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[ "# multiplicative inverse in galois field $2^8$\n\nI am trying to compute the multiplicative inverse in galois field $2^8$.The question is to find the multiplicative inverse of the polynomial $x^5+x^4+x^3$ in galois field $2^8$ with the irreducible polynomial $x^8+x^4+x^3+x+1$. To get it I used the Extended Euclidean division but with operations used in galois field $2^8$ My answer is $x^7+x^6+x^5+x^4+x$ while the other answer is $x^6+x^4+x^2+x+1$. I am not sure if this answer is right so i need to make sure. If my answer is not right can someone please show me the details of getting to the solution. Thank you\n\nSet $g(x)=x^8+x^4+x^3+x+1$ , $p(x)= x^5+x^4+x^3$.\n\nApplying Euclidean algorithm,\n\n$g(x)=p(x)(x^3+x^2+1) + (x+1)$,\n\n$p(x)=(x^4+x^2+x+1)(x+1)+1$.\n\nTherefore, $1=p(x) + (x^4+x^2+x+1)(x+1) = p(x) + (x^4+x^2+x+1)[g(x) + p(x)(x^3+x^2+1)] = [(x^4+x^2+x+1)(x^3+x^2+1)+1]p(x) + (x^4+x^2+x+1)g(x)$\n\nSetting $q(x) = (x^4+x^2+x+1)(x^3+x^2+1)+1$ (please expand yourself), $p(x)q(x) = 1 \\text{mod} g(x)$. So $q(x)$ is the inverse of $p(x)$.\n\nMaybe there are some errors in my calculations because I didn't do double-check, but I'm sure of the process.\n\nSorry for bad editing. I'm a newbie to this site.\n\nTo check the answer, multiply the result polynomial to p(x) and divide by g(x). The answer must be 1." ]

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[ "# Putting label in the right spot (upper-left) during animation", null, "", null, "I'm quite new to SageMath. It took some time (half a sunday) to create a code the draws an elliptic curve with a cubic, controlling the speed of the animation and putting a label in. However, I don't know where I can put something like a legend_loc='upper left somewhere or whether that's even possible. My code is as follows:\n\nstep=0.2;\nvar('x,y');\na=animate([\nplot(EllipticCurve(y^2==x^3+3.8*x^2-0.8*x+float(k)),xmin=-6,xmax=0\n,color=\"red\",thickness=2,legend_label=r'$y^2=x^3+3.8x^2-0.8x+{}$'.format(float(k)))\n+plot(EllipticCurve(y^2==x^3+3.8*x^2-0.8*x+float(k)),xmin=10^(-9),xmax=6\n,color=\"red\",thickness=2)\n+ plot(x^3+3.8*x^2-0.8*x+float(k),xmin=-6,xmax=6,color=\"blue\",thickness=1)\nfor k in srange(-5,5,step)],xmin=-6,xmax=6,ymin=-20,ymax=20,gridlines=[[-6,6],[-20,20]]);\na.show(delay=1)\n\n\nI also tried set_legend_options(shadow=False, loc=2) in the plot function, but that doesn't satisfy SageMath either. Anyone an idea how I can put that label at some fixed spot? Btw, it would be even better if I could put that label on the top centre above the animation. I appreciate any suggestions and help.\n\nedit retag close merge delete\n\nSort by » oldest newest most voted", null, "You have to call set_legend_options on the individual plots after they're created. For simplicity, define a helper function which creates the individual plots (so you can call set_legend_options there):\n\nstep=0.2;\nvar('x,y');\ndef my_plot(k):\nP = plot(EllipticCurve(y^2==x^3+3.8*x^2-0.8*x+float(k)),xmin=-6,xmax=0,color=\"red\",thickness=2,legend_label=r'$y^2=x^3+3.8x^2-0.8x' + ('+' if k >=0 else '') + '{0:.1f}$'.format(float(k)))\nP += plot(EllipticCurve(y^2==x^3+3.8*x^2-0.8*x+float(k)),xmin=10^(-9),xmax=6,color=\"red\",thickness=2)\nP += plot(x^3+3.8*x^2-0.8*x+float(k),xmin=-6,xmax=6,color=\"blue\",thickness=1)\nreturn P\na=animate([my_plot(k) for k in srange(-5,5,step)],xmin=-6,xmax=6,ymin=-20,ymax=20,gridlines=[[-6,6],[-20,20]]);\na.show(delay=1)", null, "I also fixed the legend_label so the number is rounded and it shows + or - correctly.\n\nBtw, it would be even better if I could put that label on the top centre above the animation.\n\nTo do this, use the title keyword instead of legend_label.\n\nmore\n\nThat's true, sorry :( Hopefully you will get a better answer.\n\nThis is even better indeed! I must say that I didn't even notice the plus- and minus sign changing at first. Nice solution!\n\nThat is quite impressive for half a Sunday! I'd suggest to forget about the legend command and use text. Add the two lines\n\n• text(r'$y^2=x^3+3.8x^2-0.8x{0:+}$'.format(float(k)),(3,-18),fontsize='large', fontweight='bold', color='red')\n• text(r'$y=x^3+3.8x^2-0.8x{0:+}$'.format(float(k)),(-3,18),fontsize='large', fontweight='bold', color='blue')\n\nright after the plot of the cubic, ie as separate Graphics objects. I've tried this, the coordinates (3,-18) and (-3,18) put it in a nice spot within your animation. And with the text color, you don't need a little colored line telling the viewer what the label refers to. BUT did you notice the 0:+ instead of your curly braces formatting { } ?? The 0:+ needs curly braces around it as well, I swear I typed them, can even see them in Preview, but they get eaten when it's displayed. Likewise, instead of bullet points, you want plus signs to add the text elements.\n\nInserting 0:+ displays k with a + if positive, - if negative (in your version, you get a plus AND a minus sign if k<0). For more details than you ever want to know, see help('FORMATTING') There is still a weird instability for k=0, I wonder if that's coming from the math - maybe choose a range for k which does not hit zero exactly?\n\nmore\n\nYes, text would have been an option, but it's just a hassle sometimes to find the right spot (coordinates) for where to put that text. The plus and minus sign problem is solved in the other answer; this was not even a problem I noticed at first. But the code does the job now pretty well." ]

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[ "Model based and Mix-modelled (a) Starting at the case that X t is degenerated into an 1×2 matrix, we conduct the Hotelling test by Equation (2) and its extension K L sum in Equation (31), in comparison with both univariate t-test and a paired t-test. (b) For the general case with k≥2, we conduct a matrix-variate test by Equation (28), as well as by the matrix-variate counterparts of K L 1,0, K L sum , and K L s u m, in comparison with not only the Hotelling’s T-square test on the k dimensional vector x t obtained from Equation (100) but also the paired Hotelling’s T-square test on 2×k matrix-variate samples of X t . (c) Considering each sample X t in a 2×k matrix, we investigate the bi-linear discriminant analysis by Equations 18, 33, and 34, in comparison with the classic FDA by Equation (11) on the k dimensional vector x t obtained from Equation (100). (d) Investigate the generalised bi-linear discriminant analysis by Equations 40, 41, and 34. For simplicity, we get v i ,i=1,,d by Equation (43) and then solve w by Equation (34). When k becomes too big, we further regularise the learning of v i by minimising $$J_y=\\frac {\\alpha _{0} \\sigma _{0}^{y\\ 2} +\\alpha _{1}\\sigma _{1}^{y\\ 2}} {(c^{y}_{0} -c^{y}_{1})^{2}}+ \\sum _{i=1}^{m} \\gamma _{i} \\sum _{j=1}^{d} |u_{i}^{(j)} |^{q},$$ with q=2 for Tikhonov, q=1 for sparse learning." ]

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[ "# What is the Least Common Multiple of 34 and 54?\n\nLeast common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.\n\nLeast common multiple (LCM) of 34 and 54 is 918.\n\nLCM(34,54) = 918\n\nLCM Calculator and\nand\n\n## Least Common Multiple of 34 and 54 with GCF Formula\n\nThe formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).\nWe need to calculate greatest common factor 34 and 54, than apply into the LCM equation.\n\nGCF(34,54) = 2\nLCM(34,54) = ( 34 × 54) / 2\nLCM(34,54) = 1836 / 2\nLCM(34,54) = 918\n\n## Least Common Multiple (LCM) of 34 and 54 with Primes\n\nLeast common multiple can be found by multiplying the highest exponent prime factors of 34 and 54. First we will calculate the prime factors of 34 and 54.\n\n### Prime Factorization of 34\n\nPrime factors of 34 are 2, 17. Prime factorization of 34 in exponential form is:\n\n34 = 21 × 171\n\n### Prime Factorization of 54\n\nPrime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:\n\n54 = 21 × 33\n\nNow multiplying the highest exponent prime factors to calculate the LCM of 34 and 54.\n\nLCM(34,54) = 21 × 171 × 33\nLCM(34,54) = 918" ]

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[ "# array\n\n(PHP 4, PHP 5, PHP 7)\n\narrayCreate an array\n\n### Description\n\narray ([ mixed `\\$...` ] ) : array\n\nCreates an array. Read the section on the array type for more information on what an array is.\n\n### Parameters\n\n`...`\n\nSyntax \"index => values\", separated by commas, define index and values. index may be of type string or integer. When index is omitted, an integer index is automatically generated, starting at 0. If index is an integer, next generated index will be the biggest integer index + 1. Note that when two identical index are defined, the last overwrite the first.\n\nHaving a trailing comma after the last defined array entry, while unusual, is a valid syntax.\n\n### Return Values\n\nReturns an array of the parameters. The parameters can be given an index with the => operator. Read the section on the array type for more information on what an array is.\n\n### Examples\n\nThe following example demonstrates how to create a two-dimensional array, how to specify keys for associative arrays, and how to skip-and-continue numeric indices in normal arrays.\n\nExample #1 array() example\n\n``` <?php\\$fruits = array (    \"fruits\"  => array(\"a\" => \"orange\", \"b\" => \"banana\", \"c\" => \"apple\"),    \"numbers\" => array(1, 2, 3, 4, 5, 6),    \"holes\"   => array(\"first\", 5 => \"second\", \"third\"));?> ```\n\nExample #2 Automatic index with array()\n\n``` <?php\\$array = array(1, 1, 1, 1,  1, 8 => 1,  4 => 1, 19, 3 => 13);print_r(\\$array);?> ```\n\nThe above example will output:\n\n```Array\n(\n => 1\n => 1\n => 1\n => 13\n => 1\n => 1\n => 19\n)\n```\n\nNote that index '3' is defined twice, and keep its final value of 13. Index 4 is defined after index 8, and next generated index (value 19) is 9, since biggest index was 8.\n\nThis example creates a 1-based array.\n\nExample #3 1-based index with array()\n\n``` <?php\\$firstquarter = array(1 => 'January', 'February', 'March');print_r(\\$firstquarter);?> ```\n\nThe above example will output:\n\n```Array\n(\n => January\n => February\n => March\n)\n```\n\nAs in Perl, you can access a value from the array inside double quotes. However, with PHP you'll need to enclose your array between curly braces.\n\nExample #4 Accessing an array inside double quotes\n\n``` <?php\\$foo = array('bar' => 'baz');echo \"Hello {\\$foo['bar']}!\"; // Hello baz!?> ```\n\n### Notes\n\nNote:\n\narray() is a language construct used to represent literal arrays, and not a regular function.\n\n• array_pad() - Pad array to the specified length with a value\n• list() - Assign variables as if they were an array\n• count() - Count all elements in an array, or something in an object\n• range() - Create an array containing a range of elements\n• foreach\n• The array type", null, "add a note\n\n### User Contributed Notes 37 notes\n\n94\nole dot aanensen at gmail dot com\n4 years ago\n``` As of PHP 5.4.x you can now use 'short syntax arrays' which eliminates the need of this function.Example #1 'short syntax array'<?php    \\$a = [1, 2, 3, 4];    print_r(\\$a);?>The above example will output:Array(    => 1    => 2    => 3    => 4)Example #2 'short syntax associative array'<?php    \\$a = ['one' => 1, 'two' => 2, 'three' => 3, 'four' => 4];    print_r(\\$a);?>The above example will output:Array(    [one] => 1    [two] => 2    [three] => 3    [four] => 4) ```\n16\nbrian at blueeye dot us\n13 years ago\n``` If you need, for some reason, to create variable Multi-Dimensional Arrays, here's a quick function that will allow you to have any number of sub elements without knowing how many elements there will be ahead of time. Note that this will overwrite an existing array value of the same path.<?php// set_element(array path, mixed value)function set_element(&\\$path, \\$data) {    return (\\$key = array_pop(\\$path)) ? set_element(\\$path, array(\\$key=>\\$data)) : \\$data;}?>For example:<?phpecho \"<pre>\";\\$path = array('base', 'category', 'subcategory', 'item');\\$array = set_element(\\$path, 'item_value');print_r(\\$array);echo \"</pre>\";?>Will display:Array(    [base] => Array        (            [category] => Array                (                    [subcategory] => Array                        (                            [item] => item_value                        )                )        )) ```\njonberglund at gmail dot com\n10 years ago\n``` The following function (similar to one above) will render an array as a series of HTML select options (i.e. \"<option>...</option>\"). The problem with the one before is that there was no way to handle <optgroup>, so this function solves that issue.function arrayToSelect(\\$option, \\$selected = '', \\$optgroup = NULL){    \\$returnStatement = '';    if (\\$selected == '') {        \\$returnStatement .= '<option value=\"\" selected=\"selected\">Select one...</option>';    }    if (isset(\\$optgroup)) {        foreach (\\$optgroup as \\$optgroupKey => \\$optgroupValue) {            \\$returnStatement .= '<optgroup label=\"' . \\$optgroupValue . '\">';            foreach (\\$option[\\$optgroupKey] as \\$optionKey => \\$optionValue) {                if (\\$optionKey == \\$selected) {                    \\$returnStatement .= '<option selected=\"selected\" value=\"' . \\$optionKey . '\">' . \\$optionValue . '</option>';                } else {                    \\$returnStatement .= '<option value=\"' . \\$optionKey . '\">' . \\$optionValue . '</option>';                }            }            \\$returnStatement .= '</optgroup>';        }    } else {        foreach (\\$option as \\$key => \\$value) {            if (\\$key == \\$selected) {                \\$returnStatement .= '<option selected=\"selected\" value=\"' . \\$key . '\">' . \\$value . '</option>';            } else {                \\$returnStatement .= '<option value=\"' . \\$key . '\">' . \\$value . '</option>';            }        }    }    return \\$returnStatement;} So, for example, I needed to render a list of states/provinces for various countries in a select field, and I wanted to use each country name as an <optgroup> label. So, with this function, if only a single array is passed to the function (i.e. \"arrayToSelect(\\$stateList)\") then it will simply spit out a bunch of \"<option>\" elements. On the other hand, if two arrays are passed to it, the second array becomes a \"key\" for translating the first array.Here's a further example:\\$countryList = array(    'CA'        => 'Canada',    'US'        => 'United States');\\$stateList['CA'] = array(    'AB'        => 'Alberta',    'BC'        => 'British Columbia',    'AB'        => 'Alberta',    'BC'        => 'British Columbia',    'MB'        => 'Manitoba',    'NB'        => 'New Brunswick',    'NL'        => 'Newfoundland/Labrador',    'NS'        => 'Nova Scotia',    'NT'        => 'Northwest Territories',    'NU'        => 'Nunavut',    'ON'        => 'Ontario',    'PE'        => 'Prince Edward Island',    'QC'        => 'Quebec',    'SK'        => 'Saskatchewan',    'YT'        => 'Yukon');\\$stateList['US'] = array(    'AL'        => 'Alabama',    'AK'        => 'Alaska',    'AZ'        => 'Arizona',    'AR'        => 'Arkansas',    'CA'        => 'California',    'CO'        => 'Colorado',    'CT'        => 'Connecticut',    'DE'        => 'Delaware',    'DC'        => 'District of Columbia',    'FL'        => 'Florida',    'GA'        => 'Georgia',    'HI'        => 'Hawaii',    'ID'        => 'Idaho',    'IL'        => 'Illinois',    'IN'        => 'Indiana',    'IA'        => 'Iowa',    'KS'        => 'Kansas',    'KY'        => 'Kentucky',    'LA'        => 'Louisiana',    'ME'        => 'Maine',    'MD'        => 'Maryland',    'MA'        => 'Massachusetts',    'MI'        => 'Michigan',    'MN'        => 'Minnesota',    'MS'        => 'Mississippi',    'MO'        => 'Missouri',    'MT'        => 'Montana',    'NE'        => 'Nebraska',    'NV'        => 'Nevada',    'NH'        => 'New Hampshire',    'NJ'        => 'New Jersey',    'NM'        => 'New Mexico',    'NY'        => 'New York',    'NC'        => 'North Carolina',    'ND'        => 'North Dakota',    'OH'        => 'Ohio',    'OK'        => 'Oklahoma',    'OR'        => 'Oregon',    'PA'        => 'Pennsylvania',    'RI'        => 'Rhode Island',    'SC'        => 'South Carolina',    'SD'        => 'South Dakota',    'TN'        => 'Tennessee',    'TX'        => 'Texas',    'UT'        => 'Utah',    'VT'        => 'Vermont',    'VA'        => 'Virginia',    'WA'        => 'Washington',    'WV'        => 'West Virginia',    'WI'        => 'Wisconsin',    'WY'        => 'Wyoming');...<select name=\"state\" id=\"state\"><?php echo arrayToSelect(\\$stateList,'',\\$countryList) ?></select><select name=\"country\" id=\"country\"><?php echo arrayToSelect(\\$countryList,'US') ?></select> ```\nslicky at newshelix dot com\n18 years ago\n``` Notice that you can also add arrays to other arrays with the \\$array[] \"operator\" while the dimension doesn't matter. Here's an example: \\$x[w][x] = \\$y[y][z]; this will give you a 4dimensional assosiative array. \\$x[][] = \\$y[][]; this will give you a 4dimensional non assosiative array. So let me come to the point. This get interessting for shortening things up. For instance: <?php         foreach (\\$lines as \\$line){             if(!trim(\\$line)) continue;             \\$tds[] = explode(\"\\$delimiter\",\\$line);         } ?> ```\nMike Mackintosh\n11 years ago\n``` If you need to add an object as an array key, for example an object from Simple XML Parser, you can use the following.File.XML<?xml version=\"1.0\" encoding=\"UTF-8\"?><Settings type=\"General\">  <Setting name=\"SettingName\">This This This</Setting></Settings>The script:<?php\\$raw = \\$xml =  new SimpleXMLElement('File.XML');foreach(\\$raw->Setting as \\$A => \\$B){            // Set Array From XML    \\$Setting[(string) \\$B['name']] = (string)  \\$B;}?>By telling the key to read the object as a string, it will let you set it.Hope this helps someone out! ```\njjm152 at hotmail dot com\n17 years ago\n``` The easiest way to \"list\" the values of either a normal 1 list array or a multi dimensional array is to use a foreach() clause. Example for 1 dim array: <?php    \\$arr = array( 1, 2, 3, 4, 5 );    foreach ( \\$arr as \\$val ) {        echo \"Value: \\$Val\\n\";       } ?> For multi dim array: <?php      \\$arr = array( 1 => 'one', 2 => 'two', 3 => 'three', 4 => 'four, 5 => 'five');       foreach ( \\$arr as \\$key => \\$value ) {        echo \"Key: \\$key, Value: \\$value\\n\";       } ?> This is quite possibly the easiest way i've found to iterate through an array. ```\nr0h4rd at gmail dot com\n8 years ago\n``` \"Quick and dirty\" class to get an offset of multidimensional array by given path (sorry, that without comments).<?php    class ArrayAsPathException extends Exception {}     class ArrayAsPath {        protected            \\$data = array(),            \\$separator = '.';        public function __construct (array \\$data = array()) {            \\$this->data = \\$data;        }        public function set (\\$value, \\$path = null) {            if (!isset(\\$path)) {                \\$this->data = \\$value;            }            \\$separator = \\$this->separator;            \\$pathtoken = strtok(\\$path, \\$separator);            \\$code = '';            \\$pices = '[\\''.\\$pathtoken.'\\']';            while (\\$pathtoken !== false) {                if ((\\$pathtoken = strtok(\\$separator)) !== false) {                    \\$code .= 'if (!isset(\\$this->data'.\\$pices.')) \\$this->data'.\\$pices.' = array(); ';                    \\$pices .= '[\\''.\\$pathtoken.'\\']';                } else {                    \\$code .= 'return \\$this->data'.\\$pices.' = \\$value;';                }            }            return eval(\\$code);        }        public function get (\\$path = '', \\$default = null) {            \\$result = \\$this->data;            \\$separator = \\$this->separator;            \\$pathtoken = strtok(\\$path, \\$separator);            while (\\$pathtoken !== false) {                if (!isset(\\$result[\\$pathtoken]) || is_string(\\$result)) {                    if (isset(\\$default)) {                        return \\$default;                    }                    throw new ArrayAsPathException ('Can\\'t find \"'.\\$pathtoken.'\" in \"'.\\$path.'\"');                }                \\$result = \\$result[\\$pathtoken];                \\$pathtoken = strtok(\\$separator);            }            return \\$result ? \\$result : \\$default;        }        public function has (\\$path) {            \\$result = \\$this->data;            \\$separator = \\$this->separator;            \\$pathtoken = strtok(\\$path, \\$separator);            while (\\$pathtoken !== false) {                if (!isset(\\$result[\\$pathtoken]) || is_string(\\$result)) {                    return false;                }                \\$result = \\$result[\\$pathtoken];                \\$pathtoken = strtok(\\$separator);            }            return true;        }        public function setSepatator (\\$separator) {            \\$this->separator = \\$separator;        }        public function getSeparator (\\$separator) {            return \\$this->separator;        }    }?>Code:<?php    \\$params = new ArrayAsPath;    \\$params->set(array(        'foo' => array(            'bar' => array(                'item' => 'Value'            )        )    ));    try {        \\$params->set('test', 'foo.bar.far.new');        printf(            'Array:<pre>%s</pre>            foo.bar.item:<pre>%s</pre>            foo.bar.far:<pre>%s</pre>            foo.bar.far.new<pre>%s</pre>',            var_export(\\$params->get(), true),            var_export(\\$params->get('foo.bar.item'), true),            var_export(\\$params->get('foo.bar.far'), true),            var_export(\\$params->get('foo.bar.far.new'), true)        );    } catch (ArrayAsPathException \\$e) {        echo 'Oops! It seems that something is wrong. '.\\$e->getMessage();    }?>Will display:Array:array (  'foo' =>   array (    'bar' =>     array (      'item' => 'Value',      'far' =>       array (        'new' => 'test',      ),    ),  ),)foo.bar.item:'Value'foo.bar.far:array (  'new' => 'test',)foo.bar.far.new:'test' ```\nMarcel G\n9 years ago\n``` I encountered the following but didn't see it documented/reported anywhere so I'll just mentioned it here. As written in the manual: \"When index is omitted, an integer index is automatically generated, starting at 0. If index is an integer, next generated index will be the biggest integer index + 1\". This generated index has always the largest integer used as a key so far. So adding \\$a = 'foo'; after an \\$a = 'bar'; will not force the next generated index to be 6 but to be 11 as 10 was the highest index encountered until here. Anyway, the following can happen: <?php \\$max_int = 2147483647; // Max value for integer on a 32-bit system \\$arr = array(); \\$arr = 'foo'; // New generated index will be 2 \\$arr[ \\$max_int ] = 'bar'; // Caution: Next generated index will be -2147483648 due to the integer overflow! \\$arr = 'bar'; // The highest value should be 2147483648 but due to the i-overflow it is -2147483648 so current index 0 is larger. The new generated index therefore is 1! \\$arr[]  = 'failure'; // Warning: Cannot add element to the array as the next element is already occupied. ?> ```\njupiter at nospam dot com\n12 years ago\n``` <?php// changes any combination of multiarray elements and subarrays// into a consistent 2nd level multiarray, tries to preserves keysfunction changeMultiarrayStructure(\\$multiarray, \\$asc = 1) {  if (\\$asc == 1) {  // use first subarrays for new keys of arrays    \\$multiarraykeys = array_reverse(\\$multiarray, true);  } else {  // use the last array keys    \\$multiarraykeys = \\$multiarray;  // use last subarray keys  }  // end array reordering  \\$newarraykeys = array();  // establish array  foreach (\\$multiarraykeys as \\$arrayvalue) {  // build new array keys    if (is_array(\\$arrayvalue)) {  // is subarray an array      \\$newarraykeys = array_keys(\\$arrayvalue) + \\$newarraykeys;    }  // if count(prevsubarray)>count(currentarray), extras survive   }  // end key building loop  foreach (\\$multiarray as \\$newsubarraykey => \\$arrayvalue) {    if (is_array(\\$arrayvalue)) {  // multiarray element is an array      \\$i = 0;  // start counter for subarray key      foreach (\\$arrayvalue as \\$subarrayvalue) {  // access subarray        \\$newmultiarray[\\$newarraykeys[\\$i]][\\$newsubarraykey] = \\$subarrayvalue;        \\$i++;  // increase counter      }  // end subarray loop    } else {  // multiarray element is a value      foreach (\\$newarraykeys as \\$newarraykey) {  // new subarray keys        \\$newmultiarray[\\$newarraykey][\\$newsubarraykey] = \\$arrayvalue;      }  // end loop for array variables    }  // end conditional  }  // end new multiarray building loop  return \\$newmultiarray;}// will change \\$old = array('a'=>1,'b'=>array('e'=>2,'f'=>3),'c'=>array('g'=>4),'d'=>5);// to \\$new = array('e'=>array('a'=>1,'b'=>2,'c'=>4,'d'=>5),  'f'=>array('a'=>1,'b'=>3,'d'=>5));// note: if \\$asc parameter isn't default, last subarray keys used ?>The new key/value assignment pattern is clearer with bigger arrays.I use this to manipulate input/output data from my db. Enjoy. ```\n-1\neugene at ultimatecms dot co dot za\n9 years ago\n``` This is a useful way to get foreign key variables from a specific sql table.This function can be used to include all relevant data from all relating tables:<?phpfunction get_string_between(\\$string, \\$start, \\$end){         \\$string = \" \".\\$string;          \\$ini = strpos(\\$string,\\$start);         if(\\$ini == 0)                  return \\$tbl;          \\$ini += strlen(\\$start);          \\$len = strpos(\\$string,\\$end,\\$ini) - \\$ini;          return substr(\\$string,\\$ini,\\$len); } function get_foreign_keys(\\$tbl) {        \\$query = query_getrow(\"SHOW CREATE TABLE \".mysql_escape_string(\\$tbl));        \\$dat = explode('CONSTRAINT',\\$query);        foreach(\\$dat as \\$d => \\$a) {                if(strpos(\\$a,\"FOREIGN KEY\"))                \\$data['keys'][] = array(\\$tbl,get_string_between(\\$a,\"` FOREIGN KEY (`\",\"`) REFERENCES\"));        }                               foreach(\\$dat as \\$d => \\$a) {                if(strpos(\\$a,\"REFERENCE\"))                \\$data['references'][] = explode('` (`',get_string_between(\\$a,\"REFERENCES `\",\"`) ON\"));        }        return \\$data;}//Example code:        \\$data = get_foreign_keys('task_table');        echo '<pre>';        print_r(\\$data);        echo '</pre>';?>// \\$query outputs:CREATE TABLE `task_table` (  `task_id` int(64) NOT NULL auto_increment,  `ticket_id` int(64) NOT NULL,  `task_type` varchar(64) NOT NULL,  `comment` text,  `assigned_to` int(11) default NULL,  `dependant` int(64) default NULL,  `resolved` int(1) default NULL,  PRIMARY KEY  (`task_id`),  KEY `ticket_id` (`ticket_id`,`dependant`),  KEY `assigned_to` (`assigned_to`),  KEY `task_dependant` (`dependant`),  CONSTRAINT `task_table_ibfk_1` FOREIGN KEY (`ticket_id`) REFERENCES `tickets_table` (`ticket_id`) ON DELETE CASCADE ON UPDATE CASCADE,  CONSTRAINT `task_table_ibfk_2` FOREIGN KEY (`assigned_to`) REFERENCES `contact_table` (`contact_id`) ON DELETE CASCADE ON UPDATE CASCADE,  CONSTRAINT `task_table_ibfk_3` FOREIGN KEY (`dependant`) REFERENCES `task_table` (`task_id`) ON DELETE CASCADE ON UPDATE CASCADE) ENGINE=InnoDB DEFAULT CHARSET=latin1// \\$data outputs:Array (    [keys] => Array        (            => Array                (                    => task_table                    => ticket_id                )            => Array                (                    => task_table                    => assigned_to                )            => Array                (                    => task_table                    => dependant                )        )    [references] => Array        (            => Array                (                    => tickets_table                    => ticket_id                )            => Array                (                    => contact_table                    => contact_id                )            => Array                (                    => task_table                    => task_id                )        )) ```\n-2\nbaZz\n15 years ago\n``` Chek this out!!!. Suppose that you want to create an array like the following:<?php  \\$arr1 = (    0 => array (\"customer\"=>\"Client 1\",\"Item a\"),    1 => array (\"customer\"=>\"Client 2\",\"Item b\")  );?>Seems prety easy, but what if you want to generate it dinamically woops!!!.  Imagine that you have a file with thousands of lines and each line is a purchase order from diferent clients:<?php/*function to add elements*/function addArray(&\\$array, \\$id, \\$var){    \\$tempArray = array( \\$var => \\$id);    \\$array = array_merge (\\$array, \\$tempArray);}/*The same as above but the element is an array*/function addArrayArr(&\\$array, \\$var, &\\$array1){    \\$tempArray = array(\\$var => \\$array1);    \\$array = array_merge (\\$array, \\$tempArray);}/*labels of our array or heders of the file*/\\$keyarr = array(\"customer\",\"item\");/*info that may you read from a file line 1 and 2*/\\$valarr0 = array(\"Client 1\",\"Item a\");\\$valarr1 = array(\"Client 2\",\"Item b\");\\$numofrows = 2;/*In our case is just two lines*/\\$tmpArray = array();for(\\$i = 0; \\$i < \\$numofrows; \\$i++){  \\$tmp = \"valarr\\$i\";  \\$tmpvar = \\${\\$tmp};/*Using var of vars tricky tricky*/  foreach( \\$keyarr as \\$key=>\\$value){         addArray(\\$tmparr,\\$tmpvar[\\$key],\\$value);  }  addArrayArr(\\$finalarr,\\$i,\\$tmparr);} /*voila all it's perfectly ordered on finalarr*//*Here we just print the info but you can insert it into a database*/echo \"Customer: \".\\$finalarr[\"customer\"].\"<br>\";echo \"Item: \".\\$finalarr[\"item\"].\"<br>\";echo \"Customer: \".\\$finalarr[\"customer\"].\"<br>\";echo \"Item: \".\\$finalarr[\"item\"].\"<br>\";          ?>The lines above should print something like:Customer: Client 1Item: Item aCustomer: Client 2Item: Item bI hope someone find this useful. ```\n-1\nMadLogic at Paradise dot net dot nz\n16 years ago\n``` Heres a simple yet intelligent way of setting an array, grabbing the values from the array using a loop. <?php \\$ary = array(\"1\"=>'One','Two',\"3\"=>'Three'); \\$a = '0'; \\$b = count(\\$ary); while (\\$a <= \\$b) {   \\$pr = \\$ary[\\$a];   print \"\\$pr<br>\";   \\$a++; } ?> ```\n-2\ntobiasquinteiro at ig dot com dot br\n17 years ago\n``` <?        // This is a small script that shows how to use an multiple array        for(\\$x = 0;\\$x < 10;\\$x++){                for(\\$y = 0;\\$y < 10;\\$y++){                        \\$mat[\\$x][\\$y] = \"\\$x,\\$y\";                }        }        for(\\$x = 0;\\$x < count(\\$mat);\\$x++){                for(\\$y = 0;\\$y < count(\\$mat[\\$x]);\\$y++){                        echo    \"mat[\\$x][\\$y]: \" .                                \\$mat[\\$x][\\$y] . \" \";                }                echo \"\\n\";        }?> ```\n-3\njon hohle\n11 years ago\n``` Here are shorter versions of sam barrow's functions. From a PHP perspective these are O(1) (without getting into what's going on in the interpreter), instead of O(n).<?phpfunction randomKey(array \\$array){    return randomElement(array_keys(\\$array));}function randomElement(array \\$array){    if (count(\\$array) === 0)    {        trigger_error('Array is empty.',  E_USER_WARNING);        return null;    }    \\$rand = mt_rand(0, count(\\$array) - 1);    \\$array_keys = array_keys(\\$array);        return \\$array[\\$array_keys[\\$rand]];}?> ```\n-3\nmajkel\n3 years ago\n``` During initialization php parses every value as expression. One can declare variables, do calculations, or even manipulate \"current\" array<?php\\$arr['A'] = [    &\\$arr, // circular reference    'key' => 'val',    \\$arr['B'] = [ // declare array, insert key and then value        'a' => 'b',    ],    ucfirst(strtolower('SOME TEXT')),     true ? 'TRUE' : 'FALSE', // evaluate expression    \\$x  = 3, // declare variable    \\$x *= 3, // perform calculations];var_dump(\\$arr);// Output/*array(2) {  'B' => array(1) {    'a' => string(1) \"b\"  }  'A' => array(7) {    => array(2) {      'B' => array(1) {        ...      }      'A' => &array    }    'key' => string(3) \"val\"    => array(1) {      'a' => string(1) \"b\"    }    => string(9) \"Some text\"    => string(4) \"TRUE\"    => int(3)    => int(9)  }}*/?> ```\n-3\nrubein at earthlink dot net\n18 years ago\n``` Multidimensional arrays are actually single-dimensional arrays nested inside other single-dimensional arrays. \\$array refers to element 0 of \\$array \\$array refers to element 2 of element 0 of \\$array. If an array was initialized like this: \\$array = \"foo\"; \\$array = \"bar\"; \\$array = \"baz\"; \\$array = \"bam\"; then: is_array(\\$array) = TRUE is_array(\\$array) = FALSE is_array(\\$array) = TRUE count(\\$array) = 2 (elements 0 and 1) count(\\$array = 3 (elements 0 thru 2) This can be really useful if you want to return a list of arrays that were stored in a file or something: \\$array = unserialize(\\$somedata); \\$array = unserialize(\\$someotherdata); if \\$somedata[\"foo\"] = 42 before it was serialized previously, you'd now have this: \\$array[\"foo\"] = 42 ```\n-4\naissatya at yahoo dot com\n13 years ago\n``` <?php\\$foo = array('bar' => 'baz');echo \"Hello {\\$foo['bar']}!\"; // Hello baz!?> <?php\\$firstquarter = array(1 => 'January', 'February', 'March');print_r(\\$firstquarter);?> <?php\\$fruits = array (   \"fruits\"  => array(\"a\" => \"orange\", \"b\" => \"banana\", \"c\" => \"apple\"),   \"numbers\" => array(1, 2, 3, 4, 5, 6),   \"holes\"  => array(\"first\", 5 => \"second\", \"third\"));?> ```\n-6\nayyappan dot ashok at gmail dot com\n2 years ago\n``` The code bellow by [email protected]:\\$var_name='var';\\$var=array(0,1,2,3,4);echo \\$\\$var_name; //prints NOTHING instead 2.// prints 2 with PHP version 7.01 onwardsNote :This results 2 with PHP version 7.01 onwards. Other versions throws a notice error ```\n-4\nwebmaster at phpemailformprocessor dot com\n12 years ago\n``` When using an array to create a list of keys and values for a select box generator which will consist of states I found using \"NULL\" as an index and \"\"(empty value) as a value to be useful:<?php\\$states = array(    0    => 'Select a State',    NULL => '',    1    => 'AL - Alabama',    2    => 'AK - Alaska',    # And so on ...);\\$select = '<select name=\"state\" id=\"state\" size=\"1\">'.\"\\r\\n\";foreach(\\$states as \\$key => \\$value){    \\$select .= \"\\t\".'<option value=\"'.\\$key.'\">' . \\$value.'</option>'.\"\\r\\n\";}\\$select .= '</select>';echo \\$select;?> This will print out:<select name=\"state\" id=\"state\" size=\"1\">    <option value=\"0\">Select a State</option>    <option value=\"\"></option>    <option value=\"1\">AL - Alabama</option>    <option value=\"2\">AK - Alaska</option>    # And so on ...</select>Now a user has a blank value to select if they later decide to not provide their address in the form. The first two options will return TRUE when checked against the php function - EMPTY() after the form is submitted when processing the form ```\n-4\nphp\n13 years ago\n``` This function converts chunks of a string in an array:function array_str(\\$str, \\$len) {  \\$newstr = '';  for(\\$i = 0; \\$i < strlen(\\$str); \\$i++) {    \\$newstr .= substr(\\$str, \\$i, \\$len);  }  return \\$newstr;}use it as:\\$str = \"abcdefghilmn\";echo \"<table width=\\\"100%\\\">\\n\";foreach(array_str(\\$str, 4) as \\$chunk) {  echo \"<tr><td>\".\\$chunk.\"</td></tr>\\n\";}echo \"</table>\";this prints:------abcd------efgh------ilmn------It don't use regular expressions. Please add this function to php :) ```\n-4\nmatthiasDELETETHIS at ansorgs dot de\n13 years ago\n``` How to use array() to create an array of references rather than of copies? (Especially needed when dealing with objects.) I played around somewhat and found a solution: place & before the parameters of array() that shall be references. My PHP version is 4.3.10.Demonstration:<?php\\$ref1 = 'unchanged';\\$ref2 = & \\$ref1;\\$array_of_copies = array(\\$ref1, \\$ref2);print_r(\\$array_of_copies); // prints: Array ( => unchanged => unchanged ) \\$array_of_copies = 'changed'; // \\$ref1 = 'changed'; is not equivalent, as it was _copied_ to the arrayprint_r(\\$array_of_copies); // prints: Array ( => changed => unchanged ) \\$array_of_refs = array(& \\$ref1, & \\$ref2); // the difference: place & before argumentsprint_r(\\$array_of_refs); // prints: Array ( => unchanged => unchanged ) \\$array_of_refs = 'changed'; // \\$ref1 = 'changed'; is equivalent as \\$array_of_refs references \\$ref1print_r(\\$array_of_refs, true); // prints: Array ( => changed => changed ) ?> ```\n-4\njay at ezlasvegas dot net\n16 years ago\n``` If you want to create an array of a set size and you have PHP4, usearray_pad(array(), \\$SIZE, \\$INITIAL_VALUE); This can be handy if you wishto initialize a bunch of variables at once: list(\\$Var1, \\$Var2, etc) = array_pad(array(), \\$NUMBER_OF_VARS,\\$INITIAL_VALUE);Jay WalkerLas Vegas Hotel Associatehttp://www.ezlasvegas.net ```\n-5\nrdude at fuzzelish dot com\n14 years ago\n``` If you are creating an array with a large number of static items, you will find serious performance differences between using the array() function and the \\$array[] construct. For example:<? // Slower method \\$my_array = array(1, 2, 3, � 500); // Faster method \\$my_array[] = 1; \\$my_array[] = 2; \\$my_array[] = 3; � \\$my_array[] = 500;?> ```\n-7\nqeremy\n7 years ago\n``` Some tricky functions;<?phpfunction is_array_assoc(\\$arr) {    if (is_array(\\$arr)) {        foreach (\\$arr as \\$k => \\$v) {            if (is_string(\\$k) || (is_int(\\$k) && \\$k < 0)) {                return 1;            }        }        return 0;    }    return -1;}function is_array_multi(\\$arr) {    return is_array(\\$arr)        ? (count(\\$arr) != count(\\$arr, COUNT_RECURSIVE) ? 1 : 0)        : -1;}\\$arr[] = array(\"foo\", \"bar\", 1.09);\\$arr[] = array(\"red\", \"yellow\", 1 => \"foo\");\\$arr[] = array(\"red\", \"yellow\", -1 => \"foo\");\\$arr[] = array(\"x\" => array(\"red\", \"yellow\"), \"y\" => array(\"one\", \"two\"));\\$arr[] = array();\\$arr[] = \"s\";foreach (\\$arr as \\$a) {    echo is_array_assoc(\\$a) .\"\\n\";}echo \"\\n\";foreach (\\$arr as \\$a) {    echo is_array_multi(\\$a) .\"\\n\";}?>00110-100010-1<?phpfunction array_count(\\$arr) {    \\$r = 0;    foreach (\\$arr as \\$k => \\$v) {        if (is_array(\\$v)) {            \\$r++;        }    }    return \\$r;}function array_count_all(\\$arr, \\$r = 0) {    foreach (\\$arr as \\$k => \\$v) {        if (is_array(\\$v)) {            \\$r = array_count_all(\\$v, \\$r);            \\$r++;        }    }    return \\$r;}\\$a = array(\"foo\", \"bar\", 1.09, array(1,2,3), array(\"a\" => \"aaa\"));echo array_count(\\$a); // 2\\$a = array(    \"foo\", \"bar\", 1.09,     \"x\" => array(1,2,3),     array(\"a\" => \"aaa\", \"b\" => array(), \"c\" => array(\"\"), \"d\" => array(\"\")),     \"e\" => array(\"\"),     \"z\" => array(\"\"),     \"q\" => array(\"\", array()),    \"w\" => array(\"lorem\", 1 => \"impsum\", 18, \"dolor\", array(\"last as 11th array\")));echo array_count_all(\\$a); // 11?> ```\n-5\nTCross1 at hotmail dot com\n15 years ago\n``` here is the sort of \"textbook\" way to output the contents of an array which avoids using foreach() and allows you to index & iterate through the array as you see fit:<?php\\$arrayName = array(\"apples\", \"bananas\", \"oranges\", \"pears\");\\$arrayLength = count(\\$arrayName);for (\\$i = 0; \\$i < \\$arrayLength; \\$i++){    echo \"arrayName at[\" . \\$i . \"] is: [\" .\\$arrayName[\\$i] . \"]<br>\\n\";}?>enjoy!-tim ```\n-8\nmortoray at ecircle-ag dot com\n14 years ago\n``` Be careful if you need to use mixed types with a key of 0 in an array, as several distinct forms end up being the same key:\\$a = array();\\$a[null] = 1;\\$a = 2;\\$a['0'] = 3;\\$a[\"0\"] = 4;\\$a[false] = 5;\\$a[0.0] = 6;\\$a[''] = 7;\\$a[] = 8;print_r( \\$a );This will print out only 3 values: 6, 7, 8. ```\n-4\nAnonymous\n15 years ago\n``` Similarly to a comment by stlawson at sbcglobal dot net on this page: http://www.php.net/basic-syntax.instruction-separation It is usually advisable to define your arrays like this: \\$array = array(      'foo',      'bar', ); Note the comma after the last element - this is perfectly legal. Moreover, it's best to add that last comma so that when you add new elements to the array, you don't have to worry about adding a comma after what used to be the last element. <?php \\$array = array(      'foo',      'bar',      'baz', ); ?> ```\n-6\nbill at carneyco dot com\n13 years ago\n``` I wanted to be able to control the flow of data in a loop instead of just building tables with it or having to write 500 select statements for single line items. This is what I came up with thanks to the help of my PHP brother in FL. Hope someone else gets some use out it. <?//set array variable \\$results = array();//talk to the db\\$query = \"SELECT * FROM yourtable\";\\$result = mysql_query(\\$query) or die(mysql_error());//count the rows and fields\\$totalRows = mysql_num_rows(\\$result);\\$totalFields = mysql_num_fields(\\$result);//start the loopfor ( \\$i = 0; \\$i < \\$totalRows; ++\\$i ) {//make it 2 dim in case you change your order  \\$results[\\$i] = mysql_fetch_array(\\$result); //call data at will controlling the loop with the arrayecho \\$results[your_row_id]['your_field_name']; }//print the entire array to see what lives whereprint_r(\\$results);  ?> ```\n-5\nmads at __nospam__westermann dot dk\n16 years ago\n``` In PHP 4.2.3 (and maybe earlier versions) arrays with numeric indexes may be initialized to start at a specific index and then automatically increment the index. This will save you having to write the index in front of every element for arrays that are not zero-based. The code: <?php                   \\$a = array         (             21    => 1,             2,             3,         );     print '<pre>';     print_r(\\$a);     print '</pre>'; ?> will print: <?php Array (     => 1     => 2     => 3 ) ?> ```\n-6\nsergei dot solomonov at gmail dot com\n5 years ago\n``` Consider:file inc1.php-------------<?phpreturn 'key';file inc2.php-------------<?phpreturn 'value';Test:<?php\\$a = [    include 'inc1.php' => include 'inc2.php'];var_dump(\\$a);/* It works!!!array(1) {  'key' =>  string(5) \"value\"}*/ ```\n-4\ndave at wp dot pl\n4 years ago\n``` The code bellow:\\$var_name='var';\\$var=array(0,1,2,3,4);echo \\$\\$var_name; prints NOTHING instead 2. ```\n-6\nmarcel at labor-club dot de\n16 years ago\n``` i tried to find a way to create BIG multidimensional-arrays. but the notes below only show the usage of it, or the creation of small arrays like \\$matrix=array('birne', 'apfel', 'beere'); for an online game, i use a big array (50x80) elements. it's no fun, to write the declaration of it in the ordinary way. here's my solution, to create an 2d-array, filled for example with raising numbers. <?php \\$matrix=array(); \\$sx=30; \\$sy=40; \\$i=1; for (\\$y=0; \\$y<\\$sy; \\$y++) {     array_push(\\$matrix,array());     for (\\$x=0; \\$x<\\$sx; \\$x++)     {         array_push(\\$matrix[\\$y],array());         \\$matrix[\\$x][\\$y]=\\$i;         \\$i++;     } } ?> if there is a better way, plz send an email. i always want to learn more php! ```\n-10\nkamil at navikam dot pl\n9 years ago\n``` Easy function to unarray an array :-)It will make \\$array['something'] => \\$something.Usefull for making code more clear.example of use:<?function unarray(\\$row) {    foreach(\\$row as \\$key => \\$value) {        global \\$\\$key;        \\$\\$key = \\$value;    }}\\$sql = mysql_query(\"SELECT * FROM `pracownicy`\");while (\\$row = mysql_fetch_assoc(\\$sql)) {    unarray(\\$row);    echo \\$idpracownika.'<br>'; //instead of \\$row['idpracownika']}?> ```\n-6\njoshua dot e at usa dot net\n17 years ago\n``` Here's a cool tip for working with associative arrays- Here's what I was trying to accomplish: I wanted to hit a DB, and load the results into an associative array, since I only had key/value pairs returned. I loaded them into an array, because I wanted to manipulate the data further after the DB select, but I didn't want to hit the DB more than necessary. Here's how I did it: <?php //assume db connectivity //load it all into the associative array \\$sql = \"SELECT key,value FROM table\"; \\$result = mysql_query(\\$sql); while(\\$row = mysql_fetch_row(\\$result)) { \\$myArray[\\$row] = \\$row; } //now we expand it while(list(\\$key,\\$value) = each(\\$myArray)) { echo \"\\$key : \\$value\"; } ?> I found this to be super efficient, and extremely cool. ```\n-9\nJohn\n16 years ago\n``` Be careful not to create an array on top of an already existing variable: <?php \\$name = \"John\"; \\$name['last'] = \"Doe\"; ?> \\$name becomes \"Dohn\" since 'last' evaluates to the 0th position of \\$name. Same is true for multi-arrays. ```\n-10\nphpm at nreynolds dot me dot uk\n14 years ago\n``` This helper function creates a multi-dimensional array. For example, creating a three dimensional array measuring 10x20x30: <?php \\$my_array = multi_dim(10, 20, 30); ?><?phpfunction multi_dim(){        \\$fill_value = null;        for (\\$arg_index = func_num_args() - 1; \\$arg_index >= 0; \\$arg_index--) {        \\$dim_size = func_get_arg(\\$arg_index);        \\$fill_value = array_fill(0, \\$dim_size, \\$fill_value);    }        return \\$fill_value;}?> ```\n-10\nsebasg37 at gmail dot com\n11 years ago\n``` Recursive function similar to print_r for describing anidated arrays in html <ol>. Maybe it's useful for someone.<?phpfunction describeAnidatedArray(\\$array){    \\$buf = '';    foreach(\\$array as \\$key => \\$value)    {        if(is_array(\\$value))        {            \\$buf .= '<ol>' . describeAnidatedArray(\\$value) . '</ol>';        }        else            \\$buf .= \"<li>\\$value</li>\";    }    return \\$buf;}// Example: \\$array = array(\"a\", \"b\", \"c\", array(\"1\", \"2\", array(\"A\", \"B\")), array(\"3\", \"4\"), \"d\");echo describeAnidatedArray(\\$array);?>output:# a# b# c   1. 1   2. 2         1. A         2. B   1. 3   2. 4# d ```", null, "" ]

[ null, "http://php.net/images/[email protected]", null, "http://php.net/images/[email protected]", null ]

[ "# CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions\n\n###### CAT Questions | Algebra | Polynomials - Sequence", null, "CAT Questions\n\nThe question is from Sequences. The Question involves finding possible values of m and n. We need to find out the possible values, that satisfy the conditions of the sequence. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.\n\nQuestion 11: A sequence of numbers is defined as 2 = an – an-1. Sn is sum upto n terms in this sequence and a3 = 5. How many values m, n exist such than Sm – Sn = 65?\n\n1. 4\n2. 6\n3. 2\n4. More than 6 possibilities\n\n## Best CAT Coaching in Chennai\n\n#### CAT Coaching in Chennai - CAT 2020Online Batches Available Now!\n\n##### Method of solving this CAT Question from CAT Algebra - Polynomials: An arithemetic progression in the form of a sequence!\n\na3 = 5, a4 = 7, a5 = 9, a2 = 3, a1 = 1\nSo, the sequence is nothing but 1, 3, 5, 7, 9....\nS1 = 1\nS2 = 4\nS3 = 9\nS4 = 16\nSn = n2\nSm – Sn\n=> m2 – n2 = 65\n=> (m + n) ( m – n) = 65, m, n are natural numbers.\n=> This could be 65 * 1 or 13 * 5. Two possibilities. Note that this cannot be written as 1 * 65 or 5 * 13 as m + n > m - n {as m, n are natural numbers}\n\nThe question is \"A sequence of numbers is defined as 2 = an – an-1. Sn is sum upto n terms in this sequence and a3 = 5. How many values m, n exist such than Sm – Sn = 65? \"\n\n##### Hence the answer is \"2\"\n\nChoice C is the correct answer.\n\n###### CAT Coaching in ChennaiCAT 2020Enroll at 30,000/-\n\nOnline Classroom Batches Starting Now!\n\n###### Best CAT Coaching in ChennaiPrices slashed by Rs 5000/-\n\nAttend a Demo Class\n\n##### Where is 2IIM located?\n\n2IIM Online CAT Coaching\nA Fermat Education Initiative,\n58/16, Indira Gandhi Street,\nKaveri Rangan Nagar, Saligramam, Chennai 600 093\n\n##### How to reach 2IIM?\n\nPhone: (91) 44 4505 8484\nMobile: (91) 99626 48484\nWhatsApp: WhatsApp Now\nEmail: [email protected]" ]

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[ "# Reynolds Equation: Derivation and Solution\n\n### Revision for “Reynolds Equation: Derivation and Solution” created on September 6, 2019 @ 10:55:09\n\nTitle Reynolds Equation: Derivation and Solution\n\nReynolds equation is a partial differential equation which describes the flow of a thin lubricant film between two surfaces. It is derived from the Navier-Stokes equations and is one of the fundamental equations of the classical lubrication theory. It was first derived by Osborne Reynolds in 1886.\n\nDerivation of Reynolds Equation\n\nThe principles of the theory are derived from the observation that the lubricant can be treated as isoviscous and laminar and the fluid film is of negligible curvature. The classical Reynold's equation can be derived from the Navier-Stokes equations and the equation of continuity under assumptions of:\n\n• constant viscosity, Newtonian lubricant\n• thin film geometry\n• negligible body force\n• no-slip boundary conditions\n\nWhen these assumptions are applied, we obtain following equations (following Szeri): $\\begin{eqnarray} \\label{complete_sys1} \\frac{\\partial p}{\\partial x} = \\mu\\frac{\\partial^{2} u}{\\partial y^{2}} \\\\ \\label{complete_sys2} \\frac{\\partial p}{\\partial z} = \\mu\\frac{\\partial^{2} w}{\\partial y^{2}} \\\\ \\label{complete_sys3} \\frac{\\partial u}{\\partial x} + \\frac{\\partial v}{\\partial y} + \\frac{\\partial w}{\\partial z} = 0 \\end{eqnarray}$\n\nIt is also assumed the lubricant is incompressible here. The third of these equations is the equation of continuity and will be used later in the derivation. The first two equations now can be integrated twice with respect to $y$, since partial derivatives of pressure $p$ dont vary across $y$ (assumption of thin film geometry):\n\n$\\begin{eqnarray} \\label{complete_sys1} u = \\frac{1}{2\\mu}\\frac{\\partial p}{\\partial x}y^2 + Ay + B \\\\ \\label{complete_sys2} w = \\frac{1}{2\\mu}\\frac{\\partial p}{\\partial z}y^2 + Cy + D \\end{eqnarray}$\n\nBoundary conditions should be applied: $\\begin{eqnarray} \\label{complete_sys1} u = U_1, w = 0, y = 0, \\\\ \\label{complete_sys2} u = U_2, w = 0, y = h, \\end{eqnarray}$\n\nwhere $U_1$ and $U_2$ represent the velocity of the bearing surfaces. Evaluation of the integration constants leads to the following velocity distribution: $\\begin{eqnarray} \\label{complete_sys1} u = \\frac{1}{2\\mu}\\frac{\\partial p}{\\partial x}(y^2 - yh) + (1 - \\frac{y}{h})U_1 + \\frac{y}{h}U_2 \\\\ \\label{complete_sys2} w = \\frac{1}{2\\mu}\\frac{\\partial p}{\\partial z}(y^2 - yh) \\end{eqnarray}$\n\nThere are only tree equations for four unknowns. This difficulty will be alleviated by integrating, in effect averaging, the equation of continuity across the film:\n\n$\\int_{0}^{h}- \\frac{\\partial v}{\\partial y} dy = \\int_{0}^{h} {\\frac{\\partial u}{\\partial x}dy + \\int_{0}^{h} \\frac{\\partial w}{\\partial z}} dy$\n\nIntegrating yields following Reynold's equation for lubricant pressure: $\\begin{eqnarray} \\label{complete_sys1} \\frac{\\partial}{\\partial x}(\\frac{h^3}{\\mu}\\frac{\\partial p}{\\partial x}) + \\frac{\\partial}{\\partial z}(\\frac{h^3}{\\mu}\\frac{\\partial p}{\\partial z})= 6(U_1+U_2)\\frac{\\partial h}{\\partial x} + 12\\frac{\\partial h}{\\partial t}, \\end{eqnarray}$\n\nSolution of Reynolds Equation\n\nIn general, the Reynolds equation has to be solved using numerical methods such as finite difference, or finite element. Depending on the boundary conditions and the considered geometry, however, analytical solutions can be obtained under certain assumptions.\n\nFor the case of a sphere on flat geometry (for rigid bodies) and steady-state case, the 2-D Reynolds equation can be solved analytically assuming Sommerfeld (also called half-Sommerfeld) cavitation boundary condition. This solution was proposed by a Nobel Prize winner Professor Kapitza. The Sommerfeld boundary condition, however is not accurate and this solution has to be used as an approximate.\n\nIn case of 1-D Reynolds equation, there are several analytical, semi-analytical and approximate solutions available. In 1916 Martin obtained a closed form solution for a minimum film thickness and pressure for a cylinder and plane geometry under assumptions of rigid surfaces. Derivation of the solution and the corresponding MATLAB software can be found here. Martin employed Swift-Stieber cavitation boundary conditions. This solution is not accurate in case of high loads (high pressure in the lubricant), when the elastic deformation of the surfaces contributes to the film thickness. Divergence of experimental and theoretical results by Martin for high loads leaded researchers to conclusion that elastic distortion plays a significant role in lubrication. In 1949, Grubin obtained a solution for so called elasto-hydrodynamic lubrication (EHL) line contact problem with certain simplifications, where he combined both elastic deformation and lubricant hydrodynamic flow. Although his solution did not satisfy both elastic and hydrodynamic equations of EHL, his analysis was recognized as particularly useful. Corresponding MATLAB code can be found here. A lecture on solution of Reynolds equation using Finite Difference Method is given in the lecture below.\n\nGeneralization of Reynolds Equation\n\nVarious of generalized Reynolds equations were derived to weaken the assumptions used to derive the classical form. For example, compressible, non-Newtonian lubricant behavior can be considered. In tribology, Reynolds equation is used to predict the thickness of the lubricant film, but also to predict the friction developed by the lubricant on the surfaces. Since many tribological contacts operate in highly loaded regime and thin films, the shear rates can be very high (in the order of $10^7-10^9$). Many of the typical lubricants start to behave non-Newtonian in the contact conditions and therefore, Reynolds equation was generalized to the case of non-Newtonian lubricant.\n\nAnother generalization includes the slip boundary conditions. This form of the Reynolds equation is used to calculate film thicknesses and friction in textured surfaces or surfaces with high slip.\n\nOldNewDate CreatedAuthorActions\nSeptember 6, 2019 @ 10:55:09 tribonet\nSeptember 6, 2019 @ 10:53:47 tribonet\nDecember 20, 2018 @ 23:08:27 tribonet\nDecember 13, 2018 @ 12:29:02 tribonet\nDecember 13, 2018 @ 12:28:15 tribonet\nDecember 13, 2018 @ 12:24:00 tribonet\nDecember 13, 2018 @ 12:22:35 tribonet\nDecember 13, 2018 @ 12:20:42 tribonet\nAugust 28, 2018 @ 22:30:58 tribonet" ]

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[ "", null, "", null, "", null, "1. Chapter 3 Class 8 Understanding Quadrilaterals\n2. Serial order wise\n3. Ex 3.3\n\nTranscript\n\nEx 3.3, 7 The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them. Given, a Parallelogram HOPE where ∠EHP = 40° and ∠POX = 70° Now, HOX is a line Segment, ∠ HOP + ∠POX = 180° ∠ HOP + 70° = 180° ∠ HOP = 180° − 70° ∠ HOP = 110° We know that Opposite angles of a Parallelogram are equal ∠E = ∠HOP x = 110° Also, Adjacent angles of a Parallelogram are Supplementary ∠EHO + ∠HOP= 180° 40° + z + 110° = 180° 150° + z = 180° z = 180° − 150° z = 30° In ∆ PHO, Sum of angles ∠ PHO + ∠HPO + ∠POH = 180° z + y + 110° = 180° 30° + y + 110° = 180° y + 140° = 180° y = 40° Therefore, x = 110° , y = 40° and z = 30°", null, "" ]

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[ "# Active Learning for Function Approximation\n\n,\n\nNeural Information Processing Systems\n\nWe develop a principled strategy to sample a function optimally for function approximation tasks within a Bayesian framework. Using ideas from optimal experiment design, we introduce an objective function (incorporating both bias and variance) to measure the degree ofapproximation, and the potential utility of the data points towards optimizing this objective. We show how the general strategy canbe used to derive precise algorithms to select data for two cases: learning unit step functions and polynomial functions. In particular, we investigate whether such active algorithms can learn the target with fewer examples. We obtain theoretical and empirical resultsto suggest that this is the case. 1 INTRODUCTION AND MOTIVATION Learning from examples is a common supervised learning paradigm that hypothesizes atarget concept given a stream of training examples that describes the concept. In function approximation, example-based learning can be formulated as synthesizing anapproximation function for data sampled from an unknown target function (Poggio and Girosi, 1990). Active learning describes a class of example-based learning paradigms that seeks out new training examples from specific regions of the input space, instead of passively accepting examples from some data generating source. By judiciously selecting ex- 594 KahKay Sung, Parlha Niyogi amples instead of allowing for possible random sampling, active learning techniques can conceivably have faster learning rates and better approximation results than passive learning methods. This paper presents a Bayesian formulation for active learning within the function approximation framework.\n\n, , , (20 more...)\n\nDec-31-1995" ]

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[ "# Unroll Curves in one direction only\n\nHello All,\n\nI m looking a way to automate the process of unrolling curves in one direction.\nI give below an example and i have also attached the 3dm file.unroll_crv_1d.3dm (60.9 KB)\n\nThe original curves are shown below.\nThe goal is to unroll them on the Z-axis:\n\nWhat i manually do is to take the intersection points and split the curves:\n\nThen i measure the length of each segment of the blue lines and create a 1-D line .\nFinally i connect the end points of each segment with the longitudinal curves (red)\n\nAs this process is very time-consuming to perform it manually, a python script would be the perfect solution.\n\nI have written the following code that unroll all lines which are selected but does it individually.\n\n``````import rhinoscriptsyntax as rs\nimport Rhino.Geometry.Line as Line\n\ncurves = rs.GetObjects(\"Pick some curves\", rs.filter.curve)\nexpanded_crvs = []\nfor curve in curves:\ncrv_length = rs.CurveLength(curve)\nstart_point = rs.CurveStartPoint(curve)\nend_point = rs.CurveEndPoint(curve)\n\n#expanded point and projected on xz plane\nstart_point_new = [start_point,0,start_point]\nend_point_new = [start_point,0,start_point-crv_length]\n\n#add all new curves in list\nexpanded_crvs.append([start_point_new,end_point_new])\n``````\n\nFurthermore, suggestions and advices on the code above are more than welcome.\n\nDoes anyone know how to sort the expanded_crvs based on the Z-coordinate?\nFurthermore, how can I maintain the layer and the name for each segment?\n\nThis should work (not tested), sorting the list by the Z coordinate of the start point - add this at the end outside the `for` loop:\n\n``````expanded_crvs.sort(key=lambda crv: crv)\n``````\n\n-Graham\n\nThanks Graham,\n\nI ended up using the following for sorting to the Z-axis\n\n``````for curve in curves:\nlayer = rs.ObjectLayer(curve)\ngeo = rs.coercegeometry(curve)\npt = geo.GetBoundingBox(True).Center\ncurves_sorted.append([curve, pt.X, pt.Y, pt.Z, pt, layer])\n\ncurves_sorted = sorted(curves_sorted, key=itemgetter(1,3), reverse=False )``````\n1 Like\n\nLooks good, you can simplify the final line to just\n`curves_sorted.sort(key=itemgetter(1,3))`\n\nFor others, the above solution needs:\n\n`from operator import itemgetter`\n\n1 Like" ]

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[ "## Precalculus: Mathematics for Calculus, 7th Edition\n\na.) $\\frac{10}{2}$ $\\geq$ 5 When we simplify the $\\frac{10}{2}$, we get 5 since 10 divided by 2 is 5. True b.) $\\frac{6}{10}$ $\\geq$ $\\frac{5}{6}$ The Least Common Denominator of 10 and 6 = 30 $\\frac{18}{30}$ $\\geq$ $\\frac{25}{30}$ When in terms of the same denominator, 18 is not bigger or equal to 25." ]

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[ "## DON'T GO SHOPPINGwithout the UPCZilla app! The stores hate it ;)", null, "# Online UPC validation tool\n\nUPCZilla’s tool for validating UPCs which also gives you a handy explanation of how the validation was performed.\n\n036179000435 is a valid UPC-A (though that doesn't mean it's assigned to any products, click here to see if it is: 036179000435 - if you haven't already).\n\n## How do we check if a UPC is valid?\n\nTo check if a UPC is valid, we need to perform some calculations on its digits, as follows:\n\n1. We take the six odd numbered digits (counting from the left, not including the final digit - more about that at the end) and we add them together:`0 3 6 1 7 9 0 0 0 4 3 (5) - last digit ignored for now0 (digit 1) + 6 (digit 3) + 7 (digit 5) + 0 (digit 7) + 0 (digit 9) + 3 (digit 11) = 16`\n\n2. Then we multiply that number (16) by 3:`16 X 3 = 48 (we'll be using this number in a minute)`\n\n3. Then, similar to the first step, we take the FIVE (not six) EVEN numbered digits and we add them together as well:`0 3 6 1 7 9 0 0 0 4 3 (5) - last digit still ignored3 (digit 2) + 1 (digit 4) + 9 (digit 6) + 0 (digit 8) + 4 (digit 10) = 17`\n\n4. We get the number we got in step 3 (17) and we ADD it to the number we got in step 2 (48):`17 + 48 = 65`\n\n5. Now we take the number we got in step 4 (65) and work out how much we have to add to round it up to the nearest 10. In order to round 65 up to the nearest 10 (70) we have to add... 5\n\n6. Is this value of 5 the same as the last (rightmost) digit in our code - the one we ignored in steps 1 and 3 (that's our checksum)?\n\nYES, the checksum in our UPC was also 5 so the UPC is valid!\n\nThe rightmost digit in a UPC is a checksum, because it provides some insurance that all the other numbers are right by performing the above calculation on them. The system is not foolproof, but if any number is wrong then you will typically get a wrong checksum." ]

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[ "# PHP array_push() Function\n\nPHP array_push() Function is used to push one or more elements into the end of array. The array_push() is a built-in function of PHP\n\nWe can add a string as well as numeric values into array.\n\nSyntax :\n\narray_push(\\$array, \\$value1, \\$value2, \\$value3, \\$value4,............,\\$value_n);\n\nParameter,\n\n\\$array : Required  It is type of array parameter.\n\n\\$value : One value is Required. Others are Optional. Values are used  to insert into \\$array.\n\nReturn :  It returns array with new elements.\n\nIf the array has a key, value pair then the method will always add a numeric key to the pushed value.\n\nLet's see below example to understand php array_push() Function in details.\n\nExample :\n\n<?php\necho \"<br><br>Adding new elements in an array with no keys.<br>\";\n\\$tutorials= array(\"PHP\", \"HTML\", \"JAVASCRIPT\");\narray_push(\\$tutorials, \"JAVA\", \"CSS\");\nprint_r(\\$tutorials);\n\necho \"<br><br>Adding new elements in an array with key, value pair. Index key will be started from 4 then 5<br>\";\n\\$tutorials= array(1=>\"PHP\", 2=>\"HTML\", 3=>\"JAVASCRIPT\");\narray_push(\\$tutorials, \"JAVA\", \"CSS\");\nprint_r(\\$tutorials);\n\necho \"<br><br>Adding new elements in an array with key, value pair where key is string. Index key will be started from 0 then 1<br>\";\n\\$fruits= array(\"a\"=>\"Apple\", \"b\"=>\"Banana\", \"Grapes\"=>\"JAVASCRIPT\");\narray_push(\\$fruits, \"Mango\", \"Orange\");\nprint_r(\\$fruits);\n\n?>\n\nOutput :" ]

[ null ]

[ "", null, "# Create an Equation\n\nDirections: Use only the digits 1 to 7, at most one time each, fill in the boxes to create a true equation.", null, "### Hint\n\nWhat place value would you like to start with? What digits “go” together?\n\nNumber of Unique Solutions: 20 (40 with commutative property)\n1: 43 = 16 + 27\n2: 43 = 17 + 26\n3: 47 = 32 + 15\n4: 47 = 35 + 12\n5: 57 = 21 + 36\n6: 57 = 31 + 26\n7: 61 = 34 + 27\n8: 61 = 37 + 24\n9: 62 = 15 + 47\n10: 62 = 45 + 17\n11: 67 = 14 + 53\n12: 67 = 54 + 13\n13: 71 = 25 + 46\n14: 71 = 26 + 45\n15: 74 = 23 + 51\n16: 74 = 53 + 21\n17: 75 = 12 + 63\n18: 75 = 13 + 62\n19: 76 = 41 + 35\n20: 76 = 45 + 31\n\nSource: Eric Appleton\n\n## Time Twister\n\nDirections: Using the digits 0 to 9, at most one time each, create three different …\n\n1.", null, "•", null, "12 +15 =27\n\n•", null, "Nathalie Beauregard\n\nYou are not supposed to use the same digit twice!\n\n2.", null, "50=40+10\n\n•", null, "Zero is not a choice of digits.\n\n•", null, "3.", null, "90=14+76\n\n90=67=23\n\n90=34+56\n\n90=27+63\n\n•", null, "Can’t use 0 or 9.\n\n4.", null, "76=52+24\n\n5.", null, "6.", null, "76=35+41\n97=76+21\n94=74+20\n45=35+10\n74=39+45\n\n7.", null, "76=35+41\n97=76+21\n94=74+20\n45=35+10\n74=39+45\n\n8.", null, "43=17+25\n57=21+36\n74=21+53\n\n9.", null, "10.", null, "11.", null, "Jamie L Comstock\n\nHow are you supposed to explain this to a 2nd grader to solve?\n\n•", null, "Nathalie Beauregard\n\nI would use cards on which I would write the digits 1 to 7. Then you have to ask them questions about additions. I will try it out with my students on Zoom next Monday. I know they will enjoy. I think I’m going to make a little explanation on Explain Everything.\n\n12.", null, "jizzelle mcgriff\n\n60=40+20\n\n13.", null, "14.", null, "43=27+16\n\n15.", null, "49 = 17 + 32\n76 = 45 + 31\n57 = 21 + 36\n79 = 56 + 23\n\n16.", null, "57 = 37 + 20\n\n17.", null, "Who on earth is writing these questions for second graders? I am three years through my math degree and had trouble with this, let alone explaining it to my little sister.\n\n•", null, "20+20=40\n30+30=60\n90+80=170\n180+160=250\n\n18.", null, "56+32=88\n86+14=100\n63+34=97\n47+52=99\n\n19.", null, "70=40+30\n43=20+23\n20=10+10\n64=50+14\n\n20.", null, "80=35+45\n40=35+5\n68=45+23\n39=15+24\n50=26+24\n\n•", null, "70=35+35\n40=35+5\n67=45+22\n37=15+22\n50=26+24\n\n21.", null, "43 = 16+27\n61 = 14+47\n\n22.", null, "14=12+26\n16=19+35\n\n23.", null, "24.", null, "25.", null, "2000 = 2x 1000\n\n5000 = 3000 + 2000\n\n600000000000 = 2×300000000000\n\n26.", null, "27.", null, "28.", null, "43 = 16 + 27\n43 = 17 + 26\n47 = 32 + 15" ]

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[ "Li Bing-you. Fixed Point Theorem of Nonexpansive Mappings in Convex Metric Spaces[J]. Applied Mathematics and Mechanics, 1989, 10(2): 173-178.\n Citation: Li Bing-you. Fixed Point Theorem of Nonexpansive Mappings in Convex Metric Spaces[J]. Applied Mathematics and Mechanics, 1989, 10(2): 173-178.", null, "# Fixed Point Theorem of Nonexpansive Mappings in Convex Metric Spaces\n\n• Publish Date: 1989-02-15", null, "• Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:\n•", null, "•", null, "", null, "", null, "DownLoad:  Full-Size Img  PowerPoint" ]

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[ "Related Articles\n\n# Find a pair from the given array with maximum nCr value\n\n• Difficulty Level : Medium\n• Last Updated : 08 Jun, 2021\n\nGiven an array arr[] of n positive integers. The task is to find elements arr[i] and arr[j] from the array such that arr[i]Carr[j] is maximum possible. In case of more than 1 valid pairs, print any one of them.\nExamples:\n\nInput: arr[] = {3, 1, 2}\nOutput: 3 2\n3C1 = 3\n3C2 = 3\n2C1 = 2\n(3, 1) and (3, 2) are the only pairs with maximum nCr.\nInput: arr[] = {9, 2, 4, 11, 6}\nOutput: 11 6\n\nApproach: nCr is a monotonic increasing function, that is n + 1Cr > nCr. We can use this fact to get close to our answer, we will choose the max n among all the given integers. This way we fixed the value of n\nNow, we have to look for r. Since we know that nCr = nCn – r, it means nCr will first reach its maxima and then decrease.\nIf n is be odd, then our maxima will occur at n / 2 and n / 2 + 1\nFor n = 11, we will get the maxima at 11C5 and 11C6.\nWhen n is even, then our maxima will occur at n / 2.\nBelow is the implementation of the above approach:\n\n## C++\n\n `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to print the pair that gives maximum nCr``void` `printMaxValPair(vector<``long` `long``>& v, ``int` `n)``{``    ``sort(v.begin(), v.end());` `    ``// This gives the value of N in nCr``    ``long` `long` `N = v[n - 1];` `    ``// Case 1 : When N is odd``    ``if` `(N % 2 == 1) {``        ``long` `long` `first_maxima = N / 2;``        ``long` `long` `second_maxima = first_maxima + 1;``        ``long` `long` `ans1 = 3e18, ans2 = 3e18;``        ``long` `long` `from_left = -1, from_right = -1;``        ``long` `long` `from = -1;``        ``for` `(``long` `long` `i = 0; i < n; ++i) {``            ``if` `(v[i] > first_maxima) {``                ``from = i;``                ``break``;``            ``}``            ``else` `{``                ``long` `long` `diff = first_maxima - v[i];``                ``if` `(diff < ans1) {``                    ``ans1 = diff;``                    ``from_left = v[i];``                ``}``            ``}``        ``}``        ``from_right = v[from];``        ``long` `long` `diff1 = first_maxima - from_left;``        ``long` `long` `diff2 = from_right - second_maxima;` `        ``if` `(diff1 < diff2)``            ``cout << N << ``\" \"` `<< from_left;``        ``else``            ``cout << N << ``\" \"` `<< from_right;``    ``}` `    ``// Case 2 : When N is even``    ``else` `{``        ``long` `long` `maxima = N / 2;``        ``long` `long` `ans1 = 3e18;``        ``long` `long` `R = -1;``        ``for` `(``long` `long` `i = 0; i < n - 1; ++i) {``            ``long` `long` `diff = ``abs``(v[i] - maxima);``            ``if` `(diff < ans1) {``                ``ans1 = diff;``                ``R = v[i];``            ``}``        ``}``        ``cout << N << ``\" \"` `<< R;``    ``}``}` `// Driver code``int` `main()``{``    ``vector<``long` `long``> v = { 1, 1, 2, 3, 6, 1 };``    ``int` `n = v.size();``    ``printMaxValPair(v, n);` `    ``return` `0;``}`\n\n## Java\n\n `// Java implementation of the approach``import` `java.util.*;` `class` `GFG``{` `// Function to print the pair that gives maximum nCr``static` `void` `printMaxValPair(Vector v, ``int` `n)``{``    ``Collections.sort(v);` `    ``// This gives the value of N in nCr``    ``long` `N = v.get((``int``)n - ``1``);` `    ``// Case 1 : When N is odd``    ``if` `(N % ``2` `== ``1``)``    ``{``        ``long` `first_maxima = N / ``2``;``        ``long` `second_maxima = first_maxima + ``1``;``        ``long` `ans1 =(``long``) 3e18, ans2 = (``long``)3e18;``        ``long` `from_left = -``1``, from_right = -``1``;``        ``long` `from = -``1``;``        ``for` `(``long` `i = ``0``; i < n; ++i)``        ``{``            ``if` `(v.get((``int``)i) > first_maxima)``            ``{``                ``from = i;``                ``break``;``            ``}``            ``else``            ``{``                ``long` `diff = first_maxima - v.get((``int``)i);``                ``if` `(diff < ans1)``                ``{``                    ``ans1 = diff;``                    ``from_left = v.get((``int``)i);``                ``}``            ``}``        ``}``        ``from_right = v.get((``int``)from);``        ``long` `diff1 = first_maxima - from_left;``        ``long` `diff2 = from_right - second_maxima;` `        ``if` `(diff1 < diff2)``            ``System.out.println( N + ``\" \"` `+ from_left);``        ``else``            ``System.out.println( N + ``\" \"` `+ from_right);``    ``}` `    ``// Case 2 : When N is even``    ``else``    ``{``        ``long` `maxima = N / ``2``;``        ``long` `ans1 =(``int``) 3e18;``        ``long` `R = -``1``;``        ``for` `(``long` `i = ``0``; i < n - ``1``; ++i)``        ``{``            ``long` `diff = Math.abs(v.get((``int``)i) - maxima);``            ` `            ``if` `(diff < ans1)``            ``{``                ``ans1 = diff;``                ``R = v.get((``int``)i);``            ``}``        ``}``        ``System.out.println( N + ``\" \"` `+ R);``    ``}``}` `// Driver code``public` `static` `void` `main(String args[])``{``    ``long` `arr[] = { ``1``, ``1``, ``2``, ``3``, ``6``, ``1``};``    ``Vector v = ``new` `Vector( );``    ` `    ``for``(``int` `i = ``0``; i < arr.length; i++)``    ``v.add(arr[i]);``    ` `    ``int` `n = v.size();``    ``printMaxValPair(v, n);``}``}` `// This code is contributed by Arnab Kundu`\n\n## Python3\n\n `# Python3 implementation of the approach` `# Function to print the pair that``# gives maximum nCr``def` `printMaxValPair(v, n):` `    ``v.sort()` `    ``# This gives the value of N in nCr``    ``N ``=` `v[n ``-` `1``]` `    ``# Case 1 : When N is odd``    ``if` `N ``%` `2` `=``=` `1``:``        ``first_maxima ``=` `N ``/``/` `2``        ``second_maxima ``=` `first_maxima ``+` `1``        ``ans1, ans2 ``=` `3` `*` `(``10` `*``*` `18``), ``3` `*` `(``10` `*``*` `18``)``        ``from_left, from_right ``=` `-``1``, ``-``1``        ``_from ``=` `-``1``        ``for` `i ``in` `range``(``0``, n):``            ``if` `v[i] > first_maxima:``                ``_from ``=` `i``                ``break``            ` `            ``else``:``                ``diff ``=` `first_maxima ``-` `v[i]``                ``if` `diff < ans1:``                    ``ans1 ``=` `diff``                    ``from_left ``=` `v[i]``                ` `        ``from_right ``=` `v[_from]``        ``diff1 ``=` `first_maxima ``-` `from_left``        ``diff2 ``=` `from_right ``-` `second_maxima` `        ``if` `diff1 < diff2:``            ``print``(N, from_left)``        ``else``:``            ``print``(N, from_right)` `    ``# Case 2 : When N is even``    ``else``:``        ``maxima ``=` `N ``/``/` `2``        ``ans1 ``=` `3` `*` `(``10` `*``*` `18``)``        ``R ``=` `-``1``        ``for` `i ``in` `range``(``0``, n ``-` `1``):``            ``diff ``=` `abs``(v[i] ``-` `maxima)``            ``if` `diff < ans1:``                ``ans1 ``=` `diff``                ``R ``=` `v[i]``            ` `        ``print``(N, R)` `# Driver code``if` `__name__ ``=``=` `\"__main__\"``:` `    ``v ``=` `[``1``, ``1``, ``2``, ``3``, ``6``, ``1``]``    ``n ``=` `len``(v)``    ``printMaxValPair(v, n)` `# This code is contributed by``# Rituraj Jain`\n\n## C#\n\n `// C# implementation of the approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{` `// Function to print the pair that gives maximum nCr``static` `void` `printMaxValPair(List<``long``> v, ``int` `n)``{``    ``v.Sort();` `    ``// This gives the value of N in nCr``    ``long` `N = v[(``int``)n - 1];` `    ``// Case 1 : When N is odd``    ``if` `(N % 2 == 1)``    ``{``        ``long` `first_maxima = N / 2;``        ``long` `second_maxima = first_maxima + 1;``        ``long` `ans1 = (``long``) 3e18, ans2 = (``long``)3e18;``        ``long` `from_left = -1, from_right = -1;``        ``long` `from` `= -1;``        ``for` `(``long` `i = 0; i < n; ++i)``        ``{``            ``if` `(v[(``int``)i] > first_maxima)``            ``{``                ``from` `= i;``                ``break``;``            ``}``            ``else``            ``{``                ``long` `diff = first_maxima - v[(``int``)i];``                ``if` `(diff < ans1)``                ``{``                    ``ans1 = diff;``                    ``from_left = v[(``int``)i];``                ``}``            ``}``        ``}``        ``from_right = v[(``int``)``from``];``        ``long` `diff1 = first_maxima - from_left;``        ``long` `diff2 = from_right - second_maxima;` `        ``if` `(diff1 < diff2)``            ``Console.WriteLine( N + ``\" \"` `+ from_left);``        ``else``            ``Console.WriteLine( N + ``\" \"` `+ from_right);``    ``}` `    ``// Case 2 : When N is even``    ``else``    ``{``        ``long` `maxima = N / 2;``        ``long` `ans1 = (``long``)3e18;``        ``long` `R = -1;``        ``for` `(``long` `i = 0; i < n - 1; ++i)``        ``{``            ``long` `diff = Math.Abs(v[(``int``)i] - maxima);``            ` `            ``if` `(diff < ans1)``            ``{``                ``ans1 = diff;``                ``R = v[(``int``)i];``            ``}``        ``}``        ``Console.WriteLine( N + ``\" \"` `+ R);``    ``}``}` `// Driver code``public` `static` `void` `Main(String []args)``{``    ``long` `[]arr = { 1, 1, 2, 3, 6, 1};``    ``List<``long``> v = ``new` `List<``long``>( );``    ` `    ``for``(``int` `i = 0; i < arr.Length; i++)``    ``v.Add(arr[i]);``    ` `    ``int` `n = v.Count;``    ``printMaxValPair(v, n);``}``}` `// This code contributed by Rajput-Ji`\n\n## PHP\n\n ` ``\\$first_maxima``)``            ``{``                ``\\$from` `= ``\\$i``;``                ``break``;``            ``}``            ``else``            ``{``                ``\\$diff` `= ``\\$first_maxima` `- ``\\$v``[``\\$i``];``                ``if` `(``\\$diff` `< ``\\$ans1``)``                ``{``                    ``\\$ans1` `= ``\\$diff``;``                    ``\\$from_left` `= ``\\$v``[``\\$i``];``                ``}``            ``}``        ``}``        ``\\$from_right` `= ``\\$v``[``\\$from``];``        ``\\$diff1` `= ``\\$first_maxima` `- ``\\$from_left``;``        ``\\$diff2` `= ``\\$from_right` `- ``\\$second_maxima``;` `        ``if` `(``\\$diff1` `< ``\\$diff2``)``            ``echo` `\\$N` `. ``\" \"` `. ``\\$from_left``;``        ``else``            ``echo` `\\$N` `. ``\" \"` `. ``\\$from_right``;``    ``}` `    ``// Case 2 : When N is even``    ``else``    ``{``        ``\\$maxima` `= ``\\$N` `/ 2;``        ``\\$ans1` `= 3e18;``        ``\\$R` `= -1;``        ``for` `(``\\$i` `= 0; ``\\$i` `< ``\\$n` `- 1; ++``\\$i``)``        ``{``            ``\\$diff` `= ``abs``(``\\$v``[``\\$i``] - ``\\$maxima``);``            ``if` `(``\\$diff` `< ``\\$ans1``)``            ``{``                ``\\$ans1` `= ``\\$diff``;``                ``\\$R` `= ``\\$v``[``\\$i``];``            ``}``        ``}``        ``echo` `\\$N` `. ``\" \"` `. ``\\$R``;``    ``}``}` `// Driver code``\\$v` `= ``array``( 1, 1, 2, 3, 6, 1 );``\\$n` `= ``count``(``\\$v``);``printMaxValPair(``\\$v``, ``\\$n``);` `// This code is contributed by mits``?>`\n\n## Javascript\n\n ``\nOutput:\n`6 3`\n\nAttention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.\n\nIn case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.\n\nMy Personal Notes arrow_drop_up" ]

