In the mathematics mathematical field of knot theory , an algebraic link is a link knot theory link formed by taking the numerator closure of an tangle mathematics algebraic tangle . References Colin Adams, The Knot Book , American Mathematical Society, ISBN 0 8050 7380 9 Category Knot theory knottheory stub ... more details
Summary Vector version available Sub super num dem.svg This shows the difference between subscript superscript characters, and numerator denominator characters. The font is Myriad Pro. Licensing PD self date August 2007 Orphan image Copy to Wikimedia Commons bot Fbot ... more details
Image Partchdiamond.svg thumb 350px Harry Partch , 11 limit tonality diamond. In musical tuning , a numerary nexus is an identity tuning identity shared by two or more interval ratio s in their numerator or denominator , with different identities in the other ref Rasch, Rudolph 2000 . A Word or Two on the Tunings of Harry Partch , Harry Partch An Anthology of Critical Perspectives , p.28. Dunn, David, ed. ISBN 9057550652. ref . For example, in the Otonality the denominator is always 1, thus 1 is the numerary nexus 1 2 3 4 5 etc. 1 1 1 1 1 3 5 2 4 In the Utonality the numerator is always 1 and the numerary nexus is thus also 1 1 1 1 1 1 etc. 1 2 3 4 5 4 8 3 5 For example, in a tonality diamond , such as Harry Partch s 11 limit diamond to the right, each ratio of a right slanting row shares a numerator and each ratio of a left slanting row shares an denominator. Each ratio of the upper left row has 7 as a denominator, while each ratio of the upper right row has 7 or 14 as a numerator. See also Tonality flux Sources reflist Category Harry Partch Category Musical tuning music stub ... more details
and numerator remain that are too large to ensure they are coprime by inspection, a greatest ... domain any element of such a field can be written as a fraction in which denominator and numerator ... of denominator and numerator by the same invertible element. In the case of the rational ... numerator and denominator this ambiguity can be removed by requiring the denominator to be positive ... more details
The normalization model is an influential model of responses of neurons in primary visual cortex . David Heeger developed the model in the early 1990s ref name pmid1504027 Cite pmid 1504027 ref , and later refined it together with Matteo Carandini and J Anthony Movshon ref name pmid9334433 Cite pmid 9334433 ref . The model involves a divisive stage. In the numerator is the output of the classical receptive field . In the denominator, a constant plus a measure of local stimulus Contrast vision contrast . References Reflist Category Visual perception neuroscience stub ... more details
ShouldBeSVG alphabet Summary Information Description Shows how Apple Chancery renders the decomposed character sequence for 4 and 221 225ths where all consecutive Number digits before the fraction slash get rendered as the numerator and the consecutive ones after the denominator get rendered as the denominator. This image uses the font Apple Chancery to render the exact string literal 4 221 225 Source I created this work entirely by myself. Date Author User Indexheavy Indexheavy User talk Indexheavy talk other versions Licensing PD self date February 2009 Copy to Wikimedia Commons bot Fbot priority true ... more details
Orphan date October 2011 File Imagekey.jpg thumb The symbol key to Bishop s Cipher. Bishop s Cipher is a combination of a substitution cipher and transposition cipher useful for extracting a message from any collection of text. As with any substitution cipher , the units of text are altered according to a Key cryptography key and like a transposition cipher those units are then arranged in a complex order. File Imagesymbolexample.jpg thumb The symbols for 11 and 25. Rather than the units of ciphertext corresponding to letters, the symbols in Bishop s Cipher correspond to the digits 1 9 and 0. Thus, the first step in deciphering the code is to apply the Key cryptography key and receive the numbers. File Imageexample.jpg thumb An example of the cipher being applied to text. Each symbol will come in a pair a numerator and denominator so each symbol unit will yield a pair of digits or more if the symbols refer to a double or triple digit number, for example, the symbols below correspond to the numbers 11 and 25 . The symbols should be read left to right and top to bottom like a book. The upper numbers the numerator