there is no warning.
Comment: No reference, just experience. Recently updated Chrome, FF, Safari, IE10 & IE9 seem to all be fine with it. So my comment may not reflect 100% of browsers.
Comment: Do you have a reference for that specific behaviour? Different browsers handle mixed content in different ways.


Vendor list page - Only list vendors with items in stock

Question: I have a page on my site that lists all the vendors in my shop like so:

        {% assign current = "" %}
        {% capture alphabet %}
            -A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z
        {% endcapture %}
        {% assign letters = alphabet | split: '-' %}
        {% assign its_a_letter = false %}
        {% for vendor in shop.vendors %}
            {% assign vendor_first_letter = vendor | strip | upcase | slice : 0 %}
            {% for letter in letters %}
                {% if vendor_first_letter == letter %}
                    {% assign its_a_letter = true %}
                    {% break %}
                {% endif %}
            {% endfor %}
            {% if its_a_letter %}
                {% unless vendor_first_letter == current %}

{{ vendor_first_letter }}

                {% endunless %}

                    {{ vendor }}

            {% else %}
                {% assign vendor_first_letter = "#" %}
                {% unless vendor_first_letter == current %}

{{ vendor_first_letter }}

                {% endunless %}

                    {{ vendor }}

            {% endif %}
            {% assign current = vendor_first_letter %}
        {% endfor %}

Some of these vendors don't currently have any items in stock so it's pointless to have them show up here. Is it possible to display only the vendors that have items in stock within their collection?
I currently have 2 collection tags in my store for 'in-stock' and 'sold-out' to help filter them with our filter menu and that is appended to the url so we only show customers in stock items.
Answer: Since a product has a vendor, and a product has inventory, you could just check that way. It would be insanely slow and obnoxious but hey! That is what a hosted platform is for, to turn crazy Liquid into the right tight HTML.
Note the Liquid for product.available
Returns true if a product is available for purchase. Returns false if all of the products variants' inventory_quantity values are zero or less, and their inventory_policy is not set to "Allow users to purchase this item, even if it is no longer in stock."

So while you loop through your vendor list, loop through all the products, checking the product vendor for a match, and the availability. If they don't suit you... skip the vendor.
Would be interesting to see how slow this is... but you never know till you try...
Another approach, perhaps smarter, is to iterate all your in-stock products once. Build your vendor list out of that, instead of shop.vendors.
Comment: It doesn't seem like I'd be able to keep them organized by their first letter this way ( in reference to the last idea you suggested )
Comment: And would looping through all available products cause any api issues if my store has 10,000+ products to go through?
Comment: You're right. Sorting is not a strong point of this algorithm. Having 10,000 products will also surely slow you down...
Comment: you might want to invest in an outside process for this. Keep your info up to date outside Shopify, and call it into play when needed so it is always fast.
Comment: David, please see my answer. It sort of worked but couldn't handle the scale of my live site
Answer: I was able to get this working by writing it like this:
{% for vendor in shop.vendors %}
    {% for collection in collections %}
        {% if collection.title == vendor %}
            {% if collection.all_tags contains 'in-stock' %}
                then the conditions for checking the first letter and displaying the vendor, etc. nothing new

It only worked, however, on my dev site that I was testing it on and when I pushed it to production I got liquid error: memory limits exceeded. My dev site is definitely lacking in collections and products compared to my live site so this may work for people who have smaller sites.
Comment: Ha... yes.. there are limits to everything... easy to do small things.. not so easy to scale to reality


Show a fullscreen modal with a spinner when clicking button

Question: I have a login form that, when the user clicks on the submit button, I want to show a fullscreen modal with a white and slightly transparent background, and a spinner in the middle, while the app communicates with the server. I then want to hide that layout when the app gets a response from the server.
I have set up a view controller with the above layout (white background and spinner). However, I'm not sure how to show this view over the login view when the login button is clicked.
Here is the action I've made for the login button:
@IBAction func onSubmit(_ sender: Any) {

}

How do I show the view over the entire screen, that disables user interaction?
Comment: There are many ways you could implement this. For example you could create a view and add it on top of the current view, this new view would have the activity spinner and an opacity styled how you want it.
Answer: This is really simple. Modals are presented full-screen by default.
If you want the view controller to show the contents from the view controller below, but blurred, then you need to add a UIVisualEffectView to your view controller. See this link for info on using UIVisualEffectView: Creating a blurring overlay view
Your code to present a modal can be as simple as:
let modal = storyboard.instantiateViewController(withIdentifier: "modal")
present(modal, animated: true)

Comment: While valid, this probably isnt the best thing to do. Simply adding a view ontop of the current view would suffice and prevent the OP getting confused with where they are in the nav stack!


