How to set placeholder to dropdown in contact form 7?

Question: I am new to WordPress contact form 7 plugin and I need to add this to my contact form.. Anybody can help me please?
Answer: As per contact form 7 setting placeholder. You can use the placeholder option for the following types of form tags: text, email, url, tel, textarea, number, range, date, and captchar.
But its little bit tricky for adding custom placeholder in dropdown. Sometimes we need match custom designed form with contact form but for adding placeholder in dropdown,enter link description hereYou need to add some extra code in your theme functions.php
Here is filter that will add custom placeholder in contact form 7 dropdown menu.
Hope this will help you to add custom placeholder, happy coding !!!
Comment: If it's useful and working. Please upvote for the answer. @SandiT


Could not determine jupyterlab build status without nodejs

Question: I'm seeing this error in the terminal: "Could not determine jupyterlab build status without nodejs". Even when latest version of nodejs is installed on my PC.
Please guide what should I do?
Answer: I ran into a similar issue this morning and ended up here.  The diagnostic message appears to be harmless:
[W 07:35:51.998 LabApp] Could not determine jupyterlab build status without nodejs

However, the way I resolved it for my configuration (Windows 10, Anaconda distribution of Python 3.7) was to download NodeJS from the source.  Choose the LTS (Long Term Support) version of Node.js rather than the "Current with the latest features" edition.
Next, ensure the node executable is in the search path.  On Windows, hold the Windows key and Break.  Click on Advanced System Settings -> Environment Variables -> System Variables.  Double click PATH to edit.  Click OK until you're out.
In a new command window, run:
jupyter lab

You're looking for something like this in the output:
[I 07:16:26.721 LabApp] Node v10.15.3

Comment: best answer for sure, thanks for the full explanation and fix
Comment: Any idea how to ensure it picks up in a new environment. Since path returns node when no environment is activated, but when I try after activating an environment it doesn't return node path
Comment: @Eswar Chitirala: activate the environment and then run conda:
conda install -c conda-forge nodejs
Answer: On Unbuntu 20.04, just activate the environment and install by conda:

conda install -c conda-forge nodejs
Answer: Try the command below, follow through the prompt and see if it helps in your issue.
jupyter lab --debug

You can check your installation of npm or nodes by using
node -v
npm -v

Answer: FWIW, I got the same error message, on Win10, and just restarted the virtual environment, restarted jupyter lab and have not had the error since (several days). Doesnt help of course if there is an underlying issue:)
Answer: For Mac OS/Windows: install LTS version of Node.js from here and restart jupyter lab.
Answer: I installed it from source but it looks like a version had installed on conda that was old, which was causing this issue. If you've installed nodejs with conda  (or something similar) you will get an outdated version, uninstall it and install it from the nodejs website manually. The error will fix.
Answer: Just for completeness, on Linux Mint LMDE 5, installing with pip solved the problem:
pip install nodejs
Answer: I've just installed nodejs (in an environment other than base), but that message still persists. (Windows 11)
pip install nodejs
(I check with conda list nodejs, pip and conda know either other's installation)
Comment: Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer).
Answer: still need python binding for nodejs
sudo pip install nodejs

Comment: Is the `sudo` important? If so, please explain why. If not, then don't add duplicate answers: https://stackoverflow.com/a/72779246/


Why is normal force at the bottom dependent on normal force on top?

Question:
Why does the normal force on bottom of the track have anything to do with the normal force on top of the track? Why isn't the normal force at the bottom simply $mg$?
Comment: If the normal force at the bottom was exactly $mg$, then the normal force would cancel the gravitational force, and the net force on the car would be zero. This would mean that the car is traveling at constant velocity at this point, but it's clearly *not*, because it's changing its direction by moving in a circle.
Comment: No. I just explained why that intuition is wrong (this is a common misconception among students first taking an intro physics class!). $N_y > mg$ and is pointed upwards so that there can be a net force upward leading to the car moving in a circle. At the top, $N_y$ is pointed downward and *helps* the gravitational force move the car in a circle.
Comment: To be specific, you use Newton's 2nd Law (which involves the net force and the instantaneous acceleration) along with knowledge about the situation (e.g. that it's moving in a circle) to infer/derive what the forces should be. Your last sentence about $V_y$ is correct.
Comment: @march but $N_y$ cancels, correct?
Comment: @march oh, I get it. $ma_y \neq 0$ because there is a change in velocity.
Comment: So when looking at forces in general, we're looking at the instantaneous change in acceleration/velocity at that point? And in this case there's an instantaneous change in $V_y$ because the direction changes
Comment: @march I forgot to tag u in the last comment. Is it correct?
Answer: It is not equal to $mg$, because the body is not traversing in a straight line. Here it is circular motion, and normal reaction is always directed towards center, so here normal reaction is acting as centripetal force.
But here $mg$ is also acting, and for upper and lower semicircular tracks, it has different directions. So here we have to consider net force acting as centripetal force.
Bottom scenario:
$mg$ is acting downwards, and $N$ upwards. Net force must be upwards which acts as centripetal force.
$$N-mg=\frac{mv^2}{R_{track}}$$
$$N=mg+\frac{mv^2}{R_{track}}$$
Top scenario:
$mg,\,N$ both act downward. Net force must be downward which act as centripetal force.
$$N+mg=\frac{mv^2}{R_{track}}$$
$$N=\frac{mv^2}{R_{track}}-mg$$
Note*: the centripetal force must act always towards center. It is the force responsible for keeping the object bound to circular motion or any curvilinear motion
Answer: Normal force is a special force. According to the situation, it can be greater or lesser than $mg$. More precisely, if an object $A$ has mass $m$, and it's exerting $F$ force on the surface normal on it, then $F$ is also the normal force experienced by the object (Newton's III Law)
So, if the object is freely falling in a lift, it is not in contact of anything, and hence normal force on it is zero.
If the object is going around a vertical loop, it has to push the ground hard enough to get enough centripetal acceleration.
In your example, it is indeed a vertical loop-the-loop problem. For the car to go in a circular motion, the force should be radially inwards. At the bottom, only the track can provide such a force (which means the car would have to really press against the track).
At the top however, gravity is going to push the car downwards towards the centre, so the car can escape at sufficiently high speeds without even touching the track. (i.e. $F_N = 0$ is possible at the top; gravity would maintain the centripetal acceleration)
Answer: This really is a centripetal acceleration equation, compounded by gravity. You know when you get to a1g acceleration, the normal force at the bottom is double it's resting Force and would be a normal force of zero at the top. To get to point six at the top you would have to add 75% more centripetal acceleration, and I believe you would have a normal force of 2.2 kg at the bottom. If my math is correct your velocity would have to be 9.3 meters per second.
Answer: You need to know that a motion can be accelerated in two independent ways or any combination of these; either when there is a change in velocity, or when there is a change in direction of motion.
The above problem has a constant velocity but the direction of car at every point of the loop changes, which mean the motion is accelerated.
Newton's laws tell us that for a motion to be accelerated, a net force must act on the body.
Enters centripetal force:
If $mg$ was the only normal, it would mean there is no force to keep the car in circular motion and it would continue in a straight line which is not the case, so there must exist some mysterious force that is keeping the car from going straight, which is indeed, the centripetal force.
Imagine this: from the car's frame of reference, it would be exerting more than just its weight on the loop; if you were inside, you'd be pushed to the floor of the car.
This is why you have another force in play. I hope you can take over from here.
P.S. you intuition isn't wrong but it would apply when the car has not to move in a loop in the next lap, meaning, if it leaves the circular motion at that very precise moment when it reaches the bottom. Then, there would be no force required to keep it in circular motion and thus only mg would act in it in vertical direction.
Answer: The connection is that the centripetal force that keeps the car going in a circle is the same at the top of the track as at the bottom (because the car is travelling at a constant speed). If this centripetal force is $F$ then at the top of the track we have
$F = N_{top} + mg$
where $N_{top}$ is the normal force at the top of the track. At the bottom of the track we have
$F = N_{bot} - mg$
where $N_{bot}$ is the normal force at the bottom of the track. We can elimiate $F$ from these two equations to get
$N_{top}+mg = N_{bot}-mg \\ \Rightarrow N_{bot} = N_{top}+2mg$


How can I score wet bread dough more easily?

Question: I've noticed that it is dramatically easier to score firm bread dough than wet bread dough. But, sometimes it's good to work with a wet dough for other reasons. Any tips on how to score wet bread dough without squashing/ripping/mutilating?
Comment: Not a native English speaker am I. What does score mean here?
Comment: @AnishaKaul Specifically with bread, it's the cuts you make in the loaf before baking that then get stretched out in the oven as the bread expands. If you image search for scored bread - or just baguettes - you'll see a ton of examples of what this looks like.
Comment: @AnishaKaul In the context of breadmaking, this is a commonly used English term, and it's pretty easy to find a definition online (all you have to do is search for scoring bread). The site's in English, and while we can always try to be clear, it's not really feasible for us to define all the terms that people might not have heard before - we also want to be concise.
Comment: @AnishaKaul- score in this context means to partially cut something to weaken it. For example- when cutting glass the glass is scored with the glass cutter and then broken along the score line.
Comment: @Jefromi Can you edit the title in some way which makes it easier for non english speakers to understand?
Answer: A very sharp blade with minimum drag.
The traditional tool is called a lame- basically just a curved classic razor blade on a handle. If you make a lot of bread you might consider buying this unitasker. (link to google images of lames)
You can use a kitchen knife if yours are very sharp but I've had the best results with a straight razor blade. I've read of people using serrated blades but they always mutilated my bread.
A little bit of non stick spray will do wonders at keeping the blade from binding up in the dough.
The rest is technique. Make each score in a single cut if possible. Instructions often say to make "deliberate slashes". Plan out where you want the cut then slash confidently. Multiple slashes or slow or halting cuts will do more damage to the loaf.
Comment: Serrated blades do work reasonably well if they're pretty sharp, as opposed to the kind that only cuts because it's serrated.
Answer: If you're willing to go for a "leaf" shape, I recommend scissors. It's a very easy alternative to traditional scoring and works very well for wet dough.
Comment: Good tip! But I'm wondering what exactly is the leaf shape - do you have any pictures?
Answer: I like to use a serrated bread knife to score my dough.  It works very well and I just put it on the dough lightly and saw back and forth until I have the serrations I want.
Hope this helps!
Answer: So the key with wet dough is to proof in the fridge over night 12 hours or so depending on your fridge temp. You might want to adjust your fridge temp but you might ruin other food. usually fridge temp is way to low for any yeast activity.
Cold dough stiffens and it becomes 100000 million times easier to score. Some people put oil on the blade.