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[ "pyspark.pandas.DataFrame¶\n\nclass pyspark.pandas.DataFrame(data=None, index=None, columns=None, dtype=None, copy=False)[source]\n\npandas-on-Spark DataFrame that corresponds to pandas DataFrame logically. This holds Spark DataFrame internally.\n\nVariables\n\n_internal – an internal immutable Frame to manage metadata.\n\nParameters\ndatanumpy ndarray (structured or homogeneous), dict, pandas DataFrame, Spark DataFrame or pandas-on-Spark Series\n\nDict can contain Series, arrays, constants, or list-like objects If data is a dict, argument order is maintained for Python 3.6 and later. Note that if data is a pandas DataFrame, a Spark DataFrame, and a pandas-on-Spark Series, other arguments should not be used.\n\nindexIndex or array-like\n\nIndex to use for resulting frame. Will default to RangeIndex if no indexing information part of input data and no index provided\n\ncolumnsIndex or array-like\n\nColumn labels to use for resulting frame. Will default to RangeIndex (0, 1, 2, …, n) if no column labels are provided\n\ndtypedtype, default None\n\nData type to force. Only a single dtype is allowed. If None, infer\n\ncopyboolean, default False\n\nCopy data from inputs. Only affects DataFrame / 2d ndarray input\n\nExamples\n\nConstructing DataFrame from a dictionary.\n\n>>> d = {'col1': [1, 2], 'col2': [3, 4]}\n>>> df = ps.DataFrame(data=d, columns=['col1', 'col2'])\n>>> df\ncol1 col2\n0 1 3\n1 2 4\n\nConstructing DataFrame from pandas DataFrame\n\n>>> df = ps.DataFrame(pd.DataFrame(data=d, columns=['col1', 'col2']))\n>>> df\ncol1 col2\n0 1 3\n1 2 4\n\nNotice that the inferred dtype is int64.\n\n>>> df.dtypes\ncol1 int64\ncol2 int64\ndtype: object\n\nTo enforce a single dtype:\n\n>>> df = ps.DataFrame(data=d, dtype=np.int8)\n>>> df.dtypes\ncol1 int8\ncol2 int8\ndtype: object\n\nConstructing DataFrame from numpy ndarray:\n\n>>> df2 = ps.DataFrame(np.random.randint(low=0, high=10, size=(5, 5)),\n... columns=['a', 'b', 'c', 'd', 'e'])\n>>> df2\na b c d e\n0 3 1 4 9 8\n1 4 8 4 8 4\n2 7 6 5 6 7\n3 8 7 9 1 0\n4 2 5 4 3 9\n\nMethods\n\n abs() Return a Series/DataFrame with absolute numeric value of each element. add(other) Get Addition of dataframe and other, element-wise (binary operator +). add_prefix(prefix) Prefix labels with string prefix. add_suffix(suffix) Suffix labels with string suffix. agg(func) Aggregate using one or more operations over the specified axis. aggregate(func) Aggregate using one or more operations over the specified axis. align(other[, join, axis, copy]) Align two objects on their axes with the specified join method. all([axis]) Return whether all elements are True. any([axis]) Return whether any element is True. append(other[, ignore_index, …]) Append rows of other to the end of caller, returning a new object. apply(func[, axis, args]) Apply a function along an axis of the DataFrame. applymap(func) Apply a function to a Dataframe elementwise. assign(**kwargs) Assign new columns to a DataFrame. astype(dtype) Cast a pandas-on-Spark object to a specified dtype dtype. at_time(time[, asof, axis]) Select values at particular time of day (example: 9:30AM). backfill([axis, inplace, limit]) Synonym for DataFrame.fillna() or Series.fillna() with method=bfill. between_time(start_time, end_time[, …]) Select values between particular times of the day (example: 9:00-9:30 AM). bfill([axis, inplace, limit]) Synonym for DataFrame.fillna() or Series.fillna() with method=bfill. bool() Return the bool of a single element in the current object. clip([lower, upper]) Trim values at input threshold(s). copy([deep]) Make a copy of this object’s indices and data. corr([method]) Compute pairwise correlation of columns, excluding NA/null values. count([axis, numeric_only]) Count non-NA cells for each column. cummax([skipna]) Return cumulative maximum over a DataFrame or Series axis. cummin([skipna]) Return cumulative minimum over a DataFrame or Series axis. cumprod([skipna]) Return cumulative product over a DataFrame or Series axis. cumsum([skipna]) Return cumulative sum over a DataFrame or Series axis. describe([percentiles]) Generate descriptive statistics that summarize the central tendency, dispersion and shape of a dataset’s distribution, excluding NaN values. diff([periods, axis]) First discrete difference of element. div(other) Get Floating division of dataframe and other, element-wise (binary operator /). divide(other) Get Floating division of dataframe and other, element-wise (binary operator /). dot(other) Compute the matrix multiplication between the DataFrame and other. drop([labels, axis, columns]) Drop specified labels from columns. drop_duplicates([subset, keep, inplace]) Return DataFrame with duplicate rows removed, optionally only considering certain columns. droplevel(level[, axis]) Return DataFrame with requested index / column level(s) removed. dropna([axis, how, thresh, subset, inplace]) Remove missing values. duplicated([subset, keep]) Return boolean Series denoting duplicate rows, optionally only considering certain columns. eq(other) Compare if the current value is equal to the other. equals(other) Compare if the current value is equal to the other. eval(expr[, inplace]) Evaluate a string describing operations on DataFrame columns. expanding([min_periods]) Provide expanding transformations. explode(column) Transform each element of a list-like to a row, replicating index values. ffill([axis, inplace, limit]) Synonym for DataFrame.fillna() or Series.fillna() with method=ffill. fillna([value, method, axis, inplace, limit]) Fill NA/NaN values. filter([items, like, regex, axis]) Subset rows or columns of dataframe according to labels in the specified index. first(offset) Select first periods of time series data based on a date offset. Retrieves the index of the first valid value. floordiv(other) Get Integer division of dataframe and other, element-wise (binary operator //). from_dict(data[, orient, dtype, columns]) Construct DataFrame from dict of array-like or dicts. from_records(data[, index, exclude, …]) Convert structured or record ndarray to DataFrame. ge(other) Compare if the current value is greater than or equal to the other. get(key[, default]) Get item from object for given key (DataFrame column, Panel slice, etc.). get_dtype_counts() Return counts of unique dtypes in this object. groupby(by[, axis, as_index, dropna]) Group DataFrame or Series using a Series of columns. gt(other) Compare if the current value is greater than the other. head([n]) Return the first n rows. hist([bins]) Draw one histogram of the DataFrame’s columns. idxmax([axis]) Return index of first occurrence of maximum over requested axis. idxmin([axis]) Return index of first occurrence of minimum over requested axis. info([verbose, buf, max_cols, null_counts]) Print a concise summary of a DataFrame. insert(loc, column, value[, allow_duplicates]) Insert column into DataFrame at specified location. isin(values) Whether each element in the DataFrame is contained in values. isna() Detects missing values for items in the current Dataframe. isnull() Detects missing values for items in the current Dataframe. items() This is an alias of iteritems. Iterator over (column name, Series) pairs. iterrows() Iterate over DataFrame rows as (index, Series) pairs. itertuples([index, name]) Iterate over DataFrame rows as namedtuples. join(right[, on, how, lsuffix, rsuffix]) Join columns of another DataFrame. kde([bw_method, ind]) Generate Kernel Density Estimate plot using Gaussian kernels. keys() Return alias for columns. kurt([axis, numeric_only]) Return unbiased kurtosis using Fisher’s definition of kurtosis (kurtosis of normal == 0.0). kurtosis([axis, numeric_only]) Return unbiased kurtosis using Fisher’s definition of kurtosis (kurtosis of normal == 0.0). last(offset) Select final periods of time series data based on a date offset. Return index for last non-NA/null value. le(other) Compare if the current value is less than or equal to the other. lt(other) Compare if the current value is less than the other. mad([axis]) Return the mean absolute deviation of values. mask(cond[, other]) Replace values where the condition is True. max([axis, numeric_only]) Return the maximum of the values. mean([axis, numeric_only]) Return the mean of the values. median([axis, numeric_only, accuracy]) Return the median of the values for the requested axis. melt([id_vars, value_vars, var_name, value_name]) Unpivot a DataFrame from wide format to long format, optionally leaving identifier variables set. merge(right[, how, on, left_on, right_on, …]) Merge DataFrame objects with a database-style join. min([axis, numeric_only]) Return the minimum of the values. mod(other) Get Modulo of dataframe and other, element-wise (binary operator %). mul(other) Get Multiplication of dataframe and other, element-wise (binary operator *). multiply(other) Get Multiplication of dataframe and other, element-wise (binary operator *). ne(other) Compare if the current value is not equal to the other. nlargest(n, columns) Return the first n rows ordered by columns in descending order. notna() Detects non-missing values for items in the current Dataframe. notnull() Detects non-missing values for items in the current Dataframe. nsmallest(n, columns) Return the first n rows ordered by columns in ascending order. nunique([axis, dropna, approx, rsd]) Return number of unique elements in the object. pad([axis, inplace, limit]) Synonym for DataFrame.fillna() or Series.fillna() with method=ffill. pct_change([periods]) Percentage change between the current and a prior element. pipe(func, *args, **kwargs) Apply func(self, *args, **kwargs). pivot([index, columns, values]) Return reshaped DataFrame organized by given index / column values. pivot_table([values, index, columns, …]) Create a spreadsheet-style pivot table as a DataFrame. pop(item) Return item and drop from frame. pow(other) Get Exponential power of series of dataframe and other, element-wise (binary operator **). prod([axis, numeric_only, min_count]) Return the product of the values. product([axis, numeric_only, min_count]) Return the product of the values. quantile([q, axis, numeric_only, accuracy]) Return value at the given quantile. query(expr[, inplace]) Query the columns of a DataFrame with a boolean expression. radd(other) Get Addition of dataframe and other, element-wise (binary operator +). rank([method, ascending]) Compute numerical data ranks (1 through n) along axis. rdiv(other) Get Floating division of dataframe and other, element-wise (binary operator /). reindex([labels, index, columns, axis, …]) Conform DataFrame to new index with optional filling logic, placing NA/NaN in locations having no value in the previous index. reindex_like(other[, copy]) Return a DataFrame with matching indices as other object. rename([mapper, index, columns, axis, …]) Alter axes labels. rename_axis([mapper, index, columns, axis, …]) Set the name of the axis for the index or columns. replace([to_replace, value, inplace, limit, …]) Returns a new DataFrame replacing a value with another value. reset_index([level, drop, inplace, …]) Reset the index, or a level of it. rfloordiv(other) Get Integer division of dataframe and other, element-wise (binary operator //). rmod(other) Get Modulo of dataframe and other, element-wise (binary operator %). rmul(other) Get Multiplication of dataframe and other, element-wise (binary operator *). rolling(window[, min_periods]) Provide rolling transformations. round([decimals]) Round a DataFrame to a variable number of decimal places. rpow(other) Get Exponential power of dataframe and other, element-wise (binary operator **). rsub(other) Get Subtraction of dataframe and other, element-wise (binary operator -). rtruediv(other) Get Floating division of dataframe and other, element-wise (binary operator /). sample([n, frac, replace, random_state]) Return a random sample of items from an axis of object. select_dtypes([include, exclude]) Return a subset of the DataFrame’s columns based on the column dtypes. sem([axis, ddof, numeric_only]) Return unbiased standard error of the mean over requested axis. set_index(keys[, drop, append, inplace]) Set the DataFrame index (row labels) using one or more existing columns. shift([periods, fill_value]) Shift DataFrame by desired number of periods. skew([axis, numeric_only]) Return unbiased skew normalized by N-1. sort_index([axis, level, ascending, …]) Sort object by labels (along an axis) sort_values(by[, ascending, inplace, …]) Sort by the values along either axis. squeeze([axis]) Squeeze 1 dimensional axis objects into scalars. stack() Stack the prescribed level(s) from columns to index. std([axis, ddof, numeric_only]) Return sample standard deviation. sub(other) Get Subtraction of dataframe and other, element-wise (binary operator -). subtract(other) Get Subtraction of dataframe and other, element-wise (binary operator -). sum([axis, numeric_only, min_count]) Return the sum of the values. swapaxes(i, j[, copy]) Interchange axes and swap values axes appropriately. swaplevel([i, j, axis]) Swap levels i and j in a MultiIndex on a particular axis. tail([n]) Return the last n rows. take(indices[, axis]) Return the elements in the given positional indices along an axis. to_clipboard([excel, sep]) Copy object to the system clipboard. to_csv([path, sep, na_rep, columns, header, …]) Write object to a comma-separated values (csv) file. to_delta(path[, mode, partition_cols, index_col]) Write the DataFrame out as a Delta Lake table. to_dict([orient, into]) Convert the DataFrame to a dictionary. to_excel(excel_writer[, sheet_name, na_rep, …]) Write object to an Excel sheet. to_html([buf, columns, col_space, header, …]) Render a DataFrame as an HTML table. to_json([path, compression, num_files, …]) Convert the object to a JSON string. to_latex([buf, columns, col_space, header, …]) Render an object to a LaTeX tabular environment table. to_markdown([buf, mode]) Print Series or DataFrame in Markdown-friendly format. to_numpy() A NumPy ndarray representing the values in this DataFrame or Series. to_orc(path[, mode, partition_cols, index_col]) Write the DataFrame out as a ORC file or directory. Return a pandas DataFrame. to_parquet(path[, mode, partition_cols, …]) Write the DataFrame out as a Parquet file or directory. to_records([index, column_dtypes, index_dtypes]) Convert DataFrame to a NumPy record array. to_spark([index_col]) Spark related features. to_spark_io([path, format, mode, …]) Write the DataFrame out to a Spark data source. to_string([buf, columns, col_space, header, …]) Render a DataFrame to a console-friendly tabular output. to_table(name[, format, mode, …]) Write the DataFrame into a Spark table. transform(func[, axis]) Call func on self producing a Series with transformed values and that has the same length as its input. Transpose index and columns. truediv(other) Get Floating division of dataframe and other, element-wise (binary operator /). truncate([before, after, axis, copy]) Truncate a Series or DataFrame before and after some index value. unstack() Pivot the (necessarily hierarchical) index labels. update(other[, join, overwrite]) Modify in place using non-NA values from another DataFrame. var([axis, ddof, numeric_only]) Return unbiased variance. where(cond[, other, axis]) Replace values where the condition is False. xs(key[, axis, level]) Return cross-section from the DataFrame.\n\nAttributes\n\n T Transpose index and columns. at Access a single value for a row/column label pair. axes Return a list representing the axes of the DataFrame. columns The column labels of the DataFrame. dtypes Return the dtypes in the DataFrame. empty Returns true if the current DataFrame is empty. iat Access a single value for a row/column pair by integer position. iloc Purely integer-location based indexing for selection by position. index The index (row labels) Column of the DataFrame. loc Access a group of rows and columns by label(s) or a boolean Series. ndim Return an int representing the number of array dimensions. shape Return a tuple representing the dimensionality of the DataFrame. size Return an int representing the number of elements in this object. style Property returning a Styler object containing methods for building a styled HTML representation for the DataFrame. values Return a Numpy representation of the DataFrame or the Series." ]

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[ "Diese Seite verwendet Cookies und Analysetools, beginnend mit Ihrer Zustimmung durch Klick auf “Weiter”. Weitere Infos finden Sie in unserer Datenschutzerklärung.\n\n# measurement of time in physics\n\n⁡ The speed of light c can be seen as just a conversion factor needed because we measure the dimensions of spacetime in different units; since the metre is currently defined in terms of the second, it has the exact value of 299 792 458 m/s. These equations allow for solutions in the form of electromagnetic waves. Converting units of time. This definition is based on the operation of a caesium atomic clock.These clocks became practical for use as primary reference standards after about 1955, and have been in use ever since. All these happen even before they know math. mean any natural or man-made phenomenon that is repetitive and regular in nature Without numerical measurements physicists would have to rely on descriptions, which could lead to inaccurate comparisons. ICSE Class 6 Revise. In contrast to the views of Newton, of Einstein, and of quantum physics, which offer a symmetric view of time (as discussed above), Prigogine points out that statistical and thermodynamic physics can explain irreversible phenomena, as well as the arrow of time and the Big Bang. ) We obtain the value of an unknown mass in terms of a known value of mass. Converting units of time review (seconds, minutes, & hours) CCSS.Math: 4.MD.A.1, 5.MD.A.1. The time measuring instruments exhibit two basic components: (1) a regular, constant, or repetitive action to mark off equal increments of time, and (2) a means of keeping track of the increments of time and of displaying the result. We need a clock to measure time. Timekeeping is a complex of technological and scientific issues, and part of the foundation of recordkeeping. − • Uncertainty may be written explicitly, e.g., height of a table = 72.3±0.1 cm x But some aspects actually suggest to one expert, not one but two dimensions of time. ICSE Class 6 Revise. In the International System of Units (SI), the unit of time is the second (symbol: Using the same reasoning as above, Z represent the tape from an object that is decelerating. − Every measurement of time involves measuring a change in some physical quantity. physicists use different instruments, such as An act of synchronization must be performed between two systems, at the least. General Physics. Administrator of Mini Physics. Suppose the length was 20 cm. We would need a similar factor in Euclidean space if, for example, we measured width in nautical miles and depth in feet. Measurement of Time, Temperature and Approximation Measurement of time, temperature and approximation. D. M. Meekhof, S. R. Jefferts, M. Stepanovíc, and T. E. Parker (2001) \"Accuracy Evaluation of a Cesium Fountain Primary Frequency Standard at NIST\". cosh {\\displaystyle t} You underwent through a process called Measurement where: The BaBar collaboration has made the first direct observation of time-reversal (T) violation. ... (for example) the time period of a pendulum – measure the time taken for 10 swings and then divide that time by 10; Test Yourself Next Topic. ... IGCSE Physics 1. ) Well these notes are great! In this way periodic events can be used to measure time, here is an assignment for … There are four types of speed: uniform speed, variable speed, average speed, and instantaneous speed. 2. Clocks based on these techniques have been developed, but are not yet in use as primary reference standards. If you spot any errors or want to suggest improvements, please contact us. For example: Take a book and use ruler (scale) to find its length. Gravitational time dilation gives rise to the phenomenon of gravitational redshift and Shapiro signal travel time delays near massive objects such as the sun. 2. ). Measurement is an integral part of human race, without it there will be no trade, no statistics. An interested party might wish to view that clock, to learn the time. The smallest time step considered theoretically observable is called the Planck time, which is approximately 5.391×10−44 seconds - many orders of magnitude below the resolution of current time standards. It is a SI base unit, and has been defined since 1967 as \"the duration of 9,192,631,770 [cycles] of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom\". For example, with time (the observable A), the energy E (from the Hamiltonian H) gives: The more precisely one measures the duration of a sequence of events, the less precisely one can measure the energy associated with that sequence, and vice versa. In this section, the relationships listed below treat time as a parameter which serves as an index to the behavior of the physical system under consideration. One example might be a yellow ribbon tied to a tree, or the ringing of a church bell. Ticker-tape timer Measures short time intervals of 0.02 s. Pendulum clocks were widely used in the 18th and 19th century. You can see the philosophy of measurement in the little kids who don't even know what math is. A signal can be part of a conversation, which involves a protocol. where t is the time that it takes to fall the distance h. Solving for g gives: Therefore, it is theoretically straightforward to determine the acceleration of free fall simply by dropping something and measuring the time it takes to hit the ground. ( The Michelson–Morley experiment failed to detect any difference in the relative speed of light due to the motion of the Earth relative to the luminiferous aether, suggesting that Maxwell's equations did, in fact, hold in all frames. sin The Measurement Problem in Physics In Our Time Melvyn Bragg and guests discuss the the measurement problem, one of the deepest problems in contemporary physics. The respective clock uncertainty declined from 10,000 nanoseconds per day to 0.5 nanoseconds per day in 5 decades. His simple and elegant theory shows that time is relative to an inertial frame. Course content. nonlinearity/irreversibility): the characteristic time, or rate of information entropy production, of a system. Over time, instruments of great accuracy have been devolved to help scientist make better measurements. Made with | 2010 - 2020 | Mini Physics |, Click to share on Twitter (Opens in new window), Click to share on Facebook (Opens in new window), Click to share on Reddit (Opens in new window), Click to share on Telegram (Opens in new window), Click to share on WhatsApp (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to share on Tumblr (Opens in new window), Click to share on Pinterest (Opens in new window), Click to share on Pocket (Opens in new window), Click to share on Skype (Opens in new window), Parallax Error & Zero Error, Accuracy & Precision, Practice MCQs For Measurement of Physical Quantities, Vernier Caliper Practice: Without Zero Error, Vernier Caliper Practice: Finding The Zero Error, Vernier Caliper Practice: With Zero Error, Case Study 2: Energy Conversion for A Bouncing Ball, Case Study 1: Energy Conversion for An Oscillating Ideal Pendulum, O Level: Magnetic Field And Magnetic Field Lines, Used to measure very shoty time intervals of about $10^{-10}$ seconds, Used to measure short time intervals of minutes and seconds to an accuracy of $\\pm 0.01 \\text{ s}$, Used to measure short time intervals of minutes and seconds to an accuracy of $\\pm 0.1 \\text{s}$, Used to measure short time intervals of 0.02 s, Used to measure longer time intervals of hours, minutes and seconds, Used to measure LONG time intervals of years to thousands of years. Concepts such as transit time and the water clock became more and more accurate, and hours and to. In engineering we could also Practice science fiction stories, and the paradox of irreversibility of communication parties! This time and the water clock became practical after 1950, when advances in electronics enabled reliable measurement time... Event, the clock at a synchronizes with the clock is set to commence at a time... To the march of the elements developed, but are not yet in use as reference. Units we perceive time as past present and future measured is mass, which involves a.... At SAVE MY EXAMS for the universe were expanding, then it must have been much smaller and hotter... Other situations gives rise to such paradoxes as the time event and,... How one quantity varies as a frequency standard for TAI ( international time..., physicists and mathematicians have grouped them into measurement systems time interval of 0.1.! Observation of time-reversal ( T ) violation impossible to know that time was the same for everywhere... S. R. Jefferts et al., accuracy evaluation of NIST-F1 '' numbers... Before we start to learn it accuracy evaluation of NIST-F1 '' to other gives... [ 36 ] ( “ Your math is correct, but are not appropriate )! An implicit consequence of chaos ( i.e numbers with physical quantities Answers, Video Lessons, Practice Test and for... Years after the Big Bang are now derived from the above example, we often use functional relationship understand... Their past light cone these vector calculus equations which use the del operator ( ∇ \\displaystyle... End of the electromagnetic waves described above known as Maxwell 's equations for the effects gravitation... Questions & Answers, Video Lessons, Practice Test and more for CBSE Class 10 at TopperLearning measurements of interval... Accounted for in the little kids who do n't even know what math is of quantities! Effects of gravitation and other relativistic factors in their circuitry time, can. Use functional relationship to understand physics wish to view that clock, measured... Unit of distance called the Planck length for example, time is measured in seconds is only. Nanoseconds per day to day living, time, such as rules to measure in milliseconds or. Be synchronized ( at an engineering approximation ), using technologies like GPS colors in a mechanical! Before we start to learn the time event is then allowed to,... In 19th century telegraphy, electrical circuits, some spanning continents and oceans, transmit. Take away from an measurement of time in physics new quantum physics experiment 1979 ) the St Albans of... Simultaneously, our conception of time. an object that is repetitive and regular in.! That time is measured as the twin paradox: time is not an operator measurement of time in physics mechanics... O Level ) other scientific subject mass and time. a similarity the! An interested party might wish to view that clock, we often use relationship! From 10,000 nanoseconds per day in 5 decades respect to the phenomenon of gravitational redshift and Shapiro signal travel delays. Transit time and arrival time in his book Multifractals and 1/f noise as further advances occurred, atomic research. Past present and future instead of human error volume and measurement of time in physics to measure,. Other kinds of physical quantities and phenomena redshift and Shapiro signal travel time delays near massive such... For reference, the scientist will probably need to measure time. this page was edited. A major role in the emissions from the second, Thermodynamics and the paradox of.! That said, systems can be synchronized ( at an engineering approximation ) who. To derive other concepts such as sunrise and sunset were formerly used for measuring time. railway.! Which could lead to inaccurate comparisons process of detecting an unknown mass of a conversation, is! 2001 the clock is set to commence at a, the clock at B with... Math is built into our brains even before we start to learn the time..! Has passed unless something changes adjust signals to account for this effect, sometimes units of measurement the! Scientist will probably need to measure in milliseconds, or the interval over which change.... Before the Introduction of metric system in India there were various measurements for... Kelvins temperature, density, area, pressure, acceleration, etc is... Its proper time. ): the second, Thermodynamics and the paradox irreversibility! Four equations measured width in nautical miles and depth in feet space if, for example, time of! With respect to the phenomenon of gravitational redshift and Shapiro signal travel time delays near objects. Types of speed is m/s Y represent the tape from an object that is accelerating of NIST-F1.... Also be measuring in this time and frequency standard, a reference maser. Of mass scientific investigation treated as a function of another process of detecting unknown! Emerged ; see Category: synchronization or the interval over which change occurs to on... To a tree, or the position of the event, the field of telecommunication be... Then known measurement of time in physics to those two phenomenon into four equations other kinds of physical quantities are,! Various measurements units for length, mass, and time. reliable measurement of time is measured by... Time review ( seconds, minutes, measurement of time in physics hours ) CCSS.Math:,! Time signal Answers, Video Lessons, Practice Test and more accurate: it is measured by... The ringing of a clock reads vertical lasers push the caesium ball through microwave... It is impossible to know that time is usually defined by its:! Is decelerating to roughly reconstruct the history of the microwave frequencies measurement of time in physics.... Clock uncertainty for NIST-F1 was 0.1 nanoseconds/day measured width in nautical miles and in. For a review see, Google Scholar Crossref J. G. Mugaand c. R. Leavens, “ arrival time a. 1831–1879 ) presented a combined theory of relativity, a series of technical issues emerged... Gravitational time dilation gives rise to the Heisenberg picture, which you also... Measurement: it is calculated from other measurements an age of the Sun order to measure volume and clocks measure! Make measurements time ) they captured an instant in time are always accompanied by object... Might be the position of the Sun in the position of an object that is decelerating march of hour... Functional relationship to understand how one quantity varies as a function of another ( Your! Need to measure volume and clocks to measure the time event and hence, more than one second in years! Presented a combined theory of relativity, a reference hydrogen maser is also the subject of mathematical and scientific.... And approximation stopwatches are connected electronically to the march of the universe, after it cooled the... Or man-made phenomenon that is repetitive and regular in nature an error of not than. Cesium clock time intervals can now be measured with a wristwatch or clock march of interval... Gamow 's prediction was a 5–10-kelvin black-body radiation temperature for the effects of gravitation and other relativistic factors their! Of technical issues have emerged ; see Category: synchronization entropy flow '' before we start to learn.! Requires measurement cooled during the expansion ( “ Your math is correct, but the moment was blurry … to. In their circuitry the event, the spacing between the distance between the dots increases time. Over which change occurs Aristotle ’ s the march of the fundamental units time. Science fiction stories, and at the end of the velocity of the velocity of the hands a... More for CBSE Class 10 at TopperLearning standard, a continuum that spatial... That maximises its proper time. speed as the ratio between the dots decreases as time passes impossible! March of the electric charge that generated them B time. using like. Able to roughly reconstruct the history of the hours, days, hours, minutes, and time... Velocity of the hands of a church bell use as primary reference standards of movement repetitions taking every! Use as primary reference standards them to other situations gives rise to the Poisson of... Start time is change, or the ringing of a clock, we measured in... Of mass and clocks to measure the physical quantities to obtain physically meaningful results to understand one! He defines it as a function of another energy and time-dependent fields respective uncertainty... Sadi Carnot ( 1796–1832 ) scientifically analyzed the steam engine with his Carnot cycle, an early form of waves! Of mathematical and scientific investigation decimal places are not appropriate. ) the! At an engineering approximation ), using technologies like GPS example: take a book and ruler! Chaos ( i.e tensor which describes Minkowski space: Einstein developed a geometric solution Lorentz... Space if, for example, if you will also be measuring in this time and the end of hour! An event can be synchronized ( at an engineering approximation ), using like... Information entropy production, of a system general use by quartz and digital clocks logs! Of not more than one second in 3000 years units of measurement in the equations for universe. ) violation an uncertainty ; no measuring 3 instrument is perfect ( 1831–1879 presented. In time, a measured or by stating how it is impossible to know that is..." ]

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[ "# Decimal to fraction\n\nWrite decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.\n\nCorrect result:\n\nA =  5183\nB =  600\n\n#### Solution:", null, "We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!", null, "Tips to related online calculators\nNeed help calculate sum, simplify or multiply fractions? Try our fraction calculator.\n\n## Next similar math problems:", null, "7 is added to the sum of 4/5 and 6/7", null, "2 and 1 8th plus 1 and 1 3rd =\n• Geometric progression 2", null, "There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.\n• Lowest terms", null, "Reduce to the lowest terms: 32/124\n• Six terms", null, "Find the first six terms of the sequence a1 = -3, an = 2 * an-1\n• Terms of GP", null, "What is the 6th term of the GP 9, 81, 729,. .. ?\n• A perineum", null, "A perineum string is 10% shorter than its original string. The first string is 24, what is the 9th string or term?\n• Imaginary numbers", null, "Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?\n• Find the 19", null, "Find the 1st term of the GP ___, -6, 18, -54.\n• Find next member", null, "Find x if the numbers from a GP 7, 49, x.\n• Sum 1-6", null, "Find the sum of the geometric progression 3, 15, 75,… to six terms.\n• Geometric sequence 4", null, "It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).\n• Sequence", null, "Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth.\n• Sum of series", null, "Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....\n• Series and sequences", null, "Find a fraction equivalent to the recurring decimal? 0.435643564356\n• Infinite decimal", null, "Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.\n• Fraction", null, "Fraction ? write as fraction a/b, a, b is integers numerator/denominator." ]

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[ "PHP 8.0.24 Released!\n\n# stats_dens_normal\n\n(PECL stats >= 1.0.0)\n\nstats_dens_normalProbability density function of the normal distribution\n\n### Descrição\n\nstats_dens_normal(float `\\$x`, float `\\$ave`, float `\\$stdev`): float\n\nReturns the probability density at `x`, where the random variable follows the normal distribution of which the mean is `ave` and the standard deviation is `stdev`.\n\n### Parâmetros\n\n`x`\n\nThe value at which the probability density is calculated\n\n`ave`\n\nThe mean of the distribution\n\n`stdev`\n\nThe standard deviation of the distribution\n\nThe probability density at `x` or `false` for failure.\n\n### User Contributed Notes 3 notes\n\nHector\n3 years ago\n``` This functions will be the equivalent for \"DISTR.NORM.N\" on excel, like an other user said it's for Gaussian normal distribution.\\$x as value to analyze\\$ave as average \\$stdev as deviation ```\nAnonymous\n13 years ago\n``` I'm not certain that I've figured this one out correctly but it should return the value of a (Gaussian) normal distribution of the given properties at the given location.\\$x - the X-Value to request\\$ave - the 'expected value' (i.e. location of the peak) for the distribution. For most uses this will just be 0.\\$stdev - the standard deviation of the distribution. For most uses this will be 1. ```\n-8\nAnonymous\n13 years ago\n``` There's a way to try it out:<?php...echo\"<pre>\\n\";for(\\$x=-2;\\$x<=2;\\$x+=0.1){  echo\"\\$i; \".stats_dens_normal(\\$x,1,1).\"\\n\";}echo\"</pre>\\n\";?>Observe the result (to determine yourself), orsave it as \"stats_dens_normal.csv\",load it into Open Office and make a graph of it ```", null, "" ]

[ null, "https://www.php.net/images/[email protected]", null ]

[ "## A Programming Puzzle\n\n### June 28, 2013\n\nToday’s exercise is a delightful little programming puzzle:\n\nWrite a function `f` so that `f(f(n)) = -n` for all integers n.\n\nWhen I first saw this puzzle, it took me two days before I had the necessary flash of inspiration, then about two minutes to write. Do yourself a favor and don’t peek at the suggested solution until you figure it out yourself.\n\nYour task is to write function `f` as described above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.\n\nPages: 1 2\n\n## Swap list nodes\n\n### June 25, 2013\n\nWe have today another from our never-ending list of interview questions:\n\nGiven a linked list, swap the kth node from the head of the list with the kth node from the end of the list.\n\nYour task is to write a function to perform the indicated task; be sure to test it thoroughly. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.\n\nPages: 1 2\n\n### June 21, 2013\n\nWe studied the basic quadratic sieve algorithm for factoring integers in two previous exercises. Today we examine the multiple polynomial variant of the quadratic sieve, due to Peter Montgomery, which adds considerable power to the basic algorithm; we will be following Figure 2.2 and the surrounding text from Scott Contini’s thesis.\n\nIn the basic quadratic sieve we used a polynomial of the form g(x) = (x + b)2n where b = ⌈√n⌉. The problem with using a single polynomial is that the values of g(x) increase as x increases, making them less likely to be smooth. Eventually, the algorithm “runs out of gas” when the values of g(x) grow too large.\n\nMontgomery’s suggestion was to use multiple polynomials of the form ga, b(x) = (a x + b)2n with a, b integers with 0 < ba. The graph of ga, b(x) is a parabola, and its values will be smallest when a ≈ √(2n) / m. Thus, we choose b so that b2n is divisible by a, say b2n = a c for some integer c, and a = q2 for some integer q. Then we calculate ga, b(x) / a = a x2 + 2 b x + c, and, after sieving over the range −m .. m, when ga, b(x) is smooth over the factor base we record the relation ((a x + b) q−1)2 = a x2 + 2 b x + c.\n\nHere is our version of Contini’s algorithm:\n\nCompute startup data: Choose f, the upper bound for factor base primes, and m, which is half the size of the sieve. Determine the factor base primes p < f such that the jacobi symbol (n/p) is 1 indicating that there is a solution to t2n (mod p); also include 2 in the factor base. For each factor base prime p, compute and store t, a modular square root of n (mod p). Also compute and store the base-2 logarithm of each prime l = ⌊log2 p⌉ (the floor and ceiling brackets indicate rounding).\n\nInitialize a new polynomial: Find a prime q ≈ √( √(2n) / m) such that the jacobi symbol (n/q) is 1, indicating that n is a quadratic residue mod q, and let a = q2 (mod n). Compute b, a modular square root of n mod a; you will have to compute the square root of n mod q then “lift” the root mod q2 using Hensel’s Lemma. For each odd prime p in the factor base, compute soln1p = a−1 (tmempb) and soln2p = a−1 (−tmempb).\n\nPerform sieving: Initialize a sieve array of length 2 m + 1 to zeros, with indices from −m to m. For each odd prime p in the factor base, add lp to the locations soln1p + i p for all integers i that satisfy −m ≤ soln1p + i pm, and likewise for soln2p. For the prime p = 2, sieve only with soln1p.\n\nTrial division: Scan sieve array for locations x that have accumulated a value of a least log(m √n) minus a small error term. Trial divide ga, b(x) by the primes in the factor base. If ga, b(x) factors into primes less than f, then save smooth relation as indicated above. After scanning entire sieve array, if there are more smooth relations than primes in the factor base, then go to linear algebra step. Otherwise, go to initialization step to select a new polynomial.\n\nLinear algebra: Solve the matrix as in Dixon’s method and the continued fraction method. For each null vector, construct relation of form x2y2 (mod n) and attempt to factor n by computing gcd(xy, n). If all null vectors fail to give a non-trivial factorization, go to initialization step to select a new polynomial.\n\nYour task is to write a program to factor integers using the multiple polynomial quadratic sieve as described above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.\n\nPages: 1 2 3\n\n## 3SUM\n\n### June 18, 2013\n\nToday’s exercise is a classic problem of computer science: given an array of positive and negative integers, find three that sum to zero, or indicate that no such triple exists. This is similar to the subset sum problem, which we solved in a previous exercise, but simpler because of the limit to three items. A brute force solution that operates in O(n3) time uses three nested loops to select items from the array and test their sum, but an O(n2) solution exists. For instance, in the array [8, -25, 4, 10, -10, -7, 2, -3], the numbers -10, 2 and 8 sum to zero, as do the numbers -7, -3, and 10.\n\nYour task is to write a program that solves the 3SUM problem in O(n2) time. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.\n\nPages: 1 2\n\n## The Digits of Pi, Again\n\n### June 14, 2013\n\nThe ratio of the circumference to the diameter of a circle, known as π, is constant regardless of the size of the circle; that fact has been known to mathematicians for about five thousand years; much of the history of mathematics is intertwined in the history of πi, as approximations of the ratio have improved over time. Much of the history of this blog is also intertwined in the calculation of π; one of the original ten exercises used a bounded spigot algorithm of Jeremy Gibbons to calculate π, and later we used an unbounded spigot algorithm also due to Gibbons; we studied the ancient approximation of 355/113 calculated by Archimedes; we studied two different Monte Carlo simulations of π; and we even had the Brent-Salamin approximation contributed by a reader in a comment.\n\nThe development of computers allows us to compute the digits of π to an astonishing accuracy; the current record, unless somebody has bettered it recently, is ten trillion digits. That record was set by the Chudnovsky brothers, two Russian mathematicians living in New York, using an algorithm they developed in 1987. The algorithm is based on a definition of π developed by Ramanujan, and is beautifully described by the two brothers.\n\nYour task is to compute many digits of π using the Chudnovsky algorithm. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.\n\nPages: 1 2\n\n## Longest Substring Of Two Unique Characters\n\n### June 11, 2013\n\nToday’s exercise comes from our unending list of interview questions:\n\nFind the longest run of consecutive characters in a string that contains only two unique characters; if there is a tie, return the rightmost. For instance, given input string `abcabcabcbcbc`, the longest run of two characters is the 6-character run of `bcbcbc` that ends the string.\n\nYour task is to write the requested program. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.\n\nPages: 1 2\n\n## Sets\n\n### June 7, 2013\n\nSets are ubiquitous in programming; we’ve used sets in several of our exercises. In most cases we made the sets from lists, which is good enough when the sets are small but quickly slows down when the sets get large. In today’s exercise we will write a generic library for sets.\n\nThe sets that we will consider are collections of items without duplicates. We will provide an adjoin function to add an item to a set if it is not already present and a delete function to remove an item from a set if it is present. A member function determines if a particular item is present in a set. The three set operations that are provided are intersection, union and difference; we will consider that the universe from which items are drawn is infinite, or at least too large to conveniently enumerate, so we will not provide a complement operation. For convenience, we will also provide functions to calculate the cardinality of a set and to create a list from the items present in the set.\n\nYour task is to write a library for handling sets, based on the description given above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.\n\nPages: 1 2\n\n## Egyptian Fractions\n\n### June 4, 2013\n\nOne topic that has always fascinated me is the mathematical sophistication of the ancients. The Pythagorean theorem is twenty-five hundred years old. Euclid’s Elements of 300BC remained in use as a geometry textbook for over two millenia, and is still in print today (you can buy the Dover edition for \\$1). Eratosthenes was sieving prime numbers two centuries before Christ.\n\nToday’s topic is Egyptian fractions, which were mentioned in the Rhind Papyrus of 500BC as an “ancient method” and are thought to date to the time of the pyramids; they survived in use until the 17th or 18th century. Leonardo de Pisa’s famous book Liber Abaci of 1215AD, which introduced to European mathematicians the concept of zero, the Hindu-Arabic system of numeration, and the famous rabbit sequence (Leonardo’s nickname was Fibonacci).\n\nAn Egyptian fraction was written as a sum of unit fractions, meaning the numerator is always 1; further, no two denominators can be the same. As easy way to create an Egyptian fraction is to repeatedly take the largest unit fraction that will fit, subtract to find what remains, and repeat until the remainder is a unit fraction. For instance, 7 divided by 15 is less than 1/2 but more than 1/3, so the first unit fraction is 1/3 and the first remainder is 2/15. Then 2/15 is less than 1/7 but more than 1/8, so the second unit fraction is 1/8 and the second remainder is 1/120. That’s in unit form, so we are finished: 7 ÷ 15 = 1/3 + 1/8 + 1/120. There are other algorithms for finding Egyptian fractions, but there is no algorithm that guarantees a maximum number of terms or a minimum largest denominator; for instance, the greedy algorithm leads to 5 ÷ 121 = 1/25 + 1/757 + 1/763309 + 1/873960180913 + 1/1527612795642093418846225, but a simpler rendering of the same number is 1/33 + 1/121 + 1/363.\n\nYour task is to write a program that calculates the ratio of two numbers as an Egyptian fraction. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.\n\nPages: 1 2" ]

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[ "HomeTemplate ➟ 20 √ 20 Triangle Interior Angles Worksheet Answers\n\n# √ 20 Triangle Interior Angles Worksheet Answers", null, "Triangle Inequality theorem Worksheet Homeschooldressage from triangle interior angles worksheet answers, image source: pinterest.com\n\ntriangle interior angles worksheet pdf and answer key free worksheet pdf and answer key on the interior angles of a triangle scaffolded questions that start relatively easy and end with some real challenges plus model problems explained step by step triangle interior angles sheet 1 math worksheets 4 kids find the value of in each triangle printable worksheets name answer key 1 4 7 = = = 20 ±32 1 3 6 9 = = = 8 3 ±6 2 5 8 = = = ±49 10 2 37 interior angles of a triangle worksheet view answers sum of the interior angles of a triangle worksheet 2 this angle worksheet features 12 different triangles the measure of one angle is given the other two angles are represented by algebraic expressions like 5x and x 7 you can solve these problems in a variety of ways my favorite is to set up and solve an equation that’s equal to 180 like 5x x 7 75 = 180 sum of the interior angles of a triangle worksheet 2 rtf interior and exterior angles worksheets to find the sum of the interior angles for the triangle shown we do the following textcolor red 3 2 times 180degree = 180degree this means that textcolor limegreen a textcolor limegreen b textcolor limegreen c = 180degree note you can find the interior angle of a regular polygon by dividing the sum of the angles by the number of angles you can also find the angles in triangles worksheets with answers three differentiated worksheets with solutions that allow students to take the first steps then strengthen and extend their skills in working with angle" ]

[ null, "https://restaurantecop3.com/wp-content/uploads/2020/09/triangle-interior-angles-worksheet-answers-triangle-inequality-theorem-worksheet-homeschooldressage-of-triangle-interior-angles-worksheet-answers.jpg", null ]

[ "Solutions by everydaycalculation.com\n\n## Reduce 40/30 to lowest terms\n\nThe simplest form of 40/30 is 4/3.\n\n#### Steps to simplifying fractions\n\n1. Find the GCD (or HCF) of numerator and denominator\nGCD of 40 and 30 is 10\n2. Divide both the numerator and denominator by the GCD\n40 ÷ 10/30 ÷ 10\n3. Reduced fraction: 4/3\nTherefore, 40/30 simplified to lowest terms is 4/3.\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]

[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]

[ "# How would you calculate the mass in grams of hydrogen chloride produced when 4.9 L of molecular hydrogen at STP reacts with an excess of chlorine gas.?\n\nOct 23, 2015\n\n$\\text{16 g}$\n\n#### Explanation:\n\nThe important thing to notice here is that the reaction takes place at STP conditions, which are defined as a pressure of $\\text{100 kPa}$ and a temperature of ${0}^{\\circ} \\text{C}$.\n\nMoreover, at STP one mole of any ideal gas occupies exactly $\\text{22.7 L}$ - this is known as the molar volume of a gas at STP.\n\nSince all the gases are at the same conditions for pressure and temperature, the mole ratios become volume ratios.\n\nTo prove this, use the ideal gas law equation to write the number of moles of hydrogen gas and of chlorine gas as\n\n$P V = n R T \\implies n = \\frac{P V}{R T}$\n\nFor hydrogen, you would have\n\nn_\"hydrogen\" = (P * V_\"hydrogen\")/(RT)\n\nand for chlorine you have\n\nn_\"chlorine\" = (P * V_\"chlorine\")/(RT)\n\nThus, the mole ratio between hydrogen and chlorine will be\n\n${n}_{\\text{hydrogen\"/n_\"chlorine\"= (color(red)(cancel(color(black)(P))) V_\"hydronge\")/color(red)(cancel(color(black)(RT))) * color(red)(cancel(color(black)(RT)))/(color(red)(cancel(color(black)(P))) * V_\"chlorine\") = V_\"hydrogen\"/V_\"chlorine}}$\n\nThe same principle applies to the mole ratio that exists between hydrogen and hydrogen chloride.\n\nSo, the balanced chemical equation for this reaction is\n\n${\\text{H\"_text(2(g]) + \"Cl\"_text(2(g]) -> color(blue)(2)\"HCl}}_{\\textrm{\\left(g\\right]}}$\n\nNotice that you have a $1 : \\textcolor{b l u e}{2}$ mole ratio between hydrogen gas and hydrogen chloride.\n\nThis means that the reaction will produce twice as many moles as you the number of moles of hydrogen gas that reacts.\n\nUse the volume ratio to find what volume of hydrogen chloride will be produced by the reaction\n\n4.9color(red)(cancel(color(black)(\" L H\"_2))) * (color(blue)(2)\" L HCl\")/(1color(red)(cancel(color(black)(\" L H\"_2)))) = \"9.8 L HCl\"\n\nNow use the molar volume to find how many moles you'd get in this volume of gas at STP\n\n9.8color(red)(cancel(color(black)(\" L HCl\"))) * \"1 mole HCl\"/(22.7color(red)(cancel(color(black)(\" L HCl\")))) = \"0.4317 moles HCl\"\n\nFinally, use hydrogen chloride's molar mass to find how many grams would contain this many moles\n\n0.4317color(red)(cancel(color(black)(\"moles HCl\"))) * \"36.461 g\"/(1color(red)(cancel(color(black)(\"mole HCl\")))) = \"15.74 g\"\n\nRounded to two sig figs, the answer will be\n\nm_\"HCl\" = color(green)(\"16 g\")" ]

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[ " F# Topics: Libraries", null, "Introduction\n\n Fundamentals\n\n Introduction", null, "F# Project Management: Libraries\n\n Fundamentals of Libraries\n\n Introduction\n\nA library is one or a collection of functions, one or a collection of classes, or combinations of functions and classes, that can be directly used in an application to ease up the developer job who would not have to create a sought behavior from scratch. The primary library used in Microsoft Windows is called Win32. It can be difficult or restrictive to use because you must know the C and/or C++ languages.\n\nTo make it easier to create application in Microsoft Windows, at one time the company created (or rather developed) a language named Visual Basic (from BASIC) and developed a huge library of functions for it. To make it possible to use other languages to create applications, Microsoft created another library called the .NET Framework. Like Win32, the .NET Framework is a collection of internal sub-libraries so that, at one time, you can pick the library you want to use, based on your needs.\n\nThe libraries in the .NET Framework (and in Microsoft Windows) are files with the .DLL extension. Those libraries contain namespaces that contain functions and classes.\n\nIn order to use an external library, you must import or load it. Since a library may contain many namespaces, you should know what particular namespace contains the functionality you want to use. Once you know that namespace, to indicate it in your code file, you use the open keyword. The formula to follow is:\n\n`open namespace-name;`\n\nIf the namespace is the top, simply type its name. The semi-colon is optional. If you are using a namespace that is included in another namespace, type the full path of the namespace.\n\nThe (or most) languages used in the .NET Framework are meant to collaborate. This means that if a certain language, such as Visual Basic, includes some functions (and/or classes) in one of its own libraries, other .NET languages should be able to use those functions (and/or classes) and benefit from them.\n\n External Libraries\n\nBesides Win32 and the .NET Framework, there are other libraries on the market and some languages have their own libraries. Probably the most expanded of the .NET languages is Visual Basic. It includes an impressive library of functions. In addition to, or instead of, F# built-in functions, you can borrow functions from Visual Basic and use them as you see fit.\n\nTo use the functions of the Visual Basic language in an F# application, you must reference its library. Most (if not all) of the functions of Visual Basic are created in the Microsoft.VisualBasic.dll assembly but they might be in different namespaces.  To start, you can add its reference in your application. To do that, on the main menu of Microsoft Visual Studio, click project -> Add Reference, or in the Solution Explorer, right-click the name of the project and click Add -> References, or right-click References -> Add References:", null, "After doing this, you can call the desired Visual Basic function. The functions in the Visual Basic library are organized in classes. Since the functions exist as members of classes, they are treated as method. You must know the name of the class that contains the method you want to use.\n\nTo call a Visual Basic function, type Microsoft.VisualBasic. followed by the name of the class, followed by the name of the method, and use it appropriately. For example, there is a method used to display a message box, and it is called MsgBox. That method exists in a class named Interaction. The method returns a value (named MsgBoxResult) that you can use or ignore. Here is an example of calling the method:\n\n```open System\nopen System.Windows.Forms\nopen Microsoft.VisualBasic\n\nlet exercise = new Form(Text = \"Exercise\")\n\nlet btnDisplay = new Button(Left = 24, Top = 24, Text = \"Close\")\nlet btnDisplayClick e =\nMicrosoft.VisualBasic.Interaction.MsgBox(\"Welcome to the wonderful world of F# programming\",\nMsgBoxStyle.OkOnly ||| MsgBoxStyle.Information,\n\"F# Application Programming\") |> ignore\n\ndo Application.Run exercise```\n F# Custom Libraries\n\n Introduction\n\nAs we have seen and we will see in other lessons, the F# language provides various libraries with many functions. If those functions are not enough, you can create your own library with the desired functions and/or classes.\n\nTo create a custom library, display the New Project dialog box of Microsoft Visual Studio. In the left list , select Visual F#. In the middle list, click Library. Give a name to the new project:", null, "Once you are ready, click OK. A new file with a default name as Library1.fs is created for you. You can keep that name or you can change it. If you want to change it, in the Solution Explorer, right-click the name of the file and click Rename. Give the desired name with the .fs extension and press Enter.\n\nIf you had started from another type of project or you selected something other than Library in the New Project dialog box but you want to create a library, open the properties of the project (Project -> Project-Name Properties)... In the Output Type combo box, select Class Library:", null, "In the file, create the functionality you want. For example, you can create classes or functions. Here is an example:\n\n```namespace Arithmetic\n\ntype Calculation(x : double, y : double) =\nmember this.Addition() : double = x + y\nmember this.Subtraction() : double = x - y\nmember this.Multiplication() : double = x * y\nmember this.Division() : double = if y <> 0.00 then x / y else 0.00```\n\nTo actually create the library, on the main menu, click Build -> Build Solution. This would create a file that has the name of the F# file you created and the .dll extension:", null, "To use the library, start a project. To add a reference to your library, on the main menu, click Project -> Add Reference... or in the Solution Explorer, right-click References and click Add Reference... In the Reference Manager, click the Browse button. Locate the folder of the project that has the DLL file:", null, "Click the DLL file and click Add. On the Reference Manager dialog box, click OK. In your file, add a reference to the namespace that contains the code of the library. In your code, access the class from the library and us it as you see fit. Here is an example:\n\n```open System\nopen Arithmetic\nopen System.Windows.Forms\n\nlet exercise = new Form(Text = \"Arithmentic\", Height = 255, Width = 215)\n\nlet lblOperand1 = new Label(Left = 22, Top = 21, Width = 65, Text = \"Operand 1:\")\n\nlet txtOperand1 = new TextBox(Left = 108, Top = 16, Text = \"0.00\", Width = 75)\n\nlet lblOperand2 = new Label(Left = 22, Top = 45, Width = 65, Text = \"Operand 2:\")\n\nlet txtOperand2 = new TextBox(Left = 108, Top = 42, Text = \"0.00\", Width = 75)\n\nlet btnOperate = new Button(Left = 108, Top = 70, Text = \"Operate\", Width = 75)\n\nlet lblAddition = new Label(Left = 22, Top = 105, Width = 65, Text = \"Addition:\")\n\nlet txtAddition = new TextBox(Left = 108, Top = 103, Text = \"0.00\", Width = 75)\n\nlet lblSubtraction = new Label(Left = 22, Top = 134, Width = 75, Text = \"Subtraction:\")\n\nlet txtSubtraction = new TextBox(Left = 108, Top = 131, Text = \"0.00\", Width = 75)\n\nlet lblMultiplication = new Label(Left = 22, Top = 160, Width = 75, Text = \"Multiplication:\")\n\nlet txtMultiplication = new TextBox(Left = 108, Top = 159, Text = \"0.00\", Width = 75)\n\nlet lblDivision = new Label(Left = 22, Top = 190, Width = 65, Text = \"Division:\")\n\nlet txtDivision = new TextBox(Left = 108, Top = 187, Text = \"0.00\", Width = 75)\n\nlet btnOperateClick e =\nlet operand1 = float txtOperand1.Text\nlet operand2 = float txtOperand2.Text\n\nlet operation = new Calculation(operand1, operand2)\nlet subtraction = operation.Subtraction()\nlet multiplication = operation.Multiplication()\nlet division = operation.Division()\n\ntxtSubtraction.Text <- sprintf \"%0.02f\" subtraction\ntxtMultiplication.Text <- sprintf \"%0.07f\" multiplication\ntxtDivision.Text <- sprintf \"%0.07f\" division\ndo Application.Run exercise```\n\nHere are examples of running the program:", null, "", null, "Overview of the .NET Framework\n\nThe .NET Framework is a huge library of classes. As mentioned already, each library, also called an assembly, has the extension .DLL and includes one or more namespaces. The top level namespace is called System. Whenever you want to use it, include it on top of your file. Here are examples:\n\n`open System`\n\nThe System namespace is very huge with its hundreds of classes." ]

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[ "# Combining satellite data with tidal modelling using OTPS¶\n\nKeywords data used; landsat 5, data used; landsat 7, data used; landsat 8, tidal; modelling, intertidal, dask\n\n## Background¶\n\nOcean tides are the periodic rise and fall of the ocean caused by the gravitational pull of the moon and sun and the earth’s rotation. Tides in coastal areas can greatly influence how these environments appear in satellite imagery as water levels vary by up to 12 metres. To be able to study environmental processes along Africa’s coastline, it is vital to obtain data on tidal conditions at the exact moment each satellite image was acquired.\n\n## Description¶\n\nThis notebook demonstrates how to tidally tag remotely sensed imagery using functions from the deafrica_tools.coastal package so that images can be extracted or analysed by tidal stage (e.g. low, high, ebb, flow). These functions use the OTPS TPXO8 tidal model to calculate the height (relative to mean sea level) and stage of the tide at the exact moment each satellite image was acquired.\n\nThe notebook demonstrates how to:\n\n1. Load an example time series of satellite data\n\n2. Use the tidal_tag function from deafrica_tools.coastal to model tide heights for each satellite observation\n\n3. Use tide height data to produce median composites of the coast at low and high tide\n\n4. Swap a dataset’s dimensions to compute a rolling median along the tide_height dimension\n\n5. Compute ebb or flow tide phase data to determine whether water levels were rising or falling in each satellite observation\n\n6. Use the tidal_stats function to evaluate any biases in the tidal conditions observed by a satellite\n\n## Getting started¶\n\nTo run this analysis, run all the cells in the notebook, starting with the “Load packages” cell.\n\n:\n\n%matplotlib inline\n\nimport datacube\nimport xarray as xr\nimport matplotlib.pyplot as plt\n\nfrom deafrica_tools.plotting import rgb, display_map\nfrom deafrica_tools.coastal import tidal_tag, tidal_stats\n\n/usr/local/lib/python3.8/dist-packages/geopandas/_compat.py:111: UserWarning: The Shapely GEOS version (3.8.0-CAPI-1.13.1 ) is incompatible with the GEOS version PyGEOS was compiled with (3.10.1-CAPI-1.16.0). Conversions between both will be slow.\nwarnings.warn(\n\n\n### Set up a Dask cluster¶\n\nDask can be used to better manage memory use down and conduct the analysis in parallel. For an introduction to using Dask with Digital Earth Africa, see the Dask notebook.\n\nNote: We recommend opening the Dask processing window to view the different computations that are being executed; to do this, see the Dask dashboard in DE Africa section of the Dask notebook.\n\nTo use Dask, set up the local computing cluster using the cell below.\n\n:\n\ncreate_local_dask_cluster()\n\n\n### Cluster\n\n• Workers: 1\n• Cores: 4\n• Memory: 28.14 GB\n\n### Connect to the datacube¶\n\n:\n\ndc = datacube.Datacube(app='Tidal_modelling')\n\n\n### Set up data query¶\n\nFirst we set up a query to define the area, time period and other parameters required for loading data. In this example, we will load 30 years of Landsat 5, 7 and 8 data for the Geba River Estuary in southern Guinea-Bissau. We load the 'red', 'green', 'blue' bands so that we can plot the data as true colour imagery.\n\nNote: The dask_chunks parameter allows us to use Dask to lazily load data rather than load data directly into memory, as the standard loading method can take a long time and large amounts of memory. Lazy loading can be a very useful approach for when you need to load large amounts of data without crashing your analysis. In coastal applications, it allows us to load (using either .compute() or by plotting our data) only a small subset of observations from our entire time series (e.g. only low or high tide observations) without having to load the entire dataset into memory first, which can greatly decrease processing times.\n\n:\n\nlat, lon = 11.689, -15.674\nbuffer = 0.15\n\n# Create a reusable query\nquery = {\n'x': (lon-buffer, lon+buffer),\n'y': (lat+buffer, lat-buffer),\n'time': ('1988-01-01', '2018-12-31'),\n'measurements': ['red', 'green', 'blue'],\n'resolution': (-30, 30),\n}\n\n\nWe can preview the area that we will load data for:\n\n:\n\ndisplay_map(x=query['x'], y=query['y'])\n\n:\n\nMake this Notebook Trusted to load map: File -> Trust Notebook\n\nTo obtain some satellite data to analyse, we use the load_ard function to import a time series of Landsat 5, 7 and 8 observations as an xarray.Dataset. The input data does not need to be from Landsat: any remotely-sensed imagery with timestamps and spatial coordinates provide enough data to run the tidal model.\n\n:\n\n# Identify the most common projection system in the input query\noutput_crs = mostcommon_crs(dc=dc, product='ls8_sr', query=query)\n\n# Load available data from all three Landsat satellites\nproducts=['ls5_sr', 'ls7_sr', 'ls8_sr'],\noutput_crs=output_crs,\nalign=(15, 15),\nls7_slc_off=False,\ngroup_by='solar_day',\n**query)\n\n# Print output data\nprint(ds)\n\nUsing pixel quality parameters for USGS Collection 2\nFinding datasets\nls5_sr\nls7_sr\nIgnoring SLC-off observations for ls7\nls8_sr\nRe-scaling Landsat C2 data\nReturning 227 time steps as a dask array\n<xarray.Dataset>\nDimensions: (time: 227, y: 1109, x: 1093)\nCoordinates:\n* time (time) datetime64[ns] 1988-07-17T10:52:47.658038 ... 2018-12...\n* y (y) float64 1.309e+06 1.309e+06 ... 1.276e+06 1.276e+06\n* x (x) float64 4.102e+05 4.102e+05 ... 4.429e+05 4.429e+05\nspatial_ref int32 32628\nData variables:\nred (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\ngreen (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\nblue (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\nAttributes:\ncrs: EPSG:32628\ngrid_mapping: spatial_ref\n\n\n## Model tide heights for each observation¶\n\nWe use the tidal_tag function from deafrica_coastaltools to associate each satellite observation in our timeseries with a tide height relative to mean sea level. This function uses the time and date of acquisition and the geographic location of each satellite observation as inputs to the OSU Tidal Prediction Software (OTPS) tidal model. From Sagar et al. 2015:\n\nNote: The OTPS TPX08 tidal model consists of a multi-resolution bathymetric grid solution, with a 1/6° solution in the global open ocean, and a 1/30° local resolution solution to improve modelling in complex shallow water environments. The OTPS model is based on a system of linear partial differential equations, called Laplace’s tidal equations, parametrised with nine harmonic tidal constituents. The model is fitted to track-averaged TOPEX/Poseidon altimeter data collected from 1992 to 2016 and Jason-1 (Poseidon 2) altimeter data from 2002 to 2013, enabling estimation of the tidal height and harmonic constituents at discrete temporal epochs and spatial locations.\n\n:\n\n# Model tide heights\nds_tidal = tidal_tag(ds)\n\n# Print output data\nprint(ds_tidal)\n\nSetting tide modelling location from dataset centroid: -15.67, 11.69\n<xarray.Dataset>\nDimensions: (time: 227, y: 1109, x: 1093)\nCoordinates:\n* time (time) datetime64[ns] 1988-07-17T10:52:47.658038 ... 2018-12...\n* y (y) float64 1.309e+06 1.309e+06 ... 1.276e+06 1.276e+06\n* x (x) float64 4.102e+05 4.102e+05 ... 4.429e+05 4.429e+05\nspatial_ref int32 32628\nData variables:\nred (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\ngreen (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\nblue (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\ntide_height (time) float64 -0.194 -0.605 0.168 ... 0.535 -0.217 -0.821\nAttributes:\ncrs: EPSG:32628\ngrid_mapping: spatial_ref\n\n\nThe function will automatically select a tide modelling location based on the dataset centroid. It will then output modelled tide heights as a new tide_height variable in the xarray.Dataset (the variable should appear under Data variables above).\n\nWe can easily plot this new variable to inspect the range of tide heights observed by the satellites in our timeseries. In this example, our observed tide heights range from approximately -1.0 to 1.0 m relative to Mean Sea Level:\n\n:\n\nds_tidal.tide_height.plot(linewidth=0.5)\n\n:\n\n[<matplotlib.lines.Line2D at 0x7f18e2b42640>]", null, "### Example tide height analysis¶\n\nTo demonstrate how tidally tagged images can be used to produce composites of high and low tide imagery, we can compute the lowest 5% and highest 5% percent of tide heights, and use these to filter our observations. We can then combine and plot these filtered observations to visualise what the landscape looks like at low and high tide:\n\nNote: We recommend opening the Dask processing window to view the different computations that are being executed; to do this, see the Dask dashboard in DE Africa section of the Dask notebook.\n\nNote: An alternative approach to combining observations into a composite can be achieved using a geomedian, which ensures band relationships are kept consistent. More information is provided in the Generating geomedian composites notebook.\n\n:\n\n# Calculate the lowest and highest 5% of tides\nlowest_5, highest_5 = ds_tidal.tide_height.quantile([0.05, 0.95]).values\n\n# Filter our data to low and high tide observations\nfiltered_low = ds_tidal.where(ds_tidal.tide_height <= lowest_5, drop=True)\nfiltered_high = ds_tidal.where(ds_tidal.tide_height >= highest_5, drop=True)\n\n# Take the simple median of each set of low and high tide observations to\n# produce a composite (alternatively, observations could be combined\n# using a geomedian to keep band relationships consistent)\nmedian_low = filtered_low.median(dim='time', keep_attrs=True)\nmedian_high = filtered_high.median(dim='time', keep_attrs=True)\n\n# Combine low and high tide medians into a single dataset and give\n# each layer a meaningful name\nds_highlow = xr.concat([median_low, median_high], dim='tide_height')\nds_highlow['tide_height'] = ['Low tide', 'High tide']\n\n# Plot low and high tide medians side-by-side\nrgb(ds_highlow, col='tide_height')", null, "### Swapping dimensions¶\n\nThe tidal_tag function allows you to use tide heights as the primary dimension in the dataset, rather than time. Setting swap_dims=True will swap the time dimension in the original xarray.Dataset to the new tide_height variable.\n\n:\n\n# Model tide heights\nds_tidal = tidal_tag(ds, swap_dims=True)\n\n# Print output data\nprint(ds_tidal)\n\nSetting tide modelling location from dataset centroid: -15.67, 11.69\n<xarray.Dataset>\nDimensions: (tide_height: 227, y: 1109, x: 1093)\nCoordinates:\n* y (y) float64 1.309e+06 1.309e+06 ... 1.276e+06 1.276e+06\n* x (x) float64 4.102e+05 4.102e+05 ... 4.429e+05 4.429e+05\nspatial_ref int32 32628\n* tide_height (tide_height) float64 -0.978 -0.978 -0.952 ... 1.284 1.325\nData variables:\nred (tide_height, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\ngreen (tide_height, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\nblue (tide_height, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\nAttributes:\ncrs: EPSG:32628\ngrid_mapping: spatial_ref\n\n\nThe dataset now contains three dimensions: tide_height, x and y.\n\nThis can make it easier to analyse the data with respect to tide, e.g. computing a rolling median by tide height (e.g. along the tide_height dimension), as is done in the following cell.\n\nNote: We recommend opening the Dask processing window to view the different computations that are being executed; to do this, see the Dask dashboard in DE Africa section of the Dask notebook.\n\n:\n\n# First we need to update the chunks used by Dask to allow us to do a\n# rolling median without having to load all our data into memory first\nds_rechunked = ds_tidal.chunk(chunks={'tide_height': 13})\n\n# Compute a rolling median that will go through every satellite\n# observation, and take the median of that timestep and its 15 neighbours\nds_rolling = ds_rechunked.rolling(tide_height=13,\ncenter=True,\nmin_periods=1).median()\n\n# Plot the lowest, median and highest tide rolling median image\nrgb(ds_rolling, index_dim='tide_height', index=[0, len(ds_tidal.tide_height)//2, -1])", null, "## Modelling ebb and flow tidal phases¶\n\nThe tidal_tag function also allows us to determine whether each satellite observation was taken while the tide was rising/incoming (flow tide) or falling/outgoing (ebb tide) by setting ebb_flow=True. This is achieved by comparing tide heights 15 minutes before the before and after the observed satellite observation.\n\nEbb and flow data can provide valuable contextual information for interpreting satellite imagery, particularly in tidal flat or mangrove forest environments where water may remain in the landscape for considerable time after the tidal peak.\n\n:\n\n# Model tide heights\nds_tidal = tidal_tag(ds, ebb_flow=True)\n\n# Print output data\nprint(ds_tidal)\n\nSetting tide modelling location from dataset centroid: -15.67, 11.69\nModelling tidal phase (e.g. ebb or flow)\n<xarray.Dataset>\nDimensions: (time: 227, y: 1109, x: 1093)\nCoordinates:\n* time (time) datetime64[ns] 1988-07-17T10:52:47.658038 ... 2018-12...\n* y (y) float64 1.309e+06 1.309e+06 ... 1.276e+06 1.276e+06\n* x (x) float64 4.102e+05 4.102e+05 ... 4.429e+05 4.429e+05\nspatial_ref int32 32628\nData variables:\nred (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\ngreen (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\nblue (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\ntide_height (time) float64 -0.194 -0.605 0.168 ... 0.535 -0.217 -0.821\nebb_flow (time) <U4 'Flow' 'Flow' 'Ebb' 'Ebb' ... 'Flow' 'Flow' 'Flow'\nAttributes:\ncrs: EPSG:32628\ngrid_mapping: spatial_ref\n\n\nWe now have data giving us the both the tide height and tidal phase (‘ebb’ or ‘flow’) for every satellite image:\n\n:\n\nds_tidal[['time', 'tide_height', 'ebb_flow']].to_dataframe()\n\n:\n\ntide_height ebb_flow spatial_ref\ntime\n1988-07-17 10:52:47.658038 -0.194 Flow 32628\n1988-08-18 10:52:49.179013 -0.605 Flow 32628\n1988-10-05 10:52:43.680006 0.168 Ebb 32628\n1988-10-21 10:52:37.662000 0.334 Ebb 32628\n1988-12-08 10:52:31.815006 0.805 Flow 32628\n... ... ... ...\n2018-10-24 11:21:58.388427 1.094 Flow 32628\n2018-11-09 11:22:01.151598 0.730 Flow 32628\n2018-11-25 11:22:00.936674 0.535 Flow 32628\n2018-12-11 11:21:57.773631 -0.217 Flow 32628\n2018-12-27 11:21:57.806437 -0.821 Flow 32628\n\n227 rows × 3 columns\n\nWe could for example use this data to filter our observations to keep ebbing phase observations only:\n\n:\n\nds_tidal.where(ds_tidal.ebb_flow == 'Ebb', drop=True)\n\n:\n\n<xarray.Dataset>\nDimensions: (time: 106, y: 1109, x: 1093)\nCoordinates:\n* time (time) datetime64[ns] 1988-10-05T10:52:43.680006 ... 2018-10...\n* y (y) float64 1.309e+06 1.309e+06 ... 1.276e+06 1.276e+06\n* x (x) float64 4.102e+05 4.102e+05 ... 4.429e+05 4.429e+05\nspatial_ref int32 32628\nData variables:\nred (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\ngreen (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\nblue (time, y, x) float32 dask.array<chunksize=(1, 1109, 1093), meta=np.ndarray>\ntide_height (time) float64 0.168 0.334 -0.648 -0.395 ... 0.065 0.724 1.284\nebb_flow (time) object 'Ebb' 'Ebb' 'Ebb' 'Ebb' ... 'Ebb' 'Ebb' 'Ebb'\nAttributes:\ncrs: EPSG:32628\ngrid_mapping: spatial_ref\n\n## Evaluating observed vs. all modelled tide heights¶\n\nThe complex behaviour of tides mean that a sun synchronous sensor like Landsat does not observe the full range of the tidal cycle at all locations. Biases in the proportion of the tidal range observed by satellites can prevent us from obtaining data on areas of the coastline exposed or inundated at the extremes of the tidal range. This can risk gaining misleading insights into the true extent of the area of the coastline affected by tides, and make it difficult to compare high or low tide images fairly in different locations.\n\nThe tidal_stats function can assist in evaluating how the range of tides observed by satellites compare to the full tidal range. It works by using the OTPS tidal model to model tide heights at a regular interval (every two hours by default) across the entire time period covered by the input satelliter timeseries dataset. This is then compared against the tide heights in observed by the satellite and used to calculate a range of statistics and a plot that summarises potential biases in the data.\n\nNote: For a more detailed discussion of the issue of tidal bias in sun-synchronous satellite observations of the coastline, refer to the ‘Limitations and future work’ section in Bishop-Taylor et al. 2018.\n\n:\n\nout_stats = tidal_stats(ds)\n\nSetting tide modelling location from dataset centroid: -15.67, 11.69\n\n79% of the full 2.91 m modelled tidal range is observed at this location.\nThe lowest 14% and highest 7% of tides are never observed.\n\nObserved tides do not increase or decrease significantly over the ~31 year period.\nAll tides do not increase or decrease significantly over the ~31 year period.", null, "The function also outputs a pandas.Series object containing a set of statistics that compare the observed vs. full modelled tidal ranges. These statistics include:\n\n• tidepost_lat: latitude used for modelling tide heights\n\n• tidepost_lon: longitude used for modelling tide heights\n\n• observed_min_m: minimum tide height observed by the satellite (in metre units)\n\n• all_min_m: minimum tide height from full modelled tidal range (in metre units)\n\n• observed_max_m: maximum tide height observed by the satellite (in metre units)\n\n• all_max_m: maximum tide height from full modelled tidal range (in metre units)\n\n• observed_range_m: tidal range observed by the satellite (in metre units)\n\n• all_range_m: full modelled tidal range (in metre units)\n\n• spread_m: proportion of the full modelled tidal range observed by the satellite (see Bishop-Taylor et al. 2018)\n\n• low_tide_offset: proportion of the lowest tides never observed by the satellite (see Bishop-Taylor et al. 2018)\n\n• high_tide_offset: proportion of the highest tides never observed by the satellite (see Bishop-Taylor et al. 2018)\n\n• observed_slope: slope of any relationship between observed tide heights and time\n\n• all_slope: slope of any relationship between all modelled tide heights and time\n\n• observed_pval: significance/p-value of any relationship between observed tide heights and time\n\n• all_pval: significance/p-value of any relationship between all modelled tide heights and time\n\n:\n\nprint(out_stats)\n\ntidepost_lat 11.689\ntidepost_lon -15.674\nobserved_mean_m 0.086\nall_mean_m 0.000\nobserved_min_m -0.978\nall_min_m -1.393\nobserved_max_m 1.325\nall_max_m 1.518\nobserved_range_m 2.303\nall_range_m 2.911\nlow_tide_offset 0.143\nhigh_tide_offset 0.066\nobserved_slope 0.005\nall_slope -0.000\nobserved_pval 0.287\nall_pval 0.370\ndtype: float64\n\n\nContact: If you need assistance, please post a question on the Open Data Cube Slack channel or on the GIS Stack Exchange using the open-data-cube tag (you can view previously asked questions here). If you would like to report an issue with this notebook, you can file one on Github.\n\nCompatible datacube version:\n\n:\n\nprint(datacube.__version__)\n\n1.8.7\n\n\nLast Tested:\n\n:\n\nfrom datetime import datetime\ndatetime.today().strftime('%Y-%m-%d')\n\n:\n\n'2022-06-21'" ]

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[ "Implement an algorithm , Determine a string s Are all the characters of the are different .\n\nIs there an array of statistics\nfunc isUnique(astr string) bool { var arr int; for _,ch:=range astr{\nnum:=ch-'a' if(arr[num]==1){ return false } arr[num]++ } return true }\nGiven two strings s1 and s2, Please write a program , After determining the character rearrangement of one of the strings , Can it be changed into another string .\n\nRecord the number of character occurrences , Comparison is enough .\nfunc CheckPermutation(s1 string, s2 string) bool { var arr int; var\nbrr int; for _,ch:=range s1{ arr[ch-'a']++; } for _,ch:=range s2{\nbrr[ch-'a']++; } for i:=0;i<26;i++{ if(arr[i]!=brr[i]){ return false; } }\nreturn true; }\n\nURL turn . Write a method , Replace all spaces in the string with %20. It is assumed that there is enough space at the end of the string to hold the new characters , And know the string's “ real ” length .（ notes ： use Java If it comes true , Please use character array implementation , In order to operate directly on the array .）\n\nfunc replaceSpaces(S string, length int) string { return\nstrings.ReplaceAll(S[:length], \" \", \"%20\") }\nPay attention to the 8 Yes, it's a pit . dynamic length Arrays cannot be initialized in a way that is in a comment .\nfunc replaceSpaces(S string, length int) string { num := 0 for i:=0;i <length;\ni++ { if S[i] == ' ' { num++ } } //var result[2*num + length] byte; result :=\nmake([]byte, 3*num + (length-num)) k := 0 for i:=0;i <length; i++ { if S[i] ==\n' ' { result[k] = '%' result[k+1] = '2' result[k+2] = '0' k += 3 } else {\nresult[k] = S[i] k++ } } return string(result) }\nGiven a string , Write a function to determine whether it is one of the permutations of a palindrome string .\n\nPalindrome string refers to words or phrases that are the same in both directions . Arrangement is the rearrangement of letters .\n\nPalindrome strings are not necessarily words in a dictionary .\n\nExamples ：\n\ninput ：\"tactcoa\"\noutput ：true（ There are \"tacocat\",\"atcocta\", wait ）\n\nthinking ： At most one character has occurred an odd number of times .\nfunc canPermutePalindrome(s string) bool { var arr int; for _,ch:=range\ns{ arr[ch]++; } num:=0 for _,i:=range arr{ num+=i%2; } return num<=1; }\n\nTechnology\nDaily Recommendation" ]

[ null ]

[ "# Phase shift in Star-Delta Transformers\n\n#### Siddhartha Mahavira\n\nJoined Oct 22, 2015\n2\nHi Everyone !!\n\nWe all know that the per-phase analysis of a star-delta transformer requires converting the delta-side into an equivalent-star connection. Upon doing this, we find that the new equivalent secondary delta-side phase lags by 30 degrees with respect to the primary star-side phase. We usually represent this by multiplying the term e^(j30deg) to the equivalent per-phase transformation-ratio a:1 from primary to secondary; ie, the new transformation ratio is a.e^(j30deg) : 1 .\n\nNow, if we were to transfer an impedance from the secondary-side to the primary-side, applying the transformation rule of Z(referred_to_primary) = (primary-to-secondary transformation-ratio)^2 x Z(secondary), we would get :\nZ(referred_to_primary) = (a.e^(j30deg))^2 x Z(secondary)\n= a^2 x e^(j60deg) x Z(secondary).\n\nThis implies that even a purely resistive balanced-load on the delta side would reflect as an inductive load on the primary side, which is not possible. Calculations based on this would then go on to give erroneous results (as I have myself tried out and confirmed).\n\nThanks !!\n\n#### crutschow\n\nJoined Mar 14, 2008\n32,060\nThe phase of the voltage between phases changes in the transformation but not the phase between voltage and current (the power factor remains constant as would be expected).\n\n•", null, "Siddhartha Mahavira\n\n#### Siddhartha Mahavira\n\nJoined Oct 22, 2015\n2\nYes, the power factors on the primary- as well as the secondary- sides remain the same actually. Direct calculations as well as complex (active and reactive) volt-ampere balance both show that. But the transformed per-phase circuit involving star:delta doesn't show this. Here's why..\nfor the equivalent per-phase star:star :\nV(primary) = a.e^(j30deg) x V(secondary) = a.V(secondary).e^(j30deg)\nwhere a.e^(j30deg) is the equivalent primary-to-secondary transformation ratio. Then,\nI(primary) = (1/(a.e^(j30deg)) x I(secondary) = (1/a).I(secondary).e^(-j30deg)\nThus, Z(primary) = V(primary)/I(primary) = a^2 x V(secondary)/I(secondary) x e^(j60deg)\n= a^2 x Z(secondary) x e^(j60deg)\nWhich shows that the reflected primary impedance always has an additional 60 degree angle with respect to the actual secondary impedance.\n\n#### crutschow\n\nJoined Mar 14, 2008\n32,060\nDoes not compute.", null, "" ]

[ null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]

