Distributions other than the normal where mean and variance are independent

Question: I was wondering if there are any distributions besides the normal where the mean and variance are independent of each other (or in other words, where the variance is not a function of the mean).
Comment: Please consider modifying your question, then, because the response you checked as your preferred answer does *not* answer the question as it stands (and the other one does).  Currently you are using the word "independent" in an idiosyncratic way.  Your example with Gamma shows this: one could simply reparameterize Gamma in terms of the mean (mu) and variance (sigma), because we can recover theta = sigma/mu and kappa = mu^2/sigma.  In other words, *functional* "independence" of the parameters is usually meaningless (except for single-parameter families).
Comment: Srikant is right.  If the question is asking about "sample mean and variance" then the answer is "no".  If the question is about population mean and variance, then the answer is yes;  David gives good examples below.
Comment: I am not sure if I understand the question correctly. Are you asking if there are any distributions apart from the normal that are completely specified by the mean and the variance? In some sense, variance is a function of the mean as it is a measure of the dispersion around the mean but I guess this is not what you have in mind.
Comment: Just to clarify, what I meant is this. For the normal distribution, the mean $\mu$ and the variance $\sigma^2$ fully characterizes the distribution and $\sigma^2$ is not a function of $\mu$. For many other distributions, this is not so. For example, for the binomial distribution, we have the mean $\pi$ and the variance $n\pi(1-\pi)$, so the variance is a function of the mean. Other examples are the gamma distribution with parameters $\theta$ (scale) and $\kappa$ (shape), where the mean is $\mu = \kappa \theta$ and the variance is $\kappa theta^2$, so the variance is actually $\mu \theta$.
Comment: you mean the sample mean $\bar{X}=\frac{1}{n}\sum_{i=1}^nX_i$ and sample variance $\frac{1}{n}\sum_{i=1}^n(X_i-\bar{X})^2$ are independant. Good question ! maybe projecting a gaussian random variable will keep independance ?
Answer: In fact, the answer is "no".  Independence of the sample mean and variance characterizes the normal distribution.  This was shown by Eugene Lukacs in "A Characterization of the Normal Distribution", The Annals of Mathematical Statistics, Vol. 13, No. 1 (Mar., 1942), pp. 91-93.
I didn't know this, but Feller, "Introduction to Probability Theory and Its Applications, Volume II" (1966, pg 86) says that R.C. Geary proved this, too.
Comment: @onestop  I guess it is an unfortunate artifact of my age.  It is not an understatement to say that Feller's books revolutionized how probability was done -  worldwide. A large part of our modern notation is due to him. For decades, his books were **the** probability books to study. Maybe they still should be.  BTW: I've added the title for those that haven't heard of his books.
Comment: Jay, thanks for the reference to the paper by Lukacs, who nicely shows that the sampling distributions of the sample mean and variance are only independent for the normal distribution. As for second central moment, there are some distributions where it is not a function of the first moment (David gave some nice examples).
Comment: I have aske the question about other funy characterisation ... http://stats.stackexchange.com/questions/4364/what-is-the-most-surprising-characterization-of-gaussian-distribution
Comment: Geary, R. C. (1936), "The Distribution of 'Student's' Ratio for Non-Normal Samples," Journal of the Royal Statistical Society, Suppl. 3, 178–184.
Answer: Note: Please read answer by @G. Jay Kerns, and see Carlin and Lewis 1996 or your favorite probability reference for background on the calculation of mean and variance as the expectated value and second moment of a random variable.
A quick scan of Appendix A in Carlin and Lewis (1996) provides the following distributions which are similar in this regard to the normal, in that the same distribution parameters are not used in the calculations of the mean and variance. As pointed out by @robin, when calculating parameter estimates from a sample, the sample mean is required to calculate sigma.
Multivariate Normal
$$E(X) = \mu$$
$$Var(X) = \Sigma$$
t and multivariate t:
$$E(X) = \mu$$
$$Var(X) = \nu\sigma^2/(\nu - 2)$$
Double exponential:
$$E(X) = \mu$$
$$Var(X) = 2\sigma^2$$
Cauchy:
With some qualification it could be argued that the mean and variance of the Cauchy are not dependent.
$E(X)$ and $Var(X)$ do not exist
Reference
Carlin, Bradley P., and Thomas A. Louis. 1996. Bayes and Empirical bayes Methods for Data Analysis, 2nd ed. Chapman and Hall/CRC, New York
Comment: In *any* location-scale family the mean and variance will be functionally independent in this fashion!
Comment: David, the double exponential is an excellent example. Thanks! I did not think of that one. The t-distribution is also a good example, but isn't E(X) = 0 and Var(X) = v/(v-2)? Or does Carlin et al. (1996) define a generalized version of the t-distribution that is shifted in its mean and scaled by sigma^2?
Comment: You are correct, the t-distribution appears to be frequently characterized with a mean = 0 and variance = 1, but the general pdf for t provided by Carlin and Louis explicitly includes both sigma and mu; the nu parameter accounts for the difference between the normal and the t.


Euclidean geometry book for math contests

Question: I'm a last year high school student, I'm looking for a "short" (by short I mean, not over 250 pages) Euclidean geometry book that covers topics linked to euclidean geometry of math contests, I have a decent knowledge in the topic thus I'm looking for a book to tackle a bit more advanced stuff. By searching a bit on the internet I found this one book: "Geometry revisited by Coxeter & Greitzer", I've read through the content and it seemed what I was looking for, is the book good for my purpose? any better suggestion?
Comment: See [my FAQ](http://www.cip.ifi.lmu.de/~grinberg/about.html#books) for a few suggestions (Honsberger is a fun read, Altshiller-Court is comprehensive and systematic, Johnson is somewhat obsolete but has some gems), but keep in mind that several new books have come out since 2006 (in particular, Hadamard's Planimetry in English with 2-3 companion volumes containing problems and solutions).
Answer: There are two following very good books:

A.V.Akopyan. Geometry in pictures.

2.V.V.Prasolov. Problems in Plane Geometry.
Answer: A great book is
Evan Chen, Euclidean Geometry in Mathematical Olympiads
While something a bit more elementary, but containing some hard problems is
Louridas & Rassias, Problem-Solving and Selected Topics in Euclidean Geometry
A great Dover edition with famous problems and less famous is
Aref & Wernick, Problems and Solutions in Euclidean Geometry
Comment: while EGMO is a fantastic book, it's slightly over OP's request of 250 pages. I still think it's worth a read though
Answer: I haven't read the book myself, but a former participant in the International Mathematical Olympiads that I am acquainted with suggested Plane Euclidean Geometry: Theory and Problems, by A. D. Gardiner and C. J. Bradley, a suggestion which is also given here.


How to protect my DIY bench power supply from reverse polarity?

Question: I have been playing with arrays of 18650 batteries for the last 10 months, charging and discharging them all the time with my LM338K based power supply, that, until tonight, where I inadvertently connected (backwards) a semi charged array (pack) of 2P3S delivering 10v and who knows how many amperes in shortcircuit, and it looks like I fried the LM338K, I know I can avoid that with just a single beefy diode in series, my question is: is there any other way where I don't lose the 0.7V voltage drop in the diode? Should the regulator have survived? The circuit for the regulator is the one in the datasheet and surely it does have overload protection and overcurrent/thermal and whatnot, but I think hooking my battery pack in reverse was just too much and unexpected.
Comment: Schottky diodes have lower dropout; a simple part swap. also, the lm338 does not have OCP, I exploded two last week hooking up a shunt to the wrong wire. twice. i hate hearing "POP"...
Comment: A small suggestion - use mechanical polarity connection. If you (semi) permanently connect a polarized connector to the battery pack, with the mating connector connected to the power supply (as well as your load), it's simply a matter of plugging and unplugging the connector. Be careful to select a connector which is rated for the current and avoid plugging and unplugging while much current is flowing.
Comment: @dandavis Schottky diodes do have greater leakage currents. This could mean that you have higher errors if you are drawing very low currents.
Answer: You will need two sets of protection and separate the charge input from the discharge output.  If you just put a diode in series with the pack, it will be reverse biased when you try to charge the pack.
Depending on the level of performance needed, you can use a simple PFET circuit (http://www.ti.com/lit/an/slva139/slva139.pdf) or an ideal diode controller with an external FET.  Some of the ideal diode controllers use NFETs which (apples for apples) have lower Rds-on resulting in lower losses (and less heat).


What is the importance of spherical and cylindrical coordinates in physics?

Question: I was studying about spherical and cylindrical coordinates but I still cannot understand what its importance in physics and math, that is, what was the motivation for its discovery? Solve a problem in physics or is its importance different?
Comment: Have you tried solving e.g. the heat or wave equation for a spherical domain in Cartesian xyz coordinates?
Comment: it's just a choice of coordinate system to make use of a symmetry of the problem youre looking at
Comment: It seems you don't have a very good teacher if they couldn't come up with physical examples.
Answer: Let's consider an example: The gravity of the earth. Suppose the earth is a sphere (its center of the mass defines the origin of our coordinate system) and that we are interested in  the gravity at a hight $h$ above the ground. Newtons law tells us that the gravitational force at a position $\vec r = \vec r_{probe}= (r,\varphi, \theta)$ is given by
$$
\tag{1}
\vec F_g =
\vec F_g(r,\varphi, \theta) =
- \gamma \frac{m_{probe} M_{earth}}{r^2} \; \vec e_r
$$
where $r = R_{earth} + h$ is the distance of the probe to the earth's center, and $\vec e_r$ is the vector connecting these two points. Note that  $\vec e_r=(1,0,0)_{r,\varphi, \theta}$ in spherical coordinates.
Eq. (1) is a  simple formula, because it consists only of a single variable, $r$. The two angles $(\varphi, \theta)$ do not appear in the formula. Hence, the 3D problem is reduced to a 1D problem, which is much simpler to solve and understand:  From the formula it is evident that the force scales with the distance squared and that it is directed towards the earth's center.
Now, let's  express this formula in cartesian coordinates $(x,y,z)$,
$$
\vec F_g =
\vec F_g(x,y,z) =
- \gamma \frac{m_{probe} M_{earth}}{(x^2+y^2 + z^2)^{3/2}} \;
\left(
\begin{matrix}
x\\
y\\
z
\end{matrix}
\right)
$$
Since the cartesian coordinates do not capture the symmetry of the problem, we have to use all three coordinates $(x,y,z)$. Hence, the   3D problem is not reduced to 1D. Note that both descriptions are equivalent: What is true/false for one is also true/false for the other.
The importance of other coordinate systems in physics is that they allow us to understand the problem on a much deeper level. Also, since the math is much simpler they allow us to solve problems which were otherwise beyond our ability.


Baggage restrictions

Question: I am traveling back to Ireland from India next week through gulf air. Just wondering how many cartons of cigarettes am I allowed to carry with me and also is it possible for me to carry cricket bat in its bag along with my laptop bag ? Or should I keep it in check in baggage?
Please let me know the possible ways. Thanks in advance
Comment: Will need to check this up but I recall it is 2 cartons.
Answer: You would need to consult with your carrier to determine whether your bat would be allowed in the cabin.