HELP with brining a Turkey and still have regular tasting gravy?

Question: So last year I made a phenomenal brine with kosher salt, pure maple syrup and a few seasonings. I loved the turkey, it was awesome. However the pan drippings that became my gravy turned out very sweet and tasted like maple syrup. I really want to brine. I need help with a brine that will make it flavorful yet give me normal tasting gravy when done.
Comment: Did you properly rinse and dry the turkey before cooking it ?
Answer: In my opinion it can't be done without cheating. A fully brined turkey will always make overly salty drippings, and a maple brined turkey will produce overly sweet/salty drippings. Some cooks have successfully made gravy with brined turkey drippings (see Can you make pan gravy if the turkey was brined?), but I suspect that those turkeys were under brined.
A solution is to buy inexpensive turkey parts. Necks, wings, backs and giblets (if you like them) are all good for this. Don't brine them, just roast them in a another pan at the same time you roast the brined turkey. Use those drippings for your gravy. You can cook those parts way past the temperature that you cook the brined turkey to give you more drippings and yummy brown bits for gravy. The meat can then be shredded to add to your dressing or gravy if you like.
Little by little you can add some of the drippings from the brined turkey to the drippings from the miscellaneous parts, tasting after each addition. Carefully adding some of the brined drippings to the plain drippings could result in a spectacular gravy.
Answer: Using unsalted offal bits may temper the saltiness but I agree it will probably always have a strong taste of salt.
If you can get a chicken with the Giblets then you may want to roast it with the Giblets present, this may also improve the meaty flavour of your gravy.


What's the "Hello, World!" for proof assistants?

Question: Many programming language tutorials start with a simple program which just outputs "Hello, World!" to the console or another output. For the various proof assistants, is there some widely-known equivalent for this? Maybe a simple proof by induction?
Comment: I can write a detailed answer promoting coq.io if you upvote this comment 5 times :-)
Comment: Why not an actual hello world? You can certainly do that with coq, cf. eg. http://coq-blog.clarus.me/tutorial-a-hello-world-in-coq.html
Comment: Also I could add as separate answer about building Formal Web Site with Lean 4: https://lean4.dev/ on the same contract conditions. Btw lean4.dev has its own package manager https://bum.pm written also in Lean 4 (before official). Leonardo de Moura gave a like to us, give us yours! :-)
Answer: The proof of commutativity for addition of natural numbers has been used as a simple pedagogical example in some places, including the Wikipedia page for Coq. It is a bit longer than just "Hello World" but it is an example that is about as simple as one can imagine for a proof, while still remaining non-trivial. This is what the proof term (quoted from the Wikipedia page) would look like for Coq:
plus_comm =
fun n m : nat =>
nat_ind (fun n0 : nat => n0 + m = m + n0)
  (plus_n_0 m)
  (fun (y : nat) (H : y + m = m + y) =>
   eq_ind (S (m + y))
     (fun n0 : nat => S (y + m) = n0)
     (f_equal S H)
     (m + S y)
     (plus_n_Sm m y)) n
     : forall n m : nat, n + m = m + n

However, Coq users rarely write such proof terms directly. Rather, they prove theorems with tactics. Here is a tactic-based proof of the same theorem (leading to a slightly different proof term):
Lemma plus_comm : forall n m, n + m = m + n.
  intros; induction n.
  - simpl.
    symmetry.
    apply Nat.add_0_r.
  - simpl.
    rewrite Nat.add_succ_r.
    f_equal.
    apply IHn.
Qed.

Comment: Would it be interesting to write a question asking for the proofs of commutativity of the natural numbers in different proof assistants, so one can compare them?
Comment: @WillSawin That sounds like it could be a useful question, but I would recommend maybe to wait a bit for the site to cool-down a bit.
Comment: Thanks for adding this answer. Please consider adding `Require Import Coq.Arith.PeanoNat.` (or another means of getting `Nat` in scope (?)) to the top of the proof to make it self-contained. I tried following along in this proof in ProofGeneral and wasn't sure where `Nat.add_0_r` lived.
Comment: @Zimmi48, please see somment by Gregory Nisbet!
Comment: Indeed, just `Require Import Arith.` or what Gregory wrote should work.
Answer: These might be somewhat advanced for an honest "Hello, world!" but I think that the irrationality of $\sqrt 2$ and the infinitude of primes are two very common get-the-feet-wet projects for people looking at the mathematical side of proof assistants.
The infinitude of primes in different languages:

Agda
Coq
Lean
Metamath
Comment: About the proof of the irrationality of the square root of 2: Freek Wiedijk wrote a [book](http://www.cs.ru.nl/~freek/comparison/comparison.pdf) about the comparison of the various existing proof assistants (in the year 2007) referring exactly to this theorem.
Answer:
Defining lists, usually:

list A := Nil | Cons of A * list A

Defining append for lists:

append Nil ys := ys
append (Cons x xs) ys := Cons x (append xs ys)

Showing that append is associative, usually:

**left as an exercise**

Of course this would look different for a proof assistant which is not based on inductive types.
Answer: Another example could be the definition of natural numbers (for type-theoretic assistants):
inductive nat : Type
| zero : nat
| succ : nat → nat

This also shows off the induction principle for naturals being automatically generated, which can be quite surprising.
Comment: Maybe this, plus the definition of addition, then 2+2=4...
Comment: This is not a proof of a theorem, is it?
Comment: this wasn't stated as a requirement in the question, and I guess this proves things like `nat.rec`
Answer: A "Hello, World!" of proof assistants should be available in as many languages as possible.  As pointed out by Clément in his answer to a different question, there are around twenty provably-correct implementations of the "leftpad" function at the lets-prove-leftpad repository.  Quoting from that repository:

Leftpad is a function that takes a character, a length, and a string, and pads the string to that length. It pads it by adding the character to the left. So it's adding padding on the left. Leftpad.
>> leftpad('!', 5, "foo")
!!foo
>> leftpad('!', 0, "foo")
foo

This is more relevant if you are interested in software verification than mathematical proofs, as it has a rather different flavours than the examples of natural numbers or lists that showcase the use of inductive types.
Answer: Many proof assistants based on an intensional type theory equipped with inductive types may choose the commutativity (or simpler, associativity) of addition as the "Hello world".
This shows two important things:

The proof assistant is able to recognize the natural numbers as a legitimate definition, and to generate the appropriate induction/recursion principle for it.
The proof assistant is able to handle equality and quantifiers. This shows that it has basic functionalities in logic and reasoning, without which it may no longer be regarded as a proof assistant.

However it is also a little bit away from the "day-to-day math". But considering that a "Hello world" program is also quite far from industrial programs, it's totally acceptable.
Answer: Proving some elementary results on propositions but using the language of types could be a good option for languages where that makes sense, since it makes clear some of the motivation behind the "propositions as types" paradigm. Here are what two of these results could look like in Agda:
data ∅ : Set where

double-negation : {P : Set} → P → ((P → ∅) → ∅)
double-negation p f = f p

triple-negation : {P : Set} → (((P → ∅) → ∅) → ∅) → (P → ∅)
triple-negation f p = f λ g → g p

Beginners could also ponder about how to simplify the proof of the second result using the first.
Answer: For a "Hello World" for proof assistants I personally use the fact that reversing a list is an involution:
theorem rev_rev {l : List α} : l.reverse.reverse = l

Usually, the proof showcases induction, using lemmas (manually or automatically), rewriting and working with equality. The equality might not be that straightforward in, say, cubical provers.
Answer: Most answers seem to be metaphorical, but a literal answer also seems warranted as many proof assistants are programming languages too.  In Lean:
def main : IO Unit := IO.println "Hello, world!"


What's the difference between normal beer and trappist?

Question: What's the difference between normal beer and trappist? Is there any difference in flavour or brewing style?
Comment: What is a "normal" beer. For me Trappist beer IS normal beer.
Answer: Trappist beers are all abbey beers, but not all abbey beers are trappist. It's a bit like champagne, it's a protected product name to designate a certain type of classical brewn beers.Trappist is the enumeration of beers brew within the walls of an abbey inhabitted by the Trappist monks of the Tre Fontane.
Currently (Okt. 2015) there are 11 recognized trappists, of which 10 are actively producing:
Six Belgian trappists:

Chimay
Orval
Westmalle
Westvleteren (St. Sixtus)
Achel (St.  Benedictus of the Achelse kluis)
Rochefort

Netherlands:

La Trappe (Brouwerij de Koningshoeven)
Zundert (Brouwerij Abdij Maria Toevlucht)

Austria:

Stift Engelszell

Italy:

Tre Fontane Abbey

United States of America:

Spencer

There's also one aspiring Trappist brewery in the US named St. Joseph's Abbey.
There are some strict rules to obtain "Authentic Trappiste Product":

The beer must be brewed within the walls of a Trappist monastery,
either by the monks themselves or under their supervision.
The brewery must be of secondary importance within the monastery and
it should witness to the business practices proper to a monastic way
of life
The brewery is not intended to be a profit-making venture.  The
income covers the living expenses of the monks and the maintenance
of the buildings and grounds.  Whatever remains is donated to
charity for social work and to help persons in need.

There are some standardized naming conventions, for instance the Double (orginally used by Westmalle) is a brown ale which has an alcohol level of around 7%.
The Tripple is another name first used by Westmalle, which are often blond and have an alcohol level of about 8% to 10%.
For future reference you can always visit the Trappiste website here.
Comment: Although not strictly necessary, it would be nice if you could elaborate on where you obtained this information - whether you're drawing from external sources or your own experience, noting that in the answer can be helpful to future readers.
Comment: @BryanCain that actually changed recently, they only got their first batch last month I think.
Comment: I'll update the answer :)
Comment: Your own link also talks about the Spencer in the US, which you left out.
Comment: Ah  yes, I missed the date of your original answer - sorry about that.
Answer: Lucas Kauffman has given a lot of details about the question you asked. I want only to add that all Trappist beers have this logo

on their label except Westvleteren beer which does not have any kind of label on the bottle.
Answer: The wort in a trappist beer contains several kinds of malt and 'candy' (sugar) to increase the alcohol content.
Comment: Not necessarily. There are many styles of beer brewed by the Trappists. The tripels would have candi sugar, but lower gravity ones may not. The various styles use several kinds of malt, but so do most British ales, American micro-brews, etc.