are one unit, as are the bottom numbers the denominator . The second step is to apply those numbers to the collection of text to which they correspond. The numerator number corresponds to the vertical line of text counting from the top. The number in the denominator corresponds to a specific letter in that line counting from the left. So the above symbol would correspond to the 25th letter on the 11th line of text from the top. Note When dechipering Bishop s Cipher you do not count the punctuation, slashes, hyphens, or spaces, only the letters and numbers. If you have deciphered everything correctly you should now have the coded message. Category Cryptography ... more details
Summary A graph showing the relationship between urban density and petrol use Newman and Kenworthy s 1989 study is often referred to in demonstrating a relationship between overall urban density and transport energy use. Newman and Kenworthy s statistical methods have been criticised by a number of authors. The essential problem is examining the relationship between motor spirit use per person and persons per hectare . Because population is in the denominator in one term and the numerator in the other, a spurious correlation emerges. Reanalysis of the primary data comparing gasoline use per person to area per person shows a more complex relationship. The revised graph shows this. Licensing GFDL self with disclaimers migration relicense Copy to Wikimedia Commons bot Fbot ... more details
In mathematics , Spijker s lemma is a result in the theory of rational mapping s of the Riemann sphere . It states that the image mathematics image of a circle under a complex rational map with numerator and denominator having degree of a polynomial degree at most n has length at most 2 n . See also Buffon s needle External links MathWorld title Spijker s Lemma urlname SpijkersLemma References cite journal last Wegert first Elias coauthors Trefethen, Lloyd N. title From the Buffon Needle Problem to the Kreiss Matrix Theorem journal The American Mathematical Monthly volume 101 issue 2 pages 132 139 month February year 1994 doi 10.2307 2324361 jstor 2324361 Category Complex analysis Category Lemmas ... more details
Summary image Revised petrol use urban density.JPG right thumb Revised graph. A graph showing the relationship between urban density and petrol use Newman and Kenworthy s 1989 study is often referred to in demonstrating a relationship between overall urban density and transport energy use. Newman and Kenworthy s statistical methods have been criticised by a number of authors. The essential problem is examining the relationship between motor spirit use per person and persons per hectare . Because population is in the denominator in one term and the numerator in the other, a spurious correlation emerges. Reanalysis of the primary data comparing gasoline use per person to area per person shows a more complex relationship. The revised graph shows this. Licensing GFDL migration relicense ... more details
In elementary algebra , an algebraic fraction is the indicated quotient of two algebraic expression s. ref cite book last1 Slaught first1 H. E. last2 Lennes first2 N.J. title Intermediate algebra page 41 url http books.google.com books?id 01l2b7SP9sIC&pg PA41&dq 22algebraic fraction 22 2Bdefinition&hl fr&ei LXi1TpzaENO5hAfD7dWXBA&sa X&oi book result&ct book preview link&resnum 9&ved 0CF0QuwUwCA v onepage&q 22algebraic 20fraction 22 20 2Bdefinition&f false ref Two examples of algebraic fractions are math frac 3x x 2 2x 3 math and math frac sqrt x 2 x 2 3 math . Algebraic fractions are subject to the same laws as arithmetic fraction s. Terminology In the algebraic fraction math tfrac a b math , the dividend a is called the numerator and the divisor b is called the denominator . The numerator and denominator are called the Term mathematics terms of the algebraic fraction. A complex fraction is a fraction whose numerator or denominator, or both, contains a fraction. A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the denominator is 1. An expression which is not in fractional form is an integral expression . An integral expression can always be written in fractional form by giving it the denominator 1. A mixed expression is the algebraic sum of one or more integral expressions and one or more fractional terms. Rational fractions Main Rational function If the expressions a and b are polynomial s, the algebraic fraction is called a rational algebraic fraction ref cite book author Bansi Lal title Topics in Integral Calculus page 53 year 2006 url http books.google.com books?id RlQ tHlWcxcC&pg PA53&dq 22rational algebraic fraction 22&hl fr&ei cyWcTqe1I5CPswaz5oTsAw&sa X&oi book result&ct result&resnum 1&ved 0CC0Q6AEwAA ref or simply rational fraction . ref name Vinberg cite book author rnest Borisovich Vinberg title A course in algebra page 131 year 2003 url http b ... more details
