UK citizen entering UK on US passport
Do I have to enter the UK on my UK passport?
How do we see? Where do the photons disappear? I know that the light is reflected from a object to my eyes, but I don't understand exactly how. The photons appear from the light source and disappear in my eye! Can someone explain the phenomenon of where the photons go and do to allow us to see? I'm asking about someone who's employed by a company and does different jobs (both a qualified and unqualified person). Who knows; maybe in English those two are two different words? What are they called in English?  All I know is a navvy but that usually means physical work.  Let me just try a few things here. These are just wild guesses, nothing more.    odd job man/worker   shiftman   (unskilled) labourer Can we say that $\frac{0}{0}$ is every number? How much money do I need to show as proof of support when applying for a UK Standard Visitor visa? How can I use JUnit4 idiomatically to test that some code throws an exception?  While I can certainly do something like this:  @Test public void testFooThrowsIndexOutOfBoundsException() {   boolean thrown = false;    try {     foo.doStuff();   } catch (IndexOutOfBoundsException e) {     thrown = true;   }    assertTrue(thrown); }   I recall that there is an annotation or an Assert.xyz or something that is far less kludgy and far more in-the-spirit of JUnit for these sorts of situations. I'm well aware of the combinatorial variant of the proof, i.e. noting that each formula is a different representation for the number of subsets of a set of $n$ elements. I'm curious if there's a series of algebraic manipulations that can lead from $\sum\limits_{i=0}^n \binom{n}{i}$ to $2^n$. How do you concatenate characters in java? Concatenating strings would only require a + between the strings, but concatenating chars using + will change the value of the char into ascii and hence giving a numerical output. I want to do System.out.println(char1+char2+char3... and create a String word like this.  I could do   System.out.print(char1); System.out.print(char2); System.out.print(char3);   But, this will only get me the characters in 1 line. I need it as a string. Any help would be appreciated.  Thanks What exactly are censored data? I have read different descriptions of censored data:  A) As explained in  thread, unquantified data below or above a certain threshold is censored. Unquantified means data is above or below a certain threshold but we do not know the exact value. Data is then marked at the low or high threshold value in the regression model. It matches the description in this , which I've found very clear (2nd slide on first page). In other words $Y$ is capped to either a minimum, a maximum value or both because we do not know the true value outside of that range.   B) A friend told me that we can apply a censored data model to partially unknown $Y$ observations, provided we have at least some limit information about the unknown $Y_i$ outcomes. For example, we want to estimate the final price for a mix of silent and open auctions based on some qualitative criteria (type of goods, country, bidders wealth, etc.). While for the open auctions we know all final prices $Y_i$, for the silent auctions we only know the first bid (say, $1,000) but not the final price. I was told that in this case data is censored from above and a censored regression model should be applied.  C) Finally there is the definition given by the  where $Y$ is missing altogether but the predictors are available. I'm not sure how this example is different from truncated data.  So what exactly are censored data? Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$ Given that $C_n$ is a cyclic group of order $n$, what conditions must integers $n$ and $m$ satisfy such that the group $C_n \times C_m$ is isomorphic to C$_{mn}$?   So I attempted to investigate a few lower-order cyclic groups to find a pattern. In particular, I looked at $C_2 \times C_3$ and compared it to $C_6$. Here are a couple of diagrams:  $C_2 \times C_3$ -   $C_6$ -   They Cayley tables look pretty different (identity elements are all over the place for $C_2 \times C_3$) so I concluded that they are not isomorphic.  I did the same for $C_2 \times C_4$ and $C_8$:  $C_2 \times C_4$ -   $C_8$ -   Again, I arrived at the conclusion that the 2 groups are not isomorphic due to their Cayley table structure.  It seems I'm stuck now. Are my conclusions wrong for the examples I examined? If so, how do I find the conditions for the general case of comparing $C_m \times C_n$ with $C_{mn}$? The use of imaginary and complex values comes up in many physics and engineering derivations. I have a question about that: Is the use of complex numbers simply to make the process of derivation easier, or is it an essential ingredient, without which it would be impossible to derive some results?   I can identify two different settings where the answer may be different:   It doesn't look like it is mandatory for results in Newtonian mechanics, General Relativity and classical electrodynamics. Can we say the same thing about quantum mechanics either way for sure?   Could this be a difference in quantum mechanics over the classical picture? In PHP, what does the ${$ } syntax do? Is there a way to take a screenshot using Java and save it to some sort of image? Simple as the title states: Can you use only Java commands to take a screenshot and save it?  