Not a particularly complex question but I'm looking for a efficient/clean way to generate all possible permutations of tuples.  For example, given a size value (ex. 3) for an n x n grid.   (1,1) (2,1) (3,1) (1,2) (2,2) (3,2) (1,3) (2,3) (3,3)   I'd like to generate comparisons between rows and columns.  So for rows, comparisons would go as (1,1) vs (2,1), (1,1) vs (3,1), (2,1) vs (3,1) ... (1,2) vs (2,2), (2,2) vs (3,2) ... etc  And for columns, comparisons would go as (1,1) vs (1,2), (1,1) vs (1,3), (1,2) vs (1,3), .. (2,1) vs (2,2), (2,1) vs (2,3), (2,2) vs (2,3) ... etc  Does anyone know of an easy way to generate each pair of tuples? I'd like to pass the two tuples from the comparison into a separate function (tuple1, tuple2). Got an idea but it uses multiple for loops and seems inefficient. Assistance would be appreciated.
How do you generate all the permutations of a list in Python, independently of the type of elements in that list?  For example:  permutations([]) []  permutations([1]) [1]  permutations([1, 2]) [1, 2] [2, 1]  permutations([1, 2, 3]) [1, 2, 3] [1, 3, 2] [2, 1, 3] [2, 3, 1] [3, 1, 2] [3, 2, 1]
Finding net magnetic and electric force on charged particle This is from my textbook, it is not an assigned problem, but I want to understand.   It says:      Consider the situation in the figure, in which there is a uniform electric field in the x direction and a uniform magnetic field in the y direction. For each example of a proton at rest or moving in the x, y, or z direction, what is the direction of the net electric and magnetic force on the proton at this instant?   I believe I need to use the equation   $$ F_{net}=(q\overrightarrow{E})+q(\overrightarrow{v} \times \overrightarrow{B}) $$  But I'm not sure exactly how. We've just started to learn about this, and I want to get a head start. Could anyone put me on the right track? Integral of $\sin x \cos x$ using two methods differs by a constant? $$ \int \sin \theta\cos \theta~d \theta= \int \frac {1} 2  \sin 2\theta~ d \theta=-\frac {1} 4  \cos 2\theta$$ But, if I let  $$ u=\sin \theta , \text{ then }du=\cos \theta~d\theta $$ Then $$ \int \sin \theta\cos \theta~d \theta= \int u ~ du =\frac { u^2 } 2 =\frac {1} 2 \sin^2 \theta $$ Since $$ \sin^2 \theta =\frac {1} 2 - \frac {1} 2 \cos 2\theta$$ The above can be written as $$ \int \sin \theta\cos \theta~d \theta= \frac {1} 2 \sin^2 \theta =\frac {1} 2 \left( \frac {1} 2 - \frac {1} 2 \cos 2\theta \right)=\frac {1} 4-\frac {1} 4 \cos 2\theta   $$ Why are the two results differ by the constant $1/4$? Thank you. Incorrectly answered 'No' to "Any previous visa refusals..." on a UK Standard Visitor visa application. How can I fix my mistake? Access denied for user 'root@localhost' (using password:NO) How to permanently set environmental variables My variables are   LD_LIBRARY_PATH=/usr/lib/oracle/11.2/client64/lib ORACLE_HOME=/usr/lib/oracle/11.2/client64   How to save these variables permanently ? Turning fullscreen on made Minecraft crash, and now it crashes on start every time I switched to full screen on minecraft, the screen turned black as if it were loading it took a while so i closed minecraft and reopened it. When I logged on it gave me a program on my taskbar saying "minecraft minecraft" then when i closed the program it gave me this error message:   java(tm) platform SE binary has stopped working.    Is there a way to fix this? I'm new to Linux (currently running Ubuntu 10.04) and I have just finished setting up SSH access to my Linux Machine.  Currently, I have to use ssh root@x.x.x.x to connect but would much rather be able to swap the IP for the computer name (like in Windows with \\name) or a domain name (like computername.example.com). I don't really know where to start so any help would be most appreciated.  Please go slowly, as mentioned - I am still new to this.  EDIT 1 Completely forgot to mention that I am trying to connect from Windows 7 (via PuTTY) - sorry. Eclipse CDT - Copy static resource file to bin_dir I am having trouble getting onto a server in Minecraft PE on iOS. When I tap on the person's server it just says invalid name:    I have tried turning off and restarting the iPad, going to home screen and logging back into the server but I have had no luck and no change. Is there a reason why this is so? Local SEO Strategies What are your strategies for local SEO? For example, if you had a web design company in Lincoln, Nebraska, what would you do for your website from an SEO perspective? What is the name of this kind of character illustration? I have seen lots of UI designer nowadays including this kind of illustration i want to know the name of this style so that i can also learn and try this in my designs. Finding the perimeter of a right triangle with area given Let's say we have $2$ particles facing each other and each traveling (almost) at speed of light.    Let's say I'm sitting on #$1$ particle so in my point of view #$2$ particle's speed is (almost) $c+c=2c$, double light speed? Please say why I am incorrect :)    EDIT: About sitting me is just example, so in point of view of #1 particle, the second one moves at (almost) $c+c=2c$ speed? How do you show monotonicity of the $\ell^p$ norms? I can't seem to work out the inequality $(\sum |x_n|^q)^{1/q} \leq (\sum |x_n|^p)^{1/p}$ for $p \leq q$ (which I'm assuming is the way to go about it). I am very new to cryptography (so be kind), but I have a question that may seem silly.   