, statistics , and the mathematical science s, a parameter Greek language G auxiliary measure ..., the term may have special uses. Parameter is a computation from data values recorded but it is not actually a data value recorded from a subject. Example for a population of test scores, a parameter ... use of the word parameter Cquote W.M. Woods...a mathematician...writes... ...a variable is one of the many things a parameter is not. ... The dependent variable, the speed of the car, depends on the independent ... position... but in a...different manner . You have changed a parameter A equalization parametric equaliser ... relation between x and y . Thus a is considered to be a parameter it is less variable than the variable ... the parameter a gives a different though related problem, whereas the variations of the variables ... worked is easily changed, but the wage is more static. This makes wage a parameter in this formula ... , and c are parameters that determine which quadratic function one is considering. The parameter could be incorporated into the function name to indicate its dependence on the parameter for instance one may define the base a logarithm by math log a x frac log x log a math where a is a parameter that indicates ... the status of symbols between parameter and variable changes the function as a mathematical object ... n k 1 math , defines a polynomial function of n when k is considered a parameter , but is not a polynomial function of k when n is considered a parameter indeed, in the latter case, it is only defined ... Parameter Estimation , page 11, Academic Press ref Analytic geometry In analytic geometry , curve s are often given as the image of some function. The argument of the function is invariably called the parameter ... form math x 2 y 2 1 math parametric form math x,y cos t, sin t math where t is the parameter . A somewhat ... analysis , integrals dependent on a parameter are often considered. These are of the form ... hand side the parameter on which the integral depends. When evaluating the integral ... more details
wiktionarypar parameter A parameter is a quantity which changes characteristics of a system or a function. The term is used in this way in many mathematical sciences. The term may also have the following meanings Parameter computer science Parameters journal , a journal of the U.S. Army War College In linguistics, see Principles and parameters disambig da Parameter de Parameter es Par metro fr Param tre homonymie ja sl Parameter ... more details
In probability theory and statistics , a shape parameter is a kind of numerical parameter of a parametric family of probability distribution s. ref Everitt B.S. 2002 Cambridge Dictionary of Statistics. 2nd Edition. CUP. ISBN 0 521 81099 x ref Definition A shape parameter is any parameter of a probability distribution that is neither a location parameter nor a scale parameter nor a function of either of both or these only, such as a rate parameter . Such a parameter must affect the shape of a distribution rather than simply shifting it as a location parameter does or stretching shrinking it as a scale parameter does . Examples The following continuous probability distributions have a shape parameter Beta distribution Burr distribution Erlang distribution Exponential power distribution Gamma distribution Generalized extreme value distribution Log logistic distribution Inverse gamma distribution Pareto distribution Pearson distribution Tukey lambda distribution Weibull distribution By contrast, the following continuous distributions do not have a shape parameter, so their shape is fixed and only their location or their scale or both can change. It follows that where they exist the skewness and kurtosis of these distribution are constants, as skewness and kurtosis are independent of location and scale parameters. Exponential distribution Cauchy distribution Logistic distribution Normal distribution Raised cosine distribution Uniform distribution Wigner semicircle distribution See also skewness kurtosis References references Category Theory of probability distributions Category Statistical terminology es Par metro de forma fa fr Param tre de forme pl Parametr kszta tu sl Parameter oblike ... more details
A statistical parameter is a parameter that indexes a family of probability distribution s. It can be regarded as a numerical characteristic of a population or a model. ref Everitt, B.S. 2002 The Cambridge Dictionary of Statistics. CUP. ISBN 0 521 81099 X ref Among parametric family parameterized families of distributions are the normal distribution s, the Poisson distribution s, the binomial distribution s, and the exponential distribution s. The family of normal distribution s has two parameters, the mean and the variance if these are specified, the distribution is known exactly. The family of chi squared distribution s, on the other hand, has only one parameter, the number of degrees of freedom. In statistical inference , parameters are sometimes taken to be unobservable, and in this case the statistician s task is to infer what he can about the parameter based on