Entering the UK as a tourist then as a student
Can I visit the UK as a tourist before my Student Visa starts?
I often have to sort a dictionary, consisting of keys &amp; values, by value. For example, I have a hash of words and respective frequencies, that I want to order by frequency.  There is a SortedList which is good for a single value (say frequency), that I want to map it back to the word.   orders by key, not value. Some resort to a , but is there a cleaner way? Order of general- and special linear groups over finite fields. Breitbart today:   What is the source for the term nothing-burger? $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$ Consider a finite-dimensional vector space $V$ over the field $\mathbb{F}$ with a linear operator $T.$ Prove that we have $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2 \operatorname{rank}(T^2).$   First, let us assume that $\dim_{\mathbb{F}}(V) = n.$ Our immediate observations include that $T^3(V) \subseteq T^2(V) \subseteq T(V)$ so that $\operatorname{rank}(T^3) \leq \operatorname{rank}(T^2) \leq \operatorname{rank}(T)$ and $\operatorname{rank}(T^3) \geq \operatorname{rank}(T) + \operatorname{rank}(T^2) - n$ by Sylvester's Rank Inequality. Can we do some manipulations with what we have to get the desired inequality, or do we require something else? Why are more powerful tools using higher voltage? AFAIK each of the world leading cordless power tools manufacturers produces several "product lines" of cordless power tools with different voltages. For example, Bosch currently produces tools with Li-Ion batteries with 10,7V, 14,4V, 18V and 36V output and the higher the voltage the more powerful a tool is.  Now those tools are powered by batteries that are assembled from cells with lower voltage (something like 3,7 volts for Li-Ion cells I guess) and cells are connected in sequence until the target voltage is reached.  They could instead connect cells in parallel. They would have the same voltage, but higher current and that would again yield higher power.  Why do they choose higher voltage over same voltage and higher current to get higher power in electric tools? I need to find a bottleneck and need to accurately as possible measure time.  Is the following code snippet the best way to measure the performance?  DateTime startTime = DateTime.Now;  // Some execution process  DateTime endTime = DateTime.Now; TimeSpan totalTimeTaken = endTime.Subtract(startTime); In the 1960s I read book--an older children's book, I think--which I loved, and still remember, roughly.  I have no idea what the title is or who the author is, and I'm wondering if anyone knows this one:  Scientists had invented a device which they didn't fully understand, and which had puzzling effects.  For example, when a pencil was put into the machine, it disappeared, and then reappeared inside out: The lead was on the outside.  When people went into the machine, they came back dead, having died from fright.  Finally they sent a very open-minded person into the machine.  She was an artist, I think.  She was able to return alive, and described an alternate universe in which geometry was very different.  I distinctly remember that there were supposedly square triangles or four-sided triangles--or was it three-sided squares?  (This is, of course, a literally contradictory claim, but I didn't see the matter as clearly then.)  Thanks! Prevent specific sites from being overrepresented in the hot questions list Some sites appear far more often in the hot questions list than other sites. I don't have any hard data on that, as that kind of data is just not publicly available, but I'm pretty sure my subjective impression on that is reasonably accurate.  Those sites don't appear more often because they are inherently more interesting, but because they have certain voting and answering patterns that favor them in the hot questions algorithm. I would argue that the goal of the hot questions list is to present questions from a large variety of SE sites to the whole network, and to show possibly interesting questions to users that would not have found them otherwise.   To achieve this goal, the spots in the hot questions list should be distributed among all SE sites. The algorithm should try to get a good sampling of all sites, and it should try to normalize the results for varying voting behaviour. At the moment, sites that intrinsically get more votes and more answers per question seem favored in the algorithm.  So I think one part of the algorithm should try to identify questions that get an unusally high amount of votes and views for that site, and give the smaller sites a chance this way.  I'm not sure on how exactly this weighting should be done, as a complete normalization would likely not work across the huge difference in scale for all the SE sites.  As a specific example that the current algorithm is broken I'll present . I don't think any site should occupy a third of the whole list.   Here's another instance where one site is overrepresented at the top of the list: I am looking for a quick way to sleep without closing the lid, or using the mouse.  If it matters, I have Lion version OS and a MacBook Air. If the magnetic field doesn't polarize does it follow the electric field path of propagation? or does it vanish? Automate keystrokes in Windows 7 64-bit I need to automate the pressing of the  key then pressing 5 digits then press  in Windows 7 64-bit.  I have an app that comes up on the screen and I need the "script" to press the keys.  I don't even need mouse support.  What can I use to do this?  Any examples or links? How can I get my external IP address in a shell script? I need to install more applications - can I use my external HD (samsung T5) and add an additional applications folder? I have loads of space on it and it the speeds are great. Show Previous/Next Posts navigation only inside the same category Is it possible to force previous/next navigation to browse through the posts (back and forth) that are only inside the same category (and to exclude other categories)? This is Problem 6 of the 2007 Indian National Math Olympiad (INMO).  If $x, y, z$ are positive real numbers, prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2).$  My best idea was to expand this and simplify. Although that doesn't look very feasible. Another idea is to see that $x^2+y^2+xy \geq x^2+y^2$. Then we just have to show that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(x^2+y^2)(x^2+z^2)(y^2+z^2)$ if that is even true. Sum of odd Fibonacci Numbers Trying to prove that the sum of odd-index consecutive Fibonacci numbers is the next even-index Fibonacci number. I have a gap in my proof that I cannot figure out. I know that induction would be easier and I have already done it that way, I am looking to use alpha and beta. $$\sum_{i=1}^n F_{2i-1} = F_{2n}$$  $$\begin{align*} \sum_{i=1}^n F_{2i-1}&amp;=\sum_{i=1}^1  \frac{1}{\sqrt{5}}(\alpha^{2i-1}-\beta^{2i-1})\\ &amp;=\frac{1}{\sqrt{5}}\left(\sum_{i=1}^1\alpha^{2i-1}-\sum_{i=1}^1\beta^{2i-1}\right)\\ &amp;\;\;\vdots\\ &amp;=\frac{1}{\sqrt{5}}[(\alpha^n-\beta^n)(\alpha^n+\beta^n)]\\ &amp;=\frac{1}{\sqrt{5}}(\alpha^{2n}-\beta^{2n})\\ &amp;=F_{2n} \end{align*}$$ What is the best program for image optimizing for the web? What programs besides Photoshop are good for saving and optimizing images for web? How can I animate the Restrict Visibility property of an object? How can I remove myself from India's visa blacklist? How to tail multiple files using tail -0f in Linux/AIX I tried tailing two files using the option:  tail -0f file1.log -0f file2.log   In Linux I see an error "tail : can process only one file at a time".  In AIX I see the error as "Invalid options".  This works fine when I use:  tail -f file1 -f file 2   in Linux but not in AIX.  I want to be able to tail multiple files using -0f or -f in AIX/Linux  multitail is not recognized in either of these OS.