File DiagnostWaxUP.JPG thumb right 350px An idealized diagnostic wax up for a partially edentulous maxilla . In dentistry , diagnostic wax up is used to visualize the results of a prosthodontist prosthetic case prior to the treatment being executed. References Reflist Prosthodontology Category Prosthodontology ... more details
Infobox Company company name Diagnostic Health Corporation company logo Image DiagnosticHealthLogo.png 200px company type private sector Private foundation 2007 location Birmingham, Alabama , United States USA key people industry Healthcare products Diagnostic Imaging revenue gain 200 million United States dollar USD 2006 num employees homepage http www.dxhealthcorp.com www.dxhealthcorp.com Diagnostic Health Corporation , based in Birmingham, Alabama , is one of the nation s largest independent diagnostic imaging companies. The company is the former diagnostic division of HealthSouth Corporation . The company has network of 53 free standing diagnostic imaging centers located in 19 states and the District of Columbia . Category Medical imaging Category Companies based in Birmingham, Alabama Category Health care companies of the United States US company stub ... more details
Refimprove date January 2010 In mathematics , an algebraic equation , also called polynomial equation over a given Field mathematics field is an equation of the form math P Q math where P and Q are possibly ... 2 frac x 3 3 xy 2 y 2 frac 1 7 math is an algebraic equation over the rationals. Two equations are equivalent if they have the same set of Equation solutions . In particular the equation math P Q math ... to the study of polynomials. An algebraic equation over the rationals can always be converted to an equivalent ... 3 7 and grouping its terms in the first member, the algebraic equation above becomes the algebraic equation math 42y 4 21xy 14x 3 42xy 2 42y 2 6 0 math Although the equation math e T x 2 frac 1 T xy sin T z 2 0 math is not an algebraic equation in four variables x , y , z and T over the rational numbers because sine , exponentiation and 1 T are not polynomial functions . It is an algebraic equation ... T 3 3 frac T 5 5 frac T 7 7 cdots math 1 T and 2 are all elements of Q T . As for any equation, the solutions of an equation are the values of the variables for which the equation is true, but for algebraic ... of the algebraic equation P 0 are the roots of the polynomial P . When solving an equation, it is important to specify in which Set mathematics set the solutions are allowed. For example, for an equation .... In this case the equation is a diophantine equation . One may also look for solutions in the field of complex numbers the fundamental theorem of algebra asserts that a non constant equation has always ... has found the solution of the Cubic function equation of degree 3 and Lodovico Ferrari has solved the Quartic function equation of degree 4 . Finally Niels Henrik Abel has proved in 1824 that the quintic equationequation of degree 5 and the equations of higher degree are not always solvable using radicals. Galois theory , named after variste Galois , were introduced to give criteria deciding if an equation is solvable using radicals. References MathWorld title Algebraic Equation urlname AlgebraicEquation ... more details
Unreferenced date December 2009 In mathematics , LHS is informal shorthand for the left hand side of an equation . Similarly, RHS is the right hand side . Each is solely a name for a term as part of an expression and they are in practice interchangeable, since equality mathematics equality is equivalence relation symmetric . This abbreviation is seldom if ever used in print it is very informal. More generally, these terms may apply to an inequation or inequality mathematics inequality . In the inequality case , there is no symmetry. The right hand side is everything on the right side of a test operator in an Expression mathematics expression . Conversely, the left hand side is everything on the left side. Some examples The expression on the right side right part of the sign is the right side of the equation and the left of the is the left side left part of equation. br br Take x 5 y 8 where x 5 would be the left hand side and y 8 would be the right hand side Homogeneous and inhomogeneous equations In solving mathematical equations, particularly linear simultaneous equations , differential equation s and integral equation s, the terminology homogeneous is often used for equations with the RHS set equal to zero. The corresponding inhomogeneous or nonhomogeneous equation then has the RHS ... operator L , with the difference being that between the equation Lf 0, to be solved for a function f , and the equation Lf g , with g a fixed function, to solve again for f . The point of the terminology appears for L a linear operator . Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution. For example in mathematical physics , the homogeneous equation may correspond to a physical theory formulated in empty space , while the inhomogeneous equation asks for more realistic solutions with some matter, or charged ..., though. See also equal sign DEFAULTSORT Sides Of An Equation Category Mathematical terminology es ... more details