observations of random variables distributed according to the probability distribution in question, or, more concretely stated, based on a random sample taken from the population of interest. In other situations, parameters may be fixed by the nature of the sampling procedure used or the kind of statistical procedure being carried out for example, the number of degrees of freedom statistics degrees of freedom in a Pearson s chi squared test . Even if a family of distributions is not specified, quantities such as the mean and variance can still be regarded as parameters of the distribution of the population from which a sample is drawn. Statistical procedures can still attempt to make inferences about such population parameters. Parameters of this type are given names appropriate to their roles, including location parameter dispersion parameter or scale parameter shape parameter Where a probability distribution ... parameter is used for quantities that index how variable the outcomes would be. Analogy A parameter ... also Precision statistics , another parameter not specific to any one distribution Parametrization ... more details
Unreferenced date December 2009 In probability theory and statistics , a scale parameter is a special kind of numerical parameter of a parametric family of probability distribution s. The larger the scale parameter, the more spread out the distribution. Definition If a family of probability distribution s is such that there is a parameter s and other parameters for which the cumulative distribution function satisfies math F x s, theta F x s 1, theta , math then s is called a scale parameter , since ... parameter set, then the density as a function of the scale parameter only satisfies math ... parameter is called an estimator of scale. Simple manipulations We can write math f s math .... Rate parameter Some families of distributions use a rate parameter which is simply the reciprocal of the scale parameter . So for example the exponential distribution with scale parameter and probability ... parameter as math f x lambda lambda e lambda x , x ge 0. math Examples The normal distribution has two parameters a location parameter math mu math and a scale parameter math sigma math . In practice ... in terms of a scale parameter math theta math or its inverse. Special cases of distributions where the scale parameter equals unity may be called standard under certain conditions. For example, if the location parameter equals zero and the scale parameter equals one, the normal distribution is known .... Estimation A statistic can be used to estimate a scale parameter so long as it Is location invariant, Scales linearly with the scale parameter, and Converges as the sample size grows. Various ... these. In order to make the statistic a consistent estimator for the scale parameter, one must in general ... value of the value obtained by dividing the required scale parameter by the asymptotic value .... See also Central tendency Invariant estimator Location parameter Location scale family Statistical dispersion DEFAULTSORT Scale Parameter Category Theory of probability distributions Category ... more details
Unreferenced date December 2009 In statistics , a location family is a class of probability distributions parametrized by a scalar or vector valued parameter , which determines the location or shift of the distribution. Formally, this means that the probability density function s or probability mass function s in this class have the form math f mu x f x mu . math Here, is called the location parameter . In other words, when you graph the function, the location parameter determines where the origin will be located. If is positive, the origin will be shifted to the right, and if is negative, it will be shifted to the left. A location parameter can also be found in families having more than one parameter, such as location scale family location scale families . In this case, the probability density function or probability mass function will have the form math f mu, theta x f theta x mu math where is the location parameter, represents additional parameters, and math f theta math is a function of the additional parameters. Additive noise An alternative way of thinking of location families is through the concept of additive noise . If is an unknown constant and w is random noise with probability density math f w math , then math x mu w math has probability density math f mu x f x mu math and is therefore a location family. See also Location test Invariant estimator Location scale family Scale parameter Statistics descriptive state collapsed DEFAULTSORT Location Parameter Category Summary statistics Category Theory of probability distributions Category Statistical terminology de Parameter Statistik Lageparameter fa fr Param tre de location nl Plaatsparameter pl Parametr po o enia ru sl Parameter lokacije ... more details
