I'm trying to remember a problem in classical mechanics involving a special surface that allows a ball to roll to the top and lose all it's momentum in finite time.   This leads to some interesting problems with time reversibility, as it implies the ball will spontaneously roll down the surface.  I'm not looking for an explanation, so much as a name and link to study it some more.
This question is in the spirit of , an example of an apparently non-deterministic system in Newtonian mechanics. Under certain restrictions, the  guarantees the existence and uniqueness of solutions to differential equations with initial conditions. However, Norton's dome does not satisfy these restrictions. The ball may sit on top of the dome for an arbitrary period of time before sliding down in a particular trajectory, without violating Newton's laws of motion.    Is there a plausible example of a system of interacting point-particles such that the equations of a point-particle are continuous but not , and therefore fail to have a unique solution?
What does this phrase from The adventures of Tom Sawyer sentence mean: "True, the knife would not cut anything, but it was a "sure-enough" Barlow, and there was inconceivable grandeur in that -- though where the Western boys ever got the idea that such a weapon could possibly be counterfeited to its injury is an imposing mystery and will always remain so, perhaps."  Thank you! I read  and thought that would easily be solved (not that it isn't solvable without) if one could write:   @Override public String toString() {     return super.super.toString(); }   I'm not sure if it is useful in many cases, but I wonder why it isn't and if something like this exists in other languages.  What do you guys think?  EDIT: To clarify: yes I know, that's impossible in Java and I don't really miss it. This is nothing I expected to work and was surprised getting a compiler error. I just had the idea and like to discuss it. The day before yesterday I think, my daughter asked me where we were going and since I was not planning to do the weekly shopping on that day and I just wanted to buy some stuff from two stores, I said offhand we are going to the shops! Looking back, it seems when I don't find a NAmE word I turn to UK if I know of.  So what do you say when:   go shopping (it's just go shopping!) you go to buy something specific; I mean you're not going shopping, and it's usually found in any store. You don't have to shop around. you want to buy non grocery or clothing stuff, maybe a can of paint and a spare part for your car together.    I have found some kind of answer for this question on , but I prefer to get a clear answer to my points above, and also if you agree with this native speaker about using store in singular form not plural:     Just as a side note, we don't use the plural in American English. "I'm   going to the store" (even if I may visit several stores), not "I'm   going to the stores". (If we know we are going to several stores I   think it would be more likely to say "I'm going shopping" or even "I'm   going downtown" in smaller towns.) We're trying to debug some applications performing broadcast.  What is the difference between the broadcast address 255.255.255.255 and as e.g. reported by ifconfig,  Bcast:192.168.1.255 How does Java's PreparedStatement work? Modern textbook on statistical field theory with an emphasis on applications to non-equilibrium phenomena? Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$ One of our SQL Server 2014 database transaction logs is growing very fast and I cannot find the root cause for this.  Database in Simple recovery mode. During full backup the log file grows to its limits (800GB) and backup fails.  I checked the transactions during the backup and did not find anything strange.  All transactions are our regular loading and no maintenance jobs (index rebuilds etc.)  I am aware of that backup keep the log from reuse but this mean 800GB changes during the backup period and this does not make any sense.  I had compared this DB to similar DB size, loading and backup duration. The second DB Log is not growing more than 400GB.  DB size is 7TB. Backup time is ~20H. The only time log is growing is during backup. Log_reuse shows correct Backup_Restore. No long running transactions.  The problem is the "speed" of log growth - compared to similar sites with same load and same backup duration, the log is 4 time less. In books the equation for length contraction is derived by supposing that the velocity of the spacecraft is the same for both observers. So the question is that, is the velocity really the same for both observers? Whereas there must be some trouble in the velocities noted by observers. I mean: If the observer on the spacecraft measures the velocity of the spacecraft to be $v$ then is it possible for the other observer to measure the same velocity from the Earth? Defaulting on credit cards before leaving the country I have a colleague who is going back to his country after staying for a couple of years in US. He has 3-4 credit cards plus a personal loan. His total debt would come to around $10,000. Some days ago, he told me he is going to default on the accounts. He figures, since he is not planning to come back to US, it should not matter to him.  Question is, is this a bad move on his part, and if it is, how can I convince him? How to install driver for TP-Link TL-WN722N(EU)V2 on Ubuntu 17.04 Kylin I can not install the TP-LINK WN722N V2, which includes a 8188 EUS chip. Then I tried to install the backports v4.4.2,but   do not want to recognize either.  The TP-Link driver installation errors thrown out:  man@kman-livve:~$ cd '/home/kman/Documents/Tplink 722 N V2/rtl8188EUS_linux_v4.3.0.8_13968.20150417' kman@kman-livve:~/Documents/Tplink ...