Logic high preventing sleep mode STM32?

Question: I have a fairly simple question that I can't find the answer to in the datasheet or reference manual for an STM32L073RZ. Put simply: is there a mechanism within the processor that prevents entering Standby mode with WKUP pins enabled when the voltage supplied to either of those pins is greater than or equal to logic high?
I ask because this is the behaviour I'm observing but, as previously stated, can't find mention of this in any documentation.
I currently have a board whereby the GPO of an NFC EEPROM (M24SR64-YMN6T/2) is attached to a WKUP pin. The GPO is active low and configured for SESSION OPENED mode. This means that the GPO line usually sits high, but, when an RF session is underway, will go low. When the RF session is finished the line pulls high again and would trigger a WKUP. This is the intended outcome, at least.
However, as I've already mentioned, I believe that the GPO line being high is preventing the processor from going into Standby mode. If this is the case it's a simple hardware fix, but I just want to make sure that I'm not missing anything.
I should mention that, if I disconnect the GPO line from the WKUP pin the processor goes into Standby mode as expected. I should also mention that, if I drive the WKUP line high from another source then it seems to prevent Standby mode. Lastly, if I have the GPO line connected to the WKUP pin but pulled low externally, then the processor goes into Standby mode.
Answer: Take a look at the comment at the bottom of page 170 of the reference manual:

Note:   An additional wakeup event is detected if the WKUP pins are enabled (by setting the EWUPx (x=1, 2, 3) bits) when the WKUP pin levels are already high
Comment: Thanks, I'd missed that. Unfortunately, clearing the CWUF bit after enabling the wakeup pins but before sleeping still leads to increased power consumption.

Logic high preventing sleep mode STM32?


How do I find Queen Endregas?

Question: I'm having problems with luring out the Queen Endregas to complete the Endrega Contract mission. I understand from reading up on the lore that Endrega queens only appear when I find their cocoons and set fire to them. However, when I use the spell that seems to set things on fire, Igni, on the cocoons, nothing happens. How do I light the cocoons on fire?
Answer: As StrixVaria already mentioned, you only need to open each cocoon and hit it with your sword. There are two groups of three cocoons each, destroying all cocoons of a group will spawn one of the Queen Endregas.
I've marked the locations of the six Endrega cocoons on a map:
Comment: Thank you for the locations. This is a very fun action adventure rpg.
Answer: You don't have to light the cocoons on fire.  Beating them to death with your sword is sufficient.  Make sure you open them up first.   In order to be able to open them, however, you must have the knowledge about the Endrega.  You can accomplish this either by killing three of them or buying the book from the dwarf in the nonhuman district who sells books.
Comment: @Mana - you're probably missing one. There's 3 cocoons for each queen. She only appears when the last one is slain.
Comment: Wait, really? I had beaten them to death but no queens emerged...I guess I had been impatient or something and left too soon.

How do I find Queen Endregas?


How to label duplicate geometric features avoiding text overlap for more than 16 duplicates?

Question: It seems that the strategy of using the increase the distance of the label placement together with use callout lines to connect the labels to the features, only works with less than 17 duplicate values. Above 17 records they overlap again as shown in the attached screenshot. Is there any alternative to solve this casuistic?
Comment: It might be a bit of an obvious question, but have you tried increasing the distance even more? It seems that the seventh value should logically be displayed at the very top or at the very bottom and for some reason it's overlapping the top right one.
Comment: Confirmed that increasing the distance is not the solution. With less than 17 duplicates, partially solved by modifying the Placement Mode option to Point around, but after 16 duplicates the problem persists
Answer: If your points are exactly the same, what you can do is the following (if not, the same approach can be taken by adapting the geometric criterion).
Collect all 'VALUETXT' for points which intersect and display one label as the list of this list.
array_to_string(array_prepend(overlay_intersects('points',text),"text"))
This generates a list like: 'text1,text2,text3,text4,text5'
Make sure the Never Overlap is configured so that only one of the overlapping points generates a label.
And then ask for the Label to be wraped around the ',' separator:

If you want to sort labels, you can use:
array_to_string(     array_sort(array_prepend(overlay_intersects('points',text),"text")))


in-memory table quota reached in error

Question: Edit 1:
From article posted by first answer > this:

Additionally, if you are using memory optimized table in the context of table valued parameters repeatedly, you may encounter this error even you use them in a separate batch and memory gets released.  We are looking to address this issue in future cumulative updates.  For now, you either need to use enterprise edition or periodically restart SQL or offline/online the database.

I use in-memory table valued parameters continually.  However as a troubleshooting step, I re-deployed the solution and removed all memory optimization.  I still received this error message.  After restarting the service the message is gone and I'm able to use in-memory tables once again.
Original Post:
I'm receiving this message (Sql Server Standard 2016 sp1 on VM):

Could not perform the operation because the database has reached its quota for in-memory tables.

However, in-memory table usage is zero as shown here.  Any idea how to recover from this state or even start to investigate what is going on?
Comment: Were you performing any operation/running any query when you got this error message? Where did you get this message? Was there any other message in the errorlog at the same time?
Answer: You may be running into this:
https://blogs.msdn.microsoft.com/psssql/2017/06/07/you-may-see-out-of-user-memory-quota-message-in-errorlog-when-you-use-in-memory-oltp-feature/

in-memory table quota reached in error


why two pair of terminals are used in a shunt?

Question: The working principle of two pair of terminals of a shunt is required here.
Comment: That's *one* pair, not two.
Answer: Imagine the shunt looks something like this, where R1~R4 represent connection and wire resistances, and are variable with tightness of the connections, temperature and so on. R5 is the shunt resistance itself (usually made of a low temperature coefficient alloy such as Manganin or Constantan.

simulate this circuit – Schematic created using CircuitLab
Provided only that the meter is high resistance compared to the values of the resistors the voltage measured will accurately reflect the current I1 multiplied by R5 (only).
It is important to use the larger connections for the high current and the smaller ones for the measured voltage because the larger ones are (or should be) on the 'outside' of the smaller ones. If you were to just parallel them all in my example there would be a large (and variable) 5m\$\Omega\$ resistance on each side so the error would be a very large (and variable) 10% of reading! Even if you calibrate that out, it would change if you tighten the connections or if they relax, and it would change more than the tolerance of most shunts for a few degrees C change in temperature.
It's possible to use Kelvin connections to surface mount resistors, for example. Some have 4 terminals, but you can split the ends of something like an 0805 to improve performance (not quite as good, but better than nothing).
Comment: I think the schematic is an excellent way of explaining it!
Answer: It's called a Kelvin connection, or four-wire resistance measurement.
The issue is that the resistance of the shunt is not so very different from the resistance of the wires connecting to it, so sharing the same connection points for connecting power, and for measurement, the connections themselves would add enough resistance to affect the measurement.
So a large (low resistance) connection is used to connect power at each end of the shunt, and a second connection closer to the shunt itself takes voltage to the measurement device. (This can be relatively thin, as it doesn't carry significant current, without affecting measurement accuracy).
Answer: A shunt is a part with a very small resistance (typically know,  not always small). It's connect at two points of a circuit. Hence it has two terminals or connection points. To measure a voltage across it, you need to measure it across those two points.
Comment: @Passerby, quite right. A current shunt is simply an additional parallel path that a current can take. It can be of calculated resistance to assist in a measurement, or to reduce current flow in the other path, such as a jumper or switch. It's not purely about measurement resistors, as you say.
Comment: I'd add that it typically has a very small, _but known_ resistance - so that you can measure across it and do your maths.
Comment: Well, I've seen people call shunts jumpers. So their specific resistance isn't important all the times.
Answer: In some shunt resistors resistance is so small, it is not very different from pcb trace resistance. So taking measurement from there is a bad idea. They arrange another two pads such way that current will not flow there, so you can take measurements of voltage drop on tbe exact resistance you know.
Answer: With shunts intended for measuring large currents, there can be significant voltage drops (small, but significant compared to the intended measurement voltage) in the high current terminals.  Additional connection points are added for the connection to the measuring instrument, so the voltage drops in the high current connections won't affect the acuracy of the measurement.


What is the true meaning of a minimum phase system?

