How is Lyft iOS app able to detect reinstall?
Apps retaining data after being deleted
limsup of intersection of events as a subset of intersection of limsups Let $A_1, A_2, \ldots$ and $B_1, B_2, \ldots$ be two sequences of events in some probability triple $(\Omega, \mathcal{F}, \mathbf{P})$. Now, it is true that $\left(\limsup_n A_n\right) \cap \left(\limsup_n B_n\right) \supseteq \limsup_n (A_n \cap B_n)$, and I can think of many different cases where this relation holds true for equality (e.g., let $A_n = B_n$, or $A_n = B_n^c$, or $B_n = \emptyset$, or $B_n = \Omega$). However, I cannot think of any case where $\left(\limsup_n A_n\right) \cap \left(\limsup_n B_n\right) \supset \limsup_n (A_n \cap B_n)$ holds for strict inclusion.  My proof for the relation is simple. Since $A_n \cap B_n \subseteq A_n$ and $A_n \cap B_n \subseteq B_n$, then we can perform some set algebra as follows:  $$\bigcup_{k=n}^\infty (A_k \cap B_k) \subseteq \bigcup_{k=n}^\infty A_k$$ $$\bigcap_{n=1}^\infty \bigcup_{k=n}^\infty (A_k \cap B_k) \subseteq \bigcap_{n=1}^\infty \bigcup_{k=n}^\infty A_k$$  Then we can use the same logic for $B_n$, and come to the conclusion as stated in the beginning. Why use swap when there is more than enough free space in RAM? Using swap space instead of RAM can drastically slow down a PC.  So why, when I have more than enough RAM available, does my Linux system (Arch) use the swap?  Checkout my conky output below:    Also, could this be the cause of speed and system-responsiveness issues I'm having?  Output of free -m :  $ free -m              total       used       free     shared    buffers     cached Mem:          1257       1004        252          0         51        778 -/+ buffers/cache:        174       1082 Swap:          502        144        357 I have county data in which the &quot;FIP&quot;s (actually State &quot;FIP&quot;s and County &quot;FIP&quot;s combined). I have data imported as CSV with the sames &quot;FIP&quot;s data titled 'STCounty'. However, the shapefile &quot;FIP&quot;s is listed as a Real and the CSV came in as an Integer and the Join function does not seem to work.  The drop boxes are greyed out/empty. So the bigger questions is how do you change the attribute type in a table? I tried to create a new column in the shapefile (county data) and set it to an integer and then multiply the &quot;FIP&quot;s*1, but got a column full of NULL. I am new to QGIS and have a lot of experience in MapInfo, so the join concept is not new to me, just the syntax in QGIS. Solder does not stick to tip of soldering iron? Basic question here, but it's driving me insane!  The solder does not seem to stick to the tip of my soldering iron. After the iron heats up, the tip appears black (sometimes on all sides and sometimes on one side), then either it doesn't melt the solder at all, or it I fiddle around with it for a while; it melts the solder, but the solder rolls into itself into a ball and doesn't stick to the tip.  I've seen this many times while soldering before and usually it's solved by cleaning the tip on a soldering sponge or cooling it down and scraping the tip off with a blade, but I have scraped this particular one many times and still it's the same problem: it heats up and gets black, then the solder doesn't stick to it.  It doesn't help that this soldering iron has a very fine tip and I have to use it to solder very tiny chips and wires under a microscope (I'm just starting to learn soldering under microscopes).  Any ideas on what I can do?    PS: Is scraping the tip a bad idea? I have been doing it with my other bigger soldering irons and it seemed to work (at least in most cases) but I am not sure whether it is a good solution or not. How to evaluate this trigonometric limit? I have been struggling to solve this limit.  What is the limit as $x$ approaches $45^0$ of $$\frac{\sqrt{2}\cos x-1}{\cot x-1}?$$   I know how to use L'Hospital's rule to calculate this limit and got the answer as $0.5$. But, how do I calculate the limit by manipulating the function? Please provide only some hints to proceed. Is $(B_t^2)$ Markov where $(B_t)$ is Brownian motion? I am pretty sure $(B_{t}^{2})$ not Markov because the squared random walk is not.    I guess I can repeat the method since to be Markov it must satisfy the discrete.  Thanks Any javascript event occurring when user clicks Stop load button? Why does light in a room not form constructive and destructive interference patterns? NOTE: I would appreciate it if you provided a hint and not the whole solution.  BdMO 2014 Nationals:     In acute angled triangle ABC, considering a portion of side BC as diameter a    circle is drawn whose radius is 18 units and it touches AB and AC side. Similarly,    considering a portion of sides AC and AB as diameters, two other circles are    drawn whose radii are 6 and 9 units respectively. What is the radius of the incircle    of ∆ABC?   The main problem with this  problem is that the figure is incredibly messy.So I drew one circle,and tried getting information from it.I noticed that if $O$ is a centre of one of the above (semi)circles,and if $O$ is located on $AB$, then $CO$ is an angle bisector.Therefore,if we connect all the vertices with the centres,their intersection would be the incentre.Then we need to drop a perpendicular from this point to get the inradius.But that hardly helps us.I have found some similar triangles in the figure.But that does not help me at all.  I have also tried backtracking.I tried to put myself in the problem-maker's shoes and tried to imagine what I would do if I had to create a problem like this.Unfortunately,I couldn't do it..  