The official Android app is giving me old push notifications. That's also in opposite order, meaning most recent one was pushed first. I am getting push messages every few minutes.
Version of the app: 1.0.51. (It is up to date at the time of writing according to Google Play.)  This started happening after the network problem that happened earlier this morning. Both my tablet and my phone are popping up notifications for events (comments, and probably edits too) that happened prior to the network issue. I had received notifications for these events already and had already cleared them before the network issue happened.  The repeated notifications do not show up in the bar displayed at the top of the Stack Exchange sites. In other words, I get notified again in Android but do not get notified again on the SE web sites.
General relativity is expressed in terms of differential geometry, which allows you to do interesting things with the coordinates: multiple coordinates may refer to a single point, eg. the  has whole lines at the top and the bottom that correspond to the North and South poles, respectively; or a single coordinate may refer to multiple points, for example by using inverse geometry the origin refers to all the points infinitely far away.  So, is the singularity just a single point in the curved spacetime, or can it be a more extended object, described by a single coordinate? I've got a development webserver on an Ubuntu box inside of VMWare Workstation 7.1.3. I'd like to run a web browser on a Windows machine (the host OS) for actually testing a web page I'm working on -- hard to run IE tests in Ubuntu :)  However, if I simply try to ping the IP given to the ubuntu VM (192.168.83.137) (or open it in my browser for that matter), it seems the host cannot communicate with the guest.  How do I allow the guest OS to communicate with the host when the guest is running in NAT mode? Central limit theorem and the law of large numbers I have a very beginner's question regarding the Central Limit Theorem (CLT):  I am aware that the CLT states that a mean of i.i.d. random variables is approximately normal distributed (for $n \to \infty$, where $n$ is the index of the summands) or the standardized random variable would have a standard normal distribution.  Now the Law of Large Number states roughly speaking that the mean of i.i.d random variables converges (in probability or almost surely) to their expected value.  What I don't understand is: If, as the CLT states, the mean is approximately normally distributed, how then can it also converge to the expected value at the same time?   Convergence would imply for me that with time the probability that the mean takes a value which is not the expected value is almost zero, hence the distribution would not really be a normal but almost zero everywhere except at the expected value.  Any explanation is welcome. Position of "only" in “We 𝒐𝒏𝒍𝒚 have two possibilities” Is there any difference in meaning between the three following sentences?   We only have two possibilities. We have only two possibilities. We have two possibilities only.   I have already read  and I know that the position of only and the emphasis (written or oral) may change the meaning of some sentences, but I am not sure if it does here.  Note: It is clear that “only we have two possibilities” has a different meaning. My question is restricted to the sentences I’ve listed above. How do I find the particular solution of this second order inhomogenous differential equation? (Using undetermined coefficients).  $y''-4y'+5y = 4e^{2x} (\sin x)$  I can find the generel homogenous solutions but I need help for the particular. Feature selection with Random Forests Here's my attempt at it:  $query = $database-&gt;prepare('SELECT * FROM table WHERE column LIKE "?%"');  $query-&gt;execute(array('value'));  while ($results = $query-&gt;fetch())  {     echo $results['column']; } $\dfrac{pq}{r}+\dfrac{qr}{p}+\dfrac{pr}{q}\in\Bbb Z\,\Rightarrow\, \dfrac{pq}{r},\dfrac{qr}{p},\dfrac{pr}{q}\in\Bbb Z$ Let $p,q,r$ be integers such that the symmetric sum of fractions $\dfrac{pq}{r}+\dfrac{qr}{p}+\dfrac{pr}{q}$ is an integer. Prove that each of the numbers: $\dfrac{pq}{r},\dfrac{qr}{p},\dfrac{pr}{q}$ is an integer. How to do this? Someone posted but deleted soon. (I am not asking how to block my posts on my timeline.)  I am asking how I can block my activity, such as posting in open groups, making comments on people's posts, adding a friend, liking a photo, liking a post, etc., from people seeing it in their news feeds?  