Question: What is the true meaning of a minimum phase system? Reading the Wikipedia article and Oppenheim is some help, in that, we understand that for an LTI system, minimum phase means the inverse is causal and stable. (So that means zeros and poles are inside the unit circle), but what does "phase" and "minimum" have to do with it? Can we tell a system is minimum phase by looking at the phase response of the DFT somehow?
Comment: Welcome do Signal Processing! This is a great question. Make sure to read our [FAQ](http://dsp.stackexchange.com/faq) which contains a lot of useful info about the site.
Answer: The relation of "minimum" to "phase" in a minimum phase system or filter can be seen if you plot the unwrapped phase against frequency.  You can use a pole zero diagram of the system response to help do a incremental graphical plot of the frequency response and phase angle.  This method helps in doing a phase plot without phase wrapping discontinuities.
Put all the zeros inside the unit circle (or in left half plane in the continuous-time case), where all the poles have to be as well for system stability.  Add up the angles from all the poles, and the negative of the angles from all the zeros, to calculate total phase to a point on the unit circle, as that frequency response reference point moves around the unit circle.  Plot phase vs. frequency.  Now compare this plot with a similar plot for a pole-zero diagram with any of the zeros swapped outside the unit circle (non-minimum phase).  The overall average slope of the line with all the zeros inside will be lower than the average slope of any other line representing the same LTI system response (e.g. with a zero reflected outside the unit circle).  This is because the "wind ups" in phase angle are all mostly cancelled by the "wind downs" in phase angle only when both the poles and zeros are on the same side of the unit circle line.  Otherwise, for each zero outside, there will be an extra "wind up" of increasing phase angle that will remain mostly uncancelled as the plot reference point "winds" around the unit circle from 0 to PI.  (...or up the vertical axis in the continuous-time case.)
This arrangement, all the zeros inside the unit circle, thus corresponds to the minimum total increase in phase, which corresponds to minimum average total phase delay, which corresponds to maximum compactness in time, for any given (stable) set of poles and zeros with the exact same frequency magnitude response.  Thus the relationship between "minimum" and "phase" for this particular arrangement of poles and zeros.
Also see my old word picture with strange crank handles in the ancient usenet comp.dsp archives: https://groups.google.com/d/msg/comp.dsp/ulAX0_Tn65c/Fgqph7gqd3kJ
Comment: hotpaw- Great analogy. I have a book that uses the Argument Principle from complex analysis instead. It's an elegant proof, but not for non-mathematicians.
Comment: @Bryan This seems very interesting. What is the title of the book?
Comment: Hmm, interesting - so we CAN tell that a system is min-phase by looking at the phase response from its DFT then it looks like, correct?
Comment: @Mohammad : One issue with using a DFT for phase response is unwrapping phase, which may or may not have a unique or closed form solution.  (Especially a problem if there are "discontinuities" in the impulse response.)
Comment: @hotpaw2 With unwrapping we are undoing the modulo 2*pi or -2*pi, (two ways of doing it), but even then I didnt think it would be an issue.
Comment: Complicated, hard to understand!
Answer: As you've already seen, the minimum phase has many physical meanings and implications. Where the phase comes from is that, for a given magnitude of frequency response, it corresponds to the filter that has the least amount of group delay. That is, you can have several filters with the same magnitude of frequency response, but one of them can be realized with the smallest amount of filter delay. In this sense, it's highly desired in control systems where filtering delay can be critical to stability. I'm abusing some notation here, as the phase "delay" can have many meanings, but the gist is there (and for group delay, it's a fact).
In other realms, if a system is a minimum phase, its inverse will have all of its poles inside the unit circle and be causal. So a minimum phase system has a stable inverse. This is important in many other applications for obvious reasons. If you must solve a linear system of equations, knowing the system is minimum phase guarantees its inverse will be minimum phase, and so stability is guaranteed (outside of any quantization effects).
It may not be obvious if a system is a minimum phase by looking at the DFT. There is a relationship between the magnitude of a minimum phase system and its phase, but it may not be visually obvious. However, adaptive lattice filters have the neat feature in that minimum phase filters are easily identified if all of the reflection coefficients are less than or equal to one in magnitude. That way, filters adaptively calculated can be determined if they're stable on the fly with little logic.
Comment: I would add that the "poles inside the unit circle" stability criterion is valid for discrete-time systems, while for continuous-time systems, you would want poles to be in the left half of the $s$-plane.
Comment: There is no reason that a minimum-phase filter can't be FIR. The only condition is that all of the filter zeros must be inside the unit circle. Given a non-minimum-phase filter, you can always transform it to a minimum-phase filter that has the same magnitude response by moving any zeros outside of the unit circle to their conjugate reciprocal. That is, for all of the filter zeros $z_i$, if $|z_i| > 1$, replace $z_i$ with $\frac{1}{z_i^*}$.
Comment: The "relationship" between log amplitude and minimum-phase is the Hilbert transform
Comment: Ah yes, excellent point. For those unfamiliar with the bilinear transform (which effectively maps the left hand s-plane into the unit circle on the z-plane), that's an important distinction. Thanks.
Comment: Minimum phase filter seems to be IIR, but how minimum is their phase compared to FIR?
Comment: @TheGrapeBeyond : FIR filters are usually not designed with a pole-zero plot in mind, thus requiring much more computational effort to find (or approximate) and move the zeros.  It's far easier with IIR filters to just factor the numerator.
Answer: One of the most useful properties of minimum phase system is that they have an impulse response that is the most compact in time as is possible for any given amplitude function. Technically this can be expressed as $$\sum_{i=0}^{k}h[i]^2 = min, k\epsilon \mathbb{N}$$
Comment: Shouldn't it be *max* rather than *min* if $h[n]$ has most of its energy upfront?
Answer: Reading
This paper seems to have some wisdom on the subject of minimum phase systems:

John Bechhoefer, "Kramers-Kronig, Bode, and the meaning of zero", American Journal of Physics 79, 10 (2011).
Answer: This video explains this nicely and goes into more depth.
TLDR: The minimality is w.r.t. all systems which produce the same bode magnitude plot. There are infinitely many systems that can produce the same magnitude plot but only one which has minimum phase delay. Predictably, an easy way to make a minimum phase system non-minimum phase is by adding a delay, which obviously increases the phase delay but doesn't affect the magnitude plot.


How to use HiDPI mode / scaling in Shotcut?

Question: How to increase UI size, density, font size, and UI scaling to HiDPI mode in Shotcut (using QT) open source editing program?
Answer: There is no DPI or font size settings within Shotcut. But the program is built with QT and scaling environmental flags enabled.
If you add export QT_SCALE_FACTOR=1.25 to your bash profile, or just run in terminal before you run shotcut the scaling will update. Can play around with the values to increase or decrease.
(Adding question, because finding this information was not easy at the time.


Singular value decomposition over finite fields?

Question: What is the definition of a singular value over a finite field $\mathcal{F}$ of a matrix ${\bf A}$ in $\mathcal{F}^{m\times n}$? Is there a geometric intuition in the same manner as with the real case where the eigenvalues are the radii of the ellipse $\frac{\|{\bf A}{\bf x}\|^2}{\|{\bf x}\|^2}$?
Comment: @gmatt: There are no interesting such inner products, because any real-valued bilinear or sesquilinear form on a vector space over a finite field is necessarily identically zero.  Proof: multiply either input by the characteristic to get zero, and note that R is uniquely divisible.
Comment: The entire notion and utility of the SVD depends on the concept of positive definite matrices, which makes little or no sense over an unordered field.
Comment: You can still use an unordered field, you just need that the inner-product maps to non-negative reals.
Answer: There is no definition of a singular value of a matrix over a finite field.  You could
define it to be a non-zero eigenvalue of $A^TA$, but this does not really work as you might expect.
Over the reals, the eigenvalues of $A^TA$ are non-negative and the smallest singular value
is a measure of how close $A$ is to being a non-invertible matrix.  Further, there are
stable algorithms to compute it, whereas we cannot compute the rank of $A$ in a stable fashion.
Over the complex numbers, you would use the eigenvalues of ${\bar A}^TA$ as singular values
instead the eigenvalues of $A^TA$.  Over finite fields you might use $\sigma(A^T)A$,
where $\sigma$ is a field automorphism.  This is a problem, we have ore choice than we do over the reals and complexes.
There is no difficulty in computing ranks over matrices over finite fields anyway.
Over finite fields, eigenvalues are of limited use.  We can get the characteristic polynomial of a matrix, and factor it; the zeros of the factors are the eigenvalues.  These eigenvalues
would lie in some extension $E$ of your finite field $F$; if I came along with $E$ and asked
which elements of $E$ were the eigenvalues, you would have a lot of work and your final
answer would depend on exactly how I described $E$.  (Even over the reals, eigenvalues
are useful if the matrix is small, or normal, but they are much less use otherwise.
Google 'pseudospectra')


Difference between meter and rhythm in poetry

Question: What is the difference between meter and rhythm in poetry? The explanations found from googling were highly confusing.
Comment: A great book to consult is the late Paul Fussell's "Poetic Meter and Poetic Form." He also wrote a book on 18th century prosody. The books are quite good and very helpful in dealing with these questions concerning rhythm and meter.
Answer: There are situations where they mean the same thing.
But rhythm is the general term, applying to all speech, in every language, as well as sounds in general, provided the sounds are continuous or repetitive, and show some pattern in their continuity or repetition. Music is a good example; it has rhythms, but no meter.
Meter, on the other hand, in the sense intended (there are plenty of others), applies strictly to poetry (or vocal song), and refers to certain specific repetitive patterns of syllables, in a particular language.
Languages vary a lot in how meter works in their poetry. Stress-timed languages like English tend towards rhythms that exploit the "stress group" -- syllables between major stresses -- as in Longfellow's famous

One if by
land, and
two if by
sea, and
I on the
op-osite
shore will
be ..

On the other hand, syllable-timed languages like Latin, French, or Japanese tend to count syllables, distinguishing (as in Latin or Greek) between "heavy" syllables, which end with a consonant, or contain phonetically long vowels or diphthongs, and "light" syllables, ending in a short vowel. Patterns of these are also "meter", and the traditional Greek names that mplungjan mentioned were developed by ancient Greeks to describe their poetry.
Meter in syllable-timed language doesn't sound like poetry to speakers of stress-timed languages. For example, while Classical Latin was syllable-timed, and had distinctive long and short vowels, Medieval Latin was stress-timed, and did not retain vowel length distinctions, so Classical poetry is quite different from Medieval.
Virgil's Aeniad (composed in the first century BC) has the following first lines,

Arma virumque canō Trōiae qui primus ab ōris
Ītaliam fātō profugus  Lāvīnaque vēnit
lītora - multum ille et terrīs  iactātus et altō
vī superum saevae memorem Iūnōnis ob īram,
multa quoque et bellō passus, dum conderet urbem
īnferretque deōs Latiō—genus unde Latīnum
Albānīque patrēs atque altae moenia Rōmae.

which somehow don't feel like they're in meter, the way a Medieval Latin poem like "In Taverna" does, even though they both have strictly-regular meter.

In taverna quando sumus, non curamus quid sit humus
sed ad ludum properamus, cui semper insudamus.