An adjoint equation is a linear differential equation , usually derived from its primal equation using integration by parts . Gradient values with respect to a particular quantity of interest can be efficiently calculated by solving the adjoint equation. Methods based on solution of adjoint equations are used in wing shape optimization , fluid flow control and uncertainty quantification . References reflist cite journal last Jameson first Antony title Aerodynamic Design via Control Theory journal Journal of Scientific Computing volume 3 issue 3 year 1988 DEFAULTSORT Adjoint Equation Category Differential calculus Applied math stub Math stub Engineering stub Mech engineering stub ru ... more details
In mathematics , more specifically in the study of dynamical system s and differential equation s, a Li nard equation ref Li nard, A. 1928 Etude des oscillations entretenues, Revue g n rale de l lectricit 23 , pp. 901 912 and 946 954. ref is a second order differential equation, named after the French physicist Alfred Marie Li nard . During the development of radio and vacuum tube technology, Li nard equations were intensely studied as they can be used to model oscillating circuit s. Under certain additional assumptions Li nard s theorem guarantees the uniqueness and existence of a limit cycle for such a system. Definition Let f and g be two continuously differentiable functions on R , with g an odd function and f an even function then the second order ordinary differential equation of the form math d 2x over dt 2 f x dx over dt g x 0 math is called the Li nard equation . Li nard system The equation can be transformed into an equivalent two dimensional system of ordinary differential equation s. We define math F x int 0 x f xi d xi math math x 1 x , math math x 2 dx over dt F x math then math begin bmatrix dot x 1 dot x 2 end bmatrix mathbf h x 1, x 2 begin bmatrix x 2 F x 1 g x 1 end bmatrix math is called a Li nard system . Alternatively, since Li nard equation itself also belongs to autonomous differential equation , the substitution math v dx over dt math leads the Li nard equation to a first order differential equation math v dv over dx f x v g x 0 math which belongs to Abel equation of the second kind . ref http eqworld.ipmnet.ru en solutions ode ode0317.pdf Li nard equation at eqworld . ref ref http eqworld.ipmnet.ru en solutions ode ode0125.pdf Abel equation of the second ... dt x 0 math is a Li nard equation. Li nard s theorem A Li nard system has a unique and Stability ... also Autonomous differential equation Abel equation of the second kind Footnotes reflist External links PlanetMath title LienardSystem urlname LienardSystem DEFAULTSORT Lienard equation Category Dynamical ... more details
In geometry , the Ces ro equation of a plane curve is an equation relating curvature math kappa math to arc length math s math . It may also be given as an equation relating the Radius of curvature mathematics radius of curvature math R math to arc length . These are equivalent because math R 1 kappa math . Two congruence geometry congruent curves will have the same Ces ro equation. It is named after Ernesto Ces ro . Some curves have a particularly simple representation by a Ces ro equation. Some examples are line geometry Line math kappa 0 math . Circle math kappa 1 alpha math , where math alpha math is the radius. Logarithmic spiral math kappa C s math , where math C math is a constant. Involute Circle involute math kappa C sqrt s math , where math C math is a constant. Cornu spiral math kappa Cs math , where math C math is a constant. Catenary math kappa frac a s 2 a 2 math . The Ces ro equation of a curve is related to its Whewell equation in the following way, if the Whewell equation is math varphi f s math then the Ces ro equation is math kappa f s math . References cite book title The Mathematics Teacher year 1908 publisher National Council of Teachers of Mathematics pages 402 cite book author Edward Kasner title The Present Problems of Geometry publisher Congress of Arts and Science Universal Exposition, St. Louis year 1904 pages 574 cite book author J. Dennis Lawrence title A catalog of special plane curves publisher Dover Publications year 1972 isbn 0 486 60288 5 pages 1 5 External links MathWorld title Ces ro Equation urlname CesaroEquation MathWorld title Natural Equation urlname NaturalEquation http www.2dcurves.com derived curvature.html curvature Curvature Curves at 2dcurves.com. Category Curves eo Ekvacio de Ces ro sl Ces rojeva ena ba ... more details