Unreferenced date February 2007 Cleanup date July 2007 The coupling parameter of the resonator, specifies the part of the energy of the laser field, which is output at each round trip. The coupling parameter should not be confused with the round trip loss , which refers to the part of the energy of the ...?... , which is absorbed or scattered at each round trip of laser field in the laser resonator , and cannot be used. At the continuous wave operation, the round trip gain is determined by the coupling parameter and the round trip loss. In simple configurations of the laser cavity or laser resonator , the coupling parameter may be just the transmission coefficient of the output coupler or just square of the magnification coefficient in the case of unstable resonator . The round trip loss may limit the power scaling of the active mirror s, or disk laser s, while the size of the gain medium scales up, and the gain size product is limited by the exponential growth of the amplified spontaneous emission the powerful disk laser should work at low values of the coupling parameter and even lower values of the round trip loss . See also Disk laser DEFAULTSORT Coupling Parameter Optics stub Category Laser science ... more details
Orphan date February 2009 In computer software , the term parameter validation ref name GA ref name VF is the automated processing, in a module, to validate the spelling or accuracy of parameters passed to that module. The term has been in common use for over 30 years. small ref name GA small Specific best practices have been developed, for decades, to improve the handling of such parameters. ref name GA Parameter validation for software reliability , G.B. Alleman, 1978 see below References . ref ref name VF Parameter Validation for Floats , MSDN.Microsoft.com, 2007, webpage http social.msdn.microsoft.com forums en US sqlreportingservices thread 9cbc23b8 8709 4053 90c3 bd4818eda862 MSDN 862 . ref ref name MS Feedback Attribute based method parameter validation and error handling , 2007, webpage http connect.microsoft.com VisualStudio feedback ViewFeedback.aspx?FeedbackID 97327 VStudio 327 . ref See also data validation strong typing error handling sanity check Notes Reflist References Parameter validation for software reliability , G.B. Alleman, 1978, webpage http portal.acm.org citation.cfm?id 987517 ACM 517 paper presents a method for increasing software reliability through parameter validation. software stub Category Software testing ... more details
In cryptography , the security parameter is a variable that measures the input size of the problem. Both the resource requirements of the cryptographic algorithm or protocol as well as the adversary cryptography adversary s probability of breaking security are expressed in terms of the security parameter. The security parameter size n is usually expressed in Unary numeral system unary representation i.e. a n long string of bits 1 so that the cryptographic algorithm execution efficiency can be polynomial time in the length of the input size. Typical security parameters The length, in bits, of the key used in a cryptographic scheme. See also Key size Negligible function cryptography Negligible function Category Cryptography crypto stub ... more details
Unreferenced date September 2010 In probability theory and statistics , a concentration parameter is a special kind of numerical parameter of a parametric family of probability distribution s. Concentration parameters occur in conjunction with distributions whose domain is a probability distribution, such as the symmetric Dirichlet distribution and the Dirichlet process . The larger the value of the concentration parameter, the more evenly distributed is the resulting distribution the more it tends towards the uniform distribution . The smaller the value of the concentration parameter, the more sparsely distributed is the resulting distribution, with all but a few parameters having a probability near zero in other words, the more it tends towards a distribution concentrated on a single point, the degenerate distribution defined by the Dirac delta function . In the case of a Dirichlet distribution, a concentration parameter of 1 results in all sets of probabilities being equally likely, i.e. in this case the Dirichlet distribution of dimension k is equivalent to a uniform distribution over a k dimensional simplex. Note that this is not the same as what happens when the concentration parameter tends towards infinity. In the former case, all resulting distributions are equally likely the distribution over distributions is uniform . In the latter case, only near uniform distributions are likely the distribution over distributions is highly peaked around the uniform distribution . Meanwhile, in the limit as the concentration parameter tends towards zero, only distributions with nearly ... of where a sparse prior concentration parameter much less than 1 is called for, consider a topic model ... mass. Accordingly, a reasonable setting for the concentration parameter might be 0.01 or 0.001. With a larger .... See also Dirichlet distribution Dirichlet process Pitman&ndash Yor process Location parameter Scale parameter Category Theory of probability distributions Category Statistical terminology ... more details