Of course, the fact that end rhyme wasn't invented until the first few centuries AD helps make this sound like poetry.
The point is that poetic meter is specific, and varies between languages, and may not sound metric to speakers of other languages; while rhythm is far more general, extending even to human contraception.
Comment: Well, I thought digressing into Greek poetry might be a little off topic.
Comment: How does music have no meter? (ignoring songs which are poetry). There's repetition of musical phrases and patterns in that repetition.
Comment: True. But it's not called _meter_ unless it's got words; that's the difference. To be fair, the Greeks might not have felt that way; they tended to think of poetry as a form of music, or vice versa. But that's the way it gets used these days.
Comment: OK, I didn't notice the point in your last paragraph, given the long digression into Latin poetry.
Comment: @John Lawler - Thanks. Makes me appreciate the aesthetics of music and poetry all the more. I even wonder if some of the experimental kinds of songs with changing time signatures were inspired by the meter of poetry. Delighted to have found this site. Didn't know that end rhyme wasn't invented until the first few centuries AD. Can you recommend a few great sources that survey the history of poetry? (popular/academic book, academic journal...doesn't matter) If not, no worries. I'll find something. But it'd be a helpful starting point if some come to mind off the top of your head.
Comment: @JohnLawler I really love that particular drinking song, and know it by heart (thanks to having performed Orff so many times).  And your Greek digression may well be the funniest thing of yours I've ever read.
Comment: Would time signature be the musical equivalent of meter? We're used to 4-4 and some others but like meter varying with languages and not sounding metric, some songs use time signatures that feel awkward. Most songs stick with one time signature, but some (that sound strange and experimental) change time signature throughout. Also, depending on the time signature, natural accents (or stresses) result.
Comment: Yes, they're close; and they have possibilities for syncope and epenthesis like meter does.
Comment: Hmmmm. _Interfaces of the Word_, by Walter Ong; and some of Haj Ross's papers, like [_Languages as Poems_](http://www.umich.edu/~jlawler/Languagesaspoems.pdf) or [_FogCatFog_](http://www.umich.edu/~jlawler/FogCatFog.pdf).
Comment: @John Lawler - Much appreciated!
Answer: Rhythm describes in general the patterns of stressed and unstressed, or long and short, syllables found in language, and especially in verse. Metre describes the particular kinds of rhythm found in verse, for example, an anapaestic tetrameter (four repetitions in a line of the pattern 'dum-dum-DUM') or an iambic pentameter (five repetitions in a line of the pattern 'dum-DUM').
Comment: I'm sure you've been teaching this stuff long after I learned it, but I think what you say is the best answer here. Even in the context of discussing poetry, *rhythm* has a broader "reach" than *metre*. My recollection is that *metre* always applied to some recognised (and named) repeating pattern, but *rhythm* could be applied to more obscure aspects where it might even be difficult or impossible to identify specific repeated sequences.
Comment: @FumbleFingers: Just realised my comment could have been ambiguous. I meant not that I've never been taught it, but that I've never provided instruction in it.
Comment: I believe Rhythm and Meter/Metre are interchangeable in poetry.
Comment: @mplungjan: Here are the Oxford English Dictionary's most relevant definitions.

RHYTHM. 'Prosody.The measured flow of words or phrases in verse, forming various patterns of sound as determined by the relation of long and short or stressed and unstressed syllables in a metrical foot or line.'

METRE: 'Any specific form of poetic rhythm, its kind being determined by the character and number of recurring units of rhythm (especially feet) within the verse.'
Comment: @FumbleFingers: Never taught it, I'm afraid!
Comment: My course was pretty thinly-spread - *English and French Language and Linguistics* - but what always struck me was that only in *English Poetry* did we actually have "seminars" (half-a-dozen or less students sitting down discussing something with a tutor for an hour or two). Everything else was in classes of anywhere from 15-30, plus the completely alien experience of being in a French lecture hall alongside 200-300 other students, most of whom were obviously fluent in the language of delivery. Me, I just stopped going after a couple of weeks, and learnt French by reading, and talking in bars!
Comment: tsk. and you an *English* teacher! :)
Comment: @FumbleFingers: I am not.
Answer: Seems very clear that rhythm and meter/metre are interchangeable
Metre

In poetry, metre (meter in American English) is the basic rhythmic
  structure of a verse or lines in verse.

More:

English poetry employs five basic rhythms of varying stressed (/) and
  unstressed (x) syllables. The meters are iambs, trochees, spondees,
  anapests and dactyls. In this document the stressed syllables are
  marked in boldface type rather than the tradition al "/" and "x." Each
  unit of rhythm is called a "foot" of poetry.

Even more
Answer: Metre produces rhythm, i.e. the pattern of stressed and unstressed syllables is the metre and the music resulted from this pattern is called rhythm.


Near and far field EM radiation

Question: When we talk about radiation, we often talk about the near and far field radiation. For the near field, the Poynting vector falls off like $1/r^3$ and the far field Poynting vector falls off like $1/r^2$. Once the distance gets big, the far field term dominates, hence the name. Now, it is the far field term that is associated with the EM radiation emitted by a particle. Since the area of a sphere increases like $r^2$, the far field power emitted by the particle (the integral of the Poynting vector over the area of the sphere) is constant. My question is if the near field also has such a power (integral of Poynting over the area of a sphere) associated with it, or if the various Poynting vectors nicely cancel out as to make the total power zero (if that's the case, then I'd love a proof that it's $0$). I know that the far field dominates over large distances, but if the near field also has such a power associated with it, then the total power must change with distance, which would seem to break energy conservation. And if the near field also has a power and it somehow doesn't break energy conservation, then why is it only the far field power that is associated with the energy emitted by the particle?
Answer: In the near field of a Hertzian dipole, $\tilde{\mathbf{E}}\times\tilde{\mathbf{H}}^*$ is (almost) purely imaginary, so the time-averaged Poynting vector
\begin{align}
\mathbf{S}=\frac{1}{2}\text{Re}\left[\tilde{\mathbf{E}}\times\tilde{\mathbf{H}}^*\right]=0\, .
\end{align}
In fact the electric field phasor in this case is basically the same as that of a static electric dipole.
This also holds true for finite antennas, although the expressions are more complicated.
In the near-field region the field is basically described by Biot-Savart and Coulomb's law.
Answer: At any point of space, there is just one EM field and there is just one associated Poynting vector
$$
\mathbf S = \mathbf E \times \mathbf B/\mu_0.
$$
At large enough distances, the total field can be approximated by the "far field", i.e. by a component that decays as $1/r$. That's why one can use the far field there instead of total field - they are almost the same.
The vector field $\mathbf S$ obeys local conservation law, there is no energy conservation breaking anywhere.
It does not matter that near field decays with distance differently than the far field; because near field isn't a tranversal wave but has strong static component, total field Poynting vector isn't directed radially everywhere, some of the flux goes "around" and "back to the radiator". So the total energy flux that goes away through a small imagined sphere (where near field is strong) is much smaller than the simplistic idea about radial Poynting vector of near field would suggest.
Comment: Yes, I know, but if you expand the Poynting vector by writing the electric and magnetic field as a sum of a "velocity" field and "acceleration field", you get four terms, one with a 1/r^4 dependence (neglected in the question so as to not get into too much detail), two with a 1/r^3 dependence and one with a 1/r^2 dependence. My question is if the sum of the other three Poynting vectors (the ones other than the one with 1/r^2 dependence) can have a non-zero power, and if yes, then I wanna know where that energy cones from, if not from the charge.
Comment: Or, rather, I guess that this non-zero power would have to come from the EM field itself (which has a certain energy density), but then why can't I say that the power from the 1/r^2 dependent Poynting vector also comes from the field, and not from the charge.
Comment: Yes, sum of the three terms can be non-zero at any point, that is obvious, so there is in general a non-zero energy flux density, it can be zero at some points but not all. When integrated over a sphere in the near field region, we get flux due to those three non-wave-field terms. This flux does not have to be zero, as energy at any interspherical space can decrease of increase in time, depending on the motion of the charge. Only in stationary oscillation, the time average of this flux has to be zero, because energy in the interspherical space is a bounded function.
Comment: "Where the energy comes from, from charge or the field" it comes from both, and also can come from other bodies.  Whatever makes the charge accelerate against electric force that acts on it, does the work that increases energy of EM field.

Near and far field EM radiation


Equation of the parabola

Question: Given the vertex of a parabola $A(-2,-1)$ and the equation of its directrix $x+2y-1=0$ find the equation of this parabola. I send my procedure, I just need to write the equation of the parabola, I tried to equate $PF = PA$ but I remove the $x$ and $y$ square. Thank you very much.
Comment: By ''guideline'' you means the directrix?
Comment: Yes @EmilioNovati
Comment: See https://math.stackexchange.com/a/1429421/265466 for an answer to a similar question (not coincidentally, written by @EmilioNovati).
Answer: Hint:
1) find the line  $s$ orthogonal to the directrix $d$ an passing thorough $A$  ( this is the symmetry axis of the parabola)
2)find the  point $D$ that is the intersection of $r$ and $d$.
3) fine the focus of the parabola that is the point $F$ on the axis such that $\overline{FA}=\overline{AD}$
4) now you can write the equation of the parabola as the locus of points equdistant from $F$ and $d$ ( see here)
Answer: What you have done so far is fine, and you have the coordinates of the focus as $(-3,-3).$
Therefore using the focus-directrix property of the ellipse, and the formula for the distance from a point to a line, the equation of the parabola is $$\frac{(x+2y-1)^2}{5}=(x+3)^2+(y+3)^2$$
Answer: What you've done so far is good. You just need to complete the calculation by using the focus-directrix property of a parabola and using the squared distances, as David Quinn describes in his answer. I'd like to show you a different way to find the focus using vectors that might be a little less work than what you did.
From the equation of the directrix we can read that the vector $\vec n=\langle1,2\rangle$ is normal (perpendicular) to it. The formula for the signed distance of a point from a line gives us $$-{-2+2(-1)-1\over\sqrt{1^2+2^2}}=\sqrt5$$ for the distance from $A$ to the directrix. That is, if we go $\sqrt5$ units in the direction of $\vec n$ from $A$ to the point $A+\sqrt5{\vec n\over\|\vec n\|}$ we reach the directrix. Since the vertex is halfway between the focus and directrix, this means that the focus $F$ is the same distance in the other direction, therefore $$F=A-\sqrt5{\vec n\over\|\vec n\|}=(-2,-1)-\sqrt5{\langle1,2\rangle\over\sqrt5}=(-3,-3).$$ (The above divisions by the length of $\vec n$ are in order to get a unit vector in the same direction.)

