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  • Treating differential operator as algebraic entity

    - by chappar
    I know that this question is offtopic and don't belong here. But i didn't know somewhere else to ask. So here is the question. I was reading e:the story of a number by Eli Maor, where he treats differential operator as just like any algebraic entity. For example if we have a differential equation like y’’ + 5y’ - 6y = 0. This can be treaed as (D^2 + 5D – 6)y = 0. So, either y = 0 (trivial solution) or (D^2 + 5D – 6) = 0. Factoring out above equation we get (D-1)(D+6)= 0 with solutions as D = 1 and D = -6. Since D does not have any meaning on its own, multiplying by y on both the sides we get Dy = y and Dy = -6y for which the solutions are Ae^x and Be^-6x. Combining these 2 solutions we get Ae^x + Be^-6x. Now my doubt is this approach break when we have an equation like D^2y = 0. Which means y = 0 (again trivial) or D^2 = 0 which means D = 0. Now Dy = y*0 = 0. That means y = C ( a constant). The actual answer should be Cx. I know that it is stupidity to treat D^2 = 0 as D = 0, it led me to doubt the entire process of treating differential equation as algebraic equation. Can someone throw light on this? Or any other site where i might get answer?

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  • Fixing VB6 inaccurate mathmetical results due to rounding

    - by jay
    Try running this in a .VBS file MsgBox(545.14-544.94) You get a neat little answer of 0.199999999999932! This rounding issue also occurs unfortunately in Sin(2 * pi) since VB can only ever see the (user defined) variable pi as accurate as 3.14159265358979. Is rounding it manually (and loosing accuracy) the only way to improve the result? What is the most effective way of dealing with this kind of problem?

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  • integer division in php

    - by oezi
    hi guys, i'm looking for the fastest way to do an integer division in php. for example, 5 / 2 schould be 4 | 6 / 2 should be 3 and so on. if i simply do this, php will return 2.5 in the first case, the only solution i could find was using intval($my_number/2) - wich isn't as fast as i want it to be (but gives the expected results). can anyone help me out with this?

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  • Scientific Algorithms that can produce imagery, pseudocode perhaps?

    - by Ross
    Hello, I have a client who are based in the field of mathematics. We are developing, amongst other things, a website. I like to create a mock-up of a drawing tool that an produce some imagery in the background based on some scientific algorithms. The intention being that the may client, later, may create there own. (They use emacs for everything, great client.) I'm look for an answer of where or what to go looking for. Not code specific, pseudocode even, as we can adapt and have not yet settled on a platform. I'm afraid my mathematic stops at the power of two and some trigonometry. Appreciated if they're are any mathematics related students/academics how could enlighten me? What to search for will be accepted? Edit: To summarise/clarify, I want to draw pretty pictures (the design perspective). I want them to have some context (i.e. not just for the sake of pretty images but have some explanation available). In essence I would to create a rendering engine which we can draw the images and we set the style parameters: line, colour, etc... But to pursue this option I want to experiment myself. Thanks Ross

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  • Algorithm for assigning a unique series of bits for each user?

    - by Mark
    The problem seems simple at first: just assign an id and represent that in binary. The issue arises because the user is capable of changing as many 0 bits to a 1 bit. To clarify, the hash could go from 0011 to 0111 or 1111 but never 1010. Each bit has an equal chance of being changed and is independent of other changes. What would you have to store in order to go from hash - user assuming a low percentage of bit tampering by the user? I also assume failure in some cases so the correct solution should have an acceptable error rate. I would an estimate the maximum number of bits tampered with would be about 30% of the total set. I guess the acceptable error rate would depend on the number of hashes needed and the number of bits being set per hash. I'm worried with enough manipulation the id can not be reconstructed from the hash. The question I am asking I guess is what safe guards or unique positioning systems can I use to ensure this happens.

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  • Given an even number of vertices, how to find an optimum set of pairs based on proximity?

    - by Alex Z
    The problem: We have a set of n vertices in 3D euclidean space, and there is an even number of these vertices. We want to pair them up based on their proximity. In other words, we'd like to be able to find a set of vertex pairs, where the vertices in each pair are as close as possible together. We want to minimise sacrificing the proximity between the vertices of any other pairs as much as possible in doing this. I am not looking for the most optimal solution (if it even strictly exists/can be done), just a reasonable one that can be computed relatively quickly. A relatively awful brute force approach involves choosing a vertex and looping through the rest to find its nearest neighbor and then repeating until there are none left. Of course as we near the end of the list the closest vertex could be very far away, but it is the only choice, therefore this can fail badly on the third point above.