Or, do I need to use an OS specific program to take the screenshot and then grab it off the clipboard? I've got this situation:  ./ ./myscript.sh ./arguments.txt ./test.sh   Inside myscript.sh, I have to run the file test.sh, passing to it the arguments contained inside arguments.txt.  myscript.sh is:  arguments=$(cat arguments.txt) source test.sh $arguments   This works well if if arguments.txt contains at most one argument:  firstargument    The substitution is:  ++ source test.sh 'firstargument'   But the problem is with two or more arguments. It does this:  ++ source test.sh 'firstargument secondargument'   Also, I don't know in advance the number of arguments inside arguments.txt. There can be zero or more. This is a canonical question that will hopefully encompass all of the questions we get asking us to determine what year a bicycle was manufactured (how old is my bike, how old is my frame, etc.). Each "answer" should address a different way to determine the manufacturing year of a bicycle. To some extent, these will also help you narrow down the model as well as it will tell you what distinguishing features to look at.  The span of answers would include things such as:      Skiptooth cranks Cartridge bottom brackets (BB30/90 etc) Elliptical chainring Quick releases versus contemporary through-axles How the steerer attaches to the fork (quill vs. threadless)  Braking system (especially with mountain bikes: v-brake, direct pull, etc.)   Shifting ramps and pins on cassettes/sprockets and chainrings (versus flat sprockets) Frame material (e.g., shift from tubular steel to use of CF and hydroformed aluminium)  Frame tubing type (e.g. Reynolds 531 tubing introduced around 1934, still used today; Reynolds 501 tubing introduced around 1983). So a frame with an original 501 decal can't be from the 70', 531 decal doesn't help as much because of the range of years produced. Also, see Decals.   *Decals: style/design, amount, placement, color, etc. can help not only determine models, but also year of manufacture. Many changed decal design for the same model bike often yearly, with special/limited editions even more specific. This applies only if decals are original or have been replaced with the identical design. Tubing decals (Reynolds, Columbus, etc.) also changed designs for same tubing made in different years, although the changes aren't made as often, and manufacturers didn't always put tubing Brand decals on every model. Earlier bikes tended to have less fancy, less colorful, less quantity of decals.   Headbadges: most early bikes had actual "badges", often quite detailed and fancy, made of metal, then plastic, and finally just using decals on the headtube. Most bikes lost their metal badges in the 60's and early 70's, although some brands still have actual badges to this day, but in general a real badge indicates an earlier model bike. Dropout style (including the later inclusion of lawyers lips) Presence or absence of CPSC reflectors (USA only) Manufacturing method (shift from lugs to TIG welding, for example)  Number of gears (shift from 2x5 ten-speed to 3x8, 2x9, 1x11, etc.)  Inspection of lug design: pantographs, cut-out, stampings, custom brazing/filing, chrome, fork crow n sweep, etc. Frame/Fork Braze-ons. Race bikes tended have less braze-ons the earlier the year of manufacture. Most 60's racers and earlier had few or none with cable guides/stops, shifters, bidons, etc. being clamp-on. By the 80's if it was clamp-on, it was a sign of very cheap models and most frames had braze-ons for all cables, with multiple bottle and accessory bosses depending on style and use.   and so forth. Please edit this question if you have an answer that isn't in the index above.   A couple of caveats:   A previous owner could have replaced or upgraded components on a bicycle, so this guide only applies to original equipment There is a delay between the introduction of a technology (such as indexed shifting) and when manufacturers start selling products that use it. Low-end manufacturers may continue using technology that is severely outdated (such as one-piece cranks, freewheels, or quill stems) because it is cheaper to do so. A number of bikes are built in a Retro style, but with modern components.  Dutch bikes, trendy coffee cruisers, and beach cruisers may be modern but appear to be 1950s styling.  These tend to have modern rims and brakes as a giveaway.     Note that bicycles.stackexchange does not do valuations of bicycles. How much your bicycle is worth depends on the location of the buyer and seller, how much the buyer wants the bike, etc. etc. etc. Convergence test of the series $\sum\sin100n$ I need to prove that $$\sum_{n=1}^{\infty} {\sin{100n}} \; \text{diverges}$$ I think the best way to do it is to show that $\lim_{n\to \infty}{\sin{100n}}\not=0$. But how do I prove it? Fire (at, on, in, to) target How to correctly choose the preposition in "fire (at, on, in, to) target"? I use both GNOME and KDE SC. In GNOME, I use Docky but I do not use it with KDE. So, I would like Docky to start up only when I login into GNOME not KDE. In KDE, there is an option to make a program autostart only in KDE. But I cannot find any such option in GNOME.    How can I do this?    Thanks in advance. Symmetry condition for continuous coordinate transformations I'm running a witcheling, a changeling witch who, because of a GM's homebrew magic ring, can transform into a .  What effects does this pixie transformation have? Specifically...   Since I'm now Small, do I apply +1 to AC, +1 to attack rolls, –1 to CMB and CMD and +4 to Stealth? Am I able to cast spells while transformed? Do I lose my racial benefits while transformed? Am I still able to use weapons such as staff, longsword, or greatsword? Is it possible to create a counter just with wiring? With the new logic gates in the 1.3.1 update, is it possible to create some wiring circuit that counts how many times a trigger was activated? In other words, is it possible to make a circuit that outputs a trigger every two input triggers?  I've done some experimenting but the nature of wires and there being no intrinsic on/off state in Terraria makes it pretty counter-intuitive compared to real world logic circuits.