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[Journal of mathematics at home University] 250th questions about the Postgraduate Entrance Exam of mathematics analysis at the University of Chinese Emy of Sciences in 2013

) = \ int_0 ^ x F (x-T) \ sin t \ rd t = \ int_0 ^ x F (s) \ sin (X-S) \ RD s \ EEx $ Zhi $ \ Bex G' (x) = \ int_0 ^ x F (s) \ cos (X-S) \ rd s, \ quad g'' (x) = f (x)-\ int_0 ^ x F (s) \ sin (X-S) \ rd s. \ EEx $ then $ \ Bex g'' + G = F, \ quad g (0) = G' (0) = 0. \ EEx $ 3 ($ 15' $) calculates the maximum curvature of the curve $ Y = e ^ x $. Answer: curvature $ \ Bex \ Kappa (x) = \ frac {y''} {(1 + y' ^ 2) ^ {3/2 }}=\ frac {e ^ x} {(1 + e ^ {2x}

How to draw an ellipse on canvas

beziercurveto Curve Since I think the scaling method above is not accurate, I really want to find a precise method for drawing an ellipse. Finally, I found it on stackoverflow: Function Drawellipse (CTX, X, Y, W, h ){ VaR Kappa = 0.5522848 ; Ox = (W/2) * kappa,// Control Point offset horizontal Oy = (H/2) * kappa, // Control Point offset vertical Xe = x +

Disposition of special characters in XML

"), str = Str.replaceall ("Delta;", "Δ"), str = Str.replaceall ("Epsilon;" , "Ε"), str = Str.replaceall ("Zeta;", "Ζ"), str = Str.replaceall ("Eta;", "Η"), str = Str.replaceall ("Theta;" , "Θ"), str = Str.replaceall ("Iota;", "Ι"), str = Str.replaceall ("Kappa;", "Κ"); str = Str.replaceall (" Lambda, "," Λ "), str = Str.replaceall (" Mu; "," Μ "), str = Str.replaceall (" Nu; "," Ν "); str = Str.replaceall (" Xi; "," Ξ "); str = Str.replaceall (" Omic

Use Python to convert the mid and url of Sina Weibo (10 hexadecimal and 62 hexadecimal) instances)

When using Sina Weibo APIs, we sometimes need to get a Weibo url, but the Weibo status field obtained from interfaces such as statusespublic_timeline does not include any, status contains a mid field. we can calculate the url through mid. Before starting the calculation, it is necessary to describe what is base62 encoding. It is actually an interchange between decimal and 62-digit. For the 62-digit system, after the value ranges from 0 to 9, 10 is represented by the lowercase letter a, followed

Use Python to convert the mid and url of Sina Weibo (10 hexadecimal and 62 hexadecimal) instances)

However, status contains a mid field. We can actually obtain the url through mid calculation. Before starting the calculation, it is necessary to describe what is base62 encoding. It is actually an interchange between decimal and 62-digit. For the 62-digit system, after the value ranges from 0 to 9, 10 is represented by the lowercase letter a, followed by 26 letters, and z is 35. Then 36 is the capital letter, until 61 is the capital letter Z. Therefore, we can implement the encode and decode en

Use Python to convert the mid and URL of Sina Weibo to each other (10 binary and 62 binary)

However, the status contains a mid field, and through mid we can actually get the URL by calculating it. It is necessary to explain what is BASE62 encoding before starting the calculation. It is actually the interchange of decimal and 62-bit binary. For 62 binary, from 0 to 9, 10 is denoted by a lowercase letter A, followed by 26 letters, to Z 35, then 36 to uppercase A, and to 61 for capital Letter Z. So, we can implement the decimal number BASE62 encoded encode and decode. The following code

Use Python for the mid and URL conversion instances of Sina Weibo (10-in and 62-binary) _python

However, the status contains a mid field that, through mid, we can actually compute to get the URL. It is necessary to explain what the BASE62 encoding is before starting the calculation. It is actually a decimal and 62-bit binary interchange. For 62 binary, from 0 to 9, 10 is represented in lowercase a, followed by 26 letters, to Z 35, then 36 to uppercase A, until 61 is capital Letter Z. So, we can implement decimal digit base62 encoding encode and decode. The following code actually comes fr

Python Standard library 3.4.3-random

slightly faster than the normalvariate () function defined below. Random. lognormvariate ( mu, Sigma ) Log normal distribution. If you take the natural logarithm of this distribution, you'll get a normal distribution with mean mu and Standar D deviation Sigma. Mu can has any value, and Sigma must is greater than zero. Random. normalvariate ( mu, Sigma ) Normal distri

Distance of understanding (Mathematics)

Central Moment, if defined, of zero. the normalized third central moment is called The skewness, often Gamma. A distribution that is skewed to the left (the tail of the distribution is heavier on the left) will have a negative skewness. A distribution that is skewed to the right (the tail of the distribution is heavier on the right), will have a positive skewness. For distributions that are not too different from the normal distribution, the median will be somewhere near μ−γ σ/6; the mode about

[Journal of mathematics, jiaricang University] 055th image filtering model of direction Diffusion

}\\\\frac {I _y ^ 2I _ {XX}-2i_xi_yi _ {XY} + I _x ^ 2I _ {YY }{| \ n I | ^ 2 }. \ EEx $ \ bee \ label {1: df_xy} I _t = \ frac {I _y ^ 2I _ {XX}-2i_xi_yi _ {XY} + I _x ^ 2I _ {YY} {| \ n I | ^ 2 }. \ EEE $ notice $ I $ level set $ \ Bex \ Chi _ \ Lambda (I) =\ sed {(x, y ); \ I (x, y) \ geq \ Lambda} \ EEx $ suitable for $ \ Bex \ lambda_1 \ Leq \ lambda_2 \ Ra \ Chi _ {\ lambda_2} (I) \ subset \ Chi _ {\ lambda_1} (I ), \ EEx $ a normal vector of curves with $ {\ BF \ Xi} $ in the tangent dir