Gulf Air has the pleasure in carrying your Special baggage, sporting equipment or musical instruments as part of your free baggage allowance. Normal excess baggage charges will apply if you exceed your free allowance. Each item must not exceed the maximum single piece weight of 32 kg or the following dimensions 190 cm (79in) x 75 cm (29.5in) x 65 cm (25.5in).
Duty-free limits
If you're arriving in Ireland from outside the EU, you can bring in certain goods free of duty subject to these limits:

200 cigarettes or 100 cigarillos or 50 cigars or 250g of smoking tobacco (Allowances are on a fractional basis, for example 100 cigarettes plus 50 cigarillos would be the limit together.)
1 litre of spirits (more than 22%) or 2 litres of intermediate products (e.g. port, sherry, etc. but not sparkling wine)
4 litres of wine or 16 litres of beer
50g of perfume and 250ml of eau de toilette

Customs duty, excise duty and VAT (sales tax), where applicable, are charged on goods in excess of the duty-free allowances.

Baggage restrictions


Why does β=α give a symmetric standard beta pdf?

Question: I know that β=α is what will give a symmetric standard beta pdf, but why is this so?
Answer: I guess by symmetric, you mean symmetric about $x=\frac{1}{2}$, where
$$f(x;\alpha,\beta) = \frac{x^{\alpha-1} (1-x)^{\beta-1}}{B(\alpha,\beta)}$$ is the beta pdf.
If $\alpha=\beta$ the numerator becomes
$$x^{\alpha-1} (1-x)^{\alpha-1}=\Big(x(1-x)\Big)^{\alpha-1}.$$
Now $x(1-x)=x-x^2 = \frac{1}{4} - (x- \frac{1}{2})^2$ is obviously symmetric about $x=\frac{1}{2}$ and so is
$$f(x;\alpha,\alpha) =\frac{\Big(\frac{1}{4} - (x- \frac{1}{2})^2\Big)^{\alpha-1}}{B(\alpha,\alpha)}$$


Can a superpartner be less massive than its SM counterpart?

Question: Theoretically, can a superpartner be less massive than its standard model counterpart? I realize there are experimental constraints.
Comment: Though I am nowhere near an expert, this would require the SUSY breaking scale to be very small, right?
Comment: Yeah it would. But I don't know whether a low SUSY breaking scale implies that the superpartners' masses are absolutely small, or just that their mass increase relative to their SM partner's is small.
Comment: Without SUSY breaking, the masses would be equal. Naively, any SUSY breaking seems like it would add mass, but I don't know that the mass matrix from SUSY breaking wouldn't include negative eigenvalues, so that for bosons, e.g., m^2 => m^2 - \lambda, and for fermions m => m - \lambda, reducing the masses. But maybe there is some requirement that the mass eigenvalues from SUSY breaking be positive?
Comment: Exactly, this is what I would like to know! Thanks for helping to clarify this question!
Answer: If you think about it, in a theory with supersymmetry (think about chiral supermultiplets of $\mathcal{N}=1 \; d=4$  for clarity) it's merely a convention to call some particles superpartner of the other particles.
Therefore yes, theoretically there aren't problems, even though we know that superpartner of the usual Standard Model particles must be heavier from experimental constraints.
EDIT: You may be interested in pag. 90 of A Supersymmetry Primer, Martin (2011).
As you can see in (8.1.1), the potential of the MSSM (Minimal Supersymmetric Standard Model, the most simple model!) is ridiculously complicated, but the point is that you now have two Higgs doublets:
$$H_u=(H^+_u,H^0_u) \;\;\; H_d=(H^0_d,H^-_d)$$
in which $H_u$ is the old Higgs doublet. You have the corresponding fermions too, usually denoted as $\tilde{H}_u$ and $ \tilde{H}_d$. Mass terms arise from typical Yukawa terms calculated in the minimum of the potential, for example $H\psi \psi$ for leptons and sleptons. There are many complications in this process: you have to identify the correct mass eigenstates, the supersymmetry can't be broken explicitly, therefore you have to mediate the breaking from an "hidden sector" to the "visible" one (many possible models: Gauge-mediated, Extra Dimensions-mediated , anomaly-mediated, and so on).
Anyway, both the masses of particles and sparticles involve the VEV of $H_u$ and $H_d$ in some complex way, for instance see (8.1.12) for $m^2_Z$ and (8.2.2) for neutralinos. These parameters (and other) are not fixed, you can know the value only from experiments. So you are free, at least in principle, to arrange the mass spectrum as you wish.
Comment: Experimentally it's a convention, but theoretically they are distinguished, right? On one side they get their mass from only the Higgs mechanism, and on the other side they get their mass from SUSY breaking. So I'm asking whether the side that get's its mass from only the Higgs can be more massive than the corresponding partner that additionally gets mass from some SUSY breaking mechanism.
Comment: I'm going to start a bounty because, without addressing this comment, you haven't actually answered my question. Thanks!
Answer: Yes, superpartners can have masses smaller than the mass they get from the Higgs mechanism.
For this the contribution to the squared mass parameter in the Lagrangian must be negative, which can be arranged but is very severely constrained experimentally.
In your comment I see a misconception though:
In supersymmetry, both the "regular" particle and its superpartner get the very same mass from the Higgs mechanism, SUSY breaking is just an additional source of mass for the partners. As Rexcirus mentions, thereotically all components of the superfield are treated with equal rights. It is only when we have supersymmetry breaking, that we can call the fields affected by the breaking the "superpartner" of the unaffected field.
Comment: Or wait, maybe I do have a misconception: are you saying that some of our SM particles could in fact get mass from SUSY breaking, and what we call its (as yet undiscovered) "superpartner" only gets mass from the Higgs?
Comment: I don't see what my misconception is. I pointed out that supersymmetry breaking breaks the symmetry, which is what you are repeating. So my question comes down to whether the mass parameter from SUSY breaking must be positive. You say it can be negative, which effectively answers my question. Do you have a citation that says as much, so I can be sure you are right about this? Thanks!
Comment: @user1247 "On one side they get their mass from only the Higgs mechanism, and on the other side they get their mass from SUSY breaking." This sentence sounded to me like the misconception that "superpartners" get their mass ONLY through susy breaking, which is not true.
Comment: If you read my sentence immediately after that one you see I meant "additional" mass from SUSY breaking. In any case I still would like a citation (or equation, or some argument rather than just a statement) that shows the additional mass from SUSY breaking could be negative.
Comment: @user1247 True, that was too shallow reading of mine. But yes, there are models with negative susy breaking contributions to the masses, but those are uninteresting since they are basically ruled out. The only possibility for a "sparticle" mass smaller than the "particle" mass is the stop, where a stop with a mass slightly lower than the top mass can evade collider constraints because its decay possibilities are very constrained.


Thermodynamics Question: Does measuring the temperature of an object change its temperature?

Question: Suppose that I want to measure the temperature of an object, such as a pot of hot water. When I stick the thermometer into the pot, I know that the temperature measured by the thermometer is its own temperature when it reaches thermal equilibrium, which, according to the Zeroth Law of Thermodynamics, is equal to the temperature of the object (the pot of hot water) at thermal equilibrium. Does this imply that the temperature of the object that I am now measuring is different than the initial temperature, and if so, is the change significant? Also, can I somehow use the information of the system at thermal equilibrium to find the initial temperature of the object?
Answer: Yes. The amount differs by the method used, as well as the dominant heat transfer mechanism (conduction, convection or radiation).
Therfore even a thermal imaging camera draws/emits heat from/towards the object.
Answer: Yes the thermometer affects the temperature of the body that you are measuring.  The change in temperature can be found doing some simple calorimetry (so you have to know the temperature, mass, and specific heat of the thermometer before you use it). And the change in temperature might be significant (but typically isn't at all), it just depends.  Suppose you are measuring the temperature of a very small amount of a low specific heat substance and your thermometer is particularly cold (or hot, relative to the material of interest); here the change in temperature might be significant.  Again, understanding how much the temperature will change just boils down to calorimetry.
Answer: If you use a temperature measuring device that has mass, the answer is "yes", you slightly changed the temperature of the pot of water.  If you use a temperature measuring device that doesn't have mass, such as an infra-red thermometer, the answer would be "no", since you didn't contact the water with anything that has any thermal inertia.  Regarding how much the temperature changed in the first case, you have to use calorimetry to solve for the final temperature.  Examples of calorimetry can be found at
http://www.physicsclassroom.com/class/thermalP/Lesson-2/Calorimeters-and-Calorimetry
Comment: But it must radiate energy for an ir-thermometer to be able to measure anything.
Comment: Yes, David, how can you experimentally gain information from an object without affecting its energy content?
Answer: Short answer is "yes" but in general is insignificant.


latest openbox Yum package standalone install centos

Question: i am trying to install openbox on centos.
when i try yum install openbox
i get
no openbox package available
nothing to do

how can I install this standalone with the yum command?
Answer: You will have to find someone who is running a yum repository which includes an openbox package, and include the details in your yum configuration.  I've had a brief look, and can't find such a repository, so it seems a little pointless to describe how to add it to your yum config.
However, http://rpm.pbone.net/index.php3/stat/4/idpl/9221302/dir/centos_5/com/openbox-184.108.40.206-5.el5.kb.x86_64.rpm.html has an RPM package for RHEL5 on x86_64 (and therefore for CentOS on x86_64, assuming that you're running CentOS5).  Interestingly, it claims the package comes from Karanbir Singh, who is one of the driving forces behind CentOS.
If you're willing to trust an unsigned RPM from the internet (which I might do on a dev system, but never on anything important) you can download the RPM from the link above and install it with yum localinstall openbox-22.214.171.124-5.el5.kb.x86_64.rpm.  If you need an i386 RPM, then I recommend poking a little more on rpmbone.
Answer: RPMfusion.org now can be installed as a repository on CentOS, and might contain the openbox package (rpmfusion.org)
If that doesn't work, perhaps freshrpms can help, too.
Answer: You can try adding EPEL.
CentOS 7
## RHEL/CentOS 7 64-Bit ##
# wget http://dl.fedoraproject.org/pub/epel/7/x86_64/e/epel-release-7-5.noarch.rpm
# rpm -ivh epel-release-7-5.noarch.rpm

CentOS 6
## RHEL/CentOS 6 32-Bit ##
# wget http://download.fedoraproject.org/pub/epel/6/i386/epel-release-6-8.noarch.rpm
# rpm -ivh epel-release-6-8.noarch.rpm

## RHEL/CentOS 6 64-Bit ##
# wget http://download.fedoraproject.org/pub/epel/6/x86_64/epel-release-6-8.noarch.rpm
# rpm -ivh epel-release-6-8.noarch.rpm

CentOS 5
## RHEL/CentOS 5 32-Bit ##
# wget http://download.fedoraproject.org/pub/epel/5/i386/epel-release-5-4.noarch.rpm
# rpm -ivh epel-release-5-4.noarch.rpm

## RHEL/CentOS 5 64-Bit ##
# wget http://download.fedoraproject.org/pub/epel/5/x86_64/epel-release-5-4.noarch.rpm
# rpm -ivh epel-release-5-4.noarch.rpm

Answer: rpm -Uvh http://dl.fedoraproject.org/pub/epel/7/x86_64/e/epel-release-7-10.noarch.rpm
yum install openbox

In case the rpm package is not available, go to http://dl.fedoraproject.org/pub/epel/7/x86_64/e/ to find out the latest epel-release file.
Comment: Answers should include more information than a link, or a command. You should explain what these are doing.