Any insightful comment,hint will be very much  appreciated. Irreducible cyclotomic polynomial I want to know if there is a way to decide if a cyclotomic polynomial is irreducible over a field $\mathbb{F}_q$? I see people say statement as question while speaking by raising their voice at the of it to mean it's a question.   For example consider followings.         You want to stay here? ==> Is used to mean "Do you want to stay here?"   You guys spoke to anyone? ==> Is used to mean "Did you guys speak to anyone?"      Are these really used by native speaker in casual speech? And can I write them in the same way while writing them as dialogue by putting them between quotes? Are there any special grammar rules for these kind of questions? System of congruences with variable I am looking over , and I came across a solution containing this:  Problem Bernardo chooses a three-digit positive integer $N$ and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer $S$. For example, if $N = 749$, Bernardo writes the numbers $10,\!444$ and $3,\!245$, and LeRoy obtains the sum $S = 13,\!689$. For how many choices of $N$ are the two rightmost digits of $S$, in order, the same as those of $2N$? $\textbf{(A)}\ 5 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 15 \qquad\textbf{(D)}\ 20 \qquad\textbf{(E)}\ 25$ Solution 1 First, we can examine the units digits of the number base 5 and base 6 and eliminate some possibilities. Say that $N \equiv a \pmod{6}$ also that $N \equiv b \pmod{5}$ Substituting these equations into the question and setting the units digits of $2N$ and $S$ equal to each other, it can be seen that $b &lt; 5$ (because otherwise $a$ and $b$ will have different parities), and thus $a=b$. $N \equiv a \pmod{6}$, $N \equiv  a \pmod{5}$, $\implies N=a \pmod{30}$, $0 \le a \le 4$ Therefore, $N$ can be written as $30x+y$ and $2N$ can be written as $60x+2y$ Just keep in mind that $y$ can be one of five choices: $0, 1, 2, 3,$ or $4$, ; Also, we have already found which digits of $y$ will add up into the units digits of $2N$. Now, examine the tens digit, $x$ by using $\mod{25}$ and $\mod{36}$ to find the tens digit (units digits can be disregarded because $y=0,1,2,3,4$ will always work) Then we take $N=30x+y$ $\mod{25}$ and $\mod{36}$ to find the last two digits in the base $5$ and $6$ representation.[N \equiv 30x \pmod{36}][N \equiv 30x \equiv 5x \pmod{25}]Both of those must add up to[2N\equiv60x \pmod{100}] $N\equiv{30x\mod{36}}\\N\equiv{30x}\equiv{5x\mod{25}}$ Both of these must add up to $2N\equiv{60x\mod{100}}$ [...]  I'm not really sure which modular arithmetic rule to apply in the final three congruences, or where to start. How would I go about understand this? This is somewhat of a beginner's question, but how does one interpret an exp(B) result of 6.012 in a multinomial logistic regression model?  1) is it 6.012-1.0 = 5.012 = 5012% increase in risk?  or  2) 6.012/(1+6.012) = 0.857 = 85.7% increase in risk?  In case both alternatives are incorrect, can someone please mention the correct way?  Ive searched many resources on the internet and I get to these two alternatives, and I am not entirely sure which one is correct. Look and you shall find (a correlation) I have several hundred measurements. Now, I am considering utilizing some kind of software to correlate every measure with every measure. This means that there are thousands of correlations. Among these there should (statistically) be a high correlation, even if the data is completely random (each measure has only about 100 datapoints).  When I find a correlation, how do I include the information about how hard I looked for a correlation, into it?   I am not at a high level in statistics, so please bear with me. Watch Filesystem in Real Time on OS X and Ubuntu I'm looking for a CLI tool which will watch a directory and spit out the names of files that change in real time.   some_watch_command /path/to/some/folder | xargs some_callback   I'm aware of inotify (inotify-tools?) and it seems to be what I need, but I need something that is both Linux (in my case Ubuntu) and OSX compatible.  It doesn't need to be lightning fast, but it does need to trigger upon changes (within a second is reasonable). Also, I don't necessarily need the exact CLI program mentioned above.  If some underlying tech exists and is easily scriptable on both platforms that would be great too. Let $X$ and $Y$ be independent $Exp(1)$-distributed random variables. Find the conditional distribution of $X$ given that $X + Y = c$ ($c$ is a positive constant).  this is my idea:  $$f_{X \mid X+Y}(x\mid c) = \frac{f_{X,X+Y}(x,c)}{f_{X+Y}(c) } $$  if this is the right definition then i might calculate the righthand side to obtain the distribution but Iam unsure How do I edit a file in /proc that can be viewed with cat, but is not editable by mousepad and abiword? What does [&] mean before function? Multigroup (CCK3) / FlexiField-like solution for compound fields? I've used  in the past to do multiply occurring series of field groups; now, working on a Drupal 7 project, I'm setting up a "Resume" content type and need a way to set up repetitive entries for education/work experience.   IE: for "Education", I need the ability to dynamically add new rows comprised of a combination of dates and places for each institution studied at.  What is the best way to accomplish CCK3 multigroup/FlexiField-like functionality in Drupal 7?  Thanks! t-test or z-test: assume normality or s≈σ? Let's say I have a large sample ($n&gt;30$) with mean $\bar{X}$ and standard deviation $S$. I can calculate only: $T=\frac{\bar{X}-\mu}{S/\sqrt{n}}$.  If I want to use t-test for a hypothesis, then I have to assume normality of the population. If I want to use z-test for a hypothesis, then I have to assume that $\boldsymbol{s\approx\sigma}$.  What is the less important assumption? What test should I do? Should I do t-test, z-test or doesn't matter?