This is what I understood (it may be wrong, so please correct me): since every particle is "divided" into a lefthand and a righthand partner, which is what guarantees the particles to have mass, and since it's finally proved that neutrinos have mass, why only lefthand neutrinos have been observed hereto?
I am learning P&amp;S's Introduction of quantum field theory. My teacher said that if the mass of neutrino is exactly 0, then we should not observe any right-handed neutrinos and left-handed anti-neutrinos according to Weyl's theory. It is because $$ \left( i\gamma^\mu \partial_\mu - m \right) \psi = \left( \begin{array}{cc} -m &amp;  i\left(\partial_0 + \vec\sigma \cdot \vec\nabla\right) \\ i\left(\partial_0 - \vec\sigma \cdot \vec\nabla\right) &amp; -m \end{array} \right) \left( \begin{array}{c} \psi_L \\ \psi_R \end{array} \right) =0. $$  If we set m=0, then we will have:  \begin{align} i\left(\partial_0 - \vec\sigma \cdot \vec\nabla\right) \psi_L &amp;= 0; \\ i\left(\partial_0 + \vec\sigma \cdot \vec\nabla\right) \psi_R &amp;= 0. \end{align}  And if these formulas can describe neutrinos we must conclude that there are two types of neutrinos.  My confusions are:   It is known that the mass of neutrino is not 0, therefore there are chances (depending on the mass) to find right-handed neutrinos and left-handed anti-neutrinos. But we don't. If I accept that there are only these two types of neutrinos (right-handed anti-neutrinos and left-handed neutrinos), this property of neutrino causes the parity violation, so parity violation must relate to angular momentum and therefore spinor space. Am I write? Are there any reasons why neutrino is so weird that is has mass but still has helicity + Or - 1. This goes against with what I have learned that only when a particle  moves at the speed of light can its spin aligned with its momentum.
I have a couple of illustrations done in Illustrator and I am planing to animate it for a website that I am working on, I've heard of  toolkit with flash, but is it the best way to go or is there another "better" way of doing it?  Here's an example of the kind of animations I am aiming for: How can I create Light Streaks in Cycles? What is currently the most reliable VPN for China? I will soon be spending a few months travelling across China and want to get a VPN service to get around the Golden Firewall.   When I was in China in 2014/15 the general consensus was that Astrill offered the most reliable service, but I heard that they have been targeted quite strongly by the government over the last year.   Therefore, I am wondering what is the best VPN for China these days? Is Astrill still as good as it used to be?   Any recent experiences would be very helpful! Testing for coefficients significance in Lasso logistic regression [A similar question was asked  with no answers] I have fit a logistic regression model with L1 regularization (Lasso logistic regression) and I would like to test the fitted coefficients for significance and get their p-values. I know Wald's tests (for instance) are an option to test the significance of individual coefficients in full regression without regularization, but with Lasso I think further problems arise which do not allow to apply the usual Wald formulas. For instance, the variance estimates neded for the test do not follow the usual expressions. The original Lasso paper:  suggests a bootstrap-based procedure to estimate the coefficients variance, which (again, I think) may be needed for the tests (section 2.5, last paragraph of page 272 and beginning of 273):  One approach is via the bootstrap: either $t$ can be fixed or we may optimize over $t$ for each bootstrap sample. Fixing $t$ is analogous to selecting the best subset (of features) and then using the least squares standard error for that subset  What I understand is: fit a Lasso regression repeatedly to the whole dataset until we find the optimal value for the regularization parameter (this is not part of the bootstrap), and then use only the features selected by the Lasso to fit OLS regressions to subsamples of the data and apply the usual formulas to compute the variances from each of those regressions. (And then what should I do with all those variances of each coefficient to get the final variance estimate of each coefficient?) Furthermore, is it correct to use the usual significance tests (for instance Wald's test which makes use of the estimated betas and variances) with