Applying Stone -Weierstrass theorem

Question: Prove or disprove that vector space generated by $\{1\}$ and $\{x^{an+b}: n \in \mathbb{N}\}$ where $a,b$ are fixed positive integers is dense in $C([0,1])$
Comment: Please give your thoughts on this. What have you tried?
Comment: If $a|b$ , it can be proved.
Answer: The beautiful result of Muntz-Szasz says that if $0<p_1<p_2 < \dots,$ then the linear span of $ \{1, t^{p_1}, t^{p_2}, \dots \}$ is dense in $C([0,1])$ iff
$$\sum_{n=1}^{\infty}\frac{1}{p_n}=\infty.$$
The answer to this specific problem is then yes. But there may be a more elementary way.
Answer: Here is an elementary proof of the statement. If $a\mid b$ then the element
$$x^{an+b}x^{am+b} = x^{a\left(n+m+\frac{b}{a}\right)+a}$$
is an element of the vectorspace for all $n,m\in\mathbb{N}$ making it a subalgebra of $C([0,1])$. Since the vectorspace separate points and contains a non-zero constant function the desired result follows from the Stone-Weierstrass theorem. This can in fact also be proven using the weaker Weierstrass approximation theorem (WA) and for the case $a\not\mid b$ proven below this is all we will need.
If $f(x)\in C([0,1])$ then $f(x^{1/a})\in C([0,1])$ so the problem is equivalent to proving that the vector space $$A_c=\text{span}\{1,x^{1+c},x^{2+c},x^{3+c},\ldots\}$$ where $c = \frac{b}{a}$ is dense in $C([0,1])$. We can without loss of generality assume $0<c<1$.
Fix $\epsilon>0$. By WA there exists a polynomial $P_\epsilon(x)$ that approximate $f(x^{1/a})$ to (uniform) accuracy $\frac{\epsilon}{2}$ on $[0,1]$. Next we have that the function $\frac{P_\epsilon(x)-P_\epsilon(0)}{x^c} \in C([0,1])$ since $c < 1$ so again by WA there exists a polynomial $Q_\epsilon(x)$ that approximate it to (uniform) accuracy $\frac{\epsilon}{2}$ on $[0,1]$.
We now have that the function $$R_\epsilon(x) \equiv P_\epsilon(0) + x^c Q_\epsilon(x)$$
is an element of $A_c$ which satisfy
$$|f(x^{1/a})-R_\epsilon(x)| \leq |f(x^{1/a})-P_\epsilon(x)| + |P_\epsilon(x) - P_\epsilon(0) - x^cQ_\epsilon(x)|\\ \leq \frac{\epsilon}{2} + \left|x^c\right|\left|\frac{P_\epsilon(x)-P_\epsilon(0)}{x^c} - Q_\epsilon\right| \leq \frac{\epsilon}{2} + \frac{\epsilon}{2} = \epsilon$$
where $|\cdot|$ is the uniform norm. Since $f$ and $\epsilon$ was abitrary it follows that $A_c$ is dense in $C([0,1])$.
Comment: Great! For me, this is a nice approach. I don't see  any mistake. Thank you very much. Really helpful.

Applying Stone -Weierstrass theorem


Torque - Why does a block topple and net torque when net force is non-zero?

Question:
Suppose there's an inclined plane with friction $\mu$ (possibly $\mu = 0$), and there's a rigid cuboid block on it. Now while it's physically intuitive to me that the block will topple over only when it's very tall, but in the below picture after some gory calculation, it looks like the net torque around $P$ is nonzero?

Also, through where the normal force acts? Somewhere I read that it acts through the center of mass, but in a video, I was watching regarding toppling it somehow magically shifted to the perpendicular to the plane at point P (bottom right of the block)!

Suppose I have a rigid body with a net force acting on it $\mathbf{\vec{F}}$. Now the net acceleration of the centre of mass would be $\mathbf{\vec{a_{cm}}} = \frac{\mathbf{\vec{F}}}{M}$. Now when $\mathbf{\vec{F}} = 0$, it's easy to see if the body will spin or not - we should just calculate $\tau_x, \tau_y, \tau_z$ through any axes parallel to the $x,y,z$ axis respectively and check if they equal to zero or not. But when $\mathbf{\vec{F}} \neq 0$, then how we know if a body will spin or not? Through which axis we need to calculate the torque? (It may happen, say, for some axis parallel to the $x$ axis the torque is nonzero though for some other axis parallel to the $x$ axis !)
Comment: Why do you think the normal should always pass through the c.o.m.? See [this question](https://physics.stackexchange.com/questions/314729/does-the-normal-reaction-shift-when-a-force-is-applied?noredirect=1&lq=1) .. and [this one might be helpful as well](https://physics.stackexchange.com/questions/322239/where-does-the-reaction-force-act-does-it-act-on-the-centre-of-mass)
Answer: Let's start with $\theta=0$. As the block rests on a horizontal plane, the net plane reaction force does indeed act through the center of the bottom face. On a microscopic level, the block deforms the surface underneath equally, so each subforce $df$ acting on a each subarea $dA$ (pressure) is the same, resulting in a net reaction torque as if the net reaction force was acting through the center.
Now let's incline the plane slightly ($theta>0$). At the very first moment, we have ruined the torque balance (the torque of gravity has increased while the torque of reaction force has not). The block starts to rotate clockwise. As it has rotated very-very-very tiny angle, it dents the plane in the front more and release the deformation in the rear. So pressure becomes not the same across the bottom face: it is larger closer to the point P. Macroscopically, it results in the net reaction force shifting its application point towards point P, and the torque balance is restored.
As we increase $\theta$, the application point is shifting closer and closer to P and at some $\theta$ it has nowhere to go, as it reaches P. That's why when your video is actually discussing the toppling moment, it has the reaction force acting through P.
The toppling takes place when focusing all the reaction force in the end point of the face (point P) isn't enough to restore the torque balance.
P.S. But if you in some way provide the application point with the means to go further, you can prevent the toppling. That's how you can perform Michael Jackson moves on skis.
Answer: Good questions all.  I'll answer them out of order.

Question 2:  The normal force can act anywhere it needs to along the surface of contact.  More precisely, it can act everywhere along the surface of contact:  the single vector you've drawn is really the result of skillions of tiny vectors all along the contact surface.  We can define a "center of force" of all these infinitesimal force vectors, similar to the idea of a "center of mass" for a bunch of masses.  We can then mentally replace all of these infinitesimal force vectors with a single normal force vector whose magnitude is the sum of all the infinitesimal vectors, and which acts at the "center of force".   From this argument, though, it should be evident that the "center of force" can be anywhere along the contact surface;  the only restriction is that it can't lie outside of the surface of contact.  The  distribution of normal force along the surface can't actually be determined from the laws of statics acting on rigid bodies, and so you can't really calculate it a priori.  Effectively, this is an indeterminate system if you don't use the fact that the net torque is zero, and you'd have to resort to elasticity and deformation techniques.
Question 1:  From above, we know that the position of the "center of force" for the normal force can shift.  This means that if we know that the block is static, we can use this fact to figure out where the "center of force" must be:  it's the location that is necessary to balance out the gravitational torque about $P$.  (Or more generally, the normal force acts at the point that is necessary to make the net torque about any point vanish.)    To illustrate this, imagine slowly increasing $\theta$ from 0.  When the angle $\theta$ is near zero, there is a relatively large positive (CCW) torque about $P$ due to gravity, and so the normal force must act relatively far away from $P$ to balance this torque out.  In fact, if you do the gory math, you'll find that it does indeed act through the CM.  However, if we increase $\theta$, then the lever arm of the gravitational force about $P$ will decrease;  and this means that the gravitational torque will decrease.  The torque about $P$ from the normal force must therefore decrease as well.  But the normal force is constrained by the fact that the block isn't accelerating;  and so the only way for the normal torque to decrease is for its lever arm to decrease.  In the limit where the block is about to topple over, the gravitational force acts directly through $P$, with zero torque;  and so the normal force must also exert zero torque, and therefore its "center of force" must be at $P$ as well.  Finally, we see from this sort of argument that a tall block will be more likely to topple than a short block.  A block will fall over once its CM moves past the point $P$ horizontally:  at that point, the gravity will exert a negative (CW) torque, and there is no possible source of positive torque to counteract it.  So it will start pivoting in a clockwise direction about $P$.  A bit of geometry should convince you that it takes a smaller angle for this to happen for a taller block than for a short block.
Question 3:  Even if a body is accelerating, it is still the case that the torque measured about the CM is the rate of change of angular momentum about the CM:
$$
\vec{\tau}_{CM} = \frac{d \vec{L}_{CM}}{dt}.
$$
In particular, if the torque about the CM vanishes, the body's rate of rotation will not change.  This isn't an entirely trivial theorem, but it is in fact true;  consult an intermediate-level text on classical mechanics for a proof.
Comment: Thanks, but regarding one part of my Question #1, why does a tall block topples while a short block doesn't when placed on the same inclined plane ? Also, we're backcalculating "centre of reaction force" based on what happens, but how do we predict it before knowing the result ?
Answer:
after some gory calculation, it looks like the net torque around P is nonzero?

If the block is static and sitting on the ramp, then the net torque you calculate about any point should be zero.
You didn't say if the block were sitting or sliding, but the sliding case is different.  If it's sliding, then it's probably accelerating, and your axis of choice ($P$) is no longer at rest in any inertial frame.  Since it's now in a non-inertial frame, fictitious forces appear in the frame in the opposite direction of the acceleration.  If you add this fictitious force (acting through the center of mass), then you'll find the net torque is once again zero (or the block is tumbling).
I think this answers your third question as well.  All the points are equal, but if your considered axis is the center of mass, you can ignore the acceleration (because the fictitious force acts as though it passes through that point, so torque there is also zero).


Is there a way to crack/recover password for MDE file?