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  • (Ordered) Set Partitions in fixed-size Blocks

    - by Eugen
    Here is a function I would like to write but am unable to do so. Even if you don't / can't give a solution I would be grateful for tips. For example, I know that there is a correlation between the ordered represantions of the sum of an integer and ordered set partitions but that alone does not help me in finding the solution. So here is the description of the function I need: The Task Create an efficient* function List<int[]> createOrderedPartitions(int n_1, int n_2,..., int n_k) that returns a list of arrays of all set partions of the set {0,...,n_1+n_2+...+n_k-1} in number of arguments blocks of size (in this order) n_1,n_2,...,n_k (e.g. n_1=2, n_2=1, n_3=1 -> ({0,1},{3},{2}),...). Here is a usage example: int[] partition = createOrderedPartitions(2,1,1).get(0); partition[0]; // -> 0 partition[1]; // -> 1 partition[2]; // -> 3 partition[3]; // -> 2 Note that the number of elements in the list is (n_1+n_2+...+n_n choose n_1) * (n_2+n_3+...+n_n choose n_2) * ... * (n_k choose n_k). Also, createOrderedPartitions(1,1,1) would create the permutations of {0,1,2} and thus there would be 3! = 6 elements in the list. * by efficient I mean that you should not initially create a bigger list like all partitions and then filter out results. You should do it directly. Extra Requirements If an argument is 0 treat it as if it was not there, e.g. createOrderedPartitions(2,0,1,1) should yield the same result as createOrderedPartitions(2,1,1). But at least one argument must not be 0. Of course all arguments must be = 0. Remarks The provided pseudo code is quasi Java but the language of the solution doesn't matter. In fact, as long as the solution is fairly general and can be reproduced in other languages it is ideal. Actually, even better would be a return type of List<Tuple<Set>> (e.g. when creating such a function in Python). However, then the arguments wich have a value of 0 must not be ignored. createOrderedPartitions(2,0,2) would then create [({0,1},{},{2,3}),({0,2},{},{1,3}),({0,3},{},{1,2}),({1,2},{},{0,3}),...] Background I need this function to make my mastermind-variation bot more efficient and most of all the code more "beautiful". Take a look at the filterCandidates function in my source code. There are unnecessary / duplicate queries because I'm simply using permutations instead of specifically ordered partitions. Also, I'm just interested in how to write this function. My ideas for (ugly) "solutions" Create the powerset of {0,...,n_1+...+n_k}, filter out the subsets of size n_1, n_2 etc. and create the cartesian product of the n subsets. However this won't actually work because there would be duplicates, e.g. ({1,2},{1})... First choose n_1 of x = {0,...,n_1+n_2+...+n_n-1} and put them in the first set. Then choose n_2 of x without the n_1 chosen elements beforehand and so on. You then get for example ({0,2},{},{1,3},{4}). Of course, every possible combination must be created so ({0,4},{},{1,3},{2}), too, and so on. Seems rather hard to implement but might be possible. Research I guess this goes in the direction I want however I don't see how I can utilize it for my specific scenario. http://rosettacode.org/wiki/Combinations

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  • Calculating intraday candlesticks by time intervals

    - by Sam
    This maybe an over asked question, but my mind draws blank at this moment. I know what a candlestick chart is and how to draw it daily. But how to draw it intraday at asked time periods. I have this server, written in Java, that gives me trade depth (each trade done since the start of the day). Its just a stream of raw data: price, shares, timestamp. How does one go about calculating candlestick data from that? Lets say, they want to have 5 min candlestick or 1min candlestick. Or is there a library that will do that for me if I feed it data? Any help is appreciated!

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  • Looking for interesting formula

    - by Thinker
    I'm creating a game where players can make an alloy. To make it less predictable and more interesting, I thought that the durability and hardness of an alloy should not be calculated by a simple formula, because it will be extremely easy to find extrema, where alloy have best statistics. So the questions is, is there any formula for a function where extrema can be found only by investigating all points? Input values will be in percents: 0.0%-100.0%. I think it should look like this: half sound wave

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  • How do i know if this is random enough?