Storing GnuPG folder in Dropbox

Question: I would like to use dropbox for backing up my gpg keys, IMHO even if dropbox admins gets a copy of the keys they still need the passphrase to use it so is it ok to assume this is safe to do so?
Comment: I also keep encrypted files in drop box that i need to access from multiple machines so i need to sync the same gpg key.
Comment: I don't actually know what kind of encryption GPG uses to protect its private keys, so I can't comment on the security of it, but I would not do this. I'd just create a different key for each computer I need one on, so that each key never leaves the computer it's created on.
Comment: in which case can you encrypt the keys with something you can unencrypt anywhere (an OTFE volume maybe) and stick that on DropBox? Or carry the key files around with you on a USB stick?
Answer: I would advise against doing this. True, they need the passphrase, but you should still always keep your private keys under your own direct control. GPG depends on the security model of requiring something you know (the passphrase) and something you have (the key). By letting your key get out there, you're running the risk of completely defeating half of the authentication scheme. I doubt that DropBox employees would ever cross you intentionally, but if they were to have a security breach allowing a 3rd party attacker to gain access, you would be in a bad situation. It would be much safer to keep your keys backed up on some type of physical media like a flash drive.
Comment: +1 You password is the weakest link in the chain (it's much smaller and so much easier to brute force (or guess!) than any other part) - if you give someone everything but the password, well, you see my point...
Answer: First, understand that "safe" is always relative. You should be thinking in terms of "safe enough for my use case", and that's ultimately going to be up to you.
GnuPG's scheme for protecting the secret keys is the best anyone currently knows how to do; it generates a symmetric key from your passphrase, and uses that protect the secret key. This symmetric key is never stored; it's derived from the passphrase each time it is required.
This provides fairly strong protection of the secret key. Enough that the best attack for recovering your secret key is guessing your passphrase. Or, put another way, making your secret key "semi-public" by putting it on something like Dropbox means that your key is only as secure as the passphrase you chose to protect it.
Since there are purpose-built tools for cracking GnuPG passphrases, and since Moore's law means cracking passwords gets exponentially easier over time, you need a really strong passphrase to make this any kind of safe.
Depending on what your secret key protects, choosing a decent passphrase may be secure enough to risk putting the key on Dropbox; and the convenience could be worth the risk. But best practice is to only ever allow the secret key on the machine that generated it and one backup/escrow location under your direct control (e.g. printed out and placed in a fireproof safe).

Storing GnuPG folder in Dropbox


If we accelerate a neutron star to move at speeds comparable to light would it become a blackhole because of the added energy?

Question: Could a neutron star turn into a blackhole if it is accelerated to near luminal velocities? And if it slows down after a while, does it become a neutron star again?
Comment: No, if an object is a black hole in any inertial frame then it's a black hole in every inertial frame. Please see https://physics.stackexchange.com/q/3436/123208 and https://astronomy.stackexchange.com/q/32578/16685
Comment: OTOH, if your speeding neutron star crashes into another body, then you will get a black hole if the total energy density (to be more precise, the [stress-energy-momentum](https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor)) in the region is high enough, in other words, if the combined mass & kinetic energy is high enough.
Comment: Also related: https://physics.stackexchange.com/q/512636/123208 BTW, some neutron stars are traveling quite fast relative to their galactic neighbours, eg https://en.wikipedia.org/wiki/IGR_J11014%E2%88%926103 but the speed is less than 1% of light speed.
Comment: @PM2Ring ...what can happen in neutron star binaries if they finally collide.
Comment: @peterh Depending on the mass & KE, you may get a larger neutron star, or a black hole. In either case, the collisions is likely to create (and eject) some heavy elements via the r-process, eg gold. See https://en.wikipedia.org/wiki/Neutron_star_merger and the periodic table at https://en.wikipedia.org/wiki/Nucleosynthesis#Timeline and https://arxiv.org/abs/1901.04138
Answer: In special relativity, changes of reference frame are symmetric between observer and observee.  If moving a neutron star gave it enough kinetic energy to become a black hole, then you could effect this change by jumping into a moving reference frame yourself.
What matters is the neutron star's mass in its rest frame.