Question: I have a mde file which i had created long back and need to do some changes. Now i don't have the source code or back up of mdb file. Is there a way to get the mdb file. I googled but most of the links are for excel. Can any expert guide me on this issue
Comment: An mde is compiled. There is no way back.
Comment: @Remou Apparently there is, although probably not easily: http://www.everythingaccess.com/mdeconversion_faqs.htm
Answer: As far as I know, the only service that can recover an MDE/ACCDe is provided by the guys at EverythingAccess.
I do not know about the quality/cost of that service, but the implementation of some of their other products show an intimate knowledge of MS Access internals that I have never seen elsewhere.
Pure wizardry.


The Geiger Counter

Question: In my class, we talked about the GM-counter and we were shown a graph with the voltage on the x-axis and intensity on the y-axis. But I do not understand why the graph has the characteristics it has, such as under a certain voltage it does not work, then it hits a plateau and suddenly it goes up again. I asked my teacher for clarification, but he was rather vague. He said that the particles need a certain voltage to get ionized (I understand this partly), but he also said that there was a continuous discharge above a certain voltage (the part I do not completely understand). I could not find the same graph as in my text book but I found one similar enough, so I have enclosed that picture. I hope someone can help me understand this concept. Thank you in advance.
Comment: https://en.wikipedia.org/wiki/Townsend_discharge
Answer: "Intensity" is the count rate, the number of voltage pulses with a height over a certain threshold value.
There is always a spread in pulse heights. A larger bias voltage will make all pulses higher. When all events due to radioactivity are higher than the threshold value, there is a plateau in count rate. This is the bias voltage that one wants to have. The count rate is stable then.
When the bias voltage gets too high, there will be spontaneous discharges that are not due to radioactivity. This must be avoided.
Comment: Thank you for your reply! I understand why the intensity goes up again now, but this part 'There is always a spread in pulse heights. A larger bias voltage will make all pulses higher. When all events due to radioactivity are higher than the threshold value, there is a plateau in count rate.' did not make much sense to me. Could you clarify please?
Comment: @YassinB. When a gamma photon or a beta electron ionizes an atom in the GM tube, it depends on where in the tube this happens how large the charge pulse on the central wire will be.  One wants all of those pulses to be counted,  so one wants them all to be large enough to be higher than the discriminator threshold. When the bias voltage is too low, one only gets maybe half of them. Or maybe 40 % when there is a little bit of change in voltage or in temperature.  So one wants the bias voltage to be on the plateau.
Comment: Thanks again for taking the effort! If I understand correctly you want to hit that plateau so that the particle will be ionized wherever it is in the tube? So the counting is most optimal. That makes sense, I think that I understand it now.
Comment: @YassinB. Yes, one wants the ionization events to be multiplied (avalanche effect) so that the charge pulse on the central wire is large enough for the discriminator threshold.

The Geiger Counter


Install Boost.Log on Fedora 17

Question: I am trying to install Boost.Log on Fedora 17 and already did yum install boost-*. All related tutorials, and answers to similar questions involve moving lib/log into boost source directory and executing bootstrap.sh. I cannot find the boost source directory, or the bootstrap.sh file in my system (did find / -name '*bootstrap.sh' 2> /dev/null). All I can find is /usr/share/boost-build/ with lots of jam files in it. Concluding that the yum installation does not contain the source directory and bootstrap.sh, I tried to build it manually but the Boost.Log source files include windows specific headers and I got double confused. Can anyone shed a light on this?
Answer: Wrote the following Makefile to compile and install, which does not include files referring to windows.h, I believe it works:
SRCS= attribute_name.cpp attribute_set.cpp attribute_values_view.cpp \
      code_conversion.cpp core.cpp \
      default_filter_factory.cpp default_sink.cpp event.cpp \
      exceptions.cpp filter_parser.cpp \
      formatter_parser.cpp global_logger_storage.cpp init_from_settings.cpp \
      init_from_stream.cpp light_rw_mutex.cpp named_scope.cpp \
      once_block.cpp parser_utils.cpp process_id.cpp \
      record_ostream.cpp severity_level.cpp syslog_backend.cpp \
      text_file_backend.cpp text_ostream_backend.cpp thread_id.cpp \
      threadsafe_queue.cpp thread_specific.cpp timer.cpp \
      timestamp.cpp trivial.cpp
OBJS=$(SRCS:.cpp=.o)
CXXFLAGS=-std=c++11 -DBOOST_FILESYSTEM_VERSION=2
libboost_log.so: $(OBJS)
  g++ -shared $^ -o $@ -lpthread -lboost_system -lboost_thread-mt -lrt -lboost_filesystem
%.o: %.cpp
  g++ $(CXXFLAGS) -fPIC -c $^ -o $@
install:
  cp libboost_log.so /usr/lib
clean:
  rm *.o

Answer: It turns out that the main build tool in the current Fedora repo's yum boost-build package is called "bjam" and not "b2" (as implied by the latest documentation).
So, if you can't find b2 use bjam.

Install Boost.Log on Fedora 17


How can we use same domain for employee email and system emails?

Question: Suppose we have a website www.abc.com. We want to send (one way) system emails to users (for email verification, password reset etc) which may be sent from email@example.com and firstname.lastname@example.com. We also want our employees to have email addresses (two way) like email@example.com (HR guys, customer-support guys etc), using which they can send and receive emails.
I am planning to look into sendGrid (system mails) and google (employee mails).
What I don't understand is that how the mappings are done? Like, when a mail is sent by some customer to firstname.lastname@example.com, how will it be sent to an employee's mail rather that being listened by sendGrid? And while sending mails from our side, how sendGrid is able to map to our domain? I want to know where and how all these mappings exist.
Comment: I dont know anything about sendGrid so that might have an influence on the outcome, but mail account from the same domain are quite normal.
Answer: One server needs to be configured to receive the emails for your domain.   It sounds like you are choosing Google for this.   To make this happen you need to change your DNS MX records to the values that Google gives you when you sign up for their system.
You need to then configure it so multiple servers can send mail on behalf of your domain.   Traditionally any server could send email from your domain and no configuration was needed to make this happen.   These days, mail sent from random places will likely get marked as spam and discarded.  You will have to configure DKIM and/or SPF records for each server that you are allowing to send email from your domain.   Both Google and sendGrid should give you instructions for configuring one or both of those.   There is no limit to the number of servers you can configure to send email from your domain.
I have this set up for my domain.   I have the mailboxes hosted with RackSpace email and I use Amazon SES to send email from the website.   RackSpace is set up as the MX records, but both places that send have DKIM or SPF set up.


Secure communication between a mobile app and a microcontroller

Question: I have a MCU-based design that essentially controls other hardware and this MCU is controlled through an app. I was hoping someone could help me figure out how to secure this communication between the app and MCU. I've tried something like SipHash which essentially appends a hash of the message with a plain text message and this is particularly useful against man-in-the-middle attacks. The other method I tried is encrypting the command packets between the two using AES. However both these methods require storing a secret key on the app and the device. Assuming this goes into production, there will be multiple devices and app downloads. It would be quite insecure to have the same key on all the MCU devices. Is there a way to get a random key on the device and then somehow have the app get this key?
Comment: What kind of "secure" do you want? Integrity and/or authenticity and/or confidentiality? How many app instances should communicate with a single MCU? Is it viable to assign a random key to each device during production and hand it to the customer in printed form to enter into the app?
Comment: @JimmyB: The main function is to prevent anybody using network scanners to read packets between the app and the device and then spoof as either one. Not sure what you mean by "number of app instances". The initial key exchange would happen once and then using the key multiple apps (on multiple phones) would be able to control a single MCU. Now that I think about it, I could create a QR code for the key that the app can scan and get the key. This would mean that there cannot be random keys across devices.
Comment: You need full-blown encryption in some form to do this right. Tacking on a hash alone is useless; if I was the MITM I'd just rewrite your message, re-hash it, tack my new hash on, and the MCU wouldn't know any difference. There must be a pre-shared key of some sort involved. AES with a pre-shared key is probably going to be your best bet.
Answer: You can use diffie hellman algorithm (https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange) to share a secret over a public chanel.
In your case I think you should also have a central server that keeps track of who owns which device. Each device should have a unique identifier and when a user purchases a device there should be a registration process that marks the device as owned by that user in the central database.


Adaptative Web Design + UX deliverables

Question: does it make sense to create UX deliverables about wireframing information design, when nowadays we are evolving to adaptive web design, with more than 2 or 3 different layouts for different devices? how is your approach for deliverables?
Comment: In the end you have X distinct states and you need to show them all to the client. If you create static wireframes, you can deliver one wireframe per state. If your deliverables are dynamic, you can have the wireframe itself change as you let the client navigate between a number of views.
Answer: One approach is to build a complete set of wireframes using the "default" - or most highly-trafficked - screen size, then show representative examples in the other screen sizes you have designed for.
If you have a few common screen patterns, you can probably get away with showing an example (or two) of each pattern.  For any interesting one-off screens, you should probably also show these at multiple screen sizes.
All of these decisions depend on the desired fidelity-level.  Early in designs, when you are getting initial feedback and expect to change things quite a bit, I would lean towards fleshing out fewer screens and leaving more "undesigned" details in the interest of faster iterations.  The more final these are, the more you need to pin down the details.
Answer: Firstly, I just want to say that adaptive and responsive web design are two different things. Adaptive design is essentially responsive design without a fluid grid/images.
At my shop, when we build responsive sites, we build the wireframes in HTML/CSS/JS with  the actual breakpoints, then move onto visual mock-ups (6-10 JPGs for review: two pages of the site with all breakpoints), and then into dev.
We charge more for responsive design because it takes longer, requires much more thought, and is generally much more difficult to design. When comparing to a fixed-width design, typically we charge about 1.5x more for responsive design.
The purpose and value in each deliverable doesn't change whether you'd doing a fixed-width or responsive/adaptive site. They're still communication tools and clients expect to see them. Responsive design is but one approach to designing for mobile experiences. It is (in my opinion) the best approach and therefore the client should expect a markup.
Answer: Build your wireframe in HTML, and make it responsive.
Then you're set.
Comment: That's all well and good, but it takes time to build the wireframes responsively in HTML. It's much faster (and therefore cheaper) to mock up designs on paper before you get anywhere near HTML. Are you going to charge your client for the time it takes to build each responsive wireframe that they then reject for various business reasons?
Comment: @Jon W Paper (or digital mockup) is not always faster.  If the designer is a strong enough coder (and the number of screens at play is higher) JS/HTML/CSS can be _faster_ to iterate on than paper/electric-paper.  (When you need three layouts of the _same pages_, a centralized stylesheet is suddenly very much worth the effort.)  That skillset is certainly not the norm, and given that the OP used the term "deliverable", probably not assumed with this question, but seems worth saying.
Comment: Even HTML wireframes need some low-level pencil'n'paper sketches.