Why does the congregation recite something different during the repetition of the hoda'ah -- but nowhere else?

Question: During the repetition of the amidah, during the hoda'ah (modim) the congregation recites a different text while the shaliach tzibbur recites the text we all did during the silent amidah.  (1) Why do we recite a different (related) text instead of listening to the sha"tz, and (2) why only here?
Comment: @IsaacMoses I understood the Rav's concern to be that everyone hear what the Chazzan says, which is usually hard while everyone is mumbling.
Comment: @IsaacMoses, are you sure about that last point? My understanding is that he is _not_ supposed to wait.
Comment: ...however, the time for the congregation to say Modim is not after the bracha of Avoda; it's when the Chazzan is saying Modim. So either the congregation should say their Modim in a 'silent' undertone, or the Chazzan should pause after the first few words to let everyone finish. If the Chazzan delays starting his Modim, I would delay starting mine.
Comment: There is an explanation of this by R' Soloveitchik quoted in [Machzor Mesoras Harav](http://www.artscroll.com/Categories/rmm.html). If no one gets there first, I'll b"n look it up tonight and post it. Note that according to R' Soloveitchik, the sha"tz is actually supposed to wait long enough for the congregation to complete Modim Derabanan before starting Modim himself.
Comment: @SethJ, I'm pretty sure it's in the "Hanhagos Harav" section of the aforementioned Machzor. I've also seen this done in the Rav's name by YU alumni (not proof by itself, I know, but reinforces what I've seen on paper). This could well be a Brisker Da'as Yachid situation, where everyone else indeed says not to wait.
Comment: @DoubleAA, now that you mention it, I believe the practice advocated by the Rav is for the Chazzan to say "Modim ananchu lach," then pause for Modim Derabanan, then continue.
Comment: @IsaacMoses See also http://www.vbm-torah.org/halakha/chazan2.htm I personally think the 1st way I mentioned is better because no one mentions the chazzan's pausing in old sources, but try convincing your whole shul to act that way.
Answer: Abudraham, in "Seder Shacharit shel Chol u-Ferushah", says( here, right column, lines 29-38):

וכשיגיע ש"ץ ל'מודים' וכורע,
    כל העם שוחין ואומרין הודאה קטנה המתחלת כמו
   כן ב'מודים', שאין דרך העבד להודות לרבו ולומר לו
   'אדוני אחה' על ידי שליח, אלא כל אדם צריך לקבל בפיו
   עול מלכות שמים, ואם יקבל על ידי שליח, אינה קבלה
   גמורה, שיוכל להכחיש ולומר לא שלחתיו. אכל בשאר
   התפלה, שהיא בקשה, יכול לתבוע צרכיו על ידי שליח,
   שכל אדם חפץ בטובתו ולא יכחיש ויאמר 'לא שלחתיו',
   וזהו שאמר דוד 'אמרתי לה׳ ה׳ אתה', אני בעצמי אמרתי
   לו ולא על ידי שליח

In my translation:

And when the Shali'ach Tzibur reaches Modim and bows, all the people bow slightly and say a small Hoda'a which also starts with Modim, as it isn't the [proper] way for a servant to thank his master and say to him 'you are my master' through a messenger, but every man has to accept the Yoke of Heavenly Kingdom with his mouth, and if he accepts through a messenger, it isn't a complete acceptance, for he can deny [it] and say 'I did not send him', and this is what [is meant by what] David said 'I said to ha-Shem ha-Shem you are', I myself said to Him and not by messenger.
Answer: I heard in a recording of R' Yisroel Simcha Shorr that this is learned from the parsha of Bikkurim.  Bikkurim is a parsha of hakaras hatov - we are thanking Hashem for the good of the land that He gave us - and the halacha is (Mishna Bikkurim 1:5) that the parsha of Bikkurim cannot be read by proxy.  From this we learn that you cannot give thanks appropriately through a messenger.
(R' Shorr didn't give a source for this idea.)
Comment: But see 3:7 that a proxy can read it for you in your presence, which is what happens during _Modim_. I don't understand R' Shorr's position.
Comment: @DoubleAA Maybe I'm missing something - it's explicit that that was a takana so that people would not get embarrassed, not normal proxy.  If someone was able to do it, they could not have a proxy do it if not for the concern for people becoming embarrassed.  By modim, which is done quietly and privately, there is no such concern
Comment: @DoubleAA Upon further review, I think you made a mistake - The mishna says מקרין אותו - they lead him in the reading.  He still has to read himself, he just has someone saying it along with him.
Comment: bikkurim might be unique because in sefer hachinuch it says……that  the reason he needs to read is to let the words be mashpia on him a sense of deeper gratification to g-d.         therefore he must read it himself and in exactly those words
Comment: another problem with the bikkurim source is….           that in bikkurim I need to read aloud myself.          but in modimm if i say along quietly I can use a shiach tzibbur. as abudraham explains that he can't say " I didn't send him"


QgisMap renderer Design Methodology

Question: I wanted to know what drawing methodology is used by qgis renderer like gdi,gdi++ or opengl. I have searched its documentation http://qgis.org/api/classQgsMapRendererJob.html
http://docs.qgis.org/testing/en/docs/pyqgis_developer_cookbook/composer.html
but didnt found any methodology used by its renderer for drawing.
Answer: It uses Qt, which abstracts away specific platform-specific technologies.
Note that you can download and build the source yourself, so you have full visibility into the detailed implementation of QGIS. Similarly, you can build Qt from source, and examine that.
Comment: i am asking about rendering maps. Like when you load shape file then how that data is rendered on qgis?
Comment: The source code is authoritative.

QgisMap renderer Design Methodology


How many automorphisms of $\Bbb Z \oplus \Bbb Z_2$

Question: The question is how many isomorphisms (of groups) exist from $\Bbb Z \oplus \Bbb Z_2$ to itself.
I tried to define isomorphism by taking generators to generators, but I want to see convincing proof for that.
Thanks
Comment: What's not convincing about the argument you have? Tell us so that we can help you fix it.
Comment: By Z2 do you mean $\mathbb{Z}/2\mathbb{Z}$?  If so, (0,1) is the unique element of order 2 so it must get sent to itself. Then you can figure out how many places you can send (1,0) to make the map surjective.
Comment: http://en.wikipedia.org/wiki/Direct_product_of_groups#Automorphisms_and_endomorphisms
Answer: Your idea is a good one, but we need to be a bit careful about which generators are sent to which generators.
First, let's suppose that $f$ is an automorphism of $\Bbb Z\oplus\Bbb Z_2.$ Now, we know that $f(0,1)\ne(0,0).$ (Why?) However, $(0,1)+(0,1)=(0,0),$ so we know that $f(0,1)+f(0,1)=f(0,0)=(0,0).$ Thus, $f(0,1)$ has order $2,$ but $(0,1)$ is the unique element of $\Bbb Z\oplus\Bbb Z_2$ having order $2.$ (Why?) Hence, we must have $f(0,1)=(0,1),$ and so for all $k\in\Bbb Z,$ we have $$f(k,1)=f(k,0)+f(0,1)=f(k,0)+(0,1)=k f(1,0)+(0,1).$$ (Why?) Now, suppose that $f(1,0)=(x,y).$ Since $(1,0)\ne(0,0),$ then $(x,y)=f(1,0)\ne f(0,0)=(0,0),$ and likewise, $f(1,0)\ne(0,1).$ (Why?) It follows that $x\ne 0.$ (Why?) Observe then that for all $k\in\Bbb Z$ we have $$f(k,0)=k f(1,0)=(kx,ky)$$ and (therefore) $$f(k,1)=(kx,ky+1).$$
Now, there must be some $k\in\Bbb Z$ and some $m\in\Bbb Z_2$ such that $$f(k,m)=(1,0).$$ (Why?) It follows that $kx=1,$ so $x=1$ or $x=-1.$ (Why?) It can be shown that any choice of $y\in\Bbb Z_2$ gives us an automorphism so long as $f(0,1)=(0,1)$ and $f(1,0)=(\pm 1,y),$ so there are $4$ such automorphisms.
So, as you suspected, our standard generating set $\bigl\{(1,0),(0,1)\bigr\}$ is indeed mapped onto a generating set. In particular, $(0,1)$ must be mapped to itself, and $(1,0)$ can be sent to any of the $4$ elements $(x,y)\in\Bbb Z\oplus\Bbb Z_2$ for which $\bigl\{(x,y),(0,1)\bigr\}$ is a generating set.
Answer: I think it will be convenient to write the operator of the group in multiplication. Let $G=\langle a, b\rangle$, where $|a|=\infty$ and $|b|=2$. Clearly, $b$ is the only element of order $2$. Hence for every $\sigma \in AutG$, we have $\sigma(b)=b$. Now assume $\sigma(a)=a^ib^j$. Now $G=\langle a^ib^j, b\rangle=\langle a^i, b\rangle$. Thus, there exists $k,l$ such $a=(a^i)^kb^l$, so we get $i=1$ or $-1$. Since $j$ can be $1$ ore $0$, we get $|Aut(G)|=4$, as given by Cameron.


Do Titans have a weak point?

Question: In Titanfall, do the different Titans have weak points that are better to shoot at? If so, are they the same on the different chassis?
Comment: possible duplicate of [What do the red areas on Titans mean?](http://gaming.stackexchange.com/questions/163621/what-do-the-red-areas-on-titans-mean)
Comment: @TheAnnoyingPyro It's still appropriate to mark it as a duplicate, because the answer is the same, and this way, this question can serve as a useful signpost that will direct users to the information they're after.
Comment: Yes they do have weak spots. But only with certain weapons and only an shield down. Then they flash video game weak spot red.
Comment: I wouldn't say it's a duplicate of that question, unless you knew about the glowing red areas on Titans beforehand and just didn't mention it.
Answer: They do have weak points... but hitting them at their weak points will deal extra damage only if their shields are depleted.
The titan's weak spots will be highlighted red when their shields are depleted.  Each titan is different so naturally the red weak points on each of the titans will be on different locations.

Then of course, there is the option to jump onto a titan as a pilot to rodeo and attack them directly bypassing their shields.  Of course, take caution going this route because you will be left very vulnerable when attacking a titan this way.  There are ways to defend against rodeoing pilots so look out when attacking a titan this way.

Do Titans have a weak point?