The Abel equation , named after Niels Henrik Abel , is special case of functional equation s which can be written in the form math f h x h x 1 , math or math alpha f x alpha x 1 math and shows non trivial properties at the iteration. Equivalence These equations are equivalent. Assuming that is an invertible function , the second equation can be written as math alpha 1 alpha f x alpha 1 alpha x 1 , . math Taking math x alpha 1 y math , the equation can be written as math f alpha 1 y alpha 1 y 1 , . math For a function f x assumed to be known, the task is to solve the functional equation for the function sup 1 sup , possibly satisfying additional requirements, such as sup 1 sup 0 1. The change of variables s sup x sup x , for a real parameter s , brings Abel s equation into the celebrated Schr der s equation , f x s x . History Initially, the equation in the more general form ref name abel cite journal url http gdz.sub.uni goettingen.de ru dms load img ?PPN PPN243919689 0001&DMDID dmdlog6 author Abel, N.H. coauthors title Untersuchung der Functionen zweier unabh ngig ver nderlichen Gr en x und y, wie f x, y , welche die Eigenschaft haben, ... journal Journal f r die reine und angewandte Mathematik volume 1 pages 11 15 year 1826 ref ref name s cite journal url http projecteuclid.org ... in the case of single variable, the equation is not trivial, and requires special analysis ref ... Jitka Laitochov title Group iteration for Abel s functional equation abstract Studied is the Abel functional equation f x x 1 ref In the case of linear transfer function, the solution can be expressed ... author G. Belitskii coauthor Yu. Lubish title The Abel equation and total solvability of linear ... Equation of tetration is special case of Abel s equation, with math f exp math . In the case of integer argument, the equation is just a recurrent procedure. See also Functional equation Abel function Schr der s equation References references Category Niels Henrik Abel Category Functional equations ... more details
. Dispersionless Hirota equation See also Integrable systems Nonlinear Schr dinger equation Nonlinear systems Davey Stewartson equation Dispersive partial differential equation Kadomtsev Petviashvili equation Korteweg de Vries equation References Kodam Y., Gibbons J. Integrability of the dispersionless ... representation and dispersionless DS equation , ArXiv 0709.4148 Konopelchenko B.G., Moro A. Integrable ... more details
In mathematics , Chaplygin s equation , named after Sergei Alekseevich Chaplygin , is a partial differential equation useful in the study of transonic fluid mechanics flow . ref cite book last1 Landau first1 L. D. authorlink1 Lev Landau last2 Lifshitz first2 E. M. authorlink2 Evgeny Lifshitz title Fluid Mechanics edition 2 year 1982 publisher Pergamon Press page 432 ref It is math Psi theta theta frac v 2 1 frac v 2 c 2 Psi vv v Psi v 0. math Here, math c c v math is the speed of sound , determined by the equation of state of the fluid and Bernoulli s principle . References Reflist DEFAULTSORT Chaplygin s Equation Category Partial differential equations Category Equations fi T aplyginin yht l ... more details
An indeterminate equation , in mathematics , is an equation for which there is an infinite set of solutions for example, 2x y is a simple indeterminate equation. Indeterminate equations cannot be directly solved from the given information. For example, the equations math ax by c math math x 2 Py 2 1 math where a, b, c, and P are given integers provided that P is not a square number , are indeterminate equations. Equations of the second form are named Pell s equation s. See also Indeterminate system Indeterminate variable Linear algebra References Unreferenced date August 2008 Category Algebra algebra stub es Ecuaci n indeterminada ko nl Onbepaalde vergelijking nn Ubestemt uttrykk uk ... more details
In the mathematics mathematical theory of partial differential equations , a Monge equation , named after Gaspard Monge , is a first order partial differential equation for an unknown function u in the independent variables x sub 1 sub ,..., x sub n sub math F left u,x 1,x 2, dots,x n, frac partial u partial x 1 , dots, frac partial u partial x n right 0 math that is a polynomial in the partial derivatives of u . Any Monge equation has a Monge cone . Classically, putting u x sub 0 sub , a Monge equation of degree k is written in the form math sum i 0 cdots i n k P i 0 dots i n x 0,x 1, dots,x k , dx 0 i 0 , dx 1 i 1 cdots dx n i n 0 math and expresses a relation between the differential of a function differentials dx sub k sub . The Monge cone at a given point x sub 0 sub , ..., x sub n sub is the zero locus of the equation in the tangent space at the point. The Monge equation is unrelated to the second order Monge Amp re equation . Category Partial differential equations mathanalysis stub ... more details