Adaptative Web Design + UX deliverables


API access to PowerShell Web Access?

Question: PowerShell Web Access allows you to run PowerShell cmdlets through a web browser. It shows a web based console window.
Is there any way to run cmdlets without typing them in to the console window? And is there any way to get the results back?
I'm envisaging an app that lets a non-technical user restart a print queue (for example) without having to know PowerShell. The app would display a list of print queues and then the user could select one and restart the queue. The app would essentially be a wrapper that takes care of the syntax and variables so that users don't need to know.
Is there a way to do that through PowerShell Web Access? Or is there some other way for a non Windows app to send arbitrary commands to a Windows server without reinventing the wheel?
Answer: Not with PowerShell Web Access**.  That is designed for an interactive session.
There are a few ways you could do this.  All examples are illustrative and may be outdated, insecure, etc.

Create an ASP.NET web application running C#.  Run PowerShell in the C#.  Use PowerShell remoting as needed.  Example.
Create GUI applications using Windows Presentation Foundation or WinForms.  Use PowerShell remoting as needed.  Example.
Create a services with an API (e.g. REST) that PowerShell can hit.
** OK, I lied.  Create a clunky solution that uses delegated, constrained endpoints accessed through PowerShell Web Access.
For each of the above solutions that uses PowerShell remoting, consider delegated and/or constrained endpoints. Example.

We have a web application that allows certain users to perform certain functions with certain parameters.  Uses ASP.NET backed by C# with a set of predefined PowerShell scripts and configuration of who can do what stored in a SQL DB.  For example...

Jane can restart application pool X on server Y.
John can restart service Z on server Q.
IT Support can unlock their own 'administrative' accounts from their standard accounts.
All of this can run from non-Windows computers.  Some of it might be carefully exposed to allow use on Mobile devices : )

If you have the use cases, the small overhead of designing the system and writing the code behind it will pay off quite quickly.
Cheers!

API access to PowerShell Web Access?


Deleted password under Solaris 11

Question: I have a very serious problem. I deleted my password with
passwd -d user, and now I can't log in to my account. I thought this would be a way to enter my account without entering the password by every login. Is there a standard UNIX/SOLARIS password to enter my account?
Answer: Login as root, and use
passwd yourusername

to set a new password for the user (change yourusername to the appropriate name).
If you, for whatever reason, can not login as root, you may need to put the system into single user mode ("runlevel S") and issue the command from there.  The steps for doing this is described in the official Oracle documentation and, for x86 platforms (not SPARC), boils down to

reboot -p (hmmm... this assumes that you are root)

"If the system displays the Press Any Key to Reboot prompt, press any key to reboot the system. Or, you can also use the Reset button at this prompt."
"If the system is shut down, turn the system on with the power switch."

"When the GRUB menu is displayed, select the boot entry that you want to modify, then type e to edit that entry."
"Using the arrow keys, navigate to the $multiboot line, then type –s at the end of the line."
"To exit the GRUB edit menu and boot the entry you just edited, press Control-X. If you are not using a serial console on a system with UEFI firmware, pressing F10 also boots the entry."
"Verify that the system is at run level S." ... with who -r.
"Perform the maintenance task that required the change to run level S." (this is where you use passwd yourusername).
"Reboot the system."

The above is untested as I do not have a Solaris system available.
Answer: Unless "PASSREQ=NO" is set in /etc/default/login, you'd not be able to login with out a password--it's set to YES by default as well as reco'd.
You'll have to have a SA reset your password.  If you're the only SA, you'll need to boot off media, mount the root pool, and manually edit the shadow or /etc/default/login file to get back in.
Another option if you're the only SA is that if you have any other boot environments (BE's), you could boot to an ABE, and from there mount the current BE to modify the shadow or /etc/default/login file to get back in on the current BE.

Deleted password under Solaris 11


How to display a geotiff-image with OpenLayers at the "right place"?

Question: I'm just starting with OpenLayers.
I have a georeferenced geotiff and the associated world file.
Now I want to display this image as an Overlay and google-maps as baselayer with OpenLayers.
Would be nice if anybody has some hints?
How to get started in the right way?
thanks, southente
Comment: I have the same issue here, so can you be more specific what should I do?
(the examples you provided doesn't make much sense. Thank u
Comment: This does not really answer the question. If you have a different question, you can ask it by clicking [Ask Question](http://gis.stackexchange.com/questions/ask). You can also [add a bounty](http://gis.stackexchange.com/help/privileges/set-bounties) to draw more attention to this question once you have enough [reputation](http://gis.stackexchange.com/help/whats-reputation).
Answer: OpenLayers supports projections.
You should know the current projection of your GeoTIFF and specify it to the layer, as EPSG code.
If you have no idea of your GeoTIFF file projection, use GDAL to know it.
In command line :
<code>gdalinfo ./path/to/your/geo.tif
</code>
You will get back the desired information
If you don't know the EPSG code, you can get it using http://spatialreference.org/
Some examples are on OpenLayers' website :

http://trac.osgeo.org/openlayers/browser/sandbox/camptocamp/canvas/openlayers/examples/raster-reprojection.html
http://dev.openlayers.org/examples/

Also, reading that page would give you some basics on how projections are handled.
Answer: The MapTiler (http://www.maptiler.com/) can be used to turn any GeoTIFF or an image with world file into a Google Maps overlay or into standalone web viewer with OpenLayers.
You just have to drag&drop the file into MapTiler and choose what sort of tiles you want to generate (if standard Mercator tiles a la Google Maps or tiles in local coordinate system or raster tiles).
The software will crunch the file, apply coordinate transformation to put the image on the right place and it produces a set of sample JavaScript viewers - powered by OpenLayers, Leaflet, Google Maps API, etc.
This way you get a ready to use JavaScript code showing your GeoTIFF - and you can start to add your own functionality (markers, place search, polygons, layer switcher, custom design and branding, etc).
If your file is a proper GeoTIFF with the geographical location and coordinate system definition embedded then the software will load it automatically as in this video: https://www.youtube.com/watch?v=-rSYFwcWVnc&list=PLGHe6Moaz52PiQd1mO-S9QrCjqSn1v-ay&index=12
If you have a World file, but the coordinate system information is missing you can specify it easily: http://www.maptiler.com/how-to/coordinate-systems/
To turn an ordinary scanned maps without any location info into a map overlay see this video: http://www.maptiler.com/how-to/overlay-image-over-map/


Display Touch Screen Keyboard in Windows Tablet through Unity 3D

Question: I am creating a registration page in my game in Unity. Data related features are working fine, but I am not getting the keyboard to Pop Up automatically/programatically when TextField is clicked.
Is touch screen keyboard support available in Unity for Windows 8 Tablet? I have searched a lot of forums but did not get the solution. All say that this feature is not provided for Windows yet.
I read a solution on Unity's Documentation for Android and IOS, but nothing is available for Windows.
I tried:
<code>Keyboard = TouchScreenKeyboard.Open("",TouchScreenKeyboardType.Default,false,false,true);
</code>
But this is not allowing me to create a build for Windows Store. Shows me an error:
Assets\Script\RegiPage.cs(15,10): error CS0246: The type or namespace name 'TouchScreenKeyboard' could not be found (are you missing a using directive or an assembly reference?)
Please help. Thanks in Advance
Answer: Currently, you cannot do the function you are looking for .
http://forum.unity3d.com/threads/186697-No-Keyboard-on-Windows-8


Replace yum with apt

Question: I have used Ubuntu for like two years now. I am very comfortable with the aptitude package manager. I recently switched to Fedora(16)[I still have ubuntu on my other drive :) ]
I am behind a university firewall (with all kind of data restrictions). In these circumstances I realized apt is better suited and effective when compared to yum. How can I replace yum with apt??
Comment: Wait, what? Do you understand the difference between the two? Why is one "better" than the other? You can't replace package managers (sanely) and expect to have a working system. Besides, Ubuntu and Fedora's package structures differ.
Comment: um... apologies! What i meant was the installer. It's been just two weeks since I installed fedora! Whenever i use yum,updates/primary_db and some more,will update themselves. I have to wait for them to update and with the restrictions we have it is very annoying(most of them stop midway). With apt that was not the case. I went ahead and installed apt (which is what i wanted basically...). Thanks! :)
Answer: See:
http://yum.baseurl.org/wiki/apt2yum
...replacing the distribution package manager is not a good idea.
Comment: ... unless you what?
Comment: Bad edit. Thought about qualifying it a bit, for the 1% of cases where it might be better ... but decided it was too much trouble to make sure people didn't take it as a 90% solution instead.
Answer: While this is technically possible, it is an awful idea.
However, if all you want is an apt-like frontend for rpm, there once was apt-rpm - but seems that it is dead (the project has not released anything in 4 years). You'd be better off just learning yum.

Replace yum with apt


Can I get multiple booster packs from one game?

Question: Is it possible to get multiple booster packs from the same game? I've just got one that I sold on the market and now I can't even find the game listed in the badges page on my profile.
Comment: Please re-check if the game is on the badges page. Also: Which game?
Comment: [It's not there](http://steamcommunity.com/profiles/76561197989922965/badges). Super Meat Boy
Answer: I've gotten two Booster Packs for Bit.Trip Presents: Runner2: Future Legend of Rhythm Alien!, though I opened, rather than sold, both of them.
Make sure you don't accidentally have a sort set for your badge page.
At the very least, you're not limited to a single booster pack per game.
Answer: I received two booster packs, and both games are still in my badges list. If I open the info popup of those games, it says that I'm still eligible for booster packs.
EDIT: A game is shown in the badge page if either:

You have still drops.
You have at least one card of that collection.
You played it recently.

For example Dota 2 wasn't showing in my badge page, since I don't have any card and I already used all drops. I started it and now it shows up in my badge page. Start Super Meat Boy and it will be shown.
Comment: Have you sold any of your booster packs? I've sold the Super Meat Boy Booster Pack which isn't in my list anymore but I got the Skyrim Booster Pack too which I have in my inventory and in the list.
Comment: Starting it did the trick.