of the cake is denoted by the fraction 1 4. Wiktionary numerator Wiktionary denominator A fraction ..., etc., consists of an integer numerator and a non zero integer denominator &mdash the numerator representing .... An example is 3 4, in which the numerator, 3, tells us that the fraction represents 3 equal parts ... number written as a b or math tfrac a b math , where the integer s a and b are called the numerator ... The numerator represents a number of equal parts and the denominator, which cannot be zero, indicates ... the numerator and the denominator are both positive, the fraction is called proper if the numerator ... can be converted to a mixed number as follows Divide the numerator by the denominator. In the example ... becomes the whole number part of the mixed number. The remainder becomes the numerator of the fractional part. In the example, 2 is the whole number part and 3 is the numerator of the fractional part ... denominator The reciprocal of a fraction is another fraction with the numerator and denominator reversed ... tfrac 1 17 math . Complex fractions In a complex fraction , either the numerator, or the denominator ... the numerator is 75 and the implied denominator is 10 to the second power, viz. 100, because there are two ... no relationship to the fraction 3 6. Special cases A unit fraction is a vulgar fraction with a numerator ... against division by zero . Equivalent fractions Multiplying the numerator and denominator ... math tfrac 1 2 math . When the numerator and denominator are both multiplied by 2, the result ... up half the cake math tfrac 1 2 math . Dividing the numerator and denominator of a fraction by the same ... the fraction. A simple fraction in which the numerator and denominator are coprime that is, the only positive integer that goes into both the numerator and denominator evenly is 1 is said to be Irreducible ... math tfrac 50 100 math . A common fraction can be reduced to lowest terms by dividing both the numerator ... the numerator and denominator by 21 math tfrac 63 462 tfrac 63 div 21 462 div 21 tfrac 3 22 math The Euclidean ... more details
Unreferenced date December 2009 A real data type is a data type used in a computer program to represent an approximation of a real number . Because the real numbers are not Countable set countable , computers cannot represent them exactly using a finite amount of information. Most often, a computer will use a rational number rational approximation to a real number. Rational numbers Main rational data type The most general data type for a rational number stores the numerator and denominator as integers. See Integer computer science Integer . Fixed point numbers Main fixed point arithmetic A fixed point data type assumes a specific denominator for all numbers. The denominator here is most often a power of two . For example, in a system whose denominator is 65,536 2 sup 16 sup , the hexadecimal number 0x12345678 means 0x12345678 65536 or 305419896 65536 or 4660 22136 65536 or about 4660.33777. See fixed point arithmetic . Floating point numbers Main floating point A floating point type is a compromise between the flexibility of a general rational type and the speed of fixed point arithmetic. It uses some of the bits in the data type to specify a power of two for the denominator. See floating point and IEEE 754 IEEE Floating Point Standard . data types DEFAULTSORT Real Data Type Category Data types ja vi Ki u s th c ... more details
Unreferenced date December 2009 In control theory , a proper transfer function is a transfer function in which the degree mathematics degree of the numerator does not exceed the degree of the denominator. Example The following transfer function is proper math textbf G s frac textbf N s textbf D s frac s 4 n 1 s 3 n 2 s 2 n 3 s n 4 s 4 d 1 s 3 d 2 s 2 d 3 s d 4 math because math deg textbf N s 4 leq deg textbf D s 4 math . The following transfer function however, is not proper math textbf G s frac textbf N s textbf D s frac s 4 n 1 s 3 n 2 s 2 n 3 s n 4 d 1 s 3 d 2 s 2 d 3 s d 4 math because math deg textbf N s 4 nleq deg textbf D s 3 math . Implications A proper transfer function will never grow unbounded as the frequency approaches infinity. math textbf G pm j infty infty math See also Strictly proper DEFAULTSORT Proper Transfer Function Category Control theory eo Pozitiva tradona funkcio pl Transmitancja w a ciwa ... more details