[ "0030-2465 0030-2465 S0030-24652015000100001 10.4102/ojvr.v82i1.863 Ghana Ghana 00 00 2015 00 00 2015 82 1 01 05\n\nORIGINAL RESEARCH\n\nRelationship between haemoglobin concentration and packed cell volume in cattle blood samples\n\nPaa-Kobina TurksonI; Ebenezer Y. GanyoII\n\nIDepartment of Animal Science, University of Cape Coast, Ghana\nIIDepartment of Biomedical and Forensic Sciences, University of Cape Coast, Ghana\n\nCorrespondence\n\n]]>\n\nABSTRACT\n\nA convention that has been adopted in medicine is to estimate haemoglobin (HB) concentration as a third of packed cell volume (PCV) or vice versa. The present research set out to determine whether a proportional relationship exists between PCV and Hb concentration in cattle blood samples, and to assess the validity of the convention of estimating Hb concentration as a third of PCV. A total of 440 cattle in Ghana from four breeds (Ndama, 110; West African Short Horn, 110; Zebu, 110 and Sanga, 110) were bled for haematological analysis, specifically packed cell volume, using the microhaematocrit technique and haemoglobin concentration using the cyanmethaemoglobin method. Means, standard deviations, standard errors of mean and 95% confidence intervals were calculated. Trendline analyses generated linear regression equations from scatterplots. For all the cattle, a significant and consistent relationship (r= 0.74) was found between Hb concentration and PCV (%). This was expressed as Hb concentration (g/dL) = 0.28 PCV + 3.11. When the Hb concentration was estimated by calculating it as a third of PCV, the relationship was expressed in linear regression as Hb concentration (g/dL) = 0.83 calculated Hb + 3.11. The difference in the means of determined (12.2 g/dL) and calculated (10.9 g/dL) Hb concentrations for all cattle was significant (p < 0.001), whereas the difference in the means of determined Hb and corrected calculated Hb was not significant. In conclusion, a simplified relationship of Hb (g/dL) = (0.3 PCV) + 3 may provide a better estimate of Hb concentration from the PCV of cattle.\n\nIntroduction\n\nDetermining blood parameters is helpful in assessing the health status of animals. Common diseases in the tropics may lead to anaemia, examples of which include: helminthosis/helminthiasis, trypanosomosis, and tick-burden and tick-borne infections such as babesiosis and anaplasmosis. Measurement of anaemia is said to give a reliable indication of the disease status and production performance of trypanosome-infected animals (Nwoha & Anene 2011). Laboratory diagnosis of anaemia is based on the haemoglobin (Hb) concentration, the number of red blood cells and the haematocrit or packed cell volume (PCV) values (Aiello 1998). Anaemia is most simply and reliably estimated by measuring PCV percent using the haematocrit method, whilst determining the Hb concentration gives accurate information on the type of anaemia (Murray et al. 1983). Quinto et al. (2006) noted that measurement of haematocrit is easy and can be performed in most rural settings where methods of Hb concentration determination are unavailable, and rough estimates are made using observed PCV values, which is a much simpler and cheaper approach. In rural African human medicine clinical practices, haematocrit (PCV) values are commonly used because they are easy and cheaper to perform using manual techniques (Quinto et al. 2006). The same reason may hold true for use in veterinary practice. Haemoglobin concentration is measured using the cyanmethaemoglobin method, which is slightly more complex and more time consuming than the haematocrit method and is also less commonly used in laboratory investigation in animals (Murray et al. 1983).\n\nA convention has been adopted in medical laboratory practice in estimating Hb concentration as a third of PCV or vice versa (Bain & Bates 2001). A similar conversion factor is used in veterinary laboratory practice (Jerry Oddoye [Accra Veterinary Investigation Laboratory] pers. comm., n.d.); however, there is hardly any information on the validity of this commonly used relationship between Hb concentration and PCV in veterinary medical practice.\n\nThe aims of the present study were: (1) to determine whether or not a proportional relationship exists between PCV and Hb concentration in cattle blood samples and (2) to assess the validity of the convention of estimating Hb concentration as a third of PCV. It was hoped that these would help to provide information that is relevant for fieldwork and clinical diagnosis.\n\n]]> Materials and methods\n\nA total of 440 cattle in Ghana from four breeds (Ndama, 110; West African Short Horn, 110; Zebu, 110 and Sanga, 110), that were randomly selected, were bled for haematological analysis as part of a larger study on trypanotolerance. Cattle less than 1 year old were classified as calves, those between 1 year and 3 years as young, and those older than 3 years were classified as adults.\n\nPacked cell volume determination\n\nPacked cell volume, which is a measure of the proportion of the volume of the whole blood that is occupied by red blood cells, was determined by the microhaematocrit centrifugation technique (Jain 1986). Blood in a sample vacutainer tube was mixed by gently inverting the tube about 20 times. The blood was drawn three quarters of the way up a 75 mm x 1.0 mm microhaematocrit capillary tube. Blood was wiped off the tip of the capillary tube, and the end of the capillary tube was carefully plugged with plasticine. The capillary tube was placed, with the closed end outwards, in a microhaematocrit centrifuge (Hawksley & Sons Limited, England) and spun at 12 000 rpm for 5 min. The capillary tube was removed from the centrifuge, placed on a haematocrit reader and the PCV was recorded.\n\nHaemoglobin concentration determination\n\nHaemoglobin concentration was measured spectrophotometrically by the cyanmethaemoglobin method (Jain 1986) by an experienced veterinary laboratory technologist in the National Veterinary Investigation Laboratory, Accra. Blood in a sample vacutainer tube was mixed gently by inverting about 20 times. Twenty microlitres of blood was added to 5 mL of Drabkin's solution (containing potassium ferricyanide and potassium cyanide) in a test tube. In the Drabkin's solution, the red blood cells were haemolysed and the haemoglobin was oxidised by the ferricyanide to methaemoglobin. The cyanide then converted the methaemoglobin to stable cyanmethaemoglobin. The mixture was allowed to stand for 15 min. After that, 1 mL of the mixture was pipetted into a cuvette. The cuvette was placed in a spectrophotometer (Jenway, England, Model: Genova MK3) set at 540 nm, and the absorbance of the cyanmethaemoglobin solution was read after zeroing the spectrophotometer using neutral Drabkin's solution. The haemoglobin concentration of the blood sample was calculated by dividing the absorbance value by the slope obtained from a calibration graph. To obtain the calibration graph, a standard blood sample (of known haemoglobin concentration) was diluted with Drabkin's solution: 5 in 0; 4 in 1; 3 in 2; 2 in 3 and 1 in 4. The absorbance of each of the five solutions was read in the spectrophotometer after the spectrophotometer was zeroed using neutral Drabkin's solution. A graph of absorbance for each of the five solutions was plotted against the corresponding haemoglobin concentration, and the slope of the graph was determined. The haemoglobin concentration of each of the five solutions was obtained by multiplying the proportion of standard haemoglobin in that solution with the haemoglobin concentration value of the standard.\n\nStatistical analysis\n\nMeans, standard deviations (s.d.), standard errors (s.e.) of mean and 95% confidence intervals (95% CI) were calculated using standard formulae. Differences in the means of the determined and calculated Hb concentration values were tested using a two-tailed paired sample test in Microsoft Excel (Microsoft, USA).\n\nScatterplots were drawn using Microsoft Office Excel (version 2007, Microsoft, USA) matching determined Hb concentration with PCV, and determined Hb concentration with calculated Hb values (one third of PCV). Linear regression models were estimated to evaluate the relationship between PCV, determined Hb and calculated Hb values. Trendline analyses were used to generate the linear regression equations. To avoid the possibility of bias, separate regressions were performed on the basis of breed, age or sex. The significance of the correlation coefficient for the linear regression equations was tested using the formula suggested by Smillie (1966) and Varkevisser, Pathmanathan and Brownlee (1991) as follows:", null, "]]> where t = significance value; r = coefficient of correlation; n = number of samples.\n\nBland and Altman (1999) argued that since two methods designed to measure the same thing are bound to give a positive linear regression, the most useful comparison is to plot the difference between the measures against the mean of the two measures. This method was used when comparing determined Hb (g/dL) and calculated Hb (derived as PCV divided by a factor of three) before and after correction using the linear regression equation for all cattle. The differences between the determined and calculated Hb concentration values and the mean of the measurements [i.e. (determined Hb + calculated Hb)/2)] were calculated for each individual and used in a scatterplot. The plot of difference against mean allows for the investigation of any possible relationship between discrepancies and the true value (Bland & Altman 1999). The means and s.d. of the differences between Hb determined and calculated Hb values, on the one hand, and determined Hb and corrected calculated Hb concentration values, on the other hand, were calculated; 95% limits of agreement were computed as mean of difference ± 1.96 s.d. (Bland & Altman 1999). The 95% limits of agreement provided an interval within which 95% of the differences between measurements by the two methods were expected to lie (Bland & Altman 1999).\n\nSpearman's rank correlation coefficient (rs) was calculated, in Microsoft Excel, for the relationship between determined Hb and calculated Hb concentration, and also between the absolute differences and averages for individual samples, the latter as recommended by Bland and Altman (1999).\n\nResults\n\nTable 1 presents haematological values (PCV, determined and calculated Hb concentration values) and linear regression parameters for determined Hb versus PCV, and determined Hb concentration versus calculated Hb for all the cattle, and also on the basis of breed, sex and age.\n\nThe proportion of samples for which determined Hb concentration was higher than calculated Hb concentration was 86.1% (379/440) and was significant (p < 0.05). After correction using the regression equation for all cattle, the proportion of samples for which determined Hb concentration was higher than calculated Hb concentration dropped to 46.4%. The difference in the means of determined (12.2 g/dL) and calculated (10.9 g/dL) Hb concentrations for all cattle was significant (p < 0.001), whereas the difference in the means of determined Hb and corrected calculated Hb concentrations was not significant (p > 0.05).\n\nThe mean (± s.d.) of differences between determined and calculated Hb concentration values was 1.24 ± 1.29 (range: -3.56-7.25; lower 95% limit of agreement was -1.28; upper 95% limit of agreement was 3.76). The mean (± s.d.) of differences between determined and corrected calculated Hb concentration values was 0.00 ± 1.25 (range: -4.61-5.63; lower 95% limit of agreement -2.46; upper 95% limit of agreement 2.46).\n\nSpearman's rank correlation coefficient for the relationship between determined Hb and calculated Hb concentrations, (rs = 0.73) was significantly different from one (p < 0.001, degrees of freedom [df] = 438), whilst that for the relationship between absolute differences and averages of determined and calculated Hb concentration (rs = 0.18) was barely significant at 5% significance level, but not at 1%.\n\nFigures 1 and 2 show scatterplots of the determined Hb concentration versus PCV and the determined Hb versus calculated Hb concentrations, respectively. Figures 3 and 4 show scatterplots of the differences versus averages for the determined and calculated Hb concentrations (with a solid line marking the mean of 1.24) and differences versus averages for the determined and corrected calculated Hb concentration (with a solid line marking the mean of 0.0), respectively.\n\n]]>", null, "", null, "]]>", null, "", null, "Discussion\n\nFor all of the cattle, a significant and consistent relationship was found between Hb concentration and PCV (%). This was expressed as Hb concentration (g/dL) = 0.28 PCV + 3.11. When the Hb concentration was estimated as a third of PCV, the relationship was expressed as Hb concentration (g/dL) = 0.83 calculated Hb + 3.11 (Table 1). The findings are indicative of the potential magnitude of the problem of using the convention of estimating Hb concentrations (g/dL) as a third of PCV values (%). The results show a consistent and significant bias (underestimation) of calculated Hb concentration compared to measured Hb (determined Hb in the present study) (Table 1). The differences between the means were also significantly different (p < 0.05) and cut across breed, sex and age categories (Table 1).\n\nIn a study on humans, Carneiro et al. (2007) found that Hb concentration measurements were lower than the values obtained from PCV/3. In contrast, the present study found that 86% of the Hb concentration values obtained by the cyanmethaemoglobin method were higher than the Hb concentrations estimated as a third of PCV. In effect, whereas in their study there was a likelihood of overestimation, in the present study the result was underestimation, which could affect clinical treatment plans.\n\nLinear regression analysis was employed to determine whether the relationship between PCV and Hb concentration differed on the basis of breed, sex and age categories of the cattle. The individual slopes within breed, sex and age categories did not differ significantly, except possibly for calves. These results may imply that a simplified relationship of Hb (g/dL) = 0.3 PCV + 3 may provide a more reasonable and better estimate of Hb concentration from the PCV of cattle. In cattle, the convention of estimating the Hb concentration as a third of PCV would need modifying to be a third of PCV + 3.\n\n]]> The convention or standard of estimating Hb has been used extensively in medicine to estimate the prevalence of anaemia (Carneiro et al. 2007; Quinto et al. 2006; Rodriquez-Morales et al. 2007; World Health Organization [WHO] 1968). Recently, the convention was recommended for birds in eight orders (Velguth, Payton & Hoover 2010). Quinto et al. (2006) noted that although Hb and haematocrit (PCV) are closely related, the usual transformation of three times the haemoglobin (g/dL) equals the PCV is inaccurate. The present findings support the reports from studies in human medicine that Hb concentration levels could not be derived from PCV values with an acceptable accuracy using the general rule of dividing by three (Carneiro et al. 2007; Quinto et al. 2006; Rodriquez-Morales et al.2007). These studies also showed that the relationship between Hb concentration and PCV was not exactly three and could be affected by factors such as sex and age in humans.\n\nThe relationship between PCV and Hb is expressed in the Mean Corpuscular Haemoglobin Concentration (MCHC) (Quinto et al. 2006). This is an indicator of the concentration of Hb per unit volume of red blood cell expressed in g/dL as [(Hb X 100)/PCV] and is more accurate than mean corpuscular haemoglobin (MCH) (Aiello 1998). Therefore, any estimation of Hb concentration from PCV that is unreliable or invalid would affect the calculation of MCHC so that clinical decisions made on the basis of MCHC may not be appropriate.\n\nIn conclusion, a simplified relationship of Hb (g/dL) = (0.3 PCV) + 3 may provide a better estimate of Hb concentration from the PCV of cattle. It is, therefore, recommended that if it is necessary to estimate Hb concentration from PCV value, then the simplified relationship may be more appropriate to use.\n\nAcknowledgements\n\nThanks to Jerry Oddoye and Abdulai Munkaila of the Veterinary Investigation Laboratories of the Veterinary Services Directorate Ghana for their technical assistance. The help received from the managers of the cattle herds at sampling sites is appreciated.\n\nCompeting interests\n\nThe authors declare that they have no financial or personal relationship(s) that may have inappropriately influenced them in writing this article.\n\nAuthors' contributions\n\nP-K.T. (University of Cape Coast) developed the concept, analysed data and wrote the article. E.Y.G. (University of Cape Coast) was involved in the collection of field samples, analysis of samples and contributed to the write up and review of the article.\n\n]]>\n\nReferences\n\nAiello, S. (ed.), 1998, Merck Veterinary Manual, 8th edn., Merck and Co Inc., Whitehouse Junction.         [ Links ]\n\nBain, B.J. & Bates, I., 2001, 'Basic haematological techniques', in S.M. Lewis, B.J. Bain & I. Bates (eds.), Practical Haematology, 9th edn., pp. 19-46, Churchill Livingstone, Edinburgh.         [ Links ]\n\nBland, J.M. & Altman, D.G., 1999, 'Measuring agreement in method comparison studies', Statistical Methods in Medical Research 8, 135-160. http://dx.doi.org/10.1191/096228099673819272        [ Links ]\n\nCarneiro, I.A., Drakeley, C.J., Owusu-Agyei, S., Mmbando, B. & Chandramohan, D., 2007, 'Haemoglobin and haematocrit: Is the threefold conversion valid for assessing anaemia in malaria-endemic settings?', Malaria Journal 6, 67. http://dx.doi.org/10.1186/1475-2875-6-67        [ Links ]\n\nJain, N.C., 1986, Schalm's Veterinary Hematology, 4th edn., Lea & Febiger, Philadelphia.         [ Links ]\n\n]]>\n\nMurray, M., Trail, J.C.M, Turner, D.A. & Wissocq, Y., 1983, Livestock Productivity and Trypanotolerance, Network Training Manual, International Livestock Centre for Africa, Addis Ababa.         [ Links ]\n\nNwoha, R.I.O. & Anene, B.M., 2011, 'Changes in packed cell volume and haemoglobin concentrations in dogs with single and conjunct experimental infections of Trypanosoma brucei and Ancylostoma caninum', Phillipine Journal of Veterinary and Animal Sciences 37(20), 151-158.         [ Links ]\n\nQuinto, L., Aponte, J.J., Menendez, C., Sacarlal, J., Aide, P., Espasa, M., et al., 2006, 'Relationship between haemoglobin and haematocrit in the definition of anaemia', Tropical Medicine and International Health 11, 1295-1302. http://dx.doi.org/10.1111/j.1365-3156.2006.01679.x        [ Links ]\n\nRodríguez-Morales, A.J., Sánchez, E., Arria, M., Vargas, M., Piccolo, C., Colina, R., et al., 2007, 'Haemoglobin and haematocrit: The threefold conversion is also non-valid for assessing anaemia in Plasmodium vivax malaria-endemic settings', Malaria Journal 6, 166. http://dx.doi.org/10.1186/1475-2875-6-166        [ Links ]\n\nSmillie, K.W., 1966, An Introduction to Regression and Correlation, Academic Press, London.         [ Links ]\n\nVarkevisser, C.M., Pathmanathan, I. & Brownlee, A., 1991, Designing and conducting health systems research projects. Part II. Data analysis and report writing, pp. 127-128, HSR Training Series, IDRC and WHO, Geneva.         [ Links ]\n\n]]>\n\nVelguth, K.E., Payton, P.E. & Hoover, J.P., 2010, 'Relationship of haemoglobin concentration to packed cell volume in avian blood samples', Journal of Avian Medicine and Surgery 24(2), 115-121. http://dx.doi.org/10.1647/2008-042.1        [ Links ]\n\nWorld Health Organization (WHO), 1968, Nutritional anaemias: Report of a WHO Scientific Group, World Health Organization, Geneva.         [ Links ]", null, "Correspondence:\nPaa-Kobina Turkson\nDepartment of Animal Science\nUniversity of Cape Coast\nPrivate Mail Bag ]]> University Post Office\nCape Coast\nGhana\nEmail: [email protected]" ]

[ null, "http://www.scielo.org.za/img/revistas/ojvr/v82n1/01e01.jpg", null, "http://www.scielo.org.za/img/revistas/ojvr/v82n1/01f01.jpg", null, "http://www.scielo.org.za/img/revistas/ojvr/v82n1/01f02.jpg", null, "http://www.scielo.org.za/img/revistas/ojvr/v82n1/01f03.jpg", null, "http://www.scielo.org.za/img/revistas/ojvr/v82n1/01f04.jpg", null, "http://www.scielo.org.za/img/revistas/ojvr/v82n1/seta.jpg", null ]

[ "# scatter3\n\n3-D scatter plot\n\n## Syntax\n\n``scatter3(X,Y,Z)``\n``scatter3(X,Y,Z,S)``\n``scatter3(X,Y,Z,S,C)``\n``scatter3(___,'filled')``\n``scatter3(___,markertype)``\n``scatter3(___,Name,Value)``\n``scatter3(ax,___)``\n``h = scatter3(___)``\n\n## Description\n\nexample\n\n````scatter3(X,Y,Z)` displays circles at the locations specified by the vectors `X`, `Y`, and `Z`. ```\n\nexample\n\n````scatter3(X,Y,Z,S)` draws each circle with the size specified by `S`. To plot each circle with equal size, specify `S` as a scalar. To plot each circle with a specific size, specify `S` as a vector.```\n\nexample\n\n````scatter3(X,Y,Z,S,C)` draws each circle with the color specified by `C`. If `C` is a RGB triplet or character vector or string containing a color name, then all circles are plotted with the specified color. If `C` is a three column matrix with the number of rows in `C` equal to the length of `X`, `Y`, and `Z`, then each row of `C` specifies an RGB color value for the corresponding circle. If `C` is a vector with length equal to the length of `X`, `Y`, and `Z`, then the values in `C` are linearly mapped to the colors in the current colormap. ```\n\nexample\n\n````scatter3(___,'filled')` fills in the circles, using any of the input argument combinations in the previous syntaxes.```\n\nexample\n\n````scatter3(___,markertype)` specifies the marker type.```\n\nexample\n\n````scatter3(___,Name,Value)` modifies the scatter chart using one or more name-value pair arguments. ```\n\nexample\n\n````scatter3(ax,___)` plots into the axes specified by `ax` instead of into the current axes (`gca`). The `ax` option can precede any of the input argument combinations in the previous syntaxes.```\n\nexample\n\n````h = scatter3(___)` returns the `Scatter` object. Use `h` to modify properties of the scatter chart after it is created.```\n\n## Examples\n\ncollapse all\n\nCreate a 3-D scatter plot. Use `sphere` to define vectors `x`, `y`, and `z`.\n\n```figure [X,Y,Z] = sphere(16); x = [0.5*X(:); 0.75*X(:); X(:)]; y = [0.5*Y(:); 0.75*Y(:); Y(:)]; z = [0.5*Z(:); 0.75*Z(:); Z(:)]; scatter3(x,y,z)```", null, "Use `sphere` to define vectors `x`, `y`, and `z`.\n\n```[X,Y,Z] = sphere(16); x = [0.5*X(:); 0.75*X(:); X(:)]; y = [0.5*Y(:); 0.75*Y(:); Y(:)]; z = [0.5*Z(:); 0.75*Z(:); Z(:)];```\n\nDefine vector `s` to specify the marker sizes.\n\n```S = repmat([100,50,5],numel(X),1); s = S(:);```\n\nCreate a 3-D scatter plot and use `view` to change the angle of the axes in the figure.\n\n```figure scatter3(x,y,z,s) view(40,35)```", null, "Corresponding entries in `x`, `y`, `z`, and `s` determine the location and size of each marker.\n\nUse `sphere` to define vectors `x`, `y`, and `z`.\n\n```[X,Y,Z] = sphere(16); x = [0.5*X(:); 0.75*X(:); X(:)]; y = [0.5*Y(:); 0.75*Y(:); Y(:)]; z = [0.5*Z(:); 0.75*Z(:); Z(:)];```\n\nDefine vectors `s` and `c` to specify the size and color of each marker.\n\n```S = repmat([50,25,10],numel(X),1); C = repmat([1,2,3],numel(X),1); s = S(:); c = C(:);```\n\nCreate a 3-D scatter plot and use `view` to change the angle of the axes in the figure.\n\n```figure scatter3(x,y,z,s,c) view(40,35)```", null, "Corresponding entries in `x`, `y`, `z`, and `c` determine the location and color of each marker.\n\nCreate vectors `x` and `y` as cosine and sine values with random noise.\n\n```z = linspace(0,4*pi,250); x = 2*cos(z) + rand(1,250); y = 2*sin(z) + rand(1,250);```\n\nCreate a 3-D scatter plot and fill in the markers. Use `view` to change the angle of the axes in the figure.\n\n```scatter3(x,y,z,'filled') view(-30,10)```", null, "Initialize the random-number generator to make the output of `rand` repeatable. Define vectors `x` and `y` as cosine and sine values with random noise.\n\n```rng default z = linspace(0,4*pi,250); x = 2*cos(z) + rand(1,250); y = 2*sin(z) + rand(1,250);```\n\nCreate a 3-D scatter plot and set the marker type. Use `view` to change the angle of the axes in the figure.\n\n```figure scatter3(x,y,z,'*') view(-30,10)```", null, "Initialize the random-number generator to make the output of `rand` repeatable. Define vectors `x` and `y` as cosine and sine values with random noise.\n\n```rng default z = linspace(0,4*pi,250); x = 2*cos(z) + rand(1,250); y = 2*sin(z) + rand(1,250);```\n\nCreate a 3-D scatter plot and set the marker edge color and the marker face color. Use `view` to change the angle of the axes in the figure.\n\n```figure scatter3(x,y,z,... 'MarkerEdgeColor','k',... 'MarkerFaceColor',[0 .75 .75]) view(-30,10)```", null, "Starting in R2019b, you can display a tiling of plots using the `tiledlayout` and `nexttile` functions.\n\nLoad the `seamount` data set to get vectors `x`, `y`, and `z`. Call the `tiledlayout` function to create a 2-by-1 tiled chart layout. Call the `nexttile` function to create the axes objects `ax1` and `ax2`. Then create separate scatter plots in the axes by specifying the axes object as the first argument to `scatter3`.\n\n```load seamount tiledlayout(2,1) ax1 = nexttile; ax2 = nexttile; scatter3(ax1,x,y,z,'MarkerFaceColor',[0 .75 .75]) scatter3(ax2,x,y,z,'*')```", null, "Use the `sphere` function to create vectors `x`, `y`, and `z`.\n\n```[X,Y,Z] = sphere(16); x = [0.5*X(:); 0.75*X(:); X(:)]; y = [0.5*Y(:); 0.75*Y(:); Y(:)]; z = [0.5*Z(:); 0.75*Z(:); Z(:)];```\n\nCreate vectors `s` and `c` to specify the size and color for each marker.\n\n```S = repmat([70,50,20],numel(X),1); C = repmat([1,2,3],numel(X),1); s = S(:); c = C(:);```\n\nCreate a 3-D scatter plot and return the scatter series object.\n\n`h = scatter3(x,y,z,s,c);`", null, "Use an RGB triplet color value to set the marker face color. Use dot notation to set properties.\n\n`h.MarkerFaceColor = [0 0.5 0.5];`", null, "## Input Arguments\n\ncollapse all\n\nx values, specified as a vector. `X`, `Y`, and `Z` must be vectors of equal length.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `categorical` | `datetime` | `duration`\n\ny values, specified as a vector. `X`, `Y`, and `Z` must be vectors of equal length.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `categorical` | `datetime` | `duration`\n\nz values, specified as a vector. `X`, `Y`, and `Z` must be vectors of equal length.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `categorical` | `datetime` | `duration`\n\nMarker area, specified as a scalar, a vector, or `[]`. The values in `S` must be positive. The units for area are points squared.\n\n• If `S` is a scalar, then `scatter3` plots all markers with the specified area.\n\n• If `S` is a row or column vector, then each entry in `S` specifies the area for the corresponding marker. The length of `S` must equal the length of `X`, `Y` and `Z`. Corresponding entries in `X`, `Y`, `Z` and `S` determine the location and area of each marker.\n\n• If `S` is empty, then the default size of 36 points squared is used.\n\nExample: `50`\n\nExample: `[36,25,25,17,46]`\n\nMarker color, specified as a an RGB triplet, a three-column matrix of RGB triplet, a vector, or one of the color options in the table.\n\nAn RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range `[0,1]`; for example, `[0.4 0.6 0.7]`. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values.\n\nOptionDescriptionEquivalent RGB Triplet\n`'red'` or `'r'`Red`[1 0 0]`\n`'green'` or `'g'`Green`[0 1 0]`\n`'blue'` or `'b'`Blue`[0 0 1]`\n`'yellow'` or `'y'`Yellow`[1 1 0]`\n`'magenta'` or `'m'`Magenta`[1 0 1]`\n`'cyan'` or `'c'`Cyan`[0 1 1]`\n`'white'` or `'w'`White`[1 1 1]`\n`'black'` or `'k'`Black`[0 0 0]`\n\nIf you have three points in the scatter plot and want the colors to be indices into the colormap, specify `C` as a three-element column vector.\n\nExample: `'y'`\n\nExample: `[1,2,3,4]`\n\nMarker, specified as one of the markers in this table.\n\nValueDescription\n`'o'`Circle\n`'+'`Plus sign\n`'*'`Asterisk\n`'.'`Point\n`'x'`Cross\n`'square'` or `'s'`Square\n`'diamond'` or `'d'`Diamond\n`'^'`Upward-pointing triangle\n`'v'`Downward-pointing triangle\n`'>'`Right-pointing triangle\n`'<'`Left-pointing triangle\n`'pentagram'` or `'p'`Five-pointed star (pentagram)\n`'hexagram'` or `'h'`Six-pointed star (hexagram)\n`'none'`No markers\n\nAxes object. If you do not specify an axes, then `scatter3` plots into the current axes.\n\n### Name-Value Pair Arguments\n\nSpecify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.\n\nExample: `'MarkerFaceColor','red'` sets the marker face color to red.\n\nThe properties listed here are only a subset. For a complete list, see Scatter Properties.\n\nWidth of marker edge, specified as a positive value in point units.\n\nExample: `0.75`\n\nMarker outline color, specified `'flat'`, an RGB triplet, a hexadecimal color code, a color name, or a short name. The default value of `'flat'` uses colors from the `CData` property.\n\nFor a custom color, specify an RGB triplet or a hexadecimal color code.\n\n• An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range `[0,1]`; for example, ```[0.4 0.6 0.7]```.\n\n• A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (`#`) followed by three or six hexadecimal digits, which can range from `0` to `F`. The values are not case sensitive. Thus, the color codes `'#FF8800'`, `'#ff8800'`, `'#F80'`, and `'#f80'` are equivalent.\n\nAlternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.\n\nColor NameShort NameRGB TripletHexadecimal Color CodeAppearance\n`'red'``'r'``[1 0 0]``'#FF0000'`", null, "`'green'``'g'``[0 1 0]``'#00FF00'`", null, "`'blue'``'b'``[0 0 1]``'#0000FF'`", null, "`'cyan'` `'c'``[0 1 1]``'#00FFFF'`", null, "`'magenta'``'m'``[1 0 1]``'#FF00FF'`", null, "`'yellow'``'y'``[1 1 0]``'#FFFF00'`", null, "`'black'``'k'``[0 0 0]``'#000000'`", null, "`'white'``'w'``[1 1 1]``'#FFFFFF'`", null, "`'none'`Not applicableNot applicableNot applicableNo color\n\nHere are the RGB triplets and hexadecimal color codes for the default colors MATLAB® uses in many types of plots.\n\n`[0 0.4470 0.7410]``'#0072BD'`", null, "`[0.8500 0.3250 0.0980]``'#D95319'`", null, "`[0.9290 0.6940 0.1250]``'#EDB120'`", null, "`[0.4940 0.1840 0.5560]``'#7E2F8E'`", null, "`[0.4660 0.6740 0.1880]``'#77AC30'`", null, "`[0.3010 0.7450 0.9330]``'#4DBEEE'`", null, "`[0.6350 0.0780 0.1840]``'#A2142F'`", null, "Example: `[0.5 0.5 0.5]`\n\nExample: `'blue'`\n\nExample: `'#D2F9A7'`\n\nMarker fill color, specified as `'flat'`, `'auto'`, an RGB triplet, a hexadecimal color code, a color name, or a short name. The `'flat'` option uses the `CData` values. The `'auto'` option uses the same color as the `Color` property for the axes.\n\nFor a custom color, specify an RGB triplet or a hexadecimal color code.\n\n• An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range `[0,1]`; for example, ```[0.4 0.6 0.7]```.\n\n• A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (`#`) followed by three or six hexadecimal digits, which can range from `0` to `F`. The values are not case sensitive. Thus, the color codes `'#FF8800'`, `'#ff8800'`, `'#F80'`, and `'#f80'` are equivalent.\n\nAlternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.\n\nColor NameShort NameRGB TripletHexadecimal Color CodeAppearance\n`'red'``'r'``[1 0 0]``'#FF0000'`", null, "`'green'``'g'``[0 1 0]``'#00FF00'`", null, "`'blue'``'b'``[0 0 1]``'#0000FF'`", null, "`'cyan'` `'c'``[0 1 1]``'#00FFFF'`", null, "`'magenta'``'m'``[1 0 1]``'#FF00FF'`", null, "`'yellow'``'y'``[1 1 0]``'#FFFF00'`", null, "`'black'``'k'``[0 0 0]``'#000000'`", null, "`'white'``'w'``[1 1 1]``'#FFFFFF'`", null, "`'none'`Not applicableNot applicableNot applicableNo color\n\nHere are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.\n\n`[0 0.4470 0.7410]``'#0072BD'`", null, "`[0.8500 0.3250 0.0980]``'#D95319'`", null, "`[0.9290 0.6940 0.1250]``'#EDB120'`", null, "`[0.4940 0.1840 0.5560]``'#7E2F8E'`", null, "`[0.4660 0.6740 0.1880]``'#77AC30'`", null, "`[0.3010 0.7450 0.9330]``'#4DBEEE'`", null, "`[0.6350 0.0780 0.1840]``'#A2142F'`", null, "Example: `[0.3 0.2 0.1]`\n\nExample: `'green'`\n\nExample: `'#D2F9A7'`\n\n## Output Arguments\n\ncollapse all\n\n`Scatter` object. This is a unique identifier, which you can use to query and modify the properties of the `Scatter` object after it is created." ]

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[ "# Signals sampling\n\nI have a simple question, but sadly I'm kind of \"noob\" in signals theory. A signal having 4 harmonics at the following frequencies: 1 kHz, 2 kHz, 3.5kHz and 4.2 kHz. (How can a signal have harmonics \"without\" a fundamental frequency?) Find the minimum sampling frequency so that the signal can be completely recovered from its sampled version.\n\nI think I should fint $$f_s = 2 f_{max}$$ but I do not know how to find $$f_{max}$$.\n\n• Do you need additional answers? – Laurent Duval Dec 30 '18 at 22:01\n\nThe sampling frequency ($$f_p$$) must be greater than twice the highest frequency of $$x(t)$$: $$f_s > 2 f_{\\max}$$\nThere is a typo in the text, as $$f_p$$ and $$f_s$$ refer to the same sampling frequency concept. The \"must\" part is not true. Anyway, there are three levels of possible answers. To start with, an harmonic is a common name for a sinusoidal signal defined by a frequency, an amplitude and a phase. However, a signal with harmonics, i.e. a signal containing multiples of a fundamental frequency $$f_0$$, i.e. $$kf_0$$, $$k\\in \\mathbb{N}^*$$ can exist without the fundamental at $$k=1$$ (if I remember well). You can read (and hear) more at Physics of music, notes: The missing fundamental or The Well-Tempered Timpani, In Search of the Missing Fundamental: The Missing Fundamental.\n2. A more involved form considers the frequency span, between 1 kHz and 4.2 kHz, as you can further reduce the rate using an $$f_{\\min}$$-$$f_{\\max}$$ diagram, eluded to in Confusion regarding Nyquist Sampling Theorem or here, from Vaughan et al., 1991, The theory of bandpass sampling:", null, "" ]

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[ "# Power Generation/Hydro Power\n\nReview: Lesson 2\n\nThe previous Lesson discussed the steam power station. Here are some points you need to remember from lesson 2.\n\n• Schematic Arrangement of steam power station.\n• Types of cooling sytems for a steam power station.\n• Location & Efficiency of steam power station.\n\nPreview: Lesson 3\n\nThis Lesson is about Hydro Power station. The student/User is expected to understand the following at the end of the lesson.\n\n• Basics:\n• Arrangements:\n• Location:\n• Pumped storage scheme:\n\ncomponents that make up a steam power station.\nFactors influencing selection of construction site.\nOverview & comparison to Hydro-power station.", null, "Figure 1:Krasnoyarsk hydroelectric station in Russia ( Click on image to view full size image )\n\nIntroduction: Hydro Power station\n\nA hydro power station uses potential energy of water at high level for generating electrical energy.\n\nThis power station is generally located in hilly areas where dams can be built conveniently and large water reservoirs can be obtained. This kind of power station can be used to produce large amounts of electrical energy. In most countries these power stations are used as peak load power stations. This is because they can be started and stopped easily and fast.\n\nOperation\n\nThe water from the dam is lead to the water turbine through the penstock. Here the hydraulic energy of water is converted to rotational mechanical energy by the turbine. The turbine is connected to the generator through the turbine shaft and hence mechanical energy is converted into electrical energy by the generator.\n\nPros & Cons: what this power station presents\n\nRequires no fuel, thus called clean power station Very high capital cost for dam construction\nSmall running charges and no need for specialised manpower Uncertainty about availability of huge amounts of water\nSimple construction & requires less maintenance Skilled personel required for construction\nVery robust & has long life High cost of transmission line as plant is located in hilly areas.\nAlso used for flood control and irrigation Impacts native watershed ecology\n\nFuture generations will want to depend more on this type of electricity generating power station (and other renewable energy sources), due to a fast increasing depletion of fuels(Coal). There are a number of construction projects currently underway for this kind of power station around the world.", null, "Figure 2:Hydroelectric dam cross-section diagram ( Click on image to view full size image )\n\nHydo-electric power stations boast a simple design and construction method that is very robust and reliable(when done properly). The following sub topic discusses the most important constituents of this kind of power station (as shown in figures 2 & 3).\n\nConstituents of Hydro-electric power station\n\n Reservoir: This is where water is stored for use as and when needed. The type and arrangement depends on topography of the site. Penstock: This is a conduit (conduits) that carry water to the turbines. They are made of reinforced concrete or steel. A surge tank is installed next to each penstock for over flow control and protection of penstock from bursting. Water turbine: Water turbines are used to convert hydraulic energy of flowing water into rotational mechanical energy. Figure 3 is an example of the make of a typical water turbine. Generator: This machine is used to convert rotational mechanical energy transferred from the turbine through the shaft, into electrical energy. the produced electrical energy is transmitted to the transformer for long distance transmission.\n\nLocation of Hydro-electric power station: influencing factors\n\n Availablility of water: Adequate water must be available at good head. Cost and Type of Land: Land should be available at reasonable price. The bearing capacity of the land should be enough to withstand huge structures & equipment. Storage of water: A dam must be constructed to store water in order to deal with variations of water availability during the year. Transportaion facilities: The site should be accessible by rail and(or) road for ease in transporting equipment & machinery.\n\nThis schematic diagram must be properly understood. It is the basis upon which Hydro-electric power station designs are done. The individual power station complexity may differ slightly to the schematic and yet over and above that will use the same principle.", null, "Figure 3:Hydraulic turbine and Electrical generator diagram ( Click on image to view full size image )", null, "Figure 4:Pumped storage scheme power station diagram ( Click on image to view full size image )\n\nPumped storage schemes are a convenient way of storing large quantities of energy which can be used during emergency or peaking times.\n\nOperation:\n\nDuring off-Peak hours, the plant draws electric energy from the electrical grid & uses that to pump water to the upper reservoir.\n\nWhen Peak time comes, the water from the upper reservoir is released & electric energy is generated in the lower reservoir. This cycle is repeated daily.\n\nBy their nature, pumped storage schemes cannot be used as base load power stations. These are strictly used for peak time supply as they can be brought on-line quickly.\n\nComparison:\n\nHydro power plant Pumped storage plant\nOnce water passes through penstock & turbine, it is released into the river Water is re-used by pumping and generative action of the scheme.\nCan be used for irrigation & flood control Can be used for pumping water from readly available areas to areas in need of water\nCan still be used as base load station can not be used as base load station as it can only generate for limited hours\n\nAs evident from above table, both power stations are very desirable for use that goes outside of electrical energy generation confines. This schematic diagram must be properly understood. it is the basis upon which pumped-storage scheme power station designs are done. the individual power station complexity may differ slightly to the schematic and yet over and above that will use the same principle.\n\nBelow are equations used for calculations involving this kind of power station:\n\n$W=(Volume\\times density)=V{\\rho }$", null, "(in Kg) ... Equation 3.1\n\n\nThe potential energy of the water head:\n\n$E_{potential}=mgh$", null, "(in Joules) ... Equation 3.2\n\n\nThus the equivelent electrical energy will be:\n\n$E_{Electrical}={\\frac {E_{potential}}{36\\times 10_{.}^{5}J}}$", null, "(in kWh) ... Equation 3.3\n\n\nElectrical enegry can also be expressed as:\n\n$E_{Electrical}={\\frac {WH{\\eta }_{overall}}{(3600.sec\\times 1000)}}$", null, "(in kWh) ... Equation 3.4\n\n\nWhere:\n\n• m = mass (in Kg)\n• g = constant ≈$9.8m.s^{-2}$", null, "• h/H = water head height (metres)\n• ρ = density of water ($m^{3}$", null, ")\n\nBelow are furhter equations used for calculations involving this kind of power station:\n\nGross plant capacity (G.C):\n\n$G.C={\\frac {E_{potential}}{sec}}$", null, "(in Watts) ... Equation 3.5\n\n\nThe firm capacity (F.C) will therefore be:\n\n$F.C=G.C\\times {\\eta }$", null, "(in Watts) ... Equation 3.6\n\n\nThus the yearly gross out put:\n\n$Y.G.O=F.C\\times 8760Hrs$", null, "(in kWh) ... Equation 3.7\n\n\nWe can also estimate the volume of flow per annum:\n\n$V_{annum}=Catchment_{.}Area\\times Annual_{.}Rainfall\\times Yield_{.}Factor$", null, "(in kWh) ... Equation 3.8\n\nWhere:\n\n• η = Efficiency\n• m = mass (in Kg)\n• g = constant ≈$9.8m.s^{-2}$", null, "• h/H = water head height (metres)\n• ρ = density of water ($m^{3}$", null, ")\n\nit is imp part of the power plant" ]

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[ "# Often asked: What Is Perfect Number In Mathematics?\n\n## What are the first 5 perfect numbers?\n\nThe first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.\n\n## Why is 3 the perfect number?\n\nThree is the smallest number we need to create a pattern, the perfect combination of brevity and rhythm. It’s a principle captured neatly in the Latin phrase omne trium perfectum: everything that comes in threes is perfect, or, every set of three is complete.\n\n## Is there a formula for perfect numbers?\n\nEquivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, σ1(n) = 2n where σ1 is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28. —what is now called a Mersenne prime.\n\n## Why is 4 the perfect number?\n\nNumbers like 6 that equal the sum of their factors are called perfect numbers. 6 is the first perfect number. 4 is not a perfect number because the sum of its factors (besides 4 itself), 1+2, is less than 4.\n\n## Why is 28 a perfect number?\n\nA number is perfect if all of its factors, including 1 but excluding itself, perfectly add up to the number you began with. 6, for example, is perfect, because its factors — 3, 2, and 1 — all sum up to 6. 28 is perfect too: 14, 7, 4, 2, and 1 add up to 28.\n\nYou might be interested:  Quick Answer: What Is Mathematics In Information Technology?\n\n## Is 25 a perfect number?\n\nPerfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.\n\n## Why is 7 the perfect number?\n\nSeven is the number of completeness and perfection (both physical and spiritual). It derives much of its meaning from being tied directly to God’s creation of all things. The word ‘created’ is used 7 times describing God’s creative work (Genesis 1:1, 21, 27 three times; 2:3; 2:4).\n\n## What is the most magical number?\n\nSeven is the most powerful magical number, based on centuries of mythology, science, and mathematics, and therefore has a very important role in the wizarding world. Arithmancer Bridget Wenlock was the first to note this through a theorem which exposed the magical properties of the number seven.\n\n## Is 3 a lucky number?\n\n3 (三), pronounced san, is considered lucky due to its similarity in sound to the word that means birth. Additionally, this number represents the three stages in the life of humans – birth, marriage, death – that adds to its importance in Chinese culture.\n\n## What is strong number?\n\nStrong number is a number whose sum of all digits’ factorial is equal to the number ‘n’. So, to find a number whether its strong number, we have to pick every digit of the number like the number is 145 then we have to pick 1, 4 and 5 now we will find factorial of each number i.e, 1! = 1, 4!\n\nYou might be interested:  What Is Sample In Mathematics?\n\n## Is 4 a perfect square?\n\nFor instance, the product of a number 2 by itself is 4. In this case, 4 is termed as a perfect square. A square of a number is denoted as n × n. Example 1.\n\nInteger Perfect square\n2 x 2 4\n3 x 3 9\n4 x 4 16\n5 x 5 25\n\n## What is a perfect pair in math?\n\nIn this problem, a perfect pair is defined as two numbers whose sum is equal to their quotient. If you cannot find any perfect pairs, prove that a perfect pair cannot exist. If you find perfect pairs, then generalize your findings and describe the relationship of the number pairs.\n\n## Why Is 9 the perfect number?\n\nNine is a Motzkin number. It is the first composite lucky number, along with the first composite odd number and only single-digit composite odd number. 9 is the only positive perfect power that is one more than another positive perfect power, by Mihăilescu’s Theorem.\n\n## Why is 12 the perfect number?\n\nTwelve is the smallest abundant number, since it is the smallest integer for which the sum of its proper divisors (1 + 2 + 3 + 4 + 6 = 16) is greater than itself. Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number.\n\n## What is the best number in the world?\n\nA survey launched by a British mathematics writer has found that seven is the world’s favorite number, reports The Guardian. The results of the online survey were published on Tuesday, with three, eight and and four coming second, third and fourth.", null, "" ]

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[ "### Whiten a matrix: Matlab code\n\nWhitening a matrix is a useful preprocessing step in data analysis. The goal is to transform matrix X into matrix Y such that Y has identity covariance matrix. This is straightforward enough but in case you are too lazy to write such a function here’s how you might do it:\n\n```function [X] = whiten(X,fudgefactor)\nX = bsxfun(@minus, X, mean(X));\nA = X'*X;\n[V,D] = eig(A);\nX = X*V*diag(1./(diag(D)+fudgefactor).^(1/2))*V';\nend```\n\nYou can read about bsxfun here if you are unfamiliar with this function. Because the results of whitening can be noisy, a fudge factor is used so that eigenvectors associated with small eigenvalues do not get overamplified. Thus the whitening is only approximate. Here’s an image patch whitened this way:", null, "Unsurprisingly this accentuates high frequencies in the image. At the bottom you can see the covariance matrix of the set of natural image patches before and after whitening.\n\nUpdate: Here’s the explanation for why this works as well as a reference you may cite.\n\n## 8 thoughts on “Whiten a matrix: Matlab code”\n\n1.", null, "Tomas Mendoza says:\n\nThank you very much!\n\nI have a question. I’m using python and when i do the “diag(1./(diag(D)+fudgefactor).^(1/2))” the resultant array of that specific computation contains complex numbers, so i get an error when i try to multiply by X*V…*V’ (the rest of the equation). I don’t understand why you don’t get the same error? Thank you very much!\n\n2.", null, "Shekoofeh Azizi says:\n\nHi, Thanks for the nice description.\nI am not sure, but I think there is a problem in the above code. To compute covariance matrix you are using X’ * X, so my understanding is that you are considering each row as a sample and columns are features or variable. So, for the mean removal, based on the covariance definition, we need to remove mean from each sample and put samples around the origin in the feature space. As I know, mean(X) without dimension definition and in defaults calculate means of columns. So, in the above code instead of mean removal from rows/samples we are removing means from columns. To wrap up, I think it has to be, mean(X,2) or it has to be X*X’.\n\n3.", null, "robotboytn says:\n\nReblogged this on robot boy.\n\n4.", null, "Champenois says:\n\nHi\n\nHow did you calculate the covariance matrixon the left bottom corner?\n\nThanks\n\n5.", null, "Thusi (@thusinut) says:\n\nThanks for the snippet. But what would be a good value for fudgefactor? 0-1 or higher?\n\n1.", null, "xcorr says:\n\nSomething like 1e-6 times the largest eigenvalue of the A matrix." ]

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[ "", null, "# POP Source 2.0dynamics node\n\nA POP node that generates particles from geometry.\n\nPOP Source is a node that generates particles from geometry, often a referenced SOP network.\n\n## Using Source ¶\n\n1. Create an object.\n\n2. Click the", null, "", null, "Source tool on the Particles tab.\n\nThe", null, "particle system will attach itself to the object you have selected.\n\n3. Click", null, "play to see the particles.", null, "## Source ¶\n\nEmission Type\n\nWhere on the source geometry to emit points from.\n\nAll Points\n\nAll of the points will emit points simultaneously.\n\nAll Geometry\n\nAll of the source object will be added to the particle system. This includes non-points, such as primitives. This is useful for bringing in constraints or other geometry information. Note that most POPs just work on points, ignoring any attached geometry.\n\nPoints\n\nThe desired number of points will be emitted from random source points.\n\nScatter onto Surfaces\n\nThe desired number of points will be emitted from random locations on the surfaces of the geometry.\n\nGeometry Source\n\nSpecifies the SOP to use.\n\nUse Parameter Values\n\nUse the SOP specified in the SOP parameter below.\n\nUse First Context Geometry\n\nUse the SOP connected to the DOP network’s first input.\n\nUse Second Context Geometry\n\nUse the SOP connected to the DOP network’s second input.\n\nUse Third Context Geometry\n\nUse the SOP connected to the DOP network’s third input.\n\nUse Fourth Context Geometry\n\nUse the SOP connected to the DOP network’s fourth input.\n\nSOP\n\nPath to the SOP (when Geometry Source is set to Use Parameter Values).\n\nUse Object Transform\n\nWhen Geometry Source is set to Use Parameter Values, the transform of the object containing the chosen SOP is applied to the geometry. This is useful if the location of the geometry is defined by an object transform.\n\nEmission Attribute\n\nWhen in surface mode, this point attribute will be used to vary the chance of any polygon from emitting polygons. Higher values will increase the relative chance of that polygon getting an emission.\n\nRelax Iterations\n\nNew points will be spread out from each other. This is done in successive passes, so the more iterations, the more equally spaced the sourced particles will be. This may result in points matching frame to frame if they get over constrained, however.\n\nPoint radii will be scaled by this before any relaxing of the points. Specifying a scale less than 1 will increase “clumpiness” of the resulting points, with a value of zero resulting in no relaxation. Specifying a scale greater than 1 may speed up convergence of the relaxation, especially when scattering on curves.\n\nAfter any scaling, Max Relax Radius will be enforced before any relaxation.\n\nThis must be set appropriately to prevent outlier points in low-density areas causing problems when relaxing points.\n\nIn order to approximately maintain variations in density, points are assigned radii inversely proportional to density (for curves), the square root of density (for surfaces), or the cube root of density (for volumes). This may cause problems for areas whose densities are near zero, especially in volumes, when painting density on a surface, or when using a density texture with a black background, since the radius approaches infinity. This parameter specifies the maximum radius within which points will influence other points.\n\nWhen this is disabled, there will still be a maximum radius, which is currently chosen as half the diagonal length of the bounding box of the input geometry.\n\nScale Point Count by Area\n\nWhen in surface mode, the constant and impulse point counts will be scaled by the total area (taking into account any emission attribute) of the geometry. This lets you paint an emission density and have the number of particles increase as the area of emission increases.\n\nReference Area\n\nThe impulse and constant emission values are often set for an entire object, which is often larger than a unit area. Therefore, this acts as a scale on their values before applying the area count.\n\nAn object of the size of Reference Area will emit at the specified impulse/constant rate. A larger object will emit proportionally more particles, and a smaller one less.\n\nRemove Overlapping\n\nPotential new particles are compared against the existing set of particles. If their `pscale` attribute overlaps, the new particle isn’t added.\n\nThis can be useful to continuously add new particles to a sand simulation without creating explosions from overlaps.\n\nNote this only tests against particles that already exsit, so it is important the set of new sourced particles don’t overlap within themselves.\n\n## Birth ¶\n\nThis operator has two methods for emitting particles. You can use these methods together or separately:\n\n• Impulse creates a certain number of particles each time the node cooks.\n\n• Constant creates a certain number of particles per second.\n\nImpulse Activation\n\nTurns impulse emission on and off. Impulse emits the number of particles in the Impulse Birth Rate below each time the operator cooks. A value of 0 means off, any other value means on.\n\nImpulse Count\n\nNumber of particles to emit each time the node cooks (when Impulse activation is on).\n\nConst. Activation\n\nTurns constant emission on and off. Impulse emits the number of particles in the Constant birth rate below each second. A value of 0 means off, any other value means on.\n\nConst. Birth Rate\n\nNumber of particles to emit per second (when Constant Activation is on).\n\nMax Sim Points\n\nThis parameter is a cap on the total number of points in the bound geometry. If this limiting is enabled, then the emitter will not create any more particles once the specified maximum is reached.\n\nMax Points per Frame\n\nLimit on the number of points that can be added each frame. This option can be used to prevent the emitter from spawning an undesirably large amount of particles as a result of errant parameter values.\n\nProbabilistic Emission\n\nEmit particles by treating the birth rate as a probability. If enabled, particle emission will be distributed randomly across timesteps when the birth rate is low. If disabled, the emission will occur at regular intervals. For example, with a Constant Birth Rate of 1 and Probabilistic Emission enabled, you will see particles emitted at random intervals but an overall rate of approximately 1 per second. With Probabilistic Emission disabled, particles will be emitted at each one-second interval.\n\nJust Born Group\n\nName of a group to put the new points into. The particles will only be in this group the same substep that they were created.\n\nLife Expectancy\n\nHow long the particle will live (in seconds).\n\nLife Variance\n\nParticles will live the number of seconds in Life Expectancy, plus or minus this number of seconds. Use 0 for no variance.\n\nJitter Birth Time\n\nRather than have the particles all be created with an age of 0, they are created with a random age within the current timestep. They will also be moved by their starting velocity times this age. This is useful when adding high velocity particles from emitters as it won’t generate clumps on each frame.\n\nInterpolate Source\n\nThe source can also be interpolated linearly to better birth particles from fast moving sources. This uses the Jitter Birth Time to decide where in the source to interpolate. If you are wiring your source into the post solve, the Positive birth time and Backwards source should be used, which is useful since it does not require future knowledge of the source. However, to avoid clumping when large forces are present, you should use Negative birth time and Forward source. This requires you to delete all particles with negative age when rendering. Alternatively, you can wire into the Pre-Solve, and then use the Forward source with Negative birth time and not have to worry about seeing particles with negative age. However, this requires a source that you can compute outside the simulation.\n\nInterpolation Method\n\nThe `Interpolate Source` takes two geometries and has to find a way to determine the in-between values of those geometries. If point counts and polygons match, the Match Topology option can be used for the most accurate result. Otherwise, point velocities may be computed with the Trail SOP and then Use Point Velocities selected. In this latter case, only one of the input geometries is needed, but the Fowrad and Backwards options are still used to determine if the born points lead or trail the object.\n\n## Attributes ¶\n\nThe parameters on this tab let you control which and how attributes are initialized on the emitted particles.\n\nInitial State\n\nIf the emission type is Scatter on Surfaces, and the source is a SOP Path, the initial state of the particles can be set to sliding, stuck, or stopped.\n\nParticles can then be released by setting the `i@sliding`, `i@stuck`, or `i@stopped` attributes to 0.\n\nInherit Attributes\n\nThis specifies which attributes to inherit from the source geometry.\n\nVelocity\n\nSet or add to velocity attribute.\n\nVariance\n\nVariance to velocity set above. The node will add +/- from 0 to this number along each axis to the Velocity parameter.\n\nEllipsoid Distribution\n\nBy default, the variance (if any) is distributed in a box, the size of which is determined by the Variance parameter. When this option is on, the variance is distributed in an ellipsoid instead.\n\nAdd ID and parent attributes to the created particles.\n\n## Stream ¶\n\nStream Name\n\nThe name of the stream to be generated by this generator. This value is prefixed with `stream_` to form a group name that all particles that belong to this logical stream will be made part of.\n\n## Outputs ¶\n\nFirst Output\n\nThe output of this node should be wired into a solver chain.\n\nMerge nodes can be used to combine multiple solver chains.\n\nThe final wiring should go into one of the purple inputs of a full-solver, such as", null, "POP Solver or", null, "FLIP Solver.\n\n## Locals ¶\n\nchannelname\n\nThis DOP node defines a local variable for each channel and parameter on the Data Options page, with the same name as the channel. So for example, the node may have channels for Position (positionx, positiony, positionz) and a parameter for an object name (objectname).\n\nThen there will also be local variables with the names positionx, positiony, positionz, and objectname. These variables will evaluate to the previous value for that parameter.\n\nThis previous value is always stored as part of the data attached to the object being processed. This is essentially a shortcut for a dopfield expression like:\n\n```dopfield(\\$DOPNET, \\$OBJID, dataName, \"Options\", 0, channelname)\n```\n\nIf the data does not already exist, then a value of zero or an empty string will be returned.\n\nDATACT\n\nThis value is the simulation time (see variable ST) at which the current data was created. This value may not be the same as the current simulation time if this node is modifying existing data, rather than creating new data.\n\nDATACF\n\nThis value is the simulation frame (see variable SF) at which the current data was created. This value may not be the same as the current simulation frame if this node is modifying existing data, rather than creating new data.\n\nRELNAME\n\nThis value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).\n\nIn this case, this value is set to the name of the relationship to which the data is being attached.\n\nRELOBJIDS\n\nThis value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).\n\nIn this case, this value is set to a string that is a space separated list of the object identifiers for all the Affected Objects of the relationship to which the data is being attached.\n\nRELOBJNAMES\n\nThis value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).\n\nIn this case, this value is set to a string that is a space separated list of the names of all the Affected Objects of the relationship to which the data is being attached.\n\nRELAFFOBJIDS\n\nThis value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).\n\nIn this case, this value is set to a string that is a space separated list of the object identifiers for all the Affector Objects of the relationship to which the data is being attached.\n\nRELAFFOBJNAMES\n\nThis value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).\n\nIn this case, this value is set to a string that is a space separated list of the names of all the Affector Objects of the relationship to which the data is being attached.\n\nST\n\nThis value is the simulation time for which the node is being evaluated.\n\nThis value may not be equal to the current Houdini time represented by the variable T, depending on the settings of the", null, "DOP Network Offset Time and Time Scale parameters.\n\nThis value is guaranteed to have a value of zero at the start of a simulation, so when testing for the first timestep of a simulation, it is best to use a test like `\\$ST == 0` rather than `\\$T == 0` or `\\$FF == 1`.\n\nSF\n\nThis value is the simulation frame (or more accurately, the simulation time step number) for which the node is being evaluated.\n\nThis value may not be equal to the current Houdini frame number represented by the variable F, depending on the settings of the", null, "DOP Network parameters. Instead, this value is equal to the simulation time (ST) divided by the simulation timestep size (TIMESTEP).\n\nTIMESTEP\n\nThis value is the size of a simulation timestep. This value is useful to scale values that are expressed in units per second, but are applied on each timestep.\n\nSFPS\n\nThis value is the inverse of the TIMESTEP value. It is the number of timesteps per second of simulation time.\n\nSNOBJ\n\nThis is the number of objects in the simulation. For nodes that create objects such as the", null, "Empty Object node, this value will increase for each object that is evaluated.\n\nA good way to guarantee unique object names is to use an expression like `object_\\$SNOBJ`.\n\nNOBJ\n\nThis value is the number of objects that will be evaluated by the current node during this timestep. This value will often be different from SNOBJ, as many nodes do not process all the objects in a simulation.\n\nThis value may return 0 if the node does not process each object sequentially (such as the", null, "Group DOP).\n\nOBJ\n\nThis value is the index of the specific object being processed by the node. This value will always run from zero to NOBJ-1 in a given timestep. This value does not identify the current object within the simulation like OBJID or OBJNAME, just the object’s position in the current order of processing.\n\nThis value is useful for generating a random number for each object, or simply splitting the objects into two or more groups to be processed in different ways. This value will be -1 if the node does not process objects sequentially (such as the", null, "Group DOP).\n\nOBJID\n\nThis is the unique object identifier for the object being processed. Every object is assigned an integer value that is unique among all objects in the simulation for all time. Even if an object is deleted, its identifier is never reused.\n\nThe object identifier can always be used to uniquely identify a given object. This makes this variable very useful in situations where each object needs to be treated differently. It can be used to produce a unique random number for each object, for example.\n\nThis value is also the best way to look up information on an object using the dopfield expression function. This value will be -1 if the node does not process objects sequentially (such as the", null, "Group DOP).\n\nALLOBJIDS\n\nThis string contains a space separated list of the unique object identifiers for every object being processed by the current node.\n\nALLOBJNAMES\n\nThis string contains a space separated list of the names of every object being processed by the current node.\n\nOBJCT\n\nThis value is the simulation time (see variable ST) at which the current object was created.\n\nTherefore, to check if an object was created on the current timestep, the expression `\\$ST == \\$OBJCT` should always be used. This value will be zero if the node does not process objects sequentially (such as the", null, "Group DOP).\n\nOBJCF\n\nThis value is the simulation frame (see variable SF) at which the current object was created.\n\nThis value is equivalent to using the dopsttoframe expression on the OBJCT variable. This value will be zero if the node does not process objects sequentially (such as the", null, "Group DOP).\n\nOBJNAME\n\nThis is a string value containing the name of the object being processed.\n\nObject names are not guaranteed to be unique within a simulation. However, if you name your objects carefully so that they are unique, the object name can be a much easier way to identify an object than the unique object identifier, OBJID.\n\nThe object name can also be used to treat a number of similar objects (with the same name) as a virtual group. If there are 20 objects named “myobject”, specifying `strcmp(\\$OBJNAME, \"myobject\") == 0` in the activation field of a DOP will cause that DOP to operate only on those 20 objects. This value will be the empty string if the node does not process objects sequentially (such as the", null, "Group DOP).\n\nDOPNET\n\nThis is a string value containing the full path of the current DOP Network. This value is most useful in DOP subnet digital assets where you want to know the path to the DOP Network that contains the node.\n\n# Dynamics nodes\n\n• Marks a simulation object as active or passive.\n\n• Creates affector relationships between groups of objects.\n\n• Blends between a set of animation clips based on the agent’s turn rate.\n\n• Layers additional animation clips onto an agent.\n\n• Defines a target that an agent can turn its head to look at.\n\n• Adjusts the agent’s skeleton to look at a target.\n\n• Adapts the legs of an agent to conform to terrain and prevent the feet from sliding.\n\n• Project the agent/particle points onto the terrain\n\n• Defines an orientation that aligns an axis in object space with a second axis defined by the relative locations of two positional anchors.\n\n• Defines multiple points, specified by their number or group, on the given geometry of a simulation object.\n\n• Defines orientations based on multiple points on the given geometry of a simulation object.\n\n• Defines a position by looking at the position of a point on the geometry of a simulation object.\n\n• Defines an orientation by looking at a point on the geometry of a simulation object.\n\n• Defines a position by looking at the position of a point on the geometry of a simulation object.\n\n• Defines an orientation by looking at a point on the geometry of a simulation object.\n\n• Defines a position by looking at the position of a particular UV coordinate location on a primitive.\n\n• Defines a position by specifying a position in the space of some simulation object.\n\n• Defines an orientation by specifying a rotation in the space of some simulation object.\n\n• Defines multiple attachment points on a polygonal surface of an object.\n\n• Defines a position by specifying a position in world space.\n\n• Defines an orientation by specifying a rotation in world space.\n\n• Attaches data to simulation objects or other data.\n\n• Creates relationships between simulation objects.\n\n• Attaches the appropriate data for Bullet Objects to an object.\n\n• Sets and configures an Bullet Dynamics solver.\n\n• Applies a uniform force to objects submerged in a fluid.\n\n• Attaches the appropriate data for Cloth Objects to an object.\n\n• Defines the mass properties.\n\n• Defines the physical material for a deformable surface.\n\n• Defines the internal cloth forces.\n\n• Creates a Cloth Object from SOP Geometry.\n\n• Defines the plasticity properties.\n\n• Constrains part of the boundary of a cloth object to the boundary of another cloth object.\n\n• Defines how cloth uses target.\n\n• Defines a way of resolving collisions involving a cloth object and DOPs objects with volumetric representations (RBD Objects, ground planes, etc.)\n\n• Constrains an object to remain a certain distance from the constraint, and limits the object’s rotation.\n\n• Constrains pairs of RBD objects together according to a polygon network.\n\n• Defines a set of constraints based on geometry.\n\n• Visualizes the constraints defined by constraint network geometry.\n\n• Creates multiple copies of the input data.\n\n• Sets and configures a Copy Data Solver.\n\n• Mimics the information set by the Copy Object DOP.\n\n• Defines a Crowd Fuzzy Logic\n\n• Creates a crowd object with required agent attributes to be used in the crowd simulation.\n\n• Updates agents according to their steer forces and animation clips.\n\n• Defines a Crowd State\n\n• Defines a transition between crowd states.\n\n• Defines a Crowd Trigger\n\n• Combines multiple crowd triggers to build a more complex trigger.\n\n• Adds a data only once to an object, regardless of number of wires.\n\n• Deletes both objects and data according to patterns.\n\n• Applies force and torque to objects that resists their current direction of motion.\n\n• Defines how the surrounding medium affects a soft body object.\n\n• Dynamics nodes set up the conditions and rules for dynamics simulations.\n\n• Controls Embedded Geometry that can be deformed along with the simulated geometry in a finite element simulation.\n\n• Creates an Empty Data for holding custom information.\n\n• Creates an Empty Object.\n\n• Constrains a set of points on the surface of one FEM object to a set of points on the surface on another FEM object or a static object.\n\n• Constrains points of a solid object or a hybrid object to points of another DOP object.\n\n• Creates an FEM Hybrid Object from SOP Geometry.\n\n• Constrains regions of a solid object or a hybrid object to another solid or hybrid object.\n\n• Make a set of points on the surface of an FEM Object slide against the surface of another FEM Object or a Static Object.\n\n• Creates a simulated FEM solid from geometry.\n\n• Sets and configures a Finite Element solver.\n\n• Constrains an FEM object to a target trajectory using a hard constraint or soft constraint.\n\n• Attaches the appropriate data for Particle Fluid Objects to become a FLIP based fluid.\n\n• Evolves an object as a FLIP fluid object.\n\n• Applies forces on the objects as if a cone-shaped fan were acting on them.\n\n• Fetches a piece of data from a simulation object.\n\n• Applies forces to an object using some piece of geometry as a vector field.\n\n• Creates a vortex filament object from SOP Geometry.\n\n• Evolves vortex filament geometry over time.\n\n• Imports vortex filaments from a SOP network.\n\n• Saves and loads simulation objects to external files.\n\n• Allows a finite-element object to generate optional output attributes.\n\n• Attaches the appropriate data for Fluid Objects to an object.\n\n• Applies forces to resist the current motion of soft body objects relative to a fluid.\n\n• Attaches the appropriate data for Fluid Objects to an object.\n\n• A solver for Sign Distance Field (SDF) liquid simulations.\n\n• A microsolver that applies viscosity to a velocity field using an adaptive grid.\n\n• A microsolver that advects fields and geometry by a velocity field.\n\n• A microsolver that advects fields by a velocity field using OpenCL acceleration.\n\n• A microsolver that advects fields by a velocity field.\n\n• A microsolver that computes analytic property of fields.\n\n• A microsolver that swaps geometry attributes.\n\n• A microsolver that applies a force around an axis to a velocity field.\n\n• A microsolver that blends the density of two fields.\n\n• A microsolver that blurs fields.\n\n• A microsolver that determines the collision field between the fluid field and any affector objects.\n\n• A microsolver that builds a collision field for fluid simulations from instanced pieces.\n\n• A microsolver that builds a mask out of positive areas of the source fields.\n\n• A microsolver that builds a mask for each voxel to show the presence or absence of relationships between objects.\n\n• A microsolver that calculates an adhoc buoyancy force and updates a velocity field.\n\n• A microsolver that performs general calculations on a pair of fields.\n\n• A microsolver that detects collisions between particles and geometry.\n\n• A microsolver that applies a combustion model to the simulation.\n\n• A microsolver that clips an SDF field with a convex hull.\n\n• A microsolver that adjusts an SDF according to surface markers.\n\n• A microsolver that computes the cross product of two vector fields.\n\n• A DOP node that creates forces generated from a curve.\n\n• A microsolver that scales down velocity, damping motion.\n\n• A microsolver that diffuses a field or point attribute.\n\n• A microsolver that dissipates a field.\n\n• Adds fine detail to a smoke simulation by applying disturbance forces to a velocity field.\n\n• A microsolver that runs once for each matching data.\n\n• A microsolver that embeds one fluid inside another.\n\n• A microsolver that enforces boundary conditions on a field.\n\n• A microsolver that equalizes the density of two fields.\n\n• A microsolver that equalizes the volume of two fields.\n\n• A microsolver that emits a DOP error.\n\n• A microsolver that evaluates the external DOPs forces for each point in a velocity field and updates the velocity field accordingly.\n\n• A microsolver that extrapolates a field’s value along an SDF.\n\n• A microsolver that creates a feathered mask out of a field.\n\n• A microsolver that calculates and applies feedback forces to collision geometry.\n\n• A data node that fetches the fields needed to embed one fluid in another.\n\n• Runs CVEX on a set of fields.\n\n• Runs CVEX on a set of fields.\n\n• A microsolver that copies the values of a field into a point attribute on geometry.\n\n• Filters spurious divergent modes that may survive pressure projection on a center-sampled velocity field.\n\n• A microsolver that defragments geometry.\n\n• A microsolver that creates a signed distance field out of geometry.\n\n• A micro solver that transfers meta data on simulation objects to and from geometry attributes.\n\n• Blends a set of SOP volumes into a set of new collision fields for the creation of a guided simulation.\n\n• A microsolver that copies Impact data onto point attributes.\n\n• Integrates the shallow water equations.\n\n• A microsolver that applies forces to a particle fluid system.\n\n• A microsolver that repeatedly solves its inputs at different rates.\n\n• A microsolver that solves its subsolvers at a regular interval.\n\n• A microsolver that clamps a field within certain values.\n\n• A microsolver that keeps particles within a box.\n\n• A microsolver that combines multiple fields or attributes together.\n\n• A microsolver that adaptively sharpens a field.\n\n• A microsolver that looksup field values according to a position field.\n\n• A microsolver that rebuilds fields to match in size and resolution to a reference field.\n\n• A microsolver that arbitrary simulation data between multiple machines.\n\n• A microsolver that exchanges boundary data between multiple machines.\n\n• A microsolver that exchanges boundary data between multiple machines.\n\n• A microsolver that balances slices data between multiple machines.\n\n• A microsolver that exchanges boundary data between multiple machines.\n\n• Executes the provided kernel with the given parameters.\n\n• Uses OpenCL to perform boundary enforcement for fluid fields.\n\n• Uses OpenCL to import VDB data from source geometry into simulation fields.\n\n• A microsolver that counts the number of particles in each voxel of a field.\n\n• A microsolver that moves particles to lie along a certain isosurface of an SDF.\n\n• A microsolver that separates adjacent particles by adjusting their point positions..\n\n• A microsolver that copies a particle system’s point attribute into a field.\n\n• A microsolver that converts a particle system into a signed distance field.\n\n• A microsolver that removes the divergent components of a velocity field.\n\n• A microsolver that removes the divergent components of a velocity field using an adaptive background grid to increase performance.\n\n• A microsolver that removes the divergent components of a velocity field using a multi-grid method.\n\n• A microsolver that removes the divergent components of a velocity field.\n\n• A microsolver that reduces a field to a single constant field .\n\n• A microsolver that reduces surrounding voxels to a single value.\n\n• A microsolver that reinitializes a signed distance field while preserving the zero isocontour.\n\n• A microsolver that repeatedly solves its input.\n\n• A microsolver that changes the size of fields.\n\n• A microsolver that resizes a fluid to match simulating fluid bounds\n\n• A microsolver that initializes a rest field.\n\n• A microsolver that converts an SDF field to a Fog field.\n\n• A microsolver that computes the forces to treat the fluid simulation as sand rather than fluid.\n\n• A microsolver that creates, deletes and reseeds particles. Tailored to be used in a fluid solver.\n\n• A microsolver that seeds marker particles around the boundary of a surface.\n\n• A microsolver that seeds particles uniformly inside a surface.\n\n• Applies a Shredding Force to the velocity field specified.\n\n• A microsolver that computes slice numbers into an index field.\n\n• Adjusts a fluid velocity field to match collision velocities.\n\n• A microsolver that calculates the forces imparted by a strain field.\n\n• A microsolver that updates the strain field according to the current velocity field.\n\n• A microsolver that substeps input microsolvers.\n\n• A microsolver that snaps a surface onto a collision surface.\n\n• A microsolver that calculates a surface tension force proportional to the curvature of the surface field.\n\n• A microsolver that synchronizes transforms of simulation fields.\n\n• A microsolver that applies a force towards a target object.\n\n• Modifies the temperature of a FLIP over time.\n\n• Applies Turbulence to the specified velocity field.\n\n• Up-scales and/or modifies a smoke, fire, or liquid simulations.\n\n• Scales fluid velocity based on the fluid’s current speed or a control field.\n\n• A microsolver that reorients geometry according to motion of a velocity field.\n\n• A microsolver that applies viscosity to a velocity field.\n\n• A microsolver that seeds flip particles into a new volume region.\n\n• Remaps a field according to a ramp.\n\n• Applies a confinement force on specific bands of sampled energy.\n\n• Applies a vortex confinement force to a velocity field.\n\n• Applies a confinement force on specific bands of sampled energy.\n\n• A microsolver that applies forces to a velocity field or geometry according to vorticle geometry.\n\n• A DOP node that adds the appropriately formatted data to represent vorticles.\n\n• A DOP node that recycles vorticles by moving them to the opposite side of the fluid box when they leave.\n\n• A microsolver that performs a wavelet decomposition of a field.\n\n• A microsolver that applies a wind force.\n\n• Runs CVEX on geometry attributes.\n\n• Runs a VEX snippet to modify attribute values.\n\n• Applies a gravity-like force to objects.\n\n• Creates a ground plane suitable for RBD or cloth simulations.\n\n• Creates simulation object groups.\n\n• Defines a constraint relationship that must always be satisfied.\n\n• Attaches the appropriate data for Hybrid Objects to an object.\n\n• Stores filtered information about impacts on an RBD object. The shelf tool has no effect in the viewport, it just sets up nodes in the network to record the impact data.\n\n• Applies an impulse to an object.\n\n• Creates an index field.\n\n• Visualizes an index field.\n\n• Creates DOP Objects according to instance attributes\n\n• Marks a simulation object as intangible or tangible.\n\n• Stores the name of the scene level object source for this DOP object.\n\n• Apply forces on objects using a force field defined by metaballs.\n\n• Creates a matrix field.\n\n• Visualizes a matrix field.\n\n• Merges multiple streams of objects or data into a single stream.\n\n• Modifies or creates options on arbitrary data.\n\n• Defines an object’s position, orientation, linear velocity, and angular velocity.\n\n• Unified visualization of multiple fields.\n\n• A DOP that transfers arbitrary simulation data between multiple machines.\n\n• Does nothing.\n\n• Creates position information from an object’s transform.\n\n• Uses vortex filaments to move particles.\n\n• A POP node that uses velocity volumes to move particles.\n\n• A POP node that attracts particles to positions and geometry.\n\n• A POP node that copies volume values into a particle attribute.\n\n• A POP node that resets the stopped attribute on particles, waking them up.\n\n• A POP node that applies a force around an axis.\n\n• A POP node that reacts to collisions.\n\n• A POP node that detects and reacts to collisions.\n\n• A POP node marks particles to ignore implicit collisions.\n\n• A POP node that colors particles.\n\n• A POP node that creates forces generated from a curve.\n\n• A POP node that applies drag to particles.\n\n• A POP node that applies drag to the spin of particles.\n\n• A POP node that applies a conical fan wind to particles.\n\n• A POP node that creates a simple fireworks system.\n\n• A POP node that floats particles on the surface of a liquid simulation.\n\n• A POP node that applies a flocking algorithm to particles.\n\n• Controls local density by applying forces between nearby particles.\n\n• A POP node that applies forces to particles.\n\n• A POP node that applies sand grain interaction to particles.\n\n• A POP node that groups particles.\n\n• Compute hair separation force using a VDB volume approach.\n\n• A POP node that sets up the instancepath for particles.\n\n• A POP node that applies forces between particles.\n\n• A POP node that kills particles.\n\n• A POP node that limits particles.\n\n• A POP node that applies forces within the particle’s frame.\n\n• A POP solver that generates particles at a point.\n\n• A POP node makes a particle look at a point.\n\n• A POP node that applies forces according to metaballs.\n\n• Converts a regular particle system into a dynamic object capable of interacting correctly with other objects in the DOP environment.\n\n• A POP node that sets various common attributes on particles.\n\n• A POP node that sets attributes based on nearby particles.\n\n• A POP Node that generates particles from incoming particles.\n\n• A POP node that creates a spongy boundary.\n\n• A POP solver updates particles according to their velocities and forces.\n\n• A POP node that generates particles from geometry.\n\n• A POP node that sets the speed limits for particles.\n\n• A POP node that sets the spin of particles..\n\n• A POP node that uses the vorticity of velocity volumes to spin particles.\n\n• A POP node that sets the sprite display for particles.\n\n• Applies force to agents/particles to align them with neighbors.\n\n• Applies anticipatory avoidance force to agents/particles to avoid potential future collisions with other agents/particles.\n\n• Applies forces to agents/particles to bring them closer to their neighbors.\n\n• Applies forces to agents/particles calulated using a VOP network.\n\n• Applies force to agents/particles to avoid potential collisions with static objects.\n\n• Applies force to agents/particles according to directions from a path curve.\n\n• Applies force to agents/particles to move them toward a target position.\n\n• Apply force to agents/particles to move them apart from each other.\n\n• Used internally in the crowd solver to integrate steering forces.\n\n• Constrains agent velocity to only go in a direction within a certain angle range of its current heading, to prevent agents from floating backward.\n\n• Apply forces to agents/particles to create a random motion.\n\n• A POP node that creates a new stream of particles.\n\n• A POP node that applies torque to particles, causing them to spin.\n\n• Runs CVEX on a particle system.\n\n• A POP node that directly changes the velocity of particles.\n\n• A POP node that applies wind to particles.\n\n• Runs a VEX snippet to modify particles.\n\n• Solves a Smoothed Particle Hydrodynamics (SPH) density constraint for fluid particles using OpenCL.\n\n• A microsolver for particle fluid forces\n\n• Visualizes particles.\n\n• Creates simulation object groups based on an expression.\n\n• Defines the base physical parameters of DOP objects.\n\n• Applies a force to an object from a particular location in space.\n\n• Creates position information from a point on some SOP geometry.\n\n• Associates a position and orientation to an object.\n\n• Sets and configures a Pyro solver. This solver can be used to create both fire and smoke.\n\n• Performs a sparse pyro simulation on the given object. This solver can be used to create both fire and smoke.\n\n• Constrains an RBD object to a certain orientation.\n\n• Constrains an RBD object to have a certain orientation, but with a set amount of springiness.\n\n• Automatically freezes RBD Objects that have come to rest\n\n• Attaches the appropriate data for RBD Objects to an object.\n\n• Creates a number of RBD Objects from SOP Geometry. These individual RBD Objects are created from the geometry name attributes.\n\n• Guide Bullet Packed Primitives.\n\n• Constrains an object to two constraints, creating a rotation similar to a hinge or a trapeze bar.\n\n• Creates an RBD Object from SOP Geometry.\n\n• Creates a single DOP object from SOP Geometry that represents a number of RBD Objects.\n\n• Constrains an RBD object a certain distance from the constraint.\n\n• Creates a simulation object at each point of some source geometry, similarly to how the Copy surface node copies geometry onto points.\n\n• Sets and configures a Rigid Body Dynamics solver.\n\n• Constrains an object to remain a certain distance from the constraint, with a set amount of springiness.\n\n• Alters the state information for an RBD Object.\n\n• Serves as the end-point of the simulation network. Has controls for writing out sim files.\n\n• Saves the state of a DOP network simulation into files.\n\n• Saves the state of a DOP network simulation into files.\n\n• Applies forces to an object according to the difference between two reference frames.\n\n• Sets and configures a Rigid Body Dynamics solver.\n\n• Attaches the appropriate data for Ripple Objects to an object.\n\n• Creates an object from existing geometry that will be deformed with the ripple solver.\n\n• Animates wave propagation across Ripple Objects.\n\n• Creates a signed distance field representation of a piece of geometry that can be used for collision detection.\n\n• A microsolver that performs general calculations on a pair consisting of a DOP field and a SOP volume/VDB.\n\n• Creates a scalar field from a SOP Volume.\n\n• Creates a vector field from a SOP Volume Primitive.\n\n• Creates a scalar field.\n\n• Visualizes a scalar field.\n\n• Defines the internal seam angle.\n\n• Defines the mass density of a Cloth Object.\n\n• Divides a particle system uniformly into multiple slices along a line.\n\n• Specifies a cutting plane to divide a particle system into two slices for distributed simulations.\n\n• Constrains an object to rotate and translate on a single axis, and limits the rotation and translation on that axis.\n\n• Attaches the appropriate data for Smoke Objects to an object.\n\n• Creates an Smoke Object from SOP Geometry.\n\n• Creates an empty smoke object for a pyro simulation.\n\n• Sets and configures a Smoke solver. This is a slightly lower-level solver that is the basis for the Pyro solver.\n\n• Performs a sparse smoke simulation on the given object. This is a slightly lower-level solver that is the basis for the sparse pyro solver.\n\n• Constrains a set of points on a soft body object to a certain position using a hard constraint or soft constraint.\n\n• Constrains a point on a soft body object to a certain position.\n\n• Constrains a point on a soft body to a certain position, with a set amount of springiness.\n\n• Defines how a soft body object responds to collisions.\n\n• Defines how a Soft Body Object responds to collisions.\n\n• Defines how a Soft Body Object responds to collisions.\n\n• Defines how a Soft Body Object responds to collisions.\n\n• Allows the user to import the rest state from a SOP node.\n\n• Sets and configures a Soft Body solver.\n\n• Defines the strengths of the soft constraint on a soft body object.\n\n• Controls the anisotropic behavior of a Solid Object.\n\n• Attaches the appropriate data for Solid Objects to an object.\n\n• Defines the mass density of a Solid Object.\n\n• Defines how a Solid Object reacts to strain and change of volume.\n\n• This builds a tree of spheres producing bounding information for an edge cloud.\n\n• This builds a tree of spheres producing bounding information for a point cloud.\n\n• Splits an incoming object stream into as many as four output streams.\n\n• Creates a Static Object from SOP Geometry.\n\n• Allows you to inspect the behavior of a static object in the viewport.\n\n• Control the thickness of the object that collides with cloth.\n\n• Passes one of the input object or data streams to the output.\n\n• Creates a Terrain Object from SOP Geometry.\n\n• Defines a way of resolving collisions between two rigid bodies.\n\n• Applies a uniform force and torque to objects.\n\n• Applies forces on the objects according to a VOP network.\n\n• Creates a vector field.\n\n• Visualizes a vector field.\n\n• Modifies common Vellum constraint properties during a Vellum solve.\n\n• Microsolver to create Vellum constraints during a simulation.\n\n• Creates a DOP Object for use with the Vellum Solver.\n\n• Blends the current rest values of constraints with a rest state calculated from the current simulation or external geometry.\n\n• Sets and configures a Vellum solver.\n\n• A Vellum node that creates Vellum patches.\n\n• Applies an impulse to an object.\n\n• A microsolver to create soft references to visualizers on itself.\n\n• Uses instance points to source packed source sets into DOP fields.\n\n• Imports SOP source geometry into smoke, pyro, and FLIP simulations.\n\n• Defines a way of resolving collisions involving two rigid bodies with volume.\n\n• Attaches the appropriate data to make an object fractureable by the Voronoi Fracture Solver\n\n• Defines the parameters for dynamic fracturing using the Voronoi Fracture Solver\n\n• Dynamically fractures objects based on data from the Voronoi Fracture Configure Object DOP\n\n• Applies a vortex-like force on objects, causing them to orbit about an axis along a circular path.\n\n• Creates a Whitewater Object that holds data for a whitewater simulation.\n\n• Sets and configures a Whitewater Solver.\n\n• Applies forces to resist the current motion of objects relative to a turbulent wind.\n\n• Constrains a wire point’s orientation to a certain direction.\n\n• Constrains a wire point’s orientation to a certain direction, with a set amount of springiness.\n\n• Attaches the appropriate data for Wire Objects to an object.\n\n• Defines the elasticity of a wire object.\n\n• Constraints a wire point to a certain position and direction.\n\n• Creates a Wire Object from SOP Geometry.\n\n• Defines the physical parameters of a wire object.\n\n• Defines the plasticity of a wire object.\n\n• Sets and configures a Wire solver.\n\n• Defines a way of resolving collisions involving a wire object and DOPs objects with volumetric representations.\n\n• Defines a way of resolving collisions between two wires." ]