the Lasso estimates of the coefficients and the bootstrap-estimated variances? I am fairly sure it is not, but any help (use a different test, use a more straightforward approach, whaterever...) is more than welcome. According to the answers  I suspect inference and p-values just cannot be obtained. In my case, p-values are an external requirement (although the use of L1 regularization was my choice). Thanks a lot EDIT What if I fit an OLS logistic regression using only the variables selected by a previous run of the Lasso logistic regression? Apparently (see ),  There's no need to run the model again after doing cross-validation (you just get the coefficients from the output of cv.glmnet), and in fact if you fit the new logistic regression model without penalisation then you're defeating the purpose of using lasso  But what if I do this with the sole purpose of being able to compute p-values while keeping the number of variables low? Is it a very dirty approach? :-) I never dealt with Android devices before so I'm completely newbie at it, please comment if something is too simple.  Say I purchase , that has got Android Froyo 2.2 installed in it.  If there is a new version of Android released tomorrow or next month, will I be able to update it (like I will be able to update my iPod Touch 4 to iOS 5)? Kinetic energy conservation in a collision Kinetic energy conservation in collision.  In any type of collision type of collision if we take the system to comprised of both bodies then the net external force is zero. So the work done by external force is also zero. By the relation $W=K_f-K_i$ as $W$ is zero hence kinetic energy is conserved. But this not the case.   Can you tell me what is the flaw in my argument? Some people say that the argument has neglected the fact that some kinetic energy is transformed into heat. But heat is created due to the interactions between bodies during collision which is thus an internal force and thus shouldn't affect kinetic energy. Nth derivative of $x^x$ A few days ago, I was wondering about a series expansion for $$f(x) = \  x^x$$ so I tried taking a couple derivatives. From these I was able to guess at some formulas for the general coefficients of the first few terms of the nth derivative as well as the last term (where I put the terms of the derivative in the order  $$f^{(n)}(x) = c_1x^x + c_2x^{x-1} + c_3x^{x-2}\ + \ ... \ +\ c_nx^{x-(n-1)}$$  Please let me know if there is a general formula for the coefficients as a function of n. In my own fooling around, I found that $$\ln(x)+1$$ appears quite a bit, so I called this $a$ in my work. Since I would like to center my expansion at $1$, and this expression evaluated to $1$, at $x=0$, I was interested in writing my formulas as functions of $n$ and $a$. I found that you get something of the form (this could very well be completely incorrect):  $$f^{(n)}(x) = ax^x + a^{n-2}{\binom n2}x^{x-1} + a^{n-4}(3{\binom n4}-a{\binom n3})x^{x-2}\\ + a^{n-6}(15{\binom n6}-10{\binom n5}a+2{\binom n4}a^2)x^{x-3}\ + \ ... \ +\ (-1)^n(n-2)! \ x^{x-(n-1)}$$  An interesting property that seemed to recur for the various coefficients was  that once I found a recursion formula for the coefficient in question and plugged in my initial value, it always seemed to be the same as taking the integral of the previous coefficient with respect to $a$. That is to say, if I plugged in the nth coefficient (a polynomial of $a$) into my recursion formula for the $(n+1)$th coefficient, this gave me the same result as integrating. In general, as reflected by the few coefficient formulas above,  the formula for the coefficient of $$x^{x-c}$$ where c is an integer such that $$0\le c&lt;n$$ "Stabilized" to a polynomial of a with c terms after the first few applications of the recursion formula. This stabilization occurred when $$n=2c$$ Also, as a direct result of the tentative and incomplete formula I have written above, the first nonzero-value for the coefficient of $$x^{x-c}$$ is $$(-1)^{c+1}(c-1)!