disambig In handwriting analysis graphonomics a Movement parameter includes slant handwriting Slant , Orientation , Amplitude , Roundness handwriting . In kinesiology a Movement parameter is an adjustable scalar physics scalar quantity to be specified in a motor system , i.e. movement control system See kinesiology , graphonomics . Examples are Velocity , Acceleration , Force , Stiffness . Category Penmanship Category Motor control writingsystem stub ... more details
Refimprove date August 2007 Context date August 2009 A free parameter is a variable used in a mathematical model and for scientific modelling which allows adjustments so the models can provide helpful insights ref http www.cosmologyscience.com glossary.htm Model Cosmology Glossary Models CosmologyScience.com 2010 ref . The values of free parameters used in models are provided by previous experiment s and by educated guesses. References Reflist DEFAULTSORT Free Parameter Category Philosophy of science Category Scientific method ... more details
More footnotes date August 2010 In science , a parameter space is the set mathematics set of values of parameter s encountered in a particular mathematical model . Often the parameters are input s of a function mathematics function , in which case the technical term for the parameter space is domain of a function . Citation needed date August 2010 Parameter spaces are particularly useful for describing families of probability distribution s that depend on parameters. More generally in science, the term parameter space is used to describe experimental variables. For example, the concept has been used in the science of soccer in the article Parameter space for successful soccer kicks. In the study, Success rates are determined through the use of four dimensional parameter space volumes. ref Cook & Goff 2006 ref In the context of statistics , parameter spaces form the background for parameter estimation . As Ross 1990 describes in his book Parameter space is a subset of p dimensional space consisting of the set of values of &Theta which are allowable in a particular model. The values may sometimes be constrainted, say to the positive quadrant or the unit square, or in case of symmetry ... the parameter space has been advanced by C. van Eeden 2006 gains in the minimax value can be very substantial when the parameter space in bounded. Examples In complex dynamics the parameter space ... is a subset of this parameter space. The function math f z z 2 c math is a complex quadratic polynomial ... the parameter space is math R times R times S 1 . math Citation needed date January 2011 History Parameter ... . For instance, the parameter space of sphere geometry spheres in three dimensions, has four dimensions ... Eric Goff 2006 http stacks.iop.org EJP 27 865 Parameter Space for Successful Soccer Kicks European Journal of Physics 27 865. Constance van Eeden 2006 Restricted Parameter Space Estimation Problems Admissibility ... History of Mathematics , 3rd edition, page 165, Dover Books . DEFAULTSORT Parameter Space Category ... more details
Notability date May 2008 Orphan date November 2006 Parameter Magazine is a biannual literary magazine based in Manchester , with issues appearing in spring and autumn. The magazine publishes poetry, prose and reviews and also features artworks in its online incarnation. Writers featured in previous issues include Forward Prize nominees Carola Luther and Mario Susko . Issue 5 was launched in Autumn 2007. Image Issue 5.gif thumb Parameter issue 5 cover External links http www.parametermagazine.org Parameter Magazine web site Category British literary magazines Category Cultural magazines Category Culture in Manchester Category Media in Manchester Category Magazines with year of establishment missing UK lit mag stub ... more details
In Celestial Mechanics , Tisserand s parameter or Tisserand s invariant is a combination of orbital elements used in a restricted N body problem Three body problem three body problem . Definition For a small body with semimajor axis math a , math , eccentricity orbit eccentricity math e , math , and inclination math i , math , relative to the orbit of a perturbing larger body with semimajor axis math a P math , the parameter is defined as follows math frac a P a 2 cdot sqrt frac a a P 1 e 2 cos i math The quasi conservation of Tisserand s parameter is a consequence of Tisserand s relation . Applications T sub J sub , Tisserand s parameter with respect to Jupiter as perturbing body, is frequently used to distinguish asteroid s typically T sub J sub 3 from Jupiter family comet s typically 2 T sub J sub 3 . The roughly constant value of the parameter before and after the interaction encounter is used to determine whether or not an observed orbiting body is the same as a previously observed in Tisserand 27s Criterion . The quasi conservation of Tisserand s parameter constrains the orbits attainable using gravity assist for outer Solar system exploration. T sub N sub , Tisserand s parameter with respect to Neptune , has been suggested to distinguish Near scattered disc Scattered Objects believed to be affected by Neptune from Extended Scattered trans Neptunian objects e.g. 90377 Sedna . Related notions The parameter is derived from one of so called Charles Eug ne Delaunay Delaunay standard variables, used to study the perturbed Energy The Hamiltonian Hamiltonian in 3 body system. Ignoring higher order perturbation terms, the following value is conserved math sqrt a 1 e 2 cos i math Consequently, perturbations may lead to the resonance between the orbit inclination and eccentricity ... links David Jewitt s page on http www2.ess.ucla.edu jewitt tisserand.html Tisserand s parameter ... Astrodynamics Category Celestial mechanics it Parametro di Tisserand sl Tisserandov parameter ... more details