I don't want people seeing my interactions with other people. Is there any significant difference between Nikon and Canon? Masking problems I am working with masking. Here is my node setting with the mask.   And here is my node settings  And what am i getting is this.    I tried invert node and many settings. It just doesnt work. Where am i going wrong For example:     Is (A &or; B &or; C) &and; (D &or; E &or; F) the same as   (A &and; D) &or; (A &and; E) &or; (A &and; F) &or; (B &and; D) &or; (B &and; E) &or; ( B &and; F) &or; (C &and; D) &or; (C &and; E) &or; (C &and; F)?   How would I check equivalence in general? What is the advantage of accepting the axiom of choice over other axioms (for e.g. axiom of determinacy)?  It seems that there is no clear reason to prefer over other axioms..  Thanks for help. Export nodes from Drupal 4? I have Ubuntu 12.04 LTS. I need the correct output because I edited it because it wasn't working but it has only made it worse. If $F_n$ is the $n$-th fibonacci number, then prove that, $$F_n={n-1 \choose 0 }+{n-2 \choose 1 }+{n-3 \choose 2 }+\ldots$$  I tried the idea of using Pascal's triangle, but it seems to need some adjustment, so I am stuck, please help.    Any combinatorial argument would be of greater help than rigorous proof.  Thank you. Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$ Need to find $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ Where $a_1\ge\dots\ge a_k\ge 0$  I thought about Cauchy Theorem on limit $\lim\limits_{n\to\infty}\dfrac{a_1+\dots+a_n}{n}=\lim a_n$ and something like what happen if all $a_i=0$ or $a_1=\dots=a_k$, but may be something I am thinking wrong?  Maybe it is too simple but I am not getting it; please help. Ideal of the twisted cubic The twisted cubic is the image of the morphism $\phi : \mathbb{P}^1 \to \mathbb{P}^3 , (x:y) \mapsto (x^3:x^2 y:x y^2:y^3)$, it is given by $X = V(ad-bc,b^2-ac,c^2-bd)$. Now I would like to compute $I(X)$, which equals by the Nullstellensatz the radical of the ideal $I := (ad-bc,b^2-ac,c^2-bd) \subseteq k[a,b,c,d]$. I think that that $I$ is already a radical ideal, even a prime ideal. Namely, I suspect that  $$\phi^* : Q:=k[a,b,c,d]/I \to k[s,t] , a \mapsto s^3, b \mapsto s^2 t , c \mapsto s t^2 , d \mapsto t^3$$ is an injection. If this is true: How can we prove that? I've already tried to find a $k$-basis of the quotient, but this turned out to be a big mess. Even the representation of the quotient as a monoid algebra doesn't seem to help. Another idea is the following: A formal manipulation of generators and relations implies $Q_a \cong k[a,b]_a$. Thus it suffices to prove that $Q \to Q_a$ is injective, i.e. that $a$ is not a zero divisor. When I get exceptions, it is often from deep within the call stack.  When this happens, more often than not, the actual offending line of code is hidden from me:  tmp.rb:7:in `t': undefined method `bar' for nil:NilClass (NoMethodError)         from tmp.rb:10:in `s'         from tmp.rb:13:in `r'         from tmp.rb:16:in `q'         from tmp.rb:19:in `p'         from tmp.rb:22:in `o'         from tmp.rb:25:in `n'         from tmp.rb:28:in `m'         from tmp.rb:31:in `l'          ... 8 levels...         from tmp.rb:58:in `c'         from tmp.rb:61:in `b'         from tmp.rb:64:in `a'         from tmp.rb:67   That "... 8 levels..." truncation is causing me a great deal of trouble.  I'm not having much success googling for this one:  How do I tell ruby that I want dumps to include the full stack? Available US State or National business (or employer) database lists? This question dovetails with this post on .  I am familiar with some of larger, paid-for business registry's like  and .  While the detailed information their business listings database include (like # of employees, annual sales, industry code, etc) is fantastic, if you are on a limited budget, sometimes the cost of purchasing the data outweighs the value you can get from it.  If you have geocoding capabilities in house, one could potentially create a reasonable surrogate by spatially-enabling (geocoding) a publicly available business listing on your own.    If you were looking to take on this type of project, where would you start your research? Do you know of US agencies at a State or National level that maintain this type of information, AND are publicly available for download or minimal purchase?