Best book for tensor products

Question: I'm trying to improve my understanding of tensor of products of modules, my algebra background is one semester of undergrad algebra and one semester of graduate algebra, in which I struggled through the section on tensor products. In my graduate course, we used Dummit and Foote and I generally liked their exposition, but found the tensor product section very confusing, so I'm looking for other sources. I'm not interested in anything specific, i.e. not just limited to vector spaces, or $\mathbb{Z}$ modules, although I don't really care about the non-commutative case. Does anyone have any recommendations?
Comment: What did you find confusing in D&F? Bosch has a nice section on tensor products in his commutative algebra book and basically all of these american general algebra books have a tensor product section iirc.
Answer: You can read about tensor products all over the place.
The wikipedia page (https://en.wikipedia.org/wiki/Tensor_product_of_modules) is reasonably good and complete if you're looking for a free resource.
Personally, I'm partial to Atiyah and Macdonald's treatment in Chapter 2 of their Commutative Algebra. It has the benefit of being quite to the point and there are some useful and pleasant exercises.
You could also try Algebra by Lang.
Keith Conrad's notes: https://kconrad.math.uconn.edu/blurbs/linmultialg/tensorprod.pdf also appear quite complete, and I've heard good things about the writing.
Comment: Thanks, I will take a look at those

Best book for tensor products


Why doesn't power generated by thermal radiation violate Carnot's theorem?

Question: It seems to me that you could use thermal radiation to drive an engine that does not require a cold reservoir. Carnot's theorem states that the only way to convert heat into work is with a temperature difference, but something as simple as glowing hot steel next to a solar panel seems to violate this. What am I missing?
Comment: The efficiency of the Carnot engine is a function of the **temperature gradient** across the engine. By definition it requires reservoirs at different temperatures. Can you ask a specific question/concept that you are finding difficult?
Comment: @boyfarrell
I think it's possible to generate electricity in an environment that has an equally distributed temperature above 0K, by converting heat directly into electricity, but all examples of thermoelectric generators I can find rely on temperature gradients. The more exotic examples I can find like http://nanoscience.gatech.edu/paper/2012/12_NL_05.pdf, and http://www.ece.tamu.edu/~noise/research_files/Therm_noise_eng_ICNF_.pdf are either not cyclic, or rely on a "hidden" temperature difference.
Is the conversion of heat to electricity (or work) strictly limited to temperature differences?
Comment: Yes, photovoltaics convert 'heat' in the form of optical radiation directly to electricity and because the solar cell has a constant temperature I can see were confusion might arise. Endoreversible thermodynamic provides a nice way of viewing this problem: the solar cell is connected to two temperature reservoirs via resistors that introduce irreversibilities (look up the work of DeVos). In photovoltaics the gradient across the Carnot engine is a chemical potential and not thermal in nature. But this gradient is ultimately driven by the temperature difference between the sun and the Earth.
Comment: Let me simplify: A negatively charged mirror next to a gloving hot steel is blown away by radiation pressure. It's an electricity generator. Wheres' the heat sink?
Answer: How do you want to convert thermal radiation to heat? I imagine this is what you have in mind: even when there is no temperature gradient, every object with a nonzero temperature radiates. This is electromagnetic radiation, so if I catch it, I can drive a current and thereby produce energy.
Here is why this cannot work: We assume here that there is no temperature gradient, which means that your engine has the same temperature as the object. This means that it, too, radiates quite a bit. In fact, it will radiate at the exact same amount that it will absorb radiation from the object - otherwise the temperature would either increase or decrease which it can't as the whole system has the same temperature. This is the definition of thermodynamic equilibrium in this case: Since the only heat transfer is by radiation, absorption and emission rate must be the same. But then, once you would switch the device on and take some of the radiation and convert it into an electric current, the temperature in your engine must decrease - and suddenly you have a gradient where before, you did not. This is prohibited by the 2nd law of thermodynamics.
To take your example: Your glowing hot steel next to a solar panel works perfectly fine. And it doesn't violate anything, because you actually have a temperature gradient: You have the hot steel and the cold solar panel. Converting the heat of the steel into electric energy, the solar panel heats up. Once it reaches the temperature of the steel (well, probably before that because it melts) it will stop producing energy.
Comment: And by this you mean that there is likely not some theoretical solar panel that can convert thermal radiation into work independent of the temperature of the panel and the temperature of the object emitting thermal radiation?
Comment: Yes - at least if the first and second law of thermodynamics hold for which there is strong evidence.
Answer: Yes, usern (where n is a large number), that's what Martin means. When he writes "absorption and emission rate must be the same", you can picture it like this: For each absorption of a photon, an electron in the solar panel has to move to a higher energy level. Now, if the solar panel is already at the same energy level as your heat source, most electrons will already be at that level. So before they can absorb a photon, they have to move down. Since per your condition, both have the same temperature, there are equal amounts of electrons moving up and down - that's the "thermodynamic equilibrium" Martin talks about.
Answer: Let's say we have an air tank filled with cool air at atmospheric pressure. What happens when we heat the air in the tank a little bit? The air gains heat energy, that's the only thing that happens, although some people might say something about pressure energy, but "pressure energy" is just heat energy, nothing else.
Now with that heat energy in the tank we can drive pneumatic tools, which do not have to get hot in the process.
Can we find a heat sink in this scenario? At the end the air is a little bit warmer than originally, the air is some kind of heat sink.
Why did I write the above? Well I planned to show that you can't find any heat sink in the above scenario, but I failed.
Now let's say we have some radiation in a tank, and that tank is inside a big tank where radiation pressure is lower than in the small tank. Now we can use the radiation in the small tank to power some tools that work by radiation pressure. Those tools don't have to get hot in the process - the tool may be a turbine, in which case the big tank is the heat sink.


What is the mathematical part called in, e.g. "a 5 × 3 matrix"?

Question: I know a 5 × 3 matrix is read a five by three matrix. But, what is the mathematical part (5 × 3) called? A mathematical expression?
Comment: In this context 5x3 is the *dimensions* of the matrix.
Comment: Can you please provide more context? For example, in what kind of sentence are you trying to use the general term for 5x3?
Comment: @Andrew E.g.: "It is noticeable that in translating the noun phrase *a 5 × 3 matrix* into Persian, proper attention has been paid to the importance of the order of the numbers in a mathematical expression."
Comment: @Juya *expression* is a general term and kinda works here, but an expression usually defines a *relationship* of some kind, e.g.  **a^2 + b^2 = c^2**.  So it depends if you're talking specifically about a particular matrix definition or about math in general.   I'm curious, though, if you swap the numbers in Persian.  That would be confusing.
Comment: @Andrew If we change the order of the numbers the meaning changes in Persian just as it does in English. The first number refers to the rows and the second number to the columns of a given matrix.
Answer: Based on comments on original question:
Short answer
dimensional expression
Explanation
A mathematical expression can be considered a "phrase" consisting of more than one "term": https://math.stackexchange.com/questions/2737525/more-formal-definitions-for-equation-expression-term . So "expression" can be used to describe "5x3"
However, "mathematical" is too broad here, especially because "mathematical" can apply to 5x3, but math also applies to matrices, so a qualifier here would be good.
To further narrow down "mathematical", I chose "dimensional", because as @Andrew mentioned, "5x3" defines the dimensions of the matrix.
Comment: I agree that *expression* works by itself but it seems imprecise for this context.  I like your answer of *dimensional expression*, although *expression of the dimensions of the matrix* sounds better to me.  But then you might as well just say *dimensions* since, if you're talking about matrices, everyone already knows what you mean.


How many blocks can a cache of 1gb (1024) hold tentitively?

Question: If I use a command geth --cache=1024, how many blocks it will hold runtime in cache. And what will be the size of each block. Is there any calculation? And is there any way using which we can force to write the data present in cache to leveldb files.?
Answer: I found this explanation from a reddit user and thought it will be useful to you in order to understand some things.

Ethereum has a gas limit rather than a block size. The gas limit is a cap on both processing and storage/bandwidth because the cost of a transaction/function is fixed in units of gas for each type of instruction.
The gas limit is voted up or down by each miner and each miner
determines what gas price it is willing to accept which is like
bitcoin transaction fees but on a per gas basis rather than a per
transaction basis.
To figure out how many transactions can fit in a block you dont need
to know what the price of gas is. You just need to know how much gas a
transaction uses and divide the gas limit by that.
If the network receives a load of spam transactions that start filling
up blocks then miners have 2 choices. They can vote up the gas limit
to fit in more transactions or they can start increasing the gas price
and reject transactions that pay too low a fee. Like with bitcoin a
transaction with a low fee might still get through but it would have
to wait until a miner that accepts a lower fee (lower gas price) is
willing to let it in.
With a sustained spam attack it would just getprogressively more
costly to do transactions until either the spammer runs out of money
or the miners make so much money that they start expanding the network
capacity...

All that this user says is true, and it's very well-explained.
As you see, it works quite different from Bitcoin scheme.
EDIT
I leave here the reddit full discussion about that
Hope it helps.
Comment: That's a nice explanation, and totally true, maybe add that the link to let us get extra info please.
Comment: one more thing I want to know that when the blocks will get written to the disk ? because when I killed the node using `kill -9 ` at **block height 1000** and then started the chain again, but it did not start from the height 1000. so If my chain gets killed, how to prevent the data loss?
And Is there any way using which I can explicitly write the cache data to disk?
Comment: The data loss can be prevented by having various nodes. This makes that at least one of them can continue recording the blockchain state. And knowing that for example on ethereum there are more than 20000 nodes, it's quite difficult that all of them crash at the same time and then have data lost.

Add that if the answer was correct for you, mark it as it in order to help other users to reach it easily.
Comment: Yes. but whenever cache gets full, blocks will be get written to disk, and we will have the empty cache again. right?
Comment: Caches can also write and read data consinuously, the objective of them is to never get full, because if they are full and a new data block arrives, it'll be lost fs the process time of the cache isn't as fast as it needs to be.


How do I make all selected lights in the scene share the same power value while negating color data

Question: I have around a hundred point lights in this city scene that have variation in both light power and color. I noticed that, far into the project, the building interior room lights are not as bright as anticipated. I only want to change the light power value in the selected lights by linking object data from one light to the other lights, but that also changes the light color which is not what I wanted. How can I make the light power data the same on all selected lights without affecting color value?
Comment: why not emission nodes instead of lights?
Comment: just because i am curious: how many weeks takes this to render just one frame?
Answer: Select all your lights, go into the Object Data panel, choose the Power value you want and press AltEnter, or select all your lights, select the one with the right Power value at the end, right click on the value and Copy To Selected.


what are some possible reasons of having duplicates in sensor signal? resulting in stair-step signal?