What is a "shallow" layer and a "deep" layer of a neural network?

Question: What does shallow, deep, shallower, deeper, mean in the context of neural network layers?
For context:
Answer: Just one comment on top of Tim's answer, "shallow" and "deeper" in the cited context are just relative descriptions. It is not referring to certain layers as shallow or deep, but stating that a certain layer $L_i$ has larger receptive field than its precedent layer $L_{i-1}$ due to the effect of convolution and pooling.
Answer: Shallower layers are the layers closer to input layer, while deeper layers are those more distant from input layer. However this is not a formal terminology, but rather informal, descriptive language.
Comment: No I mean, a single neural network has both shallow and deep layers.  I am not talking about NNs in general.  Within a single NN, which layer would be considered a shallow and which one considered a deep one.  Does deep mean number of nodes or deep means closer to the center or deep means closer to the final output?
Comment: @confused if you want to use such distinction, than closer to input layer, would be "shallower", though I don't think that such terminology is useful for anything, better just say "input layer", "first hidden layer" etc.
Comment: It's used in the Deep Learning book by Goodfellow.
Comment: I think Chien-Yao Want et al "YOLOR" paper gives insight and context for shallow and deep layers. It seems deep layers refer to those closer to the output.
"In the general definition of neural networks, the features obtained from the shallow layers are often called explicit knowledge, and the features obtained from the deep layers are called implicit knowledge. In this paper, we call the knowledge that directly correspond to observation as explicit knowledge. As for the knowledge that is implicit in the model and has nothing to do with observation, we call it as implicit knowledge."
Answer: The notion of deep neural networks actually goes way back. At the time of McCulloch and Pitts (1943) and later with Rosenblatt's perceptron (1958), no learning algorithm was available that could train neural networks with more than one hidden layer.
In 1985, the backpropagation algorithm was developed and published by Rumelhart et al. That can train neural networks with nonlinear activation nodes (in the hidden layer). 'Backprop' even works for $k$ hidden layers. Since then, deep neural networks with more than one hidden layer have been trained and tested numerous times. During the 90-ties, neural networks lost some of their 'hype' and also many researchers began systematically to compare the performance of neural networks with that of alternative classifier and regression models. There are applications where a linear discriminant outperforms a well-trained nonlinear neural network.
After the millennium, an understanding arose that more hidden layers can add higher-order (statistical) relations to neural networks (deep NNs in image processing). Specifically for computer vision, deep NNs with multiple hidden layers were developed that turned out to learn feature detection filters in the first hidden layer. Experiments have also been done with initializing the weights of this first hidden layer using the known coefficients of linear filters (edge-detection, corner detection, T-junction detection - a complete filter bank as a matter of fact). Neural networks with pixel input is a special type of application because of the spatial arrangement of an image. Deep neural networks have proven successful on many kinds of data: image, symbolic, speech, recursive and more.
So, with deep neural networks we mean more than one hidden layer.
I suggest you to have a look at the groundbreaking paper by LeCun (LeCun, Y., Bengio, Y. Hinton, G. Deep learning. Nature 521, 436–444, 2015).
Comment: Does this actually answer the question?
Comment: It does now - thanks !
Comment: I think the question does not refers to the difference between deep and shallow NN's. But it's about deep and shallow layers inside a Deep Neural Network. As mentioned in Chien-Yao Wang et al "YOLOR" paper's introduction.


Objects not appearing in the final render

Question: By final render i mean when you press F12 to get a image but when i do that one object doesn't appear although its particles appear and I've tried doing things like Ctrl + Alt + H and W but it doesn't change anything i think this is because it un-hides thing n object mode but I'm talking about when you actually RENDER it. Any help is appreciated
Comment: can you share the file? use this website: https://blend-exchange.giantcowfilms.com/
Answer: Possible causes for a Blank render:

No lights in scene.
Objects disabled for Render in outliner (camera icon).
Strips in VSE and Sequencer enabled.
Objects in different layer, or in a layer disabled in Render Layers.
Object blocked by other objects.
Active camera aiming in a different direction.
An object in the scene set as active camera.
Any, some or all of the above.


