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Here's :        At the moment, the latest entry there is October 13, which would be mistaken to mean October last year (2012), but it actually is October 2010. This applies to all the filters in the activity tab. explicit formula for recurrence relation $a_{n+1}=2a_n+\frac{1}{a_n}$ For $n\in\mathbb N$, $$a_{n+1}=2a_n+\frac{1}{a_n},\quad a_1=1. $$ Can any one give an explicit formula for all $a_n$? If such an explicit general formula doesn't exist, please explain it. I've tried to figure out the $n$-iterated function $f^{(n)}$ where $f(x)=2x+1/x$ or even $f(\tan(t))$. But in either cases, I failed.Since the recurrence isn't linear nor homogeneous,the generating function method doesn't apply here. Let $I = \{a +ib \in \Bbb Z[i] : a$ and $b$ are both multiple of $5\}$. Let $I = \{a +ib \in \Bbb Z[i] : a$ and $b$ are both multiple of $5\}$. Show that $I$ is an ideal of $\Bbb Z[i]$. Is $I$ a maximal ideal? And to find the numbers of elements of the quotient ring $\Bbb Z[i]/ I$.  I have shown that $I$ is an ideal of $\Bbb Z[i]$. But how to verify that $I$ a maximal ideal or not?   And to find the numbers of elements of the quotient ring $\Bbb Z[i]/ I$.   Is there any general way to verify when  $I = \{a +ib \in \Bbb Z[i] : a$ and $b$ are both multiple of $n\}$ will be maximal or not? How does LIGO remove the effects of environmental noise? Since LIGO is dealing with readings at nanometers, events such as vehicles driving nearby, and constant (but extremely minor) tremors of the earth can cause movement with the mirrors at nanometers.  Such tiny movements are extremely difficult to measure, but can easily cause errors when using such a small scale.  How does LIGO remove these factors, and take precautions to prevent false readings due to noise? Binding energy and mass I’ve been told that a greater binding energy means the nucleus is more tightly bound, and therefore that decreases the mass of the nucleus with respect to its nucleons when separated. But why does a tighter nucleus mean a smaller mass? I've just gotten through replacing capacitors on a trio of dead LCD screens (nothing's blown up yet, so far) - they either had one or two capacitors on their inverter circuit SLIGHTLY bloated, and not quite leaky. I ended up replacing all capacitors of the same brand/'colour', even the ones that looked fine, in case.  Now, checking a bad resistor is simple - i can use a standard multimeter to test it, and i tend to check my solders with the continuity testing option of the multimeter.  How would i test a capacitor ? Is there some standard, common way to test one? Energy conservation in General Relativity I understand that energy conservation is not a rule in general relativity, but I'd like to know under what circumstances it can still be possible. In other words, when is it possible to associate a potential energy to the gravitational field, so that the energy is constant in the evolution of the system?  Here are some examples, is there a convenient way to define energy in these scenarios?   Just a system of gravitational waves. A point mass moving in a static (but otherwise arbitrary) space-time. Equivalent (if I'm not mistaken) to a test mass moving in the field of a second much larger mass, the larger mass wouldn't move. Two rotating bodies of similar mass.   Overall, I'm trying to understand what keeps us from associating a potential energy to the metric. When we break the time translation symmetry of a system by introducing an electromagnetic field, we can still conserve energy by defining an electromagnetic potential energy. Why can't we do the same when we break TT symmetry by making space-time curved? I am firmly convinced he is innocent and his accusation is the result of the police conspiracy.     I am firmly convinced he is innocent and his accusation is the result of the police's conspiracy.    Which sentence do you think is a better choice? Some days I'm working with extremely large Excel files.  They have too many sheets that can't be shown in one sheet tab. (see image)      So, I'm wondering whether or not we can show Excel sheet on more than 1 row. Many tries with Google don't help much.    Many tries but I still can't make Excel show the sheet bar the way I want (≥ 2 rows), so I'm working with some VBA Scripts kopischke suggested.    FYI, right click on |&lt; &lt;&lt; &gt;&gt; &gt;| button on the bottom-right corner show you a list of up to 15 sheets.  For more, click on View more in the list appeared. Is the convex hull of a compact set compact? Let $V$ be a normed vector space and $K$ a compact subset of $V$. Is the convex hull of $K$ given by $$\langle K \rangle = \left\{\sum_{i=1}^n t_i x_i\mid x_i\in K, t_i≥0\text{ s.t. }\sum_i t_i=1\right\}$$ again compact? Is there a website that lets you shop for hotels with taxes and fees included in search results? Every time I book a hotel online, the price increases by 25% in "taxes and fees" at checkout, compared to the price featured in search results.  This does not occur when booking flights (I actually think there's a regulation against it for flights).  