Refimprove date February 2011 The deceleration parameter math q math in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann Lema tre Robertson Walker metric Friedmann Lema tre Robertson Walker universe . It is defined by math q stackrel mathrm def frac ddot a a dot a 2 math where math a math is the Scale factor cosmology scale factor of the universe and the dots indicate derivatives by proper time . The expansion of the universe is said to be accelerating if math ddot a math is positive recent measurements suggest it is , and in this case the deceleration parameter will be negative. ref cite book last Jones first Mark H. coauthors Robert J. Lambourne title An Introduction to Galaxies and Cosmology publisher Cambridge University Press date 2004 page http books.google.com books?id 36K1PfetZegC&lpg PP1&pg PA244 v onepage&q&f false 244 isbn 978 0521837385 ref The minus sign and name deceleration parameter are historical at the time of definition math q math was thought to be positive, now it is believed to be negative. The Friedmann equations Friedmann acceleration equation can be written as math 3 frac ddot a a 4 pi G rho 3p 4 pi G 1 3w rho, math where math rho math is the energy density of the universe, math p math is its pressure ... math H math is the Hubble parameter and math K 1,0 math or math 1 math depending on whether the universe ... hyperbolic respectively. The derivative of the Hubble parameter can be written in terms of the deceleration parameter math frac dot H H 2 1 q . math Except in the speculative case of phantom energy which violates all the energy conditions , all postulated forms of matter yield a deceleration parameter math q ge 1 math . Thus, any expanding universe should have a decreasing Hubble parameter and the local ... 0 math . This had suggested that the deceleration parameter was equal to one half the experimental ... Category Physical cosmology fr Param tre de d c l ration pl Parametr spowolnienia sk Decelera n parameter ... more details
In statistics , a nuisance parameter is any parameter which is not of immediate interest but which must be accounted for in the analysis of those parameters which are of interest. The classic example of a nuisance parameter is the variance , sup 2 sup , of a normal distribution , when the mean , , is of primary interest. Nuisance parameters are often variances, but not always for example in an errors in variables model, the unknown true location of each observation is a nuisance parameter. In general, any parameter which intrudes on the analysis of another may be considered a nuisance parameter. A parameter may also cease to be a nuisance if it becomes the object of study, as the variance of a distribution may be. Theoretical statistics The general treatment of nuisance parameters can be broadly similar between frequentist and Bayesian approaches to theoretical statistics. It relies on an attempt to partition the likelihood function into components representing information about the parameters of interest and information about the other nuisance parameters. This can involve ideas about Sufficiency statistics sufficient statistics and ancillary statistic s. When this partition can be achieved it may be possible to complete a Bayesian analysis for the parameters of interest by determining their joint posterior distribution algebraically. The partition allows frequentist theory to develop general estimation approaches in the presence of nuisance parameters. If the partition cannot be achieved it may still be possible to make use of an approximate partition. In some special cases, it is possible to formulate methods that circumvent the presences of nuisance parameters. The t test provides a practically useful test because the test statistic does not depend on the unknown variance. It is a case where use can be made of a pivotal quantity . However, in other cases no such circumvention is known. Practical statistics Practical approaches to statistical analysis treat nuisance ... more details