    - by David
    I wrote a program in java that rolls a die and records the total number of times each value 1-6 is rolled. I rolled 6 Million times. Here's the distribution: #of 0's: 0 #of 1's: 1000068 #of 2's: 999375 #of 3's: 999525 #of 4's: 1001486 #of 5's: 1000059 #of 6's: 999487 (0 wasn't an option.) Is this distribution consistant with random dice rolls? What objective statistical tests might confirm that the dice rolls are indeed random enough?

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  • How can I accelerate the generation of the an MD5 Checksum within vb.net?

    - by Richard
    I'm working with some very large files residing on P2 (Panasonic) cards. Part of the process we employ is to first generate a checksum of the file we are going to copy, then copy the file, then run a checksum on the file to confirm that it copied OK. The problem is, is that files are large (70 GB+) and take a long time to complete. It's an issue since we will eventually be dealing with thousands of these files. I would like to find a faster way to generate the checksum other than using the System.Security.Cryptography.MD5CryptoServiceProvider I don't care if this means using a specialized hardware card, provided it works and is not to ungodly expensive. I would prefer to have a method of encoding that provided some feedback as to how far the process has gone along so I can display it like I do now. The application is written in vb.net. I would prefer to be able to use it as component, library, reference within my application, but I'm willing to call an outside application if there is enough improvement in the speed of generating the checksum. Needless to say, the checksum must be consistent and correct. :-) Thank you in advance for your time and efforts, Richard

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  • Deployment of SQL Server: installing a second instance?

    - by Workshop Alex
    Simple problem. I'm working on a Delphi 2007/WIN32 application which now uses MS Access as simple data store. I have to modify it to support SQL Server Express, which is easy. These modifications are working so the application can be deployed using either SQL Server or MS Access. (Whatever the user prefers.) I did consider deploying the whole application together with the SQL Compact but this is not practicak. Using SQL Server Express 2008 instead of 2005 is an option, but also has a few nasty side-effects which we don't want to resolve for now. The problem is deploying the whole project. The installation with SQL Server would need a quiet installation so the user won't notice it. SQL Server is mentioned in the documentation so they know it's there. We just don't want to bother them with technical issues. In most cases, such an installation will go just fine. But what if the user already has an SQL Server (2005) installation which is used for something else? Personally, I would prefer to just install a second instance of SQL Server on their system so it won't conflict with the other installation. (Thus, if they uninstall the other app, the SQL instance will just stay installed.) While SQL Server 2005 and 2008 can be installed on the same system simply by using two different names for the instance, I wonder if it's also possible to install SQL Server 2005 twice on a single system to get two instances. And if possible, how?

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  • Interpolating height for a point inside a grid based on a discrete height function.

    - by fastrack20
    Hi, I have been wracking my brain to come up with a solution to this problem. I have a lookup table that returns height values for various points (x,z) on the grid. For instance I can calculate the height at A, B, C and D in Figure 1. However, I am looking for a way to interpolate the height at P (which has a known (x,z)). The lookup table only has values at the grid intervals, and P lies between these intervals. I am trying to calculate values s and t such that: A'(s) = A + s(C-A) B'(t) = B + t(P-B) I would then use the these two equations to find the intersection point of B'(t) with A'(s) to find a point X on the line A-C. With this I can calculate the height at this point X and with that the height at point P. My issue lies in calculating the values for s and t. Any help would be greatly appreciated.

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  • Implementing a hilbert map of the internet

    - by Martin
    In the XKCD comic 195 a design for a map of the internet address space is suggested using a hilbert curve so that items from a similar IPs will be clustered together. Given an IP address, how would I calculate the 2D coordinates (in the range zero to one) that this IP is located on such a map?

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  • I know my Before Tax Pay and my After Tax Pay, how can I work out how much I get taxed?

    - by Pete
    I've been entering some data into an Excel spreadsheet to work out my monthly earnings, etc. and was wondering how I can I find out how much I'm getting taxed? Say this is my current spreadsheet: Hours Worked 37.5 39.5 37.5 30 Hourly Rate $25 $25 $25 $25 Before Tax 937.50 987.50 937.50 750.00 After Tax 260.00 276.00 260.00 ??? How can I use this known data to work out my After Tax pay for the 4th column? :/

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  • Arbitrary-precision arithmetic Explanation

    - by TT
    I'm trying to learn C and have come across the inability to work with REALLY big numbers (i.e., 100 digits, 1000 digits, etc.). I am aware that there exist libraries to do this, but I want to attempt to implement it myself. I just want to know if anyone has or can provide a very detailed, dumbed down explanation of arbitrary-precision arithmetic. Thanks!