Can't see appearance in desktop settings to hide mounted drives

Question: What I have:
I am running Ubuntu server 22.04.4 LTS 64-bit on a Lenovo E30.
I have the gnome 42.9 version running.
When I login, I use the ubuntu option (selected toggling (F1)
Here is a list of the installed desktops:
ls -l /usr/share/xsessions/

-rw-r--r-- 1 root root  259 May  9  2022 gnome-classic.desktop

-rw-r--r-- 1 root root  296 May  9  2022 gnome-classic-xorg.desktop

-rw-r--r-- 1 root root  248 Apr  7  2022 gnome.desktop

-rw-r--r-- 1 root root  256 Apr  7  2022 gnome-xorg.desktop

-rw-r--r-- 1 root root  292 Apr  7  2022 ubuntu.desktop

-rw-r--r-- 1 root root  300 Apr  7  2022 ubuntu-xorg.desktop

-rw-r--r-- 1 root root 6832 Feb 16  2021 xfce.desktop

What is the problem:
I want to hide the mounted network drives off the desktop.
I cannot see the appearance setting in the Settings window to do this. Numerous sites have said this is where I need to hide them.
What have I tried:
I have tried to login using the gnome option but get an Xsession error: unsupported number of arguments (2); failing back to default at which point I cannot select the ok button and I have to power off the system.
Thanks,
Tom
Answer: Ubuntu 22.04 uses gnome-shell-extension-desktop-icons-ng. Let's change the preferences inside that:

Run gnome-extensions prefs email@example.com in terminal

Disable "Show external drives in the desktop" and "Show network drives in the desktop"


Transistors and Diodes maximum current per size

Question: As you can understand my knowledge in electronics is limited.
I am trying to find throughout the internet a way to find the maximum current I can put through a transistor or diode versus their size. Specifically in the region of nanometers and micrometers in VLSI projects. I can find a lot of info for diodes and transistors for PCBs but no info at all for applications in ICs. Any info (even with a big amount of error plus/minus, just a ballpark is fine) or a table I can find on the internet is also nice.
Thank you.
Comment: If you're using a transistor in a VLSI layout, then the manufacturing process document will have all you need. It depends on current density, heatsinking, geometry, lots of things that will make any ballpark estimate completely useless.
Comment: And to add to that: it also depends on expected lifetime (consumer devices are less strict than automotive for example), temperature range (when hot, devices cannot support as much current). A ballpark value I often see is around 1mA / 1 um width. That still doesn't tell you much as devices can be folded up and then reach much higher values.
Comment: The doping, and thus the inherent non-depletion-region ohmic behavior, will set the voltage drop at high currents, and thus set the local HEAT GENERATION, which as Bimpelrekkie explains will affect the allowed current and lifetime. The use of metallization to remove heat, to spread heat, is a design task and choice, also. However the silicon is about as good a heat path as the aluminum. Chat with your process-development people about benefits of any copper layers.
Answer: The limiting quantity is not current but power dissipation.
Therefore you should ask for power dissipation (not current) per size (i.e. chip area), a quantity with unit W/cm².
You can get the ballpark number if you look at high performance mircoprocessors.
I don't know exact up to date exact numbers but it is, quite impressing, in the same range as power densities of heating plates used for cooking:
ca. 10 W/cm²


binary up/down counter with synchronous clear and preset

Question: For a binary up/down counter with synchronous clear and preset , my question is what is the exact function of the preset here ? I have done many searches but every source assumes that the reader knows what is the preset function is and just mentions that the counter does have a preset input.
Answer:
what is the exact function of the preset here ?

The preset input is usually several parallel inputs that can be loaded into the counter via an enable input such as in the MC14516: -

Once a number is preset, you can count up or down from that value.
Another device (uses "Preset Load"): -
Answer: Since you mentioned "synchronous clear and preset", they are no different from any other counter control or counter data signals. They all traverse through combinational cloud, and finally converge at the D pin of several flip-flops. From the perspective of circuit, synchronous clear or preset are just DATA. We human beings call them clear or preset signal just because they do the clear or preset job functionally. So this is not an essential issue.


What is the best substitute for Provolone?

Question: Having recently bought the Frankies Spuntino Cookbook I want to have a go at making braciola. The recipe calls for pork steaks to be stuffed with pecorino romano and provolone.
However, in the UK provolone is hard to come by outside of Italian delis, and Italian delis are relatively rare. I understand that it's similar to mozzarella but drier.
So, what is a good substitute for provolone? Is it usually used for flavour or for its melting texture?
Comment: You can order online in the UK https://www.amazon.co.uk/Provolone-Piquant-Pasta-Filata-Cheese/dp/B00URTKJXW/ref=sr_1_2_a_it?ie=UTF8&qid=1479144468&sr=8-2&keywords=provolone+cheese Sharp provolone is pretty hard and dry so it last quite long even without refrigeration
Answer: There are two main types of provolone: piccante (sharp) and dolce (sweet).  Most braciola recipes I've seen call for the sharp version.  Sharp provolone tastes very similar to cheddar, which I assume is abundant in the UK.  The issue is that "real" cheddar is a hard cheese and provolone is only semi-hard.  Here in the US, we have a softer version of sharp cheddar-style cheese that is made in Wisconsin.  If a similar semi-hard sharp cheddar variant is available in the UK, I would recommend that.
It should also be noted that the term "braciola" (or sometimes "braciole") means a lot of different things to different people.  To most Americans, likely including the author of your book, it takes on the Sicilian meaning of an involtino.  Sometimes the meat will be filled with a soft cheese mixture like mozzarella mixed with grated pecorino romano.  However, if the recipe calls for a harder cheese like provolone, it is likely referring to a variant that is very popular in the US in which the provolone is cut into thin slices (usually using a deli slicer) and layered on the meat before the meat is rolled.  Therefore, any substitute for the provolone should ideally be thinly sliced.
Comment: The recipe is for _involtino_ braciola, calling for aged provolone, which i assime is 'sharp' as you suggest. As it happens I am near an Italian deli at the moment, I will try and find some provolone and see how cheddar like it is. Generally the more mature the cheddar here, the harder and more crumbly it is, so I'm thinking a medium cheddar would give the right texture and flavour.
Comment: I managed to find some Provolone and I would say it is closest to a medium/mature cheddar.
Comment: Aged provolone is very sharp and dry, I would use a quite mature and dry cheddar.
Answer: When limited to supermarket cheeses, I would try 1/3 mozzarella and 2/3 muenster. Braciole is served hot, so mozzarella would have lovely Italian flavor but would liquify too much, while muenster would have the right texture. The pork would not have to cook as long as beef, but you run the risk of cheese seeping out into the sauce rather than remaining as an intact layer of the meat roll.
Comment: Definitely not mozzarella. Provolone, especially aged one is a very tasty cheese and the texture is completely different from mozzarella. That said, mozzarella would also be very good in the dish, it just won't give the same type of result.
Answer: If the only issue were flavor, an aged provolone takes on a similar characteristic of other italian hard cheeses such as parmesean, and so I'd have replaced the provolone with a dry mozerella augmented with extra parmesean, or pecorino romano.  (and at least in the U.S., dry mozerella is what tends to be sold, not the fresh stuff)
As we're dealing with melting characteristics as well, as Kathi's pointed out, mozerella's just going to melt wrong.  I'd likely go with fontina, a young asiago, or manchego (a young one, not manchego viejo).
To emulate a younger provolone, use less of the aged cheese and use a better melter, like fontina, monterey jack or even a mild swiss.


Weighted sum of binomials with $r$-th power of lower index

Question: Given $r\in(0,1),$ what is the best upper (asymptotic) bound for the following expression
$$S(n,r):=\sum_{k=0}^n{n\choose k}k^r?$$
Holder's inequality gives $S(n,r)\le 2^n(\frac{n}{2})^r$ but I guess this is not optimal. Is there any better estimation?
Comment: I don't think your upper bound is correct.  It says that the weighted average of $k^r$ in the sum is at most $(n/2)^r$.  However $(n-k)^r\gt k^r$ for $k\lt n/2$ so in fact the weighted average of $k^r$ in the sum is greater than $(n/2)^r$.
Answer: Since the expression is ALMOST the $r$-th derivative of $(1+x)^n$ evaluated at $x=1,$ the asymptotic expression is $2^{n-r}n^r,$ which is, in fact, your upper bound.
Answer: Probably not.  The expression is $2^n E( {Z_n^r})$  where  $Z_n$ is the sum of n iid  0-1 valued r.v.s which are 1 with prob $\frac 12$.  However, by the SLLN $\frac {Z_n} n \approx  \frac 12$ so one expects $$ E((\frac {Z_n} n )^r) \approx  (\frac 12)^r$$  so your expression is also the asymptotics for the sum and probably can't be improved too much.  If you want to translate this into analysis you would show that the biggest contribution to the sum comes from a smallish nbhd around $\frac n 2$.
Answer: I tried a rather naive approach: Replacing the binomial by its Gaussian approximation
$$
{n \choose k} \rightarrow 2^{n} \sqrt{2 \over \pi n} \exp\left\{- {2 \over n}\left(k-{n\over 2}\right)^2\right\}
$$
and replacing the sum by an integral with upper limit $\infty$
$$
\sum_{k=0}^{n}\rightarrow \int_0^{\infty} dk
$$
Fortunately Mathematica was able to solve the resulting integral in terms of confluent hypergeometric functions, $_1F_1$,
$$
S(n,r) \approx\pi^{-1/2} 2^{n-\frac{r}{2}-1} n^{r/2} \left[\Gamma \left(\frac{r+1}{2}\right) \, _1F_1\left(-\frac{r}{2};\frac{1}{2};-\frac{n}{2}\right)+ \sqrt{2 n} \  \Gamma \left(\frac{r}{2}+1\right) \, _1F_1\left(\frac{1-r}{2};\frac{3}{2};-\frac{n}{2}\right)\right]
$$
This is a very good approximation for the original sum, though quite clumsy. To get the correction terms to $2^n(n/2)^r$ I expanded the  $_1F_1$ for large negative arguments, see, e.g., http://functions.wolfram.com/07.20.06.0019.01.I dropped exponentially small contributions, $\propto e^{-n/2}$, and found
$$
S(n,r) = 2^n \left(n \over 2\right)^r \left(1 - \frac{r(1-r)}{2 n} - \frac{r(6-11 r+6 r^2-r^3)}{8 n^2}+ O(n^{-3})\right ) + O(e^{-n/2}).
$$
Note, that the exact results $S(n,0)=2^n$ and $S(n,1)=2^n(n/2)$ seem to be preserved in the sense that all correcting terms vanish in these cases.


Designing databases: storing user stats in games(i.e. owned money) and 32bit integer overflow

Question: I am creating an little hobby database driven browser based game and I stumbled across this problem: I store money owned by users as an 32bit integer field (to be precise: two fields. One stores money in players hand, the other - money stored in bank). We all know, that maximum value, which can be stored in 32 bits is 2^32-1.
I am absolutelly sure, that 95% of players will not be able to reach the upper limit - but on the other hand (and after doing some calculations today) good players will be able to accumulate that much.
Having that in mind I came with the following ideas:

store money in 64bits, which doubles space of each record.
store money as string and convert to/from long long in the runtime.
change game mechanics so players will not be able to gain that amount of wealth.

