Ok, there are two different ways to make the American r sound. They both think they are right and that the other is wrong.   Make the r sound by retroflexing the tongue:      Make the r sound by retracting the tongue:     Note: Both methods agree that the tongue should not touch anything in the mouth.  I think the retroflexed r is more natural. I have no way to make the retracted tongue because it is very uncomfortable for me.  So which one is correct?
Following , this is how we correctly make the r sound:   Let the throat vibrate since it is voiced. Round the lip a little. Raise the tip of the tongue towards the hard bump behind the upper front teeth,  but do not let the tip of tongue touch the bump. This also makes the center of the tongue go down. The back part of the tongue is raised because you pull it into a tight ball Fold and raise the sides of the tongue so they touch the upper side-teeth.   If we follow the above requirement, our tongue should have an s shape when we pronounce the r sound as depicted in the following sketch:    Is it possible to raise the tip while raising the back and lowering the center of the tongue when making an r sound?   How do native speakers make an r?  P.S. My tongue is very short anyway!
Number of preimages of a group element under a homomorphism. How to get client date and time in ASP.NET? What are the dev-loop services that started on boot? When would you use a voltage regulator vs a resistor voltage divider?  Are there any uses for which a resistor divider is particularly bad? Table of Contents with Chapter I'm attempting to modify the Table of Contents in my document. Currently, chapter one in my document is listed as   1   Introduction   What I would like to see is  Chapter 1   Introduction   Seems like an easy enough thing to ask for, but can't seem to find a good way to do this. Any feedback would be most appreciative. How to find hydrogen wave-functions? I have found the hydrogen wave functions and would now like to calculate the function that describes the orbitals so that I can plot this function and see how they look.  I don't know how I can do that and it is crazy how I cannot find anything on the subject on the internet as if there was no relation between the wave functions and the orbitals.  Could you please tell me what I need to do to get a function $r(\theta,\phi)$ out of my wave functions $\psi(r,\theta,\phi)$. I read that this is because the mean and variance completely specify a normal distribution. However, e.g. for a Poisson distribution the mean, variance and third moment can all be expressed with the same parameter lambda. Is this not what it means to 'completely specify' a distribution?  What is an example of two Poisson distributions having the same mean, variance and different higher moments? If we treated weak stationary as if it was strict stationarity, what would happen when we try to do time series analysis? Show $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$ (inverting unit + nilpotent) Show that $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$.  Once you have found the inverse like , the verification is trivial. But how do you come up with such an inverse. Do I just try with general polynomials of all degrees and see what restrictions RHS = $1$ imposes on the coefficients until I get lucky? Also is there a general method to show an element in a ring is a unit? Limit $\lim\limits_{x\to0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$ How to install qt 4.8 from repository? How to install qt 4.8 and QtCreator from repository ? How do I increase the size of swapfile without removing it in the terminal? What differentiates the scientific method from other methods From the controversy in , I would like to know what differentiates "the scientific method" from other method.  I'm asking for differentiation, rather than a definition, because definitions call for an all encompassing answer, which is often hard to find.  If someone asks "what is an alternative to the scientific method," I would like to be able to start by being able to reliably say whether a particular method is the scientific method or not.  Of course, being a linguistic issue, the definitions of words themselves are flexible.  For instance, it is not uncommon to hear one in science talk of "truth" in a sense which is incompatable with the mathematical meaning of "truth."  Accordingly, I would like to stick to the following ideals in wording whenever possible:   Prefer mathematically accurate terminology.  Ideally the word "proof" should be used in the form found in proof theory, and "true" and "false" should be used in the form of Boolean algebra.   No method should claim a hypothesis which predicts the state of the future is "true" unless they claim soothsaying abilities (most scientific theories include a random variable to avoid needing to claim soothsaying abilities... this is legitimate)  Words which imply direction should be clarified carefully.  "Good" and "bad" are notoriously difficult, but phrases such as "advancing society" can also be very tricky as well. The physical world and the world of information theory should be treated differently.  In particular, the concept of "testing a hypothesis" will likely need to be broken down into testing and observing the physical world, taking measurements (which should have errors associated with them), and only then is the hypothesis compared against the results of the measurements. Mathematically extending arguments into infinity (such as claiming some specific cellular level learning process qualifies as the scientific method) are valid, but may rapidly make it harder to distinguish non-scientific methods from scientific ones.  Such claims should be made carefully, but they are not inherently invalid.   If these ideals are too strict, you may bend them, but you should qualify such choices with an explanation of why my recommended wording choices are too strict.  