Equation of the parabola


Mesh artifacts only on render

Question: I am making my phone in Blender and my mesh has weird artifacts on rounded corners only on render, not in viewport. Removing doubles and flipping normals doesn't help. I thought it's releated to non-quads on rounded surface but connecting verticles with knife tool also doesn't help.
What is this and how to resolve my problem?
Comment: I'm learning myself but try bridging the edge loops on that particular face.. similar to this... http://blender.stackexchange.com/questions/18177/how-fill-face-between-irregular-curves
Comment: Thank you for trying to help me but unfortunately bridge looping made artifacts a little bit less visible but that's all.
Comment: The mesh is too high-poly to model correctly. You should be using a subsurf modifier to make things detailed (smooth, high-poly) and keeping the topology much simpler.
Answer: You have a big and ugly n-gon (a polygon of more than 4 vertices) trying to bend as that curve.

You need to subdivide it into more faces.
Here's what you get when you delete that n-gon and do grid fill:

The curvature is better but far from ideal (plus you get terrible topology).
Try to create a curve that has the same number of vertices for both sides (and try to keep the rest of the topology as quads)
Answer: I got it to look "right" without much work by triangulating those trouble faces, smooth-shading the object, and setting up auto-smooth.
Here is what the topology and render look like (click on it to view it full size in your browser...it's plenty high res):

And here is the blend:

Mesh artifacts only on render


Raspberry Pi Zero MI-305 Mini USB Microphone with horrible background noise

Question: I have been trying to use a mini USB microphone, mode MI-305 with my Raspberry Pi Zero W. However, when I try to play audio recorded from it, it has this very loud background noise like a square wave buzzing sound. I have tested this microphone on a MacBook Air, and it works perfectly. I am attempting to use speech recognition, and I really need the background noise gone.

Any tips? Thanks!
Answer: I have fixed this problem by using a different USB to Mini-USB adapter which covers the USB port. The problem was that RF noise was getting in. Just get the adapter to cover the actual metal part of the microphone and it should fix it!
Answer: I disabled bluetooth completely and turned off the wifi when recording sound. Much better sound quality.


"contribute" permission for end users what it allows

Question: I have an individual that needs to update site pages on a site collection. In order to update the site pages should place them in a SharePoint group with Edit or Contribute permissions.
Answer: Regarding the content of permissions, you can go to Site Permissions-->Permission Levels, and you can see the existing Permission Levels in your site. Among them, Contribute and Edit belong to the default Permission Level. You can directly click on them to view the specific permissions contained in them (it is recommended not to modify them. If necessary, you can create a new one through Add a Permission Level). Then select the required Permission Level according to your needs.

Regarding the issue of permissions, you can go to Site Permissions-->Grant Permissions, give the group the permissions you want, and then add the user to that group through Grant permissions.

For more details, please refer to: https://learn.microsoft.com/en-us/sharepoint/understanding-permission-levels
Answer: Contribute permissions has "Read" permissions, plus:

Add Items
Edit Items
Delete Items
Delete Versions
Browse Directories
Edit Personal User Information
Manage Personal Views
Add/Remove Personal Web Parts
Update Personal Web Parts

For your requirements to update the site pages, "Contribute" permissions are enough. You can grant "Edit" permissions only if user needs to make any changes at list/library level - changing site pages library settings, etc.
Documentation: User permissions and permission levels in SharePoint


Can SDK license influence an application license?

Question: Let's say SDK is under specific license that is not compatible with some other licenses (like Flex SDK with GPLv2). Can I create an application by using for example Flex SDK, and license its distribution under GPLv2? Can my application be considered a derivative work? What is a relation between SDK license and application license that was build by using that SDK?
Comment: An SDK license *can* stipulate all kinds of things, it could say something like "Any use of this SDK to create a saleable product is strictly prohibited unless 3% of all sales of the product is given directly to the nearest 6' tall person". Or "Any use of this SDK in the creation of a product either for sale or not is prohibited except when A) the product is translated into 3 languages OR B) the product has zombies listed in it's credits." My point here is: You have to read the licenses. If you aren't used to doing that, time to practice, understanding licenses is an important part of our jobs
Answer: It might. Always read the license.


Poker Ready Reckoner

Question: This is a table with Card 1 along the top and Card 2 top to bottom  on the left. When you are dealt a particular hand, you can make notes in the appropriate box. Does anyone do this?
Comment: In most card rooms/casinos you can take notes. You cannot photograph or video tape the game. I know this is not an answer to your question, I'm not sure if players use Ready Reckoner in Poker.However doing it during a hand would be an excellent tell to all your opponents.
Comment: I agree with @RomanMik that it'd be a tell to your opponents. It also doesn't really give you much granularity in your note-taking, since your hole cards are but a single factor in how you might choose to play or think about a hand. So, IMO, it seems like a waste of time. Note-taking in general, though... that's a good idea.
Answer: I use my phone for taking notes as most people are used to seeing other players on their phones. It doesn't get other players suspicious about you taking notes. It just looks like you're distracted and texting. Most rooms do not allow you to use your phone at the table, so I just lean back after the hand is over and make my notes.
And kudos for taking notes, but you should probably just notate hands where you find something interesting or were confused about what you should do in a particular situation. Too much note taking and you will actually end up getting distracted.

Poker Ready Reckoner


Do photons experience time?

Question: I was just thinking about how electric field and magnetic field vectors oscillate in a Photon.
but then I remember that a photon doesn't experience any time so how can these vectors oscillate if the time experienced by the photon is zero.
According to Lorentz transformation formula, particles which are moving at the speed of light (in our case Photon) will experience infinite time dilation which basically means that time experienced by them is zero so if that happens to be the case then why the electric and magnetic vectors oscillate. If time experienced by the photon is zero then they should be anything happen at all but still the oscillations are happening?
Comment: Possible duplicate of [How does a photon experience space and time?](https://physics.stackexchange.com/q/54162/)
Comment: You are correct that a photon does not experience time. But that does not mean everything around a photon doesn't experience time, as well. The photon is obliterated in an instant as it experiences its entire existence in a fraction of a femtosecond, but it can still undergo changes over its lifetime. It just doesn't notice them.
Comment: @JohnRennie  it is only a duplicate if you ignore the content of the question which is asking about electric and magnetic fields.
Answer: This answer addresses this part of the question, in contrast to the duplicate which addresses only the title.

I was just thinking about how electric field and magnetic field vectors oscillate in a Photon. but then I remember that a photon doesn't experience any time so how can these vectors oscillate if the time experienced by the photon is zero.

A photon, an elementary particle in the standard model of particle physics, has as measurable quantities its energy and momentum, its spin and its mass which is equal to zero. It does not have a measurable electric or magnetic  field.
The question then becomes how does the classical electromagnetic wave emerge from the summation of photons, since it has no measurable electric and magnetic field, whereas the classical wave does.
It is because it is a quantum mechanical entity described by a complex number  wavefunction :

This wave function is derivable from a quantization of the Maxwell equations, the link gives one possible version of this. As should be known , the wavefunction itself is not measurable, as it is its square that will give the probability of finding the photon at (x,y,z,t). Finding implies observation.
The classical beam emerges from zillions of photons by a superposition, generating the collective wavefunction of the classical electromagnetic wave. How this happens in quantum field theory is described in this blog article. It is in measuring the square of this collective wave function that the E and B fields can be measured.
The difference between superposition and interaction can be seen in this laser video, where the superposition of photons in light beams generate interference patterns, although there are no photon photon interactions (just photon lasing source interactions).
The photon has no consciousness, to "know" space and time. It is the observation in a system of spacetime that defines the variables. And observables can be measured according to the probability distribution emerging from the underlying quantum mechanical framework.
Comment: I tried to access the blog article but it is invite only.
Comment: @ngc1300  It is the same for me now, unfortunately. And it is a link I have given often:(. It is due to the controversial opinions on poltical issues of the blog owner, and he must be tired of negative posts.
Luboš Motl was a very active theoretical physicist n physics SE some years ago, still getting votes for his older posts .
Answer: The nature of light is twofold: you have to distinguish between the observer-independent absolute reality (the spacetime interval) and observation.
Lightlike phenomena such as photons have a spacetime interval zero. Such an empty spacetime interval means that nothing is found between the spacetime point (event) of emission and the spacetime point of absorption of the photon.
For understanding the apparent contradiction with the electromagnetic wave it produces you have to understand what a Minkowski diagram is.
Every Minkowski diagram belongs to an observer, who observes the universe as a continuous manifold (the rectangle of the Minkowski diagram). In the Minkowski diagram the Pythagorean distance between the point of emission and the point of absorption is not zero, although the spacetime interval is zero. As an example, if a photon is traveling from Sun to Earth we do not observe that the Sun at time x and Earth at time y are adjacent. For observers, there is a gap between both points although the spacetime interval is zero. The momentum transfer of the photon from Sun to Earth is observed as an electromagnetic ray.
In summary, you must simply distinguish between reality and observation. The spacetime interval represents the "real" value all observers are agreeing on. In contrast, as it is said by the second postulate of SR, light is "observed" as moving at speed of light c.
Answer: I think you need to be more careful here... There's are classical and quantum treatments of light, and one must take care to not confuse them, and to keep them within their respective ranges of validity.
Classically, light is treated as a wave that experiences diffraction, interference, refraction, etc..... This is where electric and magnetic fields come in: an elecromagnetic wave is a classical model of a ray of light, in which the fields are mutually perpenidicular and oscillate in time in the plane perpendicular to the direction of wave propagation.
In classical special relativity and relativistic electromagnetism, a ray of light (or equivalently, a photon's worldline) is a null vector of the Lorentzian manifold and we lose the model that light is made of electric and magnetic fields oscillating in time. Instead we deal with the electromagnetic (or Maxwell) tensor, because now time is a variable instead of a parameter like in non-relativistic mechanics.
So, indeed, photons in relativistic theories do not "experience" time, but in these theories the notion of electromagnetic waves as oscillating in time doesn't make sense.
In General Relativity, the electromagnetic tensor can be used as a source for energy-momentum (since the fields carry momentum) which effects the curvature of spacetime. One can also derive radiation laws for the electromagnetic tensor source, for instance this paper considers electromagnetic radiation in the FRW spacetime.
Answer: 1) The Lorentz transformations apply to the macroscopic reference frames (RF), not to elementary particles. The Lorentz transformations connect some observation results obtained in one RF with similar observation results obtained in another RF.
2) In a trasparent medium a photon moves with the velocity smaller than $c$, and massive particles can move faster than this photon (see the Cherenkov's effect, for example).
3) A photon does not "experience itself". Its properties get into the equations of motion of other particles, so it is other particles who "experience a photon".