I know that existence of reachable upper limit is rather limiting for some players, so for me the third option is worst from the proposed ones.
Are there any other ways of dealing with this kind of problems? Which one would You go for?
Answer: Taking an example from the real world, why not have different types of coins e.g a column for a million units of the currency.
Answer: Changing to a larger datatype is likely the easiest solution and considerations of disk space/memory aren't likely to be significant unless your game is huge in scale.  Have 5,000 users playing your game?  Changing from 32-bits to 64-bits will consume roughly 20k extra.  That's not enough to lose any sleep over.
The best answer would likely come from someone familiar with how banks handle these types of situations, though their requirements may be far more complicated than what you need.
Answer: Space on memory shouldn't be a problem depending on the amount of players you'll have simultaneously, but storing as string will definitely use more disk space.
But seriously, 4 294 967 296 rupees/simoleons/furlongs? Who are they? Sim Gates?
Comment: @0/: you might want to denormalize anyway, for speed's sake. Keep both. *Normalize until it hurts, denormalize until it works.*
Comment: I thought about strings, because I am storing user stats as strings in one table - that way I wouldn't store accumulated wealth in another table, but it would be just another user stat.
Answer: Why not store money the way it should be stored, as a Money data type? This is assume of course you are using SQL Server. The money data type won't have this limitation and won't be affected by rounding issues.
Comment: On a game, having some cents lost on every transaction is a good trade with speed.
Comment: I am sorry that I didn't stated that in OP, but I am using MySQL.


How to prevent cross validation from overfitting?

Question: I a simple multiclass classification problem in which Logistic Regression works well on. (Over 65% test accuracy, which is considered good for this dataset. But the data set is small, it has 5 classes with slight imbalance, 18 features and 350 rows. Train/Test split is 75/25.)
I then tried XGBoost, and performed grid search to find the optimal hyperparameters. the CV I choose was 5 fold StratifiedKFold.
The problem I'm having is that the test error is much higher than the training error, where the training error is determined after the grid search finishes and the model is retrained on the entire training data set.
This clearly shows that the model is overfitting, and most baffling of all I know a set of parameters which is included in the grid search can achieve lower test error (error when tested against the 25% unseen data)
What am I doing wrong here? How can I prevent overfitting when during cross validation?
My entire pipeline is as follows
Data -> Train/Test split -> Cross validate on Train -> Retrain model on Train /w best hyperparameters -> Final evaluation on test
Maybe I'm leaking data somewhere?
<code>xgb_pipeline = Pipeline([('ss', StandardScaler()),
                         ('pca', PCA()),
                         ('xgb_clf', XGBClassifier(n_jobs=1))])

xgb_param_grid1 = {
    'pca__n_components':[18, 15, 12],
    'xgb_clf__n_estimators':[5],
    'xgb_clf__gamma':[0, 0.5, 1],
    'xgb_clf__colsample_bytree':[0.7, 1],
    'xgb_clf__max_depth':[3, 5],
    'xgb_clf__reg_alpha':[0, 0.5,1],
    'xgb_clf__reg_lambda':[0, 0.5,1],
}

cv = StratifiedKFold(5, shuffle=False)

xgb_grid_cv = GridSearchCV(xgb_pipeline, xgb_param_grid1, cv=cv, verbose=1, n_jobs=-1, refit=True)

xgb_grid_cv.fit(X_train, y_train)

xgb_grid_cv.score(X_train, y_train)
# Score close to 1

xgb_grid_cv.score(X_test, y_test)
# Score close to 0.4
</code>
Thanks in advance
Answer: Cross validation over the grid of hyperparameters will find the combination of hyperparameters that have the lowest test error.  Thus, you will find the set of parameters with the least amount of overfitting, but you are not guaranteed to not overfit, particularly when you place limits on the hyperparameters.  In this case, since you have a small dataset, I would start by trying to include lower max depths than 3.


How do I Derive the Green's Function for $-\nabla^2 + m^2$ in $d$ dimensions?

Question: What is the solution to this equation in $d$ dimensions:
$$(-\nabla_d^2 + m^2)G(\mathbf{x}, \mathbf{x}') = A \delta(\mathbf{x} - \mathbf{x}'),$$ with the boundary condition that $\lim_{|\mathbf{x} - \mathbf{x}'|\rightarrow \infty} G(\mathbf{x}, \mathbf{x}') = 0$?
Answer: The first step is to recognize that equation is invariant under $d$-dimensional rotations around $\mathbf{x} - \mathbf{x}' = \mathbf{0}$ and simultaneous identical translations of $\mathbf{x}$ and $\mathbf{x}'$, so we can make the following step:
$$\begin{align}(-\nabla_d^2 + m^2)G(\mathbf{x}, \mathbf{x}') &= A \delta(\mathbf{x} - \mathbf{x}') \\
& \mathrm{let: }\ r \equiv |\mathbf{x} - \mathbf{x}'| \Rightarrow \\
\frac{A}{\Omega_d r^{d-1}} \delta(r) &= - \frac{1}{r^{d-1}} \frac{\partial}{\partial r} \left[r^{d-1} \frac{\partial G(r)}{\partial r}\right] + m^2 G(r),\end{align}$$ where the factor $\Omega_d r^{d-1}$ comes from the volume element $\operatorname{d} V = \Omega_d r^{d-1} \operatorname{d}r$ and the derivatives on the right hand side (rhs) are the radial term of $\nabla_d^2$ in $d$-dimensional spherical coordinates (wiki link).
The next step is to integrate both sides of the equation over a spherical volume centered at the origin with radius $r$, then take the limit as $r \rightarrow 0$. This yields the normalization condition for $G$:
$$\lim_{r\rightarrow 0} \left[r^{d-1} \frac{\partial G}{\partial r}\right] = -\frac{A}{\Omega_d},$$ and handles the part of the equation where the delta function is non-zero.
The region where the delta function is zero, the homogeneous region, becomes: $$0 = \frac{\partial^2 G}{\partial r^2} + \frac{d-1}{r} \frac{\partial G}{\partial r} - m^2 G.$$ The equation in the homogeneous region can be brought into a more familiar form by the function substitution $G(r) = f(r) r^{-(d/2 - 1)}$ giving:
$$0 = r^2 \frac{\partial^2 f}{\partial r^2} + r \frac{\partial f}{\partial r} - \left(\frac{d}{2} - 1\right)^2 f - m^2 r^2 f.$$ The familiar form to this equation is the modified Bessel's equation. The most general solution to this equation is:
$$f(r) = C K_{d/2-1}(mr) + D I_{d/2-1}(mr),$$ with $I_{d/2-1}$ and $K_{d/2-1}$ modified Bessel functions of the first and second kind, respectively, and $C$ and $D$ constants fixed by the boundary conditions.
The boundary condition at $r\rightarrow \infty$ requires $D=0$, giving the following form for $G$: $$G(r) = \frac{C}{r^{d/2-1}} K_{d/2-1}(mr).$$ Plugging our solution for $G$ into the left hand side (lhs) of the $r \rightarrow 0$ boundary condition derived above gives:
$$\lim_{r\rightarrow0} \left[ r^{d-1} \frac{\partial G}{\partial r}\right] = -\Gamma\left(\frac{d}{2}\right) 2^{d/2-1} m^{1-d/2} C,$$ after application of the small argument limit form of $K_\nu$. This implies that:
$$\begin{align}C &= \frac{A m^{d/2-1}}{2^{d/2-1}\Gamma(d/2) \Omega_d} \\
& = \frac{A m^{d/2-1}}{2^{d/2} \pi^{d/2}},\end{align}$$ where the explicit form of $\Omega_d = S_{d-1}$ has been inserted.
Finally, replacing $C$ gives:
$$G(r) = \frac{A}{(2\pi)^{d/2}} \left(\frac{m}{r}\right)^{d/2-1} K_{d/2-1}(mr).$$
Comment: Excellent answer, resourceful and enjoyable to follow. One **question** about the analytical continuation: we can only analytical continued to Feynman propagator, right? If yes, why Feynman propagator is justified to do so while other propagator are not?  If no, how to get the other propagators?
Comment: @user143410 If the differential equation and the boundary conditions all share a symmetry ($d$-dimensional rotations, in this case), then the solution will also share that symmetry. I don't know a proof off of the top of my head, so you might consider consulting https://math.stackexchange.com/ for details.
Comment: Another **annoying question** is what cause the missing term $\delta(r_{d-1}^2-(ct)^2)$, how to fix this part to make your derivation perfect...
Comment: Excellent questions. I'd love to hear any answers you have, because I'm still working on this one in my spare time. I can tell you why this one gets the Feynman propagator, though. In the Fourier transform technique the Feynman propagator comes from moving one pole up and one pole down from the integration axis. What we've done here is the same as starting with with a vertical axis and rotating it down, so the relation of the axis to the poles is the same. The key will be redoing the boundary conditions in Minkowski space, I think.
Comment: The possible answer to the first question I can come up is:  Feynman propagator is allowed to analytical continued because by doing this we might have explicitly deformed the contour from real axis to the imaginary ones. While others are not because the placement of the two poles prevent the contour from rotating(they will pass the poles). See the other answer to my original post.
Comment: See [the Wikipedia article](https://en.wikipedia.org/wiki/Propagator#Causal_propagators). The causal propagators come from deforming the integration contour on the same sides of the poles instead of opposite.
Comment: Did your derivation assume also that the Green's function itself is invariant under $d$-dimensional rotations?  I would think, in general, that solutions to differential equations need not possess the same symmetries as the differential equations themselves.  Am I right about this?


Plymouth Don't Show On Starting Just Show on shutDown

Question: i recently installed Plymouth and use a custom theme ,i did all the things but my screen splash just show on shutdown screen and i get blank screen on booting , i use every way but i didn't get any answer, can anyone answer and help me?
Answer: 'i did all the things' and 'i use every way' is not explaining what you did. Maybe you can reinstall Plymouth, ($ sudo apt-get install --reinstall Plymouth) or check another theme. Which program did you use to install the theme or did you so by hand? maybe you can find your answer here: How do I change the plymouth bootscreen?.


Block and unfixed incline system

Question: if there is a block on top of an unfixed inline. and if the system is released from rest what is the acceleration of the block and the incline? can someone draw fbd and show? the difficulty in this problem is that you can't figure out the normal force and stuff like that. This is not an a= homework question, I'm genuinely curious about how to draw the fbd.
Comment: Does this answer your question? [Free body diagram of block on accelerating wedge](https://physics.stackexchange.com/q/277412/)
Answer: I hope the figure attached below helps you...
The observer I have taken shown in fig. is in non-inertial frame of reference. So an additional force pseudo force comes into play.
You can approach the problem through inertial frame also. The result will be the same. But the calculations get lot simpler in non-inertial frame.