Unreferenced date December 2009 In control theory , a strictly proper transfer function is a transfer function where the Degree mathematics degree of the numerator is less than the degree of the denominator. Example The following transfer function is not strictly proper math textbf G s frac textbf N s textbf D s frac s 4 n 1 s 3 n 2 s 2 n 3 s n 4 s 4 d 1 s 3 d 2 s 2 d 3 s d 4 math because math deg textbf N s 4 nless deg textbf D s 4 math . The following transfer function however, is strictly proper math textbf G s frac textbf N s textbf D s frac n 1 s 3 n 2 s 2 n 3 s n 4 s 4 d 1 s 3 d 2 s 2 d 3 s d 4 math because math deg textbf N s 3 deg textbf D s 4 math . Implications A strictly proper transfer function will approach zero as the frequency approaches infinity. math textbf G pm j infty 0 math which is true for all physical processes. See also Proper transfer function DEFAULTSORT Strictly Proper Category Control theory eo Severe pozitiva tradona funkcio pl Transmitancja ci le w a ciwa ... more details
wiktionary proper wiktionary propriety Proper may refer to Proper liturgy , the part of a Christian liturgy that is specific to the date within the Liturgical Year Proper frame , such system of reference in which object is stationary non moving , sometimes also called a co moving frame Tincture heraldry Proper Proper , in heraldry, means depicted in natural colors Proper or appropriate conduct Proper often capitalized PROPER , a corrected release in response to a previously released online video or movie that contains transcoding or other playback errors. In mathematics Proper map , in topology , a property of continuous function between topological spaces, if inverse images of compact subsets are compact Proper morphism , in algebraic geometry, an analogue of a proper map for algebraic varieties Proper transfer function , a transfer function in control theory in which the degree of the numerator does not exceed the degree of the denominator Proper equilibrium , in game theory, a refinement of the Nash equilibrium . Proper subset Proper space See also Improper disambiguation disambig fr Propre ... more details
In mathematics , in birational geometry , the Cremona group named for Luigi Cremona of order math n math over a field mathematics field math k math is the group of birational automorphism s of the n dimensional projective space over k . It is denoted by Cr P sup n sup k or Bir P sup n sup k or Cr sub n sub k . The Cremona group is naturally identified with the automorphism group of the field of the rational function s in math n math indeterminates over math k math , or in other words a pure transcendental extension of k , with transcendence degree n . The projective general linear group of order math n 1 math , of projective transformation s, is contained in the Cremona group of order math n math . The two are equal only when math n 1 math , in which case both the numerator and the denominator of a transformation must be linear. In two dimensions, the Cremona group is generated by the standard quadratic transformation , along with PGL 3, k , provided that k is an algebraically closed field . The problem of describing the Cremona group in three dimensions and higher has still not been settled. External links http eom.springer.de c c027040.htm Cremona group on Springer Online Reference Works Category Birational geometry Category Group theory pt Grupo de Cremona ... more details
orphan date December 2007 RASTA filtering and Mean Subtraction was introduced to support Perceptual Linear Prediction PLP preprocessing It uses bandpass filter ing in the log spectral domain . Rasta filtering then removes slow channel variations. It has also been applied to cepstral feature based preprocessing with both log spectral and the cepstral domain filtering. In general a RASTA filter is defined by math T z k sum n N 1 2 z n 1 rho x , math the numerator is a regression filter with N being the order must be odd and the denominator is an integrator with time decay. The pole controls the lower limit of frequency and is normally around 0.9. RASTA filtering can be changed to use mean subtraction,implementing a moving average filter. Filtering is normally performed in the cepstral domain . The mean becomes the long term cepstrum and is typically computed on the speech part for each separate utterance. A silence is necessary to detect each utterance. References http trappist.elis.ugent.be ELISgroups speech cost249 report references papers sve95b.pdf Category Signal processing ... more details