Do photons experience time?


IS ILLEGAL WORKING HARAM?

Question: I wanna ask, I currently left a job at bank, (due to it being riba based) and recently I got hired in a Real Estate company, after I joined, I came to learn that my job role i.e. Telecalling for Real Estate clients is apparently illegal in the region I work in, there are hefty fines if cold call recipient complaints to govt, however, for the most part, people do not complain, (even if they do, the company is fined, not the agent, and the company is ok with that risk) pretty much all real estate companies are doing this cold calling - which allows them to connect to potential sellers and connect them to buyers. Some people however, do not like us calling them, get bothered, however, if someone does show annoyance, we don't call them and keep their contact highlighted to not contact them. Would doing this job be haram? (Alternatively, until I found this job, I was providing car pool services to people since cab is very expensive and making money like that) which is also illegal as per law. I am studying at the moment and hope to get a good job once my studies are completed, but still I want my earnings to be halal, but this is my situation. Please advise.
Answer: السلام عليكم ورحمة الله وبركاته
Allahﷻ bless you.
your work is permissible/Halal
Country law is just a law established by a group of people, so this does not make your work forbidden،

IS ILLEGAL WORKING HARAM?


Homotopy type of linear isometric self-isomorphisms of ${\mathbb R}^\infty$

Question: In the paper "Orbispaces, orthogonal spaces, and the universal compact Lie group" by Stefan Schwede, he studies (spaces with an action of) the topological monoid $\mathbf{L}(\mathbb R^\infty,\mathbb R^\infty)$ of linear isometric self-embeddings of ${\mathbb R}^\infty$ equipped with the subset topology of $\operatorname{maps}(\mathbb R^\infty,\mathbb R^\infty)$ with compact-open-topology. The underlying space of this monoid is contractible (e.g. Remark A.12). What is known about the homotopy type of the subgroup of invertible elements of this monoid, i.e. the linear isometric self-isomorphisms of ${\mathbb R}^\infty$? In particular, is the underlying space still contractible?
Answer: There are two related questions for which the answer is known.  Put $H_0=\mathbb{R}^\infty$, and let $H$ be the Hilbert space completion of $H_0$.  Let $G_0$ be the colimit of the orthogonal groups $O(\mathbb{R}^n)$.  Let $G_1$ be the group of pairs $(g,h)\in\mathbf{L}(H_0,H_0)^2$ with $fg=gf=1$, topologised as a subspace of a product.  Let $G_2$ be the group of invertible elements of $\mathbf{L}(H_0,H_0)$.  Let $G_3$ be the group of all orthogonal automorphisms of $H$.  We then have continuous injective homomorphisms
$$ G_0 \xrightarrow{i_0} G_1 \xrightarrow{i_1} G_2 \xrightarrow{i_2} G_3 $$
The space $G_0$ is not contractible; it has $8$-periodic homotopy groups starting
$$ \mathbb{Z}/2,\mathbb{Z}/2,0,\mathbb{Z},0,0,0,\mathbb{Z}. $$
You asked about the space $G_2$.  The map $i_1$ is a continuous bijection but I suspect that it is not a homeomorphism.  Equivalently, I suspect that the inversion map on $G_2$ is not continuous, so $G_2$ is not a topological group.  So you might find that it is better to think about $G_1$.  In any case, I do not think that the homotopy type of $G_1$ or $G_2$ is known.  However, it is known that $G_3$ is contractible.  I am not aware of any natural applications of $G_1$ or $G_2$, although they certainly seem to be natural objects.  You might consider whether it would be better for you to use $G_0$ or $G_3$.
Comment: Thank you really much for your answer! I was not aware of the problem that $G_2$ might not be a topological group (I also assumed this for some applications I had in mind). I want to work with $\mathcal L$-spaces as a model for orbispaces as suggested in Schwede's paper. The space $G_2$ came up when I tried to understand homeomorphisms between $\mathcal L$-spaces or embeddings of (proper Lie) groupoids into $\mathcal L$. I don't think that I can use $G_0$ or $G_3$ without changing the whole model. Maybe it's best to avoid this issue of invertible elements of $\mathcal L$.


Mentioning graduates names in the SOP?

Question: I found many questions that ask about mentioning professors names in the SOP. However, this doesn't address my question. Is it a good idea to mention the name of a program's graduate in the SOP? I am an international student, and I contact one of the graduates who is from my country. The program has a few graduates from my country (he is the only one I am aware of and I found about him online, and he clearly was doing pretty good "high gpa"- studied both masters and phd there). I just said he thinks the program is great in both education and job opportunities. The program is a top program, and it is obvious that it has a great education and good job opportunities. However, i mentioned this to clarify that I am really interested and I tried to get more info and contact people to make sure it is a fit before applying. (Not mass applying)
Answer: I think it would be ok, if done in passing; less than a sentence, perhaps. I think it would be much better, however, if one of your letters of recommendation mentioned the earlier (successful) student instead. I once benefitted from just that situation.
But, a word of caution. Make sure that your SoP is forward looking on your own plans and goals and how you intend to meet them. Don't get side tracked from the fact that this is, perhaps, your most important application document. Having someone else say certain things gives you a few more words to make the most important points.

Mentioning graduates names in the SOP?


Standardize all predictors in R

Question: In a dataset, there are 2 binary variables and 3 continuous variables but on different scales. I am wondering, if I want standardized coefficients for these variables, do I need to standardize all three 3 continuous variables or just standardizing part of 3 variables  is fine too to run regression models? In addition, do I also need to standardize Y when do modeling?
Answer: See this answer about some of the effects and changes in interpretation when standardizing your variables. If you want to compare the beta coefficient of your continuous variables with each other you want to standardize them all. Whether you want to standardize at all depends on your goal, see this post. Some issues to consider are whether you care about comparing effects of different predictors within your sample, outside your sample, or perhaps you use standardization as a tool to deal with multicollinearity. To name a few.
Comment: Thank you so much for your comment. My main interest is to find the statistical significant predictors while keep the coefficients reasonable. Without standardization, the coefficients are so high for some predictors.

Standardize all predictors in R


Vibration of annular sector plate

Question: The deflection of the sector is assumed in the following form

But I don't know why they assumed G(θ) in the following form
and how to compute η.Can somebody help me? Thanks.
Comment: The cos and sin terms represent standing waves, and I think the cosh and sinh terms represent decay at free and clamped edges.  Your textbook should have an explanation.
Answer: The governing equation for free vibrations of a circular plate is (see Wikipedia article on vibrating Kirchhoff plates)
$$
\frac{1}{r}\frac{\partial }{\partial r}\left[r \frac{\partial }{\partial r}\left\{\frac{1}{r}\frac{\partial }{\partial r}\left(r \frac{\partial w}{\partial r}\right)\right\}\right] = -\frac{2\rho h}{D}\frac{\partial^2 w}{\partial t^2}\,.
$$
Separation of variables leads to a general solution of the form
$$
w(r,t) = \sum_{n=1}^\infty C_n\left[J_0(\lambda_n r) - \frac{J_0(\lambda_n a)}{I_0(\lambda_n a)}I_0(\lambda_n r)\right]
    [A_n e^{i\omega_n t} + B_n e^{-i\omega_n t}] \,.
$$
The term
$$
  A_n e^{i\omega_n t} + B_n e^{-i\omega_n t}
$$
can be expressed as a sum of sine, cosines, and hyperbolic sines and cosines when we take the real part of $w$.  That's why the expression for $G(\theta)$ in your book has that form.
For a annular sector of a circular plate, things are a bit more complicated and you will have to do the algebra yourself (or look it up from a book) to find out what $\eta$ is.
P.S.  The correct term for these orthogonal functions is basis functions (and not basic functions) - see Wikipedia basis function.
Answer: Biswajit covered most of it, but to build on his answer a little: when you are solving these types of problems, your answer has to satisfy both the partial differential equation and the boundary conditions.  $G(\theta)$ as given in your question is the most general solution to the PDE.  But it will not satisfy the boundary condition for all values of $\eta$, A, B, C, and D.  e.g. a clamped boundary at 0 would be expressed as $G(0)=0$, $G'(0)=0$. If you picked $A=B=D=0$, and $C=1$, you can see that this does not satisfy the boundary conditions, because $cos(0)=1$.  But there is some other combination of parameters that will satisfy it.  To solve for the 4 unknowns, you will need to apply 4 boundary conditions, 2 at each end of your sector.

Vibration of annular sector plate


LTSpice error: Time step too small

Question:
I am trying to simulate the Buck Converter LM22676 from TI for a 5V output. But LTSpice shows an error saying that the time step is too small when I try to run a transient analysis. Can someone please help me understand what I am doing wrong?
Comment: You might try some initial conditions or putting a resistance in series with V1.
Answer: If you tried replicating the schematic from the datasheet at page 14, you didn't do a good job: you missed the output feedback network. And you chose a 1k value for the output load, which is questionable for an output that's meant to deliver 3.3 V @ 3 A; I've made it 1 Ω. Not lastly, C1 and C2 are useless without some series resistance between the supply and them.
That said, the model works, though, for some reason, the output doesn't stabilize at 3.3 V. The soft-start is meant to bring up the output after some 500 µs; the duration is right, the value is not. To be sure we're talking about the same thing, this is the model I used. The symbol is auto-generated so you won't have problems replicating my schematic.
Still, I've made the following modifications (seen in the picture, below), though you may get lucky and not need any:

added Rser=1m to the bootstrap capacitor
added Rser=50m to the output filter capacitor
added Rser=10m Cpar=1m to the input voltage source
added uic to the simulation card since LTspice has trouble finding an operating point; just start from zero and it will be fine.