Discussion Tab in the side panel of each question

Question: I want to suggest to add a Discussion Tab in the side panel of each question. I think it will help users to discuss about the topic with out interfering with in the comments and share their thought about the topic. As it is Electrical Engineering forum such tab might be helpful for multiple reason. Beginners would get chance to raise thought without disturbing the main purpose of the question, experts can give suggestion and help improve the context about the topic.
Comment: As currently suggested, this would be a network-wide change and therefore would need to be posted on [main meta](https://meta.stackexchange.com). **Warning:** if you suggest it on main meta you should put a lot of thought into it, as users on main meta will likely downvote (to indicate disagreement) a suggestion that hasn't been seriously considered by the asker. Alternatively, you can use a chat room on the question for further discussion -- that is already in place.
Comment: I'm voting to close this question because while its nice to get feedback on ideas, this idea could not be implemented on EE.SE
Comment: @Ankit_Gunner As well as the points raised by others it's worth noting that the site strongly aioms at Question and answer with discussion being minimised. Comments are already meant to be about the question and not about the technical aspect, but already get used for substantial technical input. I'd probably be happy with such some version of such a feature, but it would never achieve site-wide acceptance. || The fundamental aim of the site is to provide good Q&A that attracts search engine traffic that makes money for the owners :-). All the rest is a bonus :-)
Comment: The [chat feature](https://chat.stackexchange.com/?tab=site&host=electronics.stackexchange.com) effectively handles this request, if (in my own opinion) not exceptionally well.
Comment: Thank you all for your views on this suggestion. I really appreciate your thoughts on this idea. I do see the idea  is a network-wide change rather than just EE. Yes, chat feature does deal with this issue but I think it is an isolated way to discuss rather than open panel for a topic you just came across. like @RussellMcMahon said fundamental aim is Q&A so I guess this is not the place for such panel. A version or plugin of such type would be Awesome. Moreover, Is there any other highly active discussion site out there rather than this for EE?
Comment: @Ankit_Gunner there is also a chat feature, SE is not intended for discussion, it's a Q&A site we rely on SE to make changes to the site
Comment: @Ankit_Gunner For a forum that supports discussion I suggest that you look at http://www.piclist.com (don't be put off by the presentation or the PIC in the name). Then visit http://mailman.mit.edu/mailman/listinfo/piclist, join the mailing list & say hello. Provide as much detail of your requirements as possible.
 Just like here, there are people there who know almost everything (collectively). The site supports a conversational approach. Some SE members are also PICList members (myself included). It's a very useful complement to this site for questions of this sort.
Comment: Thank you @RussellMcMahon, I really appreciate you help. I am a recent EE graduate. I want to learn more and Network with people interested in this field. Your suggestion would really help me grow, thank you.
Comment: @VoltageSpike I do understand now, Thank you!!
Comment: anytime, Your welcome
Answer: The site already has a comments section, and so having two areas to have discussion would be redundant. This would need to be site wide and site wide features are decided by stack exchange.


What International laws should one in the InfoSec industry we be aware of?

Question: What InfoSec regulations should one be aware of when dealing with 'live' cross-border communications, or the offline transport of information?
Comment: It really depends where, can you be more specific about the locations? Or specifically cross-border? E.g. any EU laws are not "international" for europeans...
Comment: I don't have enough background to scope this question further(or know a consolidated place to refer to).  With your point, I just learned about the EU datacenter laws for PII.  This caught me off guard, and left me searching on how to properly round out my knowledge.
Comment: You should include more details about your physical location. In particular, at first blush, considering your profile location of "New York," it's not immediately obvious why EU PII laws apply to you.
Answer: The world is increasingly interconnected, and it is more and more common that actions by people in one country can affect people in other countries and be regulated by laws there.
Here is a brief sampling of some of the issues to consider.

A security researcher from Russia was detained while visiting the US by authorities for distributing free copyright circumvention software.  See http://en.wikipedia.org/wiki/Dmitry_Sklyarov
Web sites can have traffic from all over the world and laws in many different countries pertaining to privacy, copyright, libel, etc. may apply to the web site owners, operators and probably even contributors.
See e.g. http://en.wikipedia.org/wiki/Information_privacy and
European Union Aiming To Create New Privacy Laws
Information considered a public service in one country can be seen by others as illegal.  See e.g. the NPR story on Seeing The Internet As An 'Information Weapon' of which this is an excerpt:

[In 2009] Russia successfully
  sponsored an even sharper version of
  its cyber disarmament proposal at a
  summit of the Shanghai Cooperation
  Organization, which includes China and
  four Central Asian countries as well
  as Russia.   The accord defined
  "information war," in part, as an
  effort by a state to undermine
  another's "political, economic, and
  social systems."

http://en.wikipedia.org/wiki/Shanghai_Cooperation_Organisation
Answer: @nealmcb gave some very good examples.
In general, since your question is quite vague, there are two types of laws that you need to consider when "going international":

Local laws relevant to your destination (including regional laws, e.g. EU, and "state" laws)
Laws of your origin country that relate to exporting your technology (e.g. the classic cryptography limitations from the U.S.).