The Immirzi parameter also known as the Barbero Immirzi parameter is a numerical coefficient appearing in loop quantum gravity , a nonperturbative theory of quantum gravity . The Immirzi parameter measures the size of the quantum of area in Planck units . ref name rovelli cite book last Rovelli first Carlo title Quantum Gravity url http www.cambridge.org uk catalogue catalogue.asp?isbn 9780521715966 accessdate 2010 Sep 25 series Cambridge Monographs on Mathematical Physics year 2004 publisher Cambridge University Press location Cambridge, UK language English isbn 0521837332 ref As a result, its ... parameter arises in the process of expressing a Lorentz connection with noncompact group SO 3,1 ... cover SU 2 . Although named after Giorgio Immirzi, the possibility of including this parameter was first pointed out by Fernando Barbero. The significance of this parameter remained obscure until ... to the Immirzi parameter. Black hole thermodynamics Copyedit section for grammar date October ... math is the Immirzi parameter and math gamma 0 ln 2 sqrt 3 pi math or math gamma 0 ln 3 sqrt 8 pi, math depending on the gauge group used in loop quantum gravity . So, by choosing the Immirzi parameter ... Immirzi parameter always the same. what date October 2010 However, Krzysztof Meissner ref name ... number instead of the logarithms of integers mentioned above. The Immirzi parameter appears in the denominator ... parameter is proportional to the area contributed by each puncture. Immirzi parameter in Spin ... sector, in the lack of energy condition and presence of gravitational propagation the Immirzi parameter ... of such a model has not yet initiated to be studied. Interpretation The parameter may be viewed as a renormalization of Newton s constant . Various speculative proposals to explain this parameter have ... were found requiring a different value of the Immirzi parameter, it would constitute evidence that loop ... hand, the Immirzi parameter seems to be the only free parameter of vacuum LQG, and once it is fixed ... more details
The Rossby parameter or simply beta math beta math is a number used in geophysics and meteorology which arises due to the meridional variation of the Coriolis force caused by the spherical shape of the Earth. It is important in the generation of Rossby wave s. The Rossby parameter math beta math is given by the equation math beta frac partial f partial y frac 1 a frac d d phi 2 omega sin phi frac 2 omega cos phi a math ref http amsglossary.allenpress.com glossary search?id rossby parameter1 Glossary of Meteorology , American Meteorological Society. ref ref http mesolab.meas.ncsu.edu linyl mea713 Ch1 Note.doc Lecture Notes for Atmospheric Science Mesoscale Dynamics MEA 713 . North Carolina State University . Accessed 14 July 2007. ref Where math phi math is the latitude, math omega math is the angular speed of the Earth s rotation, and a is the mean radius of the Earth. Although both involve Coriolis effects, the Rossby parameter describes the variation of the effects with latitude hence the latitudinal derivative , and should not be confused with the Rossby number . References references climate stub Category Atmospheric dynamics no Rossbyparameter nn Rossbyparameter ... more details
The plasma parameter is a dimensionless number, denoted by capital Lambda, . The plasma parameter is usually interpreted to be the argument of the Coulomb logarithm, which is the ratio of the maximum impact parameter to the classical distance of closest approach in Coulomb collision Coulomb scattering . In this case, the plasma parameter is given by ref Chen, F.F., Introduction to Plasma Physics and Controlled Fusion, Springer, New York, 2006 ref math Lambda 4 pi n lambda D 3 math where n is the number density of electrons, sub D sub is the Debye length . This expression is typically valid for a plasma in which ion thermal velocities are much less than electron thermal velocities. A detailed discussion of the Coulomb logarithm is available in the NRL Plasma Formulary , pages 34 35. Note that the word parameter is usually used in plasma physics to refer to bulk plasma properties in general see plasma parameters . An alternative definition of this parameter is given by the average number of electrons in a plasma physics plasma contained within a Debye sphere a sphere of radius the Debye length . This definition of the plasma parameter is more frequently and appropriately called the Debye number, and is denoted math N D math . In this context, the plasma parameter is defined as math N D frac 4 pi 3 n lambda D 3 math Since these two definitions differ only by a factor of three, they are frequently used interchangeably. Often the factor of math 4 pi 3 math is dropped. When the Debye length is given by math lambda D sqrt frac epsilon 0 k T e n e q e 2 math , the plasma parameter is given by ref Miyamoto, K., Fundamentals of Plasma Physics and Controlled Fusion, Iwanami, Tokyo ... temperature. Confusingly, some authors define the plasma parameter as math epsilon p Lambda ... plasma lectures node8.html The plasma parameter lecture notes from Richard Fitzpatrick ref table class ... parameter magnitude td tr tr bgcolor eeeeee align center td 1 td td 1 td tr tr align center ... more details