Is there a website that lets you compare the ACTUAL price of hotels with taxes and fees included, and also lets you book? Do AWS Reserved Instances need to be assigned to the instance? I have an RDS instance running of type db.t2.small.  I bought a reserved instance for 1 year of the same type, I paid the partial upfront rate.  Do I need to assign this subscription in some way to my existing instance to say 'This is the instance that is using the subscription' or does AWS just charge for the instance usage depending which instances you have running and whether an available subscription was active for it at the time which determines the running rate?  The reason that I ask is that I can't see any mention of the reduced rate on my AWS Billing area and it shows that I've used 17 hours of my reservation, but there isn't a row on my bill so far this month that indicates the new partial upfront rate that I should be charged for my instance. What test can I use to compare slopes from two or more regression models? I would like to test the difference in response of two variables to one predictor. Here is a minimal reproducible example.   library(nlme)  ## gls is used in the application; lm would suffice for this example m.set &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "setosa") m.vir &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "virginica") m.ver &lt;- gls(Sepal.Length ~ Petal.Width, data = iris,                 subset = Species == "versicolor")   I can see that the slope coefficients are different:  m.set$coefficients (Intercept) Petal.Width    4.7771775   0.9301727 m.vir$coefficients (Intercept) Petal.Width    5.2694172   0.6508306  m.ver$coefficients (Intercept) Petal.Width     4.044640    1.426365    I have three questions:   How can I test the difference between slopes? How can I test the difference between residual variances? What is a simple, effective way to present these comparisons?    A related question, , suggests re-running the model with a dummy variable to differentiate the slopes, are there options that would allow the use of independent data sets? Dryer Outlet - 4 prong to 3 prong Our new dryer has 3 prongs vs. 4. We are changing to the new 3 prong dryer outlet, but want to make sure we are grounding. The wires coming from the wall our white, red &amp; black - the the copper wire. Do I need to ground it?? Thank you! Molly Is it alright to use lowercase "i" or should you always use "I" (uppercase)? How can I have one keyboard input layout and multiples languages in Ubuntu 17.10? If I have English language I can't type "'e" and get an "é", as I can do in Portuguese and Spanish.  When I manage to do that on Settings -> Region &amp; Language, I'm able to change languages, but it also changes the keyboard layout.  Is there any way to change language (Portuguese or Spanish for example) and set the keyboard input layout (US International for example)? How can I format to show text inside ""? I've posted a lot to StackOverflow, and I've noticed something kind of irritating with the formatting in writing questions and comments. If I need to put something inside a &lt; and a >, without spaces in the middle (like right there), it will think it's code and not show up, like this   (obviously it won't come up what I wrote there, or else this wouldn't be an issue, but if you open up the question to edit you can see what's written there.)  If I want it to show up, right now I have to add an extra set of brackets inside of the originals with a junk variable, like right &lt;here> (again, open in edit window to see).  This is really annoying when trying to show variables like lists that require those brackets, and I feel like the junk variables could confuse people looking at the edits. Is there a way to get around this formatting? Thanks! I'm looking for the title of a short story by Ursula Le Guin about a scientist (?) who is given a drug that slows the timescale of his perception enormously, so that he can perceive that an alien (?) forest is actually behaving as a sentient being, reacting to current events, but at an enormously slow (from a normal human point of view) timescale. It might be in , but I don't remember the title (and it doesn't jump out at me from the list of titles) and don't have access to that collection right now. It is not &quot;The Word for World is Forest&quot;, nor &quot;Direction of the Road&quot; (from ), nor &quot;Vaster than Empires and More Slow&quot;, the latter two of which look at similar plant perception/time-scale issues. Update: it turns out that the description was right, but I had most of the details wrong: not Le Guin, not alien, not a scientist ... How To Delete This Red Box on My Screen? I was editing my mesh and I wanted to only see a part of my mesh, so I pressed alt+B to only show a selected area. However, I did ctrl+B and created a red rectangle on my screen (I don't know what it does). Does anybody know how to get it off? "Distribution not supported" when trying to install Intel Graphics Installer in Ubuntu