$$ and appears in $$f^{(c+1)}(x)$$ If these various properties are indeed true, can anyone explain why this would be the case? I am aware that this function can be expanded using the expansion for $$e^x$$ with $$x\ln(x)$$ in the exponent. This does not strike me as particularly enlightening (let me know if I'm missing something). I am most interested in the coefficients on the binomial coefficients, since these are the only things that stand between me and a general formula for the coefficients (since the form is quite standard). These are: $$1$$ then $$3,-1$$ then $$15, -10,2$$The sum of these coefficients should also give the nth derivative evaluated at zero since $$f(1) = 1$$ and $$a(1) = 1$$  Anyway, please let me know what you think! I am currently stuck due to an inability to brute force my way any further and a complete lack of cleverness. My knowledge of mathematics is quite elementary, so please explain any higher level concepts if they are necessary to explain this problem. How to escape text for regular expression in Java Does Java have a built-in way to escape arbitrary text so that it can be included in a regular expression? For example, if my users enter "$5", I'd like to match that exactly rather than a "5" after the end of input. Permanently mounting loop device I created a file   touch /datastore/virtual/pseudoblock   created a loop device with it  sudo losetup /dev/loop0 /datastore/virtual/pseudoblock   (although I got a warning about its size)  and then initialized it with random data  dd if=/dev/urandom of=/dev/loop0 bs=1M count=100   My questions are  a) why is it not displayed yet in my block devices' list?  NAME                     MAJ:MIN RM   SIZE RO TYPE  MOUNTPOINT sdb                        8:16   0 489.1G  0 disk   ├─sdb2                     8:18   0   488M  0 part  /boot ├─sdb3                     8:19   0 488.1G  0 part   │ └─sdb3_crypt           253:0    0 488.1G  0 crypt  │   ├─ubuntu--vg-root    253:1    0 472.2G  0 lvm   / │   └─ubuntu--vg-swap_1  253:2    0  15.9G  0 lvm   [SWAP] └─sdb1                     8:17   0   512M  0 part  /boot/efi sda                        8:0    0 931.5G  0 disk   └─sda1                     8:1    0 931.5G  0 part     └─sda1_crypt           253:3    0 931.5G  0 crypt      └─store--vg-store1tb 253:4    0 931.5G  0 lvm   /datastore   b) how can I permanently mount it via /etc/fstab since I cannot get its UUID?  $ blkid /dev/mapper/sdb3_crypt: UUID="fSHjbj-51K2-QfhI-G0Wb-o3lN-4pE1-BB4wCP" TYPE="LVM2_member" /dev/mapper/ubuntu--vg-root: UUID="9e452886-4d8g-fj54-854c-80bc171826e8" TYPE="ext4"   working on   $ lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 16.04.5 LTS Release:    16.04 Codename:   xenial   with  $ uname -a Linux pkara-pc01 4.15.0-42-generic #45~16.04.1-Ubuntu SMP Mon Nov 19 13:02:27 UTC 2018 x86_64 x86_64 x86_64 GNU/Linux Random errors on various sites when viewing main page Occasionally (very occasionally) when returning to the main page of a site by clicking on the logo I get the following message:     It was not possible to perform this tag search at this time due to an unexpected error.   This is odd because I'm not performing a tag search.  So far this has happened on both Movies &amp; TV and Cooking.  I have heard that others are getting this same message. How do I efficiently get "the most recent corresponding row"? I have a query pattern that must be very common, but I don't know how to write an efficient query for it.  I want to look up the rows of a table that correspond to "the most recent date not after" the rows of another table.  I have a table, inventory say, which represents the inventory I hold on a certain day.  date       | good | quantity ------------------------------ 2013-08-09 | egg  | 5 2013-08-09 | pear | 7 2013-08-02 | egg  | 1 2013-08-02 | pear | 2   and a table, "price" say, which holds the price of a good on a given day  date       | good | price -------------------------- 2013-08-07 | egg  | 120 2013-08-06 | pear | 200 2013-08-01 | egg  | 110 2013-07-30 | pear | 220   How can I efficiently get the "most recent" price for each row of the inventory table, i.e.  date       | pricing date | good | quantity | price ---------------------------------------------------- 2013-08-09 | 2013-08-07   | egg  | 5        | 120 2013-08-09 | 2013-08-06   | pear | 7        | 200 2013-08-02 | 2013-08-01   | egg  | 1        | 110 2013-08-02 | 2013-07-30   | pear | 2        | 220   I know one way of doing this:  select inventory.date, max(price.date) as pricing_date, good from inventory, price where inventory.date &gt;= price.date and inventory.good = price.good group by inventory.date, good   and then join this query again to inventory. For large tables even doing the first query (without joining again to inventory) is very slow.  