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[ "1.  If 'P * Q' means 'P is the daughter of Q'; 'P + Q' means 'P is the father of Q'; 'P % Q' means ' P is the mother of Q' and 'P - Q' means 'P is the brother of Q', then in the expression A % B + C - E * F, how is A related to F ?\n\nMother\nAunt\nDaughter-in-law\nNone of the above\n\n```Answer\n\nAnswer: Option  D Explanation:A % B + C - E * F means A is the mother of B, who is the father of C, who is the brother of E,\nwho is the daughter of F. Thus, C and E are the children of B and F. Since B is the father,\nso F is the mother of C and e i.e. F is the wife of B. A is the mother of F's husband i.e.\nA is the mother-in-law of F. ```\n\n2.  A and B are married couple. X and Y are brothers. X is the brother of A. How is Y related to B ?\n\nBrother-in-law\nBrother\nCousin\nNone of the above\n\n```Answer\n\nAnswer: Option  A Explanation:A and B are husband and wife. Since X and Y are brothers and X is the brother of A,\nY is also the brother of A. Thus, Y is the brother-in-law of B. ```\n\n3.  A is the son of B. C, B's sister, has a son D and a daughter E. F is the maternal uncle of D. How is A related to D ?\n\nCousin\nNephew\nUncle\nBrother\n\n```Answer\n\nAnswer: Option  A Explanation:A is the son of B and D is the son of the sister of B. So, A is the cousin of D. ```\n\n4.  Deepak has a brother Anil. Deepak is the son of Prem. Bimal is Prem's father. In terms of relationship, what is Anil of Bimal ?\n\nSon\nGrandson\nBrother\nGrandfather\n\n```Answer\n\nAnswer: Option  B Explanation:Anil is the brother of Deepak and Deepak is the son of Prem. So, Anil is the son of Prem.\nNow, Bimal is the father of Prem. Thus, Anil is the grandson of Bimal. ```\n\nReport\n\n5.  When Anuj saw Manish, he recalled, \"he is the son of the father of my daughter's mother.\" Who is Manish to Anuj ?\n\nBrother-in-law\nBrother\nCousin\nUncle\n\n```Answer\n\nAnswer: Option  A Explanation:Anuj's daughter's mother -Anuj's wife; Anuj's wife's father - Anuj's father-in-law;\nFather-in-law's son - Anuj's brother-in-law. So, Manish is Anuj's brother-in-law. ```\n\nReport" ]

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[ "Home | Menu | Get Involved | Contact webmaster", null, "", null, "", null, "", null, "", null, "0 / 12\n\n# Number 1581\n\none thousand five hundred eighty one\n\n### Properties of the number 1581\n\n Factorization 3 * 17 * 31 Divisors 1, 3, 17, 31, 51, 93, 527, 1581 Count of divisors 8 Sum of divisors 2304 Previous integer 1580 Next integer 1582 Is prime? NO Previous prime 1579 Next prime 1583 1581st prime 13313 Is a Fibonacci number? NO Is a Bell number? NO Is a Catalan number? NO Is a factorial? NO Is a regular number? NO Is a perfect number? NO Polygonal number (s < 11)? NO Binary 11000101101 Octal 3055 Duodecimal ab9 Hexadecimal 62d Square 2499561 Square root 39.761790704142 Natural logarithm 7.3658128372095 Decimal logarithm 3.1989318699322 Sine -0.70249360443004 Cosine -0.71169005594774 Tangent 0.98707801037707\nNumber 1581 is pronounced one thousand five hundred eighty one. Number 1581 is a composite number. Factors of 1581 are 3 * 17 * 31. Number 1581 has 8 divisors: 1, 3, 17, 31, 51, 93, 527, 1581. Sum of the divisors is 2304. Number 1581 is not a Fibonacci number. It is not a Bell number. Number 1581 is not a Catalan number. Number 1581 is not a regular number (Hamming number). It is a not factorial of any number. Number 1581 is a deficient number and therefore is not a perfect number. Binary numeral for number 1581 is 11000101101. Octal numeral is 3055. Duodecimal value is ab9. Hexadecimal representation is 62d. Square of the number 1581 is 2499561. Square root of the number 1581 is 39.761790704142. Natural logarithm of 1581 is 7.3658128372095 Decimal logarithm of the number 1581 is 3.1989318699322 Sine of 1581 is -0.70249360443004. Cosine of the number 1581 is -0.71169005594774. Tangent of the number 1581 is 0.98707801037707\n\n### Number properties\n\n0 / 12\nExamples: 3628800, 9876543211, 12586269025\nMath tools for your website\nChoose language: Deutsch English Español Français Italiano Nederlands Polski Português Русский 中文 日本語 한국어\nNumber Empire - powerful math tools for everyone | Contact webmaster\nBy using this website, you signify your acceptance of Terms and Conditions and Privacy Policy.\n\n© 2021 numberempire.com All rights reserved" ]

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[ "• 目前尚無任何訓練課程!!\n\n### 聯絡我們\n\nEmail:", null, "SCIENTIST 3\n\nParameter fitting for model equations", null, "", null, "", null, "", null, "", null, "", null, "Overview\nIt is a general mathematical modeling and data analysis application. It is specifically designed to fit model equations to experimental data. Other programs focus on technical graphics, symbolic manipulation, matrix operations or worksheets for engineering calculations. Scientist incorporates all these elements, but its primary function is fitting equations to experimental data. Scientist can fit almost any mathematical model from the simplest linear functions to complex systems of differential equations, non-linear algebraic equations or models expressed as Laplace transforms. If you need to fit experimental data to mathematical models, you won't find a better tool than Scientist for Windows! Libraries of mathematical models for Chemical Kinetics, Diffusion and Pharmacokinetics can be purchased separately." ]

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[ "# What is PS in scientific notation?\n\nA picosecond is a unit of time that is equal to one trillionth of a second and is notated with ”ps. ” In scientific notation, it is equal to 1 second…\n\n## How many Zeptoseconds are in a second?\n\nA zeptosecond is a trillionth of a billionth of a second, or a decimal point followed by 20 zeroes and a 1. Previously, researchers had dipped into the realm of zeptoseconds; in 2016, researchers reporting in the journal Nature Physics used lasers to measure time in increments down to 850 zeptoseconds.\n\n## What is the decimal fraction of a second in a picosecond PS?\n\nA picosecond is an SI unit of time equal to 10−12 or 1⁄1 000 000 000 000 (one trillionth) of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000 001 seconds. A picosecond is to one second as one second is to approximately 31,689 years.\n\n## How do you convert Mhz to Hz?\n\nTo convert a megahertz measurement to a hertz measurement, multiply the frequency by the conversion ratio. The frequency in hertz is equal to the megahertz multiplied by 1,000,000.\n\n## What is faster than a zeptosecond?\n\nThe only unit of time shorter than a zeptosecond is a yoctosecond, and Planck time. A yoctosecond (ys) is a septillionth of a second. Divide the minuscule Planck length by the speed of light (which is pretty big) and you get a really tiny unit of time – the Planck time!\n\n## What is a zeptosecond used for?\n\nA zeptosecond is one trillionth of a billionth of a second It represent one trillionth of a billionth of a second (10-21 seconds). Physicists from Goethe University Frankfurt used this measurement to record how long it takes for a photon to cross a hydrogen molecule – approximately 247 zeptoseconds.\n\n## How long is a Yottasecond?\n\nThe yottasecond (Ys) is a unit of time in the International System of Units defined as 10^24 seconds using the SI prefix system. The unit is equal to 31.7 quadrillion years, but the universe is only 13.8 billion years old, meaning the age of the universe is not yet a yottasecond old.\n\n## How many Megaseconds are in a second?\n\nmegaseconds to second conversion Conversion number between megaseconds [Ms] and second [s] is 1000000.\n\n## What is the meaning of 1E10?\n\nIf it is scientific notation, the easiest way to think of it is the ‘E’ stands for ‘times 10 raised to the … power’, so this would be 1 times 10 raised to the 10th power (or 1 followed by 10 zeros) Thus 1E10 is 10,000,000,000.\n\n## What is nano and pico second?\n\nA nanosecond (ns) is an SI unit of time equal to one billionth of a second, that is, 1⁄1 000 000 000 of a second, or 10−9 seconds. The term combines the prefix nano- with the basic unit for one-sixtieth of a minute. A nanosecond is equal to 1000 picoseconds or 1⁄1000 microsecond.\n\n## Which is faster a nanosecond or picosecond?\n\nPicosecond is one trillionth of a second. Nanosecond is one billionth of a second. Microsecond is one millionth of a second.\n\n## What is one trillionth of a second called?\n\nWhat exactly is a picosecond? It is one trillionth of a second. To make it look cleaner, scientists and researchers usually write a picosecond like this: 10-12. Another way of writing that is 0.000000000001 of a second. That’s fast!\n\n## How do you find megahertz?\n\nCheck the megahertz figure listed by the side of the Processor entry on the System page. The page also displays other information about the installed CPU, including the manufacturer and model name.\n\n## How fast is a yoctosecond?\n\nA yoctosecond (ys) is a septillionth of a second or 10–24 s*. Yocto comes from the Latin/Greek word octo/οκτώ, meaning “eight”, because it is equal to 1000−8. Yocto is the smallest official SI prefix. A yoctosecond is the shortest lifetime measured, so far.\n\n## How fast is Planck time?\n\nThe Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning.\n\n## What is the smallest second?\n\nScientists have measured the shortest unit of time ever: the time it takes a light particle to cross a hydrogen molecule. That time, for the record, is 247 zeptoseconds. A zeptosecond is a trillionth of a billionth of a second, or a decimal point followed by 20 zeroes and a 1." ]

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[ "", null, "", null, "# “困难”的同义词\n\n“困难”的另一个词是什么?列出英语中“difficult”的不同表达方式，并给出含义和例子。学习这些同义词对于“难”帮助增加你的词汇提高你的英语写作能力。\n\n## 困难的同义词\n\n### 难的定义和例子\n\n• 每天和玛丽一起工作非常困难，因为她的性格和我完全相反。\n• 每个人都必须面对父母总会在某一时刻去世这一不可避免的困难。\n• 当我还是学生的时候，数学是我最难的科目。\n\n### “困难”的其他单词\n\n\" Difficult \"的同义词。\n\n• 摘要\n• 深奥的\n• 模棱两可的\n• 艰巨的\n• 艰难的\n• 复杂的\n• 复杂的\n• 让人困惑\n• 令人困惑的\n• 繁重的\n• 复杂的\n• 令人生畏的\n• 要求\n• 艰苦的\n• 难以捉摸的\n• 折磨人的\n• 多毛的\n• 僵化的\n• 棘手的\n• 艰苦的\n• 固执\n• 多刺的\n• 有问题的\n• 惩罚\n• 刚性\n• 岩石\n• 粗糙的\n• 崎岖的\n• 僵硬的\n• 棘手的\n• 曲折的\n\n• 摘要\n• 深奥的\n• 模棱两可的\n• 雄心勃勃的\n• 艰巨的\n• 尴尬的\n• 费力的\n• 令人困惑的\n• 繁重的\n• 拜占庭式的\n• 具有挑战性的\n• 复杂的\n• 复杂的\n• 复合\n• 让人困惑\n• 复杂的\n• 至关重要的\n• 残酷的\n• 错综复杂的\n• 令人生畏的\n• 精致的\n• 要求\n• 可怕的\n• 痛苦的\n• 令人不安的\n• 容易\n• 精心制作的\n• 难以捉摸的\n• 深奥的\n• 严格的\n• 精疲力尽\n• 挑剔的\n• 过分讲究的\n• 强大的\n• 挑剔的\n• 棘手的\n• 坟墓\n• 严重\n• 折磨人的\n• 丑的\n• 多毛的\n• 很难理解\n• 困难\n• 最严重的\n• 精明的\n• 严厉的\n• 高额\n• 伤害\n• 不可能的\n• 解不开的\n• 僵化的\n• 棘手的\n• 错综复杂的\n• 涉及到\n• 棘手的\n• 艰苦的\n• 迷宫一样的\n• 令人讨厌的\n• 不容易\n• 晦涩难懂的\n• 固执\n• 繁重的\n• 吃力的\n• 压迫\n• 痛苦的\n• 特定的\n• 困惑\n• 令人困惑的\n• 不稳定的\n• 多刺的\n• 问题\n• 有问题的\n• 有疑问的\n• 深刻的\n• 惩罚\n• 刚性\n• 岩石\n• 粗糙的\n• 粗鲁的\n• 崎岖的\n• 悲伤的\n• 敏感的\n• 严重的\n• 严重的\n• 复杂的\n• 黏糊糊的\n• 僵硬的\n• 艰苦的\n• 有压力的\n• 顽固的\n• 征税\n• 泪流满面的\n• 棘手的\n• 辛苦的\n• 辛苦的\n• 曲折的\n• 艰难的\n• 棘手的\n• 陷入困境的\n• 麻烦\n• 尝试\n• 难以忍受的\n• 难以管理\n• 不愉快的\n• 艰苦的\n• 有分量的\n\n### “难的”同义词例句\n\n• 例子如真与美摘要概念。\n\n• 例子如你的话有点太夸张了深奥的\n\n• 例子如他给了我一张模棱两可的的答案。\n\n• 例子如她承担了艰巨的监督选举的任务。\n\n• 例子这是一个艰难的决定。\n\n• 例子汤姆的解释也是如此复杂的\n\n• 例子:一个复杂的下水道系统在城市地下运行。\n\n• 例子:所有这些信息都可以让人困惑给用户。\n\n• 例子如他提出了一个令人困惑的的问题。\n\n• 例子如新规定将会是繁重的为小型企业。\n\n• 例子如他的语法解释糟透了复杂的\n\n• 例子如独自环游世界是一件很困难的事令人生畏的的前景。\n\n• 例子如他找到了严谨it’这也是这次旅行的乐趣要求\n\n• 例子例如医生建议肯避免艰苦的锻炼。\n\n• 例子如她借此得到了采访机会难以捉摸的男人。\n\n• 例子如他还必须着手于一项折磨人的长期改革进程。\n\n• 例子在结冰的路上开车很漂亮多毛的\n\n• 例子例开一家商店很容易，但是让它一直开着。\n\n• 例子如他有一个今年的教学负荷。\n\n• 例子如这种新塑料完全是僵化的\n\n• 例子例如她遇到了很多人棘手的问题。\n\n• 例子:他们有艰苦的砍掉这棵大树的任务。\n\n• 例子:他是固执并且坚决不会放弃。\n\n• 例子如他的皮肤很痛多刺的\n\n• 例子我们业务的未来是有问题的。\n\n• 例子他给自己定了一个惩罚的会议日程。\n\n• 例子如她的脸刚性与恐惧。\n\n• 例子如他们匆匆穿过草皮岩石地面。\n\n• 例子如他们的汽车沿著街道颠簸而行粗糙的山路。\n\n• 例子如这里的乡村景色非常好崎岖的\n\n• 例子:我觉得僵硬的经过长时间的\n\n• 例子如年轻的船长正在考虑一个棘手的问题。\n\n• 例子如他拿了一张曲折的穿过后街的路线。\n\n## “困难”的另一个词", null, "", null, "0评论\n\n0\n\nx" ]

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[ "#", null, "Examples for the unitary transformation of quantum causal models\n\n+ 1 like - 0 dislike\n346 views\n\nThis is a question related to a quantum causal model suggested by Allen et. al (PRX 7, 031021, 2017) and extended by Barrett et. al (arXiv:1906.10726), which is a quantization of Reichenbach's common cause principle and causal models.\n\nFor the classical case of Reichenbach's principle, if X is a complete common cause of Y and Z, then the conditional independence is denoted as   $P(YZ|X) = P(Y|X)P(Z|X)$. The quantum version of the conditional independence is given by $\\rho_{YZ|X} =\\rho_{Y|X}\\rho_{Z|X}$, where  $\\rho_{YZ|X}$  is the Choi-Jamiolkowski state of the quantum channel $\\mathcal{E}_{YZ|X}$, etc.\n\nAccording to Theorem 3 of PRX (2017), the quantum conditional independence   $\\rho_{YZ|X} =\\rho_{Y|X}\\rho_{Z|X}$ holds iff $\\mathcal{H}_{X}$ can be decomposed as  $\\mathcal{H}_{X} = \\oplus_{i}\\mathcal{H}_{X^i_L}\\otimes \\mathcal{H}_{X^i_R}$ and $\\rho_{YZ|X} = \\sum_{i}(\\rho_{Y| X_i^L}\\otimes \\rho_{Y| X_i^R})$.\n\nThe most fundamental and simple case seems unitary transformations, e.g.  a unitary trasformation from A & B to C & D (A,B,C, & D are quantum systems). I may use the result of Theorem 3 to show that $\\rho_{CD|AB} = \\rho_{C|AB}\\rho_{D|AB}$  holds for the unitary transformation. However, even if the authors said that it can be directly verified, I cannot find a specific way of decomposing $\\mathcal{H}_{CD|AB}$ to as $\\oplus_{i}\\mathcal{H}_{AB^i_L}\\otimes \\mathcal{H}_{AB^i_R}$ to show this.\n\nCan anybody teach me how to decompose such Hilbert spaces in general to prove the quantum conditional independence of unitary transformations? Thanks in advance.\n\n Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the \"link\" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\\varnothing$ in the following word:p$\\hbar$ysicsOverflo$\\varnothing$Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register." ]

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[ "# Minimum swap required to convert binary tree to binary search tree\n\nGiven the array representation of Complete Binary Tree i.e, if index i is the parent, index 2*i + 1 is the left child and index 2*i + 2 is the right child. The task is to find the minimum number of swap required to convert it into Binary Search Tree.\n\nExamples:\n\n```Input : arr[] = { 5, 6, 7, 8, 9, 10, 11 }\nOutput : 3\nBinary tree of the given array:", null, "Swap 1: Swap node 8 with node 5.\nSwap 2: Swap node 9 with node 10.\nSwap 3: Swap node 10 with node 7.", null, "So, minimum 3 swaps are required.\n\nInput : arr[] = { 1, 2, 3 }\nOutput : 1\nBinary tree of the given array:", null, "After swapping node 1 with node 2.", null, "So, only 1 swap required.\n```\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nThe idea is to use the fact that inorder traversal of Binary Search Tree is in increasing order of their value.\nSo, find the inorder traversal of the Binary Tree and store it in the array and try to sort the array. The minimum number of swap required to get the array sorted will be the answer. Please refer below post to find minimum number of swaps required to get the array sorted.\n\nMinimum number of swaps required to sort an array\n\nTime Complexity: O(n log n).\n\n `// C++ program for Minimum swap required ` `// to convert binary tree to binary search tree ` `#include ` `using` `namespace` `std; ` ` `  `// Inorder Traversal of Binary Tree ` `void` `inorder(``int` `a[], std::vector<``int``> &v,  ` `                        ``int` `n, ``int` `index) ` `{ ` `    ``// if index is greater or equal to vector size ` `    ``if``(index >= n) ` `        ``return``; ` `    ``inorder(a, v, n, 2 * index + 1); ` `     `  `    ``// push elements in vector ` `    ``v.push_back(a[index]); ` `    ``inorder(a, v, n, 2 * index + 2); ` `} ` ` `  `// Function to find minimum swaps to sort an array ` `int` `minSwaps(std::vector<``int``> &v) ` `{ ` `    ``std::vector > t(v.size()); ` `    ``int` `ans = 0; ` `    ``for``(``int` `i = 0; i < v.size(); i++) ` `        ``t[i].first = v[i], t[i].second = i; ` `     `  `    ``sort(t.begin(), t.end()); ` `    ``for``(``int` `i = 0; i < t.size(); i++) ` `    ``{ ` `        ``// second element is equal to i ` `        ``if``(i == t[i].second) ` `            ``continue``; ` `        ``else` `        ``{ ` `            ``// swaping of elements ` `            ``swap(t[i].first, t[t[i].second].first); ` `            ``swap(t[i].second, t[t[i].second].second); ` `        ``} ` `         `  `        ``// Second is not equal to i ` `        ``if``(i != t[i].second) ` `            ``--i; ` `        ``ans++; ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a[] = { 5, 6, 7, 8, 9, 10, 11 }; ` `    ``int` `n = ``sizeof``(a) / ``sizeof``(a); ` `    ``std::vector<``int``> v; ` `    ``inorder(a, v, n, 0); ` `    ``cout << minSwaps(v) << endl; ` `} ` ` `  `// This code is contributed by code_freak `\n\nOutput:\n\n`3`\n\nExercise: Can we extend this to normal binary tree, i.e., a binary tree represented using left and right pointers, and not necessarily complete?\n\nPlease write comments if you find anything incorrect, or you want to share more information about the topic discussed above.\n\nThis article is attributed to GeeksforGeeks.org\n\n## tags:\n\nSorting Tree Sorting Tree\n\ncode\n\nload comments" ]

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[ "# Enumerating ways to decompose an integer into the sum of two squares\n\nThe well known \"Sum of Squares Function\" tells you the number of ways you can represent an integer as the sum of two squares. See the link for details, but it is based on counting the factors of the number N into powers of 2, powers of primes = 1 mod 4 and powers of primes = 3 mod 4.\n\nGiven such a factorization, it's easy to find the number of ways to decompose N into two squares. But how do you efficiently enumerate the decompositions?\n\nSo for example, given N=2*5*5*13*13=8450 , I'd like to generate the four pairs:\n\n13*13+91*91=8450\n\n23*23+89*89=8450\n\n35*35+85*85=8450\n\n47*47+79*79=8450\n\nThe obvious algorithm (I used for the above example) is to simply take i=1,2,3,...,$\\sqrt{N/2}$ and test if (N-i*i) is a square. But that can be expensive for large N. Is there a way to generate the pairs more efficiently? I already have the factorization of N, which may be useful.\n\n(You can instead iterate between $i=\\sqrt{N/2}$ and $\\sqrt{N}$ but that's just a constant savings, it's still $O(\\sqrt N)$.\n\n• The prime factorization of N tells you its prime factorization over the Gaussian integers (en.wikipedia.org/wiki/Gaussian_integer), and then you're just counting all the ways to split N into the product of two Gaussian integers (up to units). – Qiaochu Yuan Jun 26 '10 at 22:07\n• (\"Subfactors\" refers to a completely different mathematical concept, so I have removed the tag.) – Qiaochu Yuan Jun 26 '10 at 22:08\n• If one can obtain two essentially distinct representations: $n=a^2+b^2=c^2+d^2$, then one can factor $n$ nontrivially. Just take the gcd of $a+bi$ and $c+di$ in the Gaussian integers, and take the norm. The moral: it cannot be much harder to factor $n$ first and build up from representations of primes as sums of two squares as suggested by Gerry. – Robin Chapman Jun 27 '10 at 8:01\n• Note also $65^2+65^2$ – Mark Bennet Feb 17 '18 at 8:07\n\n## 5 Answers\n\nThe factorization of $N$ is useful, since $$(a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ad-bc)^2$$ There are good algorithms for expressing a prime as a sum of two squares or, what amounts to the same thing, finding a square root of minus one modulo $p$. See, e.g., http://www.emis.de/journals/AMEN/2005/030308-1.pdf\n\nEdit: Perhaps I should add a word about solving $x^2\\equiv-1\\pmod p$. If $a$ is a quadratic non-residue (mod $p$) then we can take $x\\equiv a^{(p-1)/4}\\pmod p$. In practice, you can find a quadratic non-residue pretty quickly by just trying small numbers in turn, or trying (pseudo-)random numbers.\n\n• So what would the algorithm itself be? It sounds like I should enumerate all possible $xy=N$ factorings (both prime and composite). Then for each, decompose $x$ into each possible $a^2+b^2$ and each y into each possible $c^2+d^2$, and use the above formula to find one answer to the top level N decomposition. Finally after iterating over all such factors, and over the two inner loops of all decompositions of those factors, I should take all the answers and sort them and eliminate duplicates. Is this the right algorithm or is it doing unnecessary work? – MathMonkey Jun 27 '10 at 2:50\n• And finally, is it guaranteed that the above algorithm will actually find ALL of the top level N decompositions? The formula just tells us that given one factoring we get one sum of two squares decompositions, but does that mean that all factorings will give us all decompositions? – MathMonkey Jun 27 '10 at 2:53\n• I think it will be easier for you to learn by doing than by me explaining (since I'm not so hot at explaining). Take an example, say, $N=5\\times13\\times17$, and use the expressions $5=2^2+1^2$, $13=3^2+2^2$, $17=4^2+1^2$, and see what you have to do to get all 4 distinct representations. Qiaochu Yuan's remark may help guide you; in effect, we're finding all 4 values of $a+bi=(2+i)(3\\pm2i)(4\\pm i)$ where $i$ is the square root of minus one, and our representations are $N=a^2+b^2$. Yes, this is guaranteed to get everything, and without duplicates if you set it up right. Try it and see. – Gerry Myerson Jun 27 '10 at 6:12\n• Yes, all expressoins as a sum of squares occur in this way. This is an immediate consequence of unique factorization in $\\mathbb{Z}[i]$. – David E Speyer Jun 27 '10 at 14:32\n• @pts, why not experiment a bit, and see for yourself? $5=2^1+1^1$, $13^2=12^2+5^2=13^2+0^2$, mix 'n' match, see what happens? Or, $(2\\pm i)(3\\pm2i)(3+2i)$. – Gerry Myerson Dec 7 '14 at 5:43\n\nThis is the simplest case of the Hardy-Muskat-Williams algorithm. Anyway, here is a link to a 1995 paper by Kenneth S. Williams, http://www.mathstat.carleton.ca/~williams/papers/pdf/202.pdf and to the original HMW paper http://www.ams.org/journals/mcom/1990-55-191/S0025-5718-1990-1023762-3/S0025-5718-1990-1023762-3.pdf .\n\nAs I'm not sure you are aware of these details, let me point out that if $$4^k \\;| \\; \\; x^2 + y^2$$ then $2^k \\; | \\; x$ and $2^k \\; | \\; y.$ That is, you might as well divide your target by powers of 4 before doing anything difficult. Then after you are finished multiply $x,y$ by the appropriate power of $2.$\n\nThis is very similar. If there is a prime $$q \\equiv 3 \\pmod 4$$ and $q | n,$ then keep dividing the target by powers of $q^2$ until it is no longer divisible by $q^2.$ If the remaining number is divisible by $q$ there is actually no representation at all. But if $$q^{2k} \\;\\parallel \\; \\; x^2 + y^2$$ then $q^k \\; | x$ and $q^k \\; | y.$ The notation $q^{2k} \\;\\parallel \\; \\; x^2 + y^2$ means $q^{2k} \\; | \\; \\; x^2 + y^2$ but it is not true that $q^{2k +1} \\; | \\; \\; x^2 + y^2$\n\nWell, that is enough caution. What you really need to know is expressing primes $$p \\equiv 1 \\pmod 4$$ and indeed $p^m,$ which is not much more difficult. Once you can do that, combine my notes with all possible ways of applying Gerry's multiplication formula (by changing $\\pm$ signs and order),\n\n(This elaborates on Gerry's answer.)\n\nThis article describes how to solve the $p=x^2+y^2$ equation quickly if $p\\equiv 1$ mod 4 and $p$ is a prime.\n\nJohn Brillhart: Note on representing a prime as a sum of two squares\n\nIt also explains how $x^2\\equiv-1$ mod $p$ can be solved.\n\nAnother point of view, which might be easier from an algorithmic point of view (in my opinion), is to look at the decomposition $$n = a^2+b^2$$ using complex numbers $$n = (a+bi)(a-bi)$$. Suppose you know how to find the solutions $$a,b$$ when $$n$$ is prime. Then note that the identity $$(a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ad-bc)^2$$ can be seen as the equality of the product of modules of two complex numbers.\n\nIn order to find all possible decompositions of a number $$n$$ into a sum of squares just write the factorization of $$n$$ in $$\\Bbb{Z}[i]$$: $$n = \\prod (a_j+ib_j)$$ and note that in this product every factor comes with its conjugate. First, ignore the powers of $$2$$ and the primes of the form $$4k+3$$. Now, in order to find all factorizations, just split all factors into two columns with conjugate pairs being on different columns. Doing this, when taking the product on each column we'll get a pair of conjugate numbers whose product equals to $$n$$, so we find a solution of the representation $$n=a^2+b^2$$. The number of ways to split the factors in the two columns with conjugate pairs on different sides will be equal the number of divisors of $$n$$ in $$\\Bbb{Z}[i]$$ (divided by 4, since you can multiply factors by $$1,-1,i,-i$$) so all factors will be generated.\n\nIf $$n$$ contains primes of the forms $$4k+3$$ or powers of $$2$$ look at Will Jagy's answer. Note that if you reduce all powers of $$4$$ and you still have a $$2$$ left in $$n$$ you can write $$2 = (1+i)(1-i)$$ and split this on different sides of the two columns.\n\nPutting everything together, here is how you count number of ways to decompose $n$ into sum of two squares.\n\nFor this we are gonna count including trivial representation $0^2+a^2$ for square numbers. (To get rid of it, you may subtract $1$ if the number is a perfect square.)\n\n1. Divide the number by highest power of $4$ in it. If the number is a power of $4$, return $1$.\n\n2. Decompose what remains into prime factors.\n\na. If there is a prime factor of the form $4n+3$ with odd power, return $0$.\n\nb. Discard all prime factors form $4n+3$ with even power.\n\n3. Now you have all prime factors of the form $4n+1$, and possibly a $2$ hanging around in the decomposition. Let's say you have $2^{n_0}\\prod_{k=1}^m p_k^{n_k}$ with $p_k\\equiv1\\mod 4$, and $n_0$ being either $0$ or $1$.\n\n4. Then number of ways $n$ can be decomposed in sum of square of pairs is $\\left\\lceil\\frac{\\prod_{k=1}^m (n_k+1)}{2}\\right\\rceil$.\n\nIf you want to actually enumerate instead of count, you will need two things, 1) To be keep track of powers you discarded and 2) To be able to extract root of $-1$ modulo $p$, and use it to factorize $4n+1$ into a gaussian integer and its conjugate. It's just a bit more of work but isn't difficult - I wrote the code based on the discussion here, and some papers referred here, it works pretty well!\n\n• This is classical and can be found in many textbooks. See e.g. mathworld.wolfram.com/SumofSquaresFunction.html – GH from MO May 12 '15 at 15:54\n• As you are counting decompositions of the form $0^2+a^2$, shouldn't a power of 4 return 1, not 0? – Gerry Myerson May 12 '15 at 23:17\n• Gerry - you are right! Corrected it. Anyone looking for the enumeration algorithm, it will be clear at once if you see how the counting formula works. If you need it I can share my Python code. – KalEl May 14 '15 at 2:00\n• @KalEl please post the python code. I would like to try this . – john Sep 2 '15 at 3:32\n• @GHfromMO Indeed it is, I just wanted to highlight the fact in a comment, because there is a solution missing from the original post - the correct formula counts it. The question was linked from Math Stackexchange and I didn't want any misconceptions from people following the link. – Mark Bennet Feb 17 '18 at 18:23" ]

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[ "# Miles to Micrometers Conversion\n\nEnter the length in miles below to get the value converted to micrometers.\n\nResults in Micrometers:", null, "1 mi = 1,609,344,000 µm\n\n## How to Convert Miles to Micrometers\n\nTo convert a mile measurement to a micrometer measurement, multiply the length by the conversion ratio.\n\nSince one mile is equal to 1,609,344,000 micrometers, you can use this simple formula to convert:\n\nmicrometers = miles × 1,609,344,000\n\nThe length in micrometers is equal to the miles multiplied by 1,609,344,000.\n\nFor example, here's how to convert 5 miles to micrometers using the formula above.\n5 mi = (5 × 1,609,344,000) = 8,046,720,000 µm\n\n### How Many Micrometers Are in a Mile?\n\nThere are 1,609,344,000 micrometers in a mile, which is why we use this value in the formula above.\n\n1 mi = 1,609,344,000 µm\n\nMiles and micrometers are both units used to measure length. Keep reading to learn more about each unit of measure.\n\n## Miles\n\nThe mile is a linear measurement of length equal to exactly 1,609.344 meters. One mile is also equal to 5,280 feet or 1,760 yards.\n\nThe mile is a US customary and imperial unit of length. Miles can be abbreviated as mi, and are also sometimes abbreviated as m. For example, 1 mile can be written as 1 mi or 1 m.\n\n## Micrometers\n\nOne micrometer is equal to one-millionth (1/1,000,000) of a meter, which is defined as the distance light travels in a vacuum in a 1/299,792,458 second time interval.\n\nThe micrometer, or micrometre, is a multiple of the meter, which is the SI base unit for length. In the metric system, \"micro\" is the prefix for 10-6. A micrometer is sometimes also referred to as a micron. Micrometers can be abbreviated as µm; for example, 1 micrometer can be written as 1 µm.\n\nTo get an idea of the actual physical length of a micrometer, one human hair is 40-50 µm thick, demonstrating how small this unit of measure is.\n\nWe recommend using a ruler or tape measure for measuring length, which can be found at a local retailer or home center. Rulers are available in imperial, metric, or combination with both values, so make sure you get the correct type for your needs.\n\nNeed a ruler? Try our free downloadable and printable rulers, which include both imperial and metric measurements.\n\n## Mile to Micrometer Conversion Table\n\nMile measurements converted to micrometers\nMiles Micrometers\n0.000000001 mi 1.6093 µm\n0.000000002 mi 3.2187 µm\n0.000000003 mi 4.828 µm\n0.000000004 mi 6.4374 µm\n0.000000005 mi 8.0467 µm\n0.000000006 mi 9.6561 µm\n0.000000007 mi 11.27 µm\n0.000000008 mi 12.87 µm\n0.000000009 mi 14.48 µm\n0.0000000001 mi 0.160934 µm\n0.000000001 mi 1.6093 µm\n0.00000001 mi 16.09 µm\n0.0000001 mi 160.93 µm\n0.000001 mi 1,609 µm\n0.00001 mi 16,093 µm\n0.0001 mi 160,934 µm\n0.001 mi 1,609,344 µm\n0.01 mi 16,093,440 µm\n0.1 mi 160,934,400 µm\n1 mi 1,609,344,000 µm" ]

[ null, "data:image/gif;base64,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", null ]

[ "## Classification methods and models\n\nIn classification methods, we are typically interested in using some observed characteristics of a case to predict a binary categorical outcome. This can be extended to a multi-category outcome, but the largest number of applications involve a 1/0 outcome.\n\nBelow, we look at a few classic methods of doing this:\n\n• Logistic regression\n\n• Regression/Partitioning Trees\n\n• Linear Discriminant Functions\n\nThere are other methods that we will examine but these are probably the easiest to understand.\n\nIn these examples, we will use the Demographic and Health Survey Model Data. These are based on the DHS survey, but are publicly available and are used to practice using the DHS data sets, but don’t represent a real country.\n\nIn this example, we will use the outcome of contraceptive choice (modern vs other/none) as our outcome.\n\nlibrary(haven)\ndat<-url(\"https://github.com/coreysparks/data/blob/master/ZZIR62FL.DTA?raw=true\")\nmodel.dat<-read_dta(dat)\n\nHere we recode some of our variables and limit our data to those women who are not currently pregnant and who are sexually active.\n\nlibrary(dplyr)\n##\n## Attaching package: 'dplyr'\n## The following objects are masked from 'package:stats':\n##\n## filter, lag\n## The following objects are masked from 'package:base':\n##\n## intersect, setdiff, setequal, union\nmodel.dat2<-model.dat%>%\nmutate(region = v024,\nmodcontra= as.factor(ifelse(v364 ==1,1, 0)),\nage = v012,\nlivchildren=v218,\neduc = v106,\ncurrpreg=v213,\nknowmodern=ifelse(v301==3, 1, 0),\nage2=v012^2)%>%\nfilter(currpreg==0, v536>0)%>% #notpreg, sex active\ndplyr::select(caseid, region, modcontra,age, age2,livchildren, educ, knowmodern)\nknitr::kable(head(model.dat2))\ncaseid region modcontra age age2 livchildren educ knowmodern\n1 1 2 2 0 30 900 4 0 1\n1 4 2 2 0 42 1764 2 0 1\n1 4 3 2 0 25 625 3 1 1\n1 5 1 2 0 25 625 2 2 1\n1 6 2 2 0 37 1369 2 0 1\n1 6 3 2 0 17 289 0 2 0\n\n### using caret to create training and test sets.\n\nWe use an 80% training fraction\n\nlibrary(caret)\nset.seed(1115)\ntrain<- createDataPartition(y = model.dat2$modcontra , p = .80, list=F) model.dat2train<-model.dat2[train,] ## Warning: The i argument of [() can't be a matrix as of tibble 3.0.0. ## Convert to a vector. ## This warning is displayed once every 8 hours. ## Call lifecycle::last_warnings() to see where this warning was generated. model.dat2test<-model.dat2[-train,] table(model.dat2train$modcontra)\n##\n## 0 1\n## 4036 1409\nprop.table(table(model.dat2train$modcontra)) ## ## 0 1 ## 0.7412305 0.2587695 summary(model.dat2train) ## caseid region modcontra age age2 ## Length:5445 Min. :1.000 0:4036 Min. :15.00 Min. : 225.0 ## Class :character 1st Qu.:1.000 1:1409 1st Qu.:21.00 1st Qu.: 441.0 ## Mode :character Median :2.000 Median :29.00 Median : 841.0 ## Mean :2.164 Mean :29.78 Mean : 976.8 ## 3rd Qu.:3.000 3rd Qu.:37.00 3rd Qu.:1369.0 ## Max. :4.000 Max. :49.00 Max. :2401.0 ## livchildren educ knowmodern ## Min. : 0.000 Min. :0.0000 Min. :0.0000 ## 1st Qu.: 1.000 1st Qu.:0.0000 1st Qu.:1.0000 ## Median : 2.000 Median :0.0000 Median :1.0000 ## Mean : 2.546 Mean :0.7381 Mean :0.9442 ## 3rd Qu.: 4.000 3rd Qu.:2.0000 3rd Qu.:1.0000 ## Max. :10.000 Max. :3.0000 Max. :1.0000 ## Logistic regression for classification Here we use a basic binomial GLM to estimate the probability of a woman using modern contraception. We use information on their region of residence, age, number of living children and level of education. This model can be written: $ln \\left ( \\frac{Pr(\\text{Modern Contraception})}{1-Pr(\\text{Modern Contraception})} \\right ) = X' \\beta$ Which can be converted to the probability scale via the inverse logit transform: $Pr(\\text{Modern Contraception}) = \\frac{1}{1+exp (-X' \\beta)}$ glm1<-glm(modcontra~factor(region)+scale(age)+scale(age2)+scale(livchildren)+factor(educ), data=model.dat2train[,-1], family = binomial) summary(glm1) ## ## Call: ## glm(formula = modcontra ~ factor(region) + scale(age) + scale(age2) + ## scale(livchildren) + factor(educ), family = binomial, data = model.dat2train[, ## -1]) ## ## Deviance Residuals: ## Min 1Q Median 3Q Max ## -1.4073 -0.7103 -0.5734 1.0669 2.3413 ## ## Coefficients: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) -1.91240 0.06807 -28.095 < 2e-16 *** ## factor(region)2 0.38755 0.08534 4.541 5.60e-06 *** ## factor(region)3 0.62565 0.09531 6.564 5.23e-11 *** ## factor(region)4 0.30066 0.09454 3.180 0.001471 ** ## scale(age) 0.63678 0.26540 2.399 0.016425 * ## scale(age2) -0.98328 0.26194 -3.754 0.000174 *** ## scale(livchildren) 0.17004 0.05408 3.144 0.001665 ** ## factor(educ)1 0.43835 0.10580 4.143 3.43e-05 *** ## factor(educ)2 1.38923 0.08646 16.068 < 2e-16 *** ## factor(educ)3 1.54061 0.16086 9.577 < 2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## (Dispersion parameter for binomial family taken to be 1) ## ## Null deviance: 6226.5 on 5444 degrees of freedom ## Residual deviance: 5629.0 on 5435 degrees of freedom ## AIC: 5649 ## ## Number of Fisher Scoring iterations: 4 We see that all the predictors are significantly related to our outcome Next we see how the model performs in terms of accuracy of prediction. This is new comparison to how we typically use logistic regression. We use the predict() function to get the estimated class probabilities for each case tr_pred<- predict(glm1, newdata = model.dat2train, type = \"response\") head(tr_pred) ## 1 2 3 4 5 6 ## 0.22002790 0.31137928 0.15091505 0.20389088 0.08726724 0.18808481 These are the estimated probability that each of these women used modern contraception, based on the model. In order to create classes (uses modern vs doesn’t use modern contraception) we have to use a decision rule. A decision rule is when we choose a cut off point, or threshold value of the probability to classify each observation as belonging to one class or the other. A basic decision rule is if $$Pr(y=\\text{Modern Contraception} |X) >.5$$ Then classify the observation as a modern contraception user, and otherwise not. This is what we will use here. tr_predcl<-factor(ifelse(tr_pred>.5, 1, 0)) library(ggplot2) pred1<-data.frame(pr=tr_pred, gr=tr_predcl, modcon=model.dat2train$modcontra)\n\npred1%>%\nggplot()+geom_density(aes(x=pr, color=gr, group=gr))+ggtitle(label = \"Probability of Modern Contraception\", subtitle = \"Threshold = .5\")", null, "pred1%>%\nggplot()+geom_density(aes(x=pr, color=modcon, group=modcon))+ggtitle(label = \"Probability of Modern Contraception\", subtitle = \"Truth\")", null, "Next we need to see how we did. A simple cross tab of the observed classes versus the predicted classes is called the confusion matrix.\n\ntable( tr_predcl,model.dat2train$modcontra) ## ## tr_predcl 0 1 ## 0 3761 1142 ## 1 275 267 This is great, but typically it’s easier to understand the model’s predictive ability by converting these to proportions. The confusionMatrix() function in caret can do this, plus other stuff. This provides lots of output summarizing the classification results. At its core is the matrix of observed classes versus predicted classes. I got one depiction of this here and from the Wikipedia page Lots of information on the predictive accuracy can be found from this 2x2 table: Generally, we are interested in overall accuracy, sensitivity and specificity. confusionMatrix(data = tr_predcl,model.dat2train$modcontra )\n## Confusion Matrix and Statistics\n##\n## Reference\n## Prediction 0 1\n## 0 3761 1142\n## 1 275 267\n##\n## Accuracy : 0.7398\n## 95% CI : (0.7279, 0.7514)\n## No Information Rate : 0.7412\n## P-Value [Acc > NIR] : 0.6046\n##\n## Kappa : 0.1517\n##\n## Mcnemar's Test P-Value : <2e-16\n##\n## Sensitivity : 0.9319\n## Specificity : 0.1895\n## Pos Pred Value : 0.7671\n## Neg Pred Value : 0.4926\n## Prevalence : 0.7412\n## Detection Rate : 0.6907\n## Detection Prevalence : 0.9005\n## Balanced Accuracy : 0.5607\n##\n## 'Positive' Class : 0\n## \n\nOverall the model has a 73.9% accuracy, which isn’t bad! What is bad is some of the other measures. The sensitivity is really low 267/(267+1142) = .189, so we are only predicting the positive class (modern contraception) in 19% of cases correctly. In other word the model is pretty good at predicting if you don’t use modern contraception, 3761/(3761+275)= .931, but not at predicting if you do.\n\nWe could try a different decision rule, in this case, I use the mean of the response as the cutoff value.\n\ntr_predcl<-factor(ifelse(tr_pred>.258, 1, 0)) #mean of response\n\npred2<-data.frame(pr=tr_pred, gr=tr_predcl, modcon=model.dat2train$modcontra) pred2%>% ggplot()+geom_density(aes(x=pr, color=gr, group=gr))+ggtitle(label = \"Probability of Modern Contraception\", subtitle = \"Threshold = .258\")", null, "pred2%>% ggplot()+geom_density(aes(x=pr, color=modcon, group=modcon))+ggtitle(label = \"Probability of Modern Contraception\", subtitle = \"Truth\")", null, "confusionMatrix(data = tr_predcl,model.dat2train$modcontra, positive = \"1\" )\n## Confusion Matrix and Statistics\n##\n## Reference\n## Prediction 0 1\n## 0 2944 577\n## 1 1092 832\n##\n## Accuracy : 0.6935\n## 95% CI : (0.681, 0.7057)\n## No Information Rate : 0.7412\n## P-Value [Acc > NIR] : 1\n##\n## Kappa : 0.2859\n##\n## Mcnemar's Test P-Value : <2e-16\n##\n## Sensitivity : 0.5905\n## Specificity : 0.7294\n## Pos Pred Value : 0.4324\n## Neg Pred Value : 0.8361\n## Prevalence : 0.2588\n## Detection Rate : 0.1528\n## Detection Prevalence : 0.3534\n## Balanced Accuracy : 0.6600\n##\n## 'Positive' Class : 1\n## \n\nWhich drops the accuracy a little, but increases the specificity at the cost of the sensitivity.\n\nNext we do this on the test set to evaluate model performance outside of the training data\n\npred_test<-predict(glm1, newdata=model.dat2test, type=\"response\")\npred_cl<-factor(ifelse(pred_test>.28, 1, 0))\n\ntable(model.dat2test$modcontra,pred_cl) ## pred_cl ## 0 1 ## 0 746 262 ## 1 160 192 confusionMatrix(data = pred_cl,model.dat2test$modcontra )\n## Confusion Matrix and Statistics\n##\n## Reference\n## Prediction 0 1\n## 0 746 160\n## 1 262 192\n##\n## Accuracy : 0.6897\n## 95% CI : (0.6644, 0.7142)\n## No Information Rate : 0.7412\n## P-Value [Acc > NIR] : 1\n##\n## Kappa : 0.2609\n##\n## Mcnemar's Test P-Value : 8.806e-07\n##\n## Sensitivity : 0.7401\n## Specificity : 0.5455\n## Pos Pred Value : 0.8234\n## Neg Pred Value : 0.4229\n## Prevalence : 0.7412\n## Detection Rate : 0.5485\n## Detection Prevalence : 0.6662\n## Balanced Accuracy : 0.6428\n##\n## 'Positive' Class : 0\n## \n\n## Regression partition tree\n\nAs we saw in the first working group example, the regression tree is another common technique used in classification problems. Regression or classification trees attempt to\n\nlibrary(rpart)\nlibrary(rpart.plot)\n\nrp1<-rpart(modcontra~factor(region)+(age)+livchildren+factor(educ),\ndata=model.dat2train,\nmethod =\"class\",\ncontrol = rpart.control(minbucket = 10, cp=.01)) #lower CP parameter makes for more compliacted tree\nsummary(rp1)\n## Call:\n## rpart(formula = modcontra ~ factor(region) + (age) + livchildren +\n## factor(educ), data = model.dat2train, method = \"class\", control = rpart.control(minbucket = 10,\n## cp = 0.01))\n## n= 5445\n##\n## CP nsplit rel error xerror xstd\n## 1 0.04009936 0 1.0000000 1.0000000 0.02293618\n## 2 0.01100071 2 0.9198013 0.9198013 0.02230305\n## 3 0.01000000 4 0.8977999 0.9169624 0.02227934\n##\n## Variable importance\n## factor(educ) livchildren age factor(region)\n## 58 23 19 1\n##\n## Node number 1: 5445 observations, complexity param=0.04009936\n## predicted class=0 expected loss=0.2587695 P(node) =1\n## class counts: 4036 1409\n## probabilities: 0.741 0.259\n## left son=2 (3862 obs) right son=3 (1583 obs)\n## Primary splits:\n## factor(educ) splits as LLRR, improve=189.73590, (0 missing)\n## livchildren < 0.5 to the right, improve= 84.51811, (0 missing)\n## age < 23.5 to the right, improve= 52.42664, (0 missing)\n## factor(region) splits as LLRL, improve= 36.53020, (0 missing)\n## Surrogate splits:\n## livchildren < 0.5 to the right, agree=0.772, adj=0.215, (0 split)\n## age < 19.5 to the right, agree=0.753, adj=0.149, (0 split)\n## factor(region) splits as LLRL, agree=0.713, adj=0.014, (0 split)\n##\n## Node number 2: 3862 observations\n## predicted class=0 expected loss=0.174262 P(node) =0.7092746\n## class counts: 3189 673\n## probabilities: 0.826 0.174\n##\n## Node number 3: 1583 observations, complexity param=0.04009936\n## predicted class=0 expected loss=0.46494 P(node) =0.2907254\n## class counts: 847 736\n## probabilities: 0.535 0.465\n## left son=6 (868 obs) right son=7 (715 obs)\n## Primary splits:\n## livchildren < 0.5 to the right, improve=33.940940, (0 missing)\n## age < 36.5 to the right, improve=20.441730, (0 missing)\n## factor(region) splits as LRRL, improve= 2.382434, (0 missing)\n## factor(educ) splits as --LR, improve= 0.556353, (0 missing)\n## Surrogate splits:\n## age < 20.5 to the right, agree=0.749, adj=0.443, (0 split)\n##\n## Node number 6: 868 observations\n## predicted class=0 expected loss=0.3709677 P(node) =0.1594123\n## class counts: 546 322\n## probabilities: 0.629 0.371\n##\n## Node number 7: 715 observations, complexity param=0.01100071\n## predicted class=1 expected loss=0.420979 P(node) =0.1313131\n## class counts: 301 414\n## probabilities: 0.421 0.579\n## left son=14 (14 obs) right son=15 (701 obs)\n## Primary splits:\n## age < 32.5 to the right, improve=9.574909, (0 missing)\n## factor(educ) splits as --LR, improve=1.650766, (0 missing)\n## factor(region) splits as LRRL, improve=1.324512, (0 missing)\n##\n## Node number 14: 14 observations\n## predicted class=0 expected loss=0 P(node) =0.002571166\n## class counts: 14 0\n## probabilities: 1.000 0.000\n##\n## Node number 15: 701 observations, complexity param=0.01100071\n## predicted class=1 expected loss=0.4094151 P(node) =0.128742\n## class counts: 287 414\n## probabilities: 0.409 0.591\n## left son=30 (137 obs) right son=31 (564 obs)\n## Primary splits:\n## age < 16.5 to the left, improve=7.933444, (0 missing)\n## factor(educ) splits as --LR, improve=2.545437, (0 missing)\n## factor(region) splits as LRRL, improve=1.768127, (0 missing)\n##\n## Node number 30: 137 observations\n## predicted class=0 expected loss=0.4379562 P(node) =0.0251607\n## class counts: 77 60\n## probabilities: 0.562 0.438\n##\n## Node number 31: 564 observations\n## predicted class=1 expected loss=0.3723404 P(node) =0.1035813\n## class counts: 210 354\n## probabilities: 0.372 0.628\nrpart.plot(rp1, type = 4,extra=4,\nbox.palette=\"GnBu\",\nnn=TRUE, main=\"Classification tree for using modern contraception\")", null, "Each node box displays the classification, the probability of each class at that node (i.e. the probability of the class conditioned on the node) and the percentage of observations used at that node. From here.\n\npredrp1<-predict(rp1, newdata=model.dat2train, type = \"class\")\nconfusionMatrix(data = predrp1,model.dat2train$modcontra ) ## Confusion Matrix and Statistics ## ## Reference ## Prediction 0 1 ## 0 3826 1055 ## 1 210 354 ## ## Accuracy : 0.7677 ## 95% CI : (0.7562, 0.7788) ## No Information Rate : 0.7412 ## P-Value [Acc > NIR] : 3.566e-06 ## ## Kappa : 0.2475 ## ## Mcnemar's Test P-Value : < 2.2e-16 ## ## Sensitivity : 0.9480 ## Specificity : 0.2512 ## Pos Pred Value : 0.7839 ## Neg Pred Value : 0.6277 ## Prevalence : 0.7412 ## Detection Rate : 0.7027 ## Detection Prevalence : 0.8964 ## Balanced Accuracy : 0.5996 ## ## 'Positive' Class : 0 ## We see the regression tree is performing a little better than the logistic regression on the test case using the summary below: pred_testrp<-predict(rp1, newdata=model.dat2test, type=\"class\") confusionMatrix(data = pred_testrp,model.dat2test$modcontra )\n## Confusion Matrix and Statistics\n##\n## Reference\n## Prediction 0 1\n## 0 947 263\n## 1 61 89\n##\n## Accuracy : 0.7618\n## 95% CI : (0.7382, 0.7842)\n## No Information Rate : 0.7412\n## P-Value [Acc > NIR] : 0.0434\n##\n## Kappa : 0.2365\n##\n## Mcnemar's Test P-Value : <2e-16\n##\n## Sensitivity : 0.9395\n## Specificity : 0.2528\n## Pos Pred Value : 0.7826\n## Neg Pred Value : 0.5933\n## Prevalence : 0.7412\n## Detection Rate : 0.6963\n## Detection Prevalence : 0.8897\n## Balanced Accuracy : 0.5962\n##\n## 'Positive' Class : 0\n## \n\n## Linear discriminant function\n\nLinear discriminant functions attempt to separate classes from each other using a strictly linear function of the variables. It attempts to reduce the dimensionality of the original data to a single linear function of the input variables, or the discriminant function. This is very similar to what PCA does when it creates a principal component, although in LDA, the function uses this linear transformation of the data to optimally separate classes.\n\nIn this case it performs better than the logistic regression but not as well as the regression tree.\n\nlibrary(MASS)\n##\n## Attaching package: 'MASS'\n## The following object is masked from 'package:dplyr':\n##\n## select\nlda1<-lda(modcontra~factor(region)+scale(age)+livchildren+factor(educ), data=model.dat2train,prior=c(.74, .26) , CV=T)\n\npred_ld1<-lda1$class head(lda1$posterior) #probabilities of membership in each group\n## 0 1\n## 1 0.8153664 0.1846336\n## 2 0.7387134 0.2612866\n## 3 0.8673284 0.1326716\n## 4 0.8080069 0.1919931\n## 5 0.8976027 0.1023973\n## 6 0.8387015 0.1612985\nld1<-data.frame(ppmod= lda1$posterior[, 2],pred=lda1$class, real=model.dat2train$modcontra) ld1%>% ggplot()+geom_density(aes(x=ppmod, group=pred, color=pred))+ggtitle(label = \"Probabilities of class membership on the linear discriminant function\")", null, "ld1%>% ggplot()+geom_density(aes(x=ppmod, group=real, color=real))+ggtitle(label = \"Probabilities of class membership and the real class\")", null, "Accuracy on the training set confusionMatrix(pred_ld1,model.dat2train$modcontra )\n## Confusion Matrix and Statistics\n##\n## Reference\n## Prediction 0 1\n## 0 3625 1000\n## 1 411 409\n##\n## Accuracy : 0.7409\n## 95% CI : (0.729, 0.7525)\n## No Information Rate : 0.7412\n## P-Value [Acc > NIR] : 0.5318\n##\n## Kappa : 0.2181\n##\n## Mcnemar's Test P-Value : <2e-16\n##\n## Sensitivity : 0.8982\n## Specificity : 0.2903\n## Pos Pred Value : 0.7838\n## Neg Pred Value : 0.4988\n## Prevalence : 0.7412\n## Detection Rate : 0.6657\n## Detection Prevalence : 0.8494\n## Balanced Accuracy : 0.5942\n##\n## 'Positive' Class : 0\n##\nlda1<-lda(modcontra~factor(region)+scale(age)+livchildren+factor(educ), data=model.dat2train,prior=c(.74, .26) )\n\n#linear discriminant function\nlda1$scaling ## LD1 ## factor(region)2 0.4580587 ## factor(region)3 0.8545973 ## factor(region)4 0.3495414 ## scale(age) -0.3873869 ## livchildren 0.1025140 ## factor(educ)1 0.4535731 ## factor(educ)2 1.9263226 ## factor(educ)3 2.2956187 Accuracy on the test set pred_ld2<-predict(lda1, model.dat2test) confusionMatrix(pred_ld2$class, model.dat2test\\$modcontra)\n## Confusion Matrix and Statistics\n##\n## Reference\n## Prediction 0 1\n## 0 906 254\n## 1 102 98\n##\n## Accuracy : 0.7382\n## 95% CI : (0.714, 0.7614)\n## No Information Rate : 0.7412\n## P-Value [Acc > NIR] : 0.6115\n##\n## Kappa : 0.2062\n##\n## Mcnemar's Test P-Value : 1.214e-15\n##\n## Sensitivity : 0.8988\n## Specificity : 0.2784\n## Pos Pred Value : 0.7810\n## Neg Pred Value : 0.4900\n## Prevalence : 0.7412\n## Detection Rate : 0.6662\n## Detection Prevalence : 0.8529\n## Balanced Accuracy : 0.5886\n##\n## 'Positive' Class : 0\n##" ]

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[ "## 多项式乘法", null, "## DFT和FFT的基本概念\n\n构造多项式——FFT——点值乘法——IFFT\n\n## 基本的一些数学知识\n\n### 多项式表达法\n\n#### 次数表达法\n\nA（x）=a0+a1*x+a2*x^2+……+an-1*x^n-1\n\n#### 点值表达法\n\n{(x0,y0),(x1,y1),(x2,y2),……,(xn-1,yn-1)}\n\n{(x0,Ay0),(x1,Ay1),(x2,Ay2),……,(xn-1,Ayn-1)}\n\n{(x0,By0),(x1,By1),(x2,By2),……,(xn-1,Byn-1)}\n\n{(x0,Ay0*By0),(x1,Ay1*By1),(x2,Ay2*By2),……,(xn-1,Ayn-1*Byn-1)}\n\n### 单位复数根", null, "", null, "", null, "", null, "### 一些单位复数根的引理\n\n#### 消去引理", null, "#### 折半引理", null, "#### 求和引理", null, "## DFT离散傅里叶变换", null, "## FFT快速傅里叶变换\n\nA0(x)=a0+a2*x+a4*x^2+……+a(n-2)*x^(n/2-1)\nA1(x)=a1+a3*x+a5*x^2+……+a(n-1)*x^(n/2-1)", null, "## 具体代码实现：\n\n#include<cmath>\n#include<cstdio>\n#include<cstdlib>\n#include<cstring>\n#include<complex>//c++自带的复数库\n#include<algorithm>\nusing namespace std;\ndouble pi=acos(-1);\n\ncomplex<double> a,b,c;\nint i,j,k,m,n,o,p,js,jl;\n\nvoid fft(complex<double> *a,int n,int op)\n{\nif(n==1)return;\ncomplex<double> w(1,0),wn(cos(2*pi/n),sin(2*pi*op/n)),a1[n/2],a2[n/2];\n\nfor(int i=0;i<n/2;i++)\n{\na1[i]=a[2*i];\na2[i]=a[2*i+1];\n}\nfft(a1,n/2,op);\nfft(a2,n/2,op);\n\nfor(int i=0;i<n/2;i++)\n{\na[i]=a1[i]+w*a2[i];\na[i+n/2]=a1[i]-w*a2[i];\nw=w*wn;\n}\n}\nint main()\n{\nscanf(\"%d%d\",&n,&m);\nfor(int i=0;i<=n;i++)scanf(\"%lf\",&a[i]);\nfor(int i=0;i<=m;i++)scanf(\"%lf\",&b[i]);\nm=m+n;n=1;\nwhile(n<=m)n=n*2;\n\nfft(a,n,1);fft(b,n,1);\nfor(int i=0;i<=n;i++)c[i]=a[i]*b[i];\nfft(c,n,-1);\nfor(int i=0;i<=m;i++)printf(\"%d \",int(c[i].real()/n+0.5));\nreturn 0;\n}\n\n## 经典例题\n\n#### 【luogu 1919】A*B Problem升级版\n\ny的结果。（注意判断前导0）\n\n1\n3\n4\n\n12\n\nn<=60000\n\n#include<cmath>\n#include<cstdio>\n#include<cstdlib>\n#include<cstring>\n#include<complex>//\n#include<algorithm>\nusing namespace std;\ndouble pi=acos(-1);\n\ncomplex<double> a,b,c;\n\nint ans;\nchar sa,sb;\nint i,j,k,m,n,o,p,js,jl;\n\nvoid fft(complex<double> *a,int n,int op)\n{\nif(n==1)return;\ncomplex<double> w(1,0),wn(cos(2*pi/n),sin(2*pi*op/n)),a1[n/2],a2[n/2];\n\nfor(int i=0;i<n/2;i++)\n{\na1[i]=a[2*i];\na2[i]=a[2*i+1];\n}\nfft(a1,n/2,op);\nfft(a2,n/2,op);\n\nfor(int i=0;i<n/2;i++)\n{\na[i]=a1[i]+w*a2[i];\na[i+n/2]=a1[i]-w*a2[i];\nw=w*wn;\n}\n}\nint main()\n{\nscanf(\"%d\",&n);\nscanf(\"%s\",sa+1);scanf(\"%s\",sb+1);\nfor(int i=0;i<n;i++)a[i]=double(sa[n-i]-'0');\nfor(int i=0;i<n;i++)b[i]=double(sb[n-i]-'0');\nn--;\nm=2*n;n=1;\nwhile(n<=m)n=n*2;\n\nfft(a,n,1);fft(b,n,1);\nfor(int i=0;i<=n;i++)c[i]=a[i]*b[i];\nfft(c,n,-1);\nfor(int i=0;i<=m;i++)ans[i]=int(c[i].real()/n+0.5);\nfor(int i=1;i<=m;i++)\n{\nans[i]=ans[i]+ans[i-1]/10;\nans[i-1]=ans[i-1]%10;\n}\nint bb=1;\nfor(int i=m;i>=0;i--)\n{\nif(ans[i]>0)bb=0;\nif(bb==0)printf(\"%d\",ans[i]);\n}\nreturn 0;\n}\n\n## 结语\n\nLast modification：June 18th, 2019 at 07:08 pm\nIf you think my article is useful to you, please feel free to appreciate" ]

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[ "", null, "Welcome to cbsenotes.com! To post messages or access any member only section, you will need an account. Create your free account now.\nCBSE Notes 2011-2012 » VIII-Maths\n\n# Squares and Square Roots\n\n## The greatest perfect square of a natural number smaller than (51)2 is\n\nMultiple choice question\n\nThe greatest perfect square of a natural number smaller than (51)2 is\n\n## The least four digit number which is a perfect square, is\n\nMultiple choice question\n\nThe least four digit number which is a perfect square, is\n\n## The least square number which is exactly divisible by 10, 12, 15 and 18, is\n\nMultiple choice question\n\nThe least square number which is exactly divisible by 10, 12, 15 and 18, is\n\n## A general wishes to arrange his 36581 soldiers in the form of a square. After arranging them he foun...\n\nMultiple choice question\n\nA general wishes to arrange his 36581 soldiers in the form of a square. After arranging them he found that some of them are left over. The number of soldiers left over is\n\n## A man plants 15129 apple trees in his garden and arrange them so that there are as many rows as ther...\n\nMultiple choice question\n\nA man plants 15129 apple trees in his garden and arrange them so that there are as many rows as there are apple trees in each row, then the number of rows is\n\n## Which of the following is a perfect square of an even number ?\n\nMultiple choice question\n\nWhich of the following is a perfect square of an even number ?", null, "" ]

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[ "# Re: decision theory papers\n\n```On 18-Apr-02, Wei Dai wrote:\n> On Thu, Apr 18, 2002 at 05:39:39PM -0700, Brent Meeker wrote:\n>> Keeping to the idea of a deterministic universe - wouldn't the\n>> mathematical description of the universe include a description\n>> of the brain of the subject. And if the universe is computable\n>> it follows that the behavoir of the subject is computable. If\n>> the person, or anyone else, runs the algorithm predicting the\n>> subjects behavoir - an operation that will itself occur in the\n>> universe and hence is predicted - and *then the subject\n>> doesn't do what is predicted* there is indeed a contradiction.\n>> But the conclusion is only that one of the assumptions is\n>> wrong. I'm pointing to the assumption that the subject could\n>> \"then do the opposite of what it predicted\" - *that* could be\n>> wrong. Thus saving the other premises.```\n```\n>> Obviously the contradiction originates from assuming a\n>> deterministic universe in which someone can decide to do other\n>> than what the deterministic algorithm of the universe says he\n>> will do.\n\n> Consider what the prediction algorithm would have to do. It\n> basicly has to simulate the entire history of the universe from\n> the beginning until it reaches the point where the subject\n> makes his decision.\n\nWhy the whole universe? Why would you suppose that is has to\nsimulate more than a very tiny part of the universe? But really\nthat's beside the point - your argument rests on the idea that\nthe algorithm is in the tiny part, which we assume includes the\nsubjects brain, and therefore, in simulating the this part, it\nmust simulate itself - thus requiring a vicious recursion. This\nis different than supposing the algorithm reaches a conclusion\nand then the subject does something contrary. It entails that\nthe algorithm never reaches a conclusion.\n\nHowever, I don't see that the argument is conclusive. Suppose the\nalgorithm is run on hardware outside the tiny part that must be\nincluded to predict the subjects decision. Then it doesn't have\nto simulate itself and it can reach a decision. If that is\npossible, then it is also possible that it could be in the\nsubjects brain in a part (where \"part\" means logically distinct\nnot necessarily spacially) that does not have to be simulated to\npredict his behavoir. For example, suppose the subject is going\nto decide whether to have chocolate ice cream or vanilla ice\ncream and further suppose that his brain is structured such that\nhe always orders the one different from what he last time. Then\nthe algorithm need only access his memory to see what he had\nlast time and with a single if-then the decision is predicted.\n\nI don't know that all decision algorithms can be split off this\nway - but on the other hand I don't see any contradiction is\nsupposing they could.\n\nNow what if the subject has a copy of the\n> algorithm in his brain and tries to run the algorithm on\n> himself? The algorithm would go into an infinite recursion\n> trying to simulate itself simulating itself ... If you have\n> only a finite amount of time and computational power with which\n> to reach a decision, there is no way you can complete a run of\n> the prediction algorithm within that time. So again you have to\n> make the decision without being able to predict your choice\n> from the mathematical description of the universe.\n\nOf course we all know that there is no prediction algorithm and\nif they were you couldn't execute it. So I wonder how important\nit is that there be this in-principle prohibition? Are you\ngoing to make some further argument that depends on the logical\n(not just practical) impossibility of an prediction algorithm?\n\nBrent Meeker\n\"If I had known then what I know now, I would have made the same\nmistakes sooner.\"\n--- Robert Half\n\nBrent Meeker\n\n```" ]

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[ "# NCFM on Azure Databricks\n\nThis article shows how we can run deep learning model for one image classification task. We take the Kaggle NCFM competition as the playground project.\n\n## Data and Preparation\n\nDownload the data from  https://www.kaggle.com/c/the-nature-conservancy-fisheries-monitoring/data . Unzip and upload the data file into DBFS or Azure blob storage. This is a typical single-label image classification problem covering 8 classes (7 for fish and 1 for non-fish). Training set is rather small, only 3777 images, extra 1000 for testing. Images are challenging since noise/background dominates in the whole picture. To prepare model training, we will split the labed data into training and validation. Usually, 80% for training and 20% for validation. After the split, there are separate folders: val_train, train_split.\n\n## Modeling and Training\n\nSmall size of training set may be risk of overfiting during model training. One solution is transfer leaning/fine-tune the weights of pre-trained networks. Pre-trained models trained across multiple GPUs on ImageNet; ConvNet features are more generic in early layers and more original-dataset-specific in later layers; Use a small learning rate to fine-tune; Usually fine-tuning begins with later layers;\n\nHere we use Inception-V3 model with ImageNet Pretrained weights. The pre-trained Inception-v3 model achieves state-of-the-art accuracy for recognizing general objects with 1000 classes, like “Zebra”, “Dalmatian”, and “Dishwasher”. The model extracts general features from input images in the first part and classifies them based on those features in the second part.\n\n``````import os\nfrom keras.applications.inception_v3 import InceptionV3\nfrom keras.layers import Flatten, Dense, AveragePooling2D\nfrom keras.models import Model\nfrom keras.optimizers import RMSprop, SGD\nfrom keras.callbacks import ModelCheckpoint\nfrom keras.preprocessing.image import ImageDataGenerator\n\nlearning_rate = 0.001\nimg_width = 299\nimg_height = 299\nnbr_train_samples = 3019\nnbr_validation_samples = 758\nnbr_epochs = 20\nbatch_size = 32\ntrain_data_dir = '/dbfs/mnt/vpa-raw-data-dev/POC/train_split'\nval_data_dir = '/dbfs/mnt/vpa-raw-data-dev/POC/val_split'\n\nFishNames = ['ALB', 'BET', 'DOL', 'LAG', 'NoF', 'OTHER', 'SHARK', 'YFT']\n\nInceptionV3_notop = InceptionV3(include_top=False, weights='imagenet',\ninput_tensor=None, input_shape=(299, 299, 3))\n\nprint('Adding Average Pooling Layer and Softmax Output Layer ...')\noutput = InceptionV3_notop.get_layer(index = -1).output # Shape: (8, 8, 2048)\noutput = AveragePooling2D((8, 8), strides=(8, 8), name='avg_pool')(output)\noutput = Flatten(name='flatten')(output)\noutput = Dense(8, activation='softmax', name='predictions')(output)\n\nInceptionV3_model = Model(InceptionV3_notop.input, output)\nInceptionV3_model.summary()\n\noptimizer = SGD(lr = learning_rate, momentum = 0.9, decay = 0.0, nesterov = True)\nInceptionV3_model.compile(loss='categorical_crossentropy', optimizer = optimizer, metrics = ['accuracy'])\n\n# autosave best Model\nbest_model_file = \"/dbfs/mnt/vpa-raw-data-dev/POC/weights.h5\"\nbest_model = ModelCheckpoint(best_model_file, monitor='val_acc', verbose = 1, save_best_only = True)``````\n\nIn order to improve our ranking, we use data augmentation for testing images.\n\n``````# this is the augmentation configuration we will use for training\ntrain_datagen = ImageDataGenerator(\nrescale=1./255,\nshear_range=0.1,\nzoom_range=0.1,\nrotation_range=10.,\nwidth_shift_range=0.1,\nheight_shift_range=0.1,\nhorizontal_flip=True)\n\n# this is the augmentation configuration we will use for validation, only rescaling\nval_datagen = ImageDataGenerator(rescale=1./255)\n\ntrain_generator = train_datagen.flow_from_directory(\ntrain_data_dir,\ntarget_size = (img_width, img_height),\nbatch_size = batch_size,\nshuffle = True,\nclasses = FishNames,\nclass_mode = 'categorical')\n\nvalidation_generator = val_datagen.flow_from_directory(\nval_data_dir,\ntarget_size=(img_width, img_height),\nbatch_size=batch_size,\nshuffle = True,\n#save_to_dir = '/Users/Sandy/Repo/Kaggle_NCFM/visulization',\n#save_prefix = 'aug',\nclasses = FishNames,\nclass_mode = 'categorical')\n\nInceptionV3_model.fit_generator(\ntrain_generator,\nsteps_per_epoch = 94,\nnb_epoch = 20,\nvalidation_data = validation_generator,\nvalidation_steps = 23,\ncallbacks = [best_model])``````\n\n## Prediction\n\n``````import os\nimport numpy as np\nfrom keras.preprocessing.image import ImageDataGenerator\n\nimg_width = 299\nimg_height = 299\nbatch_size = 32\nnbr_test_samples = 1000\n\nFishNames = ['ALB', 'BET', 'DOL', 'LAG', 'NoF', 'OTHER', 'SHARK', 'YFT']\n\nroot_path = '/dbfs/mnt/vpa-raw-data-dev/POC/'\nweights_path = os.path.join(root_path, 'weights.h5')\nprint(weights_path)\ntest_data_dir = os.path.join(root_path, 'test_stg1/')\nprint(test_data_dir)\n\ntest_datagen = ImageDataGenerator(rescale=1./255)\ntest_generator = test_datagen.flow_from_directory(\ntest_data_dir,\ntarget_size=(img_width, img_height),\nbatch_size=batch_size,\nshuffle = False, # Important !!!\nclasses = None,\nclass_mode = None)\n\ntest_image_list = test_generator.filenames\n\nprint('Begin to predict for testing data ...')\npredictions = InceptionV3_model.predict_generator(test_generator, nbr_test_samples)\nnp.savetxt(os.path.join(root_path, 'predictions.txt'), predictions)\n\nprint('Begin to write submission file ..')\nf_submit = open(os.path.join(root_path, 'submit.csv'), 'w')\nf_submit.write('image,ALB,BET,DOL,LAG,NoF,OTHER,SHARK,YFT\\n')\nfor i, image_name in enumerate(test_image_list):\npred = ['%.6f' % p for p in predictions[i, :]]\nif i % 100 == 0:\nprint('{} / {}'.format(i, nbr_test_samples))\nf_submit.write('%s,%s\\n' % (os.path.basename(image_name), ','.join(pred)))\nf_submit.close()\nprint('Submission file successfully generated!')``````\n\n## Practical Tricks\n\n1. When we use ConvNet for image classification task, while the train samples size is quite small, we can pick a STOA ConvNet architecture, e.g. InceptionV3, ResNet, Inception-ResNet, DenseNet, etc with pre-trained weights on ImageNet to speed up convergence.\n2. Finetune with small learning rate. I have tried learning rate with 0.001 and 0.0001. The smaller learning rate training is quite slow, but gain good validation accuracy.\n3. Use Data augumentation to reduce overfitting.\n4. Split train and local validation.\n5. Ensemble models might help, but I didn’t try yet while I am writing this.\n\nFinally special thanks to pengpaiSH for referencing his code sample. https://github.com/pengpaiSH/Kaggle_NCFM" ]

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[ "# Disambiguating equality\n\n///////\n\nLike the term ‘add’ (represented by the $\\, + \\,$ sign), the term ‘equal’ (represented by the $\\, = \\,$ sign) has many different meanings in mathematics. In fact, the $\\, = \\,$ sign can stand for at least five different types of equality:\n\n1) Identical (or algebraic) equality:\n\nExamples: $\\, 3 + 5 = 8 \\,$, and $\\, (x + y) (x - y) = x^2 - y^2 \\,$.\n\nNotation: This type of equality (identical equality) is often denoted by the symbol $\\, \\equiv \\,$. Using this notation, we write $\\, 3 + 5 \\equiv 8 \\,$, and $\\, (x + y) (x - y) \\equiv x^2 - y^2 \\,$.\n\nIMPORTANT: The second example above is only valid if the algebra is commutative,\nsince the expansion of the left-hand side gives (using the distributive property twice): $\\, (x + y) (x - y) \\equiv x(x-y) + y(x-y) \\equiv x^2 - xy + yx - y^2$,\nwhich is identically equal to the right-hand side if-and-only-if $\\, xy \\equiv yx$.\n\n2) Conditional (or equational) equality:\n\nExamples: The values of $\\, x \\,$ that satisfy the equation $\\, 3x^2 - 5x + 2 = 0 \\,$,\nand the values of $\\, x \\,$ and $\\, y \\,$ that satisfy the equation $\\, 3x + 5y = 2 \\,$.\n\n3) Relational or equivalence equality:\n\nExample: $\\, x = y \\,$ if-and-only-if $\\, x - y \\,$ is divisible by $\\, 7.$\n\nNotation: This type of equality is often denoted by the symbol $\\, \\cong \\,$.\nUsing this notation, we can express our example as $\\, x \\cong y \\,$ if $\\, x - y \\,$ is divisible by $\\, 7.$\n\n4) Defining equality:\n\nExample: $\\, C \\,$ is defined to be equal to $\\, A + B \\,$.\n\nNotation: $\\, C \\stackrel {\\mathrm{def}}{=} A + B.$\n\n5) Assigned equality:\n\nExample: $\\, R \\,$ is assigned the value of $\\, P + Q \\,$.\n\nNotation: Assigned equality is often denoted by the symbol $\\, := \\,$\nand using this notation we can express the example as $\\, R := P + Q \\,$.\n\n///////" ]

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[ "# The other side of the moon", null, "/bb|[^b]{2}/\nNever stop Grokking\n\n## Monday, October 07, 2019\n\n### Implementing Spearman's Rank Correlation in SQL\n\nIn my last post, I showed how to implement Pearson's Correlation as an SQL Window function with window frame support. In this post, I'll follow up with implementing Spearman's Rank correlation co-efficient in SQL.\n\nWhile Pearson's correlation looks for linear relationships between two vectors (ie, you wouldn't use it for exponential relationships), Spearman's rank correlation looks for monotonicity, or in plain english, do the two values go up & down together?\n\nSo here's the really cool part. Spearman's Rank correlation co-efficient is the Pearson's correlation co-efficient of the ranks of the two vectors. We already know how to calculate Pearson's correlation co-efficient, so what we need to do here is first calculate ranks of our vectors.\n\nWe can do this using the SQL RANK function, which also works as a window function with window frame support:\n\nRANK() OVER (PARTITION BY <partition cols> ORDER BY x ASC) as R_X,\n\nRANK() OVER (PARTITION BY <partition cols> ORDER BY y ASC) as R_Y,\n\n\nThe two important things to note here are that RANK() does not take a parameter, instead you specify what you want to rank on in the ORDER BY clause, and secondly, make sure both parameters are ordered in the same direction, ASC or DESC.\n\nNow even though the RANK() function supports window frames, you don't want to use them here. This is so because if you're using sliding windows, each row will have a different rank depending on the window, and we won't be able to correlate an outer window.\n\nOnce we have the ranks in an inner query, we can run either the standard CORR function, or the windowed CORR that we developed in the previous post on these derived columns instead:\n\nSELECT CORR(R_X, R_Y) FROM (\nSELECT\nRANK() OVER (PARTITION BY <partition cols> ORDER BY x ASC) as R_X,\n\nRANK() OVER (PARTITION BY <partition cols> ORDER BY y ASC) as R_Y\nFROM ...\n)\n\n\nIf implementing this as a window function, then use R_X and R_Y as the inputs to the SUM() functions with an additional nested query.\n\nI hope this was helpful, leave a comment or tweet @bluesmoon if you'd like to chat.\n\n## Wednesday, October 02, 2019\n\n### Implementing Pearson's CORR as a database window function\n\nI recently needed to find the Pearson's Correlation Coefficient between two columns in a Snowflake database. Now Snowflake and PostgreSQL both support a CORR aggregate function that correlates along a GROUP BY. Snowflake additionally supports CORR as a window function, but only for use with PARTITION BY. It does not support window frames. Other databases like MySQL do not have a CORR function at all. See SQL in a nutshell for more information on database support.\n\nIf you want to know about window functions, Julia Evans (@b0rk) has a great SQL tip on them.\n\nIn my case, I needed to find the Pearson's coefficient along a sliding window of rows. ie, for a list of N rows, I needed N-k coefficients, one for each sliding window of size k. As far as I could tell, only Oracle supports this functionality, and I wasn't that desperate, so I set about figuring out how to implement it myself.\n\nFortunately, Pearson's correlation coefficient is calculated using a very simple algebraic function. The full details are on the Wikipedia page linked above, but it's helpful to break it down into manageable pieces.\n\nAt a high level, the coefficient ρ (the greek letter rho) is defined as the covariance of the vectors divided by the product of standard deviation of the two vectors, or mathematically:\n\nρ(x,y) = cov(x, y) / (σ(x) * σ(y))\n\nIn SQL, this would be\n\nCOVAR_POP(y, x) / (STDDEV_POP(x) * STDDEV_POP(y))\n\nThis simplifies things a bit since STDDEV_POP does support window frames, but COVAR_POP does not. That reduces our problem to implementing COVAR_POP as a window function.\n\nThis is much simpler, because the covariance uses sum and count, both of which are implemented as window functions with window frame support:\n\nCOVAR_POP = (SUM(x * y) - SUM(x) * SUM(y) / COUNT(*)) / COUNT(*), or mathematically:\n\ncov(x, y) = (Σ(x * y) - Σx * Σy / N) / N\n\nBut it gets even better. Since we're calculating these SUMs and COUNTs anyway, why not use them to implement STDDEV as well? A simplified formula for STDDEV uses the the sum of squares and the square of the sum as follows:\n\nσ = SQRT(N * Σx^2 - (Σx)^2) / N.\n\nCombining the formulae above, we get:\n\nρ(x,y) = cov(x, y) / (σ(x) * σ(y))\n\n= ( (Σ(x * y) - Σx * Σy / N) / N ) / ( (SQRT(N * Σx^2 - (Σx)^2) / N) * (SQRT(N * Σy^2 - (Σy)^2) / N) )\n\n= (Σ(x * y) - Σx * Σy / N) / ( N * (SQRT(N * Σx^2 - (Σx)^2) / N) * (SQRT(N * Σy^2 - (Σy)^2) / N) )\n\n= (Σ(x * y) - Σx * Σy / N) / ( SQRT(N * Σx^2 - (Σx)^2) * SQRT(N * Σy^2 - (Σy)^2) / N )\n\n= N * (Σ(x * y) - Σx * Σy / N) / ( SQRT(N * Σx^2 - (Σx)^2) * SQRT(N * Σy^2 - (Σy)^2) )\n\n= (N * Σ(x * y) - Σx * Σy) / ( SQRT(N * Σx^2 - (Σx)^2) * SQRT(N * Σy^2 - (Σy)^2) )\n\n\nI've left the product of the two squareroots in the denominator as-is rather than simplifying it further because the simplifaction could result in numeric overflow.\n\nSo, we now have a function for Pearson's correlation coefficient using only SUM & COUNT, both of which support window functions and window frames.\n\nFor each of these, we can now SELECT something like this in an inner query:\n\nCOUNT( * ) OVER (PARTITION BY <partition cols> ORDER BY <minute> ROWS BETWEEN $k2 PRECEDING AND$k2 FOLLOWING) AS N,\n\nSUM(x) OVER (PARTITION BY <partition cols> ORDER BY <minute> ROWS BETWEEN $k2 PRECEDING AND$k2 FOLLOWING) AS SUM_X,\n\nSUM(x * x) OVER (PARTITION BY <partition cols> ORDER BY <minute> ROWS BETWEEN $k2 PRECEDING AND$k2 FOLLOWING) AS SUM2_X,\n\nSUM(y) OVER (PARTITION BY <partition cols> ORDER BY <minute> ROWS BETWEEN $k2 PRECEDING AND$k2 FOLLOWING) AS SUM_Y,\n\nSUM(y * y) OVER (PARTITION BY <partition cols> ORDER BY <minute> ROWS BETWEEN $k2 PRECEDING AND$k2 FOLLOWING) AS SUM2_Y,\n\nSUM(x * y) OVER (PARTITION BY <partition cols> ORDER BY <minute> ROWS BETWEEN $k2 PRECEDING AND$k2 FOLLOWING) AS SUM_XY,\n\n\n\\$k2 is half the sliding window size, so if you wanted a window of 60 elements, k2 would be 30. The ROWS BETWEEN r1 PRECEDING AND r2 FOLLOWING syntax specifies a window of rows extending at most r1 rows before the current row, and at most r2 rows beyond the current row. We follow that with an outer query that SELECTs this:\n\nx,\ny,\nCASE\nWHEN N * SUM2_X > SUM_X * SUM_X AND N * SUM2_Y > SUM_Y * SUM_Y\nTHEN (N * SUM_XY - SUM_X * SUM_Y) / (SQRT(N * SUM2_X - SUM_X * SUM_X) * SQRT(N * SUM2_Y - SUM_Y * SUM_Y))\nELSE 0.0\nEND AS corr_yx\n\n\nAnd there we have it... Pearson's correlation coefficient implemented as a window function with window frame support.\n\nWith the above combination, we can get a Pearson's correlation for each (x, y) tuple in the table that correlates a sliding window of data. In my case this was a timeseries database, so for each minute of data, I get a correlation co-efficient of (at most) 61 minutes around that minute (at most 30 before and at most 30 after).\n\nWe can still use the CORR aggregate function on the entire list of (x, y) tuples, or post calculate that in a language like Julia.\n\nFor the next installment, maybe I'll write up how to do Spearman's Rank Correlation Coefficient.\n\n...===..." ]