Infobox journal title Journal of Diagnostic Medical Sonography cover File Journal of Diagnostic Medical Sonography.jpg editor Michelle Bierig, MPH, RDMS, RDCS, FASE, FSDMS discipline Obstetrics former names abbreviation J. Of Diagnostic Medical Sonography publisher SAGE Publications country frequency Bi monthly history 1985 present openaccess license impact impact year website http www.uk.sagepub.com journals Journal201412?siteId sage uk&prodTypes any&q Journal of Diagnostic Medical Sonography&fs 1 link1 http jdm.sagepub.com content current link1 name Online access link2 http jdm.sagepub.com content by year link2 name Online archive ISSN 8756 4793 eISSN OCLC 535496115 LCCN The Journal of Diagnostic Medical Sonography is a Peer review peer reviewed academic journal that publishes papers six times a year in the field of Obstetrics . The journal s Editor in Chief editor is Michelle Bierig, MPH, RDMS, RDCS, FASE, FSDMS. It has been in publication since 1985 and is currently published by SAGE Publications in association with Society of Diagnostic Medical Sonography . Scope The Journal of Diagnostic Medical Sonography seeks to present the latest diagnostic techniques and interpretation methods, case reports and research applications. This interdisciplinary journal covers areas such as OB GYN, echocardiography, neurosonology, and breast sonography. The Journal of Diagnostic Medical Sonography is intended as a primary resource for graduates to and practice sonographers, publishing reports of CME self tests and diagnostic challenges. Abstracting and indexing The Journal of Diagnostic Medical Sonography is abstracted and indexed in the following databases Academic Onefile EMBASE General Onefile SCOPUS External links Official website 1 http jdm.sagepub.com Category SAGE academic journals Category English language journals Category Obstetrics journals ... more details
Noref date November 2009 The Prony equation named after Gaspard de Prony is a historically important equation in hydraulics , used to calculate the head loss due to friction within a given run of pipe. It is an empirical equation developed by France Frenchman Gaspard de Prony in the 19th century math h f frac L D aV bV 2 math where h sub f sub is the head loss due to friction, calculated from the ratio of the length to diameter of the pipe L D , the velocity of the flow V , and two empirical factors a and b to account for friction. This equation has been supplanted in modern hydraulics by the Darcy Weisbach equation , which used it as a starting point. Category Equations of fluid dynamics mathapplied stub ca Equaci de Prony es Ecuaci n de Prony fr quation de Prony pt Equa o de Prony ru sl Pronyjeva ena ba uk ... more details
Orphan date July 2011 The Rodrigues equation is an equation used in chromatography to describe the efficiency of a bed of permeable large pore particles. It is thus an extension of Van Deemter s equation . It was developed by Alirio E. Rodrigues et al. . ref name Rodrigues1997 cite journal title Permeable packings and perfusion chromatography in protein separation journal Journal of Chromatography B author Alirio E. Rodrigues volume 699 issue 1 2 date 10 October 1997 pages 47 61 doi 10.1016 S0378 4347 97 00197 7 ref Equation The equation is math HETP A frac B u C cdot f lambda cdot u math Where HETP is the height equivalent to a theoretical plate A Eddy diffusion B Longitudinal diffusion C Resistance to mass transfer u Flow rate math f lambda frac 3 lambda left frac 1 tanh lambda frac 1 lambda right math math lambda math Intraparticular P clet number References reflist Category Chromatography Category Equations analytical chem stub ... more details
In mathematics, the replicator equation is a deterministic monotone non linear and non innovative game dynamic used in evolutionary game theory . The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness landscape ... type constant. This important property allows the replicator equation to capture the essence of selection . Unlike the quasispecies equation, the replicator equation does not incorporate mutation ... form is given by the differential equation math dot x i x i f i x phi x , quad phi x sum i 1 n ..., the equation is defined on the n dimensional simplex . The replicator equation assumes a uniform population ... equations, such as the quasispecies equation. In application, populations are generally finite, making ... upon the population distribution, which allows the replicator equation to be written in the form ... to be stochastic. Since the replicator equation is non linear, an exact solution is difficult to obtain even in simple versions of the continuous form so the equation is usually analyzed in terms of stability. The replicator equation in its continuous and discrete forms satisfies the Folk theorem ... of the equation. The solution of the equation is often given by the set of evolutionarily stable state ... equation once a strategy becomes extinct there is no way to revive it. Phase portrait solutions for the continuous linear fitness replicator equation have been classified in the two and three dimensional ... portraits increases rapidly. Relationships to other equations The continuous replicator equation on math n math types is equivalent to the Generalized Lotka&ndash Volterra equation in math n 1 math dimensions ... Volterra variable. The continuous replicator dynamic is also equivalent to the Price equation see ... equation which incorporates mutation is given by the replicator mutator equation, which ... j math to type math i math . This equation is a simultaneous generalization of the replicator equation ... more details