The accelerations of the block are calculated in the above image.(a2 : acc. of block. a1: acc. of wedge).

Block and unfixed incline system


Why in Digital Design only Capacitive load?

Question: Why in designing of CMOS logic we only consider the capacitive load of fanout? There is some wire resistance. So, why don't we consider resistive load?
Comment: In some cases we do consider resistance, often adding external resistors to improve signal integrity.
Answer: When the wiring resistance becomes significant, then we do include it. As long as the wiring resistance is much, much less than the \$R_{DS}\$ of the MOSFET then it can be ignored.
Answer: Wiring resistance is usually less than 1Ω and most wiring resistance being in the mΩ range. With many digital logic families maxing out at 50mA, if you were to calculate the equivalent resistance of most push pull GPIO's, the source resistance would be somewhere in the range of 100Ω to 50Ω at DC. Because of 50Ω is much bigger than mΩ's the wiring resistance can be neglected in allmost all cases.
However, if you have long wires or small wires that make the wiring resistance more than ~1Ω then you should consider wiring resistance in your calculation.
Answer: We do.  Internal to the CMOS chips, the resistance of the deep-sub-micron metal layer wiring contributes significantly to the RC delays even a small distance across an SOC (less than 1mm) in or between logic blocks.  That analysis is a large part of timing closure to meet clock rate specs.
In PCB design, another consideration is inductance: mutual inductance can be a cause of crosstalk between long traces, reducing signal integrity.  Trace inductance can also contribute to ringing of steep transients, causing signal under/overshoot.
Answer: Why C and not R, what about Zo = sqrt (L/C)?

Attenuation occurs when the source impedance is not zero or the load is not infinity.  Although 5V logic is around 50 Ohms is considered low relative to the expected gigaohm gate input resistance so we can neglect trace resistance as well as load resistance.

5V (1Gohm)/(1 GOhm + 50 ohm) = 5V as a voltage divider on R there is no attenuation , so we neglect load R.

Impedance of CMOS transmission signals do matter when the 2~3ns rise time reduces to make reflection echos visible in the  echos from mismatched Z load reflections. These delays show as 35% typ overshoot & decayed ringing unless terminated with matched impedance.

However increased risetime and for longer traces , ringing can degrade signal quality.

Typical trace width, W with a height, H over ground planes and trace length , L has an impedance based on ratios of these parameters.

When typical PCB FR4 trace  geometry has a ratio H/W=2,  Zo = 83 Ohms, L < 5 nH/cm , C ~ 0.7 pF/cm with a propagation speed, v = < 18 cm/ns  (Ref Saturn PCB.exe)

Rise time, Tr is defined as the 0 to 64% Vmax by a standard T=RC load capacitance (e.g.15pF) and the logic family standard source resistance.  For 5.5V logic this is 50 Ohms +/-50% and for 3.6V logic this is 25 Ohms +/-50% typically.  Lowering the gate + supply voltage increases RdsOn so 3.6V logic was designed to use a lower Vgs(th) and lower RdsOn to improve rise times but then cannot be used at 5V as it would go into shoot-thru or cross-conduction with both hi & lo side drivers active.
Tr = RC is the rated at 15pF but your design may be more or less depending on trace width over ground planes, trace length , fan out of gate loads and logic family.
Ringing occurs when the prop delay approaches the rise time the mismatched load reflection causes an observable change with oscillation.

When the signals go on cables, we are either limiting the data rate and slew rate (e.g. RS-232) or we terminate the cable with a load resistance matched to the cable ( e.g. 120 Ohms for ribbon or 50 typ. for coax.)
Answer: CMOS logic input draws no DC current, so there is not much resistance or resistive load to consider when a CMOS output drives CMOS inputs. The speed how fast a signal can transition between states depends mainly on output current drive strength and capacitances it needs to drive. PCB wiring has very little resistance in comparison, though wiring does add capacitance easily.
Answer: Resistance is included, in the sense that the output voltage level of a CMOS device is specified at a given current.  From these two numbers, the output resistance of the device can be estimated, and from that you can assess the effect of an ohm or two of wiring resistance.  Here's an example from a 74C04 data sheet.

Note the Voh is spec'd to be at least 2.4 V at a current of -360 uA.
You'll find a similar set of specs on almost any digital device.
The capacitance has to do with how fast a device can change the voltage on a node.  It's a dynamic, switching, or AC specification.  This spec impacts how fast a circuit can switch (though it's not the only thing), and also impacts the dynamic power dissipation of the device.


Strange light bulb phenomenon

Question: Let me explain.  My son has a small typical night light that occasionally will go out, even if the bulb isn't dead.  Usually I'll tap on it repetitively or shake it to get it to work again. When I hold it under another light,  I can see the "coils" or string-looking things moving around uncontrollably, unattached to the points.  Now, here's the weird thing.  Sometimes, when I get it to work again, it will actually appear brighter than before.  Usually it's an orangey-yellow dim light, but after it goes out and I "fix" it, it becomes whiter and brighter.  How can this be?  Is it because the coils are no longer connected in their usual triangular shape, instead forming an irregular shape?  How could that effect it?
It looks something like this.  Just your average night light
Comment: If the filament is not attached to its holders, it could be simply shorting out a small section if the coil touches in two places (hence it would get brighter). Solution? Don't lose sleep over it, just get a new bulb...
Comment: It sounds like there is a loose electrical connection in the lamp somewhere. Considering that you "fix" it by tapping it, I would seriously consider either replacing the entire lamp or getting a qualified electrician to mend it. Maybe there is somewhere like a domestic applicance repair place near you - they would be able to check and repair it for you.
Comment: @TomCarpenter That's what I thought at first, but I've never known tungsten filament lamps to be *repeatedly* fixable with percussive maintenance.
Comment: I was meaning a photo of the actual broken/misbehaving one, but worry not you have your answer.
Comment: This is common on some types of lamp with very flexible poorly supported filaments.  If it goes out and sometimes lights with a tap then the buld is burnt out and needs replacing.  The risk of fire is fractionally increased as it may dissipate mote heat and run hotter but usually the filament will burn out again if it is far outside the design current.  Replace with LED lamp if you want it to be mechanically more robust in future.
Answer: The coil is a resistor lets say its divided into three parts, they all have equal resistance (same material). If the coil in the bulb comes loose, it can short out at a different point. You have less resistance and more current through the same section of coil. This will make it brighter and also hotter and reduce the lifetime of the coil.

simulate this circuit – Schematic created using CircuitLab
Comment: Does this also mean that the current consumption can quite double in rare case? If it is controlled by a relay or a switch, then the whole design is subjected to stress. This is a good example for use case stress test.
Answer: I've seen that before.  You have a burned out incandescent bulb.  The tungsten coil filament has disconnected from one end, but is being held onto the other reasonably well, and is acting like a spring.  If it's jostled, the coil will sometimes strike its terminal and reconnect for a time.
When it does, there's no telling what part of the filament will connect, and as laptop2D describes, that's either cutting out part of the element (making it brighter) or paralleling elements that were meant to be in series (likewise).
I doubt it can overload like this for very long.  Perhaps it's not overloading, and the effect you see is just a trick of perception.

Strange light bulb phenomenon


Where is the EDITOR env variable originally set?

Question: Where is the EDITOR environment variable initialized? so far I have checked the following files and could not find where it is:

~/.bashrc
~/.bash_profile
~/.profile
/etc/profile
/etc/bashrc
/etc/environment
Comment: What do you mean by "originally"? By default it's **not** set at all.
Answer: Nowhere. You are thinking about it from a wrong perspective.
Each application has its own preferred editor (or pager, or whatever else it needs). That is built in into application. Defined at compile time and never changes.
If creator of application wants to allow user to change it later - then an application can take a look at environment variable EDITOR, PAGER, etc and use whatever user defined there.
Some applications with capability to switch to a user preferred editor do not look at environment variable EDITOR, but at its own configuration files. Or both (git for example).
Answer: I'm going to guess that $EDITOR is set in your current shell but you are not sure how and where it got set? If that's the case, and you are on a system with strace installed like Linux you may want to try to look at all the files that BASH for instance opens. I modified the answer in this question slightly Find out what scripts are being run by bash at login
echo exit | strace -e open bash -li
From the BASH man page:
      -i        If the -i option is present, the shell is interactive.
       -l        Make bash act as if it had been invoked as a login shell (see INVOCATION below).

Another way, in another comment from that answer is to invoke bash with the -x flag enabling echo of each command that is executed:
/bin/bash -x -l -i -c 'exit' 2>&1 | less

I would do this first to make sure that $EDITOR is somehow even being set on startup and not exported by some other script or program you are running after your shell has already initialized.


Whether registered LLC which is Inactive has to file Tax?

Question: Whether a registered LLC which is Inactive has to file Tax? There is no business operation happening. Just LLC is set up. In this scenario, do i need to file the tax? State : NJ
Answer: As with most laws, typically the "need" is based on the consequences of non-compliance.
In this case, inactive and "file tax" can mean several things. Many states have an annual tax for keeping the LLC active, but if it is already in inactive status then it means you already didn't pay.
The consequence is merely a higher cost to bring it active again.
If thats not the kind of 'inactive' you meant, then you have to pay that annual tax to keep it from becoming inactive.
Or ... don't.
Disclaimer: Not a lawyer and there are many states.
Comment: To keep an LLC active, you pay an annual fee, which isn't a tax.  It is actually a business expense that you deduct from your income at tax time!
Comment: @JeffO'Neill yes, I'm aware. Many states call it an annual fee or franchise tax. Many non-federal business taxes are deductible, or were deductible. That semantical distinction isn't important.
Answer: If the LLC is a single-member LLC taxed as a sole proprietorship (pass through income) then I expect that you do not need to do anything.  If this LLC makes money, it is just one more form to your personal income taxes so it is no big deal.  To be safe, you could add that form with $0 income.
If the LLC is taxed as a partnership or S-Corp, then I expect that you would need to file a return, but I am not sure.


What's wrong with my aloe?