Image impctprmtr.png right 288px thumb Impact parameter b and scattering angle . The impact parameter math b math is defined as the perpendicular distance between the path of a projectile and the center of the field math U r math created by an object that the projectile is approaching see diagram . It is often referred to in Nuclear Physics see Rutherford Scattering , as well as in Classical Mechanics . The impact parameter is related to the scattering angle math theta math by ref Landau LD and Lifshitz EM 1976 Mechanics , 3rd. ed., Pergamon Press. ISBN 0 08 021022 8 hardcover and ISBN 0 08 029141 4 softcover . ref math theta pi 2b int r mathrm min infty frac dr r 2 sqrt 1 b r 2 2U mv infty 2 math where math v infty math is the velocity of the projectile when it is far from the center, and math r mathrm min math is its closest distance from the center. See also Tests of general relativity References reflist http hyperphysics.phy astr.gsu.edu hbase nuclear rutsca2.html Category Classical mechanics physics stub de Sto parameter ja pt Par metro de impacto zh ... more details
Orphan date February 2009 In X ray crystallography , the Flack parameter is a factor used to estimate the absolute configuration of a structural model determined by single crystal structure analysis. In this approach, one determines the absolute structure of a noncentrosymmetric crystal. The processes used to decide the absolute structure use the anomalous dispersion effect . If atomic scattering factors did not have Complex number imaginary parts , the Friedel pair s would have exactly the same amplitude s i.e., the scattering intensity math F h k l 2 math from crystal plane h k l is equal to math F h k l 2 math . However, atomic scattering factors have imaginary part s due to the anomalous dispersion effect , and Friedel s law is broken by this effect. There are several ways to determine the absolute structure by X ray crystallography. For example, a comparison of the intensities of Bijvoet pairs or of the R factors for the two possible structures can suggest the correct absolute structure. One of the more powerful and simple approaches is using the Flack parameter, because this single parameter clearly indicates the absolute structure. The Flack parameter is calculated during the structural refinement using the equation given below math I hkl 1 x F h k l 2 x F h k l 2 math explain this formula where x is the Flack parameter, I is the square of the scaled observed structure factor and F is the calculated structure factor. By determining x for all data, x is usually found to be between 0 and 1. If the value is near 0, with a small standard uncertainty , the absolute structure given by the structure refinement is likely correct, and if the value is near 1, then the inverted structure is likely correct. If the value is near 0.5, the crystal may be racemic or twinned. The technique is most effective when the crystal contains both lighter and heavier atoms. Light atoms usually show only a small anomalous dispersion effect. This parameter, introduced by H. D. Flack ref cite ... more details
In the geometry of complex algebraic curve s, a local parameter for a curve C at a smooth point P is just a meromorphic function on C that has a simple zero at P . This concept can be generalized to curves defined over fields other than math mathbb C math or even scheme mathematics scheme s , because the local ring at a smooth point P of an algebraic curve C defined over an algebraically closed field is always a discrete valuation ring . ref J. H. Silverman 1986 . The arithmetic of elliptic curves . Springer. p. 21 ref This valuation will endow us with a way to count the order at the point P of rational functions which are natural generalizations for meromorphic functions in the non complex realm having a zero or a pole at P . Local parameters, as its name indicates, are used mainly to properly count multiplicities in a local way. Introduction When C is a complex algebraic curve, we know how to count multiplicities of zeroes and poles of meromorphic functions defined on it ref R. Miranda 1995 . Algebraic curves and Riemann surfaces . American Mathematical Society. p. 26 ref . However, when discussing curves defined over fields other than math mathbb C math , we do not have access to the power of the complex analysis, and a replacement must be found in order to define multiplicities of zeroes and poles of rational functions defined on such curves. In this last case, we say that the germ of the regular function math f math vanishes at math P in C math if math f in m P subset mathcal O C,P math . This is in complete analogy with the complex case, in which the maximal ideal of the local ... with the concept of a Discrete valuation ring Uniformizing parameter uniformizing parameter ... parameter for the DVR R, m is just a generator of the maximal ideal m . The link comes from the fact that a local parameter at P will be a uniformizing parameter for the DVR math mathcal O C ... on the local ring math mathcal O C,P math , math m P math . A local parameter for C at P is a function ... more details
both source distributions are central either with a zero mean or a zero noncentrality parameter ... distributions that are not usually formulated in terms of a noncentrality parameter see noncentral hypergeometric distributions , for example. The noncentrality parameter of the t distribution may be negative ... more details
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