However, the same problem is quickly solved if I simply use my programming language to issue one max(price.date) ... where price.date &lt;= date_of_interest ... order by price.date desc limit 1 query for each date_of_interest from the inventory table, so I know there is no computational impediment.  I would, however, prefer to solve the whole problem with a single SQL query, because it would allow me to do further SQL processing on the result of the query.  Is there a standard way to do this efficiently? It feels like it must come up often and that there should be a way to write a fast query for it.  I'm using Postgres, but an SQL-generic answer would be appreciated. I don't know if this is a well-known fact, but I have observed that every number, no matter how large, that is equally divided by $9$, will equal $9$ if you add all the numbers it is made from until there is $1$ digit. A quick example of what I mean:  $9*99 = 891$ $8+9+1 = 18$ $1+8 = 9$  This works even with really long numbers like $4376331$ Why is that? This doesn't work with any other number. Similarly for $11$ and alternating digits sums. Are getters and setters poor design? Contradictory advice seen I'm currently working on a simple game in Java with several different modes. I've extended a main Game class to put the main logic within the other classes. Despite this, the main game class is still pretty hefty.  After taking a quick look at my code the majority of it was Getters and Setters (60%) compared to the rest that is truly needed for the logic of the game.  A couple of Google searches have claimed that Getters and Setters are evil, whilst others have claimed that they are necessary for good OO practice and great programs.  So what should I do? Which should it be? Should I be changing my Getters and Setters for my private variables, or should I stick with them? During my upcoming holiday to the USA I'm thinking about buying a new guitar as the exchange rate is extremely favorable. Excuse my naivety but I have never flown with a guitar before. What is a recommended way to go about this? Could I take it as carry on luggage or would it have to be checked? If checked luggage what kind of precautions should I take to keep it safe? Are there any problems with flying US budget carriers? If I do buy the guitar I'm expecting to have to make two flights with it, one domestic flight with Virgin America and an international flight with Air NZ. How many passes do you need to wipe/shred your files to make them not undeletable? What kind of components are black blobs on a PCB? What does a type followed by _t (underscore-t) represent? This seems like a simple question, but I can't find it with the Stack Overflow search or Google. What does a type followed by a _t mean? Such as  int_t anInt;   I see it a lot in C code meant to deal closely with hardware—I can't help but think that they're related. Is there a label/goto in Python? Is there a goto or any equivalent in Python to be able to jump to a specific line of code? Provide an easily discoverable way to get the full URL to an answer , clicking &quot;link&quot; &quot;share&quot; for anwers yields a short (traceable) URL in the &quot;share a link to this answer&quot; dialog, such as †:  These short URLs show no clue about the linked question whatsoever. Also, when different people use a short URL for the very same post, then the user id suffix makes those be different URLs for a browser. Such links will then not be shown as visited‡. I know how to get URLs that have a proper slug. But as I see  pop up on these sites (where referrals ), I assume many others just don't realize full URLs would be better for use on these sites themselves? Or many don't want to do the little effort to get the full URL? So: can we please have an easy way to get the full URL as well, in a way that is easily found for those who don't know about the different links? (Currently for questions, clicking &quot;link&quot; has the same effect. But then one can also right-click the title, or take the URL from the location bar, to get the full human-readable URL. Once, Jeff .)  † The short links for answers are not (yet) [automatically converted][6] into a clickable question title either, unlike links such as `https://meta.stackexchange.com/questions/74274/privacy-leak-in-permalink#75963`, which renders as https://meta.stackexchange.com/questions/74274/privacy-leak-in-permalink#75963 But I guess that will change soon.  ‡ On Meta the CSS for posts doesn't indicate such difference anyway, which is a different issue. How to find the joint PDF?