Question:
I am using an cellphone application to record cellphone gyroscope signal. I put the sampling rate to "fastest" which means the highest sampling rate the cellphone is able to do. What is strange is that when I try to plot the signal it is stair like "broken" (I dont know what to call a signal like this if anyone can help) What I dont understand is why is it like this? is it because of the resolution? or because the phone can't do a sampling rate say "500Hz" so it samples say "100Hz" and it duplicates each value 5 times so it gets us under the illusion that it was 500 Hz? anyone have some kind of reasoning for this?
Also I would like to ask whether there is a way to interpolate or filter this kind of signal?
Answer: There are multiple possibilities.
One, as you said, cellphone may not be capable of 500Hz so it duplicates values. Did you verify whether cellphone is capable of it?
Two, gyroscope output itself may be duplicated. That is even if cellphone programs 500Hz, gyroscope may not be capable of it. Did you check data sheet of gyroscope how it reutrns values?
Three, Plotting tool will plot like this stair-case style. But that possibility may be ruled out in this case by looking at the plot and sample resolution.
So my advice would be to first check data sheet of gyroscope. It may not be able to sample at 500Hz, so it samples at lower rate and holds the value till next sample. This will result in such a kind of plot.
Answer: Your application that is triggering the internal HW of the phone System on Chip (via the OS), is triggering the sampling at lower rates (even though you set it to max)
There are also limitations of the sensor refresh rates. For ex: very comonly in today's cell phones we can get a temperature measurement at a maximum rate of 1ms (in high end phones). So, there are limitations of the application usage on the Hardware usage and also of the sensor itslef. In such cases what you see is a "sample and hold" till new value is available. Hence the stair like waveform
Answer: This appears to be either representing the lower sampled data using a zero-order hold process (which is what "sample and hold" would be referred to), or could simply be an artifact of the plotting tool (without seeing the source data). I assume the former since the OP mentioned 500 and 100 Hz sampling; so the data is sampled at 100 Hz and each value is held to provide a 500 Hz sampled signal- this is cheap and easy interpolation.
To answer the OP's question regarding interpolation or filtering: To clarify, I will refer to "original" data as the 100 Hz sampled signal and "resampled" or "interpolated" data as the 500 Hz sampled signal shown in the OP's plot.  The data has already been interpolated using a zero-order hold (hold each original value for 4 more samples) which is very simple but doing this introduces "droop" in the frequency spectrum where the amplitude rolls off over frequency. The droop is really only an issue if the data has higher frequency content relative to the original sampling rate, so this may be of no consequence for the OP's application but something to be aware of. This is also very efficient and easy to do so the droop is often accepted or subsequently compensation for in such interpolation approaches.
However to understand how to do a better interpolation, below describes a typical zero-insert and filter interpolation approach that can be performed on this data. First, since there is no information added in the additional samples provided, and they introduce frequency droop as I described, select every 5th sample as the starting data ("original data") to the process described below:
General Interpolation Process, Interpolate by I
Step 1. Insert I-1 zeros in between each of the data samples
This will upsample the data to the higher rate $If_s$. Inserting zeros preserves the original spectrum with no distortion in band, but will replicate the spectrum $I-1$ times within the new frequency span from $f=0$ to $f=If_s$ where $f_s$ is the original sampling rate and $If_s$ is the new sampling rate multiplied by the factor $I$.

Step 2. Filter out the images
To complete the interpolation, we just need to remove all the images that were added within the spectrum. This is done with an interpolation filter. Since the original spectrum is not modified in the original bandwidth in any way, then perfect interpolation would be achieved with an interpolation filter that passes the passband with no distortion and completely reject the images. Perfect is not achievable but presents the design goals of the filter balanced with the acceptable distortion.
An excellent choice for image rejection filters are linear phase multiband FIR filters readily provided by the least-squares algorithm in MATLAB/Octave and Python Scipy. A demonstration of this using a 21 tap linear phase multi-band filter with Octave follows (increasing the N provides for more rejection at the expense of filter complexity):
<code>N = 21;
coeff = firls(N, [0 .02 .18 .22 .38 .42 ]*2,[1 1 0 0 0 0]);
out = filter(coeff,1,sig);
</code>
The frequency response of the filter is shown overlaid with the zero-insert spectrum to show how the filter rejection is optimized at the image locations. Using the multi-band filter approach maximizes the rejection where it is needed for a given filter complexity (number of taps).

Resulting in the following spectrum:

An overlay of the two spectrums in vicinity of the passband signal is shown below:

A zoom in of the time domain plot shows specifically how the interpolated samples are placed in comparison to the zero-order hold (sample and hold). Note the interpolated samples have been offset by the delay of the interpolation filter.


To what extent should relevant background be discussed vs. just referenced?

Question: Is is perfectly appropriate to refer reviewers to other papers for understanding a concept or writer must include the concept in his paper too?
What should be done while keeping brevity, plagiarism and complexity of idea in mind?
Comment: Plagiarism should entirely be taken out of the equation here. Paraphrasing and appropriately referencing other people's work are standard tools for every researcher.
Comment: How do other papers in your research area do it?
Comment: Sorry, I'm not sure what you mean. Which reviewers? Papers sometimes include a Background section that cites some foundational papers. Or Related Information.
Answer: It depends.

What do your readers need to know to appreciate the main result of your paper? If your paper builds on the ideas of others, these ideas must be stated (included explicitly) and accompanied by a citation. If you simply note in passing that there are other relevant ideas, reference may be enough. Having said that, as a reviewer, I will question and discourage an excessively long list of references [1-22]. Authors should do their work to identify and tell the reader what they can find in each paper separately, not dump the whole reading list on them.
How long is your paper? If you are writing a 100+ page manuscript, then brevity is not as important as if you were restricted to 1 or 2 pages for your extended abstract.
Whom are you writing for? If this is a highly specialised journal, you can expect your readers to already know some sacred texts by heart, and a reference is sufficient. For a more general readership, you need to support your reader and tell them more , i.e. explain the main ideas and then refer to the texts.
Comment: Point 3 is the key one: Before you start writing, you should think about and define who your audience is. That includes thinking about what they will know and what you have to explain.
Comment: the readers of my domain already know some basic key points that keep repeating in almost every research paper. My problem is: I got an idea form a paper of another domain and I have implemented in my research field. To whom I am writing for, may not know that idea. So should I refer them to a specific research paper for learning basics and advanced ideas or should I have to include them in my paper. If I add them in my paper, it seems useless and I can't explain in detail as original author did. But I don't want reviewer to convey that I superficially know the idea.


Beginner: Is there another book?

Question: Is there another book I can use to study for my test?
This ARRL Ham Radio License Manual book (Level 1 ) is HORRIBLE!
I never had electronics anything in school nor electricity.
I got through the explanations about frequency even though I am still confused. One paragraph referred to a term that wasn't explained until the next page. DUH.
Then I got to the electronics section. OMG!!! It's horrible. One unfamiliar term after another after another with limited explanations.
I have absolutely no idea what this guy is talking about.
No wonder people get scared away.
If I can't find another way to learn this (no classes within 400 miles), I am just going to give up.
I haven't even gotten to the place where I learn how to use my radio yet.
Comment: You may benefit from the [ARRL Ham Radio License Support Page](http://www.arrl.org/ham-radio-license-manual). And you may be disappointed - the License Manual does not teach you how to actually use your radio. The License Manual focuses on the topics required to pass the license exam.
Comment: I'm afraid this question is off-topic because it is [a request for a shopping recommendation](http://ham.stackexchange.com/help/on-topic).
Answer: I studied for my technician class exam using Gordon West's book:
http://www.amazon.com/Technician-2014-2018-manual-HamStudy-software/dp/0945053800
It basically just goes through each question in the question pool and explains how to understand the question. I studied for about a month, just memorizing each question and getting a basic understanding. You should also supplement your learning with QRZ practice tests. Try to meet other people in your area and ask them lots of questions.
Comment: Thanks. I really *want* to understand this stuff but the explanations are so AAAARRRGGGG! horrible.
Comment: If I can add my $0.02, don't just use practice tests to study - that's not a study method, it's an ongoing "how am I doing?" benchmark. There are a few ham radio study websites out there that have actual study tools like flashcards, use one of those.  My site is https://hamstudy.org but hamexam.org also has decent ones.

Beginner: Is there another book?