As Neal mentioned, each of these laws may apply, depending on country/law:

the country where your company is legally registered
the country you are selling into
the country where your technology is being developed
the country where your users are located / citizens of
the country where your web servers are physically located
the country where your database is physically located
the country/ies where your cloud provider may migrate your cloudy instance/s to (good luck with that one).

As mentioned, some of the big ones to know about, besides the non-country regulations such as PCI-DSS and depending on industry, are EU Data Protection, Basel II, and the Chinese Firewall.
If you ask a more targeted question, it may be easier to provide more specific answers.


Sigma 70-300mm 1:4-5.6 APO Macro super lens

Question: Is there an adapter to fit the Sigma 70-300mm 1:4-5.6 APO Macro super lens to the body of a Sony a200
Comment: Sigma makes lenses for many different mounts. Do you know which mount your Sigma lens is, or what camera it was used on?
Comment: Possible duplicate of [Can I use lens brand X on interchangeable lens camera brand Y?](http://photo.stackexchange.com/questions/62000/can-i-use-lens-brand-x-on-interchangeable-lens-camera-brand-y)
Answer: That lens is available from Sigma with a Sony mount, so there's no need for an adapter if you haven't yet bought the lens -- just buy the Sony version.
If you already have the lens for some other mount, see Can I use lens brand X on interchangeable lens camera brand Y? for information about which mounts can be adapted to which others and what drawbacks might be involved.
It looks like the a200 has a Sony/Konica/Minolta A-mount, which has flange focal distance (FFD) of 44.5mm. So, if you have the Sigma 70-300mm lens with a Canon EF mount, you won't be able to adapt it because the Sony's 44.5mm FFD is greater than the 44.0mm FFD that EF lenses require. On the other hand, the Nikon F-mount's FFD is 46.5mm, so if you have the Sigma lens built for Nikon, you may be able to use that lens on your a200 with an adapter like this one.


US company Warrants issued in Europe

Question: Can one bank issue another companies warrants ? I have been searching for warrants on US companies and turns out that a lot of these warrants are issued in Euro instead and by different banks rather than the US companies they represent. Any help will be very much appreciated.  is that even possible?
Answer: This is quite common that a bank in country X will issue warrants representing stock of company traded in country Y. People living in the country X wanting to invest in that stock, may not have a direct access to a stock exchange in the country Y, and buying these warrants (while the bank itself buys the actual stocks to cover them) is the only way.
Such a warrant is sometimes called "Global Depository Receipt".

US company Warrants issued in Europe


Accidental voting

Question: I didn't mean to vote on this answer but have accidently clicked 'vote up'. Then I clicked 'vote down' to undo previous vote. I think it doesn't do what I expected, it just adds 10 and then subtracts 2 from reputation of one who gave the answer, and subtracts 1 from voter's reputation. Is there any way to undo such actions ?
Answer: Yes. If you accidentally click an upvote, click again to remove it. Same for a downvote.
Clicking a downvote (after clicking an upvote) will remove your upvote and issue a downvote instead.
Comment: You however need to be on time. After 5 minutes it's locked until he (or someone else) edits the post.
Comment: @Yasir: I edited the other answer as well. You can now remove your second accidental downvote. In the future, watch out! And remember, click the orange arrow once again to remove it ;)
Comment: Daaaaaaaaaaaamn
Comment: @Yasir: I have edited the answer. You should now be able to remove the downvote. Just click the orange arrow once again.
Comment: @Josh: So clicking upvote then clicking downvote is the same as clicking upvote then clicking it again to undo and eventually clicking downvote? Also it turns out the same [person](http://stackoverflow.com/users/35448/bjnortier) gave two answer, thus accident seems to occur with both answers. I'm sorry for inconvencies, probably I'm to tired to use SO today.
Comment: @Yasir: That's correct. Clicking the other arrow immediately will inverse the vote. Clicking the arrow once again removes it.
Comment: @BaluS: Yes, I've removed a downvote from the answer beginning 'Parameterized Modules! From..'.
Comment: @BalusC: probably I did that because of pictures being disabled in browser :) Thanks.

Accidental voting