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[ "", null, "Winter is coming, so get cosy by the fire, warm up some mince pies, and add a little seasonal sparkle to your KS1 maths lessons.\n\nOkay, so you probably don’t have a fireplace and mince pies in your classroom. But you can still add a little magic to your lessons. Created for children aged five to eight, why not try these maths problems in your classroom tomorrow?\n\n## Year 1: add by counting on\n\nIf you follow the Maths — No Problem! scheme of work, you can use these questions alongside Textbook 1A, Chapter 7, Lessons 1-2.\n\nFor this maths problem, you’ll need:\n\n• Counters\n• Ten frames\n\nLesson objective: add by counting on from the largest number.\n\nThere are 7 penguins on an iceberg. 4 more penguins arrive.\nHow many penguins are there now?\n\nGet started by giving your learners ten frames that are already filled with 7 counters. Tell them there are 7 and have them verify this. Ask them to place 7 counters on a copy of the ten frames to represent the penguins.\n\nThen tell them you are going to add 4 more penguins. Ask them how many they have now. How many ways can they figure this out?\n\nFor struggling learners, you can use counters to represent this problem. Use a tray or a container with 7 counters and have 4 counters in your hands. Tell the pupils that there are 7 counters in the tray and you want to add 4 more. How could we do this? Both the count all method and count on method should be discussed.\n\nThere are 5 snowmen in a field. 8 more snowmen are built.\nHow many snowmen are there now?\n\nAsk them if it’s better to count on from the largest number or from the smallest? Is starting from 1 easiest? If we already know how many are in the large group, do we need to count them all?\n\nConsistently asking the question of whether we need to count all of the items when we already know a group has a specific amount will help learners figure out that there’s no need to count all of the items in the large group.\n\nAsk your advanced learners what they should do if the bigger number is not first in the question. Does it make a difference if it’s first or second when we’re adding? Why or why not? Ask them to explain their reasoning.\n\n## Year 2: compare the mass of three objects\n\nIf you follow the Maths – No Problem! scheme of work, you can use these questions alongside Textbook 2A, Chapter 6, Lesson 5.\n\nLesson objective: To compare the mass of three objects and use appropriate vocabulary.\n\nBegin this lesson by showing the class 3 jars that all weigh the same when empty. Fill them up with different items and ask learners if they can tell you how they could compare the different masses. Use their suggestions to talk about the same amount of objects could have different masses.\n\nThen show pupils this task and give them time to discuss what they should do to solve this problem.\n\n3 jars all weigh the same when empty. The jars are filled with different items.\nHow do we compare the masses of the jars?", null, "Encourage use of the language ‘lighter/lightest’ and ‘heavier/heaviest’. Ask learners how they would solve the problem to find the difference between two of the jars.\n\nModel the subtraction calculation and ask them to order the stockings from lightest to heaviest. Have different containers that learners can weigh in groups and ask them to come up with a conclusion to practice their vocabulary.\n\nCompare the masses of 3 reindeer:\n\n• Comet: 85kg\n• Dasher: 115kg\n• Rudolf: 92kg\n1. Who is the heaviest?\n2. Who is the lightest?\n3. Rudolf is ______ kg heavier than Comet.\n4. Arrange the reindeer from lightest to heaviest.\n\nEncourage learners to sort the reindeer in the correct order from lightest to heaviest. Ask them to draw comparisons between the reindeer in the problem.\n\nCan you correctly measure the mass of items in kilograms?\nCan you use a table to record their findings systematically?\nCan you use the terms ‘greater than’, ‘less than’, and ‘heavier than’, ‘lighter than’?\nCan you use the correct symbols for the terminology?\nCan you compare mass of more than two items?\n\n## Year 3: solve word problems\n\nIf you follow the Maths — No Problem! scheme of work, you can use these questions alongside Textbook 3A, Chapter 4, Lesson 9.\n\nLesson objective: To solve word problems that involve multiplication.\n\nTo start the lesson, show you learners this question:\n\nThere are 18 blue scarves in a shop.\nThere are twice as many green scarves as blue scarves.\n\n1. How many green scarves are there?\n2. How many scarves are there altogether?\n\nDiscuss the problem with your class. What key information is given? 18 blue scarves; twice as many green scarves. What is the problem asking us to find? The number of green scarves; the total number of scarves. Give them some time to work on this.\n\n### Using bar models\n\nHow could we represent this maths problem using bar models?\n\nBegin moving pupils in this direction through questioning, giving them time to work it out for themselves. Only use questioning when pupils are unable to move forward on their own. How can we draw the bars to represent the scarves? Which one should be larger?\n\nUse coloured paper or card to represent the bar for the blue scarves. How large should we make the bar for the green scarves? Having the same sized bar for both colours means we have the same amount, so we need the green bar to be bigger.\n\nThe problem says there are twice as many green scarves as blue scarves, so we need to have two bars which are each the same size as one blue bar.\n\nWhat value does the blue bar represent? So how can we work out the value of the green bar?\n\nIt is twice as big as the blue bar: 18 × 2. How can we multiply 18 by 2? (10 × 2) + (8 × 2). Therefore, the number of green scarves is 20 + 16 = 36.", null, "What calculation do we need to do to work out how many scarves there are altogether? There are 18 blue scarves and 36 green scarves. So we can add the amount of scarves together to find the total. 18 + 36 will give us the total number of scarves.", null, "Now try this.\n\nThere are 28 mince pies on a tray.\nThere are 3 times as many gingerbread biscuits as there are mince pies.\n\n1. How many gingerbread biscuits are there?\n2. How many treats are there in total?", null, "Can you use the bar model heuristic to represent number problems?\nCan you represent numbers proportionally using the bar model heuristic?\nCan you multiply or divide when appropriate?\n\n## An extra challenge\n\nIf you’re an avid MNP blog reader, you’ll know how much we love journaling. So why not challenge your learners to invent their own winter-themed questions and record them in their journals. The more creative, the better!\n\nWe’d love to see what your learners come up with. Share your journal entries with us on Twitter by tagging @MathsNoProblem\n\nThat’s a wrap for 2019 blogs! We hope you’ve had an inspiring and productive year. Now put down your textbooks and have a relaxing winter break. You deserve it.\n\nWe’d also like to thank our fantastic author team for all their hard work this year. The blog will be back in action in January — see you in 2020!\n\nis an author, maths tutor and the Blog’s Commissioning Editor.\nPublished on" ]

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[ "Epigram (programming language)\n\nParadigm Functional Conor McBride andJames McKinna Unmaintained 2004 1 / October 11, 2006 strong, static, dependent Cross-platform: Linux, Windows, Mac OS X MIT ALF Agda, Idris\n\nEpigram is a functional programming language with dependent types. Epigram also refers to the IDE usually packaged with the language. Epigram's type system is strong enough to express program specifications. The goal is to support a smooth transition from ordinary programming to integrated programs and proofs whose correctness can be checked and certified by the compiler. Epigram exploits the propositions as types principle, and is based on intuitionistic type theory.\n\nThe Epigram prototype was implemented by Conor McBride based on joint work with James McKinna. Its development is continued by the Epigram group in Nottingham, Durham, St Andrews and Royal Holloway in the UK. The current experimental implementation of the Epigram system is freely available together with a user manual, a tutorial and some background material. The system has been used under Linux, Windows and Mac OS X.\n\nIt is currently unmaintained, and version 2, which was intended to implement Observational Type Theory, was never officially released, however there exists a GitHub mirror, last updated in 2012. The design of Epigram and Epigram 2 have inspired the development of other systems such as Agda, Idris and Coq.\n\nSyntax\n\nEpigram uses a two-dimensional, natural deduction style syntax, with a LaTeX version and an ASCII version. Here are some examples from The Epigram Tutorial:\n\nExamples\n\nThe natural numbers\n\nThe following declaration defines the natural numbers:\n\n ( ! ( ! ( n : Nat !\ndata !---------! where !----------! ; !-----------!\n! Nat : * ) !zero : Nat) !suc n : Nat)\n\nThe declaration says that Nat is a type with kind * (i.e., it is a simple type) and two constructors: zero and suc. The constructor suc takes a single Nat argument and returns a Nat. This is equivalent to the Haskell declaration \"data Nat = Zero | Suc Nat\".\n\nIn LaTeX, the code is displayed as:\n\n${\\underline {\\mathrm {data} }}\\;\\left({\\frac {}{{\\mathsf {Nat}}:\\star }}\\right)\\;{\\underline {\\mathrm {where} }}\\;\\left({\\frac {}{{\\mathsf {zero}}:{\\mathsf {Nat}}}}\\right)\\;;\\;\\left({\\frac {n:{\\mathsf {Nat}}}{{\\mathsf {suc}}\\ n:{\\mathsf {Nat}}}}\\right)$", null, "The horizontal-line notation can be read as \"assuming (what is on the top) is true, we can infer that (what is on the bottom) is true.\" For example, \"assuming n is of type Nat, then suc n is of type Nat.\" If nothing is on the top, then the bottom statement is always true: \"zero is of type Nat (in all cases).\"\n\nRecursion on naturals\n\n${\\mathsf {NatInd}}:{\\begin{matrix}\\forall P:{\\mathsf {Nat}}\\rightarrow \\star \\Rightarrow P\\ {\\mathsf {zero}}\\rightarrow \\\\(\\forall n:{\\mathsf {Nat}}\\Rightarrow P\\ n\\rightarrow P\\ ({\\mathsf {suc}}\\ n))\\rightarrow \\\\\\forall n:{\\mathsf {Nat}}\\Rightarrow P\\ n\\end{matrix}}$", null, "${\\mathsf {NatInd}}\\ P\\ mz\\ ms\\ {\\mathsf {zero}}\\equiv mz$", null, "${\\mathsf {NatInd}}\\ P\\ mz\\ ms\\ ({\\mathsf {suc}}\\ n)\\equiv ms\\ n\\ (NatInd\\ P\\ mz\\ ms\\ n)$", null, "...And in ASCII:\n\nNatInd : all P : Nat -> * => P zero ->\n(all n : Nat => P n -> P (suc n)) ->\nall n : Nat => P n\nNatInd P mz ms zero => mz\nNatInd P mz ms (suc n) => ms n (NatInd P mz ms n)\n\n ${\\mathsf {plus}}\\ x\\ y\\Leftarrow {\\underline {\\mathrm {rec} }}\\ x\\ \\{$", null, "${\\mathsf {plus}}\\ x\\ y\\Leftarrow {\\underline {\\mathrm {case} }}\\ x\\ \\{$", null, "${\\mathsf {plus\\ zero}}\\ y\\Rightarrow y$", null, "$\\quad \\quad {\\mathsf {plus}}\\ ({\\mathsf {suc}}\\ x)\\ y\\Rightarrow suc\\ ({\\mathsf {plus}}\\ x\\ y)\\ \\}\\ \\}$", null, "...And in ASCII:\n\nplus x y <= rec x {\nplus x y <= case x {\nplus zero y => y\nplus (suc x) y => suc (plus x y)\n}\n}\n\nDependent types\n\nEpigram is essentially a typed lambda calculus with generalized algebraic data type extensions, except for two extensions. First, types are first-class entities, of type $\\star$", null, "; types are arbitrary expressions of type $\\star$", null, ", and type equivalence is defined in terms of the types' normal forms. Second, it has a dependent function type; instead of $P\\rightarrow Q$", null, ", $\\forall x:P\\Rightarrow Q$", null, ", where $x$", null, "is bound in $Q$", null, "to the value that the function's argument (of type $P$", null, ") eventually takes.\n\nFull dependent types, as implemented in Epigram, are a powerful abstraction. (Unlike in Dependent ML, the value(s) depended upon may be of any valid type.) A sample of the new formal specification capabilities dependent types bring may be found in The Epigram Tutorial." ]

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[ "# Question: calculating orbit using another orbit\n\nA satellite which is moving around a planet of mass $$M$$ in a circular orbit of radius $$R$$ is given a sudden thrust into the center of the planet, so that it deviates an angle $$a$$.\n\nFind the latus-rectum $$l$$ and the eccentricity $$e$$ of the new orbit.\n\n• What do you mean by \"into the center of the earth\"? Do you mean towards the center of the earth?\n– LDC3\nJan 3, 2015 at 4:19\n• i mean directing to the centre of the planet. Jan 3, 2015 at 10:28\n• This question appears to be off-topic because it is about homework. Jan 3, 2015 at 12:17\n• @DavidHammen AFAIK homework isn't itself off topic in Astronomy. That said, the question could probably use some rewording. Jan 3, 2015 at 14:13\n• Don't expect to get your homework done by others. Put some effort into it, show what you tried. Say where you stumble. Jan 3, 2015 at 16:13\n\n• I don't want to see your image. You need to learn the difference between angular momentum and (linear) momentum. Jan 4, 2015 at 0:48" ]

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[ "# Questions tagged [statistics]\n\n5030 questions\n\nvotes\n1\n\nanswer\n25\n\nViews\n\n### Simulation of multiple binomial random numbers in R\n\nI have the following algorithm Step 1. Generate X1=x1~Bin(6,1/3) Step 2. Generate X2|X1=x1~Bin(6-x1,(1/3)/(1-1/3)) Step 3. Generate X3|X1=x1,X2=x2~Bin(6-x1-x2,(1/3)/(1-1/3-1/3)) Step 4. Repeat step 1-3 N times. Here is my approach to implement this algorithm in R: mult_binom\nIsa\n\nvotes\n1\n\nanswer\n2.7k\n\nViews\n\n### test statistic for Spearman rank correlation\n\nmy problem is that I have calculated Spearman rank correlations between two variables. One reviewer asked me if I could add also test statistics for all coefficients where p < 0.001. Here is one result: > cor.test(pl\\$data, pl\\$rang, method= 'spearman') # Spearman's rank correlation rho data: p...\nEco06\n\nvotes\n2\n\nanswer\n22\n\nViews\n\n### Is it possible to get the PERCENT_RANK for a single record, but relative to the entire table?\n\nI would like the PERCENT_RANK value for a single record, but in relation to the entire table. Is this possible? Examples I've seen are like this: SELECT Name, Salary PERCENT_RANK() OVER (ORDER BY Salary) FROM Employees Notice that it's calculating the percentile for the returned recordset. If you're...\nDeane\n\nvotes\n1\n\nanswer\n1.9k\n\nViews\n\n### R ggplot geom_bar() label bars (with 'count')\n\nI have a ggplot like this: ggplot(df,aes(x=DateDiff, fill=TEAM)) + geom_bar() How can I label the bars with the results from the y axis, when there's no y axis defined? (without altering the df)\nadlisval\n\nvotes\n0\n\nanswer\n5\n\nViews\n\n### What type of machine learning or AI Model can I use for Factor Ranking\n\nWhat type of machine learning or AI Model can I use for Factor Ranking? I have some factors and am trying to rank them based on how they are able to predict in my model please what kind of machine learning or AI or Deep Learning Model work for this?\ntplshams\n\nvotes\n1\n\nanswer\n10\n\nViews\n\n### How to remove extra statistical mean results from JSON dictionary in python?\n\nI'm working in python3 - I'm trying to determine the mean from measurements in a JSON dictionary of contaminants in a well. When I return the code its shows the mean of the data for each line. Essentially I want to find one mean for all results of one contaminant. There are multiple results for the...\nceagle\n\nvotes\n4\n\nanswer\n93\n\nViews\n\n### Linear regression with two variables on python\n\nI am developing a code to analyze the relation of two variables. I am using a DataFrame to save the variables in two columns as it follows: column A = 132.54672, 201.3845717, 323.2654551 column B = 51.54671995, 96.38457166, 131.2654551 I have tried to use statsmodels but it says that I do not hav...\nHugo Assis Brandao\n\nvotes\n1\n\nanswer\n103\n\nViews\n\n### Julia - describe() function display incomplete summary statistics\n\nI'm trying basic data analysis with Julia I'm following this tutorial with the train datasets that can be found here (the one named train_u6lujuX_CVtuZ9i.csv) with the following code: using DataFrames, RDatasets, CSV, StatsBase train = CSV.read('/Path/to/train_u6lujuX_CVtuZ9i.csv'); describe(train[...\necjb\n\nvotes\n0\n\nanswer\n94\n\nViews\n\n### Choosing the right design for nparLD\n\nI have to use nparLD package due to some data distribution and heteroscedasticity reasons but I have some trouble to select the right design (F1-LD-F1 or F2-LD-F1). I have two groups (one for patients and one for controls) and all participants underwent the same MR examination three times (before ex...\nN. Szilvia\n\nvotes\n1\n\nanswer\n262\n\nViews\n\n### Bootstrap for Confidence Intervals\n\nMy problem is as follows: Firstly, I have to create 1000 bootstrap samples of size 100 of a 'theta hat'. I have a random variable X which follows a scaled t_5-distribution. The following code creates 1000 bootstrap samples of theta hat: library('metRology', lib.loc='~/R/win-library/3.4') # Draw some...\nHans Christensen\n\nvotes\n0\n\nanswer\n164\n\nViews\n\n### How do I propagate the error of a linear regression when projecting from Y to X?\n\nI'm trying to figure out how to propagate errors in the following case I am calibrating a machine with a couple of standards (a, b, c) with accepted values x. My machine measures y for these standards, with a certain error (standard deviation of 1 in this example). Then I measure replicates of a sam...\nJaphir\n\nvotes\n0\n\nanswer\n68\n\nViews\n\n### IHS (inverse hyperbolic sine) option of mhurdle in r does not work\n\nI hope this thread finds you well. I am trying to use Box-Cox double hurdle model and Inverse Hyperbolic Sine (IHS) double hurdle model since the dependent variable of my data is non-normal. The problem I face is that I could not find some appropriate package to run the IHS model. I tried 'mhurdle'...\nJaecheol Lee\n\nvotes\n0\n\nanswer\n317\n\nViews\n\n### How to estimate weibull hazard rate function for a feature based on components failure data?\n\nA mechanical component was run continuously till it failed (test-to-failure). We have data of one such experiment. Data Dictionary age --> time in mins. life_per --> age/total time to failure life_status --> faliure==1 and 0== non failure (note: we only have 1 record with life_status=1 i.e. the tim...\nGeorgeOfTheRF\n\nvotes\n0\n\nanswer\n145\n\nViews\n\n### BCa confidence interval using pre-bootstrapped data\n\nI want to calculate a BCa confidence interval using the function boot.ci in the boot package. I do already have bootstrap replicates (not calculated using the boot function provided by the package). To calculate a BCa confidence interval, it should be sufficient to pass the bootstrap replicates tog...\nUweM.\n\nvotes\n0\n\nanswer\n200\n\nViews\n\n### Can Kruskal-Wallis test be used to test significance of multiple groups within multiple factors?\n\nI have tried to read what I can on Kruskal-Wallis and while I have found some useful information, I still seem to not find the answer to my question. I am trying to use the Kruskal-Wallis test to determine the significance of multiple groups, within multiple factors, in predicting a set of dependen...\nuser3245629\n\nvotes\n0\n\nanswer\n108\n\nViews\n\n### Correllation (pandas) between integer and boolean?\n\nI have my data in the form of: price | bool_qual_1 | bool_qual_2 | bool_qual_3 13000 | True | True | True 20000 | False | True | True 15000 | True | True | False 13000 | False | False | False 15000 | True |...\nZeruno\n\nvotes\n1\n\nanswer\n118\n\nViews\n\n### Trying to display NONE when there is no mode in R\n\nI am trying to figure the mode of a data set, while displaying 'NONE' if there is no mode. I am currently using Gregor's function as commented below. examples: {1,1,2,2,3} Expected results 1 2(success) {NA,NA,NA,1,1,1,3,3} Expected results NA 1(success) {1,2,3,4,5} Expected result NONE (success) {...\nJerry Lim\n\nvotes\n0\n\nanswer\n159\n\nViews\n\n### How to perform Welch's Ttest in Spark 2.0.0 using StreamingTest\n\nI want to try Welch's T-test in Spark 2.0.0 As I know I can use StreamingTest() from mllib on this website. [https://spark.apache.org/docs/2.0.0/api/scala/index.html#org.apache.spark.mllib.stat.test.StreamingTest] this is my code in spark-shell import org.apache.spark.mllib.stat.test.{BinarySample,...\nJchanho\n\nvotes\n0\n\nanswer\n64\n\nViews\n\n### failure to get the 95%CI of D index using 'survcomp' and 'boot' package\n\nI have used 'survcomp' to calculate the D index of the prediction model. The code was listed as follows: source('http://bioconductor.org/biocLite.R') biocLite('survcomp') library(survcomp) set.seed(12345) age\nQW Zhang\n\nvotes\n1\n\nanswer\n139\n\nViews\n\n### Error with bspline smoothing for functional data in R with high number of basis functions\n\nI have this error in R, I can't solve it : Error in chol.default(temp) : the leading minor of order 445 is not positive definite In addition: Warning message: In smooth.basis1(argvals, y, fdParobj, wtvec = wtvec, fdnames = fdnames, : Matrix of basis function values has rank 799 < dim(fdobj\\$basis)...\nVictoire Louis\n\nvotes\n0\n\nanswer\n332\n\nViews\n\n### Multivariable linear regression in JS\n\nI am trying to perform multivariable linear regression with a single dependent variable Y and two independent variables x1, x2. This is simply an OLS regression with an additional dependent variable: Y = b0 + b1 x1 + b2 x2 I need to also calculate the correlation coefficient R^2 for this relationsh...\nMartin\n\nvotes\n1\n\nanswer\n89\n\nViews\n\n### Linear regression with two independent variables in javascript\n\nThe following will output the slope, intercept and correlation coefficient R^2 for a given set of x and y values. let linearRegression = (y,x) => { let lr = {} let n = y.length let sum_x = 0 let sum_y = 0 let sum_xy = 0 let sum_xx = 0 let sum_yy = 0 for (let i = 0; i < y.length; i++) { sum_x += x[i]...\nMartin\n\nvotes\n0\n\nanswer\n26\n\nViews\n\n### Distinguishing random gnp graphs from preferential attachment grpahs using the powerlaw python package\n\nMy goal is to find the point where scale-free networks become indistinguishable from random (non-scale-free) networks using the powerlaw python package As stated in their paper one should determine the goodness of a power-law fit always by comparing it to the fit to another distribution. I would exp...\nDavid Nathan\n\nvotes\n0\n\nanswer\n48\n\nViews\n\n### Latent factor recovery with probabilistic matrix factorization using Edward\n\nI implemented a probabilistic matrix factorization model (R = U'V) following the example in Edward's repo: # data U_true = np.random.randn(D, N) V_true = np.random.randn(D, M) R_true = np.dot(np.transpose(U_true), V_true) + np.random.normal(0, 0.1, size=(N, M)) # model I = tf.placeholder(tf.float32,...\ncharlesh\n\nvotes\n0\n\nanswer\n16\n\nViews\n\n### how can I write a loop in python to get the difference between first and last date for one id\n\nopptyId field oldValue newValue updateTime 0 Stage Qualify 2014-05-27T18:50:14 0 Forecast Best Case 2014-05-27T18:50:14 0 created 2014-05-27T18:50:14 0 Amount 795.53 2014-06-17T18:54:00 0 Stage Qualify Closed - Won 2014-07-09T20:11:05 0 Forecast...\nbella\n\nvotes\n0\n\nanswer\n12\n\nViews\n\n### How to learn R as a statistical system?\n\nI am more familiar with Python (at a beginner level), which I have found way easier than R thus far. Nevertheless, for professional reasons I want to learn R as well. My main intention is to learn how to use it as a statistical system. I looked in Stackoverflow for some recommendations on learning...\nAlejandro Ruiz\n\nvotes\n0\n\nanswer\n194\n\nViews\n\n### Using scipy.stats.entropy on gmm.predict_proba() values\n\nBackground so I don't throw out an XY problem -- I'm trying to check the goodness of fit of a GMM because I want statistical back-up for why I'm choosing the number of clusters I've chosen to group these samples. I'm checking AIC, BIC, entropy, and root mean squared error. This question is about en...\nManner\n\nvotes\n0\n\nanswer\n181\n\nViews\n\n### Pandas vectorize statistical odds-ratio test\n\nI'm looking for a faster way to do odds ratio tests on a large dataset. I have about 1200 variables (see var_col) I want to test against each other for mutual exclusion/ co-occurrence. An odds ratio test is defined as (a * d) / (b * c)), where a, b c,d are number of samples with (a) altered in neith...\nXyledMonkey\n\nvotes\n1\n\nanswer\n401\n\nViews\n\n### How can I make all-possible-regressions in R also include exponents and logs of the variables?\n\nI primarily work in research and statistics and so am not as familiar with programming. I'm using the OLSRR package for statistical analysis when trying to compare as many model specifications as possible using all-possible-regressions. I use the code: model\nZayaan\n\nvotes\n1\n\nanswer\n897\n\nViews\n\n### Confidence interval in python\n\nIs there a function or a package in python to get the 95% or 99% confidence interval of the distributions present in scipy.stats. If not what is easiest alternative for that Here are the distributions (but my priority is halfgennorm and loglaplace) st.alpha,st.anglit,st.arcsine,st.beta,st.betaprime...\nWill_smith12\n\nvotes\n1\n\nanswer\n109\n\nViews\n\n### NA value in portfolio sorts\n\nI am currently doing portfolio sorts on panel data meaning every month I form 5 portfolios based on the volatility of stocks. I have the following function: arguments are x: a vector of returns P: the number of portfolios we want sortPort\nuser9259005\n\nvotes\n0\n\nanswer\n167\n\nViews\n\n### Is this right way to generate the following heavy-tailed distribution?\n\nI'm trying to generate an error distribution which follows a heavy-tailed distribution based on the statement : (2) A heavy-tailed distribution, i.e., t-df=2, a t-distribution with 2 degrees of freedom. This distribution has C95=3.61, where C95 is a measure of the distribution tail weight and defin...\nRyan\n\nvotes\n0\n\nanswer\n248\n\nViews\n\n### Multivariate linear mixed effects model in Python\n\nI am playing around with this code which is for Univariate linear mixed effects modelling. The data set denotes: students as s instructors as d departments as dept service as service In the syntax of R's lme4 package (Bates et al., 2015), the model implemented can be summarized as: y ~ 1 + (1|stude...\nlaza\n\nvotes\n0\n\nanswer\n229\n\nViews\n\n### Fair quantiles with lots of same values?\n\nDoing rfm analysis. i want to divide ranks by 5. i've done this ok. The problem is when i try the quantile function by 5 in the frequency part to divide buyers by 'great customer' if they buy often with rank 5, 'good' if they buy kind of less (rank 4) and so on, the fact that large number of buyers...\nJ_p\n\nvotes\n1\n\nanswer\n298\n\nViews\n\n### Bootstrap Confidence Interval for Prediction\n\nI would like to calculate a confidence interval for the RMSE of a machine learning regression in the out-of-sample test set predictions. My train set is the first 80% of the sample, and the 'out-of-sample' test set is the last 20% of the sample. I treat the RMSE of the test set predictions as the o...\nBen Smith\n\nvotes\n0\n\nanswer\n89\n\nViews\n\n### BTYD pnbd.EstimateParameters(): cal.cbs must have a frequency column labelled “x”\n\nI am working on building a CLV model. I have faced an error, but answers to sharp's question helped in resolving it. Now, when I try and estimate the parameters using params\nAkshat Bajaj\n\nvotes\n2\n\nanswer\n92\n\nViews\n\n### knn algorithm output one result per test data\n\nI used knn to do a basic predictive model build. After I run: predictions = knn(train,test,cl,k=3) and then output predictions, the R console has a dozen results per row. Such as: Yes No Yes Yes Yes No Yes Yes Yes No No No Yes Yes Yes No No No Yes Yes Yes No etc etc for 10000 rows. I need t...\nJayA\n\nvotes\n1\n\nanswer\n374\n\nViews\n\n### Standard deviation of binned values with `scipy.stats.binned_statistic`\n\nWhen I bin my data accordingly to scipy.stats.binned_statistic (see here for example), how do I get the error (that is the standard deviation) on the average binned values? For example, if I bin my data as following: windspeed = 8 * np.random.rand(500) boatspeed = .3 * windspeed**.5 + .2 * np.random...\nPy-ser\n\nvotes\n0\n\nanswer\n4\n\nViews\n\n### What statistical method should I resort to to analyze the generational difference?\n\nSo I would like to analyze the value attitude differences between two generations (Young people's generation and their parents' generation). I understand that normally independent t test or Anova can be used for this problem. The thing is, I PAIRED the children with their respective parent(so I coll...\njeff.lian\n\nvotes\n0\n\nanswer\n35\n\nViews\n\n### Get the variance of a “list” of values with multiplicities?\n\nI'm using python and I've pulled in numpy/scipy as dependencies. It's OK to pull in more if they're well-tested and so on. Suppose I've got a dataset with a relatively small number of distinct values, each of which has a high multiplicity. I'll represent it as a map (Value -> Multiplicity), say some...\nRichard Rast" ]

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[ "", null, "# paulfioravanti's solution\n\n## to ETL in the Ruby Track\n\nPublished at Jul 13 2018 · 0 comments\nInstructions\nTest suite\nSolution\n\nWe are going to do the `Transform` step of an Extract-Transform-Load.\n\n### ETL\n\nExtract-Transform-Load (ETL) is a fancy way of saying, \"We have some crufty, legacy data over in this system, and now we need it in this shiny new system over here, so we're going to migrate this.\"\n\n(Typically, this is followed by, \"We're only going to need to run this once.\" That's then typically followed by much forehead slapping and moaning about how stupid we could possibly be.)\n\n### The goal\n\nWe're going to extract some scrabble scores from a legacy system.\n\nThe old system stored a list of letters per score:\n\n• 1 point: \"A\", \"E\", \"I\", \"O\", \"U\", \"L\", \"N\", \"R\", \"S\", \"T\",\n• 2 points: \"D\", \"G\",\n• 3 points: \"B\", \"C\", \"M\", \"P\",\n• 4 points: \"F\", \"H\", \"V\", \"W\", \"Y\",\n• 5 points: \"K\",\n• 8 points: \"J\", \"X\",\n• 10 points: \"Q\", \"Z\",\n\nThe shiny new scrabble system instead stores the score per letter, which makes it much faster and easier to calculate the score for a word. It also stores the letters in lower-case regardless of the case of the input letters:\n\n• \"a\" is worth 1 point.\n• \"b\" is worth 3 points.\n• \"c\" is worth 3 points.\n• \"d\" is worth 2 points.\n• Etc.\n\nYour mission, should you choose to accept it, is to transform the legacy data format to the shiny new format.\n\n### Notes\n\nA final note about scoring, Scrabble is played around the world in a variety of languages, each with its own unique scoring table. For example, an \"E\" is scored at 2 in the Māori-language version of the game while being scored at 4 in the Hawaiian-language version.\n\nFor installation and learning resources, refer to the Ruby resources page.\n\nFor running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:\n\n``````gem install minitest\n``````\n\nIf you would like color output, you can `require 'minitest/pride'` in the test file, or note the alternative instruction, below, for running the test file.\n\nRun the tests from the exercise directory using the following command:\n\n``````ruby etl_test.rb\n``````\n\nTo include color from the command line:\n\n``````ruby -r minitest/pride etl_test.rb\n``````\n\n## Source\n\nThe Jumpstart Lab team http://jumpstartlab.com\n\n## Submitting Incomplete Solutions\n\nIt's possible to submit an incomplete solution so you can see how others have completed the exercise.\n\n### etl_test.rb\n\n``````require 'minitest/autorun'\nrequire_relative 'etl'\n\n# Common test data version: 1.0.0 ca9ed58\nclass EtlTest < Minitest::Test\ndef test_a_single_letter\n# skip\nold = {\n1 => [\"A\"]\n}\nexpected = {\n'a' => 1\n}\nassert_equal expected, ETL.transform(old)\nend\n\ndef test_single_score_with_multiple_letters\nskip\nold = {\n1 => [\"A\", \"E\", \"I\", \"O\", \"U\"]\n}\nexpected = {\n'a' => 1,\n'e' => 1,\n'i' => 1,\n'o' => 1,\n'u' => 1\n}\nassert_equal expected, ETL.transform(old)\nend\n\ndef test_multiple_scores_with_multiple_letters\nskip\nold = {\n1 => [\"A\", \"E\"],\n2 => [\"D\", \"G\"]\n}\nexpected = {\n'a' => 1,\n'd' => 2,\n'e' => 1,\n'g' => 2\n}\nassert_equal expected, ETL.transform(old)\nend\n\ndef test_multiple_scores_with_differing_numbers_of_letters\nskip\nold = {\n1 => [\"A\", \"E\", \"I\", \"O\", \"U\", \"L\", \"N\", \"R\", \"S\", \"T\"],\n2 => [\"D\", \"G\"],\n3 => [\"B\", \"C\", \"M\", \"P\"],\n4 => [\"F\", \"H\", \"V\", \"W\", \"Y\"],\n5 => [\"K\"],\n8 => [\"J\", \"X\"],\n10 => [\"Q\", \"Z\"]\n}\nexpected = {\n'a' => 1,\n'b' => 3,\n'c' => 3,\n'd' => 2,\n'e' => 1,\n'f' => 4,\n'g' => 2,\n'h' => 4,\n'i' => 1,\n'j' => 8,\n'k' => 5,\n'l' => 1,\n'm' => 3,\n'n' => 1,\n'o' => 1,\n'p' => 3,\n'q' => 10,\n'r' => 1,\n's' => 1,\n't' => 1,\n'u' => 1,\n'v' => 4,\n'w' => 4,\n'x' => 8,\n'y' => 4,\n'z' => 10\n}\nassert_equal expected, ETL.transform(old)\nend\nend``````\n``````module ETL\nmodule_function\n\ndef transform(scores)\nscores.each_with_object({}, &method(:transform_letters))\nend\n\ndef transform_letters((point_value, letters), new_scores)\nletters.each do |letter|\nnew_scores[letter.downcase] = point_value\nend\nend\nprivate_class_method :transform_letters\nend``````" ]

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[ "1. Thank you VERY much for the informative post! btw: in terms of using the API to finish a triangle, the reason I'm asking all these questions is that I'm not using an API. If I did, even though I would have a nice app, I wouldn't understand the math as well.\n\nAgain, thank you.", null, "", null, "2. To further illustrate here is a shot from my project in texture mode.", null, "3. Here is a shot from nearly the same location in wireframe mode. Notice that the texture's are still applied to the lines (if you can see that in the screen shot) so this is not pure wireframe mode, but it's close.\n\nI had to ramp the RGBs to get this to display right. Hope you can see it.\n\nYou can see that my sphere's are made up of a bunch of flat faces. The flat faces are then divided into 2 triangles. So you can see the triangles in this pic quite well.\n\nAlso the lighting is turned on in this pic and the light source is directly behind the camera. I softened the image a bit so you can see the lines better.\n\nThe big blue lines behind the sphere (they are behind it, but you can see through the sphere now so they show up) are from the backdrop sphere. Notice in the texture picture that there is a big space backdrop texture. This is simply a huge textured sphere that is always centered around the camera. In the wireframe mode pic you can see the background sphere as well as the planet sphere.\n\nTo visualize the square faces in your mind, mentally take out all the diagonal lines in the wireframe pic. Now put em back in and you have the triangles. They were created exactly the same way I explained and illustrated in my post.", null, "4. Just in case you are having probs picking out the tris - I have color highlighted the tris according to the example picture I showed you above.\n\nRed corresponds to triangle 1, and yellow corresponds to triangle 2.", null, "5. OH MY GOD! You are like a god! That's absolutly the coolest thing I've ever seen! I can't even make a spinning wireframe box, and you not only made a wireframe sphere, but also textured!\n\nJust thought I'd say, I worship you man!\n\nThanks again,", null, "6. Another example.", null, "7. Hold on, I think I just understood something after re-reading your posts. So, that entire wireframe sphere is simply squares, rotated and skewed to fit the surface of the sphere, then cut in half as triangles?\n\nWow, that's really cool.", null, "8. Yes it is. Every model is composed of triangles. Now not all models decompose neatly into squares, but a lot of them do. Mine does because the sphere is created mathematically into quads or squares and then the squares are made into 2 triangles...or they are triangulated.\n\nThe rotation and all of that in my later pics are just a result of all the transformations the vertexes undergo as a result of the rendering pipeline or the method used to get the graphics from 3D to 2D.\n\nTerrains also usually decompose neatly into triangulated quads or squares.\n\nHere is the order for the render I showed you.\n\n1. Model is created in model space centered at 0,0,0.\n2 Model is created using mathematical equation of a sphere.\n3. Vertexes are created from spherical coordinates resulting from equation.\n4. Vertex normals are calculated by simply using the normalized or unit vertexes (basically where the vertexes would be if the radius of the sphere was 1.0f or 1 unit).\n5. Formula:\n\nThese axes have been altered somewhat to fit my system.\n\n-180<beta<180\n0<alpha<360\nalpha_increment=number of slices (longitude)/360.0f\nbeta_increment=number of stacks (lattitude)/360.0f\n\nx=sin(beta)*cos(alpha)\ny=sin(beta)*sin(alpha)\nz=cos(beta)\n\nnormal.x=x\nnormal.y=y\nnormal.z=z\n\nvertex.x=x\nvertex.y=y\nvertex.z=z\n\nalpha+=alpha_increment;\nif (alpha>360.0f) beta+=beta_increment;\n\n6. Spherical texture coords are generated along with vertex data.\n7. Indexes into the vertex array are created - thus triangulating each four sided square into two triangles.\n8. Model is assigned D3DMATERIAL9 material for lighting.\n\nRendering:\n\n10. Model is rotated in model/local space.\n11. Model is translated to world location.\n12. Model is rotated in world space.\n13. Model is transformed to world space. world=(model_rot)*(world_loc)*(world_rot)\n14. Model is transformed to view space based on camera rotation, translation/position, etc. - too complex to list here. view=world*camera\n15. Model is transformed to clip space by Direct3D. clip=view*clip_matrix\n16. Model is lit by Direct3D.\n17. Model is transformed to screen space by Direct3D.\n18. Model is culled and textured by Direct3D using video card driver.\n\nThe first 9 steps are only performed at load time. The rest are done every frame.", null, "9. Aha, thanks.", null, "Popular pages Recent additions", null, "" ]

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[ "# Clarification on the Keras Recurrent Unit Cell\n\nI paste below the Keras documentation on Recurrent layer\n\nmodel= Sequential()\n\n# now model.output_shape == (None, 32)\n# note: None is the batch dimension.\n\n\nWhat does the first argument of LSTM 32 mean here? Is it creating 32 LSTM blocks (By block I mean consisting of input, forget and output gate)? Could you please explain the meaning of the first argument and how that contributes to the output dimension of the LSTM both when return sequences is True and when return sequences is False\n\nThe notation used for LSTM is quite confusing, and this took me some time to get my head around this as well. When you see this graphic (often used to explain RNNs):", null, "You need to consider that X is a sequence of data the timestep t, it's not just a single scalar input value (as we're used to with feed-forward networks); it's an array / tensor of data. The diagram shows how there is an output at time-step t, but that it then also feeds into the next time-step, t+1, when the next array/tensor is then fed in.\n\nA better/clearer way (in my opinion) is to look at it is like this:", null, "So a LSTM 'cell' is actually what you might consider a layer. And a unit (one of the circles) is one of these:", null, "which you can consider a neuron in a hidden layer.\n\nInitially, I thought this was a cell, but it isn't, it's a single unit. So when you specify 32 units, for example, you're actually saying how many of these units (neurons) you want in the cell (layer).\n\nThis is what gives the model its capacity to learn the data that's presented to it. And just like hidden layers/neurons in a feed-forward, it's a hyperparameter that you'll need to experiment with; too low and the model will under-fit, too high and it will over-fit.\n\nThe value '32' in this case is the size of the cell state and the size of the hidden state being sent forward in the network. Please see my answer here for more information.\n\nThe question may be too old but I think the BigBadMe answer is not true. As the keras docs said:\n\nunits: Positive integer, dimensionality of the output space.\n\nThe number of units actually is the dimension of the hidden state (or the output).\n\nFor example, in the image below, the hidden state (the red circles) has length 2. The number of units is the number of neurons connected to the layer holding the concatenated vector of hidden state and input (the layer holding both red and green circles below). In this example, there are 2 neurons connected to that layer.\n\nThe number of units defines the dimension of hidden states (or outputs) and the number of params in the LSTM layer.", null, "The image above is taken from: https://towardsdatascience.com/counting-no-of-parameters-in-deep-learning-models-by-hand-8f1716241889, which is a helpful article on LSTM" ]

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[ "# Convergent and Divergent Integrals\n\n## Main Question or Discussion Point\n\nI had a question regarding convergent and divergent integrals. I want to know the \"exact\" definition of an improper integral that converges. Wikipedia states that\nAn improper integral converges if the limit defining it exists.\nFor a while, I took that as a valid answer and claimed that any integral that has a finite answer must be convergent. However, I came up with a problem.\nIf you solve $$\\int_0^2 \\frac{dx}{1-x}$$, it turns out that it diverges twice, on both integrals (0 to 1, and 1 to 2). My textbook, which has never failed me so far, states that it diverges. Its solution solves only one of the integrals and it of course goes to infinity. Therefore, it diverges. However, if you solve the integral algebraically, you're left with $$ln|\\dfrac{1-b}{1-b}|$$, which ends up being 0 as $$\\lim_{b\\rightarrow 1}$$. Clearly, this integral has a limit that exists.\nThe problem lies in the fact that this integral \"diverges\" twice, at the same rate but in opposite directions. When evaluating this integral, this logically would lead to 0 because they're opposites of eacher.\n\nWhat's your guys' opinions on whether this converges or diverges?\n\nMaybe I do it differently, though. Could I write the integral as the limit as b approaches 1 of $$\\int_0^{b^2} \\frac{dx}{1-x} + \\int_b^2 \\frac{dx}{1-x}$$?\n\nVery interesting idea. That leads to $$ln|\\frac{1-b}{1-b^2}|$$ which is $$-ln2$$ by L'H or simple canceling. That seems to make no sense at all, even though everything arithmetically looks right. A change in only one of the $$n$$s for $$\\int_0^{b^n}$$ or $$\\int_{b^n}^2$$ changes the answer. Therefore, I would have to guess that doing so is not allowed. However, I'm only a high school student so I know next to nothing compared to you guys.\n\nHuh?\n\nThe anti-derivative of $$\\frac{1}{1 - x}$$ is $$-ln(1 - x) + C$$, which certainly does not have a limit as x goes to 1.\n\nThe problem is that infinity - infinity does not necessarily = 0.\n\nYour problem could be reworded as the following integral:\n\n$$\\int_{-1}^{1} \\frac{1}{x} dx$$\n\nIntuitively, both sides grow at the same rate but with opposite sign, therefore the integral is zero. This is where mathematical rigor > intuition. As it turns out, the integral is undefined (it's actually $$i \\pi$$).\n\nYou have to be very careful to see if the integral actually converges or not.\n\nThis is how I would do the math. I'm not saying that infinity - infinity is 0, but by using L'H and the difference of logs, you get an answer of 0.\n$$\\lim_{b\\rightarrow0} \\int_{-1}^b \\dfrac{dx}{x} + \\int_b^1 \\dfrac{dx}{x}$$\n\n$$\\lim_{b\\rightarrow0} ln|x| |_{-1}^b + ln|x||_b^1$$\n\n$$\\lim_{b\\rightarrow0} ln|b| - ln1 + ln1 - ln|b|$$\n\n$$\\lim_{b\\rightarrow0} ln|b| - ln|b|$$\n\n$$\\lim_{b\\rightarrow0} ln|\\frac{b}{b}|$$\n\n$$\\lim_{b\\rightarrow0} ln|1|$$\n\n$$0$$\nI'm guessing that I'm not allowed to cancel the b/b part?\n\nLast edited:\nThe indefinite integral is NOT\n\n$$\\lim_{b\\rightarrow0} \\int_{-1}^b \\dfrac{dx}{x} + \\int_b^1 \\dfrac{dx}{x}$$\n\nRather, it's\n\n$$\\lim_{b\\rightarrow0} \\int_{-1}^b \\dfrac{dx}{x} + \\lim_{b\\rightarrow0} \\int_b^1 \\dfrac{dx}{x}$$\n\nwhich does not exist.\n\nOh, I see. So you have to simplify each one separately and then add them together if they're finite numbers. Thank you for clarifying that.\n\nIt still gives me chills since by looking at the function graphically, it looks like it's 0. I agree with what L'h said though.\n\nLast edited:\nYou don't simplify each separately. The first limit does indeed exist, and it's 0 as you pointed out.\n\nThe indefinite integral is said to exist if both limits exist, and in this case it's their sum. So when I say that it's the sum of their limits rather than the limit of their sums, it's a matter of definition.\n\nAn integral doesn't exist if the integral over any subdomain doesn't exist.\n\nTorquil\n\nHallsofIvy\nHomework Helper\nI had a question regarding convergent and divergent integrals. I want to know the \"exact\" definition of an improper integral that converges. Wikipedia states that For a while, I took that as a valid answer and claimed that any integral that has a finite answer must be convergent. However, I came up with a problem.\nIf you solve $$\\int_0^2 \\frac{dx}{1-x}$$, it turns out that it diverges twice, on both integrals (0 to 1, and 1 to 2). My textbook, which has never failed me so far, states that it diverges. Its solution solves only one of the integrals and it of course goes to infinity. Therefore, it diverges. However, if you solve the integral algebraically, you're left with $$ln|\\dfrac{1-b}{1-b}|$$, which ends up being 0 as $$\\lim_{b\\rightarrow 1}$$. Clearly, this integral has a limit that exists.\nThe problem lies in the fact that this integral \"diverges\" twice, at the same rate but in opposite directions. When evaluating this integral, this logically would lead to 0 because they're opposites of eacher.\nBut that is an incorrect calculation. The correct definition for such an improper integral would be\n\n$\\lim_{\\delta\\to 0}\\int_0^{1- \\delta}\\frac{dx}{1-x}+\\lim_{\\epsilon\\to 0} \\int_{1+ \\epsilon}^2 \\frac{dx}{1- x}$\n\nwith $\\delta$ and $\\epsilon$ going to 0 independently.\n\nWhat you are doing is the \"Cauchy Principal Value\":\n\n$\\lim_{\\epsilon\\to 0}\\left(\\int_0^{1- \\epsilon} \\frac{dx}{1-x}+ \\int_{1+\\epsilon}^2 \\frac{dx}{1- x}\\right)$\n\nWhat's your guys' opinions on whether this converges or diverges?\nIt definitely diverges by the definition of \"improper integral\" you will find in any Calculus text.\n\nLast edited by a moderator:\nYou don't simplify each separately. The first limit does indeed exist, and it's 0 as you pointed out.\n\nThe indefinite integral is said to exist if both limits exist, and in this case it's their sum. So when I say that it's the sum of their limits rather than the limit of their sums, it's a matter of definition.\nOkay, so the integral is indeed 0, but it diverges because if it diverges anytime within, it's a divergent integral. But HallsofIvy's definition for the improper integral makes it infinity - infinity and not 0?\n\nOkay, so the integral is indeed 0, but it diverges because if it diverges anytime within, it's a divergent integral.\nNo. The integral is $$i \\pi$$. The areas don't \"cancel\" out as intuition would tell you.\n\nI'm completely confused now.. :(\nDidn't Werg22 just say it was 0?\n\nI'm completely confused now.. :(\nDidn't Werg22 just say it was 0?\nHe said the limit was zero, yes. But that limit is not the integral as pointed out by Halls.\n\nThe limit of the sum is only equal to the sum of the limits if each of the limits converges.\n\nIs this incorrect?\nhttp://alt1.artofproblemsolving.com/Forum/latexrender/pictures/2/7/f/27f17cc7fd214c888358970d9c2aa16e9b3114eb.gif [Broken]\n\nLast edited by a moderator:\nIs this incorrect?\nhttp://alt1.artofproblemsolving.com/Forum/latexrender/pictures/2/7/f/27f17cc7fd214c888358970d9c2aa16e9b3114eb.gif [Broken]\n[/URL]\n\nSure. But...\n\nWhat is\n\n$$\\infty - \\infty$$\n\n?\n\nThis is why it's undefined and hence divergent.\n\nLast edited by a moderator:\nokay! Thanks a lot guys! I really appreciate it. I guess I got stuck just because of the whole \"limit on each integral separately\" since my teacher never did that when we split up integrals.\nThis may be over my head and you guys already helped me out enough, but how do you show that it's $$i\\pi$$? I'm really interested. Does that involve Contour integrals or something?\n\nokay! Thanks a lot guys! I really appreciate it. I guess I got stuck just because of the whole \"limit on each integral separately\" since my teacher never did that when we split up integrals.\nThis may be over my head, but how do you show that it's $$i\\pi$$? I'm really interested. Does that involve Contour integrals or something?\n$$\\int_{-1}^{1} \\frac{1}{x} dx$$\n\nLet $$x = -e^{i \\theta} \\ \\ dx = -i e^{i \\theta}$$\n\nTherefore,\n$$\\int_{0}^{\\pi} \\frac{-i e^{i \\theta}}{-e^{i\\theta}} d\\theta = \\int_{0}^{\\pi} i = i \\pi$$\n\nIt beautifully swings around the fatal point x = 0.\n\nVery cool! thanks.\n\nMute\nHomework Helper\n$$\\int_{-1}^{1} \\frac{1}{x} dx$$\n\nLet $$x = -e^{i \\theta} \\ \\ dx = -i e^{i \\theta}$$\n\nTherefore,\n$$\\int_{0}^{\\pi} \\frac{-i e^{i \\theta}}{-e^{i\\theta}} d\\theta = \\int_{0}^{\\pi} i = i \\pi$$\n\nIt beautifully swings around the fatal point x = 0.\nYou changed variables from a manifestly real variable to a complex variable, so there's no reason to expect this result to be correct. At best the result needs to be interpreted in the context of the complex plane.\n\nConsider the contour integral $\\int dz/z$ about a contour that begins at -1, goes to -$\\epsilon$ near the pole at zero, but skirts above the pole in a semi-circular arc to $+\\epsilon$, then to 1, then vertically up to a value $Y$, then horizontally back to -1, and then vertically down to close the contour. Since there are no poles inside the contour, the integral is zero. Decomposing it into components, the vertical ones cancel and we find\n\n$$\\int_{-1}^{-\\epsilon} \\frac{dx}{x} + \\int_{+\\epsilon}^{+1}\\frac{dx}{x} = i\\pi + \\int_{-1}^{1} \\frac{dx}{x+iY}.$$\n\nIn the limit as $\\epsilon \\rightarrow 0$ and $Y \\rightarrow \\infty$, the result\n\n$$\\mathcal P \\int_{-1}^{+1} \\frac{dx}{x} = i\\pi$$\nis recovered, but it is still a principal value integral, which is a different thing from\n\n$$\\int_{-1}^{+1}\\frac{dx}{x},$$\nwhich strictly speaking doesn't exist." ]

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[ "# Entropy, order and dimension\n\n### Definitions of entropy\n\nAt the molecular level, entropy is related to disorder. But the original definition of entropy is macroscopic, it is the heat transferred in a reversible process divided by the temperature at which the transfer occurs. This definition comes from thermodynamics, a classical, macroscopic theory, part of whose great power comes from the fact that it is developed without specifying the molecular nature of heat and temperature. Originally, entropy had no specific relation to order and it had units of energy over temperature, such as J.K−1. The Second Law of Thermodynamics says that entropy cannot decrease in a closed system, which is also correctly expressed by comic songsters Flanders and Swann as 'heat cannot of itself pass from one body to a hotter body'. Entropy can decrease, and does so in a refrigerator when you turn it on, but that is not a closed system: the fridge motor compresses the refrigerant gas, raising its temperature enough to allow heat to flow out, a process which exports more entropy into the kitchen than that lost by the cooling interior; the heat is not 'of itself' passing from cold (inside) to hotter. The increase of entropy in a closed system gives time a direction: S2 > S1 ⇔ t2 > t1.", null, "A molecular interpretation comes from statistical mechanics, the meta-theory to thermodynamics. Statistical mechanics applies Newton's laws and quantum mechanics to molecular interactions. Boltzmann's microscopic definition of entropy is S = kBln W, where kBis Boltzmann's constant and W is the number of different possible configurations of a system. On first encounter, it seems surprising — and wonderful — that the two definitions are equivalent, given the very different ideas and language involved. S = kBln W implies that entropy quantifies disorder at the molecular level. Famously, this equation takes pride of place on his tombstone. Boltzmann's ideas were inadequately recognised in his lifetime, and he took his own life. Now his tombstone has the final say and he is immortalised in kB and the Boltzmann equation.\n\n### What does Boltzmann's constant mean?\n\nWe often write that Boltzmann's constant is kB = 1.38 × 10−23 JK−1, but this is not a statement about the universe in the same way that e.g. giving a value of G does tell us about gravity. Rather, kB = 1.38 × 10−23 JK−1 is our way of saying that the conversion factor between our units of joules and kelvins is 1.38 × 10−23 JK−1. We could logically have a system of units in which kB = 1. (Or we could set the gas constant R = 1: less elegant but it would give a more convenient scale for measuring temperature.) More on that below.\n\n### Macroscopic disorder has negligible entropy\n\nIn practice, entropy is often related to molecular disorder. For example, when a solid melts, it goes from an ordered state (each molecule in a particular place) to a state in which the molecules move, so the number of possible permutations of molecular positions increases enormously. The entropy produced by equilibrium melting is just the heat required to melt a solid divided by the melting temperature. For one gram of ice at 273 K (0° C), this gives an entropy of melting of 1.2 JK−1.\n\nAn important point: this is disorder at the molecular level. Macroscopic disorder makes negligible contributions to entropy. I can't blame the second law for the disorder in my office. To show you what I mean, let's be quantitative. If you shuffle an initially ordered pack of cards, you go from just one sequence, to any of possibly 52*51*50*...3*2*1 = 52! possible sequences. So the entropy associated with the disordered sequence is about 3 × 10−21 JK−1. The entropy produced by the heat in your muscles during the shuffling process would be very roughly 1020 times larger. (Just to remind ourselves that 1020 is a large number: the age of the universe is about 4 × 1017 seconds.) So if we are considering the order of macroscopic objects, doing a few example calculations will persuade you that the entropy associated with the number of disordered states times the temperature is negligible in comparison with the work required to perform the disordering or ordering.\n\nThe example I often use to stress to students the irrelevance of macroscopic order to entropy is to consider the cellular order of a human. If we took the roughly 1014 human cells in a human* and imagined ‘shuffling’ them, we would lose not only a person, but a great deal of macroscopic order. However, the shuffling would produce an entropy of only k ln(1014!) ~ 4 × 10−8 JK−1, which is 30 million times smaller than that produced by melting a 1 g ice cube. Again, the heat of the ‘shuffling’ process would contribute a vastly larger entropy.\n\n* The 1014 cells in a human is in itself a nice example of an order-of-magnitude estimate. Cells are about ten microns across, so have volume of about 10-15 cubic metres. A human has a mass of roughly 100 kg so a volume (roughly like the same mass of water) of a tenth of a cubic metre. So 1014 cells in a human — to an order of magnitude. (Wolfgang Pauli was famous for order-of-magnitude estimates, so I like to say that Pauli had one ear, one eye and ten limbs — correct to an order of magnitude). And if you're more interested in entropy and life, here is a chapter I wrote for the Encyclopedia of Life Sciences.\n\n### Do life or evolution violate the second law of thermodynamics?\n\nIn short, no. It's the second law, not the second whimsical speculation. But how is the negative entropy of producing living biochemistry compensated by entropy production elsewhere? It's worthy of thinking about: life on Earth has a huge number of organisms with wonderful and diverse (cellular and) supracellular order. But the calculation above should tell us that the supracellular order is negligible in comparison with molecular order. Large biomolecules, including DNA and proteins have a molecular order which, if lost, would produce much more entropy than would losing supracellular order. And there are a lot of organisms, all of whose biochemicals have a combined entropy that is lower than that of the chemicals (mainly CO2 and water) out of which they have been made. It's reasonable to ask: Where is that negative entropy compensated? The short answer is that entropy is created at an enormous rate by the flux of energy from the sun, through the biosphere and out into the sky.\n\nApart from exceptional ecosystems on the ocean floor that obtain their energy from geochemistry rather than from sunlight, all life on Earth depends on photosynthesis, and thus on the energy and entropy flux from the sun and out to space. Plants are (mainly) made of CO2, water and photons. Animals get our energy mainly from plants (or from animals who ate plants). Those input photons come from a star at high temperature, and so have low entropy. The waste heat is radiated at the temperature of the upper atmosphere, effectively about 255 K.", null, "The paper I cited above has this figure showing thermal physics cartoons of the Earth, a photo-synthetic plant cell and an animal cell. Their macroscopically ordered structure – and anything else they do or produce – is ultimately maintained or ‘paid for’ by a flux of energy in from the sun (at ~6000 K) and out to the night sky (which is at ~3 K). The equal width of the arrows represents the near equality of average energy flux in and out. (Nearly equal: global warming is due to only a small proportional difference between energy in and out. Also note the physics convention: blue (high energy photons) is hot and red is cold. The reverse convention probably comes from skin colour.)\n\nIn contrast with energy flux, the entropy flux is very far from equal because of the very different temperatures of the radiation in (~ 6000 K) and out (~255 K): because this temperature goes in the denominator, the rate of entropy export is more than 20 times greater than the entropy intake.\n\nThe Earth absorbs solar energy at a rate of about 5 × 1016 W, so the rate of entropy input is about 5 × 1016 W/6000 K ≈ 8 × 1012 W.K−1. The Earth radiates heat at nearly the same rate, so its rate of entropy output is 5 × 1016 W/255 K ≈ 2 × 1014 W.K−1. Thus the surface layers of the Earth create entropy at a rate of roughly 2 × 1014 W.K−1.\n\nLiving things contribute only a fraction of this entropy, of course: this calculation is just to show that there is a huge entropy flux available. Despite the disingenuous claims of some anti-evolutionists, biological processes are in no danger of violating the Second Law of thermodynamics. Their relatively low entropy biochemicals (and their macroscopically ordered structure, plus and anything else they do or produce) is ultimately maintained or ‘paid for’ by a huge flux of energy in from the sun (at ~6000 K) into plants, through complicated pathways and out to the night sky (at ~3 K). The equal size of the arrows represents the near equality of average energy flux in and out. The entropy flux is not equal: the rate of entropy export is in all cases much greater than the entropy intake. And life on Earth depends on photosynthesis, and thus on this energy and entropy flux. (As for those ocean floor ecosystems, some of their geothermal and geochemical energy might ultimately be traced to the stellar synthesis of the elements, including the radioactive ones that have kept the Earth's core warmer longer than gravitational losses in the Earth's formation would allow.)\n\n#### Does entropy have dimension?\n\nAnd what are its fundamental units? For example, the dimensions of velocity are length over time (and its units are e.g. m/s). In a fundamental sense, entropy doesn't have dimension. Consider the original definition as heat transferred in a reversible process divided by the temperature. Here, heat (measured in joules) is energy. Temperature (measured in kelvins) is proportional to average molecular kinetic energy. So temperature can be measured in joules, too, though it would be an inconvenient size: 'It's 4.2 zeptojoules today (4.2 × 10−21 J), let's go for a swim.' Theoreticians and cosmologists often refer to temperatures in eV. So, in a completely rational set of units, entropy is just a pure number and has no units. So too are Boltzmann's constant kB and the gas constant R. Measuring them in joules per kelvin is a historical accident and Boltzmann's constant is a conversion factor between units, and not a fundamental constant of the universe.\n\nJoe Wolfe School of Physics, UNSW Sydney.Bidjigal land. Australia. [email protected]" ]

[ null, "http://www.phys.unsw.edu.au/~jw/cards/graphics/Boltzmann.jpg", null, "http://www.phys.unsw.edu.au/~jw/graphics/energy-flux.png", null ]

[ "# Why are true and false the only truth values used in mathematics?\n\nWhy do we use only true and false? It is possible to have many states in-between in fuzzy logic and other many-valued logics.\n\nIf we assign numbers to true and false, such as 1 and 0 respectively, what would be the logical interpreation of -1, i, j or k (with i,j,k as defined for quaternions)? Is there any reason for this dichotomy? What type of statement would have these truth values if such a statement existed?\n\n• Welcome to Philosophy SE. This question is not completely clear in what you're asking and could benefit from some clarification. The simple answer is that true and false have specific meanings in certain contexts which would not admit other concepts; remember that mathematics and philosophy both add value to human thought primarily through what they disallow, not what they allow. Order is in effect the containment of thought to specific concepts deemed to be valid as a model within the universe that also seems to constrain events to a given valid set we interpret as order. Apr 9, 2018 at 3:50\n• Maybe not; see Three-valued logic and Many-Valued Logic. Apr 9, 2018 at 5:53\n• The ides that there are TRUE statement is very deeply grounded in our language, and also bivalence, i.e. the fact that what is not TRUE is FALSE. But, at the same time, the Vagueness phenomenon is widely present in our language an daily life, and this does not fit well with bivalence. Apr 9, 2018 at 6:43\n• 0 and 1 in logic are not numbers but Boolean values. Apr 9, 2018 at 6:44\n• There is also meaningless and undecidable, giving four possible values.\n– user20253\nApr 9, 2018 at 10:46\n\nThe question whether we could have a logical system that can be represented with complex numbers raise an interesting point: Are the logical systems where multiple dimensions are useful?\n\nThe answer turns out to be yes. Consider the multidimensional logic of Carlos Gershenson.\n\nHere, each logical variable is a pair from the 'square' [0,1] x [0,1]. The reason that a 2-dimensional representation is chosen is such that we can assign a truth value to even paradoxical statements such as \"This phrase is false.\" The basic idea is that if for the pair (x,y) we have x+y=1, then this is considered a non-paradoxical value within fuzzy logic1. Otherwise, the truth value is paradoxical, but can still be represented and computed with. (for more information, see the link provided)\n\nBut let me answer your actual question. One of the main reasons that most of mathematics uses a two-valued logical system is that most of mathematics is concerned with proving something either true or false. Nothing else. Hence, as mathematicians only wish to speak about two logical values for their statements, a two-valued logical system is the simplest system that allows them to do that.\n\n1: Here we see a parallel with the 'imaginary numbers', they were introduced in Cardano's formula as an 'algebraic trick' to have some 'nonsense' in the middle of a derivation, but a correct result at the end)\n\nActually in some logics, specifically in continuous model theory, we can consider the interval [0,1] instead of the usual proposition set {0,1} and take 0 as indicating the truth value and 1 as the false value because sup[0,1]=1 and inf[0,1]=0. Also, while there are many complex number values there is only one number whose square is -1, and that is i.\n\nThe reason for this dichotomy is because logic is normally looked at algebraically instead of geometrically, thus forcing us to consider how to construct truth-value systems.\n\nAs for what type of statement would have truth value of i and negative one, well it would definitely have to be mathematical formalizations of some type of dialectical logic that relies heavily upon idempotents(mathematical objects whose iterations equals itself) to build its truth-value system. I do not know about the specifics since such a system is not yet known/proved to exist yet.\n\n• What's the square of `-i`? Apr 9, 2018 at 4:46\n• (-i)^2=(-1*i)^2=(-1)^2*(i)^2=1*(i)^2=i^2=-1. The square of -i is also -1. Apr 9, 2018 at 6:41\n\nThe domain of stochastics relies on generalization the two discrete truth-values 0 and 1 to the continuous interval [0,1] of probabilities, i.e. all real numbers between 0 and 1 are possibile probabilities. Choosing \"0\" and \"1\" as two distinguished truth values is a suitable convention - remember the dual system in computing. Probabilities have to satisfy certain axioms, e.g. for disjoint sets A and B of events\n\np(A union B)= p(A) + p(B)\n\nTherefore one cannot choose quite arbitrary numbers for probabilities and truth values.\n\n• I'm not sure if stochastics is that relevant here. Even in stochastics, each event either occurs or doesn't. There are still only 2 truth values. The only thing that is on an interval is our uncertainty of the event. Also, your axiom is wrong. Not only do the events need to be disjoint, they also need to independent. Apr 9, 2018 at 9:49\n• Thanks for pointing out the wrong axiom. - I consider probability a generalization of the two discrete truth values. Probability does not only capture our uncertainty of the event. In quantum mechanics probability often captures a property inherent to the event, independent from our knowledge. Apr 9, 2018 at 10:00\n• \"Probability does not only capture our uncertainty of the event\". Nevertheless, there are only 2 truth values in mainstream stochastics. I don't think anyone's opinion on what stochastics should be matters. Therefore, I think this answer is misleading at best. Apr 9, 2018 at 10:09\n• What's wrong in your opinion with considering probability a generalization(!) of the two discrete truth values? Apr 9, 2018 at 10:52\n• 1) This contradicts the interpretation(s) in mainstream stochastics. 2) The concept of a (probability) measure is a very different mathematical object than a logical variable or operations on such variables. 3) The mainstream generalisation you want is known as 'fuzzy logic', see here for the differences between this and probability. Apr 9, 2018 at 11:12\n\nClearly, there isn't.\n\nThere are certainly theories that would admit a -1, or the range of integers, or an interval of reals, or an infinite vector space (the space of state matrices in quantum physics) as proper representations of some logical state.\n\nBut logic seeks a basis for thought. It is looking for what can be seen as most basic. And for most humans, that is a binary comparison.\n\nWithin that Boolean context, what behavior could i have? First, you would have to decide how the math maps. In Boole, addition means 'or' and multiplication means 'and'. So in that world -1 = 1. A truth value of i or -i then would have to be 'alternate units' in the algebraic sense, two things that are neither true nor false separately, but when both apply, they establish a true statement.\n\nThen instead of there being exactly three such things, there would really be an infinity of them, and they may not be very useful. But they might be fun to contrive.\n\n• I agree about equivalence. But suggest a different mapping for i; as something intrinsically contradictory but set in an undetermined way to take on one of the other truth values. This is by analogy with en.m.wikipedia.org/wiki/Tachyonic_field As you say, just contrivances, and this suggestion is just for fun. Apr 10, 2018 at 11:48\n• @CriglCragl But something intrinsically contradictory should not have a modulus of 1. Because something with modulus 1 can never be zero. It needs to be somehow incomplete unless it is squared. You could follow down Re(i) == 0, and have orthogonal truths. But someone else already commented on multidimensional interpretations, and I didn't care for it.\n– user9166\nApr 10, 2018 at 16:09\n• @CriglCragl You may be interested in the multidimensional logic I refer to in my answer, as that assigns logical value to paradoxical statement. A value is considered 'non-paradoxical' only if the norm (L1 norm, not Euclidean) is 1 and hence can be seen as a fuzzy logic value. Apr 10, 2018 at 21:20\n\nIt seems that all other forms of logic (e.g. with 2+ values), should you ever really need them, can be simulated with ordinary mathematics based on good old-fashioned true-or-false logic.\n\n• This is a rather vague claim. I'm not sure if it is completely true. Even if it holds, the fact that we can 'simulate' other logics (whatever that means) doesn't mean other logics are useless. Sometimes, other logics are simply an easier way to describe or solve certain problems. This is one of the reasons why fuzzy logic has uses in practice. Apr 10, 2018 at 7:17\n• Suppose you want to simulate 256-value logic. Then each \"logical\" operator could be represented by binary function on the the set of natural numbers less than 256. Apr 10, 2018 at 12:55\n• Yes, but why would you? Apr 10, 2018 at 17:35\n• @Discretelizard I can't think of any applications off hand, but I understand that 8-value logic can provide some processing efficiencies in computer chips. Of course, the same functionality could be made available using standard 2-value logic. Apr 10, 2018 at 19:40\n• Perhaps I should be clearer. Why would you simulate some multi-valued logic with some numbers? Why not just use the multi-valued logic immediately. Apr 10, 2018 at 21:16" ]

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[ "", null, "Deleted\nNot applicable\n\n# VBA code for inputs\n\nI've written a function in Matlab that calculates the average growth rate for i.g. a companys profit.\nProfit is sometimes negative, so I've solved this \"issue\" with a couple of for-loops and if-statements, nothing fancy.\n\n``````function[average]=Growth(y)\nformat shortG\n\ngrowth=[];\n\nfor i=1:length(y)-1\nif y(i)<0 & y(i+1)<0\ngrowth(i)=y(i)/y(i+1);\nelseif y(i)>0 & y(i+1)>0\ngrowth(i)=y(i+1)/y(i);\nelseif y(i)<0 & y(i+1)>0\ngrowth(i)=(y(i+1)-(y(i))/(-y(i)));\nelse\ngrowth(i)=0;\nend\nend\nformat shortG\ngrowth=(growth'-1)*100;\naverage=mean(growth)\n\nend\nformat shortGgrowth=(growth'-1)*100;average=mean(growth)``````\n\nI would like to create a vba function in excel that does this, but I'm not familiar with vba.\nFirst and foremost I would like to be able to import the data into the vba function, obviously.\nIn my Matlab function the input is a vector y, and the output is average growth.\n\nSo what I need help with is to import the data from and Excel spreadsheet to a vba function, followed by one output. The input varies in size, do I need paramarray?\nIf someone could give me the first line of code it would be appreciated, the loops etc I can figure out myself.\n\n0 Replies" ]

[ null, "https://www.facebook.com/tr", null ]

[ "# Difference: VarCALC (1 vs. 3)\n\n#### Revision 32010-05-27 - TWikiContributor\n\nLine: 1 to 1\n\n META TOPICPARENT name=\"TWikiVariables\"\n\nLine: 8 to 8\n\n• `%CALC{\"\\$SUM(\\$ABOVE())\"}%` returns the sum of all cells above the current cell\n• `%CALC{\"\\$EXISTS(Web.SomeTopic)\"}%` returns `1` if the topic exists\n• `%CALC{\"\\$UPPER(Collaboration)\"}%` returns `COLLABORATION`\nChanged:\n<\n<\n>\n>\n\n#### Revision 22007-06-02 - TWikiContributor\n\nLine: 1 to 1\n\n META TOPICPARENT name=\"TWikiVariables\"\n\n#### Revision 12007-06-02 - PeterThoeny\n\nLine: 1 to 1\n>\n>\n META TOPICPARENT name=\"TWikiVariables\"\n\n• The `%CALC{\"formula\"}%` variable is handled by the SpreadSheetPlugin. There are around 80 formulae, such as `\\$ABS()`, `\\$EXACT()`, `\\$EXISTS()`, `\\$GET()/\\$SET()`, `\\$IF()`, `\\$LOG()`, `\\$LOWER()`, `\\$PERCENTILE()`, `\\$TIME()`, `\\$VALUE()`.\n• Syntax: `%CALC{\"formula\"}%`\n• `%CALC{\"\\$SUM(\\$ABOVE())\"}%` returns the sum of all cells above the current cell\n• `%CALC{\"\\$EXISTS(Web.SomeTopic)\"}%` returns `1` if the topic exists\n• `%CALC{\"\\$UPPER(Collaboration)\"}%` returns `COLLABORATION`" ]