Stablising the Higgs without SUSY

Question: Should the Higgs be found at the LHC, but no supersymmetry (assuming for the sake of argument that the LHC be capable of eliminating all versions of SUSY that are motivated by solving the hierarchy problem), what then? Are there alternatives for stablising the Higgs scale that don't involve SUSY (other than Randall-Sundrum)?
Answer: Randall Sundrum doesn't really work to stabilize the Higgs scale. In those cases where people claim it does, it is a low planck scale theory and it is trivially experimentally excluded. But this is not your question.
The most natural mechanism for stabilizing the Higgs is technicolor. This is the idea that the Higgs is an emergent boson, like the pion, of a strong color force.
One motivation for this is the following: suppose you got rid of the Higgs completely, so that you consider the Higgsless standard model. Do all the Fermions become massless, and the weak interactions become long range?
The answer is no. In the absence of the Higgs, QCD vacuum condensates pick up the slack. QCD with massless quarks is not so different from QCD as we know it, except for the pions being close to massless. With more flavors, there are more chiral condensates, and there are more pions, so you break flavor SU(6)xSU(6) to SU(6) (the six massless flavors), and get a full SU(6) worth of pions. You have an udsctb condensate, instead of the ud condensate with a smaller s component, as in our world.
But the up-down condensate breaks chiral symmetry, meaning it is a condensate of left-right quarks which means it breaks chiral SU(2). The chiral condensates are Higgslike, they define a direction in SU(2) space and they have a U(1) charge. Their expectation value breaks weak SU(2)xU(1) to an "electromagnetic" U(1).
But this breaking is SU(6) symmetric, meaning it cannot give a different mass to the different quarks, and flavor isospin SU(6) is exact. Further, the leptons only interact with the condensate through the U(1) interaction, and I am not sure what their masses will be.
The idea of Technicolor is to repeat the QCD story at the Higgs scale, by producing a Higgs mechnanism by a new gauge symmetry group. The technical problem is to introduce interactions with the existing standard model fermions which give the standard model fermions a proper mass. There are technical difficulties here, which lead many people to believe that the theory must be slow running to work, this is called "walking" technicolor.
Such theories stabilize the Higgs automatically, because the Higgs is produced nonperturbatively at the analog of the QCD scale for the new confining gauge field. This also explains the QCD-Higgs coincidence problem (this doesn't have a name in the literature), the 2-order of magnitude coincidence between the QCD scale which determines the mass of the proton and the Higgs scale, which determines the mass of everything else. This is strange, because a-priori, there is no relation even in SUSY models.
The Wikipedia page on this is surprisingly detailed. The space of renormalizable theories is enormously rich, and it should be possible to make the idea work. But this is probably will be much easier once there is more LHC data to give clues.
Comment: @James: So you want to protect a scalar to be massless without SUSY? This is difficult--- the only way I can think of is to make the Higgs a Goldstone boson. If it is a Goldstone boson of a broken chiral symmetry, you're back in technicolor land. If you break something else at high energies, maybe you can get a good Higgs. I believe this is the subject of "little Higgs" theories, but these are usually in the context of large extra dimensions, and I do not read large-extra-dimension papers on principle, but perhaps one should make an exception for the purpose of answering these questions.
Comment: Thanks (I didn't really mean that RS theories "stabilise" the Higgs, I just wanted to head off answers that might go in that direction).
With regard to technicolour, I am told that an SM Higgs should be distinguishable from technicolour at the LHC (indeed, shouldn't we already be seeing technipions and their ilk appearing if it were true?), so I wanted to know if there were models with a genuinely elementary scalar Higgs that isn't troubled by hierarchy.
Comment: @RonMaimon: Speaking as someone not in HEP, I've always wondered about resolutions to the Higgs fine tuning without SUSY. Do you have any comments on things like top-condensate? It seems a bit too coincidental that top-higgs (phenomenological) coupling is about unity.
Comment: @genneth: I don't know top-condensate models, I never took them seriously enough to read the papers, but you need a new force to bind the tops together and condense them, and then why doesn't it act on other generations? It seems inelegant to break generation symmetries. I think it is best to wait a few months--- we will definitely know the answer.
Comment: Thanks, that's what I suspected. It was on my mind, since the LHC seems to be putting the squeeze on vanilla SUSY. Now I need to go off and find out what it's telling us about technicolour.
Answer: Yes, there is a mechanism. It's the strong anthropic principle. For there to be consciousness, intelligent life has to evolve in a hospitable environment. With a slightly smaller hierarchy between the Planck scale and the electroweak breaking scale, massive astronomical bodies like galactic superclusters/clusters, galaxies or stars would probably collapse into black holes. Gravity becomes too strong.
Comment: you mean like a sort of cosmological-scale Zeno effect, where by simply existing we are continuously measuring a hospitable environment, and hence making a unstable vacuum to become effectively stable?
Comment: @lurscher: The Higgs instability is not a vacuum instability, it is just a way to keep the mass low compared to the Planck scale without fine tuning.

Stablising the Higgs without SUSY


How to know when to use adverb or adverbial phrase?

Question: Ex- In the sentence "look here" here is the adverb of the verb. If I write "look at here" why is this wrong? Can't I consider "at here" as the adverbial phrase with at being the preposition and here being used in noun sense. How to know  when an adverb can be used and when an adverbial phrase can be used?
Answer: "Look here" is a common phrase so people understand "here" in this context to be an adverb modifying "look." At is a preposition that requires an object. When you make the object of "look" be "here," people are expecting here to function as an adverb instead, so it sounds unnatural. "Here" is an adverb that does not require a preposition, so why would we add the preposition "at?"  When referring to a concrete noun ("look at this") then use at. When referring to a general thing, do not use at ("look over here").
In some really weird contexts, it could actually be okay to say "look at over here," but I would not try this. "Look at here" is hard to every justify even in the weirdest of contexts.
Comment: this explanation is very helpful. Thanks!!!
Comment: In other cases such as - "look in there" in is the preposition and there is a noun. So why is it correct? In the sentence "look at here" "at here" could modify look by emphasizing that the listener must particularly look at the point. So I wanted to know that sometimes we use adverb (without preposition) and sometimes a preposition phrase as adverbial clause. So is there any specific rule in English  that says when we can use an adverb and when an adverbial phrase? Or does it come naturally with practice and more reading?
Comment: @AkshitRaj It's because "look at here" has a shortened form: "look here," whereas "look in there" has no such shortened form. If you omit the "in," there is no way to tell that you are trying to say to look "in" as opposed to "at" something. Since there is no way to shorten it, you can say "look in there," but since there is a way to shorten "look at here," the shortened "look here" should always be used instead. If an adverb alone can convey the full meaning with a verb, use the adverb without the preposition. If the adverb alone is insufficient, then use the adverbial phrase.


Components of State vector in quantum mechanics

Question: I am currently learning quantum mechanics and I am trying to understand the connection between the wave function and the state vector.
Is it correct to say that the components of the state vector of a quantum system are all possible wavefunctions in that state?
Comment: Could you clarify how (if at all) your sources define/describe what state vectors and wavefunctions are?
Answer: A state vector is just a wavefunction where the domain doesn't need to be $\mathbb{R}^d$. Similarly, you can call wavefunctions vectors because the functions used in quantum mechanics (square integrable ones) are elements of a space which is closed under addition and scalar multiplication. I.e. a vector space.
A simple example is a large atom with a magnetic moment. In the Stern-Gerlach experiment, quantum fluctuations of its position are negligible but its spin (which can be up or down) is highly probabilistic. So instead of a wavefunction $\psi: \mathbb{R}^3 \to \mathbb{C}$, we just need $\psi: \{0,1\} \to \mathbb{C}$. A function from a two element set to $\mathbb{C}$ can be regarded as a two component vector so we can write this object as
\begin{align}
\left | \psi \right > = \begin{pmatrix} a \\ b \end{pmatrix}
\end{align}
where $|a|^2$ is the spin-up probability and $|b|^2$ is the spin-down probability. This is also written
\begin{align}
\left < + | \psi \right > = a, \quad \left < - | \psi \right > = b.
\end{align}
Depending on how formal you want to be, the normalization condition $|a|^2 + |b|^2 = 1$ can also be seen as an integral of $|\psi|^2$ except using the counting measure instead of the Lebesgue measure.
We can also consider the opposite case. A particle with no spin but probabilistic position on a line. Position is a continuous degree of freedom so our $\psi: \mathbb{R} \to \mathbb{C}$ will be a vector with "a continuum of components". Instead of being able to project $\left | \psi \right >$ onto just two basis states ($\left < + \right |$ or $\left < - \right |$), we will be able to project it onto infinitely many position eigenstates. One for each position we can imagine the particle to have. The eigenstates can be labelled by $\left < x \right |$ and the projection by $\left < x | \psi \right >$ which is nothing more than $\psi(x)$ in the usual function notation.
Since we now have an all-encompassing framework that accounts for both continuous and discrete degrees of freedom, we can combine the two and consider things like $\psi: \mathbb{R} \times \{0, 1\} \to \mathbb{C}$ for particles with uncertain positions and spins. This allows us to consider projections like $\left < +, x | \psi \right >$ or $\left < -, y | \psi \right >$. In this situation, textbooks often use a hybrid notation where the $2 \times \infty$ components of the state vector are written as two functions worth of components. Something like
\begin{align}
\left | \psi \right > = \begin{pmatrix} \psi_+(x) \\ \psi_-(x) \end{pmatrix}.
\end{align}
This may have given rise to your notion of a vector consisting of many wavefunctions.
Comment: Great answer, but a small note: The notation in your last equation is a bit weird, since an $x$ appears on the RHS but not on the LHS. I guess this is a common abuse of notation, but, in my experience, also a common source of confusion when first encountering Dirac notation/ intro quantum mechanics.
Answer: The relationship between wave functions and state vectors is the exact same relationship as between vector components and vectors in Euclidean vector space.
When you have an "ordinary" vector in 3D Euclidean space, given in terms of components, such as
$$\mathbf{v} = \langle 1, -2, 5 \rangle$$
you've likely seen them written with a subscript notation, e.g. $v_x = 1$, $v_y = -2$, and $v_z = 5$. You can think of this as a function from the label, here $x$, $y$, or $z$, to the corresponding component number, here $1$, $-2$, and $5$. The function, remember, is the association between the two, not how it's written.
In the case of quantum mechanics, though, the vectors can have infinitely many - even continuously many - "components". Thus, it becomes more natural to use function notation directly, and we call such a function a "wave function". In particular, $\psi(x)$ is the "$x$th component" of the vector $|\psi\rangle$ in some basis (usually the position basis given the use of $x$ as the variable [note this $x$ is not the same as the label-$x$ from before], but other bases are possible).


How is Alice so skilled in "Resident Evil: Retribution" if she was stripped of her superhuman powers?

Question: At the end of Resident Evil Retribution, Wesker injects Alice with the T-Virus, returning her former powers, which supposedly he took away in a former movie. But in this movie, we see Alice being an excellent shooter, killing everybody and monsters, being an excellent driver, being an excellent martial artist etc. Watching Alice in other movies such as Extinction, or the Final Chapter, I don't remember seeing differences between her when she had superhuman powers and when she supposedly had not. How is this possible, which are the differences between superhuman Alice and the Alice who was taken away her powers?
Comment: "which supposedly he took away in a former movie" -> he takes her powers away in the previous movie, "Resident Evil: Afterlife"
Answer: Normal Alice was a highly trained operative we never see her disobeying the laws of physics we simply see her doing things that would hurt like hell in the morning or even 5 seconds after doing it, however as a highly trained operative Alice would have the ability to push through pain and fatigue until she was unable to function or she completed her objective.
Super Alice most likely felt less pain and fatigue than normal Alice, the regenerative effects of the T-virus acting as a kind of steroid allowing her to push her body harder and to recover faster from the intense physical activity as well as giving her a slight healing factor that allowed her to survive at the end of Apocalypse.
Super Alice also had psionic abilities however it wasnt clear how voluntary these were.