LTSpice error: Time step too small


Alternative to boxplots that illustrate MEAN

Question: What is a good alternative to boxplots that reflects the MEAN and STANDARD ERROR , not the median and its quartiles ?
A package in R that does that would help a lot.
Comment: So you want to mark a point for the mean and an interval indicating mean $\pm$ standard error? Or something else?
Comment: @Glen_b Yup that is true
Answer: You could just use a barchart with error bars that represent the standard error. Depending on your data structure you may have to summarise it and calculate the standard errors using plyr
Answer: I quite like the ggplot geom_pointrange for non-standard point and range type plots.  You supply the point and the min and max values yourself, so as long as you explicit about what you are using the range to represent (std. error, variance, quantiles, etc), you can use the geom to plot whatever you need.  Purists might disagree, and argue that the point_range geom should only be used to plot the complete range of the data, if so I'd be interested to know this.
Answer: One of the advantages of R is that you can a) Modify existing code and b) Make your own graphs "from scratch" using either base graphics or one of the packages that have been developed.
Questions about code are off topic here, but it would surely not be too difficult to either modify boxplot or build your own function.
I'd be hesitant to make it look too much like a boxplot, however, because, even if you label things clearly as mean and standard error, people are so used to boxplots that they will interpret it as one.


Understanding current flow in example

Question: When I have series circuit with 3 light bubbles the voltage in second should be less than in first and the voltage in third should be less than in second. Conventional current flow is from positive to negative while electron flow is from negative to positive. Which light bulb will get the lowest voltage - the one closest to negative charge of battery or the one closest to positive charge of battery? (correct me if my reasoning is wrong)
Comment: The current in a series circuit is the same everywhere. The bulb with the highest resistance will have the highest voltage, regardless of its position.
Answer: Assuming that the three light bulbs have identical characteristics, the voltage in their terminals will be exactly the same for each one. In this way, the sum of the voltages of the three bulbs will be equal to the voltage of the source, as follows
Vs = Vb1 + Vb2 + Vb3
where: Vs = Voltage source (battery)
       Vb1...3 = Voltage of bulb 1...3
The difference in voltages when measuring (e.g. with a voltmeter) depends on the terminal that you use for reference (negative, ground reference). If you measure with respect to the source's negative terminal (typical measurements), the bulb closer to the positive terminal will measure the maximum voltage, then the second and the lower voltage for the third.
The bottom line is that when measuring the reading is a sum of the voltages across the device's terminals, but the voltage in each device must be exactly the same.
Comment: When I measure voltage in a wire after third light bulb it shows 0. Does it mean current doesn't flow in that part of a wire? (I thought electrons always get from one side of battery to another)
Comment: When wire the three bulbs and then connect them to the battery there will always be a current (electron flow). The current (I) and the voltage (V) in a circuit are related by the resistance (R), through the circuital ohm's law: I=V/R. If you try to measure voltage across two points of wire you always will get a 0[V] reading because the resistance of such a piece of wire is really small. Special equipment, such an _electrometer_, is needed to measure voltage in common metal wires. Nonetheless, you can still measure current across the whole circuit.

Understanding current flow in example


Concealing a character in Vim without affecting how it's highlighted

Question: I would like to show '␣' instead of non-breaking spaces since they are invisible by default, and added the following lines to my vimrc:
syntax match nonbreaking "\%xa0" conceal cchar=␣
set conceallevel=1
highlight nonbreaking ctermbg=NONE guibg=NONE

While this works, it also adds a background colour to all occurrences of non-breaking spaces – even with the {cterm,gui}bg=NONE line:

Is there a way to "hide" U+00ad behind '␣' without affecting how it's highlighted at all?
Answer: well, it's not a direct answer to your question about background of concealed characters, though here is a solution to your problem:
to show non-breakable spaces as ␣ you should better use the listchars setting:
:set listchars=nbsp:␣

and here's my complete listchars setting, in case you're interested:
:set listchars=eol:¶,trail:~,extends:⫸,precedes:⫷,tab:▸ ,nbsp:␣

and this will not affect the colours.
More about it :he listchars
HTH
Comment: Nice! I didn't know there was a `nbsp` in listchars. I'll consider enabling `list` for all files. (Right now I only enable it for code.)
Answer: I'd also recommend against using the conceal feature for this, as it can interfere with the existing syntax highlighting; the use of 'listchars' as suggested by @zmo is preferable (but :set list has side effects, e.g. with wrapping, too).
For completeness, you can influence the visual appearance of the concealed characters via the Conceal highlight group.
:hi clear Conceal

clears the existing highlighting.


Importing issues from Maya 2015 to 2017

Question: I tried to import a scene (it was a glock model) from 2015 to 2017, however for some reason, the grip of the gun is all messed up: as seen with the first image.  Is it a problem with the gun itself or is it an importing problem? Also here was the original model back in Maya 2015:
Answer: have you tried to freeze and reset transformations and delete history (delete by type -> history) while in Maya 2015? That's just a guess, but it helped when I had kinda similar problem.

Importing issues from Maya 2015 to 2017


Alpha, Omega, & everlasting God?

Question: One time Jesus said: "I am Alpha and Omega, the beginning and the ending" (cf. Revelation 22:13). But at another time Jesus said that He is the everlasting God, which supposedly has no ending.
Can anyone explain this seemingly contradictory statement?
Comment: I'd just like to point out that saying He ***is*** the beginning and the end is different than saying He ***has a*** beginning and an end. So if the problem isn't a contradiction on Scripture, it's you misunderstanding what's being said.
Comment: Can you please provide a reference for where Jesus says that "He is the everlasting God".
Comment: Hi and welcome to the site! In the absence of a particular denominational or doctrinal perspective that you're looking for, this question may be better suited on [Hermeneutics.SE](http://hermeneutics.stackexchange.com/). Alternatively, you could update your question to indicate *who* (ie which type of Christian perspective) you'd like to answer. Refer to our [help centre](http://christianity.stackexchange.com/help) for more info as to what sort of questions are on-topic and off-topic here.
Answer: The saying "I am the Alpha and Omega, the Beginning and the End" can be, and has been, interpreted in the following four ways at least:
(1) As an idiom meaning eternal. Thus Albert Barnes interprets it in Barnes' Notes. Adam Clarke follows the same interpretation in his commentary on Revelation 1:8 where he says:

I am Alpha and Omega - I am from eternity to eternity. This mode of speech is borrowed from the Jews, who express the whole compass of things by א (aleph) and ת (tau), the first and last letters of the Hebrew alphabet; but as St. John was writing in Greek, he accommodates the whole to the Greek alphabet, of which Α (alpha) and Ω (omega) are the first and last letters. With the rabbins מא ועד ת (meeleph vead tau), "from aleph to tau," expressed the whole of a matter, from the beginning to the end. So in Yalcut Rubeni, fol. 17, 4: Adam transgressed the whole law from aleph to tau; i.e., from the beginning to the end.
  Ibid., fol. 48, 4: Abraham observed the law, from aleph to tau; i.e., he kept it entirely, from beginning to end.
  Ibid., fol. 128, 3: When the holy blessed God pronounced a blessing on the Israelites, he did it from aleph to tau; i.e., he did it perfectly.

So that the argument is that Alpha and Omega denote the whole of eternity.
Others have interpreted it in more limited senses:
(2) With respect to creation. That he is the Beginning, as in the Creator, and the End, as in the one who destroys the world at the end.  This is how it is interpreted, for example, in the note on Rev 1:8 in an old commentary called The People's New Testament, or Johnson's Notes:

I am the Alpha and the Omega. The first and last letters of the Greek alphabet; hence "the beginning and the end." All begins with God and he closes the drama of earthly history.

The first two interpretations, obviously, would be the interpretations most acceptable to Trinitarians. The following interpretations are more likely to be accepted by non-Trinitarians.
(3) With respect to the church. That Jesus is to the church the beginning and end of everything, the beginning and end of salvation, etc.  This is the sense in which the words were generally interpreted by the Socinians, as the following quotation from a note by an eminent Socinian (Wissowatius) in the Racovian Catechism (pages 161-162 of Thomas Rees' translation) will show:

That the Son of God is absolutely the First, none will venture to assert, who maintain that the Father is the first person of the Trinity. Erasmus well observes in his Annotations on John viii. 25: Quod in Apocalypsis dicitur principium et finis, constat intelligendum, Christum esse initium et consummationem Eccleslae, quam priore adventu constituit, posteriore perficiet. "As to what are called in the Revelation 'the beginning and the end,' it is evident that we must understand by them that Christ is the beginning and the consummation of the Church, which was founded by his first, and will be completed by his second, appearance." We read nearly to the same effect in Hermas Simil. 9; where, speaking of the Church, he calls the Son of God, "the old rock and the new gate;" and for these reasons, because the Church is founded upon him, and is older than every creature, and because he will in the last days appear for its completion, that those who are about to be saved may enter through him into the kingdom of God: which accords with the words of Paul, whose disciple he was (Col i. 15,18), and also with Revelation i. 17, and xxii. 13, as Grotius also has remarked. To the same effect are likewise Heb. ii. 10; xii. 2; Acts iii. 15, 31; Eph ii. 20, &c.  B. WISSOWATIUS.

Sometimes in connection with this explanation, Hebrews 12:2 is used (as mentioned in the note quoted): "Looking unto Jesus the author and finisher of our faith..."
(4) With respect to an authority derived from the Father. An Arian interpretation is given in the following words in Scripture proofs and Scriptural illustrations of Unitarianism by John Wilson (page 201):

The terms, Alpha and Omega, beginning and end, are, in a finite sense, justly applicable to Jesus as the first of all created existences, and the last of those who will be required to resign the authority with which he is invested by the Father.--RAMMOHUN ROY on Rev. xxii. 13: Second Appeal, Appendix No. 2.