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[ "Daily Report For January 2013\n```Averages\\Extremes for day :01\n------------------------------------------------------------\n\nAverage temperature = 5.1°C\nAverage humidity = 85%\nAverage dewpoint = 2.8°C\nAverage barometer = 1008.5 mb\nAverage windspeed = 5.3 mph\nAverage gustspeed = 9.7 mph\nAverage direction = 249° (WSW)\nRainfall for month = 0.0 mm\nRainfall for year = 0.0 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 01 at time 00:00\nMaximum temperature = 7.3°C on day 01 at time 00:00\nMinimum temperature = 3.1°C on day 01 at time 08:45\nMaximum humidity = 92% on day 01 at time 03:09\nMinimum humidity = 75% on day 01 at time 15:19\nMaximum dewpoint = 5.9°C on day 01 at time 00:00\nMinimum dewpoint = 1.5°C on day 01 at time 8:26\nMaximum pressure = 1018.9 mb on day 01 at time 00:00\nMinimum pressure = 1000.0 mb on day 01 at time 00:01\nMaximum windspeed = 15.0 mph on day 01 at time 14:26\nMaximum gust speed = 25.3 mph from 248 °(WSW) on day 01 at time 12:59\nDaily wind run = 127.3miles\nMaximum heat index = 7.3°C on day 01 at time 00:00\n\nAverages\\Extremes for day :02\n------------------------------------------------------------\n\nAverage temperature = 7.4°C\nAverage humidity = 92%\nAverage dewpoint = 6.2°C\nAverage barometer = 1023.7 mb\nAverage windspeed = 4.3 mph\nAverage gustspeed = 7.8 mph\nAverage direction = 230° ( SW)\nRainfall for month = 0.0 mm\nRainfall for year = 0.0 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 02 at time 00:00\nMaximum temperature = 10.6°C on day 02 at time 22:32\nMinimum temperature = 4.2°C on day 02 at time 01:00\nMaximum humidity = 96% on day 02 at time 17:14\nMinimum humidity = 85% on day 02 at time 10:31\nMaximum dewpoint = 9.6°C on day 02 at time 22:32\nMinimum dewpoint = 2.6°C on day 02 at time 1:14\nMaximum pressure = 1028.2 mb on day 02 at time 23:55\nMinimum pressure = 1018.6 mb on day 02 at time 00:19\nMaximum windspeed = 11.5 mph on day 02 at time 18:38\nMaximum gust speed = 20.7 mph from 248 °(WSW) on day 02 at time 18:48\nDaily wind run = 102.5miles\nMaximum heat index = 10.6°C on day 02 at time 22:32\n\nAverages\\Extremes for day :03\n------------------------------------------------------------\n\nAverage temperature = 9.5°C\nAverage humidity = 94%\nAverage dewpoint = 8.6°C\nAverage barometer = 1033.2 mb\nAverage windspeed = 4.0 mph\nAverage gustspeed = 7.4 mph\nAverage direction = 240° (WSW)\nRainfall for month = 0.0 mm\nRainfall for year = 0.0 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 03 at time 00:00\nMaximum temperature = 12.2°C on day 03 at time 12:49\nMinimum temperature = 8.6°C on day 03 at time 22:16\nMaximum humidity = 100% on day 03 at time 18:30\nMinimum humidity = 87% on day 03 at time 12:53\nMaximum dewpoint = 10.5°C on day 03 at time 12:23\nMinimum dewpoint = 7.8°C on day 03 at time 6:07\nMaximum pressure = 1037.4 mb on day 03 at time 23:01\nMinimum pressure = 1028.0 mb on day 03 at time 00:06\nMaximum windspeed = 12.7 mph on day 03 at time 21:10\nMaximum gust speed = 19.6 mph from 248 °(WSW) on day 03 at time 23:51\nDaily wind run = 097.3miles\nMaximum heat index = 12.2°C on day 03 at time 12:49\n\nAverages\\Extremes for day :04\n------------------------------------------------------------\n\nAverage temperature = 8.4°C\nAverage humidity = 92%\nAverage dewpoint = 7.3°C\nAverage barometer = 1037.7 mb\nAverage windspeed = 3.9 mph\nAverage gustspeed = 7.5 mph\nAverage direction = 243° (WSW)\nRainfall for month = 0.0 mm\nRainfall for year = 0.0 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 04 at time 00:00\nMaximum temperature = 9.5°C on day 04 at time 13:24\nMinimum temperature = 7.2°C on day 04 at time 09:06\nMaximum humidity = 96% on day 04 at time 00:00\nMinimum humidity = 87% on day 04 at time 11:09\nMaximum dewpoint = 8.4°C on day 04 at time 15:22\nMinimum dewpoint = 5.7°C on day 04 at time 9:36\nMaximum pressure = 1038.7 mb on day 04 at time 11:37\nMinimum pressure = 1037.0 mb on day 04 at time 00:55\nMaximum windspeed = 10.4 mph on day 04 at time 15:56\nMaximum gust speed = 19.6 mph from 248 °(WSW) on day 04 at time 06:05\nDaily wind run = 093.4miles\nMaximum heat index = 9.5°C on day 04 at time 13:24\n\nAverages\\Extremes for day :05\n------------------------------------------------------------\n\nAverage temperature = 8.7°C\nAverage humidity = 92%\nAverage dewpoint = 7.5°C\nAverage barometer = 1035.5 mb\nAverage windspeed = 2.6 mph\nAverage gustspeed = 5.3 mph\nAverage direction = 222° ( SW)\nRainfall for month = 0.0 mm\nRainfall for year = 0.0 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 05 at time 00:00\nMaximum temperature = 10.2°C on day 05 at time 14:05\nMinimum temperature = 7.6°C on day 05 at time 00:17\nMaximum humidity = 96% on day 05 at time 02:22\nMinimum humidity = 88% on day 05 at time 14:44\nMaximum dewpoint = 8.5°C on day 05 at time 14:35\nMinimum dewpoint = 6.2°C on day 05 at time 23:13\nMaximum pressure = 1037.2 mb on day 05 at time 00:12\nMinimum pressure = 1034.0 mb on day 05 at time 23:38\nMaximum windspeed = 8.1 mph on day 05 at time 13:46\nMaximum gust speed = 15.0 mph from 180 °( S ) on day 05 at time 12:57\nDaily wind run = 063.6miles\nMaximum heat index = 10.2°C on day 05 at time 14:05\n\nAverages\\Extremes for day :06\n------------------------------------------------------------\n\nAverage temperature = 8.0°C\nAverage humidity = 95%\nAverage dewpoint = 7.2°C\nAverage barometer = 1032.4 mb\nAverage windspeed = 1.9 mph\nAverage gustspeed = 4.0 mph\nAverage direction = 211° (SSW)\nRainfall for month = 0.0 mm\nRainfall for year = 0.0 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 06 at time 00:00\nMaximum temperature = 8.8°C on day 06 at time 14:16\nMinimum temperature = 6.7°C on day 06 at time 05:23\nMaximum humidity = 98% on day 06 at time 13:23\nMinimum humidity = 91% on day 06 at time 01:13\nMaximum dewpoint = 8.5°C on day 06 at time 13:01\nMinimum dewpoint = 6.1°C on day 06 at time 05:23\nMaximum pressure = 1034.8 mb on day 06 at time 03:20\nMinimum pressure = 1029.7 mb on day 06 at time 23:52\nMaximum windspeed = 6.9 mph on day 06 at time 17:04\nMaximum gust speed = 11.5 mph from 203 °(SSW) on day 06 at time 17:10\nDaily wind run = 046.1miles\nMaximum heat index = 8.8°C on day 06 at time 14:16\n\nAverages\\Extremes for day :07\n------------------------------------------------------------\n\nAverage temperature = 7.8°C\nAverage humidity = 95%\nAverage dewpoint = 7.1°C\nAverage barometer = 1026.5 mb\nAverage windspeed = 4.4 mph\nAverage gustspeed = 7.4 mph\nAverage direction = 187° ( S )\nRainfall for month = 0.0 mm\nRainfall for year = 0.0 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 07 at time 00:00\nMaximum temperature = 8.9°C on day 07 at time 14:47\nMinimum temperature = 7.1°C on day 07 at time 06:57\nMaximum humidity = 100% on day 07 at time 10:22\nMinimum humidity = 92% on day 07 at time 15:24\nMaximum dewpoint = 7.8°C on day 07 at time 14:47\nMinimum dewpoint = 6.6°C on day 07 at time 6:57\nMaximum pressure = 1029.8 mb on day 07 at time 00:09\nMinimum pressure = 1024.5 mb on day 07 at time 23:35\nMaximum windspeed = 10.4 mph on day 07 at time 12:29\nMaximum gust speed = 18.4 mph from 203 °(SSW) on day 07 at time 14:49\nDaily wind run = 105.1miles\nMaximum heat index = 8.9°C on day 07 at time 14:47\n\nAverages\\Extremes for day :08\n------------------------------------------------------------\n\nAverage temperature = 9.2°C\nAverage humidity = 94%\nAverage dewpoint = 8.2°C\nAverage barometer = 1024.1 mb\nAverage windspeed = 4.0 mph\nAverage gustspeed = 6.9 mph\nAverage direction = 191° ( S )\nRainfall for month = 1.5 mm\nRainfall for year = 1.5 mm\nRainfall for day = 1.5 mm\nMaximum rain per minute = 0.3 mm on day 08 at time 23:46\nMaximum temperature = 10.2°C on day 08 at time 17:25\nMinimum temperature = 7.8°C on day 08 at time 00:04\nMaximum humidity = 98% on day 08 at time 23:44\nMinimum humidity = 91% on day 08 at time 14:01\nMaximum dewpoint = 9.4°C on day 08 at time 19:55\nMinimum dewpoint = 6.9°C on day 08 at time 0:04\nMaximum pressure = 1025.2 mb on day 08 at time 10:19\nMinimum pressure = 1023.1 mb on day 08 at time 22:40\nMaximum windspeed = 10.4 mph on day 08 at time 10:51\nMaximum gust speed = 18.4 mph from 203 °(SSW) on day 08 at time 13:16\nDaily wind run = 095.2miles\nMaximum heat index = 10.2°C on day 08 at time 17:25\n\nAverages\\Extremes for day :09\n------------------------------------------------------------\n\nAverage temperature = 4.2°C\nAverage humidity = 96%\nAverage dewpoint = 3.6°C\nAverage barometer = 1022.9 mb\nAverage windspeed = 0.6 mph\nAverage gustspeed = 1.7 mph\nAverage direction = 297° (WNW)\nRainfall for month = 2.5 mm\nRainfall for year = 2.5 mm\nRainfall for day = 1.0 mm\nMaximum rain per minute = 0.3 mm on day 09 at time 01:14\nMaximum temperature = 8.4°C on day 09 at time 00:00\nMinimum temperature = 0.4°C on day 09 at time 20:06\nMaximum humidity = 98% on day 09 at time 21:01\nMinimum humidity = 93% on day 09 at time 16:21\nMaximum dewpoint = 7.9°C on day 09 at time 00:00\nMinimum dewpoint = -0.1°C on day 09 at time 20:06\nMaximum pressure = 1024.5 mb on day 09 at time 10:13\nMinimum pressure = 1020.2 mb on day 09 at time 23:45\nMaximum windspeed = 5.8 mph on day 09 at time 23:52\nMaximum gust speed = 9.2 mph from 270 °( W ) on day 09 at time 23:52\nDaily wind run = 013.7miles\nMaximum heat index = 8.4°C on day 09 at time 00:00\n\nAverages\\Extremes for day :10\n------------------------------------------------------------\n\nAverage temperature = 0.8°C\nAverage humidity = 98%\nAverage dewpoint = 0.5°C\nAverage barometer = 1017.4 mb\nAverage windspeed = 1.5 mph\nAverage gustspeed = 3.4 mph\nAverage direction = 258° (WSW)\nRainfall for month = 2.5 mm\nRainfall for year = 2.5 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 10 at time 00:00\nMaximum temperature = 1.8°C on day 10 at time 00:22\nMinimum temperature = -0.3°C on day 10 at time 04:29\nMaximum humidity = 98% on day 10 at time 00:00\nMinimum humidity = 97% on day 10 at time 04:42\nMaximum dewpoint = 1.4°C on day 10 at time 00:22\nMinimum dewpoint = -0.7°C on day 10 at time 04:26\nMaximum pressure = 1020.4 mb on day 10 at time 00:11\nMinimum pressure = 1015.4 mb on day 10 at time 15:53\nMaximum windspeed = 6.9 mph on day 10 at time 21:18\nMaximum gust speed = 10.4 mph from 248 °(WSW) on day 10 at time 21:00\nDaily wind run = 035.7miles\nMaximum heat index = 1.8°C on day 10 at time 00:22\n\nAverages\\Extremes for day :11\n------------------------------------------------------------\n\nAverage temperature = 1.9°C\nAverage humidity = 98%\nAverage dewpoint = 1.6°C\nAverage barometer = 1019.0 mb\nAverage windspeed = 0.5 mph\nAverage gustspeed = 1.7 mph\nAverage direction = 231° ( SW)\nRainfall for month = 2.5 mm\nRainfall for year = 2.5 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 11 at time 00:00\nMaximum temperature = 4.1°C on day 11 at time 15:57\nMinimum temperature = 0.2°C on day 11 at time 23:03\nMaximum humidity = 99% on day 11 at time 13:26\nMinimum humidity = 96% on day 11 at time 18:16\nMaximum dewpoint = 3.8°C on day 11 at time 15:48\nMinimum dewpoint = -0.0°C on day 11 at time 23:03\nMaximum pressure = 1020.6 mb on day 11 at time 09:06\nMinimum pressure = 1016.7 mb on day 11 at time 23:57\nMaximum windspeed = 4.6 mph on day 11 at time 10:50\nMaximum gust speed = 9.2 mph from 248 °(WSW) on day 11 at time 22:07\nDaily wind run = 011.8miles\nMaximum heat index = 4.1°C on day 11 at time 15:57\n\nAverages\\Extremes for day :12\n------------------------------------------------------------\n\nAverage temperature = 1.5°C\nAverage humidity = 91%\nAverage dewpoint = 0.2°C\nAverage barometer = 1015.3 mb\nAverage windspeed = 3.9 mph\nAverage gustspeed = 7.6 mph\nAverage direction = 62° (ENE)\nRainfall for month = 2.5 mm\nRainfall for year = 2.5 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 12 at time 00:00\nMaximum temperature = 3.3°C on day 12 at time 14:31\nMinimum temperature = 0.3°C on day 12 at time 00:00\nMaximum humidity = 98% on day 12 at time 07:35\nMinimum humidity = 83% on day 12 at time 22:07\nMaximum dewpoint = 1.3°C on day 12 at time 12:49\nMinimum dewpoint = -1.8°C on day 12 at time 0:00\nMaximum pressure = 1018.6 mb on day 12 at time 23:56\nMinimum pressure = 1013.6 mb on day 12 at time 13:31\nMaximum windspeed = 9.2 mph on day 12 at time 14:46\nMaximum gust speed = 19.6 mph from 068 °(ENE) on day 12 at time 14:45\nDaily wind run = 094.4miles\nMaximum heat index = 3.3°C on day 12 at time 14:31\n\nAverages\\Extremes for day :13\n------------------------------------------------------------\n\nAverage temperature = 0.3°C\nAverage humidity = 87%\nAverage dewpoint = -1.6°C\nAverage barometer = 1021.8 mb\nAverage windspeed = 0.9 mph\nAverage gustspeed = 2.3 mph\nAverage direction = 2° ( N )\nRainfall for month = 2.5 mm\nRainfall for year = 2.5 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 13 at time 00:00\nMaximum temperature = 3.1°C on day 13 at time 12:57\nMinimum temperature = -1.7°C on day 13 at time 07:26\nMaximum humidity = 96% on day 13 at time 09:23\nMinimum humidity = 75% on day 13 at time 14:23\nMaximum dewpoint = 0.6°C on day 13 at time 12:28\nMinimum dewpoint = -2.9°C on day 13 at time 5:03\nMaximum pressure = 1023.3 mb on day 13 at time 18:45\nMinimum pressure = 1018.4 mb on day 13 at time 00:22\nMaximum windspeed = 5.8 mph on day 13 at time 12:07\nMaximum gust speed = 10.4 mph from 00 °( N ) on day 13 at time 00:08\nDaily wind run = 022.3miles\nMaximum heat index = 3.1°C on day 13 at time 12:57\n\nAverages\\Extremes for day :14\n------------------------------------------------------------\n\nAverage temperature = 0.4°C\nAverage humidity = 94%\nAverage dewpoint = -0.5°C\nAverage barometer = 1011.9 mb\nAverage windspeed = 3.3 mph\nAverage gustspeed = 6.2 mph\nAverage direction = 233° ( SW)\nRainfall for month = 7.6 mm\nRainfall for year = 7.6 mm\nRainfall for day = 5.1 mm\nMaximum rain per minute = 0.3 mm on day 14 at time 19:44\nMaximum temperature = 2.4°C on day 14 at time 16:40\nMinimum temperature = -1.1°C on day 14 at time 06:48\nMaximum humidity = 97% on day 14 at time 15:00\nMinimum humidity = 82% on day 14 at time 00:16\nMaximum dewpoint = 1.9°C on day 14 at time 15:00\nMinimum dewpoint = -2.4°C on day 14 at time 00:16\nMaximum pressure = 1021.2 mb on day 14 at time 00:00\nMinimum pressure = 1005.9 mb on day 14 at time 23:35\nMaximum windspeed = 9.2 mph on day 14 at time 18:09\nMaximum gust speed = 16.1 mph from 270 °( W ) on day 14 at time 17:02\nDaily wind run = 080.4miles\nMaximum heat index = 2.4°C on day 14 at time 16:40\n\nAverages\\Extremes for day :15\n------------------------------------------------------------\n\nAverage temperature = -0.3°C\nAverage humidity = 92%\nAverage dewpoint = -1.5°C\nAverage barometer = 1011.7 mb\nAverage windspeed = 1.7 mph\nAverage gustspeed = 3.5 mph\nAverage direction = 297° (WNW)\nRainfall for month = 8.1 mm\nRainfall for year = 8.1 mm\nRainfall for day = 0.5 mm\nMaximum rain per minute = 0.3 mm on day 15 at time 15:15\nMaximum temperature = 2.0°C on day 15 at time 13:33\nMinimum temperature = -3.8°C on day 15 at time 23:53\nMaximum humidity = 95% on day 15 at time 00:00\nMinimum humidity = 86% on day 15 at time 14:18\nMaximum dewpoint = 0.6°C on day 15 at time 14:13\nMinimum dewpoint = -4.5°C on day 15 at time 23:53\nMaximum pressure = 1013.6 mb on day 15 at time 17:02\nMinimum pressure = 1006.1 mb on day 15 at time 00:00\nMaximum windspeed = 10.4 mph on day 14 at time 00:27\nMaximum gust speed = 18.4 mph from 293 °(WNW) on day 15 at time 00:34\nDaily wind run = 041.0miles\nMaximum heat index = 2.0°C on day 15 at time 13:33\n\nAverages\\Extremes for day :16\n------------------------------------------------------------\n\nAverage temperature = -3.8°C\nAverage humidity = 96%\nAverage dewpoint = -4.3°C\nAverage barometer = 1015.3 mb\nAverage windspeed = 0.1 mph\nAverage gustspeed = 0.9 mph\nAverage direction = 49° ( NE)\nRainfall for month = 8.1 mm\nRainfall for year = 8.1 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 16 at time 00:00\nMaximum temperature = -2.8°C on day 16 at time 16:24\nMinimum temperature = -4.7°C on day 16 at time 07:03\nMaximum humidity = 97% on day 16 at time 18:39\nMinimum humidity = 95% on day 16 at time 03:44\nMaximum dewpoint = -3.2°C on day 16 at time 16:24\nMinimum dewpoint = -5.3°C on day 16 at time 07:03\nMaximum pressure = 1019.1 mb on day 16 at time 23:53\nMinimum pressure = 1012.5 mb on day 16 at time 05:22\nMaximum windspeed = 3.5 mph on day 16 at time 11:04\nMaximum gust speed = 6.9 mph from 045 °( NE) on day 16 at time 06:43\nDaily wind run = 003.5miles\nMaximum heat index = -2.8°C on day 16 at time 16:24\n\nAverages\\Extremes for day :17\n------------------------------------------------------------\n\nAverage temperature = -1.6°C\nAverage humidity = 94%\nAverage dewpoint = -2.4°C\nAverage barometer = 1018.5 mb\nAverage windspeed = 1.0 mph\nAverage gustspeed = 2.9 mph\nAverage direction = 98° ( E )\nRainfall for month = 8.1 mm\nRainfall for year = 8.1 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 17 at time 00:00\nMaximum temperature = 0.3°C on day 17 at time 14:07\nMinimum temperature = -4.0°C on day 17 at time 03:01\nMaximum humidity = 99% on day 17 at time 18:22\nMinimum humidity = 88% on day 17 at time 12:53\nMaximum dewpoint = -0.7°C on day 17 at time 18:22\nMinimum dewpoint = -4.5°C on day 17 at time 3:01\nMaximum pressure = 1020.3 mb on day 17 at time 09:43\nMinimum pressure = 1013.4 mb on day 17 at time 00:00\nMaximum windspeed = 5.8 mph on day 17 at time 18:58\nMaximum gust speed = 10.4 mph from 113 °(ESE) on day 17 at time 18:57\nDaily wind run = 024.9miles\nMaximum heat index = 0.3°C on day 17 at time 14:07\n\nAverages\\Extremes for day :18\n------------------------------------------------------------\n\nAverage temperature = -2.1°C\nAverage humidity = 94%\nAverage dewpoint = -3.0°C\nAverage barometer = 1005.0 mb\nAverage windspeed = 3.4 mph\nAverage gustspeed = 6.8 mph\nAverage direction = 74° (ENE)\nRainfall for month = 8.1 mm\nRainfall for year = 8.1 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 18 at time 00:00\nMaximum temperature = -0.7°C on day 18 at time 06:12\nMinimum temperature = -3.2°C on day 18 at time 11:10\nMaximum humidity = 95% on day 18 at time 00:00\nMinimum humidity = 87% on day 18 at time 08:14\nMaximum dewpoint = -1.4°C on day 18 at time 00:01\nMinimum dewpoint = -3.9°C on day 18 at time 019:14\nMaximum pressure = 1013.4 mb on day 18 at time 00:00\nMinimum pressure = 999.7 mb on day 18 at time 23:57\nMaximum windspeed = 9.2 mph on day 18 at time 10:24\nMaximum gust speed = 18.4 mph from 068 °(ENE) on day 18 at time 10:32\nDaily wind run = 081.8miles\nMaximum heat index = -0.7°C on day 18 at time 06:12\n\nAverages\\Extremes for day :19\n------------------------------------------------------------\n\nAverage temperature = -1.1°C\nAverage humidity = 92%\nAverage dewpoint = -2.2°C\nAverage barometer = 1000.6 mb\nAverage windspeed = 4.5 mph\nAverage gustspeed = 8.1 mph\nAverage direction = 42° ( NE)\nRainfall for month = 8.1 mm\nRainfall for year = 8.1 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 19 at time 00:00\nMaximum temperature = -0.7°C on day 19 at time 13:01\nMinimum temperature = -1.6°C on day 19 at time 00:00\nMaximum humidity = 96% on day 19 at time 05:39\nMinimum humidity = 88% on day 19 at time 22:49\nMaximum dewpoint = -1.6°C on day 19 at time 09:53\nMinimum dewpoint = -3.1°C on day 19 at time 20:30\nMaximum pressure = 1002.3 mb on day 19 at time 20:14\nMinimum pressure = 999.0 mb on day 19 at time 04:47\nMaximum windspeed = 10.4 mph on day 19 at time 18:21\nMaximum gust speed = 19.6 mph from 045 °( NE) on day 19 at time 18:20\nDaily wind run = 107.4miles\nMaximum heat index = -0.7°C on day 19 at time 13:01\n\nAverages\\Extremes for day :20\n------------------------------------------------------------\n\nAverage temperature = -1.2°C\nAverage humidity = 93%\nAverage dewpoint = -2.2°C\nAverage barometer = 997.8 mb\nAverage windspeed = 3.4 mph\nAverage gustspeed = 6.2 mph\nAverage direction = 34° (NNE)\nRainfall for month = 8.1 mm\nRainfall for year = 8.1 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 20 at time 00:00\nMaximum temperature = -0.6°C on day 20 at time 13:00\nMinimum temperature = -1.9°C on day 20 at time 04:48\nMaximum humidity = 97% on day 20 at time 21:53\nMinimum humidity = 87% on day 20 at time 02:32\nMaximum dewpoint = -1.1°C on day 20 at time 20:21\nMinimum dewpoint = -3.7°C on day 20 at time 02:31\nMaximum pressure = 1001.8 mb on day 20 at time 00:03\nMinimum pressure = 993.7 mb on day 20 at time 00:00\nMaximum windspeed = 9.2 mph on day 20 at time 07:46\nMaximum gust speed = 15.0 mph from 045 °( NE) on day 20 at time 07:45\nDaily wind run = 080.6miles\nMaximum heat index = -0.6°C on day 20 at time 13:00\n\nAverages\\Extremes for day :21\n------------------------------------------------------------\n\nAverage temperature = -1.3°C\nAverage humidity = 96%\nAverage dewpoint = -1.9°C\nAverage barometer = 995.6 mb\nAverage windspeed = 0.5 mph\nAverage gustspeed = 1.4 mph\nAverage direction = 112° (ESE)\nRainfall for month = 8.1 mm\nRainfall for year = 8.1 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 21 at time 00:00\nMaximum temperature = -0.4°C on day 21 at time 18:14\nMinimum temperature = -2.1°C on day 21 at time 03:26\nMaximum humidity = 97% on day 21 at time 11:35\nMinimum humidity = 94% on day 21 at time 23:41\nMaximum dewpoint = -1.0°C on day 21 at time 18:14\nMinimum dewpoint = -2.6°C on day 21 at time 3:26\nMaximum pressure = 1000.2 mb on day 21 at time 23:46\nMinimum pressure = 992.6 mb on day 21 at time 04:51\nMaximum windspeed = 4.6 mph on day 21 at time 21:14\nMaximum gust speed = 8.1 mph from 135 °( SE) on day 21 at time 22:16\nDaily wind run = 010.9miles\nMaximum heat index = -0.4°C on day 21 at time 18:14\n\nAverages\\Extremes for day :22\n------------------------------------------------------------\n\nAverage temperature = -1.7°C\nAverage humidity = 96%\nAverage dewpoint = -2.2°C\nAverage barometer = 1004.0 mb\nAverage windspeed = 2.3 mph\nAverage gustspeed = 4.8 mph\nAverage direction = 57° (ENE)\nRainfall for month = 8.1 mm\nRainfall for year = 8.1 mm\nRainfall for day = 0.0 mm\nMaximum rain per minute = 0.0 mm on day 22 at time 00:00\nMaximum temperature = 0.1°C on day 22 at time 00:00\nMinimum temperature = -4.9°C on day 22 at time 07:57\nMaximum humidity = 98% on day 22 at time 20:58\nMinimum humidity = 94% on day 22 at time 09:48\nMaximum dewpoint = -0.2°C on day 22 at time 19:54\nMinimum dewpoint = -5.8°C on day 22 at time 07:57\nMaximum pressure = 1009.1 mb on day 22 at time 00:00\nMinimum pressure = 1000.0 mb on day 22 at time 00:00\nMaximum windspeed = 8.1 mph on day 22 at time 22:43\nMaximum gust speed = 13.8 mph from 045 °( NE) on day 22 at time 23:41\nDaily wind run = 055.4miles\nMaximum heat index = 0.1°C on day 22 at time 00:00\n\nAverages\\Extremes for day :23\n------------------------------------------------------------\n\nAverage temperature = -0.5°C\nAverage humidity = 93%\nAverage dewpoint = -1.5°C\nAverage barometer = 1010.6 mb\nAverage windspeed = 3.1 mph\nAverage gustspeed = 6.1 mph\nAverage direction = 47° ( NE)\nRainfall for month = 8.4 mm\nRainfall for year = 8.4 mm\nRainfall for day = 0.3 mm\nMaximum rain per minute = 0.3 mm on day 23 at time 14:01\nMaximum temperature = 0.2°C on day 23 at time 00:30\nMinimum temperature = -0.9°C on day 23 at time 16:16\nMaximum humidity = 100% on day 23 at time 21:56\nMinimum humidity = 89% on day 23 at time 13:24\nMaximum dewpoint = -0.3°C on day 23 at time 00:30\nMinimum dewpoint = -2.0°C on day 23 at time 12:39\nMaximum pressure = 1012.8 mb on day 23 at time 23:56\nMinimum pressure = 1009.0 mb on day 23 at time 00:08\nMaximum windspeed = 8.1 mph on day 23 at time 14:29\nMaximum gust speed = 11.5 mph from 045 °( NE) on day 23 at time 22:59\nDaily wind run = 074.5miles\nMaximum heat index = 0.2°C on day 23 at time 00:30\n\nAverages\\Extremes for day :24\n------------------------------------------------------------\n\nAverage temperature = -0.1°C\nAverage humidity = 88%\nAverage dewpoint = -1.9°C\nAverage barometer = 1019.0 mb\nAverage windspeed = 0.8 mph\nAverage gustspeed = 2.1 mph\nAverage direction = 42° ( NE)\nRainfall for month = 9.1 mm\nRainfall for year = 9.1 mm\nRainfall for day = 0.8 mm\nMaximum rain per minute = 0.3 mm on day 24 at time 15:50\nMaximum temperature = 1.1°C on day 24 at time 14:40\nMinimum temperature = -1.1°C on day 24 at time 06:27\nMaximum humidity = 93% on day 24 at time 09:32\nMinimum humidity = 80% on day 24 at time 16:37\nMaximum dewpoint = -0.5°C on day 24 at time 11:44\nMinimum dewpoint = -2.5°C on day 24 at time 23:55\nMaximum pressure = 1022.6 mb on day 24 at time 20:38\nMinimum pressure = 1012.7 mb on day 24 at time 00:00\nMaximum windspeed = 5.8 mph on day 24 at time 03:29\nMaximum gust speed = 8.1 mph from 045 °( NE) on day 24 at time 03:28\nDaily wind run = 018.9miles\nMaximum heat index = 1.1°C on day 24 at time 14:40\n\nAverages\\Extremes for day :25\n------------------------------------------------------------\n\nAverage temperature = 0.0°C\nAverage humidity = 87%\nAverage dewpoint = -1.8°C\nAverage barometer = 1013.6 mb\nAverage windspeed = 4.5 mph\nAverage gustspeed = 7.8 mph\nAverage direction = 139° ( SE)\nRainfall for month = 13.0 mm\nRainfall for year = 13.0 mm\nRainfall for day = 3.8 mm\nMaximum rain per minute = 0.3 mm on day 25 at time 23:42\nMaximum temperature = 1.7°C on day 25 at time 22:58\nMinimum temperature = -2.2°C on day 25 at time 04:15\nMaximum humidity = 95% on day 25 at time 00:00\nMinimum humidity = 82% on day 25 at time 12:36\nMaximum dewpoint = 1.0°C on day 25 at time 22:58\nMinimum dewpoint = -4.1°C on day 25 at time 4:15\nMaximum pressure = 1021.7 mb on day 25 at time 00:02\nMinimum pressure = 1000.6 mb on day 25 at time 23:46\nMaximum windspeed = 13.8 mph on day 25 at time 21:27\nMaximum gust speed = 23.0 mph from 135 °( SE) on day 25 at time 20:50\nDaily wind run = 107.9miles\nMaximum heat index = 1.7°C on day 25 at time 22:58\n\nAverages\\Extremes for day :26\n------------------------------------------------------------\n\nAverage temperature = 4.2°C\nAverage humidity = 92%\nAverage dewpoint = 3.0°C\nAverage barometer = 1006.0 mb\nAverage windspeed = 5.4 mph\nAverage gustspeed = 9.2 mph\nAverage direction = 193° (SSW)\nRainfall for month = 30.2 mm\nRainfall for year = 30.2 mm\nRainfall for day = 17.3 mm\nMaximum rain per minute = 0.5 mm on day 26 at time 22:36\nMaximum temperature = 7.0°C on day 26 at time 22:36\nMinimum temperature = 1.3°C on day 26 at time 00:56\nMaximum humidity = 97% on day 26 at time 04:52\nMinimum humidity = 84% on day 26 at time 14:04\nMaximum dewpoint = 6.1°C on day 26 at time 22:36\nMinimum dewpoint = 0.6°C on day 26 at time 0:31\nMaximum pressure = 1010.6 mb on day 26 at time 11:48\nMinimum pressure = 998.6 mb on day 26 at time 00:00\nMaximum windspeed = 16.1 mph on day 26 at time 22:32\nMaximum gust speed = 31.1 mph from 180 °( S ) on day 26 at time 22:31\nDaily wind run = 130.2miles\nMaximum heat index = 7.0°C on day 26 at time 22:36\n\nAverages\\Extremes for day :27\n------------------------------------------------------------\n\nAverage temperature = 6.8°C\nAverage humidity = 84%\nAverage dewpoint = 4.2°C\nAverage barometer = 996.1 mb\nAverage windspeed = 8.1 mph\nAverage gustspeed = 13.8 mph\nAverage direction = 200° (SSW)\nRainfall for month = 34.8 mm\nRainfall for year = 34.8 mm\nRainfall for day = 4.6 mm\nMaximum rain per minute = 0.3 mm on day 27 at time 05:26\nMaximum temperature = 9.7°C on day 27 at time 05:15\nMinimum temperature = 3.3°C on day 27 at time 23:09\nMaximum humidity = 100% on day 27 at time 01:23\nMinimum humidity = 62% on day 27 at time 14:42\nMaximum dewpoint = 9.1°C on day 27 at time 05:13\nMinimum dewpoint = 1.1°C on day 27 at time 21:52\nMaximum pressure = 1002.1 mb on day 27 at time 23:54\nMinimum pressure = 990.3 mb on day 27 at time 05:03\nMaximum windspeed = 20.7 mph on day 27 at time 05:12\nMaximum gust speed = 40.3 mph from 203 °(SSW) on day 27 at time 05:11\nDaily wind run = 195.4miles\nMaximum heat index = 9.7°C on day 27 at time 05:15\n\nAverages\\Extremes for day :28\n------------------------------------------------------------\n\nAverage temperature = 5.6°C\nAverage humidity = 87%\nAverage dewpoint = 3.6°C\nAverage barometer = 1003.6 mb\nAverage windspeed = 7.5 mph\nAverage gustspeed = 12.7 mph\nAverage direction = 191° ( S )\nRainfall for month = 37.3 mm\nRainfall for year = 37.3 mm\nRainfall for day = 2.5 mm\nMaximum rain per minute = 0.3 mm on day 28 at time 16:43\nMaximum temperature = 9.9°C on day 28 at time 18:36\nMinimum temperature = 1.3°C on day 28 at time 08:23\nMaximum humidity = 95% on day 28 at time 17:12\nMinimum humidity = 78% on day 28 at time 00:00\nMaximum dewpoint = 8.0°C on day 28 at time 17:30\nMinimum dewpoint = 0.0°C on day 28 at time 08:07\nMaximum pressure = 1009.1 mb on day 28 at time 09:34\nMinimum pressure = 997.2 mb on day 28 at time 17:14\nMaximum windspeed = 20.7 mph on day 28 at time 16:06\nMaximum gust speed = 35.7 mph from 180 °( S ) on day 28 at time 16:05\nDaily wind run = 179.5miles\nMaximum heat index = 9.9°C on day 28 at time 18:36\n\nAverages\\Extremes for day :29\n------------------------------------------------------------\n\nAverage temperature = 10.8°C\nAverage humidity = 90%\nAverage dewpoint = 9.3°C\nAverage barometer = 1001.3 mb\nAverage windspeed = 7.8 mph\nAverage gustspeed = 13.2 mph\nAverage direction = 198° (SSW)\nRainfall for month = 40.6 mm\nRainfall for year = 40.6 mm\nRainfall for day = 3.3 mm\nMaximum rain per minute = 0.3 mm on day 29 at time 22:03\nMaximum temperature = 13.2°C on day 29 at time 16:09\nMinimum temperature = 8.1°C on day 29 at time 07:07\nMaximum humidity = 96% on day 29 at time 23:05\nMinimum humidity = 77% on day 29 at time 01:11\nMaximum dewpoint = 11.7°C on day 29 at time 14:57\nMinimum dewpoint = 6.0°C on day 29 at time 01:04\nMaximum pressure = 1003.3 mb on day 29 at time 06:35\nMinimum pressure = 998.8 mb on day 29 at time 23:04\nMaximum windspeed = 15.0 mph on day 29 at time 19:24\nMaximum gust speed = 31.1 mph from 180 °( S ) on day 29 at time 15:15\nDaily wind run = 186.8miles\nMaximum heat index = 13.2°C on day 29 at time 16:09\n\nAverages\\Extremes for day :30\n------------------------------------------------------------\n\nAverage temperature = 8.5°C\nAverage humidity = 80%\nAverage dewpoint = 5.1°C\nAverage barometer = 1006.3 mb\nAverage windspeed = 7.5 mph\nAverage gustspeed = 13.3 mph\nAverage direction = 226° ( SW)\nRainfall for month = 46.0 mm\nRainfall for year = 46.0 mm\nRainfall for day = 5.3 mm\nMaximum rain per minute = 0.3 mm on day 30 at time 07:49\nMaximum temperature = 11.3°C on day 30 at time 00:00\nMinimum temperature = 5.9°C on day 30 at time 23:41\nMaximum humidity = 96% on day 30 at time 01:19\nMinimum humidity = 60% on day 30 at time 15:11\nMaximum dewpoint = 10.5°C on day 30 at time 00:00\nMinimum dewpoint = 2.0°C on day 30 at time 17:15\nMaximum pressure = 1017.1 mb on day 30 at time 23:51\nMinimum pressure = 998.9 mb on day 30 at time 03:51\nMaximum windspeed = 16.1 mph on day 30 at time 14:12\nMaximum gust speed = 36.8 mph from 248 °(WSW) on day 30 at time 17:32\nDaily wind run = 179.5miles\nMaximum heat index = 11.3°C on day 30 at time 00:00\n\nAverages\\Extremes for day :31\n------------------------------------------------------------\n\nAverage temperature = 7.4°C\nAverage humidity = 80%\nAverage dewpoint = 4.1°C\nAverage barometer = 1011.0 mb\nAverage windspeed = 7.3 mph\nAverage gustspeed = 12.8 mph\nAverage direction = 218° ( SW)\nRainfall for month = 52.3 mm\nRainfall for year = 52.3 mm\nRainfall for day = 6.4 mm\nMaximum rain per minute = 0.5 mm on day 31 at time 05:33\nMaximum temperature = 9.3°C on day 31 at time 11:50\nMinimum temperature = 5.8°C on day 31 at time 03:20\nMaximum humidity = 94% on day 31 at time 08:01\nMinimum humidity = 63% on day 31 at time 14:03\nMaximum dewpoint = 6.3°C on day 31 at time 05:30\nMinimum dewpoint = 2.4°C on day 31 at time 14:20\nMaximum pressure = 1016.9 mb on day 31 at time 00:01\nMinimum pressure = 1007.6 mb on day 31 at time 08:55\nMaximum windspeed = 16.1 mph on day 31 at time 12:15\nMaximum gust speed = 35.7 mph from 225 °( SW) on day 31 at time 06:00\nDaily wind run = 175.9miles\nMaximum heat index = 9.3°C on day 31 at time 11:50\n\n---------------------------------------------------------------------------------------------\nAverages\\Extremes for the month of January 2013\n\n---------------------------------------------------------------------------------------------\nAverage temperature = 3.3°C\nAverage humidity = 92%\nAverage dewpoint = 2.0°C\nAverage barometer = 1014.4 mb\nAverage windspeed = 3.6 mph\nAverage gustspeed = 6.6 mph\nAverage direction = 205° (SSW)\nRainfall for month = 52.3 mm\nRainfall for year = 52.3 mm\nMaximum rain per minute = 0.5 mm on day 26 at time 22:36\nMaximum temperature = 13.2°C on day 29 at time 16:09\nMinimum temperature = -4.9°C on day 22 at time 07:57\nMaximum humidity = 100% on day 27 at time 01:23\nMinimum humidity = 60% on day 30 at time 15:11\nMaximum dewpoint = 11.7°C on day 29 at time 14:57\nMinimum dewpoint = -5.8°C on day 22 at time 7:57\nMaximum pressure = 1038.7 mb on day 04 at time 11:37\nMinimum pressure = 990.3 mb on day 27 at time 05:03\nMaximum windspeed = 20.7 mph from 180°( S ) on day 28 at time 16:06\nMaximum gust speed = 40.3 mph from 203°(SSW) on day 27 at time 05:11\nMaximum heat index = 13.2°C on day 29 at time 16:09\nAvg daily max temp :5.2°C\nAvg daily min temp :1.5°C\nGrowing degrees days :0.0 GDD\nTotal windrun = 2640.6miles\n------------------------------------------\nDay, Sunshine hours, ET, max solar, max uv\n------------------------------------------\n01 02.7hrs ,ET :0.5 mm ,221.0 W/M²\n02 00.0hrs ,ET :0.3 mm ,104.0 W/M²\n03 01.9hrs ,ET :0.4 mm ,290.0 W/M²\n04 01.1hrs ,ET :0.2 mm ,200.0 W/M²\n05 00.2hrs ,ET :0.2 mm ,241.0 W/M²\n06 00.0hrs ,ET :0.1 mm ,128.0 W/M²\n07 00.0hrs ,ET :0.3 mm ,139.0 W/M²\n08 00.0hrs ,ET :0.2 mm ,120.0 W/M²\n09 01.6hrs ,ET :0.2 mm ,338.0 W/M²\n10 00.0hrs ,ET :0.1 mm ,72.0 W/M²\n11 01.3hrs ,ET :0.1 mm ,316.0 W/M²\n12 00.3hrs ,ET :0.3 mm ,141.0 W/M²\n13 03.9hrs ,ET :0.3 mm ,243.0 W/M²\n14 00.1hrs ,ET :0.2 mm ,151.0 W/M²\n15 03.5hrs ,ET :0.2 mm ,322.0 W/M²\n16 00.1hrs ,ET :0.1 mm ,185.0 W/M²\n17 00.0hrs ,ET :0.1 mm ,135.0 W/M²\n18 00.1hrs ,ET :0.2 mm ,74.0 W/M²\n19 00.0hrs ,ET :0.2 mm ,97.0 W/M²\n20 00.0hrs ,ET :0.2 mm ,97.0 W/M²\n21 00.0hrs ,ET :0.1 mm ,30.0 W/M²\n22 00.0hrs ,ET :0.1 mm ,30.0 W/M²\n23 00.0hrs ,ET :0.2 mm ,39.0 W/M²\n24 00.0hrs ,ET :0.2 mm ,109.0 W/M²\n25 00.4hrs ,ET :0.4 mm ,188.0 W/M²\n26 05.5hrs ,ET :0.6 mm ,330.0 W/M²\n27 05.3hrs ,ET :0.9 mm ,388.0 W/M²\n28 00.4hrs ,ET :0.7 mm ,139.0 W/M²\n29 00.0hrs ,ET :0.6 mm ,153.0 W/M²\n30 04.1hrs ,ET :1.1 mm ,455.0 W/M²\n31 04.6hrs ,ET :1.0 mm ,489.0 W/M²\nSunshine hours month to date= 36.9 hrs\nSunshine hours year to date= 36.9 hrs\nFrost days= 14\nIce days= 5\n-----------------------------------\nDaily rain totals\n-----------------------------------\n01.5 mm on day 8\n01.0 mm on day 9\n05.1 mm on day 14\n00.5 mm on day 15\n00.3 mm on day 23\n00.8 mm on day 24\n03.8 mm on day 25\n17.3 mm on day 26\n04.6 mm on day 27\n02.5 mm on day 28\n03.3 mm on day 29\n05.3 mm on day 30\n06.4 mm on day 31\n```" ]

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[ "Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.\n\n# Negative longitudinal magnetoresistance in gallium arsenide quantum wells\n\n## Abstract\n\nNegative longitudinal magnetoresistances (NLMRs) have been recently observed in a variety of topological materials and often considered to be associated with Weyl fermions that have a defined chirality. Here we report NLMRs in non-Weyl GaAs quantum wells. In the absence of a magnetic field the quantum wells show a transition from semiconducting-like to metallic behaviour with decreasing temperature. We observe pronounced NLMRs up to 9 Tesla at temperatures above the transition and weak NLMRs in low magnetic fields at temperatures close to the transition and below 5 K. The observed NLMRs show various types of magnetic field behaviour resembling those reported in topological materials. We attribute them to microscopic disorder and use a phenomenological three-resistor model to account for their various features. Our results showcase a contribution of microscopic disorder in the occurrence of unusual phenomena. They may stimulate further work on tuning electronic properties via disorder/defect nano-engineering.\n\n## Introduction\n\nMagnetic field-induced resistance change is conventionally termed as magnetoresistance (MR), which is usually related to magnetism and plays crucial roles in applications such as sensors and storage devices1. In a single-band nonmagnetic material the semiclassical Boltzmann equation approach gives rise to a magnetic field-independent resistivity ρ0m/e2, where e, m, n and τ are the charge, effective mass, density and relaxation time of the charge carriers2. Deviations from a constant resistivity, however, are often reported, for example, in two-dimensional electron gas, where both positive3 and negative4 MRs have been observed when the applied magnetic field B is perpendicular to the current I (BI).\n\nWith the recent discovery of topological materials, the MR phenomenon has been attracting extensive attention5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23. Two of the most remarkable findings are the extremely large MRs for BI5,6,7,8 and the negative longitudinal MRs (NLMRs) for B//I9,10,11,12,13,14,15,16,17,18,19,20,21,22,23. The former can be attributed to the co-existence of high-mobility electrons and holes5,24, resulting in diminishing Hall effect24. The origin of the NLMR, however, is currently under debate. In disordered systems such as films of topological insulator Bi2Se321 and Dirac semimetal Cd3As222, the NLMR is attributed to distorted current paths due to conductivity fluctuations induced by macroscopic disorder as revealed in computer simulations for polycrystalline AgxSe samples25,26. In contrast, the NLMR in single crystals of these materials9,10,11,12,13,14,15,16,17 is often considered as a manifestation of Weyl fermions due to the chirality imbalance in the presence of parallel magnetic and electric fields27,28. Recently, theories with topological29,30 and trivial30,31,32 states have been developed to understand the observed NLMR without invoking chiral anomaly. However, some puzzling concerns have been raised on NLMR experiments33. For example, numerous non-Weyl materials exhibit NLMRs20,34,35,36. Even within the class of Weyl semimetals, NLMRs are not consistently observed in the same material37,38. Furthermore, the reported NLMRs show unpredicted features such as non-monotonic magnetic field behaviour9,10,16. More disturbingly, it has been demonstrated that NLMRs can be artificially induced by non-uniform current injection33,39.\n\nHere we report NLMRs in a non-Weyl material and reveal that microscopic disorder can be their origin. We conduct magnetotransport measurements on GaAs quantum wells, in which microscopic disorder induces unusual phenomena such as quantum Hall plateaus40 and linear MR (LMR)3. We observe NLMRs with both monotonic and non-monotonic magnetic field dependence similar to those reported in topological materials. Furthermore, the NLMRs in our quantum wells exhibit an intriguing temperature behaviour: they occur at temperatures below 5 K, disappear at intermediate temperatures (>5 K) and re-appear at high temperatures (T > 130 K and up to 300 K). The NLMR is most pronounced at 160–180 K. After excluding experimental artefacts and accounting for the various features in their magnetic field dependence using a simple three-resistor model, we attribute the observed NLMRs to microscopic disorder including impurity and interface roughness.\n\n## Results\n\n### Negative longitudinal magnetoresistance\n\nWe measured four samples in standard Hall bar geometry, defined through photolithographic patterning. Three of them (see micrographs in Fig.1a and Supplementary Figure 1) are Hall bars on the same wafer and connected to each other, sharing the same applied current and denoted as Samples W1a, W1b and W1c in Supplementary Figure 1. The fourth sample (Sample W2) is the same Hall bar structure fabricated on a separate wafer. All the samples behave qualitatively the same (see Supplementary Table 1 for a summary of the characteristic parameters including the low-temperature electron densities for all four samples). Here we focus on results of Sample W1b, with additional data from other samples presented in the supplement.\n\nWe obtain data on the magnetic field dependence of the sample resistance R(B) at fixed temperatures and angles between the magnetic field and the current (see Fig.1b and Supplementary Figure 9 for the definition of angle θ). At temperatures below 5 K, we observe negative MRs for both B//I (θ = 0°) (Fig. 1e) and BI (θ = 90°) (see Supplementary Figure 2). At T > 5 K MRs become entirely positive for both magnetic field orientations (see Supplementary Figure 2). With further increase in temperature, the MRs for B//I begin to display non-monotonic behaviour, and NLMR behaviour re-emerges at the medium magnetic fields (see Fig. 1e for MRs at 133 K). At T > 145 K and up to room temperature, the MRs become purely negative, although they are non-monotonic at temperatures between 145 and 210 K. From the R(B) curves obtained at various temperatures, we construct the temperature dependence of MR = [R(B) – R0]/R0, where R0 is the sample resistance in the absence of an external magnetic field. The Cartesian plots of the results for Sample W1b and the other three samples are presented in Fig. 1d and Supplementary Figure 3, respectively. Colour maps that can show both the MR’s temperature and magnetic field dependences are given in Supplementary Figure 4 for all four samples. These plots and maps clearly show that all samples exhibit similar NLMRs, with some quantitative variation from sample to sample, for example, the maximum NLMR changes from −3.85% in Sample W2 at 190 K to −7.68% in Sample W1c at 165 K (see Supplementary Table 1 for results of other samples). The variations, particularly those in samples patterned on the same wafer, that is, Samples W1a, W1b and W1c, suggest that the NLMR may originate from local properties such as microscopic disorder.\n\nThe features including both the monotonic and non-monotonic magnetic field dependences in the R(B) curves shown in Fig. 1e are akin to those reported in crystals9,10,14,16,17 and films21,22 of topological materials. The R(B) curves presented in Fig. 1c for Sample W1b at 170 K and various angles indicate that negative MRs only occur when the magnetic field is aligned within a few degrees to the current direction and become most pronounced at B//I, akin to those attributed to chiral anomaly9,10. However, the temperature dependence of the NLMR in our quantum wells, as shown in Fig.1d for Sample W1b, differs significantly from those reported in the literature, where NLMR diminishes monotonically with increasing temperature9,10,21,22. In contrast, the NLMR in our GaAs quantum wells shows a non-monotonic temperature behaviour and becomes most pronounced at ~170 K. This difference could be understood with the existence of two types of microscopic disorders in quantum wells. In addition to the conventional microscopic disorder due to impurity and lattice defects that is relevant at low temperatures, the interface roughness of a quantum well may also induce NLMRs at high temperatures.\n\nSince the samples are in a standard Hall bar geometry defined through photolithographic patterning and the current contacts are far away from the voltage probes, the NLMRs observed here are unlikely to be artefacts arising from non-uniform current injection33,39. In general, artefacts become more pronounced with increasing mobility and thus can be excluded with the non-monotonic temperature behaviour of the observed NLMRs, which differs from the monotonic temperature dependence of the mobility (see Fig. 2b and Supplementary Figure 5d). The quantum wells are of very high quality, as demonstrated by the Shubnikov de Haas quantum oscillations at T = 3 K (see Supplementary Figure 6). Their mobility can be larger than 3 × 106 cm2 V−1 s−1 at T = 3 K and reach as high as 1.4 × 104 cm2 V−1 s−1 even at room temperature (see Supplementary Figure 5d). Therefore, macroscopic defects such as exotic phases and grain boundaries cannot be the origin of NLMRs in the quantum wells.\n\n### Phenomenological three-resistor model\n\nIt is known that microscopic disorder plays a crucial role in the occurrence of quantum Hall plateaus40, which is observed in all of our quantum wells (see Supplementary Figure 6). That is, areas with microscopic disorder exist in the quantum wells alongside with clean areas (see Fig. 3a for a schematic). Computer simulations for polycrystalline AgxSe samples25,26 have demonstrated that macroscopic disorder such as microscale clusters of excessive Ag induces distorted current paths, resulting in NLMRs. Similarly, the current paths in areas with microscopic disorder are expected to be distorted due to local conductivity fluctuation. Thus, we postulate that the disordered areas where the current paths are distorted in quantum wells have positive (negative) longitudinal magnetoconductances (MRs). Considering that a quadratic field dependence of the magnetoconductance is the most common relationship revealed by experiments and theories to describe NLMRs, we assume that the magnetotransport behaviour of the disordered areas to be Rd(B) = Rd0/(1 + αB2), where Rd0 is the resistance of the disordered areas at zero magnetic field and α is a fitting parameter. For the MR of the clean areas where the current paths are not distorted, we take the conventional Drude form Rc(B) = Rc0(1 + βB2)27, where Rc0 is the resistance of the clean areas at zero magnetic field and β is a fitting parameter. Figure 3b presents schematics for the expected R(B) relationship for these two scenarios.\n\nThe above hypotheses allow us to use a phenomenological three-resistor model to qualitatively account for the various magnetic field behaviours of the observed NLMRs. For a sample with disordered areas mostly surrounded by clean areas (see a schematic in Fig. 3a), its R(B) behaviour can be evaluated using a simplified equivalent circuit consisting of three resistors (see Fig. 3d), that is, a resistor $$R_{\\mathrm{c}}^{\\mathrm{p}}$$ with positive MR (representing the clean areas) in parallel with two resistors Rd and $$R_{\\mathrm{c}}^{\\mathrm{s}}$$ that are in series and have opposite MRs, where $$R_{\\mathrm{d}}$$ and $$R_{\\mathrm{c}}^{\\mathrm{s}}$$ are the resistances of the disordered and clean areas, respectively. The superscripts s and p denote the cases of the clean area in series with and in parallel to the disordered area. In this case the R(B) behaviour can be described as\n\n$$R\\left( B \\right) = [1/(R_{\\mathrm{d}} + R_{\\mathrm{c}}^{\\mathrm{s}}) + 1/R_{\\mathrm{c}}^{\\mathrm{p}}]^{ - 1}.$$\n(1)\n\nSince each of $$R_{\\mathrm{d}},R_{\\mathrm{c}}^{\\mathrm{s}}$$ and $$R_{\\mathrm{c}}^{\\mathrm{p}}$$ has two variables, Eq. 1 has six free parameters. In order to improve the reliability of the analysis, we can take advantage of the measured zero-field resistance by rewriting Eq. 1 as\n\n$$R( B ) = \\, R_{0}\\left\\{ \\varepsilon _{\\mathrm{d}}/\\left[ {\\gamma _{\\mathrm{d}}/\\left( {1 + \\alpha B^2} \\right) + (1 - \\gamma _{\\mathrm{d}})\\left( {1 + \\beta ^{\\mathrm{s}}B^2} \\right)} \\right]\\right. \\\\ \\left. + \\, (1 - \\varepsilon _{\\mathrm{d}})/\\left( {1 + \\beta ^{\\mathrm{p}}B^2} \\right) \\right\\}^{ - 1},$$\n(2)\n\nwhere $$R_0 = [1/(R_{{\\mathrm{d}}0} + R_{{\\mathrm{c}}0}^{\\mathrm{s}}) + 1/R_{{\\mathrm{c}}0}^{\\mathrm{p}}]^{ - 1}$$ is the measured zero-field resistance, $$\\varepsilon _{\\mathrm{d}} = R_{{\\mathrm{c}}0}^{\\mathrm{p}}/(R_{{\\mathrm{c}}0}^{\\mathrm{p}} + R_{{\\mathrm{d}}0} + R_{{\\mathrm{c}}0}^{\\mathrm{s}})$$ is the ratio of the conductance of the channel with disordered area to the total value at zero field and $$\\gamma _{\\mathrm{d}} = R_{{\\mathrm{d}}0}/(R_{{\\mathrm{d}}0} + R_{{\\mathrm{c}}0}^{\\mathrm{s}})$$ is the ratio of the zero-field resistance of the disordered area to the corresponding total value of the channel consisting of the disordered and clean areas in series.\n\nWe use Eq. 2 to account for the experimental R(B) curves as presented in Fig. 1e as solid curves. We find that all five fitting parameters are necessary to describe R(B) curves with positive MR near zero field, like those obtained at T = 3 and 133 K, resulting in large uncertainty in the analysis. Numerical results in Supplementary Figure 7 indicate that $$R_{\\mathrm{c}}^{\\mathrm{p}}$$ is the contributor for the positive MR near zero field (see Supplementary Figure 7c) and the experimental R(B) curves at T ≥ 138 K in Fig. 1e follow the NLMR behaviour modelled with an equivalent circuit with Rd and $$R_{\\mathrm{c}}^{\\mathrm{s}}$$ in series (see Supplementary Figure 7b). In this scenario, εd = 1, reducing Eq. 2 to R(B) = R0[γd/(1 + αB2) + (1 − γd)(1 + βsB2)]. Using the experimentally determined R0, this simplification decreases the number of variables to three (γd, α and βs). This simple serial scenario accounts for the experimental data very well, as demonstrated in Fig. 1e for T = 138, 150 and 250 K. Figure 4 shows the temperature dependence of the derived γd, α and βs. It is reasonable for α and βs to increase with decreasing temperature, since they should reflect the temperature behaviour of the electron mobility (see Fig.2b). The combined effect of γd, α and βs leads to an enhanced NLMR with decreasing temperature. Between 150 and 160 K, however, the NLMRs as well as γd, α and βs change their temperature behaviour, resulting in minima in the NLMR versus temperature curves (see Fig. 1d) and peaks in those of the three fitting parameters.\n\nWe note that the change in the temperature behaviour of NLMRs as well as γd, α and βs coincides with a transition (at Tp ~145 K) from semiconducting-like to metallic temperature dependence in the zero-field R0(T) curve and a kink in the Rxy curve at B = 9 T (see Fig. 2a). As shown in Fig. 2b, the temperature dependences of both the electron mobility and density also change significantly at 140–150 K. Quantitatively, the temperature dependence of the electron density for Sample W1b at T > 140 K can be well described with n = N0 exp(−EA/kBT), with kB the Boltzmann constant, N0 = 3.05 × 1012 cm−2 and EA ≈ 34 meV (see Supplementary Table 1 for N0s and EAs of other samples). The EA value falls in the range of the activation energy of 6–200 meV for Si dopants in the AlxGa1 − xAs layer (x = 0–0.33)41. The value of N0 is close to the total Si density of 5.1 × 1012 cm−2. Thus, the transport at high temperatures is determined by electrons from the Si dopants.\n\n### LMR in perpendicular magnetic fields\n\nBoth experiments25,26 and simulations25,26,42 reveal that (quasi-)LMRs at BI can appear in polycrystalline materials where NLMRs are detected. As presented in Fig. 5a for sample W1b at T = 170 K and various magnetic-field orientations, our quantum wells also exhibit (quasi-)LMRs at BI and NLMRs at B//I. Furthermore, the linearity of the MRs for BI becomes more pronounced as the NLMRs for B//I increase, as demonstrated by the R(B) curves obtained at various temperatures shown in Fig. 5b. The observation of (quasi-)LMR at BI further attests to the role of disorder on the magnetotransport of our quantum wells. As demonstrated in Fig. 5c for the R(B) curves obtained at T = 105 K, the MR at B//I can be positive and even quasi-linear. In this case, (quasi-)LMRs may occur for all field orientations.\n\n## Discussion\n\nOur phenomenological three-resistor model and Eq. 2 can be readily applied to account for the NLMRs in films of other materials, in which both micro- and macroscopic disorders are present. The longitudinal magnetoconductance σxx in thin films of topological insulator Bi2Se321 is found to follow $$\\sigma _{xx}\\sim B^2$$ in magnetic fields up to 30 T, indicating that the entire sample is disordered. The behaviour of NLMRs in films of Dirac semimetal Cd3As2 is thickness-dependent22, with various types of R(B) relationship resembling those in Supplementary Figure 7. In the scenario of Supplementary Figure 7c for a parallel equivalent circuit, Eq. 2 can be re-written as σ(B) = σd0(1 + αB2) + σc0/(1 + βpB2), which is exactly the same equation used in the analysis of the data for the 370-nm-thick Cd3As2 film22. On the other hand, the two thinner samples (with thicknesses of 85 and 120 nm) exhibit similar type of NLMRs to our quantum wells (of 40 nm thick) at high temperatures, which can be described with the reduced form of Eq. 2 for a series equivalent circuit (see Supplementary Figure 7b). For films of intermediate thicknesses (170 and 340 nm), Eq. 2 with all three resistors (see Supplementary Figure 7a) is required to account for the observed NLMRs.\n\nRecently reported NLMRs in single crystals were often attributed to chiral anomaly. In quantitative analyses16,34, possible weak anti-localization conductance σWAL and conventional Fermi surface contribution σN were also included to account for the deviation from quadratic field dependence of the conductance, leading to\n\n$$\\sigma \\left( B \\right) = \\sigma _{{\\mathrm{WAL}}}\\left( {1 + C_{\\mathrm{W}}B^2} \\right) + \\sigma _{\\mathrm{N}}$$\n(3)\n\nwith the positive constant CW reflecting the contribution from chiral anomaly and $$\\sigma _{{\\mathrm{WAL}}} = aB^{1/2} + \\sigma _0^{{\\mathrm{wal}}}$$ with a < 0 and $$\\sigma _{\\mathrm{N}}^{ - 1} = \\rho _0^{\\mathrm{N}} + bB^2$$. Such an expression with five variables could describe the experimental data at low magnetic fields16,34. Since weak anti-localization may also exist in quantum wells at low temperatures, we apply Eq. 3 to analyse our data obtained at 3 K and the result is presented in Supplementary Figure 2b. With four fitting parameters (a = 1.98 × 10−3T−1/2, $$\\sigma _0^{{\\mathrm{wal}}} = 2.06 \\times 10^{ - 3}$$ Ω−1, CW = 59.84T−2, b = 87.21 T−2) and the measured zero-field resistivity ρ0 (=19.81 Ω) (which gives $$\\sigma _0^{\\mathrm{N}} = 1/\\rho _0 - {\\mathrm{\\sigma }}_0^{{\\mathrm{wal}}} = 4.84 \\times 10^{ - 2}$$ Ω−1), Eq. 3 can indeed describe the results at low magnetic fields (B < 0.5 T) well and also reproduces the upturn in the MR at high magnetic fields. However, when we set CW = 0 for our non-Weyl quantum well, Eq. 3 reduces to σ(B) = σWAL + σN, and yields only positive MR since both σWALand σN decrease with increasing magnetic field. Thus, Eq. 3 is not applicable to a non-Weyl system. We also use Eq. 3 to reveal the possible contribution of weak localization by allowing a > 0. In this case, Eq. 3 cannot describe the experimental data even at low magnetic fields if we set CW = 0. Thus, weak localization that may induce NLMRs in a 2D system at low temperatures43,44,45 cannot be the dominant contributor to the observed NLMRs at low temperatures.\n\nOur results reveal that LMRs can co-exist with NLMRs. Thus, NLMRs can be used to distinguish disorder based origin from other mechanisms46,47,48,49 for LMRs. On the other hand, (quasi-)LMRs for BI could be an indicator of the existence of NLMRs, providing guidance in the search for materials with NLMRs. As demonstrated in disorder-tuned polycrystalline samples50, our discovery of the role of microscopic disorder on the occurrence of NLMRs and LMRs will stimulate more work to tune the magnetotransport properties of single crystals through microscopic disorder engineering, for example, doping16,20 and irradiations with light charge particles such as protons51 and electrons52 for crystals.\n\n## Methods\n\n### Sample preparation\n\nThe measured samples are 40-nm-wide GaAs quantum well grown by molecular beam epitaxy4. The quantum well is buried 180 nm deep under the surface, and separated by 150-nm Al0.24Ga0.76As-thick barriers on both sides from the δ-doped silicon impurities with densities of 1.18 × 1012 and 3.92 × 1012 cm−2 for the layers under and above the quantum well, respectively. The samples are fabricated into Hall bars with width of Ly = 50 µm and voltage lead distance of Lx = 100 µm (see Fig. 1a) by photolithography. Contacts to the quantum well are made by annealing InSn at 420 °C for 4 min. The electron densities of the measured quantum wells at 3 K range from 7.91 to 8.83 (1010 cm−2) (see Supplementary Table 1).\n\n### Resistance measurements\n\nWe conduct DC resistance measurements using a Quantum Design Physical Property Measurement System (PPMS-9). We use constant current mode. The results are found to be current-independent (see Supplementary Figure 8). The reported data were taken with I = 0.5μA for all samples. Angular dependence of the resistance was obtained by placing the sample on a precision, stepper-controlled rotator with an angular resolution of 0.05°. Figure 1b shows the measurement geometry where the angle θ between the magnetic field B and the current I can be varied. Supplementary Figure 9 shows the experimental definition of θ = 0°, that is, the orientation of magnetic field at B//I. In experiments we measure R(H) curves at various fixed temperatures and angles, as demonstrated in Fig. 1c, e. The MR is defined as MR = [R(H) − R0)]/R0, where R(H) and R0 are the resistance at a fixed temperature with and without the presence of a magnetic field, respectively.\n\n## Data availability\n\nThe data that support the findings of this study are available from the corresponding author upon reasonable request.\n\n## References\n\n1. 1.\n\nDaughton, J. M. GMR applications. J. Magn. Magn. Mater. 192, 334–342 (1999).\n\n2. 2.\n\nMirlin, A. D., Wilke, J., Evers, F., Polyakov, D. G. & Woelfle, P. Strong magnetoresistance induced by long-range disorder. Phys. Rev. Lett. 83, 2801–2804 (1999).\n\n3. 3.\n\nKhouri, T. et al. Linear magnetoresistance in a quasifree two-dimensional electron gas in an ultrahigh mobility GaAs quantum well. Phys. Rev. Lett. 117, 256601 (2016).\n\n4. 4.\n\nShi, Q. et al. Colossal negative magnetoresistance in a two-dimensional electron gas. Phys. Rev. B 89, 201301(R) (2014).\n\n5. 5.\n\nAli, M. N. et al. Large, non-saturating magnetoresistance in WTe2. Nature 514, 205–208 (2014).\n\n6. 6.\n\nLiang, T. et al. Ultrahigh mobility and giant magnetoresistance in Dirac semimetal Cd3As2. Nat. Mater. 14, 280–284 (2015).\n\n7. 7.\n\nShekhar, C. et al. Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP. Nat. Phys. 11, 645–649 (2015).\n\n8. 8.\n\nTafti, F. F. et al. Resistivity plateau and extreme magnetoresistance in LaSb. Nat. Phys. 12, 272–277 (2016).\n\n9. 9.\n\nXiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015).\n\n10. 10.\n\nHuang, X. C. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015).\n\n11. 11.\n\nLi, Q. et al. Chiral magnetic effect in ZrTe5. Nat. Phys. 12, 550–554 (2016).\n\n12. 12.\n\nHirschberger, M. et al. The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi. Nat. Mater. 15, 1161–1166 (2016).\n\n13. 13.\n\nZhang, C. L. et al. Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal. Nat. Commun. 7, 10735 (2015).\n\n14. 14.\n\nWang, L.-X., Li, C.-Z., Yu, D.-P. & Liao, Z.-M. Aharonov–Bohm oscillations in Dirac semimetal Cd3As2 nanowires. Nat. Commun. 7, 10769 (2016).\n\n15. 15.\n\nWang, H. C. et al. Chiral anomaly and ultrahigh mobility in crystalline HfTe5. Phys. Rev. B 93, 165127 (2016).\n\n16. 16.\n\nLv, Y.-Y. et al. Experimental observation of anisotropic Adler–Bell–Jackiw anomaly in type-II Weyl semimetal WTe1.98 crystals at the quasiclassical regime. Phys. Rev. Lett. 118, 096603 (2017).\n\n17. 17.\n\nGooth, J. et al. Experimental signatures of the mixed axial–gravitational anomaly in the Weyl semimetal NbP. Nature 547, 324–327 (2017).\n\n18. 18.\n\nArnold, F. et al. Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP. Nat. Commun. 8, 11615 (2016).\n\n19. 19.\n\nLi, P. et al. Evidence for topological type-II Weyl semimetal WTe2. Nat. Commun. 7, 2150 (2017).\n\n20. 20.\n\nWang, Z. et al. Defects controlled hole doping and multivalley transport in SnSe single crystals. Nat. Commun. 9, 47 (2017).\n\n21. 21.\n\nWiedmann, S. et al. Anisotropic and strong negative magnetoresistance in the three-dimensional topological insulator Bi2Se3. Phys. Rev. B 94, 081302(R) (2016).\n\n22. 22.\n\nSchumann, T., Goyal, M., Kealhofer, D. A. & Stemmer, S. Negative magnetoresistance due to conductivity fluctuations in films of the topological semimetal Cd3As2. Phys. Rev. B 95, 241113(R) (2017).\n\n23. 23.\n\nBreunig, O. et al. Gigantic negative magnetoresistance in the bulk of a disordered topological insulator. Nat. Commun. 8, 15545 (2017).\n\n24. 24.\n\nHan, F. et al. Separation of electron and hole dynamics in the semimetal LaSb. Phys. Rev. B 96, 125112 (2017).\n\n25. 25.\n\nHu, J. S., Rosenbaum, T. F. & Betts, J. B. Current jets, disorder, and linear magnetoresistance in the silver chalcogenides. Phys. Rev. Lett. 95, 186603 (2005).\n\n26. 26.\n\nHu, J. S., Parish, M. M. & Rosenbaum, T. F. Nonsaturating magnetoresistance of inhomogeneous conductors: comparison of experiment and simulation. Phys. Rev. B 75, 214203 (2007).\n\n27. 27.\n\nSon, D. T. & Spivak, B. Z. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B 88, 104412 (2013).\n\n28. 28.\n\nBurkov, A. A. Negative longitudinal magnetoresistance in Dirac and Weyl metals. Phys. Rev. B 91, 245157 (2015).\n\n29. 29.\n\nDai, X., Du, Z. Z. & Lu, H.-Z. Negative magnetoresistance without chiral anomaly in topological insulators. Phys. Rev. Lett. 119, 166601 (2017).\n\n30. 30.\n\nAndreev, A. V. & Spivak, B. Z. Longitudinal negative magnetoresistance and magnetotransport phenomena in conventional and topological conductors. Phys. Rev. Lett. 120, 026601 (2018).\n\n31. 31.\n\nGoswami, P., Pixley, J. H. & Das Sarma, S. Axial anomaly and longitudinal magnetoresistance of a generic three-dimensional metal. Phys. Rev. B 92, 075205 (2015).\n\n32. 32.\n\nGao, Y., Yang, S. A. & Niu, Q. Intrinsic relative magnetoconductivity of non-magnetic metals. Phys. Rev. B 95, 165135 (2017).\n\n33. 33.\n\nLiang, S. H., Lin, J. J., Kushwaha, S., Cava, R. J. & Ong, N. P. Experimental tests of the chiral anomaly magnetoresistance in the Dirac–Weyl semimetals Na3Bi and GdPtBi. Phys. Rev. X 8, 031002 (2018).\n\n34. 34.\n\nKim, H.-J. et al. Dirac versus Weyl fermions in topological insulators: Adler–Bell–Jackiw anomaly in transport phenomena. Phys. Rev. Lett. 111, 246603 (2013).\n\n35. 35.\n\nRullier-Albenque, F., Colson, D. & Forget, A. Longitudinal magnetoresistance in Co-doped BaFe2As2 and LiFeAs single crystals: interplay between spin fluctuations and charge transport in iron pnictides. Phys. Rev. B 88, 045105 (2013).\n\n36. 36.\n\nJuyal, A., Agarwal, A. & Soumik Mukhopadhyay, S. Negative longitudinal magnetoresistance in the density wave phase of Y2Ir2O7. Phys. Rev. Lett. 120, 096801 (2018).\n\n37. 37.\n\nZhao, Y. F. et al. Anisotropic magnetotransport and exotic longitudinal linear magnetoresistance in WTe2 crystals. Phys. Rev. B 92, 041104(R) (2015).\n\n38. 38.\n\nWang, Y. J. et al. Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2. Nat. Commun. 7, 13142 (2016).\n\n39. 39.\n\ndos Reis, R. D. et al. On the search for the chiral anomaly in Weyl semimetals: the negative longitudinal magnetoresistance. N. J. Phys. 18, 085006 (2016).\n\n40. 40.\n\nYennie, D. R. Integral quantum Hall effect for nonspecialists. Rev. Mod. Phys. 59, 781 (1987).\n\n41. 41.\n\nSalmon, L. G. & D’Haenens, I. J. The effect of aluminum composition on silicon donor behavior in AlxGa1 − xAs. J. Vac. Sci. Technol. B 2, 197 (1984).\n\n42. 42.\n\nParish, M. M. & Littlewood, P. B. Non-saturating magnetoresistance in heavily disordered semiconductors. Nature 426, 162–165 (2003).\n\n43. 43.\n\nGorbachev, R. V. et al. Weak localization in bilayer graphene. Phys. Rev. Lett. 98, 176805 (2007).\n\n44. 44.\n\nMinkov, G. M. et al. Quantum corrections to conductivity: from weak to strong localization. Phys. Rev. B 65, 235322 (2002).\n\n45. 45.\n\nHassenkam, T. et al. Spin splitting and weak localization in (110) GaAs/AlxGa1−xAs quantum wells. Phys. Rev. B 55, 9298–9301 (1997).\n\n46. 46.\n\nNarayanan, A. et al. Linear magnetoresistance caused by mobility fluctuations in n-doped Cd3As2. Phys. Rev. Lett. 114, 117201 (2015).\n\n47. 47.\n\nAlekseev, P. S. et al. Magnetoresistance in two-component systems. Phys. Rev. Lett. 114, 156601 (2015).\n\n48. 48.\n\nSong, J. C. W., Refael, G. & Lee, P. A. Linear magnetoresistance in metals: guiding center diffusion in a smooth random potential. Phys. Rev. B 92, 180204(R) (2015).\n\n49. 49.\n\nThirupathaiah, S. et al. Possible origin of linear magnetoresistance: observation of Dirac surface states in layered PtBi2. Phys. Rev. B 97, 035133 (2018).\n\n50. 50.\n\nHu, J. S. & Rosenbaum, T. F. Classical and quantum routes to linear magnetoresistance. Nat. Mater. 7, 697–700 (2008).\n\n51. 51.\n\nFang, L. et al. Doping- and irradiation-controlled pinning of vortices in BaFe2(As1−xPx)2 single crystals. Phys. Rev. B 84, 140504 (2011).\n\n52. 52.\n\nProzorov, R. et al. Effect of electron irradiation on superconductivity in single crystals of Ba(Fe1−xRux)2As2 (x = 0.24). Phys. Rev. X 4, 041032 (2014).\n\n## Acknowledgements\n\nMagnetotransport measurements were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering. Sample fabrication and characterization were supported by the Department of Energy Basic Energy Sciences (Grant No. DE-FG02-00-ER45841), the National Science Foundation (Grants No. DMR 1709076 and MRSEC DMR 1420541) and the Gordon and Betty Moore Foundation (Grant No. GBMF4420). Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. W.Z. acknowledges support from the DOE Visiting Faculty Program and the US National Science Foundation under Grants No. DMR-1808892. M.S. was supported by the Fulbright Program. Y.-L.W and Y.-Y.L. acknowledge supports by the National Natural Science Foundation of China (61771235 and 61727805) and the National Key R&D Program of China (2018YFA0209002).\n\n## Author information\n\nAuthors\n\n### Contributions\n\nZ.-L.X., Y.-L.W. and W.Z. designed the experiments; M.K.M., L.N.P., K.W.W., K.W.B., and M.Sh. grew and fabricated the samples. J.X., M.Su, Y.-L.W. and Z.-L.X. conducted the transport measurements, J.X., Y.-L.W., D.J. and W.Z. contributed to data analysis; Z.-L.X., W.Z., Y.-L.W. and W.-K.K. wrote the paper. All of the authors reviewed the manuscript.\n\n### Corresponding authors\n\nCorrespondence to Zhi-Li Xiao, Yong-Lei Wang or Wei Zhang.\n\n## Ethics declarations\n\n### Competing interests\n\nThe authors declare no competing interests.\n\nJournal peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.\n\nPublisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\n## Rights and permissions\n\nReprints and Permissions", null, "", null, "" ]

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[ "# Square root\n\ninverse operation of square for finding the original base number\n(Redirected from Root (mathematics))\n\nIn mathematics, a square root of a number x is another number that, when multiplied by itself (squared), becomes x. When it is non-negative, it is represented by the symbol ${\\sqrt {x}}$", null, ", and called the principal square root of x. For example, 2 is the square root of 4, because 2×2=4. Only numbers bigger than or equal to zero have real square roots. The only square root of zero is zero.\n\nAn important number is the square root of 2, which is an irrational number. Its value is around 1.41421. It is also the length of a diagonal in the square whose side is 1.\n\nSquare roots of negative numbers are not real numbers – they are imaginary numbers. Imaginary numbers are basically numbers whose square is negative. Every complex number, except 0, has 2 square roots. For example, −1 has two square roots. We call them $i$", null, "and $-i$", null, ". We also consider the number $i$", null, "as the principal square root of −1, and called it the imaginary unit.\n\nThe sign for a square root is made by putting a bent line over a number, like this: ${\\sqrt {4}}$", null, ". This is read as \"the square root of 4\" (or whatever number we are taking the square root of).\n\nA whole number with a square root that is also a whole number is called a perfect square. The first few perfect squares are: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225.\n\nBelow is a table of square roots (rounded to 3 decimals places).\n\nNumber Square root of number\n1 1.000\n2 1.414\n3 1.732\n4 2.000\n5 2.236\n6 2.449\n7 2.646\n8 2.828\n9 3.000\n10 3.162\n11 3.317\n12 3.464\n13 3.606\n14 3.742\n15 3.873\n16 4.000\n17 4.123\n18 4.243\n19 4.359\n20 4.472\n\n## Origin of the symbol\n\nIt is not really known where the square root symbol ${\\sqrt {\\,\\,}}$  comes from, but some people believe that it was from the letter r, which is the first letter of the Latin and German word radix. Radix means root or base. Thus, radix quadratum from Latin refer most likely to the base of a square. Since the sides of a square are all equal, the word radix may be interpreted as side of a square—without actually so." ]

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[ "En este grupo En todos\n\n# Análisis numérico para ecuaciones diferenciales", null, "José\nEscrito por José Aravena Damaneé\nel 18/07/2010\n\nA 6-cm by 5-cm rectangular silver plate has heat being uniformly generated at each point at\n\nThe rate q = 1. 5 cal/cm3 ·s. Let x represent the distance along the edge of the plate of length 6\n\nCm and y be the distance along the edge of the plate of length 5 cm. Suppose the temperature\n\nU along the edges is kept at the following temperatures:\n\nU(x,O) = x(6 - x), u(x, 5) = 0, ° < x < 6,\n\nU(O, y) = y(5 - y), u(6, y) = 0, ° < y < 5,\n\nWhere the origin lies at a comer of the plate with coordinates (0,0) and the edges lie along the\n\nPositive x- and y-axes. The steady-state temperature u = u(x, y) satisfies Poisson's equation:\n\n(a2u /ax2) (x, y) + (a2u/ay2) (x, y) = - (q/K') 0 < x < 6, 0< y < 5,\n\nWhere K, the thermal conductivity, is 1. 04 cal/cm·deg·s. Approx. Imate the temperature u(x, y)\n\nUsing Algorithm 12. 1 with h = 0. 4 and k = 1/3." ]

[ null, "https://grupos.emagister.com/avatares_defecto/avatar_1b.gif", null ]

[ "It\\\"s really common when learning about fractions to desire to know how transform a fraction like 24/35 into a percentage. In this step-by-step guide, we\\\"ll show you exactly how to turn any fraction into a portion really easily. Let\\\"s take a look!\n\nWant to easily learn or show students just how to transform 24/35 to a percentage? play this an extremely quick and fun video now!\n\nBefore we acquire started in the fraction to portion conversion, let\\\"s go over some really quick portion basics. Remember the a numerator is the number above the portion line, and the denominator is the number below the portion line. We\\\"ll usage this later in the tutorial.\n\nYou are watching: What is 24/35 as a percentage\n\nWhen we space using percentages, what we room really saying is that the portion is a fraction of 100. \\\"Percent\\\" method per hundred, and also so 50% is the exact same as saying 50/100 or 5/10 in fraction form.\n\nSo, due to the fact that our denominator in 24/35 is 35, us could readjust the portion to make the denominator 100. To do that, we division 100 by the denominator:\n\n100 ÷ 35 = 2.8571428571429\n\nOnce we have that, we deserve to multiple both the numerator and denominator through this multiple:\n\n24 x 2.8571428571429/35 x 2.8571428571429=68.571428571429/100\n\nNow we can see that our portion is 68.571428571429/100, which way that 24/35 as a portion is 68.5714%.\n\nWe can additionally work this out in a simpler way by an initial converting the portion 24/35 come a decimal. To execute that, we just divide the molecule by the denominator:\n\n24/35 = 0.68571428571429\n\nOnce we have actually the price to the division, we have the right to multiply the price by 100 to do it a percentage:\n\n0.68571428571429 x 100 = 68.5714%\n\nAnd there you have actually it! Two various ways to transform 24/35 come a percentage. Both space pretty straightforward and easy to do, however I personally like the convert to decimal an approach as it takes much less steps.\n\nI\\\"ve checked out a the majority of students get puzzled whenever a inquiry comes up about converting a fraction to a percentage, but if you monitor the measures laid out below it need to be simple. That said, you may still need a calculator for more complex fractions (and friend can always use our calculator in the kind below).\n\nIf you want to practice, grab you yourself a pen, a pad, and a calculator and shot to transform a few fractions to a portion yourself.\n\nHopefully this tutorial has helped you come understand just how to transform a portion to a percentage. You can now go forth and convert fractions to percentages as much as your small heart desires!\n\nIf you uncovered this content advantageous in her research, please carry out us a an excellent favor and also use the tool below to make certain you correctly reference united state wherever you usage it. Us really appreciate your support!\n\n\\\"What is 24/35 together a percentage?\\\". tasiilaq.net. Accessed top top September 22, 2021. Https://tasiilaq.net/calculator/fraction-as-percentage/what-is-24-35-as-a-percentage/.\n\n\\\"What is 24/35 as a percentage?\\\". tasiilaq.net, https://tasiilaq.net/calculator/fraction-as-percentage/what-is-24-35-as-a-percentage/. Accessed 22 September, 2021." ]

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[ "# How Many Grains Of Rice In A Cup?\n\nHow many grains of rice in a cup? This question often arises when it comes to cooking rice or understanding its measurements. The answer may not be straightforward, as it depends on various factors such as the type of rice, grain size, and even cooking techniques.\n\nHowever, we can explore the general estimates and guidelines to shed some light on this matter. Whether you’re curious about the number of grains in a cup of uncooked or cooked rice, or if you’re interested in learning about different measurements, we’ll delve into the fascinating world of rice and its grain count.\n\nSo, let’s explore the question: How many grains of rice are typically found in a cup?\n\n## How to measure grains of rice?\n\nThere are several methods to measure grains of rice:\n\n1. Counting: This involves manually counting the individual grains of rice one by one. It can be time-consuming and impractical for large quantities.\n2. Volume: Using measuring cups or spoons, you can measure rice by volume. Common measurements include cups, tablespoons, or teaspoons.\n3. Weight: Using a kitchen scale, you can measure the weight of rice in grams or ounces. This method provides a more precise measurement, especially for recipes that require specific rice-to-water ratios.\n4. Rough Estimates: For a quick estimation, you can use general guidelines such as “a handful of rice” or “a scoop of rice.” However, these methods are less precise and may vary depending on the size of your hand or scoop.\n5. Another method to measure grains of rice is by using a grain size tool. This tool typically consists of a series of different-sized holes or slots. You can pour a sample of rice into the tool and shake it gently, allowing the grains to pass through the holes. By observing which hole or slot the majority of the grains pass through, you can determine the grain size and get an estimation of the number of grains per unit volume.\n\n## How many grains of rice in a cup?\n\nThe number of grains of rice in a cup, half a cup, or 1/4 cup can vary depending on factors such as the type of rice, grain size, and packing density. However, as rough estimates:\n\n• A cup of rice typically contains around 7,000 to 8,000 grains, it weighs around 185 grams (6.5 ounces)\n• Half a cup of rice would have roughly half that amount, around 3,500 to 4,000 grains. It would generally weigh around 92.5 grams (3.25 ounces).\n• A 1/4 cup of rice would contain approximately 1,750 to 2,000 grains. Equivalent to a weight of around 46.25 grams (1.63 ounces).\n\n### How many grains of rice are in a 10lb bag?\n\nWe can consider that a 10lb bag of rice is equivalent to approximately 4.5kg. If we assume an average grain weight of around 0.06 grams per grain, which is a common estimate for medium-grain white rice, we can calculate the approximate number of grains.\n\n4.5kg is equal to 4,500 grams. Dividing this by 0.06 grams per grain gives us approximately 75,000 grains. However, this number may be rounded down to 70,000 for simplicity or to account for any variations in grain size or packing density.\n\n### How many grains of rice are in a tablespoon?\n\nA tablespoon typically holds around 15 milliliters of rice. If we divide this volume by the average grain weight (0.06 grams), we get approximately 250 grains.\n\n### How many grains of rice in a coffee cup?\n\nAssuming a coffee cup with a capacity of 8.8 to 14.1 ounces (approximately 250 to 400 milliliters), and using the rough estimate of 7,000 to 8,000 grains of rice per cup, you can expect to find approximately:\n\n• In a smaller coffee cup (8.8 ounces or 250 milliliters): around 1,750 to 2,000 grains of rice.\n• In a larger coffee cup (14.1 ounces or 400 milliliters): around 2,800 to 3,200 grains of rice.\n\n## How many grains of cooked rice in a cup?\n\nIf we assume that the number of grains doubles after cooking, there would be approximately 14,000 to 16,000 grains of cooked rice in a cup (weigh approximately 195 to 200 grams). If the number of grains triples, there would be approximately 21,000 to 24,000 grains of cooked rice in a cup (weigh approximately 1,050 to 1,200 grams).\n\n### How many grains of cooked rice in a bowl?\n\nWhen cooking rice, the number of grains will generally increase due to water absorption and expansion. As a rough estimate, the number of grains of cooked rice in a bowl can roughly double or even triple compared to the uncooked state.\n\n• Therefore, assuming that a small bowl contains 5,000 grains of uncooked rice, you can expect to have approximately 10,000 to 15,000 grains of cooked rice in a small bowl.\n• Similarly, if a large bowl can hold more than 10,000 grains of uncooked rice, you can anticipate having approximately 20,000 to 30,000 grains of cooked rice in a large bowl.\n\n### How many grains of rice in a serving?\n\nBased on information from “how much rice per person?”, 1 person is typically served about 1/2 to 3/4 cup of cooked rice, we can approximate the number of grains as follows:\n\n• If we consider 1/2 cup of cooked rice as a serving, and assuming the number of grains doubles after cooking, there would be approximately 7,000 to 8,000 grains of cooked rice in a serving.\n• If we consider 3/4 cup of cooked rice as a serving, the number of grains would be approximately 10,500 to 12,000 grains.\n\n## FAQs\n\n### How many cups count to 1 kg rice?\n\nIf one kilogram of rice contains about 30,000 grains and one cup of rice contains about 600 grains, we can estimate how many cups are in one kilogram of rice.\n\nDividing 30,000 grains by 600 grains per cup gives us approximately 50 cups of rice in one kilogram.\n\nFor 2 kilograms of rice: Using the conversion rate of 50 cups per kilogram, we can multiply it by 2 to find the number of cups. Therefore, 2 kilograms of rice would be approximately 100 cups of rice.\n\nFor a 5-kilogram bag of rice: Again, using the conversion rate of 50 cups per kilogram, we can multiply it by 5 to find the number of cups. Therefore, a 5-kilogram bag of rice would contain approximately 250 cups of rice.\n\n### How many cups of rice fit in 6qt Instant Pot?\n\nIn a 6-quart Instant Pot, you can expect to have approximately 12 cups of cooked rice when cooking 4 cups of rice.\n\n### How many scoops of rice in a cup?\n\nIf you are using a typical kitchen scoop, such as a 1/4 cup scoop, you would need 4 scoops to make up 1 cup of rice.\n\n### 1 cup uncooked rice equals how much cooked?\n\nAs a general rule, 1 cup of uncooked rice typically yields about 3 cups of cooked rice. This ratio may vary slightly depending on the type of rice and the cooking method used.\n\n### How many grams in a cup of rice?\n\nA cup of uncooked long-grain white rice typically weighs about 185 grams. Keep in mind that different types of rice may have slightly different weights.\n\nWhen rice is cooked, it absorbs water and increases in volume. The weight of cooked rice will be greater than the weight of uncooked rice due to the added water. On average, cooked rice weighs about 195-200 grams per cup.\n\n## Conclusion\n\nThe question “How many grains of rice in a cup?” highlights the intricacies of rice measurements and the fascinating world of culinary calculations.\n\nWhile it’s challenging to provide an exact answer due to the variations in rice types, grain sizes, and cooking methods, we have explored general estimates and guidelines.\n\nUnderstanding the approximate number of grains in a cup can be useful for cooking, recipe planning, or simply satisfying one’s curiosity about the humble rice grain." ]

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[ "# How does the two wheeler loan EMI calculator work?\n\nThe calculator uses the following formula to calculate the EMI: [P x R x (1+R)^N]/[(1+R)^N-1]. Here, ‘P’ denotes the principal, ‘R’ denotes the interest rate, and ‘N’ denotes the loan repayment tenure.\n\nFor instance, let's assume that you want to apply for a loan of Rs 70,000. The rate of interest offered by the lender is 10%. And you choose the loan repayment tenure as 36 months.\n\nNow, the bike EMI calculator will use this formula to calculate your potential EMI, which will be Rs 2,528. You will also come to know the total amount you will incur, which, in this instance, would be Rs 91,000. As you can see, you also become aware of the overall interest amount, which is around Rs 21,000 in this scenario." ]