an integer number source lang lisp 6 8 3 4 3 4 16 12 source The numerator and denominator may be obtained by their eponymous functions, that reduce a rational to canonical form and compute the numerator ... f numera.htm Function NUMERATOR, DENOMINATOR at the Common Lisp HyperSpec ref source lang lisp numerator ... more details
Definition In epidemiology , data or facts about a population is called denominator data . Denominator data is independent of any specific disease or condition. Disease specific data includes the Incidence epidemiology incidence of disease in a population, the Susceptible individual susceptibility of the population to a specific condition, the disease resistance, etc. In Mathematical modelling of infectious disease mathematical models of disease , disease specific variables often appear in the numerator . General reference data about the population typically appear in the denominator , hence the term denominator data . In an Compartmental models in epidemiology epidemiological compartment model , for example, variables are often scaled to total population. The susceptible fraction of a population is obtained by taking the ratio of the number of people susceptible to the total population. Susceptibility to a disease may depend on other factors such as age or sex. Data about a population including age distribution, male female ratios, and other demographic factors may be relevant as denominator data. Denominator data is not only limited to data describing human populations but also includes information about wild animal wild and domestic animal domestic animal populations. See also Incidence epidemiology Incidence Cumulative incidence Prevalence Attributable risk Category Epidemiology ... more details
Orphan date November 2010 Sales density is a measure of performance in retailing . It is the revenue generated for a given area of sales space, and is presented as a monetary value per square metre. The higher the figure, the more efficiently the floorspace is being used. ref name Elmbridge http www.elmbridge.gov.uk Elmbridge 20Borough 20Council Planning APPENDIX 201.pdf Planning Dept , Elmbridge Borough Council ref It is often quoted alongside other indicators such as like for like sales. ref name Deloitte http www.deloitte.com view en RO ro press release 3171bc5c6500e110VgnVCM100000ba42f00aRCRD.htm How do retailers trading performance measures stack up? , Deloitte , March 2009 ref Sales density is a ratio computed dividing the total retail sales over a year by the total surface of all the stores owned by the retailer potential wholesale franchising sales are usually not included . It is disputed whether the online sales of the retailer should be included in the numerator of the ratio given the high interdependence in the marketing strategy of online sales and own stores sales. References Reflist Category Financial ratios Category Sales ... more details
Orphan date July 2011 The Overall Nutritional Quality Index is a Nutritional rating systems nutritional rating system developed at the Yale Griffin Prevention Research Center. It assigns foods a score between 0 and 100 to reflect the overall nutrition provided. ref http www.guardian.co.uk lifeandstyle 2008 oct 22 foodanddrink healthandwellbeing ref The system has been marketed commercially as NuVal, and some consumer foods in the United States are marked with ONQI values as NuVal . The ONQI for a food is the ratio of a nominator value representing beneficial nutrients such as iron , dietary fibre and vitamins , ref http www.nuval.com Science Numerator Nutrients ref and a denominator value representing detrimental nutrients such as cholestrol and saturated fat . The following foods have the maximum ONQI of 100 ref http www.telegraph.co.uk health 3241667 Health food Yale Universitys Overall Nutritional Quality Index.html ref broccoli , blueberries , okra , Orange fruit oranges and green beans . Some of the lowest ONQIs are for white bread 9 , hot dog 5 , apple pie 2 and popsicle 1 . References reflist Category Nutrition ... more details