From page 200 of the same, what we could say is a fifth interpretation emerges, which is a much harder sell than all the others:
(5) That Jesus doesn't call himself Alpha and Omega. This argument is based around the fact that some manuscripts say "Lord God" in verse 8, not just "Lord," and some manuscripts omit the saying "I am the Alpha and Omega" in verse 11.  One eminent textual critic of the late 1700s and early 1800s, Griesbach, presents the text of verse 8 with "Lord God" and verse 11 without "I am the Alpha and Omega" which gave the unitarians of that period an argument that only the Father says "I am the Alpha and Omega"  and the Son does not. I checked that Griesbach really does present the text this way, and I checked the UBS 3rd Edition, and it presents these two verses the same way as Griesbach.  The ESV, which follows a Nestle-Aland/UBS text thus reads:

Revelation 1:8 ESV "I am the Alpha and the Omega," says the Lord God, "who is and who was and who is to come, the Almighty."
  verse 9 I, John, your brother...
  verse 10 I was in the Spirit on the Lord's day, and I heard behind me a loud voice like a trumpet
  verse 11 saying, "Write what you see in a book and send it to the seven churches, to Ephesus and to Smyrna and to Pergamum and to Thyatira and to Sardis and to Philadelphia and to Laodicea."

So unlike in the KJV, you find no statement here by Jesus in verse 11 that he is the Alpha and the Omega and the statement in verse 8 is presented not as from "the Lord" but as from "the Lord God." I don't know what anyone relying on that argument would do with Revelation 22:13, however, since that would seem to be a major problem for this theory (but I would assume that even without manuscript evidence they would view it as an interpolation or claim its the Father speaking here):

Revelation 22:12 ESV "Behold, I am coming soon, bringing my recompense with me, to repay each one for what he has done. verse 13 I am the Alpha and the Omega, the first and the last, the beginning and the end."

So basically, every different Christological position that exists in Christianity can find a way to make these words fit their position, at least to their own satisfaction.
Comment: Wow!!! Very nice answer. Thank you for all the effort. I learnt something.
Answer: It is possible that Jesus is in this particular case was emphasizing what God said back in the Old Testament:

Isaiah 41:4  Who hath wrought and done it, calling the generations from the beginning? I the LORD, the first, and with the last; I am he.
Isaiah 44:6  Thus saith the LORD the King of Israel, and his redeemer the LORD of hosts; I am the first, and I am the last; and beside me there is no God.
Isaiah 48:12  Hearken unto me, O Jacob and Israel, my called; I am he; I am the first, I also am the last.

This was said by God to emphasize that he alone was God, He was before any other god was conceived and he will out last all of them.
But the most likely probability is that what he was referring to is:
1st. Corinthians  15:45  And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.
Which is to summarize the fall and resurrection of mankind. Adam through his willful disobedience of God (Adam was not deceived he understood that he was disobeying God, yet did so of his own free will. Eve on the other hand was deceived and her disobedience was not totally willful), as a counter; to Adams willful disobedience, Jesus willful obedience brought an end to man's loss of acceptability. As Adam willfully accepted death as a punishment for his disobedience, Jesus willfully banned death as man's punishment by his obedience even unto a horrible death.
While I realize that you are seeking a more definitive answer there appears to be none in the Bible.
Hope this at least gives you some optional answers.
Answer: I can find a number of times in the New Testament (KJV) where the word "everlasting" is used, but they never refer to any person, not even the person of Jesus Christ, so without a citation (book, chapter, verse, translation), your question is based upon a false premise.
As to the phrse "alpha and omega, the beginning and the end", this is as much a poetic or literary device, rather than a description to be taken literally.
Comment: It is widely accepted among most branches of Christianity that Jesus is eternal.

Alpha, Omega, & everlasting God?


Integral expression for zeta(2)

Question: By computing the sum of all Bernoulli numbers via Borel summation (I learned this technique from Varadarajan's excellent book Euler through time. A new look at old themes, 2006) I found that $$\sum B_n = \int_0^\infty \frac{t}{e^{2t}-e^t} dt$$ and discovered numerically that this expression equals $\zeta(2)-1$. The web is not very good for finding out where this can be found in print. Where should I look, and how can equations such as $$\zeta(2) = 1 + \int_0^\infty \frac{t}{e^{2t}-e^t}\ dt$$ be proved?
Answer: The starting point is the integral
$$
\Gamma(s) = \int_{0}^{\infty}e^{-x}x^{s-1}dx
$$
for the gamma function. Make the change of variable $x = nu$ with $n$ an arbitrary positive integer. Then
$$
\Gamma(s)n^{-s} = \int_{0}^{\infty}e^{-nu}u^{s-1}du
$$
and summing over $n$ from $n = 1$ yields
$$
\Gamma(s)\zeta(s) = \int_0^{\infty}\frac{1}{e^u - 1}u^{s-1}du.
$$
This formula was the starting point of one of Riemann's two proofs of the functional equation. I am not certain who discovered it first, but it may have been Abel.
Substituting $s = 2$ gives
$$
\zeta(2) = \int_{0}^{\infty}\frac{u}{e^u - 1}du
$$
and so
$$
\zeta(2) =
\int_{0}^{\infty}\frac{ue^u}{e^{2u} - e^u}du =
\int_{0}^{\infty}\frac{u(e^u - 1) + u}{e^{2u} - e^u}du =
\int_{0}^{\infty}\left(ue^{-u} + \frac{u}{e^{2u} - e^u}\right)du =
1 + \int_{0}^{\infty}\frac{u}{e^{2u} - e^u}du.
$$
Comment: I now have a reference (from page 9 of H. M. Edwards' book Riemann's Zeta Function): N. H. Abel, Solution de quelques problemes a l'aide d'integrales définies . Mag. Naturvidenskaberne 2 (1823).

Abel does the case when $s = 2m$ is an even positive integer.

According to W. Narkiewicz on page 133 of The Development of Prime Number Theory, the early history of $\zeta(s)$ is covered by G. Schuppener in Geschichte der Zeta-Funktion von Oresme bis Poisson. Deutsche Hochschulschriften 533. Hänsel-Hohenhausen, Egersbach.
Comment: See also my answer to Why does the Gamma-function complete the Riemann Zeta-function?
http://mathoverflow.net/questions/7656/why-does-the-gamma-function-complete-the-riemann-zeta-function/7665#7665
Comment: I did have the general formula involving zeta(n), but stupidly put the n! on the wrong side of the equation and concluded that the formula for Gamma(s) zeta(s) would not help me -(. I am not aware of any work on zeta(s) done by Abel - did you mean Euler? He had a formula equivalent to that for Gamma(n) zeta(n) for n=2, 3, 4, 5.
\@engelbrekt: If you care about being referred to by your real name, please send me an email : hb3 at ix.urz.uni-heidelberg.de

Integral expression for zeta(2)


How can I get more involved in the campaign?

Question: I signed up to volunteer for the campaign of my candidate of choice but have not received any information on what to do next. I want to be one of the "making phone calls" type volunteers. What is the most effective way to get involved on this level? Is it is relatively easy or difficult to be accepted if I have no experience?
Comment: This is going to be very campaign/location specific. I think your best bet will be to go to the campaign office you would like to volunteer for and talk to the people there. I suspect they will be happy to send you out into the summer heat going door to door with pamphlets.
Comment: Same thing happened to me-filled out a form and got no response. I agree with @lazarusL though, your best bet is to actually go to the nearest campaign office and talk to a staffer about how to volunteer.
Comment: Probably jargon but the term used in campaigns for what you're talking about is phonebanking.
Answer: This typically depends on the level of campaign you're talking about, so I'll answer generally with some more specific background.
It's important to remember campaigns have limited resources below the federal level and usually can only utilize volunteers once they have the capacity to prepare for them and manage them. Usually, the person who performs this task is the Field Director or the Volunteer Coordinator.
Obviously, the first place you should go to get engaged with a campaign is their website or social media page. They will typically have a volunteer sign up page that you can fill it to begin showing up in their volunteer management database.
If you don't hear back from them, look for a headquarters phone number to call and follow up with them. If a campaign has no headquarters information, it's a pretty good indicator that the campaign doesn't have the resources available to open up a physical location. Campaigns without a physical location typically have fewer, but more large scale volunteer opportunities, like a Day of Action.
Finally, visiting the campaign in person at an event, or their physical location is going to be your best bet. Candidates are often speaking at local clubs or organizational meetings that you can attend to get more engaged.
Patience is key with campaigns, it's very typical that a campaign won't launch a full field program until mid to late August, so they may not have an opportunity available yet.


What type of tree is this?

Question: This is a tree that I have been growing. I'm wondering if this is a mulberry, and if so, what kind?  Location is Arizona.
Comment: Where is the tree growing? That's essential information for species identification questions.
Comment: It's produced fruit for about 3-4 years and it grew wild in our grass and we've had 9-11 more grow its fuitt are green, then red , then juicy purple in the end
Comment: Arizona near Kingman
Answer: It is a mulberry.  What isn't clear from the photos, and may not be clear without a DNA analysis, is whether it's a hybrid of the native red mulberry and the white mulberry imported from Asia in the hopes of starting a silk trade in North America (white mulberry is the main food source for silk caterpillars), or whether it's distinctly a red or white.  The berries won't always indicate this, and the leaves won't always indicate this.  At this point, our red mulberry has seen sufficient habitat loss that most new mulberry trees are hybrids.
Comment: Thank you we've had 9-10 grow and they're is 2 different kinds of them. All produce fruit and the fruit is red and then mostly turn dark purple/red.
Answer: I am sure it is a Mulberry (Morus sp.). I have two of them growing in my garden. The bark, leaves and flowers look exactly like my trees. Note that the Mulberry has different male and female flowers (and off course only the female produce fruit). To be 100% sure I looked it up in Blameys' "Mediterranean wild flowers".
Answer: Looking at the landscape in your area (which suggests somewhere between west Texas and southern Oregon) it might also be a black mulberry.
Here is a snippet on black mulberries
Comment: Thank you and this is in Arizona so you're correct I want to say it's a black mulberry as well.

What type of tree is this?