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  • PHP given a series of arbitrary numbers, how can I choose a logical max value on a line graph?

    - by stormist
    I am constructing a line graph in PHP. I was setting the max value of the line graph to the max value of my collection of items, but this ended up making the graph less readable you are unable to view the highest line on the graph as it intersects with the top of it. So what I need is basically a formula to take a set of numbers and calculate what the logical max value of on the line graph should be.. so some examples 3500 250 10049 45394 434 312 Max value on line graph should probably be 50000 493 412 194 783 457 344 max value on line graph would ideally be 1000 545 649 6854 5485 11545 In this case, 12000 makes sense as max value So something as simple as rounding upward to the nearest thousandth might work but I'd need it to progressively increase as the numbers got bigger. (50000 instead of 46,000 in first example) The maximum these numbers will ever be is about a million. Any recommendations would be greatly appreciated, thank you.

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  • How to write an intersects for Shapes in android

    - by Rafael T
    I have an written an Object called Shape which has a Point representing the topLeftCorner and a Dimension with represents its width and height. To get the topRightCorner I can simply add the width to the topLeftPoint.x. I use to rotate them on a certain degree around their center. The problem after the rotation is, that my intersects(Shape) method fails, because it does not honor the rotation of the Shapes. The rotation will be the same for each Shape. My current implementation looks like this inside my Shape Object: public boolean intersects(Shape s){ // functions returning a Point of shape s return intersects(s.topLeft()) || intersects(s.topRight()) || intersects(s.bottomLeft()) || intersects(s.bottomRight()) || intersects(s.leftCenter()) || intersects(s.rightCenter()) || intersects(s.center()); } public boolean intersects(Point p){ return p.x >= leftX() && p.x <= rightX() && p.y >= topY() && p.y <= bottomY(); } Basically I need functions like rotatedLeftX() or rotatedTopRight() to work properly. Also for that calculation I think it doesn't matter when the topLeft point before a rotation of ie 90 will turn into topRight... I already read this and this Question here, but do not understand it fully.

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  • XNA Track rotated pixel positions

    - by jonny adams
    Hi, Im making a game in xna where a tank has to move over a landscape. I need to be able find the bottom of the tank when it is rotated so I can make it move up and down as the player goes over the landscape. for example if i have a sprite at with its top left corner at 400,300 and i rotate it around its center by 45 degrees around its center, how do i find the new locations of the bottom track. Thanks

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  • Facebook Hacker Cup: Power Overwhelming

    - by marcog
    A lot of people at Facebook like to play Starcraft II™. Some of them have made a custom game using the Starcraft II™ map editor. In this game, you play as the noble Protoss defending your adopted homeworld of Shakuras from a massive Zerg army. You must do as much damage to the Zerg as possible before getting overwhelmed. You can only build two types of units, shield generators and warriors. Shield generators do no damage, but your army survives for one second per shield generator that you build. Warriors do one damage every second. Your army is instantly overrun after your shield generators expire. How many shield generators and how many warriors should you build to inflict the maximum amount of damage on the Zerg before your army is overrun? Because the Protoss value bravery, if there is more than one solution you should return the one that uses the most warriors. Constraints 1 = G (cost for one shield generator) = 100 1 = W (cost for one warrior) = 100 G + W = M (available funds) = 1000000000000 (1012)

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  • How are a session identifiers generated?

    - by Asaf R
    Most web applications depend on some kind of session with the user (for instance, to retain login status). The session id is kept as a cookie in the user's browser and sent with every request. To make it hard to guess the next user's session these session-ids need to be sparse and somewhat random. The also have to be unique. The question is - how to efficiently generate session ids that are sparse and unique? This question has a good answer for unique random numbers, but it seems not scalable for a large range of numbers, simply because the array will end up taking a lot of memory.

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  • syntax to express mathematical formula concisely in your language of choice

    - by aaa
    hello. I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible. Right now my language looks something like this: // implies two nested loops j=0:N, i=0,j (range(i) < j < N)[T(i,j) = (T(i,j) - T(j,i))/e(i+j)]; // implies summation over above expression sum(range(i) < j < N))[(T(i,j) - T(j,i))/e(i+j)]; I am looking for possible syntax improvements/extensions or just different ideas about expressing mathematical formulas as clearly and precisely as possible. Can you give me some syntax examples relating to my question which can be accomplished in your language of choice which consider useful. In particular, if you have some ideas about how to translate the above code segments, I would be happy to hear them Thank you

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