If the one-time pad is the perfect cipher and impossible to crack, why would the following algorithm not be one of the strongest:  To encrypt:   generate a random bit array using a pseudo number generator with the key as the seed  The generated bit array is the size of the data use a simple XOR to encrypt using the generated bit array   To decrypt:   pseudo-random number generator will generate the same bit array with the same seed (the key) generate bit array the same size of the encrypted data run XOR on encrypted data using bit array that's generated   This is very simplified, but you can imagine how for larger encryption you could break down the data into blocks, and in order to ensure that the block bit arrays are random a new seed for each can be derived from the key. So, if $f(k)$ is the pseudo random number generator, and b is the block number, you can encrypt each block with $f(k+b)$. ($k$ is key)   Instead of using a pseudo-random number generator, you could use some hash algorithm to generate the pad.    (assuming you can use equivalently strong keys) would this not be a very strong cipher method? Perhaps it may be strong and heavy on memory since the pad needs to be the size of the data. So during encryption and decryption you need to generate a pad that's equivalent to the size of the data.   Is there a flaw in this algorithm, or would something like this not be practical and much slower than current standards? Following an earlier question ,  I would love to implement the  as suggested by Russell McMahon.   That way I could switch between 4AA batteries (1.2V*4 or 1.5V*4) and USB power. The battery voltage would nicely be regulated to 5V too. And the idea was to use the shutdown pin of the chip IF USB power is detected. The device also has to work when no batteries are present.  I am not too experienced with this, but I thought to connect the 5V from the USB to the SHUTDOWN pin from the LDO chip. Pitywise, the pin function is inverted, if SHUTDOWN is low, Vout from the LDO chip is low.  I am now considering using an XOR gate to make the thing work:         &ndash; Schematic created using   I would love to limit the amount of components, but the number of diodes is already high, and the whole thing feels a bit crafted   My questions:    Is there a better suitable chip (with an inverted shutdown pin) is there a better circuit (without voltage drop) to get this (I would prefer to get rid of D1, but then, the XOR has no desired operation) Incoming light reacts with the several types of cone cells in the eye. In humans, there are three types of cones sensitive to three different spectra, resulting in trichromatic color vision. Each individual cone contains pigments composed of opsin apoprotein, which is covalently linked to either 11-cis-hydroretinal or more rarely 11-cis-dehydroretina.  The opsins (photopigments) present in the L and M cones are encoded on the X chromosome.  A very small percentage of women may have an extra type of color receptor because they have different alleles for the gene for the L opsin on each X chromosome. X chromosome inactivation means that only one opsin is expressed in each cone cell, and some women may therefore show a degree of tetrachromatic color vision. Tetrachromacy is also demonstrated among several species of birds, fish, amphibians, reptiles and insects.  Humans cannot see ultraviolet light directly because the lens of the eye blocks most light in the wavelength range of 300–400 nm.  So, besides above mentioned exceptions, is it possible due to mutations or genetic engineering to see UV or infrared. What kind of mutations should be made or are the changes to be made in the opsines to big to create 'alien' eyes? I'm still learning, but I'm trying to follow a tutorial to apply texture to a model. I only want to apply the texture to one object in the scene, so I selected it, unwrapped it, and painted over it. Now I selected it in the Edit Mode (I can't select it in the Object mode because all is locked together) and went into Node Editor, but the nodes are greyed out.  Why? Suppose all the Associated Primes are Minimal. Let $R$ be a commutative Noetherian ring with unit and let $I$ be a fixed ideal. I am sorry if the following turns out to be a very silly question.  1) Suppose $\operatorname{Ass}(R/I)$ are all minimal, then what can we say about $R/I$?  One conclusion is that $I$ has a unique primary decomposition. If $R/I$ is CM, then $\operatorname{Ass}(R/I)$ are all minimal, but I don't think the converse is true. Can someone provide a counterexample?  2) Suppose $\operatorname{Ass}(R/I)$ are all minimal and have the same height. I still dont think we can conclude that $R/I$ is CM. Can someone provide a counterexample? Theorem 2.1.6 of Bruns and Herzog, CM Rings, gives a result in this direction but it needs additional hypothesis. It says that if every ideal $I$ is generated by height $I$ elements and $\operatorname{Ass}(R/I)$ are all minimal, then $R$ is CM.  It would be nice if someone can say something nice about the ring in the special situation described in 1) and 2).  Thanks. Everybody perhaps knows of Jon Favreau's movie  which is going to be released in 2016. But quite recently I learned (and to my utter surprise) that another Jungle book movie is coming in 2017 and it's called .   Now, this movie has big names too with Christian Bale as Baghera, Benedict Cumberbatch as Sher Khan, Cate Blanchett as Kaa and a young Indian boy in the live action role as Mowgli.   How often does this happen, with two big productions with big cast making a movie on the same subject? I want to ask why this is happening and if there are any really significant differences between the two (apart from the cast, of course).