Buy 1 get 10% discounts for selected products

Question: How can give buy 1 get 10% for selected products in selected categories.
Answer: You can make good use of Shopping Cart Price Rules. You just need to set the criteria on Conditions tab. Add a rule, specify Products Subselection, then choose 1 on If total quantity  is. Then add conditions under total quantity and select SKU under Product attribute. Finally, switch to Actions, select Percent of product price discount and enter 10 on Discount Amount.
Comment: help me @  https://snag.gy/0CRG8I.jpg
Comment: I need to add one extra condition, if 2 qty of the same category then only applied discount. Now the condition is working but, another category of products also getting the discount, i need the same category of products only applicable for this discount.
Comment: Look at Step 3.7 on official document. It can define which product(s) apply the discount.


Audex unavailable in 20.04LTS

Question: My favourite CD ripper Audex more doesn't seem to be in the repositories for 20.04LTS, and installing the last available version in 16.04 LTS doesn't work because kde-runtime isn't available. Is it available by any other means? thanks!
Comment: https://github.com/KDE/audex compile and build from source to install
Comment: See answer below, it compiles normally on Ubuntu 20.04 LTS with Qt5 and KF5.
Answer: The source code on github has mentions of Qt5 and KF5, so I was preliminary wrong about its obsolescence.
We can compile and install it:
sudo apt-get install git build-essential cmake extra-cmake-modules \
qt5-default dh-buildinfo docbook2x libcdparanoia-dev pkg-kde-tools \
qtscript5-dev libqt5x11extras5-dev libkf5plasma-dev \
libkf5completion-dev libkf5crash-dev libkf5iconthemes-dev \
libkf5kcmutils-dev libkf5kio-dev libkf5cddb-dev

cd ~/Downloads
git clone https://github.com/KDE/audex.git
cd audex
cmake .
make -j3

sudo make install

And then use it as usual.
Answer: I've been using N0rbert's instructions for a while, but now qt5-default is deprecated and has no installation candidate.  So instead of qt5-default, add these packages:
apt-get install qtbase5-dev qtchooser qt5-qmake qtbase5-dev-tools libkf5textwidgets*

The make process throws a lot of warnings about deprecated declarations in the code, but it still compiles and works.

Audex unavailable in 20.04LTS


Why is $10^n-4$ always a multiple of 6?

Question: I don't have any idea on how to prove it, and I need it for one of my questions which is still unanswered: What is the largest number smaller than 100 such that the sum of its divisors is larger than twice the number itself?.
Answer: It's always even, and it has digits $999\dots996$ so it's always divisible by $3$: it's $3$ times $333\dots332$.
Comment: Good answer! You got there 43 sec before me!
Answer: Because it is even and $\;10^n-4\equiv1^n-1\equiv0\mod3$, so it's divisible by $2$ and $3$.
Answer: We see $$10^n - 4 = 6 + \sum^{n-1}_{k=1} 9\cdot 10^k$$ and $6$ divides $9\cdot 10^k$ for any $k\ge 1$ since each of those is an even number divisible by $3$.
Answer: Note that $4^n\equiv 4\mod 2$ and $4^n\equiv 4\mod 3$ so by the Chinese Remainder theorem $4^n\equiv 4\mod 6$ i.e. $10^n\equiv 4\mod 6$
Answer: Here is the standard proof for the above claim:
Prove $10^n-4$ is always a multiple of 6, for $n\in \mathbb{N}$.
That is: $10^n-4=6m$, for $m\in \mathbb{N}$.
We prove the above via induction:
Consider the base case, that is, when n = 1, we thus have:
$$10^{1}-4=10-4=6=6m \ for \ m=1 \ \checkmark$$
Consider the $n^{th}$ case, that is: $$10^n-4=6m \Rightarrow10^n=6m+4, \ for \ n,m\in \mathbb{N}$$
Then we want to prove the $(n+1)^{th}$.
So consider the following:
$$10^{n+1}-4=(10^n\cdot 10)-4=10(6m+4)-4=60m+36=6(10m+6).$$
Indeed we see $10^{n+1}-4$ is a multiple of $6$ given the $n^{th}$ case.
Therefore by induction, the claim holds for all $n\in \mathbb{N}$.

Why is $10^n-4$ always a multiple of 6?


Were Feynman diagrams important for the creation of the electroweak theory?

Question: Feynman diagrams representing the interactions of subatomic particles were introduced by Richard Feynman in 1948. The first published Feynman diagram appeared in Physical Review in 1949.
Did Feynman diagrams play a key role in the creation of the electroweak theory developed between 1949 and 1967 in the work of Yang and Mills, Glashow, Higgs, Weinberg, Salem and their collaborators?
If so, please explain how (for instance these diagrams might have rendered some difficult calculations more feasible).
Comment: See e.g. [Kibble, History of electroweak symmetry breaking](https://arxiv.org/abs/1502.06276):"*But in all these models, the symmetry breaking, giving the W and Z bosons masses, had to be inserted by hand, and theories of spin-1 bosons with explicit masses were well known to be non-renormalizable and thus unphysical. The big question therefore was: could this be a case of spontaneous symmetry breaking?*"
Comment: They played a key role already in making sense of what the renormalizability is. It is what gets you finite values of diagram amplitudes after making the high energy cutoff and inserting the measured values of masses and charges by hand. Crafting the very structure of the theory was guided by the renormalizability constraint, see [The conceptual foundations and the philosophical aspects of renormalization theory](https://www.researchgate.net/publication/225936036_The_conceptual_foundations_and_the_philosophical_aspects_of_renormalization_theory) for a historical analysis.
Comment: "*As Weinberg (1980a) remarked in his Nobel lecture, if he had not been guided by the principle of renormalizability, his theory of electroweak interactions would have received contributions not only from $SU (2) \times U (1)$-invariant vector
boson exchanges - which were believed to be renormalizable... - but also from $SU(2)\times  U(1)$-invariant
four-fermion couplings, which were known to be nonrenormalizable, and the theory would have lost most of its predictive power.*"
Comment: They played a key role in establishing the significance of renormalizability for theories generally. The electroweak theory took shape after its renormalizability was assured by the Higgs mechanism.
Comment: Do you mean they played a key role for proving the renormalizability property for theories (including electroweak theory?) or do you mean something else by "the significance of renormalizability"?
Answer: Julian Schwinger said of Feynman diagrams:

that they brought QFT to the masses.

However, he along with Sin-Itiro Tomonaga  independently developed an alternative formalism that is non-perturbative from the beginning, in contrast to Feynmans perturbative approach.
Feynmans approach, being perturbative, misses a great deal. One does not need to know QFT to see this.
After all, the functions that are perturbative on the real line are exactly the analytic functions. But these are subsumed by the smooth functions. That is there are many more smooth functions than there are analytic ones. And this is before one begins to examine the possibility that non-smooth functions also play a role - as they do with say, Diracs delta function and their derivatives.
More physically speaking, instantons are twists in vector bundles, and are global phenomena. And being global they are missed by physics which only probe locally, as Feynman diagrams do.


Baseboard heater powered by a switch, not thermostat

Question: Our finished basement has electric baseboard heat.  The baseboard is powered by a light switch, so I either have the heat on or off.  Can I take out the switch and use the wiring to connect a digital thermostat instead?
Answer: What you need is a line voltage thermostat.  Non--programmable ones are very common. Programmable (digital as you call it) line voltage stats are available but rare. I attached a pic of one that I found. Search for "line voltage thermostat" and you'll find a few.  If you don't care about programability, simple line voltage stats are as common as dirt. Just be sure it's two pole.   I don't know if single pole stats are still available, but for 240, I don't consider them safe.
Not sure what NoSparksPlease was getting at regarding the disconnecting switch (???), I would assume the existing circuit is on a breaker and that would satisfy the code.
Comment: NEC 424.19 says the disconnecting means must be within sight or lockable, lockable in 110.25 requires the means remain in place.
Comment: I wouldn't say that line voltage programmable ones are "rare" exactly, though I agree they may be less common (because they are more expensive).
Answer: You normally can, but not every digital thermostat will work. You will need to select one that specifies the proper voltage (120 or 240v), most digital thermostats are only rated for 24v or less, and some digital stats require a neutral, which may not be present if two wire cable was used on a 240v circuit.
Most line voltage digital thermostats do not satisfy electrical code requirements that may require an electrical disconnecting switch, so you may have to install a bracket in your electrical panel to make it so you can lock the breaker in the off position.
Also my recollection and checking with a couple online manufacturers webpages is the Installation Instructions that come with baseboards specify either using a built in or wall thermostat. The Installation instructions are part of the NRTL Listing (UL, ETL. CSA), and the electrical codes require following the those instructions. So it is likely that you existing installation is not legal.
Comment: The two-pole line voltage stats I've seen have an ON/OFF slideswitch on them, which I presume satisfies the disconnect requirement


Any particular god or goddess for sports?

Question: In Hinduism, do we have any particular deities for sports and other activities for the players for praying before starting playing?
Comment: Well if you take into consideration wrestling/kushti we normally see Lord Hanuman being the main god that is generally worshiped as Hanuman portrays strength, passion, agility and fearlessness. These are the characteristics that normally are associated with the sportsman.
Comment: @AnuragSingh I meant amorous sport only. ;)
Comment: Present day sports like foot ball?
Comment: whatever it may be then or now
Comment: Lord Hanuman! Read Hanuman Chalisa daily.
Comment: @Rohit.: Yeah I misunderstood.
Answer: This is how wikipedia defines Sports. https://en.wikipedia.org/wiki/Sport
Sport includes all forms of competitive physical activity or games which, through casual or organised participation, aim to use, maintain or improve physical ability and skills while providing enjoyment to participants, and in some cases, entertainment for spectators.
So if the Aim is to improve physical ability and skills. Lets see which God is associated with physical ability and skills. Yes you are right He is Hanuman.
Kushti and Kabbadi are traditional sports in India, And where ever it was practiced and taught they have images for Hanuman.
Also Shiva is also very tall and powerful physically. He sits in the cold mountains, it needs enormous physical strength to do so.
As per Scriptures Hanuman is a avatar of shiva himself.
Is Hanuman an avatar of Lord Shiva?
Hope this helps :)
Comment: Hanuman is amsha of Shiva but they are different. You can't say they are same. They have different mantras and ways of worship.
Comment: @Sarvabhouma I have never said they are same.