The Upside Potential Ratio is a measure of a return of an investment asset relative to the minimal acceptable return . The measurement allows a firm or individual to choose investments which have had relatively good upside performance, per unit of downside risk. math U sum min infty R r R min P r over sqrt sum infty min R r R min 2 P r , math where the returns math R r math have been put into increasing order. Here math P r math is the probability of the return math R r math and math R min math which occurs at math r min math is the minimal acceptable return. The Upside Potential Ratio may also be expressed as a ratio of Moment mathematics Partial moments partial moments . The measure was developed by Frank A. Sortino . Discussion The Upside Potential Ratio is a measure of risk adjusted returns. All such measures are dependent on some measure of risk. In practice, standard deviation is often used, perhaps because it is mathematically easy to manipulate. However, standard deviation treats deviations above the mean which are desirable, from the investor s perspective exactly the same as it treats deviations below the mean which are less desirable, at the very least . In practice, rational investors have a preference for good returns e.g., deviations above the mean and an aversion to bad returns e.g., deviations below the mean . Sortino further found that investors are or, at least, should be averse not to deviations below the mean, but to deviations below some minimal acceptable return MAR , which is meaningful to them specifically. Thus, this measure uses deviations above the MAR in the numerator, rewarding performance above the MAR. In the denominator, it has deviations below the MAR, thus penalizing performance below the MAR. Thus, by rewarding desirable results in the numerator and penalizing undesirable results in the denominator, this measure attempts to serve as a pragmatic measure of the goodness of an investment portfolio s returns in a sense that is not just ... more details
In mathematics , Maclaurin s inequality , named after Colin Maclaurin , is a refinement of the inequality of arithmetic and geometric means . Let a sub 1 sub , a sub 2 sub , ..., a sub n sub be positive number positive real number s, and for k 1, 2, ..., n define the averages S sub k sub as follows math S k frac displaystyle sum 1 leq i 1 cdots i k leq n a i 1 a i 2 cdots a i k displaystyle n choose k . math The numerator of this fraction is the elementary symmetric polynomial of degree k in the n variables a sub 1 sub , a sub 2 sub , ..., a sub n sub , that is, the sum of all products of k of the numbers a sub 1 sub , a sub 2 sub , ..., a sub n sub with the indices in increasing order. The denominator is the number of terms in the numerator, the binomial coefficient math scriptstyle n choose k . math Maclaurin s inequality is the following chain of inequalities math S 1 geq sqrt S 2 geq sqrt 3 S 3 geq cdots geq sqrt n S n math with equality if and only if all the a sub i sub are equal. For n 2, this gives the usual inequality of arithmetic and geometric means of two numbers. Maclaurin s inequality is well illustrated by the case n 4 math begin align & quad frac a 1 a 2 a 3 a 4 4 8pt & ge sqrt frac a 1a 2 a 1a 3 a 1a 4 a 2a 3 a 2a 4 a 3a 4 6 8pt & ge sqrt 3 frac a 1a 2a 3 a 1a 2a 4 a 1a 3a 4 a 2a 3a 4 4 8pt & ge sqrt 4 a 1a 2a 3a 4 . end align math Maclaurin s inequality can be proved using the Newton s inequalities . See also Newton s inequalities Muirhead s inequality Generalized mean inequality References cite book last Biler first Piotr coauthors Witkowski, Alfred title Problems in mathematical analysis publisher New York, N.Y. M. Dekker date 1990 pages isbn 0824783123 planetmath id 3835 title MacLaurin s Inequality Category Real analysis Category Inequalities Category Symmetric functions ko it Disuguaglianza di MacLaurin hu MacLaurin egyenl tlens ge zh ... more details
the cover up rule to solve for the new numerator of each partial fraction. Example math frac 3x 2 12x ... to the LCD. From the equation of numerators we solve for each numerator, A, B, C, D, and so on. This equation ... any value of x and solve for the numerator. Example math frac 3x 5 1 2x 2 frac A 1 2x 2 frac B 1 2x ... 13 2. Hence, numerator A equals six and one half. To solve for B Since the equation of the numerators ... more details
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