R-Basic statistical analysis-ch7

testing, the original assumption being that two nominal variables are conditionally independent in each layer of the third variable. The following code can test the treatment and improve the situation at each level of gender independence. This test assumes that there is no third-order interaction (Treatment condition x Improvement x sex).(3) Measurement of relevanceThe Assocstats () function in the VCD package is used to calculate the Phi coefficient, column contact number, and Cramer ' s v coe

8 tactics to Combat imbalanced Classes on Your machine learning Dataset

breastcancer in patients.From, Post,i recommend looking at the following performance measures, can give moreinsight into the accuracy of th E model than traditional classificationaccuracy: Confusion Matrix: A breakdown of predictions into a table showing correctpredictions (the diagonal) and the types of incorrect predictions made (whatclasses incorrect predictions were assigned). Precision: A measure of a classifiers exactness. Recall: A measure of a classifiers completeness

Use Java 8 functional programming to generate letter sequences

Use Java 8 functional programming to generate letter sequences Using functional programming to generate letter sequences in Java 8 is a big challenge. Lukas Eder happily accepts this challenge and will tell us how to use Java 8 to generate ABC sequences-of course, it is not a bad way. I was overwhelmed by an interesting question raised by "mip" on Stack Overflow. The problem is: 1 2 3 I am looking for a way to generate the following letter sequences:A, B, C, ..., Z, AA, AB, A

Php shtmlspecialchars function details

bracket of the regular expression. I wrote a test myself. [Php]$ String = 'x10p ';$ String1 = preg_replace ('/(x) ([0-9] +) p/', ' \ 1', $ string );$ String2 = preg_replace ('/x ([0-9] +) p/', ' \ 1', $ string );Echo $ string1;Echo 'Echo $ string2;?> The output results are as follows: In x, x is enclosed in brackets. 10 the first parenthesis is 10.[Php]Preg_replace ('/ (# (\ d {3, 5} | x [a-fA-F0-9] {4}) | [a-zA-Z] [a-z0-9] {2, 5 });) /',' \ 1', $ string) The result is to replace $ amp; with

[Turn]html5 Canvas Drawing Tutorial (11)-use Lineto/arc/beziercurveto to draw an oval

the horizontal direction of the canvas is enlarged, and the vertical direction of the same, so, the original arc drawn by the circle becomes an ellipse.This method is very good at first glance, the code is small, and the principle is easy to understand. But the analysis will be able to find his obvious shortcomings, that is--imprecise! For example, I need a width of 171 high 56 ellipse, at this time if we set the radius of Arc 28, then the back will be for 171/28/2 this egg pain of the unintell

HTML Escape Character Daquan

, circumflex? #235; euml; small e, Di? ESIS/umlautSecret #236; igrave; small I, grave accentÍ #237; Iacute; small I, acute accent? #238; icirc; small I, circumflex? #239; iuml; small I, Di? ESIS/umlautE #240; ETH; small Eth, Icelandic? #241; ntilde; small N, TildeRevoke #242; ograve; small O, grave accentÓ #243; oacute; small O, acute accent? #244; ocirc; small O, circumflex? #245; otilde; small O, Tilde? #246; ouml; small O, Di? ESIS/umlautDivision #247; divide; Divisio

HTML Escape Character [standby]

; small O, slash Commandid ugrave; small U, grave accent Úúo uacute; small U, acute accent ? Small ucirc; small U, circumflex Ü uuml; small U, Di? ESIS/umlaut Y route yacute; small y, acute accent T branch thorn; small thorn, Icelandic ? Examples yuml; small y, umlautsymbols, mathematical symbols, and Greek letters? Fnof; Role Alpha; Release Beta; Gamma gamma; △ Delta; Login Epsilon; Token ETA; Revoke ETA; Vertex Theta; Middleware iota; Sort

Hmm class implemented by Python

#! /Usr/bin/env python """HMM module This module implements simple Hidden Markov Model class. It follows the description inChapter 6 of Jurafsky and Martin (2008) fairly closely, with one exception: in thisImplementation, we assume that all states are initial states. @ Author: Rob Malouf@ Organization: Dept. of Linguistics, San Diego State University@ Contact: rmalouf@mail.sdsu.edu@ Version: 2@ Since: 24-march-2008""" From copy import copy Class HMM (object ): """Class for Hidden Markov ModelsAn

Ngrams-Naive Bayes method word segmentation-Python

= 1024908267229 # Number of tokens PW = pdist(datafile('count_11_txt '), N, avoid_long_words) #### Segment2: second version, with bigram counts, (p. 226-227) Def CPW (word, Prev ):"Conditional probability of word, given previous word ."Try:Return P2w [Prev + ''+ word]/float (PW [Prev])Failed t keyerror:Return Pw (word) P2w = pdist(datafile('count_20000txt '), n) @ MemoDef segment2 (text, Prev = '"Return (log P (words), words), where words is the best segmentation ."If not text: Return

Suffix array)

). Therefore, the total space occupied is at least 4 N pointers and 2n integers (at least N integers ). if other methods are used to represent the tree structure, a larger space is required. the size of the suffix array is smaller than that of the suffix tree. Finally, compare their complexity: first, according to the total number of characters | Σ | the character set Σ is divided into three types: if | Σ | is a constant, it is called sigma as constant al

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