Question:
Lately I've moved it to the patio since the summer began. The leaves started turning pale and are becoming flat. There are few brown spots on the leaves. I water it once in two weeks and it gets ample sunlight. I live in Colorado and the temperatures are high 80s. Please help!
Comment: I would guess that it got rained on and water that collected in the middle is causing it to rot.  Happened to mine a few years back under similar conditions.
Comment: It hasn't rained for a while.. maybe it's a sunburn.. I'll move it indoors.. thanks!
Answer: Plants that are indoors can not be taken out of doors and into the sun.  Aloe most certainly loves sun but if it has been grown indoors then it needs acclimation before allowed in direct sun longer than...5 minutes the first day.  This is too much sun.  Get it out of the sun and into the shade.  Do not over water or give fertilizer until your aloe responds.
If you have an awning or a porch roof that is where this plant would be happier right now.  Far more light than indoors.  Your aloe will be able to make more food for itself. Bring your plant indoors way before a chance of freeze.
Because you are in Colorado you will never want to plant your aloe out of doors.  The best thing for indoor plants is to go out on a fully covered porch for a few months when there is no chance of frost.  More light, the plants make more food for themselves, store it for winter...really revives house plants.  But a plant not used to direct sun either out of doors or even through a window can easily be killed placing it direct sun.
This is too much sun.  Sun burn.  The epidermis of indoor or plants in the shade is thinner than the epidermis of the same plants accustomed to direct sun.  Similar to 'sunscreen'?  Takes weeks to acclimate plants to direct sun, beginning with 5 minutes for a few days, doubling that for a few days, doubling that for a few days until your plant has a thicker epidermis and can handle direct sun. The sun has fried some of the chloroplasts that do photosynthesis, thus the pale yellow color.
Answer: Aloe's don't like much direct sun light, try some place where it gets plenty of indirect sunlight
Answer: Looks like too much water .i water mine once a month inside and not at all outside. The aloe I have came from the desert of Arizona it is in an 18 gallon terracotta  pot and stands 5 foot tall and loves sun. Yours looks like it is sun burned, the new leaves that emerge will be more sun resistant. You might think of changing the soil to a cactus quick draining type soil

What’s wrong with my aloe?


Should i annotate types everywhere?

Question: Should i annotate types in my unit tests functions?
What also with overridden django methods like save and get or post functions in generic view?
Comment: @WillemVanOnsem I mean though, you could have that response to pretty much any question on this site.
Comment: @Neil: most questions on these site are "why is my code not working", so then it is not much opinion based :). Furthermore a lot of questions have definitely some theoretical foundation. For example certain logic programming semantics are better than others based on the "well founded semantics".
Comment: I agree that this might be opinion based. The best approach though if you think that is probably just to mark it as opinion based and vote to close.
Answer: This is arguably an opinion question but I think that there is a generally accepted answer, which is roughly "No".
One way of categorising programming languages is into statically typed and dynamically typed. Statically typed languages are generally more robust, especially for "programming in the large", and dynamically typed languages have advantages ito programming speed, and in modelling problems where it is beneficial to be able to accept data of various types. Type hints try to strike a balance. The rough rule being: if you are using the dynamic nature of the language to achieve something, don't worry about annotating it. If however, you are writing code that doesn't make specific use of the dynamic nature of the language, annotate
Perhaps to make the point clear, consider that if you DO annotate everything, well then why not just use Cython? Same effort but you actually get some speed up as well. The reason people use Python with annotations instead of Cython is that some problems are naturally better solved without specifying types.

Should i annotate types everywhere?


Can I use a link tag for an additional attribute on the properties tab?

Question: Is there a way to call out a link alt, title, or alias tag to populate as an additional attribute on the properties tab?
Comment: What do you mean by "call out a link alt, title or alias tag"?
Comment: Hey Adam! i may not be using the correct terminology so i will try to explain more in depth. I have an additional attribute that is appending my link (a utm value) i would like to have my alt, title or alias tag from my link put in that additional attribute field. Kind of like using a %%emailaddress%%as an additional attribute. Does that make more sense?
Answer: If you have Web Analytics Connector (WAC) set up, you can automatically append the __AdditionalEmailAttribute1 to your links. If you need to append an additional parameter to your link, you can create up to 5 AdditionalEmailAttributes:

Optional field that lets you specify up to five email attributes on
  CREATE or RETRIEVE calls. Used to capture analytics or other metadata.
  Additional attributes are __AdditionalEmailAttribute 2,
  __AdditionalEmailAttribute3, and so on.

You are likely using Subscriber ID in your WAC settings since Google Analytics (you mentioned UTM tracking) stopped accepted PII information like Email Address. So you can contact support to add an %%emailaddr%% and append to your URL or use one of the 5 AdditionalEmailAttributes.
Or if you need to add the email address to the alias tag for the a href link then you can manually add that:
Comment: Thanks Jackson. We did just turn on our WAC and  __AdditionalEmailAttribute's. I was appending the utm values manually previously and had a unique content= value for each link in the email.
I am looking to see if I can do the same thing by having the __AdditionalEmailAttribute5 dynamically pull in either the alt, title, or alias tag from my unique link and put it in that __AdditionalEmailAttribute5 field. I thought I may be able to do it with ampscript. I know this might sound a little repetitious since the text i am wanting to add is already in my link but there is a reason.
Comment: You'll need to assign a variable to either the alt, title, or alias and use it for __AdditionalEmailAttribute5. Otherwise you can use these personalization strings: https://help.salesforce.com/articleView?id=mc_es_available_personalization_strings.htm&type=5
Comment: Thanks Jackson. That is what I am looking for. I am somewhat new to ampscirpt. could you tell me what adding the variable would look like?
Comment: BTW. i did try adding the personalization string of %%linkname%% as the description states that it is the Descriptive name of a hyperlink, known as the link alias, but it did not work. Just gave me back this "utm_content=%%linkname%%"
Comment: Not entirely sure what you need to do with the alias. Maybe something like this? `%%[ set @alias = "whatever"]%% `


Given that fat has a lower specific heat than water, why do meats with higher fat content take longer to cook?

Question: Meats with a low fat content, like shrimp and chicken breast are often suggested to be cooked at a high temperature for a short period of time.  However meats with a higher fat content, such as beef brisket and pork ribs, are often to suggested to be cooked low and slow. Oil has a lower specific heat than water which means it heats up faster. Given this, I would expect high fat meats to have shorter cook times. Why is it the reverse?
Comment: the fat insulates the deep insides from the heat, so heat takes longer to reach the middle than on watery lean cuts, since water is a great conductor of heat. Also the bones of ribs are a heat sink, and brisket has all sorts of weird substances you need to melt away.
Answer: The cuts you are talking abut don't just have fat, they have collagen. Collagen requires long cooking in order to be converted to gelatin and stop the meat being tough and chewy, and to add that delicious richness to the cooking liquor and succulence to the meat.
Answer: Because cooking time has nothing whatsoever to do with the specific heat of the food.  It's determined by what you want the result of cooking to be.
High-fat meats (like pork and beef) can be cooked low and slow because the fat stays in the meat and keeps it moist over long cooking.  Whereas low-fat meats (like chicken breast or seafood) primarily have water, which evaporates, making them extremely dry and unpalatable if cooked long in a dry environment.
Additionally, the "high-fat" meats are more likely to be cut into large, thick portions which are suitable for slow cooking.  They don't have to be, though; consider both bacon and Mexican-style skirt steak, either of which is cut thin and then cooked "at a high temperature for a short period of time".
Plus, see spagirl's answer about collagen.


Can a trial court create precedent?

Question: It has been said that "trial courts do not create precedent." Can a trial court create precedent?
Answer: canada
Yes, trial courts can set precedent on questions of law. See generally R. v. Sullivan, 2022 SCC 19 and Re Hansard Spruce Mills, [1954] 4 D.L.R. 590 (B.C.S.C.). Trial judges of coordinate jurisdiction are bound by the ordinary principles of horizontal stare decisis to follow prior judgments made by other trial judges of the same court (subject to limited exceptions). See Sullivan, paragraphs 44 and 75:

[44] A superior court judge in first instance [i.e. a trial court] should follow prior decisions made by their own court on all questions of law, including questions of constitutional law, unless one or more of the exceptions in Spruce Mills are met.

[75] The principle of judicial comity — that judges treat fellow judges' decisions with courtesy and consideration — as well as the rule of law principles supporting stare decisis mean that prior decisions should be followed unless the Spruce Mills criteria are met. Correctly stated and applied, the Spruce Mills criteria strike the appropriate balance between the competing demands of certainty, correctness and the even-handed development of the law. Trial courts should only depart from binding decisions issued by a court of coordinate jurisdiction in three narrow circumstances:

The rationale of an earlier decision has been undermined by subsequent appellate decisions;
The earlier decision was reached per incuriam ("through carelessness" or "by inadvertence"); or
The earlier decision was not fully considered, e.g. taken in exigent circumstances.

To be clear: courts of coordinate jurisdiction are bound as a matter of stare decisis unless one of the above exceptions are established:

[57] ... [the judge] was bound to follow precedent because as a matter of horizontal stare decisis, [the previous judgment] was binding on courts of coordinate jurisdiction in the province as a matter of judicial comity, unless an exception to horizontal stare decisis was established.
Comment: This is fascinating. I think it's generally completely different in the United States.
Answer: united-states
Generally speaking, a trial court ruling does not create a legally binding precedent in the United States. A court's rulings are only binding on courts that appeal their decisions to that court.
Unlike Canada, court in the United States do not generally observe
"horizontal stare decisis". It isn't uncommon in the U.S. (in both the state and in the federal court systems) for different judges in the same trial court to rule differently on a legal issue upon which there is no binding appellate precedent.
This said, a well reasoned unofficially reported order of a trial court, usually, but not always, a federal court, reported in West's Federal Supplement Reporter, can be a persuasive precedent that informs another court's ruling on the strength of its reasoning and analysis from a presumptively impartial person, rather than because the principle of stare decisis (which is the rule that courts must follow precedents when they apply) binds or limits the court.
Trial court rulings are particularly commonly referred to in interlocutory matters like discovery disputes or bankruptcy procedures that are difficult or impossible to obtain appellate review of, to provide guidance for reasonableness in matters reviewed for abuse of discretion (like attorney fees awards), and to gain insight into rarely litigated statutes, and to gain insight into newly enacted legislation for which not enough time has passed for any binding appellate authority to exist.
Also, while it is not precedent, the doctrines of res judicata and collateral estoppel (a.k.a. "claim preclusion" and "issue preclusion") prevent re-litigation of disputes and legal issues between parties to a previous case in which they are someone legally related to them was involved.
For example, if NATIONAL CORPORATION loses a products liability lawsuit in a case against INJURED CONSUMER, in a case that is reduced to a "final judgment" on the grounds that the product they made had a defective design, the defective design ruling is binding against NATIONAL CORPORATION in a lawsuit against SECOND INJURED CONSUMER who must still, of course, prove that the defective design caused their particular injury. This could make the case of SECOND INJURED CONSUMER much easier to win.
Comment: "_a trial court ruling does not create a legally binding precedent in the United States_" — what happens if the trial court is not the lowest one in the hierarchy? Say it has to resolve a question of law (along with finding facts). Would the lower courts not be bound by the resolution? In NZ it is not uncommon for complex/high profile cases to be tried in the High Court right away; the District Court will then be bound. Can this not happen in the US?
Comment: @Greendrake This does not happen in the U.S. In U.S. law, precedents are created only in appeals (although trial court opinions can be persuasive authority on the strength of their legal reasoning alone).
Answer: new-zealand

Can a trial court create precedent?

By all means.
Certain cases get tried in the High Court, which is not the lowest one in the hierarchy:

Certain criminal cases may or must be tried in the High Court
So do some civil cases. Especially judicial reviews.

So, guess what. In any such a trial, if there is a question of law resolved (along with fact-finding), this resolution inevitably becomes a binding precedent on the District Court.