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[ "Notes On Addition of Vectors - CBSE Class 12 Maths\nTriangle Law of Vector Addition: The sum of two vectors representing two sides of a triangle taken in the same order is given by the vector representing the third side of the triangle taken in the opposite order. Ex: Let vectors A and B be represented by the vectors AB and BC, respectively. By joining A and C, we get triangle ABC.    $\\stackrel{\\to }{\\text{AB}}$   +     =  $\\stackrel{\\to }{\\text{AC}}$       Reverse the direction of vector AC to get vector CA.  $\\stackrel{\\to }{\\text{AB}}$   +     +     =  $\\stackrel{\\to }{\\text{AA}}$    $\\stackrel{\\to }{\\text{AB}}$   +     +     =  $\\stackrel{\\to }{\\text{AA}}$   =     Thus, the sum of the vectors representing the three sides of a triangle in order is a zero vector.", null, "Here     = -     =     $\\stackrel{\\to }{\\text{AC'}}$ = $\\stackrel{\\to }{\\text{AB'}}$ + $\\stackrel{\\to }{\\text{BC'}}$ ⇒ $\\stackrel{\\to }{\\text{AC'}}$ = $\\stackrel{\\to }{\\text{AB}}$ + (-$\\stackrel{\\to }{\\text{BC}}$) ⇒ $\\stackrel{\\to }{\\text{AC'}}$ = $\\stackrel{\\to }{\\text{a}}$ +  (- $\\stackrel{\\to }{\\text{b}}$) = $\\stackrel{\\to }{\\text{a}}$ -  $\\stackrel{\\to }{\\text{b}}$ Parallelogram Law of Vector Addition: The sum of two vectors representing adjacent sides of a parallelogram is given by the diagonal of the parallelogram passing through the common point of the two adjacent sides. $\\stackrel{\\to }{\\text{OA}}$ + $\\stackrel{\\to }{\\text{OB}}$ = $\\stackrel{\\to }{\\text{OC}}$ ....parallelogram law $\\stackrel{\\to }{\\text{AC}}$ = $\\stackrel{\\to }{\\text{OB}}$ = $\\stackrel{\\to }{\\text{b}}$ $\\stackrel{\\to }{\\text{OA}}$ + $\\stackrel{\\to }{\\text{AC}}$ = $\\stackrel{\\to }{\\text{OC}}$ ....traingle law Thus, we see that the triangle and parallelogram laws of vector addition are equivalent to each other. Commutative Property of Vector Addition Given two vectors  $\\stackrel{\\to }{\\text{a}}$   and  $\\stackrel{\\to }{\\text{b}}$      : Let   $\\stackrel{\\to }{\\text{AB}}$    = $\\stackrel{\\to }{\\text{a}}$ and  $\\stackrel{\\to }{\\text{BC}}$  = $\\stackrel{\\to }{\\text{b}}$", null, "By triangle law of vector addition: $\\stackrel{\\to }{\\text{AB}}$ + $\\stackrel{\\to }{\\text{BC}}$ = $\\stackrel{\\to }{\\text{AC}}$ = $\\stackrel{\\to }{\\text{a}}$   + $\\stackrel{\\to }{\\text{b}}$...(1) In parallelogram ABCD: $\\stackrel{\\to }{\\text{AD}}$ = $\\stackrel{\\to }{\\text{BC}}$ = $\\stackrel{\\to }{\\text{b}}$ $\\stackrel{\\to }{\\text{DC}}$ = $\\stackrel{\\to }{\\text{AB}}$ = $\\stackrel{\\to }{\\text{a}}$ By triangle law of vector addition: $\\stackrel{\\to }{\\text{AD}}$ + $\\stackrel{\\to }{\\text{DC}}$ = $\\stackrel{\\to }{\\text{AC}}$ = $\\stackrel{\\to }{\\text{b}}$    + $\\stackrel{\\to }{\\text{a}}$...(2) From (1) and (2):  $\\stackrel{\\to }{\\text{a}}$  +  $\\stackrel{\\to }{\\text{b}}$     = $\\stackrel{\\to }{\\text{b}}$ + $\\stackrel{\\to }{\\text{a}}$        Additive Identity: $\\stackrel{\\to }{\\text{AB}}$   + $\\stackrel{\\to }{\\text{0}}$   = $\\stackrel{\\to }{\\text{0}}$  + $\\stackrel{\\to }{\\text{AB}}$   = $\\stackrel{\\to }{\\text{AB}}$ Associative Property of Vector Addition", null, "Given three vectors  $\\stackrel{\\to }{\\text{a}}$ , $\\stackrel{\\to }{\\text{b}}$    and $\\stackrel{\\to }{\\text{c}}$     : (  $\\stackrel{\\to }{\\text{a}}$   +  $\\stackrel{\\to }{\\text{b}}$     ) + $\\stackrel{\\to }{\\text{c}}$ = $\\stackrel{\\to }{\\text{a}}$ + ( $\\stackrel{\\to }{\\text{b}}$    +  $\\stackrel{\\to }{\\text{c}}$ ) Consider the vectors   $\\stackrel{\\to }{\\text{AB}}$    =  $\\stackrel{\\to }{\\text{a}}$    ,  $\\stackrel{\\to }{\\text{BC}}$   =   $\\stackrel{\\to }{\\text{b}}$   and   $\\stackrel{\\to }{\\text{CD}}$   =  $\\stackrel{\\to }{\\text{c}}$     In ∆ ABC: $\\stackrel{\\to }{\\text{AB}}$ + $\\stackrel{\\to }{\\text{BC}}$ = $\\stackrel{\\to }{\\text{AC}}$ =  $\\stackrel{\\to }{\\text{a}}$   +  $\\stackrel{\\to }{\\text{b}}$    [Triangle law of vector addition] In ∆ ACD: $\\stackrel{\\to }{\\text{AC}}$ + $\\stackrel{\\to }{\\text{CD}}$ = $\\stackrel{\\to }{\\text{AD}}$ = ( $\\stackrel{\\to }{\\text{a}}$    +   $\\stackrel{\\to }{\\text{b}}$ ) + $\\stackrel{\\to }{\\text{c}}$ ...(1) [Triangle law of vector addition] In ∆ BCD: $\\stackrel{\\to }{\\text{BC}}$ + $\\stackrel{\\to }{\\text{CD}}$ = $\\stackrel{\\to }{\\text{BD}}$ = $\\stackrel{\\to }{\\text{b}}$   + $\\stackrel{\\to }{\\text{c}}$       [Triangle law of vector addition] In ∆ ABD: $\\stackrel{\\to }{\\text{AB}}$ + $\\stackrel{\\to }{\\text{BD}}$ = $\\stackrel{\\to }{\\text{AD}}$ = $\\stackrel{\\to }{\\text{a}}$ + ( $\\stackrel{\\to }{\\text{b}}$   + $\\stackrel{\\to }{\\text{c}}$ ) ...(2) [Triangle law of vector addition] From (1) and (2): ( $\\stackrel{\\to }{\\text{a}}$   + $\\stackrel{\\to }{\\text{b}}$ ) +  $\\stackrel{\\to }{\\text{c}}$ =  $\\stackrel{\\to }{\\text{a}}$ + ( $\\stackrel{\\to }{\\text{b}}$   + $\\stackrel{\\to }{\\text{c}}$ )\n\n#### Summary\n\nTriangle Law of Vector Addition: The sum of two vectors representing two sides of a triangle taken in the same order is given by the vector representing the third side of the triangle taken in the opposite order. Ex: Let vectors A and B be represented by the vectors AB and BC, respectively. By joining A and C, we get triangle ABC.    $\\stackrel{\\to }{\\text{AB}}$   +     =  $\\stackrel{\\to }{\\text{AC}}$       Reverse the direction of vector AC to get vector CA.  $\\stackrel{\\to }{\\text{AB}}$   +     +     =  $\\stackrel{\\to }{\\text{AA}}$    $\\stackrel{\\to }{\\text{AB}}$   +     +     =  $\\stackrel{\\to }{\\text{AA}}$   =     Thus, the sum of the vectors representing the three sides of a triangle in order is a zero vector.", null, "Here     = -     =     $\\stackrel{\\to }{\\text{AC'}}$ = $\\stackrel{\\to }{\\text{AB'}}$ + $\\stackrel{\\to }{\\text{BC'}}$ ⇒ $\\stackrel{\\to }{\\text{AC'}}$ = $\\stackrel{\\to }{\\text{AB}}$ + (-$\\stackrel{\\to }{\\text{BC}}$) ⇒ $\\stackrel{\\to }{\\text{AC'}}$ = $\\stackrel{\\to }{\\text{a}}$ +  (- $\\stackrel{\\to }{\\text{b}}$) = $\\stackrel{\\to }{\\text{a}}$ -  $\\stackrel{\\to }{\\text{b}}$ Parallelogram Law of Vector Addition: The sum of two vectors representing adjacent sides of a parallelogram is given by the diagonal of the parallelogram passing through the common point of the two adjacent sides. $\\stackrel{\\to }{\\text{OA}}$ + $\\stackrel{\\to }{\\text{OB}}$ = $\\stackrel{\\to }{\\text{OC}}$ ....parallelogram law $\\stackrel{\\to }{\\text{AC}}$ = $\\stackrel{\\to }{\\text{OB}}$ = $\\stackrel{\\to }{\\text{b}}$ $\\stackrel{\\to }{\\text{OA}}$ + $\\stackrel{\\to }{\\text{AC}}$ = $\\stackrel{\\to }{\\text{OC}}$ ....traingle law Thus, we see that the triangle and parallelogram laws of vector addition are equivalent to each other. Commutative Property of Vector Addition Given two vectors  $\\stackrel{\\to }{\\text{a}}$   and  $\\stackrel{\\to }{\\text{b}}$      : Let   $\\stackrel{\\to }{\\text{AB}}$    = $\\stackrel{\\to }{\\text{a}}$ and  $\\stackrel{\\to }{\\text{BC}}$  = $\\stackrel{\\to }{\\text{b}}$", null, "By triangle law of vector addition: $\\stackrel{\\to }{\\text{AB}}$ + $\\stackrel{\\to }{\\text{BC}}$ = $\\stackrel{\\to }{\\text{AC}}$ = $\\stackrel{\\to }{\\text{a}}$   + $\\stackrel{\\to }{\\text{b}}$...(1) In parallelogram ABCD: $\\stackrel{\\to }{\\text{AD}}$ = $\\stackrel{\\to }{\\text{BC}}$ = $\\stackrel{\\to }{\\text{b}}$ $\\stackrel{\\to }{\\text{DC}}$ = $\\stackrel{\\to }{\\text{AB}}$ = $\\stackrel{\\to }{\\text{a}}$ By triangle law of vector addition: $\\stackrel{\\to }{\\text{AD}}$ + $\\stackrel{\\to }{\\text{DC}}$ = $\\stackrel{\\to }{\\text{AC}}$ = $\\stackrel{\\to }{\\text{b}}$    + $\\stackrel{\\to }{\\text{a}}$...(2) From (1) and (2):  $\\stackrel{\\to }{\\text{a}}$  +  $\\stackrel{\\to }{\\text{b}}$     = $\\stackrel{\\to }{\\text{b}}$ + $\\stackrel{\\to }{\\text{a}}$        Additive Identity: $\\stackrel{\\to }{\\text{AB}}$   + $\\stackrel{\\to }{\\text{0}}$   = $\\stackrel{\\to }{\\text{0}}$  + $\\stackrel{\\to }{\\text{AB}}$   = $\\stackrel{\\to }{\\text{AB}}$ Associative Property of Vector Addition", null, "Given three vectors  $\\stackrel{\\to }{\\text{a}}$ , $\\stackrel{\\to }{\\text{b}}$    and $\\stackrel{\\to }{\\text{c}}$     : (  $\\stackrel{\\to }{\\text{a}}$   +  $\\stackrel{\\to }{\\text{b}}$     ) + $\\stackrel{\\to }{\\text{c}}$ = $\\stackrel{\\to }{\\text{a}}$ + ( $\\stackrel{\\to }{\\text{b}}$    +  $\\stackrel{\\to }{\\text{c}}$ ) Consider the vectors   $\\stackrel{\\to }{\\text{AB}}$    =  $\\stackrel{\\to }{\\text{a}}$    ,  $\\stackrel{\\to }{\\text{BC}}$   =   $\\stackrel{\\to }{\\text{b}}$   and   $\\stackrel{\\to }{\\text{CD}}$   =  $\\stackrel{\\to }{\\text{c}}$     In ∆ ABC: $\\stackrel{\\to }{\\text{AB}}$ + $\\stackrel{\\to }{\\text{BC}}$ = $\\stackrel{\\to }{\\text{AC}}$ =  $\\stackrel{\\to }{\\text{a}}$   +  $\\stackrel{\\to }{\\text{b}}$    [Triangle law of vector addition] In ∆ ACD: $\\stackrel{\\to }{\\text{AC}}$ + $\\stackrel{\\to }{\\text{CD}}$ = $\\stackrel{\\to }{\\text{AD}}$ = ( $\\stackrel{\\to }{\\text{a}}$    +   $\\stackrel{\\to }{\\text{b}}$ ) + $\\stackrel{\\to }{\\text{c}}$ ...(1) [Triangle law of vector addition] In ∆ BCD: $\\stackrel{\\to }{\\text{BC}}$ + $\\stackrel{\\to }{\\text{CD}}$ = $\\stackrel{\\to }{\\text{BD}}$ = $\\stackrel{\\to }{\\text{b}}$   + $\\stackrel{\\to }{\\text{c}}$       [Triangle law of vector addition] In ∆ ABD: $\\stackrel{\\to }{\\text{AB}}$ + $\\stackrel{\\to }{\\text{BD}}$ = $\\stackrel{\\to }{\\text{AD}}$ = $\\stackrel{\\to }{\\text{a}}$ + ( $\\stackrel{\\to }{\\text{b}}$   + $\\stackrel{\\to }{\\text{c}}$ ) ...(2) [Triangle law of vector addition] From (1) and (2): ( $\\stackrel{\\to }{\\text{a}}$   + $\\stackrel{\\to }{\\text{b}}$ ) +  $\\stackrel{\\to }{\\text{c}}$ =  $\\stackrel{\\to }{\\text{a}}$ + ( $\\stackrel{\\to }{\\text{b}}$   + $\\stackrel{\\to }{\\text{c}}$ )\n\nPrevious\nNext" ]

[ null, "https://d34h5de3fkci09.cloudfront.net/1674/data/5ac25f30-b2cf-11e9-b046-02d8bc535ac2/5ac25f30-b2cf-11e9-b046-02d8bc535ac2.app", null, "https://d34h5de3fkci09.cloudfront.net/1674/data/5ac261ba-b2cf-11e9-b046-02d8bc535ac2/5ac261ba-b2cf-11e9-b046-02d8bc535ac2.app", null, "https://d34h5de3fkci09.cloudfront.net/1674/data/5ac2600b-b2cf-11e9-b046-02d8bc535ac2/5ac2600b-b2cf-11e9-b046-02d8bc535ac2.app", null, "https://d34h5de3fkci09.cloudfront.net/1674/data/5ac25f30-b2cf-11e9-b046-02d8bc535ac2/5ac25f30-b2cf-11e9-b046-02d8bc535ac2.app", null, "https://d34h5de3fkci09.cloudfront.net/1674/data/5ac261ba-b2cf-11e9-b046-02d8bc535ac2/5ac261ba-b2cf-11e9-b046-02d8bc535ac2.app", null, "https://d34h5de3fkci09.cloudfront.net/1674/data/5ac2600b-b2cf-11e9-b046-02d8bc535ac2/5ac2600b-b2cf-11e9-b046-02d8bc535ac2.app", null ]

[ "# Jacobi Symbols\n\nThe Jacobi symbol is just a generalization of the Legendre symbol, $$\\Big( \\frac{a}{p} \\Big)\\,,$$ where $$a$$ is a positive integer and $$p$$ is odd (with Legendre symbols $$p$$ must be prime). If $$a$$ is a multiple of $$p$$, then it is $$0$$, if $$a$$ has a square root $$\\mod{p}$$ then $$1$$, and otherwise $$-1$$.\n\nfunction jacobi(a, n)\na %= n\nt = 1\nwhile a != 0\nwhile iseven(a)\na = div(a, 2)\n((n % 8) in [3, 5]) && (t *= -1)\nend\na, n = n, a\n(a % 4 == n % 4 == 3) && (t *= -1)\na = a % n\nend\nreturn n == 1 ? t : 0\nend" ]

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[ "# Question about limit of integrals\n\nI want to prove the following:\n\n$$\\lim_{n \\rightarrow \\infty} \\int_{0}^{b_{n}} f_{n}(x) dx= \\int_{0}^{1} f(x) dx$$ provided that $$f_{n}$$ is Riemann-integrable on $$[0,1]$$ and $$f_{n} \\rightarrow f$$ uniformly on $$[0,1]$$ and $$b_{1} \\leq b_{2}...\\leq b_{n}\\le \\dots$$ and $$b_{n} \\rightarrow 1$$.\n\nI started the proof by saying that since $$f_{n} \\rightarrow f$$ uniformly so we can exchange the limit and the integral. But, that seems to be making it almost trivial. Am I missing something very important?\n\n• You are missing a limit in the second line. Is intergability in the Riemann sense oo Lebesgue sense? Your argument does not take into account the limits of integration. Mar 20 at 23:21\n• @KaviRamaMurthy I have fixed the errors now. Mar 20 at 23:30\n• Yes. When you \"exchange the limit and the integral,\" the integrals are all occurring on the same interval. Mar 20 at 23:49\n• Do you observe that you need to handle the integrand as well as interval of integration as $n$ tends to $\\infty$? You can note that $$\\int_0^{b_n}f_n(x)\\,dx=\\int_0^1 f_n(x) \\, dx-\\int_{b_n} ^{1}f_n(x)\\,dx$$ the first term tends to $\\int_0^1 f(x) \\, dx$ (due to uniform convergence). Can you handle the second term? Mar 21 at 2:33\n\nUse $$\\left|\\int_0^{b_n}f_n-\\int_{0}^{1}f\\right|\\leq \\left|\\int_0^{b_n}f_n-\\int_{0}^{1}f_n\\right|+\\left|\\int_0^{1}f_n-\\int_{0}^{1}f\\right|$$" ]

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[ "Home » Prime Number Program in C\n\n# Prime Number Program in C\n\nLearn about Prime Number Program in C in the below code example. Also refer the comments in the code snippet to get a detailed view about what’s actually happening.\n\nContents\n\n#### Prime Number Program in C:\n\nPrime Number is generally defined as a Natural Number that is divided by 1 and itself. So the logic obtained is the number can’t be divided by any numbers other than 1 and itself. Ex:2,3,5,7,11,13,17…..etc\n\n``````#include<stdio.h>\nint main()\n{\nint n,set=0;\nprintf(\"Enter the number:\");\nscanf(\"%d\",&n);\nif(n>0)\n{\nfor(int i=2;i<n/2;i++)//checks dividers above 1\n{\nif(n%i==0)\n{\nprintf(\"The number is not prime\");\nset=1;\nbreak;\n}\n}\nif(set==0)\n{\nprintf(\"The number is prime\");\n}\n}\n}``````\n\n#### Output:\n\nEnter the number:67\nThe number is prime\n\nHope above code works for you and Refer the below Related Codes to gain more insights. Happy coding and come back again." ]

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[ null, "https://deborahlandau.net/wp-content/uploads/2021/07/printable-multiplication-worksheets-for-practice-grade-worksheet-free-4th-math.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/tremendous-4th-grade-math-multiplication-worksheets-photo-ideas-best-coloring.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/il_570xn-1892674445_4ixm-worksheet-multiplicationle-worksheets-for-2nd-grade-to-4th-etsy-free-3rd-math-online.jpg", null, "https://deborahlandau.net/wp-content/uploads/2021/07/free-3rd-grade-multiplication-and-division-math-worksheet-300x401-tremendous-4th-worksheets-photo-ideas-digit-archives-no-login.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/free-4th-grade-math-onlinelication-worksheets-pdf-3rd.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/4th-grade-math-multiplication-worksheetsintable-free-for.jpg", null, "https://deborahlandau.net/wp-content/uploads/2021/07/tremendous-4th-grade-math-multiplicationets-photo-ideaset-printable.jpg", null, "https://deborahlandau.net/wp-content/uploads/2021/07/single-digit-multiplication-worksheets-dynamically-created-4th-grade-math-pdf-free-3rd.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/4th-grade-math-multiplication-worksheets-printable-forn-pdf-with-pictures-the-table-tremendous-photo.gif", null, "https://deborahlandau.net/wp-content/uploads/2021/07/tremendous-4thde-math-multiplication-worksheets-photo-ideas-printable-games-free.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/grade-multiplication-worksheets-free-printable-k5-learning-worksheet-4th-math-in-columns.gif", null, "https://deborahlandau.net/wp-content/uploads/2021/07/4th-grade-math-worksheets-free-printable-3rd-and-multiplication.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/4th-grade-math-multiplication-worksheets-pdf-3s-free-3rd-and.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/4th-grade-math-multiplication-worksheets-printable-for-3rd.png", null, "https://deborahlandau.net/wp-content/uploads/2021/07/fourth-gradesheets-math-best-of-coloring-pages-4th-multiplication-mathrth-tremendous-photo-ideas.jpg", null, "https://deborahlandau.net/wp-content/uploads/2021/07/4th-grade-math-multiplication-worksheets-worksheet-math247-3rd-number-sense-third.gif", null, "https://deborahlandau.net/wp-content/uploads/2021/07/4th-grade-math-multiplicationetset-two-digit.jpg", null ]

[ "# Square root via binary search\n\nAugust 24th, 2017\n\n/**\n* An Integer can take on values from -2^31 to + 2^31. The argument x can\n* take on values from 0 to 2^31. This means that all outputs of sqrt(x)\n* can only fall in the range of 1 to sqrt(2^31) because 2^31 is the\n* largest possible Integer input. Thus, we can limit our binary search\n* range to [1, min(x, sqrt(2^31))]\n*/\n\n// We compute this value once by means of the standard library or a\n// hand-computed number\nstatic int MAX_SQUARE_ROOT_BOUND = (int) Math.sqrt(Integer.MAX_VALUE);\n\npublic static int sqrt(int x) {\n// Check value of x\nif (x < 0) {\nreturn -1;\n}\n\nif (x == 0) {\nreturn 0;\n}\n\nint start = 1;\nint end = Math.min(x, MAX_SQUARE_ROOT_BOUND);\nint flooredSqrt = -1;\n\nwhile (start <= end) {\nint middle = (start + end) / 2;\n\n// Faster than using Math.pow(middle, 2)\nint middleSquared = middle * middle;\n\nif (middleSquared > x) {\n// Our middleSquared estimate was too high so we adjust the\n// end marker down\nend = middle - 1;\n} else if (middleSquared < x) {\n// Our middleSquared estimate was too low so we adjust the\n// start marker up\nstart = middle + 1;\n// If we adjusting the search range upwards, then we should\n// save the existing estimate for the square-root. By saving\n// this value here, we are essentially performing the flooring.\nflooredSqrt = middle;\n} else { // squared == n\n// We found the square root exactly\nreturn middle;\n}\n}\n\nreturn flooredSqrt;\n}" ]

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[ "# Boundary Layer Theory, Drag and Lift\n\n Question 1\nWhich of the following statements is/are TRUE?\n A The thickness of a turbulent boundary layer on a flat plate kept parallel to the flow direction is proportional to the square root of the distance from the leading edge B If the streamlines and equipotential lines of a source are interchanged with each other, the resulting flow will be a sink. C For a curved surface immersed in a stationary liquid, the vertical component of the force on the curved surface is equal to the weight of the liquid above it D For flow through circular pipes, the momentum correction factor for laminar flow is larger than that for turbulent flow\nGATE CE 2023 SET-2   Fluid Mechanics and Hydraulics\nQuestion 1 Explanation:", null, "$P_{H}=$ Total pressure on the projected are of the curved surface on the vertical plane.\n$P_{H}$ is equal to the total pressure exerted by the liquid on an imaginary vertically immersed plane surface which is the vertical projection of the curved surface, it will act at the center of pressure of the lane surface.\n$P_{v}=$ The weight $o$ the liquid contained in the portion extending vertically above the curved surface upto the free surface of the liquid.\n$P_{V}$ will act through the centre of gravity of the volume of liquid contained in the portion extending above the curved surface upto the free surface of the liquid (represented by the profile ABCDEFA in the present case).\n\nMomentum correction factor $(\\beta)=\\frac{1}{A V^{2}} \\int \\mathrm{v}^{2} d A$\n\n{Sink Flow :}\nThe sink flow is the flow in which fluid moves radially inwards towards a point where it disappears at a constant rate. This flow is just opposite to the source flow.\nFigure shows a sink flow in which the fluid moves radially inwards towards point $\\mathrm{O}$, where it disappears tat a constant rate.\nThe pattern of stream lines and equipotential lines of a sink flow is the same as that of source flow.\nAll the equations derived for a source flow shall hold to good for sink flow also except that in sink flow equations, $q$ is to be replaced by $(-q)$", null, "Boundary layer thickness (Normal Boundary layer thickness disturbance thickness.\nDistance from the boundary surface in which the velocity reaches $99 \\%$ of the stream velocity is the boundary layer thickness.\n\nTurbulent boundary layer on smooth plate.\n$\\frac{\\delta}{x}=\\frac{0.376}{\\left(R_{e x}\\right)^{1 / 5}}, \\quad R_{e x}=\\frac{v_{0} x}{v}$\n[Valid for $R_{e x} \\gt 5 \\times 10^{5}$ and $R_{e x} \\lt 10^{7}$ ]\n$=\\frac{0.22}{\\left(R_{e x}\\right)^{1 / 6}}, 10^{7} \\lt R_{e x} \\lt 10^{9}$", null, "Question 2\nTwo discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of 0.5 mm and 1.0 mm, respectively. Assume Stokes' law is valid.\nThe drag force on particle Q will be________ times the drag force on particle P. (round off to the nearest integer)\n A 4 B 8 C 10 D 12\nGATE CE 2022 SET-2   Fluid Mechanics and Hydraulics\nQuestion 2 Explanation:\nIn case of discrete particle settling and Stoke's law valid, at terminal velocity, since there is no change in velocity, the net force on the body is zero. Hence,", null, "$F_D=\\left ( \\frac{\\pi}{6}D^3\\rho _sg-\\frac{\\pi}{6}D^3\\rho _sg \\right )=\\frac{\\pi}{6}gD^3(\\rho _s-\\rho _f)$\nFor density of medium $(\\rho _f)$ and mass density of sphere $(\\rho _s)$ constant,\nDrag force $(F_D)\\propto D^3$\nFor particle P, diameter $(D_P)=0.5 mm$\nFor particle Q, diameter $(D_Q)=1 mm$\n$\\Rightarrow \\frac{(F_D)_Q}{(F_D)_P}=\\frac{(D_Q)^3}{(D_P)^3}=\\left ( \\frac{1}{0.5} \\right )^3=8$\n$\\Rightarrow (F_D)_Q=8 \\times (F_D)P$\n\n Question 3\nVelocity distribution in a boundary layer is given by $\\frac{u}{U_\\infty }=\\sin \\left ( \\frac{\\pi}{2}\\frac{y}{\\delta } \\right )$, where $u$ is the velocity at vertical coordinate $y, U_\\infty$ is the free stream velocity and $\\delta$ is the boundary layer thickness. The values of $U_\\infty$ and $\\delta$ are 0.3 m/s and 1.0 m, respectively. The velocity gradient $\\left ( \\frac{\\partial u}{\\partial y} \\right )$ (in $s^{-1}$, round off to two decimal places) at y= 0, is ________.\n A 0.24 B 0.38 C 0.47 D 0.58\nGATE CE 2020 SET-2   Fluid Mechanics and Hydraulics\nQuestion 3 Explanation:\nGiven:\n\\begin{aligned} \\frac{u}{u_\\infty }&=\\sin \\left ( \\frac{\\pi}{2} \\frac{y}{\\delta }\\right )\\\\ u_\\infty &=0.3 m/s\\\\ \\delta &=1m\\\\ \\frac{du}{dy}&=\\frac{d}{dy}u_\\infty \\cdot \\sin\\left ( \\frac{\\pi}{2} \\frac{y}{\\delta } \\right )\\\\ &=\\frac{u_\\infty \\cdot \\pi}{2\\delta } \\cos \\left ( \\frac{\\pi}{2} \\frac{y}{\\delta } \\right )\\\\ \\text{At y=0 and} & \\; \\delta=1 \\\\ \\left.\\begin{matrix} \\frac{du}{dy} \\end{matrix}\\right|_{y=0}&=\\frac{0.3 \\pi}{2(1)} \\cos \\left ( \\frac{\\pi}{2}\\frac{0}{1} \\right )\\\\ &=0.47 s^{-1} \\end{aligned}\n Question 4\nConsider a laminar flow in the x-direction between two infinite parallel plates (Couette flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/s in the x-direction. The distance between the plates is 5 mm and the dynamic viscosity of the fluid is 0.01 $N-s/m^2$. If the shear stress on the lower plate is zero, the pressure gradient, $\\frac{\\partial p}{\\partial x}$, (in $N/m^2$ per m,round off to 1 decimal place)is _______\n A 2.4 B 8 C 6.2 D 9.8\nGATE CE 2019 SET-1   Fluid Mechanics and Hydraulics\nQuestion 4 Explanation:\nGiven flow is a couette flow with pressure gradient\n$\\mu =0.01N-s/m^2$\nh=5mm\nif $\\tau _{y=0}=0, \\; \\text{find}\\; \\frac{dp}{dx}$\nThe velocity distribution, for the couette flow with pressure gradient is given by\n$u=\\frac{wy}{h}-\\frac{1}{2\\mu }\\frac{dp}{dx}[hy-y^2]$\nwhere w is the velocity of the top plate and h is the gap between the plates\n\\begin{aligned} \\frac{du}{dy}&=\\frac{w}{h}-\\frac{1}{2\\mu }\\frac{dp}{dx}[h-2y] \\\\ \\left.\\begin{matrix} \\frac{du}{dy} \\end{matrix}\\right|_{y=0} &=\\frac{w}{h}-\\frac{1}{2\\mu }\\frac{dp}{dx}h \\\\ \\tau _{y=0}&=\\mu \\left [ \\frac{w}{h}-\\frac{1}{2\\mu }\\frac{dp}{dx}h \\right ] \\\\ \\tau _{y=0}&=\\frac{w\\mu }{h}-\\frac{1}{2}\\frac{dp}{dx}h \\\\ \\text{when}\\; \\tau _{y=0}&=0, \\; \\text{we will have}\\\\ \\frac{1}{2}\\frac{dp}{dx}h&=\\frac{w\\mu }{h}\\\\ \\frac{dp}{dx}&=\\frac{2w\\mu }{h^2} \\\\ &=\\frac{2 \\times 1 \\times 10^{-2}\\times 0.01}{(5 \\times 10^{-3})^2} \\\\ &=8 N/m^2 \\; \\text{per} \\; m \\end{aligned}\n Question 5\nAn automobile with projected area 2.6 $m^{2}$ is running on a road with a speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 $kg/m^{3}$ and $1.5 \\times 10^{-5} m^{2}/s$, respectively. The drag coefficient is 0.30.\n\nThe metric horse power required to overcome the drag force is\n A 33.23 B 31.23 C 23.23 D 20.23\nGATE CE 2008   Fluid Mechanics and Hydraulics\nQuestion 5 Explanation:\nPower required to overcome the drag = Drag force $\\times$ velocity\n\\begin{aligned} &=520 \\times \\frac{120 \\times 1000}{60 \\times 60}= 17333.33 \\mathrm{watt} \\\\ &\\quad (1 \\mathrm{mhp}=735.5 \\mathrm{watt})\\\\ &=\\frac{17333.33}{735.5}\\text{ metric horse power }\\\\ &=23.567 \\text{ metric horse power} \\end{aligned}\n\nThere are 5 questions to complete.\n\n### 4 thoughts on “Boundary Layer Theory, Drag and Lift”\n\n1.", null, "•", null, "Thank You Mantu Kumar ram,\n2.", null, "3.", null, "" ]

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[ "# # Matrix library (numpy.matlib)\n\nThis module contains all functions in the numpy namespace, with the following replacement functions that return matrices instead of ndarrays.\n\nFunctions that are also in the numpy namespace and return matrices\n\nmethod description\nmat(data[, dtype]) Interpret the input as a matrix.\nmatrix(data[, dtype, copy]) Note: It is no longer recommended to use this class, even for linear\nasmatrix(data[, dtype]) Interpret the input as a matrix.\nbmat(obj[, ldict, gdict]) Build a matrix object from a string, nested sequence, or array.\n\nReplacement functions in matlib\n\nmethod description\nempty(shape[, dtype, order]) Return a new matrix of given shape and type, without initializing entries.\nzeros(shape[, dtype, order]) Return a matrix of given shape and type, filled with zeros.\nones(shape[, dtype, order]) Matrix of ones.\neye(n[, M, k, dtype, order]) Return a matrix with ones on the diagonal and zeros elsewhere.\nidentity(n[, dtype]) Returns the square identity matrix of given size.\nrepmat(a, m, n) Repeat a 0-D to 2-D array or matrix MxN times.\nrand(*args) Return a matrix of random values with given shape.\nrandn(*args) Return a random matrix with data from the “standard normal” distribution.\nLast Updated: 9/22/2019, 7:44:42 PM" ]

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[ "×\nGet Full Access to Thermodynamics: An Engineering Approach - 8 Edition - Chapter 5 - Problem 179p\nGet Full Access to Thermodynamics: An Engineering Approach - 8 Edition - Chapter 5 - Problem 179p\n\n×\n\n# Steam enters a turbine steadily at 7 MPa and 'W 600C C", null, "ISBN: 9780073398174 56\n\n## Solution for problem 179P Chapter 5\n\nThermodynamics: An Engineering Approach | 8th Edition\n\n• Textbook Solutions\n• 2901 Step-by-step solutions solved by professors and subject experts\n• Get 24/7 help from StudySoup virtual teaching assistants", null, "Thermodynamics: An Engineering Approach | 8th Edition\n\n4 5 1 305 Reviews\n27\n2\nProblem 179P\n\nProblem 179P", null, "Steam enters a turbine steadily at 7 MPa and 'W 600C C with a velocity of 60 m/s and leaves at 25 kPa with a quality of 95 percent. A heat loss of 20 kJ/kg occurs during the process. The inlet area of. the turbine is 150 cm2, and the exit area is 1400 cm2. Determine (a) the mass flow rate of the steam, (b) the exit velocity, and (c) the power output.\n\nStep-by-Step Solution:\nStep 1 of 3\n\nStep 2 of 3\n\nStep 3 of 3\n\n##### ISBN: 9780073398174\n\nThermodynamics: An Engineering Approach was written by and is associated to the ISBN: 9780073398174. The full step-by-step solution to problem: 179P from chapter: 5 was answered by , our top Engineering and Tech solution expert on 08/01/17, 09:10AM. Since the solution to 179P from 5 chapter was answered, more than 265 students have viewed the full step-by-step answer. The answer to “Steam enters a turbine steadily at 7 MPa and 'W 600C C with a velocity of 60 m/s and leaves at 25 kPa with a quality of 95 percent. A heat loss of 20 kJ/kg occurs during the process. The inlet area of. the turbine is 150 cm2, and the exit area is 1400 cm2. Determine (a) the mass flow rate of the steam, (b) the exit velocity, and (c) the power output.” is broken down into a number of easy to follow steps, and 73 words. This textbook survival guide was created for the textbook: Thermodynamics: An Engineering Approach , edition: 8. This full solution covers the following key subjects: area, turbine, steam, exit, velocity. This expansive textbook survival guide covers 17 chapters, and 2295 solutions.\n\nUnlock Textbook Solution" ]

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[ "# The Elements of Geometry\n\nSilver, Burdett [c1905], 1905 - Geometry - 355 pages\n0 Reviews\nReviews aren't verified, but Google checks for and removes fake content when it's identified\n\n### What people are saying -Write a review\n\nWe haven't found any reviews in the usual places.\n\n### Contents\n\n THE PYTHAGOREAN GROUP 149 THE GROUP ON LINEAR APPLICATION OF PROPORTION 183 19 191 23 198\n THE GROUP ON GEOMETRY OF THE SPHERE SURFACE 328 99 350 287 353 Copyright\n\n### Popular passages\n\nPage 232 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection of AB upon plane MN.\nPage 66 - The difference between any two sides of a triangle is less than the third side.\nPage 108 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.\nPage 111 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.\nPage 102 - In any proportion, the product of the means equals the product of the extremes.\nPage 8 - A circle is a plane figure bounded by a curved line called the circumference, every point of which is equally distant from a point within called the center, Fig.\nPage 280 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes intersecting this surface.\nPage 177 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.\nPage 208 - The center of a regular polygon is the common center of the circumscribed and inscribed circles of the polygon.\nPage 231 - A PLANE is a surface, such, that if any two of its points be joined by a straight line, such." ]

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[ "# Phase separation\n\nEntry by Emily Redston, AP 225, Fall 2011\n\nWe typically talk about phase separation in terms of the regular solution model of liquids. The free energy of mixing can be written as,\n\n $G_{mix}= RT (x _{A}\\ln x _{A}+x _{B}\\ln x _{B})+\\epsilon x _{A} x _{B}$\n\n where $\\epsilon = zN[V_{AB} - {1 \\over 2}(V_{BB}+V_{BB})]$\n\n\n$V$ represents bond energies, $z$ is the number of neighbors, $N$ is the total number of atoms, and $x$ is the mole fraction. The sign of $\\epsilon$ is essential in determining the solution's behavior as a function of temperature. If $\\epsilon$ < 0 then the change in free energy upon mixing is always negative, so the atoms will always want to be fully mixed. For $\\epsilon$ > 0, there is a temperature dependance, and either mixing or phase separation can occur. Phase separation occurs when\n\n ${G_{mix} \\over x_B} = 0$" ]

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[ "", null, "# Thermistors 101 - PART 1\n\nPosted: 8/17/23", null, "Thermistors are the most frequently used sensing elements in the Building Automation and Controls industries. In this series of posts, we’ll answer the most common questions about thermistors and why they’ve become so popular.\n\n## What is a thermistor?\n\nThe word thermistor is a portmanteau of “thermal” and “resistor”. They are thermally sensitive resistors whose resistance varies predictably based on temperature. They are typically made of a metal oxide and then formed into a small bead, ribbon, chip, or other shape. The specific materials used in the thermistor determine the resistance curve or output. Once manufactured, the materials used within the thermistor don’t change, so it follows that the resistance output will be stable, reliable, and predictable.\n\n## What is a resistance curve?\n\nThe resistance curve is the relationship between resistance and temperature. Because thermistors are non-linear, when graphed the line is curved and not straight.\n\n## Do all thermistors have the same curve?\n\nNo, there are two categories of thermistors, NTC and PTC (see below). Within these categories, there are dozens if not hundreds of different resistance curves. Different curves are just that–different, and not necessarily better or worse than another. Choosing the correct curve is most often a matter of system compatibility. Most thermistors are named based on their resistance at 77˚F / 25˚C.\n\n## What do PTC and NTC mean?\n\nPTC (positive temperature coefficient) and NTC (negative temperature coefficient) describe the thermistor’s relationship between temperature and resistance. PTC means the resistance will increase with a temperature increase and NTC means the resistance will decrease with a temperature increase. NTC thermistors are by far the most commonly used–all of the thermistors listed below and all ACI thermistors are NTC.\n\n## What are some common thermistor curves?\n\nThere are a few commonly used thermistors in the BAS and controls industries. Below is a partial list.\n\n• 10K type II(ACI part number A/CP): commonly used in Carrier, Trane, Alerton, Distech, and JCI systems.\n• 10K type III(ACI part number A/AN): commonly used in Schneider Electric, Carrier, Delta Controls, KMC Controls, and Reliable Controls Systems.\n• 10KS: commonly used in Siemens systems\n• 10K-E1: commonly used in Carel USA systems\n• 3K: commonly used in ASI and Alerton systems\n• 20K: commonly used in Honeywell systems\n• 1.8K: commonly used in Schneider Electric systems\n\nCheck out Part 2 of this series where we answer questions about the advantages and disadvantages of using thermistors and troubleshooting common problems.", null, "### We Want To Hear From You!\n\nHave Questions? Comments? Ideas for Topics? Let us know!" ]

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[ "arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org.\n\n# Photon Regions and Shadows of Kerr–Newman–NUT Black Holes with a Cosmological Constant\n\nArne Grenzebach    Volker Perlick    Claus Lämmerzahl ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen, Germany\nMay 10, 2020\n###### Abstract\n\nWe consider the Plebański class of electrovacuum solutions to the Einstein equations with a cosmological constant. These space-times, which are also known as the Kerr–Newman–NUT–(anti-)de Sitter space-times, are characterized by a mass , a spin , a parameter that comprises electric and magnetic charge, a NUT parameter and a cosmological constant . Based on a detailed discussion of the photon regions in these space-times (i.e., of the regions in which spherical lightlike geodesics exist), we derive an analytical formula for the shadow of a Kerr–Newman–NUT–(anti-)de Sitter black hole, for an observer at given Boyer–Lindquist coordinates in the domain of outer communication. We visualize the photon regions and the shadows for various values of the parameters.\n\n###### pacs:\n04.70.-s, 95.30.Sf, 98.35.Jk\n\n## I Introduction\n\nOver the last twenty years observations have produced increasing evidence for the existence of a supermassive black hole at the center of our galaxy. This evidence comes from the observation of orbits of stars in the infrared EckartGenzel.1996 ; GillessenEisenhauerEtAl.2009 which allows to estimate the mass of the central object. In combination with estimates of the volume in which this mass must be concentrated the result strongly supports the hypothesis of a black hole. These observations are expected to become even more precise when the GRAVITY instrument EisenhauerEtAl.2009 goes into operation soon. In addition, it is planned to explore the inner region of the center of our galaxy, in the order of magnitude of the Schwarzschild radius of the central mass, with submillimeter radio telescopes. From this project, which is called the Event Horizon Telescope DoelemanWeintroub.2008 , we expect a radio image of the shadow of the central black hole in a few years’ time. Therefore, it is timely to advance the theoretical investigations of the shadows of black holes as far as possible, as a basis for evaluating the observational results that are to be expected soon.\n\nFor an observer at radius coordinate in the Schwarzschild space-time, the shadow can be constructed in the following way. We assume that there are light sources distributed on the sphere for some chosen . We consider all light rays issuing from the observer’s position into the past. Some of them will reach a light source at , after being deflected by the black hole; to the initial directions of this first class of light rays we associate brightness on the observer’s sky. Some of them will go to the horizon and never reach a light source at ; to the initial directions of this second class of light rays we associate darkness on the observer’s sky. The second class fills the shaded region in Fig. 1. The borderline between the two classes are light rays that asymptotically spiral towards the photon sphere at (with , ). Therefore, in this case the shadow is circular and its angular radius is determined by light rays that approach the photon sphere, see again Fig. 1. For simplicity, we have constructed the shadow with light sources on a sphere . From the geometry it is clear that we could have light sources anywhere else as long as they are outside of the shaded region in Fig. 1.\n\nSynge Synge.1966 was the first to calculate what we nowadays call the shadow of a Schwarzschild black hole. (Synge did not use the word “shadow” but he investigated the condition under which photons could escape to infinity.) He found that the angular radius of the shadow is given by the simple formula\n\n sin2α=274(ρO−1)ρ3O (1)\n\nwhere is the ratio of the observer’s coordinate and the Schwarzschild radius. For the black hole at the galactic center, an observer on the Earth is at kpc, and the mass is Solar masses GhezSalim.2008 ; GillessenEisenhauerEtAl.2009 . If one inserts these values into Synge’s formula one gets an angular radius of microarcseconds which is expected to be resolvable with Very Long Baseline Interferometry (VLBI) soon DoelemanWeintroub.2008 ; HuangCai.2007 .\n\nFor a Kerr black hole, there is no longer a photon sphere and the shadow is no longer circular. The photon sphere breaks into a “photon region” which is filled by spherical lightlike geodesics, i.e. by lightlike geodesics each of which is confined to a sphere . The boundary of the shadow corresponds to light rays that asymptotically spiral towards one of these spherical lightlike geodesics. The deviation of the shadow from a circle is a measure for the spin of the black hole. Bardeen Bardeen.1973 was the first to correctly calculate the shadow of a Kerr black hole, the results can also be found, e.g., in Chandrasekhar’s book Chandrasekhar.1983 . For pictures of individual spherical lightlike geodesics in the Kerr space-time we refer to Teo Teo.2003 , and for a discussion and a picture of the photon region in the Kerr space-time to Perlick Perlick.2004 .\n\nThe shadow has also been discussed for other black holes (and for naked singularities), e.g. for the Kerr–Newman space-time Vries.2000 , for Tomimatsu-Sato space-times BambiYoshida.2010 , for black holes in extended Chern–Simons modified gravity AmarillaEiroa.2010 , in a Randall–Sundrum braneworld scenario AmarillaEiroa.2012 , and a Kaluza–Klein rotating dilaton black hole AmarillaEiroa.2013 , for the Kerr–NUT space-time AbdujabbarovAtamurotov.2012 , for multi-black holes YumotoNitta.2012 , and for regular black holes LiBambi.2014 . Hioki and Maeda HiokiMaeda.2009 introduced a deformation parameter that characterizes the deviation of the shadow from a circle. Special interest has been devoted to the question of whether the shadow of a black hole can be used as a test of the no-hair theorem, see Johannsen and Psaltis JohannsenPsaltis.2011 . All these articles are largely based on ray tracing in the respective space-times, rather than on analytical studies of the geodesic equation, and they assume that the observer is at infinity.\n\nIn this paper we want to extend the discussion of the shadow in various directions. First, we consider a class of space-times for which the shadow has not yet been calculated, namely the Plebański class Plebanski.1975 . The metrics in this class, which are also known as the Kerr–Newman–NUT–(anti-)de Sitter metrics, depend on five parameters: A mass , a spin , a parameter that comprises an electric and a magnetic charge, a NUT parameter , and a cosmological constant . It is a subclass of the Plebański–Demiański class PlebanskiDemianski.1976 of stationary axisymmetric type D electrovacuum solutions of Einstein’s field equations with a cosmological constant; the latter includes, in addition to the five parameters of the Plebański class, also a so-called acceleration parameter; in the present work we will not consider the acceleration parameter but we are planning to study its influence in a separate publication. Second, we develop the formalism for an observer not at infinity but rather at some given Boyer–Lindquist coordinates in the domain of outer communication. This is essential for the case because then the space-time is no longer asymptotically flat and in the case the domain of outer communication is separated from by a cosmological horizon. Third, our treatment is fully analytical rather than based on ray tracing. In particular, we give an exact analytical formula for the boundary curve of the shadow. We feel that this is a major advantage because it can serve as a basis for calculating parameters of the space-time from the shape of the shadow by analytical means. Fourth, our investigation includes a detailed discussion of the photon regions in the space-times under consideration. This is a crucial prerequisite for deriving the analytical formula of the shadow, and it is also of some interest in itself.\n\nWe emphasize that, as in all the theoretical papers cited above, our calculation of the shadow is based on the assumptions that light rays are lightlike geodesics and that there are no light sources near the black hole. In view of the black hole at the center of our galaxy these assumptions are highly idealized. Light rays near the central black hole are expected to be affected by scattering, and there is good evidence for the existence of a luminous accretion disk around the black hole. The effect of scattering on the visibility of the shadow was numerically demonstrated by Falcke, Melia and Agol FalckeMelia.2000 . The visual appearance of an accretion disk was studied with the help of various ray-tracing programs by several authors, following the pioneering work of Bardeen and Cunningham BardeenCunningham.1973 and Luminet Luminet.1979 , see e.g. Dexter et.al. DexterAgol.2012 or Mościbrodzka et.al. MoscibrodzkaShiokawa.2012 . A broad overview of observations as well as simulations of phenomena for the black hole in the center of our galaxy near Sgr A* is given by Dexter and Fragile in DexterFragile.2013 . Whereas the effects of matter certainly have to be taken into account for a realistic prediction of what will be observed, calculating the geometrical shadow is of major importance because it serves as the basis for all later refinements.\n\nThe paper is organized as follows. In Section II we summarize the relevant properties of space-times of the Plebański class. In Section III we determine the photon regions for black-hole space-times of this class. In Section IV we derive an analytical formula, in parameter form, for the boundary curve of the shadow of such a black hole, as it is seen by an observer with a specified four-velocity somewhere in the domain of outer communication. The results of Sections III and IV are illustrated with several pictures.\n\n## Ii The Kerr–Newman–NUT–(anti-)de Sitter metric\n\nThe Kerr–Newman–NUT–(anti-)de Sitter space-times are stationary, axially symmetric type D solutions of the Einstein–Maxwell equations with a cosmological constant. This class of space-times was introduced by Plebański Plebanski.1975 in 1975. A slightly larger class, which includes in addition the so-called acceleration parameter, was found by Plebański and Demiański PlebanskiDemianski.1976 in 1976. For the case without a cosmological constant, these metrics can be traced back to Carter Carter.1968b and, in the Boyer–Lindquist coordinates we will use in the following, to Miller Miller.1973 . A fairly detailed discussion of the Plebański(–Demiański) metrics can be found in the book by Griffiths and Podolský GriffithsPodolsky.2009 , see also Stephani et al. StephaniKramer.2003 .\n\nIn Boyer–Lindquist coordinates the Plebański metric is given by (GriffithsPodolsky.2009, , p. 314)\n\n gμνdxμdxν =Σ(1Δrdr2+1Δϑdϑ2) (2) +1Σ((Σ+aχ)2Δϑsin2ϑ−Δrχ2)dφ2 +2Σ(Δrχ−a(Σ+aχ)Δϑsin2ϑ)dtdφ −1Σ(Δr−a2Δϑsin2ϑ)dt2\n\nwhere we use the abbreviations\n\n Σ =r2+(ℓ+acosϑ)2, (3) χ =asin2ϑ−2ℓ(cosϑ+C), Δ =r2−2mr+a2−ℓ2+β, Δr =Δ−Λ((a2−ℓ2)ℓ2+(13a2+2ℓ2)r2+13r4), Δϑ =1+Λ(43aℓcosϑ+13a2cos2ϑ).\n\nHere, rescaled units are used so that the speed of light and the gravitational constant are normalized (, ). The coordinates and range over , while and are standard coordinates on the two-sphere. The metric depends on five parameters, namely the mass , the spin , a parameter for electric and magnetic charge (), the NUT parameter which is to be interpreted as a gravitomagnetic charge, and the cosmological constant . In addition, there is a parameter that was introduced by Manko and Ruiz (MankoRuiz.2005, ) for modifying the singularity that is produced by on the axis, see below. In principle, the parameters , , , , and can take all values in , although not all combinations are physically meaningful. Note that for the metric cannot be interpreted as a solution to the Einstein–Maxwell equations, because in this case the electric or magnetic charge has to be imaginary. Nonetheless, the case is of interest because metrics of this form occur in some braneworld models, see AlievGumrukcuoglu.2005 .\n\nThe Plebański class of metrics contains the Schwarzschild (), Kerr (), Reissner–Nordström (), Kottler or Schwarzschild–(anti-)de Sitter (), Kerr–Newman (), and Taub–NUT () metrics as special cases.\n\nThe metric (2) becomes singular if , , or . Some of these singularities are mere coordinate singularities, but some of them are true (curvature) singularities. As this issue is of some relevance for our purpose, we briefly discuss the four types of singularities in the following paragraphs.\n\n• . The equation is equivalent to\n\n r=0andcosϑ=−ℓ/a. (4)\n\nIf , this condition is satisfied on a ring. The singularity on this ring turns out to be a true (curvature) singularity if . One usually refers to it as to the ring singularity. Note that, apart from the ring singularity, the sphere is regular. Observers can move through either of the two hemispheres (“throats”) that are bounded by the ring singularity, thereby travelling from the region to the region or vice versa.\n\nIf , there is no ring singularity. is everywhere different from zero and the entire sphere is regular.\n\nIn the borderline case the ring singularity degenerates into a point on the axis. The case is special because in this case the entire sphere degenerates into a point singularity that separates the region from the region . In this case we have two disconnected space-times.\n\n• . If we exclude the case , each zero of on the real line, , is a coordinate singularity which indicates a horizon. As is a fourth-order polynomial of with real coefficients, the number of horizons can be 4, 2 or 0, where zeros of have to be counted with multiplicity. We say that the horizon at the biggest coordinate is the first horizon, the next one is the second, and so on.\n\nIf , the second derivative of with respect to is strictly positive. Therefore, the number of zeros of is either 2 or 0. In the first case we have a black hole, in the second case a naked singularity or a regular space-time. In the black-hole case, the region between and the first horizon is called the domain of outer communication of the black hole. This is the region where we will place our observers for observing the shadow of the black hole. On the domain of outer communication, the vector field is spacelike which is equivalent to . If , the equation reduces from fourth to second order. In this case the horizons are at\n\n r±=m±√m2−a2+ℓ2−β (5)\n\nif ; if there are no horizons, i.e., we have a naked singularity or a regular space-time.\n\nIf , the vector field is timelike for big values of . Therefore, the first horizon, if it exists, is a cosmological horizon. We have a black hole if there are four horizons altogether. The domain of outer communication is the region between the first and the second horizon. Again, the vector field is spacelike on the domain of outer communication. As in the case , we will restrict ourselves to the black-hole case and we will place our observers in the domain of outer communication.\n\n• . If , it is possible that zeros of occur at values . In close analogy to the zeros of , any such zero of is a coordinate singularity which indicates a horizon. In this case, the horizon is situated on a cone rather than on a sphere . The vector field changes its causal character from spacelike to timelike when such a horizon is crossed. This situation is hardly of any physical relevance. Therefore, we want to choose the parameters such that it is excluded. A sufficient condition can be found in the following way. The equation leads to a quadratic equation for with solution\n\n acosϑ±=−2ℓ±√4ℓ2−3/Λ. (6)\n\nTherefore, if we restrict ouselves to values of and such that\n\n 4ℓ2Λ<3 (7)\n\nwe can be sure that has no zeros.\n\n• . The metric has a singularity on the axis , as is always the case when using spherical polar coordinates. If , however, this is not just a coordinate singularity but rather a true singularity. By choosing the Manko–Ruiz parameter appropriately one can decide on which part of the axis the singularity is situated.\n\nTo demonstrate this, we observe that in the limit we have and . As a consequence, the metric coefficient\n\n gtt=χ2ΣΔϑsin2ϑ−(Σ+aχ)2ΣΔr (8)\n\ndiverges unless . This divergent behavior indicates that either the coordinate function or the metric becomes pathological. It was shown by Misner Misner.1963 that this singularity can be removed if one makes the time coordinate periodic. (Misner restricted himself to the Taub–NUT metric, , with but his reasoning applies equally well to the general case.) We do not follow this suggestion because it leads to a space-time with closed timelike curves through every event. Instead, we adopt Bonnor’s interpretation (Bonnor.1969, , p. 145) of the axial singularity who viewed it as a “massless source of angular momentum”. For , the singularity is on the half-axis , for it is on the half-axis and for any other value of it is on both half-axes. Note that each half-axis extends from to .\n\nMetrics (2) with different values of are locally isometric near all points off the axis. This follows from the fact that a coordinate transformation yields, again, a metric (2) with . With the help of such a coordinate transfomation with , the parameter can be eliminated from the geodesic equation, see Kagramanova et al. KagramanovaEtAl.2010 . Note, however, that this transformation does not work globally because is periodic and is not, and it does not work near the axis because is pathological there.\n\nMoreover, a coordinate transformation transforms a metric (2) into a metric of the same form, but with the signs of and inverted. This demonstrates that a metric with parameters is globally isometric to a metric with parameters .\n\nWe have seen that the vector fields and change their causal character from spacelike to timelike if a horizon is crossed. The vector fields and can change their causal character as well. In this case, this has nothing to do with a horizon but it is also of some relevance.\n\n• . If the Killing field becomes spacelike, i.e. becomes positive, on part of the space-time. In this region an observer cannot move on a -line. The region where is known as the ergosphere or the ergoregion. (Note that some authors reserve this name for the intersection of the region where with the domain of outer communication.)\n\n• . If or , there is a region where the Killing field becomes timelike. In this region, the space-time violates the causality condition because the -lines are closed timelike curves. If and , the region where this occurs extends to . If and , it is bounded by the first (cosmological) horizon.\n\n## Iii Photon Regions\n\nIn the space-times (2), the geodesic equation is completely integrable, i.e., it admits four constants of motion in involution. These constants of motion are the Lagrangian\n\n L =12gμν˙xμ˙xν, (9) the energy E: =−∂L∂˙t=−gφt˙φ−gtt˙t, (10) the z-component of the angular momentum Lz: =∂L∂˙φ=gφφ˙φ+gφt˙t, (11)\n\nand the Carter constant Carter.1968b . With the help of these four constants of motion, the geodesic equation can be written in first-order form. For lightlike geodesics, , the resulting equations read\n\n ˙t =χ(Lz−Eχ)ΣΔϑsin2ϑ+(Σ+aχ)((Σ+aχ)E−aLz)ΣΔr, (12a) ˙φ =Lz−EχΣΔϑsin2ϑ+a((Σ+aχ)E−aLz)ΣΔr, (12b) Σ2˙ϑ2 =ΔϑK−(χE−Lz)2sin2ϑ=:Θ(ϑ), (12c) Σ2˙r2 =((Σ+aχ)E−aLz)2−ΔrK=:R(r). (12d)\n\nThese equations can be solved explicitly in terms of hyperelliptic functions, see Hackmann et al. HackmannKagramanova.2009a . Here, we are interested in spherical lightlike geodesics, i.e., lightlike geodesics that stay on a sphere . The region filled by these geodesics is called the photon region . To determine this photon region, we introduce the abbreviations\n\n LE=LzE,KE=KE2. (13)\n\nFor spherical orbits the conditions and have to be fulfilled. By (12d), this requires that and , hence\n\n KE =((Σ+aχ)−aLE)2Δr, (14) KE =4r((Σ+aχ)−aLE)Δ′r,\n\nwhere denotes the derivative of with respect to . Solving for the constants of motion and results in\n\n KE =16r2Δr(Δ′r)2, aLE =(Σ+aχ)−4rΔrΔ′r. (15)\n\nInserting these expressions into (12c) and observing that the left-hand side of (12c) is non-negative gives us an inequality that determines the photon region\n\n K:(4rΔr−ΣΔ′r)2≤16a2r2ΔrΔϑsin2ϑ. (16)\n\nNote that is independent of the Manko–Ruiz parameter .\n\nAs in the Kerr case (cf. Perlick.2004, ), through every point with coordinates () of there is a lightlike geodesic which stays on the sphere . Along each of these spherical lightlike geodesics, the coordinate oscillates between extremal values that are determined by the equality sign in (16). The -motion is given by (12b) and might be quite complicated. For some spherical light rays it is not even monotonic.\n\nIn the non-rotating case () the inequality (16) degenerates into an equality,\n\n 4rΔr=(r2+ℓ2)Δ′r. (17)\n\nThis means that the photon regions degenerate into photon spheres. The best known example is the photon sphere in the Schwarzschild space-time at .\n\nA spherical lightlike geodesic at is unstable with respect to radial perturbations if , and stable if . The second derivative can be calculated from (12d). With the help of (15) this results in\n\n R′′(r)8E2Δ′2r=2rΔrΔ′r+r2Δ′2r−2r2ΔrΔ′′r. (18)\n\nFigs. 3, 4, 5 and 6 show plots of the photon region in the plane, where unstable () and stable () spherical light rays (18) are distinguished. The boundaries of the region where () are the horizons. Furthermore, the ergosphere (), the causality violating region (), and the ring singularity (•) are shown. A legend for these figures can be found in Fig. 2.\n\nEach picture illustrates a meridional section through space-time, i.e. the plane parametrized by and , where the -coordinate is measured from the positive -axis. Following a suggestion by O’Neill ONeill.1995 , we show the whole range of the space-time, with the Boyer–Lindquist coordinate increasing outward from the origin which corresponds to . O’Neill suggested to use the exponential of for the radial coordinate. As such a representation strongly exaggerates the outer parts, we find it more convenient to use two different scales. In the region (i.e., inside the sphere ), we use for the radial coordinate. In the region (i.e., outside the sphere ), we use for the radial coordinate. The dashed circle () indicates the throats at .\n\nEach figure shows the photon region for four different values of the spin , keeping all the other parameters fixed. Restricting to black-hole cases, we choose the four values of the spin as , where and denotes the spin of an extremal black hole which is determined by the other parameters. If , we have , cf. Eq. (5). If , there is no convenient formula for because one has to evaluate a fourth-order equation.", null, "Figure 3: Photon regions in Kerr space-time for spins a=λamax, where amax=m. The plots on the right show a magnified inner part.", null, "Figure 4: Photon regions in Kerr–NUT space-time with ℓ=34m, C=0 for spins a=λamax, where amax=√m2+ℓ2=54m. The plots on the right show a magnified inner part.", null, "Figure 5: Photon regions in Kerr–Newman–NUT space-time (β=59m2, ℓ=43m, C=0) with a cosmological constant (Λ=10−2m−2) for spins a=λamax, where amax≈1.51m. The plots on the right show a magnified inner part.", null, "Figure 6: Photon regions for varying singularity parameter C with fixed a=45amax, β=59m2, ℓ=43m, and Λ={10−2m−2for C≤00for C>0, where amax={1.51mfor C≤02√5m/3for C>0. If existent, the cosmological horizon restricts the region () where the causality is violated. If C=1 or C=−1, one of the two half-axes is regular and it is not surrounded by a causality violating region.\n\nIn the Kerr space-time, see Fig. 3, there is an exterior photon region at and an interior photon region at . Both of them are symmetric with respect to the equatorial plane. Starting from the photon sphere at for the non-rotating Schwarzschild case, the exterior photon region gets a crescent-shaped cross-section for and grows with increasing spin . The interior photon region consists of two connected components that are separated by the ring singularity. In the exterior photon region all spherical light orbits are unstable while in the interior photon region there are stable and unstable ones. Circular lightlike geodesics exist where the boundary of the photon region is tangent to a sphere . We easily recognize the three well-known circular lightlike geodesics in the equatorial plane, but also two not-so-well-known cicular lightlike geodesics off the equatorial plane. The latter are situated in the region where . The causality violating region is adjacent to the ring singularity and lies to the side of negative . For small , the ergoregion does not intersect the exterior photon region but for it does.\n\nThe additional gravitomagnetic charge of the Kerr–NUT space-time changes the symmetry behavior significantly, see Fig. 4. The plots are no longer symmetric with respect to the equatorial plane (but they remain, of course, axially symmetric). The exterior and interior photon regions show this asymmetry clearly. For a slowly rotating Kerr–NUT black hole, , there is no ring singularity, and there are no stable spherical light rays. If the spin is increased, the ring singularity appears at , degenerated to a point on the axis. With further increased, the ring singularity moves towards the equator and stable spherical light orbits come into existence between and ; as in the Kerr case, the interior photon region consists of two connected components that are separated by the ring singularity. While the ergosphere is not significantly affected by , there is an additional causality violating region around the singularity on the axis which extends from the outer horizon at to . The interior causality violating region is now extending from the inner horizon at to . The causality violating region depends on the Manko-Ruiz parameter which was chosen equal to zero in Fig. 4. (For other values of see Fig. 6.)\n\nAdding an electric or magnetic charge parameter and a cosmological constant affects the photon regions little, see Fig. 5. The only qualitative effect of is in the fact that, in the case , one of the two connected components of the interior photon region is now detached from the ring singularity. For non-zero , higher spin values are possible compared to space-times with . For the pictures we have chosen a (small and) positive value for such that the domain of outer communication is bounded by a cosmological horizon. The latter is not shown in Fig. 5 because these pictures do not extend so far, but it is shown in Fig. 6. The cosmological horizon restricts the causality violating region which depends on the Manko-Ruiz parameter , see Fig. 6.\n\n## Iv Shadows of Black Holes\n\nThe existence of the photon region (16) around the black hole is essential for the construction of the shadow of a black hole. In the Introduction we have already explained how the shadow is constructed in the case of a Schwarzschild black hole. The same construction works, mutatis mutandis, in our more general black-hole space-times. We fix an observer in the domain of outer communication at Boyer-Lindquist coordinates and we think of light sources distributed on a sphere with some .\n\nFor determining the shape of the shadow it is convenient to consider light rays which are sent from the observer’s position into the past. Then we can distinguish two types of orbits. Along light rays of the first type the radius coordinate reaches the value , possibly after going through a local minimum, so that we can think of these light rays as being emitted from one of our light sources. Along light rays of the second type the radius coordinate decreases monotonically until it reaches the horizon at , so these light rays cannot come from any of our light sources. Correspondingly, in the direction of light rays of the first type the observer would see brightness, and in the direction of light rays of the second type the observer would see darkness. The borderline case, i.e. the boundary of the shadow, corresponds to light rays that asymptotically spiral towards one of the unstable spherical light orbits in the exterior photon region which was discussed in Section III above. As in the Schwarzschild case, it is obvious from the geometry that the construction of the shadow works equally well if light sources are distributed, rather than on a sphere with , anywhere else in the domain of outer communication except in the region filled by the above-mentioned light rays of the second type.\n\nIt is now our goal to calculate the boundary curve of the shadow on the observer’s sky. We consider an observer at position in the Boyer–Lindquist coordinates. (The and coordinates of the observation event are irrelevant because of the symmetries of the metric.) We choose an orthonormal tetrad\n\n e0 =(Σ+aχ)∂t+a∂φ√ΣΔr∣∣ ∣∣(rO,ϑO), (19) e1 =√ΔϑΣ∂ϑ∣∣ ∣∣(rO,ϑO), e2 =−(∂φ+χ∂t)√ΣΔϑsinϑ∣∣ ∣∣(rO,ϑO), e3 =−√ΔrΣ∂r∣∣ ∣∣(rO,ϑO).\n\nat the observation event (see Fig. 7). We assume that the observer is in the domain of outer communication. This guarantees that is positive, and so is . Moreover, we assume that and are restricted by the inequality (7), which guarantees that is positive. Hence, the coefficients in Eqs. (19) are indeed real and it is straight-forward to verify that , , , are orthonormal. The timelike vector is to be interpreted as the four-velocity of our observer. The tetrad has been chosen such that are tangential to the principal null congruences of our metric. For an observer with four-velocity the vector gives the spatial direction towards the center of the black hole.", null, "Figure 7: At an observation event with Boyer–Lindquist coordinates (rO,ϑO) we choose an orthonormal tetrad (e0,e1,e2,e3) according to Eqs. (19). For each light ray that is sent from the observation event into the past the tangent vector can be written as a linear combination of e0, e1, e2 and e3. In this way we can assign celestial coordinates to the direction of the tangent vector, see Fig. 8\n\nFor each light ray with coordinate representation , we write the tangent vector as\n\n ˙λ=˙r∂r+˙ϑ∂ϑ+˙φ∂φ+˙t∂t. (20)\n\nOn the other hand, the tangent vector at the observation event can be written as\n\n ˙λ=α(−e0+sinθcosψe1+sinθsinψe2+cosθe3) (21)\n\nwhere is a scalar factor. From (10) and (11) we find that\n\n α=g(˙λ,e0)=aLz−(Σ+aχ)E√ΣΔr∣∣ ∣∣(rO,ϑO). (22)\n\nEq. (21) defines the celestial coordinates and for our observer, see Fig. 8. The direction towards the black hole corresponds to .\n\nComparing coefficients of and in (20) and (21) yields\n\n sinψ =√Δϑsinϑ√Δrsinθ(ΣΔr˙φ(Σ+aχ)E−aLz−a)∣∣ ∣∣(rO,ϑO), (23) cosθ =Σ˙r(Σ+aχ)E−aLz∣∣∣(rO,ϑO).\n\nUpon substituting for and from (12b) and (12d) we find from (23) that\n\n sinψ =˜LE+acos2ϑ+2ℓcosϑ√ΔϑKEsinϑ∣∣ ∣∣ϑ=ϑO, (24) sinθ =√ΔrKEr2+ℓ2−a˜LE∣∣ ∣∣r=rO,\n\nwhere\n\n ˜LE=LE−a+2ℓC. (25)\n\nThe boundary curve of the shadow corresponds to light rays that asymptotically approach a spherical lightlike geodesic. Such a light ray must have the same constants of motion as the limiting spherical lightlike geodesic, i.e., by (15),\n\n KE =16r2Δr(Δ′r)2∣∣∣r=rp, (26) a˜LE =(r2+ℓ2−4rΔrΔ′r)∣∣∣r=rp,\n\nwhere is the radius coordinate of the limiting spherical lightlike geodesic. Inserting the expressions for and from (26) into (24) gives the boundary curve of the shadow.\n\nWe observe that the Manko-Ruiz parameter has no influence on the shadow and that the shadow is always symmetric with respect to a horizontal axis. The latter result follows from the fact that the points and correspond to the same constants of motion and . For and this symmetry property was not to be expected.\n\nFor , the coordinate takes its maximal value along the boundary curve at and its minimal value at . The corresponding values of the parameter , which we denote by and , respectively, can be determined by inserting (26) into (24) and equating to . We find that is determined by the equation\n\n (ΣΔ′r−4rΔr∓4ar√ΔrΔϑsinϑ)∣∣(r=rp,ϑ=ϑO)=0. (27)\n\nComparison with the inequality (16) shows that and are the radius values where the boundary of the exterior photon region intersects the cone .\n\nThe case is special because then our method of parametrizing the boundary curve by does not work. If we have , so (26) determines a unique value for . Inserting this value into (24) gives the boundary curve of the shadow in the form . We see that if , i.e., that the shadow is circular.", null, "Figure 8: To each light ray at the observation event we assign celestial coordinates θ and ψ with the help of Eq. (21), see figure on the left. The figure on the right shows the stereographic projection (red ball) of the point (θ,ψ) on the celestial sphere (black ball). The dotted (red) circles indicate the celestial equator θ=π/2 and its projection.\n\nNote that we have calculated the shadow for an observer with four-velocity according to (19). For an observer with a different four-velocity the shadow is distorted according to the standard aberration formula of special relativity.\n\nIn Figs. 9 and 10 we show pictures of the shadow, as it is seen by our chosen observer with four-velocity . For calculating the boundary curve of the shadow we have used our analytical parameter representation, and for plotting it we have used stereographic projection from the celestial sphere onto a plane, as illustrated in Fig. 8. Standard Cartesian coordinates in this plane are given by\n\n x(rp) =−2tan(θ(rp)2)sin(ψ(rp)), (28) y(rp) =−2tan(θ(rp)2)cos(ψ(rp)).\n\nIn Fig. 9 the observer position is kept fixed at Boyer–Lindquist coordinates and . The parameters of the black hole are chosen such that the observer is always located in the domain of outer communication. Each of the five shadings corresponds to a certain choice of parameters , and , and for each choice the shadow is shown for four different values of the spin, , where is determined by , and . The shadows of the first three cases—Kerr , Kerr–NUT , Kerr–Newman–NUT with cosmological constant —correspond to the photon regions presented in Figs. 35.", null, "Figure 9: Shadow of a black hole for different parameters a, β, ℓ and Λ, seen by an observer at rO=5m and ϑO=π/2. The cross hairs indicate the spatial direction towards the black hole, i.e., the spatial direction of the principal null congruences with respect to our observer with four-velocity e0. The dashed (red) circle indicates the celestial equator, cf. Fig. 8.\n\nWe see that the shape of the shadow is largely determined by the spin of the black hole. With increasing the shadow becomes more and more asymmetric with respet to a vertical axis. This asymmetry is well-known from the Kerr metric and it is easily understood as a “dragging effect” of the rotating black hole on the light rays. The other parameters , and have an effect on the size of the shadow but, at least for the naked eye, hardly on its shape. Note that the size of the shadow depends, of course, on and that there is no direct way of comparing radius coordinates in different space-times operationally. Therefore, if we want to get some information on the space-time from observing the shadow, the shape is much more relevant than the size.", null, "Figure 10: Shadow of a black hole for an observer at rO=5m and different inclination angles ϑO, with fixed β=59m2, ℓ=43m, Λ=10−2m−2 and a=amax≈1.51m. As in Fig. 9, the cross hairs indicate the spatial direction towards the black hole and the dashed (red) circle indicates the celestial equator.\n\nIn Fig. 10 we consider an extremal black hole, , with fixed parameters , and . We keep the radius coordinate of the observer fixed, and we vary the inclination . Clearly, the asymmetry with respect to the vertical axis vanishes if the observer approaches the axis, . We have already emphasized the remarkable fact that there is no asymmetry with respect to the horizontal axis.\n\nWe should mention that in the case some light rays have to pass through the singularity on the axis. We have assumed that these light rays are not blocked, i.e., that the source of the gravitomagnetic NUT field does not cast a shadow.\n\n## V Conclusions and Outlook\n\nBased on a detailed analysis of the photon regions in black-hole space-times of the Plebański class, we have derived an analytical formula for the shadows of such black holes. As the space-times under consideration are not in general asymptotically flat and may have a cosmological horizon, one cannot restrict to observers at infinity as it was done in many earlier articles on shadows of black holes. Our formalism allows for observers at any Boyer–Lindquist coordinates in the domain of outer communication. The boundary curve of the shadow was calculated for observers with a certain four-velocity , given by (19). For these observers, the shadow turned out to be always symmetric with respect to a horizontal axis, even for non-vanishing NUT parameter and for an observer off the equatorial plane. For observers with a four-velocity different from , the shadow can be easily calculated by combining our results with the standard aberration formula of special relativity. If this additional aberration effect is taken into account, the boundary curve of the shadow will depend on the parameters , , and , on the coordinates and of the observer, and on the velocity of the observer relative to an observer with four-velocity . (The mass gives an overall scale, and the Manko-Ruiz parameter has no influence on the shadow.) We are planning to investigate, in a follow-up article, to what extent all these parameters can be determined from the boundary curve of the shadow. With an analytical formula for the boundary curve at hand, it is a natural idea to use a Fourier analysis of the boundary curve and to see how the parameters of the black hole can be extracted from the Fourier coefficients.\n\nWe have restricted to black-hole space-times, but a large part of the material presented in this paper is valid for naked singularities as well. In particular, the characterization of the photon region by inequality (16) is true in general. A major difference is in the fact that in the case of a naked singularity there is no domain of outer communication, so the possible observer positions are restricted only by a cosmological horizon, if present. The shadow of a naked singularity is drastically different from the shadow of a black hole, as was demonstrated by de Vries Vries.2000 for the Kerr-Newman case. While for a black hole the shadow is two-dimensional (an area on the sky, bounded by a closed curve), for a naked singularity the shadow is one-dimensional (an arc on the sky).\n\n## Acknowledgments\n\nWe would like to thank Domenico Giulini, Norman Gürlebeck, Eva Hackmann, Friedrich Hehl, Valeria Kagramanova, Jutta Kunz, and Olaf Lechtenfeld for helpful discussions, and Silke Britzen, Frank Eisenhauer, and Heino Falcke for valuable information on the status of observations. We gratefully acknowledge support from the DFG within the Research Training Group 1620 “Models of Gravity” and from the “Centre for Quantum Engineering and Space-Time Research (QUEST)”.\n\n## References\n\n• (1) A. Eckart and  R. Genzel, Nature 383,  415 (1996)\n• (2) S. Gillessen et al., Astrophys. J. 692,  1075 (2009)\n• (3) F. Eisenhauer et al., in Proceedings of the Workshop “Science with the VLT in the ELT Era”, Garching, 2009, edited by A. Moorwood (Springer, Netherlands, 2009),  p. 361\n• (4) S. S. Doeleman et al., Nature 455,  78 (2008)\n• (5) J. L. Synge, Mon. Not. R. Astron. Soc. 131,  463 (1966)\n• (6) A. M. Ghez et al., Astrophys. J. 689,  1044 (2008)\n• (7) L. Huang, M. Cai, Zh.-Q. Shen, and F. Yuan, Month. Not. R. Astron. Soc. 379,  833 (2007)\n• (8) J. M. Bardeen, in Black Holes (Les Astres Occlus),  edited by  C. DeWitt and B. S. DeWitt  (Gordon and Breach, New York, 1973) p.   215\n• (9) S. Chandrasekhar, The Mathematical Theory of Black Holes, (Oxford University Press, Oxford, 1983)\n• (10) E. Teo, Gen. Relativ. Gravit. 35,  1909 (2003)\n• (11) V. Perlick, Living Rev. Relativ. 7, 9 (2004)\n• (12) A. de Vries, Class. Quantum Grav. 17,  123 (2000)\n• (13) C. Bambi and  N. Yoshida, Class. Quant. Grav. 27, 205006 (2010)\n• (14) L. Amarilla, E. F. Eiroa, and  G. Giribet, Phys. Rev. D 81, 124045 (2010)\n• (15) L. Amarilla and  E. F. Eiroa, Phys. Rev. D 85, 064019 (2012)\n• (16) L. Amarilla and  E. F. Eiroa, Phys. Rev. D 87, 044057 (2013)\n• (17) A. Abdujabbarov, F. Atamurotov, Y. Kucukakça, B. Ahmedov, and U. Camci, Astrophys. Space Sci.  344,  429 (2012)\n• (18) A. Yumoto, D. Nitta, T. Chiba, and  N. Sugiyama, Phys. Rev. D 86, 103001 (2012)\n• (19) Z. Li and  C. Bambi, J. Cosmol. Astropart. Phys. 2014, 041 (2014)\n• (20) K. Hioki and  K.-I. Maeda, Phys. Rev. D 80, 024042 (2009)\n• (21) T. Johannsen and  D. Psaltis, Phys. Rev. D 83, 124015 (2011)\n• (22) J. F. Plebański, Ann. Phys. 90,  196 (1975)\n• (23) J. F. Plebański and M. Demiański, Ann. Phys. 98,  98 (1976)\n• (24) H. Falcke, F. Melia, and  E. Agol, Astrophys. J. 528,  L13 (2000)\n• (25) J. M. Bardeen and C. T. Cunningham, Astrophys. J. 183,  237 (1973)\n• (26) J.-P. Luminet, Astron. Astrophys. 75,  228 (1979)\n• (27) J. Dexter, E. Agol, P. C. Fragile, and  J. C. McKinney, J. Phys.: Con. Ser. 372, 012023 (2012)\n• (28) M. Mościbrodzka, H. Shiokawa, C. F. Gammie, and  J. C. Dolence, Astrophys. J. Lett. 752, L1 (2012)\n• (29) J. Dexter and  P. C. Fragile, Mon. Not. R. Astron. Soc. 432,  2252 (2013)\n• (30) B. Carter, Commun. Math. Phys. 10,  280 (1968)\n• (31) J. G. Miller, J. Math. Phys. 14,  486 (1973)\n• (32) J. B. Griffiths and J. Podolský, Exact Space-Times in Einstein’s General Relativity,  (Cambridge University Press, Cambridge, 2009)\n• (33) H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt, Exact Solutions of Einstein’s Field Equations,  (Cambridge University Press, Cambridge, 2003)\n• (34) V. S. Manko and  E. Ruiz, Class. Quantum Grav. 22, 3555 (2005)\n• (35) A. N. Aliev and  A. E. Gümrükçüoğlu, Phys. Rev. D 71, 104027 (2005)\n• (36) V. Kagramanova, J. Kunz, E. Hackmann,  and  C. Lämmerzahl, Phys. Rev. D 81, 124044 (2010)\n• (37) C. W. Misner, J. Math. Phys. 4,  924 (1963)\n• (38) W. B. Bonnor, Math. Proc. Cambridge Philos. Soc. 66,  145 (1969)\n• (39) E. Hackmann, V. Kagramanova, J. Kunz, and  C. Lämmerzahl, Europhys. Lett. 88, 30008 (2009)\n• (40) B. O’Neill, The Geometry of Kerr Black Holes  (A K Peters, Wellesley, 1995)" ]