Their goal is to put different methodologies on the levelest playing fields that I can manage in this medium.  Being stack exchange, bonus points for references to existing theories, though you may need to paraphrase their results to fit with the ideals I'm recommending for these answers.  Answers may be tested two ways:   Positive: If we think something is the scientific method, does it meet the requirements set forth? Negative: If we think something is not the scientific method, does the answer explain why it is not? What's the deepest reason why QCD bound states have integer charge? What's the deepest reason why QCD bound states have integer electric charge, i.e. equal to an integer times the electron charge?  Given that the quarks have the fractional electric charges they do, this is a consequence of color confinement. The charges of the quarks are constrained in the context of the standard model by anomaly cancellation, and can be explained by grand unification. The GUT explanation for the charges doesn't care about the bound state spectrum of the QCD sector, so it just seems to be a coincidence that hadrons (which are composite) have integer charge, and that leptons (which are elementary) also have integer charge.   Now maybe there's some anthropic argument for why such a coincidence is useful (in the case of proton and electron, it gives us atoms as we know them). Or maybe you can argue that GUTs naturally produce fractionally charged particles and strongly coupled sectors, and it's just not much of a coincidence.   But I remain curious as to whether Seiberg duality, anyons, some UV/IR relationship... could really produce something like the lepton-hadron charge coincidence, for deeper reasons. I suppose one is looking for a theory in which properties of bound states in one sector have a direct and nontrivial relationship to properties of elementary states in another sector. Is there anything like this out there?   (This question was prompted by muster-mark's many recent questions about fractional charge, and by a  that the hadron-lepton charge coincidence is a "semi-coincidence", which assured me that I wasn't overlooking some obvious explanation.) $f$ is irreducible $\iff$ $G$ act transitively on the roots Let $F$ be a field and $f\in F[X]$ a separable polynomial. Let $K_f$ be the splitting field of $f$ and $G_f=\text{Gal}(K_f/F)$ its Galois group. Show that $f$ is irreducible $\iff$ $G_f$ acts transitively on the roots on $f$. My work $\implies :$ Let $f\in F[x]$ irreducible, $\alpha \in K_f$ a root and $\alpha _1,...,\alpha _n$ the other roots of $f$ (so $K_f=F(\alpha ,\alpha _1,...,\alpha _n)$). What I have to show (I think) is that for all $i$ there is a $\sigma \in G_f$ s.t. $\sigma \alpha =\alpha _i.$ Q1) Is it right ? Q2) Is $f$ the minimal polynomial of $\alpha $ ? (To me it is, but my teacher said that it can be not the case, but I don't understand why). Since $\alpha $ and $\alpha _1$ have the same minimal polynomial, there is an isomorphism $\sigma :\alpha \longmapsto \alpha _1$. We can observe that $\sigma : F(\alpha )\longrightarrow K_f$. Now $F(\alpha ,\alpha _1)/F(\alpha )$ is algebraic, then we can extend $\sigma $ to a morphism $F(\alpha ,\alpha _1)\longrightarrow K_f$. Now, we can continue like that and extend $\sigma $ as $\psi: K_f\longrightarrow K_f$ s.t. $\psi(\alpha )=\alpha _1$. Q3) The fact that $\psi(\alpha )=\alpha _1$ comes from the fact that $\psi|_{F(\alpha )}=\sigma $, right ? The bijectivity is obvious since it's a field homomorphism and that $\sigma (K_f)=K_f$. Q4) How to conclude that $G_f$ act transitively on the roots ? I don't have particular problem for the converse. How to unplug a network cable that's stuck? Intuitive explanation for dividing by $n-1$ when calculating standard deviation? I was asked today in class why you divide the sum of square error by $n-1$ instead of with $n$, when calculating the standard deviation.  I said I am not going to answer it in class (since I didn't wanna go into unbiased estimators), but later I wondered - is there an intuitive explanation for this?! Who is the Lord, as referred to in the title? Frodo? Sauron? Someone else? Or is it more of an abstract title, not referring to a single person, like "He who wields the One Ring"? Can I register a domain name that contains a company name or trademark? I wonder is it legal to register a domain name that contains a company name. For example cococola.cc (considering that this domain name is available). Can I buy and use any domain names that contain a name of a trademark? I want to remove all empty lines from a file. Even if the line contains spaces or tabs it should also be removed. When I entered the -al attribute with the  command, I got the following:  anupam@JAZZ:~/blog$ ls -al total 76 drwxrwxr-x 13 anupam anupam 4096 Aug 28 21:45 . drwxr-xr-x 34 anupam anupam 4096 Aug 28 20:52 .. drwxrwxr-x  8 anupam anupam 4096 Aug 28 12:19 app drwxr-xr-x  2 anupam anupam 4096 Aug 28 12:19 bin drwxrwxr-x  5 anupam anupam 4096 Aug 28 12:19 config -rw-rw-r--  1 anupam anupam  154 Aug 28 12:19 config.ru drwxrwxr-x  3 anupam anupam 4096 Aug 28 12:37 db -rw-rw-r--  1 anupam anupam 1339 Aug 28 12:19 Gemfile -rw-rw-r--  1 anupam anupam 2871 Aug 28 12:19 Gemfile.lock drwxrwxr-x  7 anupam anupam 4096 Aug 28 21:45 .git -rw-rw-r--  1 anupam anupam  466 Aug 28 12:19 .gitignore drwxrwxr-x  4 anupam anupam 4096 Aug 28 12:19 lib drwxrwxr-x  2 anupam anupam 4096 Aug 28 12:29 log drwxrwxr-x  2 anupam anupam 4096 Aug 28 12:19 public -rw-rw-r--  1 anupam anupam  249 Aug 28 12:19 Rakefile -rw-rw-r--  1 anupam anupam  478 Aug 28 12:19 README.rdoc drwxrwxr-x  8 anupam anupam 4096 Aug 28 12:19 test drwxrwxr-x  6 anupam anupam 4096 Aug 28 12:33 tmp drwxrwxr-x  3 anupam anupam 4096 Aug 28 12:19 vendor   What does each column mean, and what does the total 76 signify here?