Can a trial court create precedent?


Switching left alt and left win

Question: I have a Thinkpad X230 (german layout, [edit]running linux[/edit]) and I want to switch the left win- and the left alt-key somehow with the right alt-key (AltGr) not being touched.
However, I haven't found a working solution yet. I know the question dealing with exactely this problem here on superuser (How do I swap Alt and Windows keys with xmodmap?), but the xmodmaps there just give me an error:

X Error of failed request:  BadValue (integer parameter out of range for operation)
Major opcode of failed request:  118 (X_SetModifierMapping)
Value in failed request:  0x17
Serial number of failed request:  13
Current serial number in output stream:  13

And as the Keyboardmodel is a different one, I don't know which setxkbmap-command is required.
What I tried so far (besides the Xmodmaps in the question mentioned above) is
* "setxkbmap -option altwin:swap_lalt_lwin", which does exactely nothing
* some xmodmap-variations (unfortunately I do not remember which combinations I tried, however, I wasn't able to make it work), my last status with most of my used commands is this one:

!!Clear Super & Alt
!clear Mod1
!clear Mod4
!remove mod1 = Alt_L
!remove mod4 = Super_L
!keycode 204 = NoSymbol NoSymbol NoSymbol NoSymbol
!keycode 205 = NoSymbol NoSymbol NoSymbol NoSymbol
!keycode 206 = NoSymbol NoSymbol NoSymbol NoSymbol
!keycode 207 = NoSymbol NoSymbol NoSymbol NoSymbol
!
!keycode 64 = Super_L Super_L Super_L Super_L
!keycode 133 = Alt_L Alt_L Alt_L Alt_L
!keysym Alt_L = Super_L
!keysym Super_L = Alt_L
!Remap Super & Alt
!add mod1    = Super_L
!add mod4    = Alt_L

Is someone experienced in using xmodmap or setxkbmap and can me help out? It would be very appreciated!
Thanks in advance!
Answer: The solution is clean and a built in function:
<code>setxkbmap -option altwin:swap_lalt_lwin
</code>
(I am using it for my Thinkpad X260) on Fedora 27 and the Windowmanager Xmonad, which uses the Super_L key as as ModMask.)

Switching left alt and left win


changing the behaviour of control signals at startup

Question: I am trying to change the default behavior of the control signals with stty.
Signals like Ctrl+C, Ctrl+D, Ctrl+Z, Ctrl+\. Can any one give me idea about how to disable and enable these signals on console with stty.
Comment: More correctly they are _special characters_ that trigger the _line discipline_ to send signals.
Answer: You can "trap" commands (and key combinations) with trap:
trap "echo CTRL+C not allowed" 2

Now when I use CTRL+C in the terminal I get this message:
CTRL+C not allowed

Or, just trap "" 2 if you simply want to trap CTRL+C without printing anything.
To clear a trap, simply do:
trap - 2

Read the man page for trap here. More information about signals and traps can be found here.
Comment: no i dont want to show any type of messages nor allow these signals to interrupt my program for some time. After some time again i need to enable these signals.
Comment: @Kumar2080 See my edit. And please **read the information** in the links I posted.
Answer: trap will not work on CTRL+Z ,when you provide CTRL+Z the handler will not
execute and your console gets non-interactive


What do you call political institutions that are not independent?

Question: If something, for example a political institution, serves only to make a false appearance that that institution exists (for example, courts or legislatures that are heavily dependent on the head of state's will in undemocratic countries), what do you call it? I thought I could use the words 'decorative' or 'decoration', but Lexico doesn't seem to support that view.
Answer: There are some specific terms such as:
-kangaroo court: "a court that ignores recognized standards of law or justice and often carries little or no official standing in the territory within which it resides, or it may ignore due process and come to a predetermined conclusion"
-puppet state/puppet government: a state/government that is legally independent but really dependent on another power e.g. the dictator or a colonial power
In general the term puppet can be used in front of most institutions.


Do I have to keep saying "_____ thought,"after I put italics?

Question: Every time a character is thinking something is it necessary to put "_____thought," if there is italics, so shouldnt they already know that's what the character was thinking not the narrator speaking?
Answer: First, you'd need to establish the convention that you use italics for thoughts. I've seen different books use italics for thoughts, telepathy, foreign-language inserts, and more. The reader would need to know what you use italics for. (See, here I've used italics to stress a word.)
Once you've established the convention, and so long as it's clear who's thinking the thought, (I'm assuming we're only hearing the POV character's thoughts?) you don't need to repeat the "_____ thought" part - it's sufficiently clear without, so reiterating it is redundant.
If you're inside the heads of multiple characters, you'd still need to make clear every time who's doing the thinking. But this can be self-evident from context, just like it is in dialogue.
Comment: I love answering questions like this, but you beat me to it. All I might add (or paraphrase) is to simply follow the rules for quotes. You don't have to say "___ said" every time; the same holds true for "___ thought".
Comment: Note also that, if you are getting inside multiple characters' heads in the same scene, you may want to designate one of them as the viewpoint character (and remove the other's inner thoughts, because people usually cannot read minds).
Comment: @Kevin not necessarily. Story might be about a telepathic character who *can* read minds.
Answer: No
You merely need to ensure the reader understands who is thinking, and that the text is thought.
E.g.
"Trevor stood before her, like an ebony sculpture, even more imposing than she remembered.
Gods, my father hasn't changed. Morgan thought to herself."
or
"Trevor stood before her, like an ebony sculpture, even more imposing than she remembered.
Gods, my father hasn't changed. The thought sluiced through Morgan's mind.
or
"Trevor stood before Morgan, erasing her preoccupations. He was an ebony sculpture, even more imposing than she remembered.
Gods, my father hasn't changed..."
or
"Gods, my father hasn't changed... The thought came unbidden as Trevor stood before her; an ebony sculpture, even more imposing than she remembered."
etc, etc, etc
Answer: If you establish it as a convention in your novel, no.
Being honest, while there are uses for outright stating thoughts as streams of dialogue-like prose, it's still a very telly form of exposition. Creative narration and use of motifs can bring about the same effect in POV-based narration as outright stating a particular stream of consciousness in italics.
Answer: My own convention is to format thoughts much like dialogue, in italics, without the quotes. So I will often start a new paragraph, in italics.
He's trying to trick me.
I will intentionally, early on, add the 'she thought' tag, to establish this convention:

He's trying to trick me, Sandra thought.

I never write to reveal the thoughts of more than one character, so this is seldom necessary, but I still do it once in a while because it sounds right, or especially for linkage:

He's trying to trick me, Sandra thought. "I'm really not interested, okay?"

Because thoughts are often not verbal in any grammatical sense, but a mix of images and feelings and intuition, I will often describe thoughts, that lead to verbatim thoughts:

So that would explain why Mark lied about where the money came from, but why would Allen agree with him? Allen couldn't possibly know what Mark was doing, not back then. Unless he did. Unless he knew all along!

IMO thoughts expressed grammatically are rare, so I would resort to descriptive prose for them most of the time. When there is a voice or sentence in their head, it is usually short, direct and without embellishment, a declaration and not a long description. Often it is a single word: Jerk. To me that is a "believable" thought, and when I want to include it, I treat it as internal dialogue; and use all the rules of dialogue, just in italics instead of quotes.

Do I have to keep saying “_____ thought,”after I put italics?


What is sealing in a blockchain?

Question: What is meant by terms like Sealing, InstantSeal, ManualSeal, etc. (please add them here if you know more kinds of seals).
Answer: Sealing means signing a block. You put a "seal" on a block to say that this its content that doesn't get modified. If someone would try to modify it, they would invalidate the seal.
Answer: Sealing a block means adding some final consensus-related information to a block to complete the block authoring process. Sealing happens on the client-side after all transactions have been executed and and other runtime logic has completed.
When other nodes in the network import your block, they will check the seal before checking other more computationally-expensive parts of the block such as executing transactions.
The exact information included in the seal depends on the consensus engine. In PoA and PoS consensus the seal is a signature. In PoW it is the mining output.
Because sealing a block usually the final step in authoring a block, people sometimes speak of "sealing" when they are really referring to the larger authoring process. This is the case for both manual seal and instant seal. The misnomer is particularly bad in this case because manual and instant seal don't actually use a cryptographic seal. A more accurate name would be "manual authoring" and "instant authoring". Learn more about what they are in What is the difference between Babe, Aura, and Grandpa?
Comment: Could you also add a brief explanation of `InstantSeal`?
Comment: @Purple_Turtle In Instant seal, the node will automatically authorise the block the second it gets a transaction. It will not create the empty blocks on the chain.

What is sealing in a blockchain?


Gas expansion and temperature

Question: A piston is freed and the gas inside is expanded, volume will increase therefore temperature will increase too according to charles law, right? But at the same time pressure will decrease and so temperature will decrease too according to gay-lussac's law? I am very confused, which law should I consider in this case and why?
Thank you..
Comment: Charles' law relates volume and temperature at constant pressure so cannot be used as the pressure decreases unless there is an input of heat into the system.

The gas will do work in expanding so its internal energy will decrease and so the temperature will decrease.
Answer: Before you apply any law, the first thing to consider is the conditions, assumptions and special cases (if any).
Charles's Law requires constant pressure. If the pressure is not constant, then you can't use this law. Does it apply here?
For Gay-Lussac's law, you need fixed mass and fixed volume. Does it apply here?
Pressure, volume, temperature, and mass all affect each other. You need two of them to be fixed in order to get direct proportionality between the remaining two.
Answer: As LostCause points out, these named laws aren't applicable to your case. But the ideal gas equation, $pV=nRT$, (which yields these laws as special cases) is applicable (provided that the gas density isn't too high).
You'll now see that you don't have enough information to deduce what happens to the temperature using the ideal gas equation. The extra information needed usually comes from the conditions under which the gas expands. For example, we could let the piston out very slowly. This will allow heat to flow into the gas through the cylinder walls, so the gas temperature hardly changes. This is isothermal expansion. At the other extreme, we could let the piston out quickly, so hardly any heat can flow in. This is adiabatic expansion. In this case the work that the gas does pushing out the piston can come only from the gas's internal energy, and its temperature drops. There are an infinite number of different conditions under which the gas could expand.

Gas expansion and temperature


Windows not showing up in grub menu

Question: I had Arch Linux installed, but for some reason the partition where the OS was, got deleted. I also had Windows 7 Ultimate on another partition and the GRUB menu use to show it. After my Arch install was deleted, I installed Linux Mint Cinnamon 18. And since then my Windows 7 Ultimate is not showing up GRUB menu. What should I do?
Answer: Give Boot-Repair a try. I had similar problems in the past and resolved it with Boot-Repair.
Start up Mint
<code>$ sudo add-apt-repository ppa:yannubuntu/boot-repair
$ sudo apt-get update
$ sudo apt-get install -y boot-repair && boot-repair
</code>
Then follow the recommended instructions from the above link.

Windows not showing up in grub menu