In mathematics , a Riccati equation is any ordinary differential equation that is quadratic function quadratic in the unknown function. In other words, it is an equation of the form math y x q 0 x q 1 ... the equation reduces to a Bernoulli differential equation Bernoulli equation , while if math q 2 x 0 math the equation becomes a first order linear ordinary differential equation . The equation is named after Count Jacopo Francesco Riccati 1676 1754 . More generally, the term Riccati equation is used ... to as the algebraic Riccati equation . Reduction to a second order linear equation The non linear Riccati equation can always be reduced to a second order linear ordinary differential equation ODE harv Ince 1956 pp 23 25 . If math y q 0 x q 1 x y q 2 x y 2 math then, wherever math q 2 math is non zero, math v yq 2 math satisfies a Riccati equation of the form math v v 2 R x v S x ... math u Ru Su 0. math A solution of this equation will lead to a solution math y u q 2u math of the original Riccati equation. Application to the Schwarzian equation An important application of the Riccati equation is to the 3rd order Schwarzian differential equation math S w w w w w 2 2 f math which ... the Riccati equation math y y 2 2 f. math By the above math y 2u u math where math u math is a solution ... C math after scaling. Thus math w U u Uu u 2 U u math so that the Schwarzian equation has solution ..., a simple integration. The same holds true for the Riccati equation. In fact, if one particular ... math y 1 u math in the Riccati equation yields math y 1 u q 0 q 1 cdot y 1 u q 2 cdot y 1 u 2 ... or math u q 1 2 , q 2 , y 1 , u q 2 , u 2, math which is a Bernoulli differential equation Bernoulli equation . The substitution that is needed to solve this Bernoulli equation is math z frac 1 u math Substituting math y y 1 frac 1 z math directly into the Riccati equation yields the linear equation math z q 1 2 , q 2 , y 1 , z q 2 math A set of solutions to the Riccati equation is then given ... more details
In mathematics , a modular equation is an algebraic equation satisfied by moduli , in the sense of moduli problem . That is, given a number of functions on a moduli space , a modular equation is an equation holding between them, or in other words an identity mathematics identity for moduli. The most frequent use of the term modular equation is in relation with the moduli problems for elliptic curve s. In that case the moduli space itself is of dimension 1. That implies that any two rational function s F and G , in the function field of an algebraic variety function field of the modular curve, will satisfy a modular equation P F , G 0 with P a non zero polynomial of two variables over the complex number s. For suitable non degenerate choice of F and G , the equation P X , Y 0 will actually define the modular curve. One should qualify that by saying that P , in the worst case, will be of high degree and the plane curve it defines will have Mathematical singularity singular points and the coefficient s of P may be very large numbers. Further, the cusps of the moduli problem, which are the points of the modular curve not corresponding to honest elliptic curves but degenerate cases, may be difficult to read off from knowledge of P . That all being said, in that sense a modular equation becomes the equation of a modular curve . Such equations first arose in the theory of multiplication of elliptic function s geometrically, the n sup 2 sup fold covering map from a 2 torus to itself given by the mapping x n x on the underlying group expressed in terms of complex analysis . References unreferenced date August 2008 Category Moduli theory ... more details
The diffusion equation is a partial differential equation which describes density fluctuations in a material ..., for instance the diffusion of alleles in a population in population genetics . Statement The equation is usually written as Equation box 1 equation math frac partial phi mathbf r ,t partial t nabla ... then the equation is nonlinear, otherwise it is linear. More generally, when D is a symmetric positive definite matrix , the equation describes Anisotropy anisotropic diffusion, which is written for three dimensional diffusion as Equation box 1 equation math frac partial phi mathbf r ,t partial t sum ..., then the equation reduces to the following linear differential equation math frac partial phi mathbf r ,t partial t D nabla 2 phi mathbf r ,t , math also called the heat equation . Historical origin The Fick s law of diffusion particle diffusion equation was originally derived by Adolf Fick ... Derivation The diffusion equation can be derived in a straightforward way from the continuity equation .... The diffusion equation can be obtained easily from this when combined with the phenomenological ... r ,t math . If drift must be taken into account, the Smoluchowski equation provides an appropriate generalization. Discretization see also Discrete Gaussian kernel The diffusion equation is continuous ... tensor diffusion equation, in standard discretization schemes. Because direct discretization of the diffusion equation with only first order spatial central differences leads to checkerboard artifacts. The rewritten diffusion equation used in image filtering math frac partial phi mathbf r ,t partial ... 