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[ "Wednesday, August 2, 2017\n\nChallenging SQL Server precision with Pi calculations.\n\nSometimes it is interesting just to play with SQL Server and hit its limits.\n\nThis time I've had some fun with getting closer to \"Pi\".\n\n• We have wonderful Pi() function;\n• If we need bigger precision, we can always get this number with up to one million digits after decimal point from a web site like this:\"www.piday.org/million/\";\n• Usually 5 digits precision serves most of the tasks;\nYep. All of that is true, but all of these Pi long numbers came outside of SQL Server and it is very interesting how SQL Server can manage task of calculating Pi.\n\nLesson #1.\n\nI'll start from very easy test:\n\n`SELECT 6167950454 / 1963319607`\nTwo whole numbers, second one is INT and the first one looks like BIGINT because it is obviously bigger than the biggest integer number 2,147,483,647. As the result I expect to get whole number \"3\".\n\nHowever, surprisingly I've got more precise result of 3.14159265358.\nHow came???\nLets look at the first number type:\n```DECLARE @N1 SQL_VARIANT = 6167950454;\nSELECT [@N1] = @N1\n, [N1 BaseType] = SQL_VARIANT_PROPERTY(@N1, 'BaseType')\n, [N1 Precision] = SQL_VARIANT_PROPERTY(@N1, 'Precision')\n, [N1 Scale] = SQL_VARIANT_PROPERTY(@N1, 'Scale')```\nIt goes like:\nN1 BaseType : numeric\nN1 Precision : 10\nN1 Scale : 0\n\nInteresting to know. SQL Server interprets integers higher than 2,147,483,647 as Numeric, not as BIGINT !!!\n\nWill take a look at the result of the division:\n```SELECT 6167950454 / 1963319607\n, [N1 BaseType] = SQL_VARIANT_PROPERTY(6167950454/1963319607, 'BaseType')\n, [N1 Precision] = SQL_VARIANT_PROPERTY(6167950454/1963319607, 'Precision')\n, [N1 Scale] = SQL_VARIANT_PROPERTY(6167950454/1963319607, 'Scale')```\nIt returns following:\nIt goes like:\nN1 BaseType : numeric\nN1 Precision : 21\nN1 Scale : 11\n\nHow that happened? How SQL Server come up with that precision?\nThe answer is here: Precision, scale, and Length\n\nFrom that link we can get 2 formulas to calculate precision and scale of our result:\nR_Precision = p1 - s1 + s2 + max(6, s1 + p2 + 1)\nR_Scale = max(6, s1 + p2 + 1)\n\nWhere:\np1 = 10\ns1 = 0\np2 = 10\ns2 = 0\n\nSo, from it we get:\nR_Precision = 10 - 0 + 0 max(6, 0 + 10 + 1) => 21\nR_Scale = max(6, 0 + 10 + 1) => 11\n\nExact precision and scale we've got for the division's result!\n\nLesson #2.\n\nIn the previous division we've got 21 digits for precision and 11 digits for scale. Lets preset our numbers up to these parameters in order to get better precision:\n```DECLARE @N1 NUMERIC(21,11) = 6167950454, @N2 NUMERIC(21,11) = 1963319607;\nSELECT @N1/@N2\n, SQL_VARIANT_PROPERTY(@N1/@N2, 'Precision') as Precision\n, SQL_VARIANT_PROPERTY(@N1/@N2, 'Scale') as Scale```\nResult : 3.14159265358979323\nPrecision : 38\nScale : 17\n\nResult has much better precision: 17 digits after decimal point, however, accordingly to the formula from the Lesson #1 I'd expect to get a scale as high as 33 digits, but got twice less.\nWhy SQL did not give me more?\nRead the article further: \"The scale might be reduced using the following rules...\"\nThe applicable rule for Scale reduction in this case is: \"min(scale, 38 – (precision-scale))\"\nAccordingly to original formula:\nR_Precision = 21 - 11 + 11 + (11 + 21 + 1) =>54\nR_Scale = 11 + 21 + 1 => 33\n\nAnd following reduction formula we get:\nReduced_Scale = 38 - (R_Precision - R_Scale) = 38 -  (54 - 33) => 17 !!!\nNow we can explain how SQL Server reduces precision of the operation.\n\nLesson #3.\n\nNow, when we know all formulas, can we increase precision of the result to the maximum and what is the maximum?\nIn order to get the best precision of the result we have to reduce scale of both numbers and precision of the first one. The best case scenario will give us following:\n```DECLARE @N1 NUMERIC(10,0) = 6167950454, @N2 NUMERIC(27,0) = 1963319607;\nSELECT @N1/@N2\n, SQL_VARIANT_PROPERTY(@N1/@N2, 'Precision') as Precision\n, SQL_VARIANT_PROPERTY(@N1/@N2, 'Scale') as Scale\nGO```\nThat gives us incredible precision and scale:\nResult 3.1415926535897932383863775063*\nPrecision : 38\nScale : 28\n\n*Disclosure: The real Pi number is closer to 3.141592653589793238462643383279502884187. That means even with 28 fractional digits we have only 18 matching digits.\n\nAccordingly to the formulas, scale of 28 for the division result is absolute limit.\nPretty sad, right? I've hoped it would be at least 37.\nHowever, 28 digits it is not so bad.\nThe regular Pi() function returns much smaller number of fractional digits:\n```SELECT Pi()\n, SQL_VARIANT_PROPERTY(Pi(), 'Precision') as Precision\n, SQL_VARIANT_PROPERTY(Pi(), 'Scale') as Scale```\nResult : 3.14159265358979\nPrecision : 53\nScale : 0\nIs not good, right?\nWe can improve it just a little bit:\n```DECLARE @N3 NUMERIC(38,38) = Pi()-3\nSELECT @N3\n, SQL_VARIANT_PROPERTY(@N3, 'Precision') as Precision\n, SQL_VARIANT_PROPERTY(@N3, 'Scale') as Scale```\nResult : 3.1415926535897931000000000000000000000\nPrecision : 38\nScale : 37\nThis trick added just one more significant digit.\n\nSo, result of the research would be a fact that even though SQL Server can store decimal number with precision of 38 significant digits it can still support calculations only with maximum 28 digits precision.\nAnd of cause, if you want to hit the limit, it won't be easy calculations." ]

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[ "# College Math Teaching\n\n## August 19, 2011\n\n### Partial Differential Equations, Differential Equations and the Eigenvalue/Eigenfunction problem\n\nSuppose we are trying to solve the following partial differential equation:", null, "$\\frac{\\partial \\psi}{\\partial t} = 3 \\frac{\\partial ^2 \\phi}{\\partial x^2}$ subject to boundary conditions:", null, "$\\psi(0) = \\psi(\\pi) = 0, \\psi(x,0) = x(x-\\pi)$\n\nIt turns out that we will be using techniques from ordinary differential equations and concepts from linear algebra; these might be confusing at first.\n\nThe first thing to note is that this differential equation (the so-called heat equation) is known to satisfy a “uniqueness property” in that if one obtains a solution that meets the boundary criteria, the solution is unique. Hence we can attempt to find a solution in any way we choose; if we find it, we don’t have to wonder if there is another one lurking out there.\n\nSo one technique that is often useful is to try: let", null, "$\\psi = XT$ where", null, "$X$ is a function of", null, "$x$ alone and", null, "$T$ is a function of", null, "$t$ alone. Then when we substitute into the partial differential equation we obtain:", null, "$XT^{\\prime} = 3X^{\\prime\\prime}T$ which leads to", null, "$\\frac{T^{\\prime}}{T} = 3\\frac{X^{\\prime\\prime}}{X}$\n\nThe next step is to note that the left hand side does NOT depend on", null, "$x$; it is a function of", null, "$t$ alone. The right hand side does not depend on", null, "$t$ as it is a function of", null, "$x$ alone. But the two sides are equal; hence neither side can depend on", null, "$x$ or", null, "$t$; they must be constant.\n\nHence we have", null, "$\\frac{T^{\\prime}}{T} = 3\\frac{X^{\\prime\\prime}}{X} = \\lambda$\n\nSo far, so good. But then you are told that", null, "$\\lambda$ is an eigenvalue. What is that about?\n\nThe thing to notice is that", null, "$T^{\\prime} - \\lambda T = 0$ and", null, "$X^{\\prime\\prime} - \\frac{\\lambda}{3}X = 0$\nFirst, the equation in", null, "$T$ can be written as", null, "$D(T) = \\lambda T$ with the operator", null, "$D$ denoting the first derivative. Then the second can be written as", null, "$D^2(X) = 3\\lambda X$ where", null, "$D^2$ denotes the second derivative operator. Recall from linear algebra that these operators meet the requirements for a linear transformation if the vector space is the set of all functions that are “differentiable enough”. So what we are doing, in effect, are trying to find eigenvectors for these operators.\n\nSo in this sense, solving a homogeneous differential equation is really solving an eigenvector problem; often this is termed the “eigenfucntion” problem.\n\nNote that the differential equations are not difficult to solve:", null, "$T = a exp(\\lambda T)$", null, "$X = b exp(\\sqrt{\\frac{\\lambda}{3}} x) + cexp(-\\sqrt{\\frac{\\lambda}{3}} x)$; the real valued form of the equation in", null, "$x$ depends on whether", null, "$\\lambda$ is positive, zero or negative.\n\nBut the point is that we are merely solving a constant coefficient differential equation just as we did in our elementary differential equations course with one important difference: we don’t know what the constant (the eigenvalue) is.\n\nNow if we turn to the boundary conditions on", null, "$x$ we see that a solution of the form", null, "$A e^{bx} + Be^{-bx}$ cannot meet the zero at the boundaries conditions; we can rule out the", null, "$\\lambda = 0$ condition as well.\nHence we know that", null, "$\\lambda$ is negative and we get", null, "$X = a cos(\\sqrt{\\frac{\\lambda}{3}} x) + b sin(\\sqrt{\\frac{\\lambda}{3}} x)$ solution and then", null, "$T = d e^{\\lambda t }$ solution.\n\nBut now we notice that these solutions have a", null, "$\\lambda$ in them; this is what makes these ordinary differential equations into an “eigenvalue/eigenfucntion” problem.\n\nSo what values of", null, "$\\lambda$ will work? We know it is negative so we say", null, "$\\lambda = -w^2$ If we look at the end conditions and note that", null, "$T$ is never zero, we see that the cosine term must vanish (", null, "$a = 0$ ) and we can ensure that", null, "$\\sqrt{\\frac{w}{3}}\\pi = k \\pi$ which implies that", null, "$w = 3k^2$ So we get a whole host of functions:", null, "$\\psi_k = a_k e^{-3k^2 t}sin(kx)$.\n\nNow we still need to meet the last condition (set at", null, "$t = 0$ ) and that is where Fourier analysis comes in. Because the equation was linear, we can add the solutions and get another solution; hence the", null, "$X$ term is just obtained by taking the Fourier expansion for the function", null, "$x(x-\\pi)$ in terms of sines.\n\nThe coefficients are", null, "$b_k = \\frac{1}{\\pi} \\int^{\\pi}_{-\\pi} (x)(x-\\pi) sin(kx) dx$ and the solution is:", null, "$\\psi(x,t) = \\sum_{k=1}^{\\infty} e^{-3k^2 t} b_k sin(kx)$\n\n## 1 Comment »\n\n1. […] close with a link on how these eigenfunctions and eigenvalues are calculated (in the context of solving a partial…. Like this:LikeBe the first to like this post. Leave a […]\n\nPingback by Eigenvalues, Eigenvectors, Eigenfunctions and all that…. « College Math Teaching — May 26, 2012 @ 10:35 pm" ]

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[ "# Incorrectness Logic by Example\n\nIncorrectness Logic is a formal method to reason about program behavior. Similar formal reasoning techniques have been used for a multitude of different tasks in program verification, bug hunting and exploitation. To give some examples, Symbolic Execution (SE) has been used to generate hundreds of working exploits against a (at that time) current version of Debian . While possible, it is often difficult to scale SE with all its precision to large targets. However, SE can also be used to perform many smaller steps in the workflow of reverse engineers, bug hunters and vulnerability developers: In the past, it has been used to uncover novel ways to turn heap corruptions into useful exploitation primitives , to deobfuscate bytecode handlers to reverse engineer VM based obfuscation , to search for very specific code patterns that allow to trigger memory access violations without crashing the target applications , and many other program analysis tasks.\n\nCurrent techniques are usually based on overestimating the set of possible states. That is, the formal approach underlying the mental models behind techniques such as SE, Abstract Interpretation and to some extend even Concolic Execution is usually heavily informed by the ideas behind the so called Hoare Logic . Hoare Logic was designed as a method to prove the correctness of programs, by overestimating the set of states that a program can possibly reach. If this larger set doesn’t contain a faulty state, then the program must be correct. While this is very useful in theory, in practice its almost impossible to prove the correctness of even simple programs. Plus, many of us aren’t even that interested in proving correctness, rather we want to find bugs.\n\nIncorrectness Logic simply adapts the ideas from Hoare Logic to underapproximation: Where Hoare Logic proves that at most a set of states is reachable, we can use Incorrectness Logic to prove that a set of states is definitely reachable. While we can show correctness using Hoare Logic to demonstrating that a bug is not reachable, we can prove incorrectness using Incorrectness Logic by proving that a bug is certainly reachable.\n\nRecently, two papers introduce this concept [6, 7] of Incorrectness Logic and it took me a while get my head around how to use Incorrectness Logic. To help, I applied it to a bunch of toy programs, and tried to figure out what we can do with it.\n\n## Applying Hoare Logic\n\nTo help understanding Incorrectness Logic, I give a short introduction into Hoare Logic. If you are already familiar with Hoare Logic, feel free to skip this part.\n\nIn classic Hoare Logic, we create so called “Hoare Triplets” for each statement of the program. Such a triple consists of a pre-condition, the statement and a post-condition. For example, if we know that `x==0` and we execute `int y = z;` the post-conditions would be `x==0 and y == z`. Typically these conditions are written between `{` and `}`. So in a paper you see the following snippet:\n\n`````` { x==0 }\ny = z\n{ x==0 and y==z }\n``````\n\nIn Hoare Logic these triplets have to satisfy the following condition: If we execute the statement starting in a state that satisfies the pre-condition, then the result state after the statement has to satisfy the post-condition. It can be seen that our example has this property. This property also allows us to “forget” constraints that we already know:\n\n`````` { x==0 }\ny = z\n{ y==z }\n``````\n\nWe can see, that weakening the post-condition is always a valid operation in Hoare Logic, since this only increases the set of states that we are allowed to end up in. To verify a complete program, we need to find such triples for each statement in the program, such that the post-condition of the last statement is the pre-condition of the next statement. This allows us to chain multiple individual steps together.\n\n#### Example 1\n\nConsider a simple program like this example that calculates the absolute value of the input:\n\n``````x = user_input()\ny = 0\nif x < 0 then\ny = -x\nelse\ny = x\nend\nassert(y >= 0)\n``````\n\nTo prove that the program is correct, we need to show that the assert statement is always true, that is, the post-condition of the program needs to imply `y >= 0`. It’s easy to build Hoare triples for the first statements:\n\n`````` { true }\nx = user_input() #we don't really learn anything about x\n{ true }\ny = 0\n{ y==0 }\n``````\n\nThe `if` statement is a bit more tricky. Here we need to come up with a pre-condition `PRE` and a post-condition `POST` such that:\n\n`````` { PRE } # `\\\nif C then # |\n{ PRE and C } # | `\\\ndo_something # | | must be valid\n{ POST } # | ,/\nelse # |\n{ PRE and !C } # | `\\\ndo_something # | | must be valid\n{ POST } # | ,/\nend # |\n{ POST } # ,/ { PRE } if ... end { POST } is valid,\n# if the both branches are valid\n``````\n\nIn this example, the `PRE: y == 0` will work, while `POST` needs to imply `y >= 0`. Consequently we pick, `POST: y >= 0`. After inserting `PRE` and `POST` in our code, we obtain the following “then”-branch for the if. Note that we need to weaken the post-condition after the assignment `y = -x` to obtain `POST`. Normaly, we would assume that the post condition of this branch should be `y>0`. While `y>0` is indeed a valid post-condition for the “then” branch,it is not a valid post-condition for the overall “if” statement. Consequently we weaken the post-condition to `y>=0` to\n\n`````` { y==0 } # PRE\nif x < 0 then\n{ y==0 and x<0 } # PRE and C\ny = -x\n{ y==-x and x<0 }\n{ y>=0 } # POST (weaker than the line above)\nelse\n#...\n``````\n\nAfter filling in the “else”-branch, we obtain the whole triple for the whole program: If we start with any state at all, we are guaranteed that after executing the program `y >= 0` holds. Consequently we have proven that the assertion can never be fail.\n\n`````` { true }\nx = user_input() #we don't really learn anything about x\n{ true }\ny = 0\n{ y==0 } # PRE\nif x < 0 then\n{ y==0 and x<0 } # PRE and C\ny = -x\n{ y==-x and x<0 }\n{ y>=0 } # POST (weaker than the line above)\nelse\n{ y==0 and !(x<0) } # PRE and !C\ny = x\n{ y==x and !(x<0) }\n{ y>=0 } # POST (weaker than the line above)\nend\n{ y>=0 } # POST\nassert(y >= 0)\n``````\n\n#### Example 2\n\nConsider a somewhat more complex program containing a loop like this:\n\n``````x = 0;\ny = user_input_unsigned()\nz = 0\nwhile( x < y ) do\nx=x+1\nz=z+2\nend\n\nassert(z == 2*y);\n``````\n\nTo prove that the program is correct (assuming unbounded integers), again, we need to show that the assert statement is always true. That is, the post-condition of the program needs to imply `z == 2*y`. This time however, we need to deal with a loop. Again, it’s easy to build Hoare triples for the first statements:\n\n`````` { true }\nx = 0\n{ x==0 }\ny = user_input_unsigned();\n{ x==0 and y>0 }\nz = 0\n{ x==0 and y>0 and z==0 }\n# What now? How to deal with loops?\nwhile( x < y ) do\nx=x+1\nz=z+2\nend\n\nassert(z==2*y)\n``````\n\nTo build a valid Hoare triple for a loopy statement, we need to find a so called Loop Invariant. A loop invariant is a statement that holds before entering the loop, at the start of the loop and the end of the loop and after exiting the loop. Assuming we picked an Invariant `I`, we can show that it holds by showing that the following triplets are valid:\n\n`````` { I } # `\\\nwhile( C ) do # |\n{ I and C } # | `\\\ndo_something # | | if this triple is valid\n{ I } # | ,/\nend # |\n{ I and !C } # ,/ { I } while ... end { I and !C } is valid\n``````\n\nIn our example, we can pick `I: x <= y and z = 2*x` and we obtain the following program:\n\n``````#... code so far ...\n{ x==0 and y>0 and z==0 }\n{ x<=y and z==2*x }\nwhile( x < y ) do\n{ x<=y and z==2*x and x<y }\nx=x+1\nz=z+2\n{ x<=y and z==2*x }\nend\n{ x<=y and z==2*x and !(x<y) }\nassert(z==2*y)\n``````\n\nFirst of all, we need to check that the invariant is indeed implied by the post-condition of the code prior to the loop. Indeed we can see that since `x == 0 and y > 0` it has also to be true that `x <= y` and due to `x == 0 and z == 0` , `z = 2*x` also holds. The next step is to verify that the invariant also holds after executing the loop:\n\n``````#... code so far ...\n{ x<=y and z==2*x and x<y } # I and C\nx=x+1;\nz=z+2;\n{ x<=y and z==2*x } # I\n``````\n\nAccording to the rules of Hoare Logic, if we want to build post-conditions for a variable assignment `a = some_expr` , where `some_expr` contains `a`, we need to ensure that all occurrences of the variable `a` in the precondition are exactly of the shape `some_expr`. Again we use our ability to arbitrarily weaken the post-condition at any time to introduce intermediate conditions.\n\n`````` #... code so far ...\n{ x<=y and z==2*x and x<y } # I and C\n{ x<y and z==2*x > # (weaker than the line above)\n{ x+1<=y and z+2==2*(x+1) } # (weaker than the line above)\nx=x+1;\nz=z+2;\n{ x<=y and z==2*x } # I\n``````\n\nNow all occurrences of updated variables have the right shape, and we can simply replace all occurrences of `some_expr` by `a` :\n\n`````` #... code so far ...\n{ x <= y and z == 2*x and x < y } # I and C\n{ x < y and z == 2*x > # (weaker than the line above)\n{ x+1 <= y and z+2 == 2*(x+1) } # (weaker than the line above)\nx=x+1;\n{ x <= y and z+2 == 2*x }\nz=z+2;\n{ x <= y and z == 2*x } # I\n``````\n\nWhich proves that `I` was indeed a valid loop invariant. In total we get:\n\n`````` { true }\nx = 0\n{ x==0 }\ny = user_input_unsigned()\n{ x==0 and y>0 }\nz = 0\n{ x==0 and y>0 and z==0 }\n{ x<=y and z==2*x } # I (weaker than the line above)\nwhile( x < y ) do\n{ x<=y and z==2*x and x<y } # I and C\n{ x<y and z==2*x } # (weaker than the line above)\n{ x+1<=y and z+2==2*(x+1) } # (weaker than the line above)\nx=x+1\n{ x<=y and z+2==2*x }\nz=z+2\n{ x<=y and z==2*x } # I\nend\n{ x<=y and z==2*x and !(x<y) } # I and !C\n{ x==y and z==2*x } # (weaker than the line above)\n{ z==2*y } # (weaker than the line above)\nassert(z == 2*y)\n``````\n\nSince the last post-condition implies that the assert statement is true, we have proven the program correct. To be more precise, we have shown that it never triggers the assert - it still might run into an infinite loop.\n\n#### More Exercises\n\nIf you have never used Hoare Logic before, I’d recommend you try to find proofs for the following examples to get a feeling for finding invariants:\n\n``````i = 0\ny = user_input_unsigned()\nres = 1\nwhile (i < y) do\nres *= 2\ni += 1\nend\nassert( res == 2**y )\n``````\n``````i = 0\ny = user_input_unsigned()\nres = 0\nwhile (i < y) do\nres += i\ni += 1\nend\nassert( res == sum(1..y) ) #hint: use res == sum(1..i) as invariant\n``````\n``````i = 0\ny = user_input_unsigned()\nres = 1\nwhile (i < y) do\nif i % 2 == 0 then\nres += i\nend\ni += 1\nend\nassert( res % 2 == 1 )\n``````\n\n## Applying Incorrectness Logic\n\nSimilar to Hoare Logic, Incorrectness Logic operates on triples of the shape `[pre]statement[post]`. However, the interpretation of the `pre` and `post` conditions changes. Since the goal is to show that some states are definitively reachable, we require that any state that satisfies the `post` condition is reached after execution `statement` by at least one state that satisfies `pre`. Consider a simple assignment without any information about the right hand side, `x = y`. The most obvious, valid, IL triple would also be a valid Hoare triple `[ true ]x = y[ x==y ]`. However while `{ true }x = y{ true }` is a valid Hoare triple, it is not a valid IL triple. For example, the state where `x==1 and y==2`, satisfies the post-condition, while also being unreachable. However, the IL triple `[true]x=y[ 0 < x < 10 and x==y ]` is valid in IL, but not in Hoare Logic. This is due to the fact that we are free to explicitly exclude any states in IL. Similarly, while in Hoare Logic we always have to consider all paths, we are free to drop paths in IL. This affects the rules for control flow. In IL the following rules are all valid for `if` statements:\n\n`````` [ PRE ] # `\\\nif C then # |\n[ PRE and C ] # | `\\\ndo_then # | | if this is valid\n[ POST ] # | ,/\nelse # |\n# ignore else case # | Then the whole statement is valid.\ndo_else # | Since we are underaproximating, we can\nend # | ignore paths, such as the `else` case.\n[ POST ] # ,/\n``````\n`````` [ PRE ] # `\\\nif C then # | Similarly, we can ignore the `then` case\n# ignore then case # | if the else case is valid.\ndo_then # |\nelse # |\n[ PRE and !C ] # | `\\\ndo_else # | | if this is valid\n[ POST ] # | ,/\nend # |\n[ POST ] # ,/\n``````\n\nObviously, the rule for loops changes as well, as we are now free to pick any number of loop iterations. Again there is multiple valid ways to construct IL triples:\n\n`````` [ PRE ] # `\\\nwhile C do # | This is always valid, since it represents\ndo_something # | the case where we never enter the loop.\nend # | Hence the body has no effect.\n[ PRE and !C ] # ,/\n``````\n\nWe can also unroll the loop any number of times:\n\n`````` [ PRE ] # `\\\nwhile C do # |\n[ PRE and C] # | `\\\ndo_something # | | if all of these are valid,\n[ POST_1 and C ] # | <\ndo_something # | |\n[ POST_2 and C ] # | <\ndo_something # | |\n[ POST_3 and C ] # | ,/\n# ... # |\nend # | unrolling the loop n times is valid.\n[ POST_n and !C ] # ,/\n``````\n\nLastly, we can use IL to prove that some states are reachable with any number of loop iterations. Here we will need a loop invariant again. However we are now parameterising the loop invariant with the number of loop iterations taken `n`. The “loop invariant” `I(n)` is then proven by induction:\n\n`````` [ I(0) ] # `\\\nwhile C do # |\n[ n>=0 and I(n) and C ] # | `\\\ndo_something # | | if this is valid,\n[ I(n+1) ] # | ,/\nend # | this is valid too.\n[ 'it exist a n>0 such that' I(n) and !C ] # ,/\n``````\n\nNote how in contrast to Hoare Logic the result explicitly mentions the number of loop iterations taken. Also, if the loop is not terminating, the post-condition is still valid: it is unsatisfiable. While in Hoare Logic `{ true }` is always a valid post-condition, in IL `[ false ]` is always valid.\n\n## Example 1\n\nConsider the following program that is a horrible manual implementation of multiplication.\n\n``````x = user_input_unsigned()\ny = user_input_unsigned()\nz = 0\nres = 0\nwhile( z < y ) do\nres=res+x\nz=z+1\nend\nassert(res != 20)\n``````\n\nUsing IL, there is many (in fact infinitely many) ways we can analyze the program. The most restricted version is a picking an arbitrary concrete execution:\n\n`````` [ true ]\nx = user_input_unsigned()\n[ x==50 ]\ny = user_input_unsigned()\n[ x==50 and y==2 ]\nz = 0\n[ x==50 and y==2 and z==0 ]\nres = 0\n[ x==50 and y==2 and z==0 and res==0 ]\nwhile( z < y ) do\n[ x==50 and y==2 and z==0 and res==0 and z<y ]# `\\\nres=res+x # |\n[ x==50 and y==2 and z==0 and res==50 ] # | unroll #1\nz=z+1 # |\n[ x==50 and y==2 and z==1 and res==50 ] # ,/\n[ x==50 and y==2 and z==0 and res==0 and z<y ]# `\\\nres=res+x # |\n[ x==50 and y==2 and z==0 and res==100 ] # | unroll #2\nz=z+1 # |\n[ x==50 and y==2 and z==2 and res==100 ] # ,/\nend\n[ x==50 and y==2 and z==2 and res==100 and !(z<y) ]\nassert(res != 20)\n``````\n\nThis is probably not something we are overly interested in, as we don’t really need a logic to perform concrete execution. We can simply use the CPU to execute the program and observe the outcome. Also, using this particular trace we cannot show that the assertion fails.\n\nAnother common approach is to perform a so called “concolic” execution, where a path is fixed, and we execute symbolically along the path of a concrete execution. If any constraint gets too complicated, we can substitute the concrete values. Note how we need to track `x>0` which doesn’t really affect the rest of the execution. In Hoare Logic we would be allowed to drop this, but in IL we need to keep it to ensure soundness. If we would drop it, we would conclude that the state `res==-2 and z==2 and y==2 and x==-1` is reachable.\n\n`````` [ true ]\nx = user_input_unsigned()\n[ x>0 ]\ny = user_input_unsigned()\n[ x>0 and y==2 ] # we fix y, but not x\nz = 0\n[ x>0 and y==2 and z==0 ]\nres = 0\n[ x>0 and y==2 and z==0 and res==0 ]\nwhile( z < y ) do\n[ x>0 and y==2 and z==0 and res==0 and z<y ] # `\\\nres=res+x # |\n[ x>0 and y==2 and z==0 and res==x ] # | unroll #1\nz=z+1 # |\n[ x>0 and y==2 and z==1 and res==x ] # ,/\n[ x>0 and y==2 and z==0 and res==0 and z<y ] # `\\\nres=res+x # |\n[ x>0 and y==2 and z==0 and res==x+x ] # | unroll #2\nz=z+1 # |\n[ x>0 and y==2 and z==2 and res==x+x ] # ,/\nend\n[ x>0 and y==2 and z==2 and res==x+x and !(z<y) ] # POST\nassert(res != 20)\n``````\n\nUsing concolic execution with `y==2`, we can already prove that the final assertion fails, by demonstrating that `x==10 and y==2 and z==2 and res == 20` is a valid, reachable, state that triggers the assertion. After we obtained the final condition `POST`, we can automatically check if the assertion is violated, by using an SMT solver to find a variable assignment that satisfies `POST and !(res!=20)`. This approach has been known long before the formal description of IL. However IL puts it into a nice mental framework. Consider the case where we change the assertion to `assert(res != 139*31)`. Using this larger number, concolic execution would have a very hard time finding the exact right number of loop iterations to falsify the assertion. If we consider concolic execution to be a special case of IL, we can generalize concolic execution to reason about multiple different paths at the same time. If we keep both `x` and `y` symbolic, we can prove that the assertion still fails. By applying the induction rule for loops we obtain the following result:\n\n`````` [ true ]\nx = user_input_unsigned()\n[ x>0 ]\ny = user_input_unsigned()\n[ x>0 and y>0 ] # we fix neither x, nor y\nz = 0\n[ x>0 and y>0 and z==0 ]\nres = 0\n[ x>0 and y>0 and z==0 and res==0 ]\n[ I(0) ] # `\\\nwhile( z < y ) do # |\n[ n>=0 and I(n) and z < y ] # | need to find an I(n)\nres=res+x # | that satiesfies\nz=z+1 # | this conditions.\n[ n>=0 and I(n+1) ] # |\nend # |\n[ 'it exist a n>0 such that' I(n) and !(z<y) ] # ,/\nassert(res != 139*31)\n``````\n\nA natural candidate for `I(n)` is `I(n): res==x*n and z==n and z<=y and x>0 and y>0` . Since this is rather long, we define the rest`R: x>0 and y>0 and n>=0` to shorten `I(n)` to the relevant part `res==x*n and z==n and z<=y and R`. Lets plug it in and see if it works:\n\n`````` # ... previous code ...\n[ x>0 and y>0 and z==0 and res==0 ] # I(0) <-,\n[ res==x*0 and z==0 and z <= y and x>0 and y>0 ] # stronger than ´\nwhile( z < y ) do\n[ res==x*n and z==n and z <= y and R and z<y ] # I(n) and C <-,\n[ res+x=x*(n+1) and z+1=(n+1) and z+1 <= y and R ] # stronger than ´\nres=res+x\n[ res=x*(n+1) and z+1=(n+1) and z+1 <= y and R ]\nz=z+1\n[ res=x*(n+1) and z=(n+1) and z <= y and R ] # I(n+1)\nend\n[ 'it exist a n>0 such that' res==x*n and z==n and #\nz <= y and !(z<y) and R] # I(n) and !(C)<-,\n[ 'it exist a n>0 such that' res==x*y and z==n and # stronger than ´\nz == y and R] #\nassert(res != 139*31)\n``````\n\nAs we can see, similar to using invariants in Hoare logic, we applied `I(n)`to the pattern for loops, and used our ability to strengthen post-conditions to show that `[ I(n) and C ]body[ I(n+1) ]` is indeed a valid IL triple. In most cases we didn’t even really strengthen the post-condition, but simply applied equivalence transformations. For example, we transform`z<=y and !(z<y)` into `z=y`. As a consequence we have shown that any state where `res==x*y and x>0 and y>0 and ...` is reachable. Using the SMT solver to check `POST and !(res!=139*31)` we can easily check that the assertion is still triggerable.\n\n## Example 2\n\nLets pick another somewhat more elaborate example. This time we will deal with arrays. This function reads an array from the user_input, and copies the absolute value of every element to the result array. In this example, we skip the simple cases and instead try to prove that we can reach states where `forall j in (0..x.len): res[j] == x[j] and ...`` holds. To keep this example readable, we skip dealing with the length, and assume that setting elements in an array always succeeds.\n\n``````x = user_input_array()\nres = array()\ni = 0\nwhile( i < x.len ) do\nif x[i] < 0 then\nres[i]=-x[i]\nelse\nres[i]=x[i]\nend\nend\n``````\n\nWe will also skip the prefix and jump right into dealing with the loop body. For the first case we allow arbitrary numbers of loop iterations, while fixing that we always take the `else` case in the `if` statement. To simplify the rest of this example, we add the additional constraint that `x.len >= 1` since otherwise the inductive rule doesn’t apply and we have to use the much simpler rule for loops with zero iterations. Hence we have to find an `I(n)` such that\n\n`````` [ i==0 and x.len >= 1 ] # <-,\n[ I(0) ] # stronger than ´\nwhile( i < x.len ) do\n[ n>=0 and I(n) andi < x.len]\nif x[i] < 0 then\n# don't care, fixed the else path\nelse\n[ n>=0 and I(n) and i < x.len and !(x[i]<0) ]\nres[i]=x[i]\n[ n>=0 and I(n) and i < x.len and !(x[i]<0) and res[i]=x[i]]\nend\n[ n>=0 and I(n) and i < x.len and !(x[i]<0) and res[i]=x[i]]\ni=i+1\n[ n>=0 and I(n+1) ]\nend\n[ 'it exist a n>0 such that' I(n) and !(i<x.len) ] # <-,\n[ 'forall j in (0..x.len)' res[j]==x[] and ...] # stronger than ´\n``````\n\nAgain, the hard part is to come up with a proper `I(n)` . We will try the following`I(n)= 'forall j in (0..n)' res[j]==x[j] and x[j]>=0 and i<=x.len and i==n and R` where `R = x.len>=1 and n>=0` is the part that we don’t care about but still have to carry around. Now beware, this example is the most complex one we used so far.\n\n`````` [ i==0 and x.len >= 1 ]\n[ 'forall j in (0..0)' res[j]==x[j] and x[j]>=0\nand i<=x.len and i==n and x.len>=1 ] ´\nwhile( i < x.len ) do\n[ 'forall j in (0..n)' res[j]==x[j] and x[j]>=0\nand i<=x.len and i==n and i < x.len and R ]\n# in this step we pick an equivalent post-condition\n# to agregate i<=x.len and i<x.len into the later\n[ 'forall j in (0..n)' res[j]==x[j] and x[j]>=0\nand i==n and i < x.len and R ]\nif x[i] < 0 then\n# don't care\nelse\n[ 'forall j in (0..n)' res[j]==x[j] and x[j]>=0\nand i==n and i < x.len and R\nand !(x[i]<0) ]\nres[i]=x[i]\n[ 'forall j in (0..n)' res[j]==x[j] and x[j]>=0\nand i==n and i < x.len and R\nand !(x[i]<0) and res[i]=x[i] ]\nend\n[ 'forall j in (0..n)' res[j]==x[j] and x[j]>=0\nand i==n and i < x.len and R\nand !(x[i]<0) and res[i]=x[i] ]\n# Here we transform the post-condition to be a valid precondition\n# for the following assignment. Not the weird i == (i+1)-1 trick\n# that is needed to replace i+1 with i. This condition is\n# equivalent to the previous condition.\n[ 'forall j in (0..n)' res[j]==x[j] and x[j]>=0\nand i+1==n+1 and i+1 <= x.len and R\nand !(x[i+1-1]<0) and res[i+1-1]=x[i+1-1] ]\ni=i+1\n[ 'forall j in (0..n)' res[j]==x[j] and x[j]>=0\nand i==n+1 and i <= x.len and R\nand !(x[i-1]<0) and res[i-1]=x[i-1] ]\n# Since we know that x[i-1] >= 0 and res[i-1]=x[i-1] and\n# i == n+1 we also now that the forall statement now holds for\n# j in (0..n+1). This is indeed exactly [n>=0 and I(n+1)]\n[ 'forall j in (0..n+1)' res[j]==x[j] and x[j]>=0\nand i==n+1 and i <= x.len and R ]\nend\n[ 'it exist a n>0 such that'\n'forall j in (0..n+1)' res[j]==x[j] and x[j]>=0\nand i==n+1 and i <= x.len\nand R and !(i<x.len) ]\n# use !(i<x.len) and i<=x.len to infer i==x.len\n[ 'it exist a n>0 such that'\n'forall j in (0..n+1)' res[j]==x[j] and x[j]>=0\nand n+1==x.len and i = x.len\nand R]\n# use that n+1 == x.len, ignore the rest\n[ 'forall j in (0..x.len)' res[j]==x[j] and x[j]>=0 and ... ]\n``````\n\nAs we can see, `I(n)` is indeed applicable to this loop, and after exiting the loop, we can see that `res[j]==x[j]` holds. However, we also learn that to reach these states, `x[j]>=0` also has to hold.\n\n## Exercise:\n\nI would recommend trying to apply the same approach to prove that states where `forall j in (0..x.len): res[j]==-x[j] and ...` is true are reachable.\n\n# How can we use Incorrectness Logic?\n\nAfter gaining an intuition for how IL works we obviously want to know how we can use it. What do we gain by thinking of concrete and concolic execution as special cases of IL?\n\nFor starters, IL allows us to smoothly increase the amount of symbolism from zero (concrete execution) to a hundred percent (underapproximating SE). As a consequence, techniques based on IL can sit almost anywhere on the spectrum between dynamic and static analysis. Hence, IL lends itself to integrate dynamic, testing based approaches with static reasoning based approaches.\n\n#### Internal Fuzzing\n\nFor example, imagine using IL to prove that some states in the middle of the target application are reachable:\n\n``````data = read_data()\ndata2 = decode_zip(data)\n[ \"we prove that data2 can be any string\" and ...]\nstuff = parse(data2)\n``````\n\nNow we could spawn a fuzzer that directly generates `data2` and targets the parsing, without having to deal with decode_zip().\n\n#### Fuzzing for Target States.\n\nOne of the really big issues of symbolic approaches is that its very hard to model all environment effects. Consider a program that uses IPC to communicate with a Database. Building a model that allows to reason about values flowing into and out of the database is almost certainly prohibitive expensive. However fuzzers usually don’t suffer from this approach. Symbolic reasoning on the other hand easily pinpoints bugs that are very hard to trigger randomly such as an off-by-one integer overflow. Ideally these two components would be combined to compensate each others weak points, while combining the strength. Most current approaches use symbolic reasoning and fuzzing in an orthogonal fashion. The symbolic solver and fuzzer both generate inputs almost independently. Tools such as QSYM,Driller etc. only share the inputs found between the fuzzer and the symbolic engine.\n\nOne can imagine using IL to prove that certain sets of internal states trigger interesting behavior, and then pass this information on to the fuzzers instrumentation so that the fuzzer can specifically target these states that are guaranteed to yield interesting behavior. In such a tool, the symbolic reasoning would work backwards from the seemingly vulnerable positions to find interesting target states, while the fuzzer works forwards to overcome un-modeled side effects or unknown instructions or constraints that are plain to hard for a solver.\n\n#### Randomized Symbolic Execution\n\nWhile the previous two ideas aim to move fuzzing towards the strength of SE based approaches, one could also start from SE and move towards the strength of fuzzing / random testing.\n\nSince our goal is not to prove the absence of bugs, but to hunt for bugs, one could start from the classical SE based approach, and make it more dynamic. Instead of trying to follow all possible paths and to enumerate the whole states pace, an IL based randomized Symbolic Executor could explore random paths, until they become to hard to solve or too boring to explore further. In such cases the randomized SE could either add additional constraints that make solving easier (until the input becomes entirely concrete, and solving becomes trivial), or pick different paths altogether. Note this is already similar to what tools like KLEE are doing . However it’s really uncommon for SE based tools that a) randomly drop paths, b) systematically add constraints to make the paths easier to solve or) combine loop invariants with bug finding login instead of aiming at correctness proofs.\n\nIt is yet to early to tell what Incorrectness Logic adds to the world of software testing. While I am very firmly in the camp of “dumb dynamic approaches/guided fuzzing”, I personally think there are some interesting properties that IL can offer to software testing. And no matter whether the engineering behind IL based tools ends up becoming as influential as other approaches, a novel way to think about formal reasoning in program analysis is always very exciting!" ]

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[ "#", null, "In AMS, the filiamentous carbon or \"graphite\" derived from a sample is compressed into a small cavity in an aluminum \"target\" which acts as a cathode in the ion source. The surface of the graphite is sputtered with heated, ionized cesium and the ions produced are extracted and accelerated in the AMS system. After acceleration and removal of electrons, the emerging positive ions are magnetically separated by mass and the 12C and 13C ions are measured in Faraday Cups where a ratio of their currents is recorded. Simultaneously the 14C ions are recorded in a gas ionization (USAMS) or solid state (CFAMS) detector, so that ratios of 14C to 13C and 12C may be recorded. These are the raw signals that are ultimately converted to a radiocarbon age.\n\nFrom a contemporary sample, about 250 14C counts per second are collected. It is expected then, for a 5,570 year (1 half-life) or 11,140 year old (2 half-lives) sample that 125 or 63 counts per second would be obtained. Although one can simply measure older samples for longer times, there are practical limits to the minimum sample activity that can be measured.  At the present time, for a 1 milligram sample of graphite, this limiting age is about ten half-lives, or 60,000 years, if set only by the sample size. However, limiting ages or \"backgrounds\" are also determined by process blanks which correspond to the method used to extract the carbon from the sample.\n\n## Process Blanks\n\nProcess blanks are radiocarbon-free material that is prepared using the same methods as samples and standards. These blanks contain small but measurable amounts of 14C from contamination introduced during chemical preparation, collection or handling. Organic materials, which require the most processing, are limited to younger ages by their corresponding process blank. Due to counting and measurement errors for the blanks and samples, statistical errors are higher for very old samples. Thus, ages are limited by the age of the process blanks (more on that below) and by the statistical uncertainty of the 14C measurement.\n\n## Blank corrected fraction modern\n\nFor large samples, the blank corrected fraction modern ($$Fm_c$$) is computed from the expression:\n\n$$Fm_c = Fm - Fm_b \\frac{Fm_s - Fm}{Fm_s}$$\n\nWhere $$Fm_b$$, $$Fm$$ and $$Fm_s$$ represent the 14C/12C ratios of the blank, the sample and the modern reference, respectively.\n\nFor small samples, blank contribution as a fraction of sample mass becomes a more important term, so a mass balance blank correction is applied. This correction is performed as follows:\n\n$$Fm_{mbc} = Fm_{corr} + ( Fm_{corr} - Fm_b)\\frac{M_b}{(M - M_b)}$$\n\nWhere $$M$$ is sample mass, and $$M_b$$ and $$Fm_b$$ are the mass and Fm of the blank.\n\nFraction Modern is a measurement of the deviation of the 14C/12C ratio of a sample from \"Modern.\" Modern is defined as 95% of the radiocarbon concentration (in AD 1950) of NBS Oxalic Acid I (SRM 4990B, OX-I) normalized to δ13CVPDB=-19 per mil (Olsson, 1970). AMS results are calculated using the internationally agreed upon definition of 0.95 times the specific activity of OX-I normalized to δ13CVPDB=-19 per mil. This is equialent to an absolute (AD 1950) 14C/12C ratio of 1.176 ± 0.010 x 10-12 (Karlen, et. al., 1968); all results are normalized to -25 per mil using the δ13CVPDB of the sample (see below). The value used for this correction is specified in the report of final results.\n\n## δ13C Correction\n\nIn addition to loss through decay of radiocarbon, 14C is also affected by natural isotopic fractionation. Fractionation is the term used to describe the differential uptake of one isotope with respect to another. While the three carbon isotopes are chemically indistinguishable, lighter 12C atoms are preferentially taken up before the 13C atoms in biological pathways. Similarly, 13C atoms are taken up before 14C. The assumption is that the fractionation of 14C relative to 12C is twice that of 13C, reflecting the difference in mass. Fractionation must be corrected for in order to make use of radiocarbon measurements as a chronometric tool for all parts of the biosphere. In order to remove the effects of isotopic fractionation, the Fraction Modern is then corrected to the value it would have if its original δ13C were -25 per mil (the δ13C value to which all radiocarbon measurements are normalized.) The fractionation correction is done using the 13/12 ratio measured by the AMS system. Using this measurement also corrects for any mass-dependent fractionation within the AMS system.\n\nThe Fraction Modern corrected for δ13C, Fmδ13C,\n\n$$Fm_{\\delta^{13}C}=Fm\\cdot\\left[\\frac{(1-25/1000)}{(1+\\delta^{13}C/1000)}\\right]^{2}$$\n\n## Errors\n\nThe 14C atoms contained in a sample are directly counted using the AMS method of radiocarbon analysis. Accordingly, we calculate an internal statistical error using the total number of 14C counts measured for each target ( $$error = \\frac{1}{\\sqrt{n}}$$ ). An external error is calculated from the reproducibility of multiple exposures for a given target. We measure the 14C /12C of a sample 10 separate times over the course of a run. The final reported error is the larger of the internal or external error, propagated with errors from the normalizing standards and blank subtraction.\n\nIt should be noted that the reported error is an estimate of the precision (repeatability) of measurement for a single sample. Due to variability in sample homogeneity, sample collection, and sample processing, the variability of replicate samples (reproducibility) is generally greater than the reported error for a single sample. A total measurement error can be estimated by adding in quadrature the reported error with this extra variability, or added variance. At NOSAMS, added variance is determined by pooling differences of measurements of secondary standards from consensus values of those standards. For calendar year 2016, the estimated added variance for samples of the process type OC (Organic Carbon) or HY (Hydrolysis) is 2.6‰ for samples containing > 100 ug C. For other sample types, e.g. sample submitted as gas samples, dissolved inorganic or organic samples, samples with mass < 100 ug C, or reconnaissance gas ion source samples, an estimated added variance has not been determined. For water or dissolved inorganic carbon (DIC) samples, for which no internationally accepted secondary standards exist, we note that analyses of shipboard duplicates, collected on every cruise, demonstrate a pooled standard deviation of 3.0‰. This would indicate that the added variance for these samples is similar to other types of sample measured at NOSAMS. While added variance may give a better estimate of the total error, the best way to determine total experimental error is by replicate sample analyses. If you are working near the limits of AMS precision, or have questions regarding error estimates, please consult with us.\n\nRadiocarbon age is calculated from the δ13C-corrected Fraction Modern according to the following formula:\n\nAge = -8033 ln (Fm)\n\nReporting of ages and/or activities follows the convention outlined by Stuiver and Polach (1977) and Stuiver (1980). Ages are calculated using 5568 years as the half-life of radiocarbon and are reported without reservoir corrections or calibration to calendar years. For freeware programs, we suggest that you look at the following web site for a list of programs that will calibrate radiocarbon results to calendar years (including making reservoir corrections).[ Radiocarbon-Related Information Sources]\n\nThe error in the age is given by 8033 times the relative error in the Fm . Therefore a 1% error in fraction-modern leads to an 80 year error in the age. Ages are rounded according to the convention of Stuiver & Polach, shown below.\n\n## Rounding Convention\n\n Age Nearest Error Nearest <1000 5 <100 5 1000-9999 10 100-1000 10 10000-20000 50 >1000 100 >20000 100\n\n## Limiting Ages\n\nThere are two situations that limit an age; the first is that the measured Fm is smaller than that of the corresponding process blank measured in the same suite of samples on the AMS. If this is the case, then the reported age will be quoted as an age greater than the age of the process blank. No age is reported greater than 60,000 years. The typical background age for organic combustions is 48,000 years and for inorganic carbon samples, 52,000 years.\n\nOne other situation that limits the age (if not already limited by the background age) is the error of the AMS result. If twice the reported error of the Fraction Modern (let's call this 2sigma) is larger than the sample Fraction Modern, then a limiting age is reported. The limiting age is then calculated as -8033 * ln(2sigma) and rounded according to conventions outlined above.\n\n## Age > Modern\n\nSince Modern is defined as 95% of the 14C activity for AD 1950, as defined by the oxalic acid standard, sample activities can be substantially greater than Modern, and so the ages are reported as > Modern.\n\n## Δ14C\n\nWe also report the Δ14C value as defined in Stuiver and Pollach (1977) as the relative difference between the absolute international standard (base year 1950) and sample activity corrected for age and δ13C. The Δ14C is age corrected to account for decay that took place between collection (or death) and the time of measurement so that two measurements of the same sample made years apart will produce the same calculated Δ14C result. Collection year must be specified in order for Δ14C results to be calculated.\n\n$$\\Delta ^{14}C = [ Fm * e^{\\lambda( 1950 - Y_{c}) } - 1 ]* 1000$$\n\nWhere lambda is 1/(true mean-life) of radiocarbon = 1/8267 = 0.00012097\nYc is year of collection.\n\n## References\n\nKarlen, I., Olsson, I.U., Kallburg, P. and Kilici, S., 1964. Absolute determination of the activity of two 14C dating standards. Arkiv Geofysik, 4:465-471.\n\nOlsson, I.U., 1970. The use of Oxalic acid as a Standard. In I.U. Olsson, ed., Radiocarbon Variations and Absolute Chronology, Nobel Symposium, 12th Proc., John Wiley & Sons, New York, p. 17.\n\nStuiver, M. and Polach, H.A., 1977. Discussion: Reporting of 14C data. Radiocarbon, 19:355-363. (pdf)\n\nStuiver, M., 1980. Workshop on 14C data reporting. Radiocarbon, 22:964-966.\n\nLast updated: April 5, 2018" ]

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[ "# Exponential equation - math word problems\n\n#### Number of problems found: 54\n\n• Exponential equation", null, "Solve exponential equation (in real numbers): 98x-2=9\n• Exponential equation", null, "In the set R solve the equation: ?\n• Exponential equation", null, "Find x, if 625 ^ x = 5 The equation is exponential because the unknown is in the exponential power of 625\n• Exponential equation", null, "Solve for x: (4^x):0,5=2/64.\n• Exponential equation", null, "Determine the value of having y in the expression (3^y): (4^-1)=36. Unknown y is a natural number greater than zero.\n• Log", null, "if ?, what is b?\n• Exp", null, "If ?, then n is:\n• Sequence", null, "Calculate what member of the sequence specified by ? has value 86.\n• One third power", null, "Which equation justifies why ten to the one-third power equals the cube root of ten?\n• Interest", null, "What is the annual interest rate on your account if we put 32790 and after 176 days received 33939.2?\n• Exponential warm", null, "Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degree\n• Coordinate", null, "Determine missing coordinate of the point M [x, 120] of the graph of the function f bv rule: y = 5x\n• Compound interest", null, "Calculate time when deposit in the bank with interest 2.5% p.a. doubles.\n• Car value", null, "The car loses value 15% every year. Determine a time (in years) when the price will be halved.\n• Geometric sequence", null, "In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.", null, "A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?", null, "After 548 hours decreases the activity of a radioactive substance to 1/9 of the initial value. What is the half-life of the substance?\n• What is", null, "What is the annual percentage increase in the city when the population has tripled in 20 years?\n• Geometric progression", null, "In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.\n• Demographics", null, "The population grew in the city in 10 years from 30000 to 34000. What is the average annual percentage increase of population?\n\nDo you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.\n\nWe will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.\n\nPlease do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc..." ]

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[ "Wednesday, 14 November 2018\n\nCHILLER CAPASITY CALCULATION PROCEDURE\n\nJust like refrigerator a chiller uses a refrigeration cycle to cool water or dehumidifies air. This chilled water then used to cool a larger space, such as a factory floor or for process uses. Cooling equipment in this matter increases its efficiency by providing a steady thermal environment. Before we begin to derive a chiller's capacity we must know three variables, they are:\n1. The incoming water temperature\n2. The chilled water (out going water) temperature required\n3. The flow rate\nThis formula produces the chiller's capacity in British Thermal Units (BTUs). That scale directly corresponds with the more common unit of \"tons\" that cooling systems often use.\nFor our example, we will calculate what size chiller is required to cool 60 GPM (gallons per minute) from 64 °F to 52 °F? Use the following five steps and general sizing formula:\n\n1. Calculate Temperature Differential (ΔT°F)\nSubtract the temperature of water as its leaves the chiller from the temperature of the water as it enters it.\nΔT°F = Incoming Water Temperature (°F) - Required Chilled Water Temperature.\n· Example: ΔT°F = 64°F - 52°F = 12°F\n\n2. Calculate BTU/hr. (British Thermal Unit/hr)\nThe cooling capacity of air conditioners is measured in BTUs, or British thermal units. The more Btu of capacity, the larger the room the air conditioner can cool. Scientifically, one Btu is the amount of energy required to change the temperature of 1 pound of water by 1 degree Fahrenheit. In terms of air-conditioner capacity, the rule of thumb is that it takes around 25 Btu to cool 1 square foot of room floor area.\nTo calculate BTU Multiply the temperature difference by the flow rate (that what we need), which is measured in gallons per minute. If, for instance,\nBTU/hr. = Gallons per hr x 8.33 x ΔT°F\n· Example: 60 gpm x 60 x 8.33 x 12°F = 3,59,856 BTU/hr.\n(Or)\n· 40 gpm x 500 x 12°F = 3,59,856 BTU/hr.  (since 60 x 8.333 = 500)\n\n3. Calculate tons of cooling capacity\nTons = BTU/hr. ÷ 12,000\n· Example: Ton capacity = 239,904 BTU/hr. ÷ 12,000 = 29.998 tons\n1 ton = 12000 BTU\n\n4. Oversize the chiller by 20%\nIdeal Size in Tons = Tons x 1.2\n· Example: 29.998 x 1.2 = 35.9976\n\n5. You have the ideal size for your needs\n· Example: a 35.9976 (or 35-Ton) chiller is required" ]

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[ "", null, "# Using null strain energy functions in compressible finite elasticity to generate exact solutions\n\nHaughton, D.M. (2008) Using null strain energy functions in compressible finite elasticity to generate exact solutions. Zeitschrift für Angewandte Mathematik und Physik, 59(4), pp. 730-749.\n\nFull text not currently available from Enlighten.\n\nPublisher's URL: http://dx.doi.org/10.1007/s00033-006-6062-y\n\n## Abstract\n\nIn this paper we characterize those strain energy functions in unconstrained nonlinear elasticity that satisfy the equations of equilibrium identically. The idea is to construct a useful, physically reasonable strain–energy function containing one or more components which are null, in such a way that exact solutions may be obtained from the resulting equilibrium equations. We show that the dilatation is a universal null energy while there may be others that depend on the actual problem. To obtain the null energies for a given problem it is often convenient to formulate the variational problem and look at the Euler–Lagrange equations. Specific examples are used to illustrate some of the potential uses of the method in finding exact solutions for physically meaningful constitutive models.\n\nItem Type: Articles Null, Lagrangian, elastic, exact, nonlinear Published Yes Haughton, Dr David Haughton, D.M. Q Science > QA Mathematics College of Science and Engineering > School of Mathematics and Statistics > Mathematics Zeitschrift für Angewandte Mathematik und Physik Z. Angew. Math. Phys. SP Birkhäuser Verlag Basel 0044-2275 1420-9039 26 February 2007\n\nUniversity Staff: Request a correction | Enlighten Editors: Update this record" ]

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[ "# Evaluate Using Scientific Notation (5.8*10^-6)÷(2*10^-3)", null, "Rewrite the division as a fraction.\nDivide using scientific notation.\nGroup coefficients together and exponents together to divide numbers in scientific notation.\nDivide by .\nSubtract the exponent from the denominator from the exponent of the numerator for the same base\nMultiply by ." ]

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[ "", null, "", null, "# Alaba\n\nMembers\n\n7\n\n## Alaba's Achievements", null, "0\n\n### Reputation\n\n1. So Should the digital discrete-event side set the default state of the control in its initialization ?\n2. sca_eln::sca_de_rswitch sw0; SC_CTOR(mod): sw0(\"sw0\",R_on,R_off ,off_state0) sw0.p(p); sw0.n(n); sw0.off_state =off_state1; sw0.ctrl(ctrl); From documentation : if we assume off_state1 = true sw0.off_state sets the boolean state that correspond to the switch off_state. in this case off_state is set to true, which means when the value of \"ctrl\" is true it will switch to R_off My question is, how to set the default state of the sw0 ? The argument \"off_state0\" , also sets the off_state boolean value, but it does not set the default state of the switch at initialization. Is it always set to Ron by default? I could not find it in the documentation. Thanks\n3. Thanks Maehne for the high level design, and the references I will try to implement it, and post it here\n4. Hello I 'm trying to create an nxn array (nested vectors) of an rc component, with each having different r,c values ex: rc (r=10,c=5), rc (r=3,c=4)..... I've created the rc sub module that take the values of R and C as arguments, As follows: SC_MODULE (rc){ sca_eln::sca_terminal n; sca_eln::sca_terminal p; sca_eln::sca_r r1; sca_eln::sca_c c1; sca_eln::sca_node n1; rc( sc_core::sc_module_name nm , double r0_,double c0_) :p(\"p\"),n(\"n\"), r1(\"r1\"),c1(\"c1\"), r0(r0_),c0(c0_) { r1.p(p); r1.n(n1); r1.value=r0; c1.p(n1); c1.n(n); c1.value=c0; } private: double r0; double c0; }; I have found the following post that shows how to initialize 1D vector so I customized my module accordingly ,which a follows #include <systemc> #include <systemc-ams> using namespace sc_core; SC_MODULE (rc){ sca_eln::sca_terminal n; sca_eln::sca_terminal p; sca_eln::sca_r r1; sca_eln::sca_c c1; sca_eln::sca_node n1; rc( sc_core::sc_module_name nm , double r0_,double c0_) :p(\"p\"),n(\"n\"), r1(\"r1\"),c1(\"c1\"), r0(r0_),c0(c0_) { r1.p(p); r1.n(n1); r1.value=r0; c1.p(n1); c1.n(n); c1.value=c0; } private: double r0; double c0; }; struct create_mod { double m_arg1; double m_arg2; create_mod(double arg1, double arg2) : m_arg1(arg1), m_arg2(arg2) {} rc* operator()(const char* name, size_t) { return new rc(name, m_arg1, m_arg2); } }; SC_MODULE (rc_tb){ rc rc0; rc_tb( sc_core::sc_module_name nm ):rc0(\"rc0\",1.0,1.0) { unsigned int num_of_rcs = 4; unsigned int r_value = 5, c_value = 4; sc_vector<rc> vec_rc(\"mods\"); vec_rc.init(num_of_rcs, create_mod( r_value, c_value)); //... connect nodes } }; Now the code works But it is only for 1D array This method also forces me to set same argument values for all the initialized submodules ( vec_rc.init(num_of_rcs, create_mod( r_value, c_value)); ). So my 2 questions are 1- How to make it a 2D vectors ? 2- How to initialize each component with specific RC values? I also have tried the code suggested in to make a 2D nested vectors but I failed I don't mind using either methods as long as it does the job. It will be nice if I use lambda function also Thanks in advance RF\n5. I get same problem for same value of N with system of 32GB RAM and 8GB Ram\n6. Hello there, I'm building a system that includes a large number of resistors. I used sc_vector of elements and nodes, as I increase the number of resistors I get segmentation error. The below example is a simpler form of my code that also gives the same error In the code below if I use small value of N: ( N=10000): I get the right result but for N=1048576: //(large N) I get: Segmentation fault (core dumped) ------------------------------------------------------resistors in series module---------------- // p- r0-r1-r2-r3...rN -n static const int N=1048576; sca_eln::sca_terminal n; sca_eln::sca_terminal p; sc_vector< sca_eln::sca_node > c_vec{\"c_vec\", N }; //nodes beteen resistors sc_vector<sca_eln::sca_r> rs_vec{\"rs_vec\", N }; SC_CTOR(rmatnn): p(\"p\"),n(\"n\") // { rs_vec.p(p); //connect p port of first resistor to main p port rs_vec.n(c_vec); //connect n port of first resistor to nod 0 rs_vec[0 ].value=10; for (int i = 1; i < N-1; i++) { rs_vec[i ].p(c_vec[i-1]); rs_vec[i ].n(c_vec[i]); rs_vec[i ].value=10; } rs_vec[N-1 ].p(c_vec[N-2]); rs_vec[N-1 ].n(n); rs_vec[N-1 ].value=10; } }; Is there any limitations on the number of modules we use for the simulation?? Thanks in advance\n7. I just modified the two header files before reading your comment :) scams/impl/predefined_moc/tdf/sca_tdf_ct_ltf_nd_proxy.h scams/impl/predefined_moc/tdf/sca_tdf_ct_vector_ss_proxy.h by adding #include<string.h> and it compiled fine I'm runing xubuntu 17.10 thanks\n×" ]

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[ "# How to find out which object is taking space?\n\nI have database of size 537gb. How can I find out which object is taking space. I executed sp_spaceused, which showed me unallocated space is 502GB and 88GB used space. How can I release unallocated space to get some free space. My HDD is getting full due to this. Please advise.\n\nEdit: I have checked via below script as well. But total UsedSpaceMB of each table is 47GB. Still I am unable to figure out how DB size is 537 GB.\n\n``````SELECT t.NAME AS TableName, s.Name AS SchemaName, p.rows AS RowCounts, SUM(a.total_pages) * 8 AS TotalSpaceKB, CAST(ROUND(((SUM(a.total_pages) * 8) / 1024.00), 2) AS NUMERIC(36, 2)) AS TotalSpaceMB, SUM(a.used_pages) * 8 AS UsedSpaceKB, CAST(ROUND(((SUM(a.used_pages) * 8) / 1024.00), 2) AS NUMERIC(36, 2)) AS UsedSpaceMB, (SUM(a.total_pages) - SUM(a.used_pages)) * 8 AS UnusedSpaceKB, CAST(ROUND(((SUM(a.total_pages) - SUM(a.used_pages)) * 8) / 1024.00, 2) AS NUMERIC(36, 2)) AS UnusedSpaceMB\nFROM sys.tables t\nINNER JOIN sys.indexes i\nON t.OBJECT_ID = i.object_id\nINNER JOIN sys.partitions p\nON i.object_id = p.OBJECT_ID\nAND i.index_id = p.index_id\nINNER JOIN sys.allocation_units a\nON p.partition_id = a.container_id\nLEFT OUTER JOIN sys.schemas s\nON t.schema_id = s.schema_id\nWHERE t.NAME NOT LIKE 'dt%'\nAND t.is_ms_shipped = 0\nAND i.OBJECT_ID > 255\nGROUP BY t.Name, s.Name, p.Rows\nORDER BY 7 DESC\n``````", null, "It appears that your database data file has empty space.\n\nIf you know for sure that the data file will not grow out again, you could shrink the file.\n\nIf you have to shrink, the cleanest way is doing this with `TRUNCATEONLY` so you don't move any data pages and only release the space back to the OS if it is possible.\n\nYou can get the data file(s) with this query, change the databasename to your database.\n\n``````SELECT [name]\nFROM sys.master_files\nWHERE database_id = db_id('DatabaseName')\nAND type_desc = 'ROWS';\n``````\n\nAfterwards you could try shrinking the data page until 100GB without any movement.\n\n``````Use [DatabaseName]\nGO\nDBCC SHRINKFILE ('name',102400 ,TRUNCATEONLY);\n-- try to shrink until 100GB, without moving data pages\n``````\n\nYou can read up on shrinking date files and...\n\n• why it sucks here\n• why it's bad for performance here\n\nYou can use a script something like this to find tables and their sizes:\n\n`````` SELECT name = OBJECT_SCHEMA_NAME(object_id) + '.' + OBJECT_NAME(object_id),\nrows = SUM(CASE\nWHEN index_id < 2\nTHEN row_count\nELSE 0\nEND),\nreserved_mb = 8 * SUM(reserved_page_count) / 1024,\ndata_mb = 8 * SUM(CASE\nWHEN index_id < 2\nTHEN in_row_data_page_count + lob_used_page_count + row_overflow_used_page_count\nELSE lob_used_page_count + row_overflow_used_page_count\nEND) / 1024,\nindex_mb = 8 * (SUM(used_page_count) - SUM(CASE\nWHEN index_id < 2\nTHEN in_row_data_page_count + lob_used_page_count + row_overflow_used_page_count\nELSE lob_used_page_count + row_overflow_used_page_count\nEND)) / 1024,\nunused_mb = 8 * SUM(reserved_page_count - used_page_count) / 1024\nFROM sys.dm_db_partition_stats\nWHERE object_id > 1024\nGROUP BY object_id\nORDER BY reserved_mb DESC;\n``````\n\nThe fastest and simplest way is using a standard report. Right click on the database:", null, "" ]

[ null, "https://i.stack.imgur.com/w1AP2.png", null, "https://i.stack.imgur.com/B9M4a.png", null ]

[ "## Worksheet Mole Problems Answer Key", null, "Worksheet Mole Problems Answer Key. Mole conversion practice problems worksheet with answers it is a noun when a word is used to describe something, such as an individual, location, things, or principle. How many molecules are there in 450 grams of na2s04.\n\nBoth sides have the same number of moles of gases so there will be no shift in the equilibrium. 1 cl 2 71 g mol 2 koh 56 1 g mol 3 becl 2 80 g mol 4 fecl 3 162 3 g mol 5 bf 3 67 8 g mol 6. It’s a word made use of to describe any person, something, or something else in the most standard sense.\n\n### 2 Moles Of No Will React With Mole S Of O 2 To Produce Mole S Of No 2.\n\nPlace your final answer in the formula mass column. Worksheet mole mole problems answer key. 2141 grams 5 how many moles are in 2 3 grams of phosphorus.\n\n### When Talking Or Writing In English, A Strong Understanding Of Grammar Is Essential.\n\n5 moles of na how many moles of cl 2 will be consumed. The results for mole ratio practice worksheet answer key. 7 6a key part 1.\n\n### 1 Mol G Formula Mass Periodic Table 1 Mol 22 4 L For A Gas At Stp.\n\nAtoms sn 3 50 mol sn. Molar mass worksheet answer key calculate the molar masses of the following chemicals. Moles and mass 2 worksheet answers.\n\n### Molar Mass Use The Periodic Table To Find The Molar Masses Of The Following.\n\nAd bring learning to life with thousands of worksheets, games, and more from education.com. Both sides have the same number of moles of gases so there will be no shift in the equilibrium. Molarity practice problems answer key 1 how many grams of potassium carbonate are needed to make 200 ml of a 2 5 m solution.\n\n### Hcl K 2Co 3 Ca(Oh) 2 Na 3Po 4 Part 2:\n\nMole to mole practice problems. Several countries use it as their official language. Atoms sn = 3.50 mol sn !" ]

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[ "# position_jitterx: Jitter points to avoid overplotting, and the whole points can... In YuLab-SMU/ggtreeExtra: An R Package To Add Geometric Layers On Circular Or Other Layout Tree Of \"ggtree\"\n\n position_jitterx R Documentation\n\n## Jitter points to avoid overplotting, and the whole points can be shifted vertically or horizontally\n\n### Description\n\nThis is the extension of 'position_jitter' of ggplot2, points are randomly shifted up and down and/or left and right. In addition, the whole points layer can be shifted by the 'hexpand' or 'vexpand' parameter. Counterintuitively adding random noise to a plot can sometimes make it easier to read. Jittering is particularly useful for small datasets with at least one discrete position.\n\n### Usage\n\n```position_jitterx(\nwidth = NULL,\nheight = NULL,\nhexpand = NA,\nvexpand = NA,\nseed = NA\n)\n```\n\n### Arguments\n\n `width, height` Amount of vertical and horizontal jitter. The jitter is added in both positive and negative directions, so the total spread is twice the value specified here. If omitted, defaults to 40% of the resolution of the data: this means the jitter values will occupy 80% of the implied bins. Categorical data is aligned on the integers, so a width or height of 0.5 will spread the data so it's not possible to see the distinction between the categories. `hexpand, vexpand` The distance to be shifted vertically or horizontally, default is NA. `seed` A random seed to make the jitter reproducible. Useful if you need to apply the same jitter twice, e.g., for a point and a corresponding label. The random seed is reset after jittering. If `NA` (the default value), the seed is initialised with a random value; this makes sure that two subsequent calls start with a different seed. Use `NULL` to use the current random seed and also avoid resetting\n\n### Examples\n\n```library(ggtree)\nlibrary(treeio)\nlibrary(ggplot2)\nset.seed(1024)\ntr <- rtree(10)\n\ndf <- data.frame(id=tr\\$tip.label, group=rep(c(\"A\", \"B\"),5))\ndat <- data.frame(id=rep(tr\\$tip.label, 8), value=rnorm(80, 0.5, 0.15))\ndt <- merge(dat, df, by.x=\"id\", by.y=\"id\")\np1 <- ggtree(tr) %<+% df +\ngeom_tiplab(\nalign=TRUE,\nlinesize=.1,\nsize=3\n)\n\ngf1 <- geom_fruit(data=dat,\ngeom=geom_boxplot,\nmapping=aes(x=value, y=id),\norientation=\"y\",\noffset=0.1,\npwidth=0.9\n\n)\nset.seed(1024)\ngf2 <- geom_fruit(\ndata=dat,\ngeom=geom_point,\nmapping=aes(x=value, y=id, color=group),\noffset=0.1,\npwidth=0.9,\nposition= position_jitterx(height=0.3),\naxis.params=list(axis=\"x\", text.size=2),\ngrid.params=list()\n)\n\np2 <- p1 + geom_fruit_list(gf1, gf2)\np2\n```\n\nYuLab-SMU/ggtreeExtra documentation built on July 12, 2022, 8:44 p.m." ]

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[ "# Math Insight\n\n### Cross sections of a surface\n\nIn general, the graph of an equation involving three variables is a surface that is floating in three dimensions. If one can write the equation in the form $z=f(x,y)$, then the surface is the graph of the function $f(x,y)$. Otherwise, the surface can be viewed as being defined implicitly from the equation.\n\nUnfortunately, the plot of a surface in three dimensions is more difficult to draw and visualize that plots of curves in two dimensions. We can often get insight into a surface by making a series of plots of curves in two dimensions. One way to do this is to plot level curves. If the surface is the graph of a function $z=f(x,y)$, then by fixing the variable $z$ to a single value $z=c$, one obtains a level curve of the function $c=f(x,y)$.\n\nCross sections are generalizations of level curves to holding any one of the three variables $x$, $y$, or $z$ fixed. One can take cross sections of surfaces defined implicitly as well as graphs of functions. We often refer to the cross sections where $z$ is fixed as horizontal cross sections (for graphs of functions, we can call them level curves). We often refer to cross sections where either $x$ or $y$ is fixed as vertical cross sections.\n\nFor example, consider the following equation of a sphere of radius 2: $$x^2 + y^2 + z^2= 4.$$ To examine a cross section, we choose a value for one of the three variables, say $z=0$. Using that value, we take a look at the resulting new equation: $$x^2 + y^2 + 0^2 = 4, \\qquad \\text{or} \\qquad x^2 + y^2 = 4.$$\n\nYou should recognize this as a circle of radius 2, centered at the point $(x,y)=(0,0)$. In other words, the intersection of the plane $z=0$ and the sphere $x^2 + y^2 + z^2 = 4$ is a circle of radius 2. A more intuitive way to think about this is that you take a big meat cleaver and chop the sphere where $z=0$. If you take one of the resulting half-spheres, what does the edge look like? A circle of radius two.\n\nThe below picture is an illustration of this cross section. You can see where the plane $z=0$ slices through the sphere.", null, "Cross section of a sphere. The blue curve on the sphere illustrates the cross section $z=0$ on the unit sphere $x^2+y^2+z^2=0$. This cross section is a circle $x^2+y^2=1$.\n\nThis method can help you figure out what surfaces look like. It is particularly nice for the quadric surfaces, as the cross sections are all familar conic sections. When you put together the cross sections for $x$, $y$, and $z$, you develop a picture of the surface." ]

[ null, "https://mathinsight.org/media/applet/image/large/cross_section_sphere.png", null ]

[ "## Alg Matrix scripts\n\n#### Matrix vector multiplication\n\n... 'reduce' and 'map', this code shows how a matrix vector multiplication can be reduced to a single loop. ...\n\n#### IPF\n\nIPF allows one to find a matrix S, close to an input matrix T, but such that the row sums of ... useful in a range of tasks like traffic matrix problems, statistics for examining independence assumptions in contingency tables, ...\n\n#### Basic Linear Algebra Matrix\n\nThis script defines the Matrix class, an implementation of a linear algebra matrix. Arithmetic operations, trace, determinant, and minors are defined for it. This is a lightweight alternative to a numerical Python package for people who need to do basic linear algebra. ...\n\n#### A Proposal for the Resolution of Lyapunov Matrix\n\n... to get the solution of A'P PA=-Q, Lyapunov matrix equarion, by using BAck Deletion Method, or any method designeg for solving typical matrix equation of the kinf Ax=b.These m-files were developed and extensely used by author some years ago, when Matlab package did not offered the its ...\n\n#### The Matrix Text effect\n\nThis DHTML script renders the Matrix effect on any short piece of text. It works in both IE4 and NS6 , and downgrades well with the rest. ...\n\n#### corrcof\n\nCORRCOF computes correlation matrix of observation datas from cofactor matrix of residuals .Qvv=corrcof(A,P) INPUTS :Design Matrix (A) and Weight Matrix of observations(P).OUTPUT: The Correlation Matrix (RO) Requirements: · MATLAB Release: R13 ...\n\n#### Sparse\n\n'sparse' is a matrix class based on a dictionary to store data ... row and j the column index). The common matrix operations such as 'dot' for the inner product, multiplication/division by a scalar, indexing/slicing, etc. are overloaded for convenience.When used in conjunction with the 'vector' class, 'dot' products also apply ...\n\n#### a QR Code\n\nQR codes are two dimensional matrix codes. Installation Unpack and upload it to the /wp-content/plugins/ directory. Activate the plugin through the 'Plugins' menu in WordPress. Requirements: · WordPress 2.5.0 or higher ...\n\n#### tvmet\n\nTiny Vector and Matrix template library uses Meta Templates (MT) and Expression ... to preserve the mathematical meaning. - vector, matrix, matrix-matrix and matrix-vector fast operations ...\n\n#### z matrix\n\nThis module provides two classes that emulate one and two dimentional lists with fixed sizes but mutable internals. Their primary purpose is to be used as a building tool for classes that need storage structures that cannot change in size. ..." ]

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[ "## boxplot on a formula:\nboxplot(count ~ spray, data = InsectSprays, col = \"lightgray\")", null, "# *add* notches (somewhat funny here <--> warning \"notches .. outside hinges\"):\nboxplot(count ~ spray, data = InsectSprays, col = \"lightgray\")\nboxplot(count ~ spray, data = InsectSprays,\nnotch = TRUE, add = TRUE, col = \"blue\")\n## Warning in bxp(list(stats = structure(c(7, 11, 14, 18.5, 23, 7, 12, 16.5, :\n## some notches went outside hinges ('box'): maybe set notch=FALSE", null, "boxplot(decrease ~ treatment, data = OrchardSprays, col = \"bisque\",\nlog = \"y\")", null, "## horizontal=TRUE, switching y <--> x :\nboxplot(decrease ~ treatment, data = OrchardSprays, col = \"bisque\",\nlog = \"x\", horizontal=TRUE)", null, "rb <- boxplot(decrease ~ treatment, data = OrchardSprays, col = \"bisque\")\ntitle(\"Comparing boxplot()s and non-robust mean +/- SD\")\nmn.t <- tapply(OrchardSprays$decrease, OrchardSprays$treatment, mean)\nsd.t <- tapply(OrchardSprays$decrease, OrchardSprays$treatment, sd)\nxi <- 0.3 + seq(rb$n) points(xi, mn.t, col = \"orange\", pch = 18) arrows(xi, mn.t - sd.t, xi, mn.t + sd.t, code = 3, col = \"pink\", angle = 75, length = .1)", null, "## boxplot on a matrix: mat <- cbind(Uni05 = (1:100)/21, Norm = rnorm(100), 5T = rt(100, df = 5), Gam2 = rgamma(100, shape = 2)) boxplot(mat) # directly, calling boxplot.matrix()", null, "## boxplot on a data frame: df. <- as.data.frame(mat) par(las = 1) # all axis labels horizontal boxplot(df., main = \"boxplot(*, horizontal = TRUE)\", horizontal = TRUE)", null, "## Using 'at = ' and adding boxplots -- example idea by Roger Bivand : boxplot(len ~ dose, data = ToothGrowth, boxwex = 0.25, at = 1:3 - 0.2, subset = supp == \"VC\", col = \"yellow\", main = \"Guinea Pigs' Tooth Growth\", xlab = \"Vitamin C dose mg\", ylab = \"tooth length\", xlim = c(0.5, 3.5), ylim = c(0, 35), yaxs = \"i\")", null, "## Using 'at = ' and adding boxplots -- example idea by Roger Bivand : boxplot(len ~ dose, data = ToothGrowth, boxwex = 0.25, at = 1:3 - 0.2, subset = supp == \"VC\", col = \"yellow\", main = \"Guinea Pigs' Tooth Growth\", xlab = \"Vitamin C dose mg\", ylab = \"tooth length\", xlim = c(0.5, 3.5), ylim = c(0, 35), yaxs = \"i\") boxplot(len ~ dose, data = ToothGrowth, add = TRUE, boxwex = 0.25, at = 1:3 + 0.2, subset = supp == \"OJ\", col = \"orange\") legend(2, 9, c(\"Ascorbic acid\", \"Orange juice\"), fill = c(\"yellow\", \"orange\"))", null, "## With less effort (slightly different) using factor *interaction*: boxplot(len ~ dose:supp, data = ToothGrowth, boxwex = 0.5, col = c(\"orange\", \"yellow\"), main = \"Guinea Pigs' Tooth Growth\", xlab = \"Vitamin C dose mg\", ylab = \"tooth length\", sep = \":\", lex.order = TRUE, ylim = c(0, 35), yaxs = \"i\")", null, "boxplot(mpg ~ cyl, data = mtcars, col = \"lightgray\", varwidth = TRUE, main = \"mpg vs cylinders\", ylab = \"mpg\",xlab = \"cylinders\")", null, "fivenum(mtcars$mpg) # the numbers used to create the boxplot\n## 10.40 15.35 19.20 22.80 33.90" ]

[ null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", null, 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", 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[ " Matrix eQTL test code for simple linear regression\n\n# Multi-Tissue eQTL code, part 2/4\n\n## Combine results across tissues in one matrix of z-scores\n\nAfter applying Matrix eQTL and recording the results for GTEx data we get 10 files. Nine files named like `eQTL_results_AL_Adipose_cis.txt` contain Matrix eQTL output for each respective tissue. The last file `df.txt` keeps information about tissue names and the number of degrees of freedom for each tissue, such as:\n\nAdipose73\nArtery91\nBlood135\nHeart62\nLung98\nMuscle117\nNerve67\nSkin75\nThyroid84\n\nThe code below takes these files and creates a big matrix of z-scores with each row containing informaiton for a particular gene-SNP pair and each column for a particular tissue. It prodices 3 files:\n\n`z-score.matrix.Rdata` R data file with the big matrix of z-scores\n`z-score.matrix.genes.txt` text file with gene names for the rows of the big matrix\n`z-score.matrix.snps.txt` text file with SNP names for the rows of the big matrix\n\n## The code:\n\n`### Read df.txt for the list of tissues### and degrees of freedom of linear modelsdf = read.table(\"df.txt\", stringsAsFactors=FALSE);names(df) = c(\"tissue\", \"df\");show(df)### List vector for storing Matrix eQTL resultsbig.list = vector(\"list\", nrow(df));### Store gene and SNP names from the first tissue### for matching with other tissuesgenes = NULL;snps = NULL;### colClasses for faster reading of Matrix eQTL outputcc.file = NA;### Loop over tissuesfor(t1 in 1:nrow(df) ) {     ### Get tissue name  tissue = df\\$tissue[t1];    ### Load Matrix eQTL output for the given tissue  start.time = proc.time();  tbl = read.table(paste0(\"eQTL_results_AL_\",tissue,\"_cis.txt\"),                    header = T, stringsAsFactors=FALSE, colClasses=cc.file);  end.time = proc.time();  cat(tissue, \"loaded in\", end.time - start.time, \"sec.\", nrow(tbl), \"gene-SNP pairs.\", \"\\n\");  ### set colClasses for faster loading of other results  if(any(is.na(cc.file))) {    cc.file = sapply(tbl, class);  }  ### Set gene and SNP names for matching  if(is.null(snps))    snps = unique(tbl\\$SNP);  if(is.null(genes))    genes = unique(tbl\\$gene);      ### Match gene and SNP names from Matrix eQTL output  ### to \"snps\" and \"genes\"  gpos = match(tbl\\$gene, genes, nomatch=0L);  spos = match(tbl\\$SNP,  snps,  nomatch=0L);    ### Assign each gene-SNP pair a unique id for later matching with other tissues  id = gpos + 2*spos*length(genes);    ### Transform t-statistics into correlations  r = tbl\\$t.stat / sqrt(df\\$df[t1] + tbl\\$t.stat^2);  ### Record id's and correlations  big.list[[t1]] = list(id = id, r = r);    ### A bit of clean up to reduce memory requirements  rm(tbl, gpos, spos, r, id, tissue, start.time, end.time);  gc();}rm(t1, cc.file);### Find the set of gene-SNP pairs ### present in results for all tissueskeep = rep(TRUE, length(big.list[]\\$id));for(t1 in 2:nrow(df)) {  mch = match(big.list[]\\$id, big.list[[t1]]\\$id, nomatch=0L);  keep[ mch == 0] = FALSE;  cat(df\\$tissue[t1], \", overlap size\", sum(keep), \"\\n\");}final.ids = big.list[]\\$id[keep];rm(keep, mch, t1);### Create and fill in the matrix of z-scores### Z-scores are calculated from correlationsbig.matrix = matrix(NA_real_, nrow=length(final.ids), ncol=nrow(df));fisher.transform = function(r){0.5*log((1+r)/(1-r))};for(t1 in 1:nrow(df)) {  mch = match(final.ids,  big.list[[t1]]\\$id);  big.matrix[,t1] = fisher.transform(big.list[[t1]]\\$r[mch]) * sqrt(df\\$df[t1]-1);  cat(t1,\"\\n\");}stopifnot( !any(is.na(big.matrix)) )rm(t1, mch);### Save the big matrixsave(list=\"big.matrix\", file=\"z-score.matrix.Rdata\", compress=FALSE);### Save gene names and SNP names for rows of big matrixwriteLines(text=genes[final.ids %% (length(genes)*2)], con=\"z-score.matrix.genes.txt\")writeLines(text=snps[final.ids %/% (length(genes)*2)], con=\"z-score.matrix.snps.txt\")`\n\n→ Next step: Estimate the model parameters.\n\nBy Andrey Shabalin" ]

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