$ sudo make  "******************************************" "NO SKRC,we will use default KSRC" "******************************************" make ARCH=x86_64 CROSS_COMPILE= -C /lib/modules/4.10.0-15-generic/build M=/home/kman/Documents/Tplink 722 N V2/rtl8188EUS_linux_v4.3.0.8_13968.20150417  modules make[1]: Entering directory '/usr/src/linux-headers-4.10.0-15-generic' arch/x86/Makefile:140: CONFIG_X86_X32 enabled but no binutils support make[1]: *** No rule to make target '722'.  Stop. make[1]: Leaving directory '/usr/src/linux-headers-4.10.0-15-generic' Makefile:1367: recipe for target 'modules' failed   A method to know him, I do not know about. Thanks  Model:TL-WN722N(EU)_V2_161112_Linux.zip Chipset:rtl8188EUS_linux_v4.3.0.8_13 An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root? Problem: Is there an irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root for $p$ prime? If there is, what is the minimal degree possible?   I can only prove that $x^2-c$ is impossible, by quadratic reciprocity and Chinese remainder theorem. Even the case of $a x^2 - c$ is unknown to me.  Meanwhile, if $f$ is not required  to be irreducible, but only have no root in $\mathbb{Z}$, then $(x^2-a)(x^2-b)(x^2-ab)$ is a solution for non-sqaure $a,b,ab$, since if both $a,b$ are not squares in $\mathbb{Z}/p\mathbb{Z}$, then $ab$ is a square. Yet I still don't know if this is of minimal degree.  Also, it is natural to pose generalizations   When $p$ is not necessarily prime (equivalently for all prime powers). When $p$ is odd prime. When $p$ represents sufficiently large primes (equivalently all but a finite number left). what does ∇ (upside down triangle) symbol mean in this problem Given $f(x) = \frac{1}{2}x^TAx + b^Tx + \alpha $   where A is an nxn symmetric matrix, b is an n-dimensional vector, and alpha a scalar. Show that  $\bigtriangledown _{x}f(x) = Ax + b$   and  $H = \bigtriangledown ^{2}_{x}f(x) = A$   Is this simply a matter of taking a derivative with respect to X, how would you attack this one? Order posts by tags count? I am trying to order posts by tag count. I want to order posts with no tags first and posts with highest count last.  I tried and got posts with no tags only.       $tags = get_tags();     $tag_ids = wp_list_pluck( $tags, 'term_id' );      $args1 = array (        'orderby'          =&gt; 'DEC',        'post_type'        =&gt; 'post',        'pagination'       =&gt; true,        'posts_per_page'   =&gt; '1',        'tag__not_in'      =&gt;  $tag_ids,        'meta_key'         =&gt; '_thumbnail_id',     );   How do I order posts based on the tags count? How do I programmatically create a new content type? I'm building a module (my_module) in Drupal 7. It has some functionality and also will create a new content type. In my_module.install, I implemented hook_install() (my_module_install()).    Can I use more hook_install() to create a new content type (my_module_install()) in this module? If the answer is yes, how should I do this? Otherwise, should I do this in another module? Estimating Uniform distribution endpoints using data with errors Suppose I have a random variable $X$ ~ $Unif(0,\theta)$ where I want to estimate $\theta$. I draw a sample $X_1,...,X_n$.One way is to get a point estimate using e.g.  maximum likelihood estimation via the sufficient statistic $X_{(n)}$.  However, suppose I want a 95% confidence interval of sorts on the value of $\theta$, how should I construct one?  The reason why I am interested in confidence interval is because of the following issue, which is actually my main question (the above prelude on confidence interval is just a suggestion on possible approach). So actually my sample came with some noise, in a sense that I actually observe $X_1+E_1,...,X_n+E_n$ where $E_i$~$N(0,\sigma_i^2)$ independently from each other and from the $X$'s. How should I make some form of statistical estimation about $\theta$? I would prefer some form of confidence estimate. There is a problem 3.3 in :     Ambiguities in the energy-momentum tensor:      (a) If you add a total derivative to Lagrangian ${\cal{L}} \rightarrow {\cal{L}} + \partial_\mu X^\mu$, how does the energy-momentum tensor change?      (b) Show that the total energy $Q = \int d^3x \; {\cal{T^{00}}}$ is invariant under such changes   Given the definition of energy-momentum tensor:  $$ {\cal{T}}^\mu{}_\nu = \sum_n \frac{\partial{\cal{L}}}{\partial \left( \partial_\mu \phi_n \right)} \partial_\nu \phi_n - g_{\mu\nu} {\cal{L}} $$  It changes as:  $$ \delta {\cal{T}}^\mu{}_\nu =  \sum_n \left( \partial_\rho \frac{\partial{X^\rho}}{\partial \left( \partial_\mu \phi_n \right)} \right) \partial_\nu \phi_n - g_{\mu\nu} {\partial_\rho X^\rho} $$  $T^{00}$ changes as:  $$ \delta {\cal{T}}^{00}= \sum_n \left( \partial_\rho \frac{\partial{X^\rho}}{\partial \dot{\phi_n}} \right) \dot{\phi_n} - \partial_\rho X^\rho $$   From this point I’m stuck. The first term doesn’t seem to disappear at all after integration over space, and the second disappears only partially:  $$ \int d^3x \; \dot{X^0} $$  So even if I’d have assumed that $X$ depends on position, and not on the fields - the total energy doesn’t seem to be invariant under it.  What is the best way to proceed forward with this? "Would" & " Used to" Countable additivity implies countable subadditivity? Suppose $\mu$ is a measure in a ring $R$ of a set $X$. So for any mutually disjoint subsets $A_1,A_2,\ldots$ such that $\sum_{i=1}^\infty A_i\in R$, we have that $\mu(\sum_{i=1}^\infty A_i) = \mu(A_1)+\mu(A_2)+\cdots$. (i.e. countable additivity)  I'm wondering: Does that imply countable subadditivity? I.e. for any subsets $A_1,A_2,\ldots$ such that $\sum_{i=1}^\infty A_i\in R$, is it always true that $\mu(\sum_{i=1}^\infty A_i)\le \mu(A_1)+\mu(A_2)+\cdots$?  I believe it should be true, because you can take the mutually disjoint subsets $A_1,A_2-A_1,A_3-(A_1\cup A_2),A_4-(A_1\cup A_2\cup A_3),\cdots$, each of which is in $R$ (because unions and differences of sets in $R$ are again in $R$), then apply countable additivity, then use monotonicity on the fact that $A_n-(A_1\cup\cdots\cup A_{n-1})\subseteq A_n$.  Is that right? I just want to make sure I didn't make any mistake in my logic. EM wave generation from different frames of reference