3 3 in 2D and 3 3 3 in 3D. See also Heat equation Fick s law of diffusion Fick s law of diffusion Second law Fick s Second Law Radiative transfer equation and diffusion theory for photon transport in biological ... behind and solution of the Diffusion Equation. http dragon.unideb.hu zerdelyi Diffusion on the nanoscale ... navbox DEFAULTSORT Diffusion Equation Category Diffusion Category Partial differential equations ... more details
In geometry , an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve s intrinsic properties, that is, properties that do not depend on the location and possibly the orientation of the curve. Therefore an intrinsic equation defines the shape of the curve without specifying its position relative to an arbitrarily defined coordinate system. The intrinsic quantities used most often are arc length math s math , tangential angle math theta math , curvature math kappa math or Radius of curvature mathematics radius of curvature , and, for 3 dimensional curves, Torsion of a curve torsion math tau math . Specifically The natural equation is the curve given by its curvature and torsion. The Whewell equation is obtained as a relation between arc length and tangential angle. The Ces ro equation is obtained as a relation between arc length and curvature. The equation of a circle including a line for example is given by the equation math kappa s Cte math where math s math is the arc length and math kappa math the curvature. These coordinates greatly simpilfy some physical problem. For elastic rods for example, the potential energy is given by math E int 0 L B kappa 2 s ds math where math B math is the bending modulus math EI math . Moreover, as math kappa s d theta ds math , elasticity of rods can be given a simple variational form. References cite book author R.C. Yates title A Handbook on Curves and Their Properties location Ann Arbor, MI publisher J. W. Edwards pages 123 126 year 1952 cite book author J. Dennis Lawrence title A catalog of special plane curves publisher Dover Publications year 1972 isbn 0 486 60288 5 pages 1 5 External links MathWorld title Intrinsic Equation urlname IntrinsicEquation Category Curves ko ... more details
distinguish Torricelli s law Torricelli s theorem Torricelli s trumpet Torricelli point Unreferenced date January 2008 Torricelli s equation is an equation created by Evangelista Torricelli to find the final velocity of an object moving with a constant acceleration without having a known time interval. The equation itself is math v f 2 v i 2 2 a Delta d , math Derivation Begin with the equation for velocity math v f v i at , math Square both sides to get math v f 2 v i at 2 v i 2 2av it a 2t 2 , math The term math t 2 , math appears in the equation for displacement, and can be isolated math d d i v it a frac t 2 2 math math d d i v it a frac t 2 2 math math t 2 2 frac d d i v it a 2 frac Delta d v it a math Substituting this back into our original equation yields math v f 2 v i 2 2av it a 2 left 2 frac Delta d v it a right math math v f 2 v i 2 2av it 2a Delta d v it math math v f 2 v i 2 2av it 2a Delta d 2av it , math math v f 2 v i 2 2a Delta d , math See also Equation of motion External links http encyclopedia2.thefreedictionary.com Torricelli 27s equation Torricelli s theorem DEFAULTSORT Torricelli s Equation Category Kinematics it Equazione di Torricelli mn km pt Equa o de Torricelli ru tr Torricelli denklemi ... more details
For specific applications of Kepler s equation Kepler s laws of planetary motion In orbital mechanics , Kepler s equation relates various geometric properties of the orbit of a body subject to a central ... of both physics and mathematics, particularly classical celestial mechanics . Equation Kepler s equation is Equation box 1 indent equation math M E epsilon sin E math border colour 50C878 background ... mathematics eccentricity . Kepler s equation is a transcendental equation because sine is a transcendental ... forms There are several forms of Kepler s equation. Each form is associated with a specific type of orbit. The standard Kepler equation is used for elliptic orbits 0 &le 1 . The hyperbolic Kepler equation is used for hyperbolic orbits 1 . The radial Kepler equation is used for linear radial orbits 1 . Barker s equation is used for parabolic orbits 1 . When 1, Kepler s equation is not associated ... length. Hyperbolic Kepler equation The Hyperbolic Kepler equation is math M epsilon sinh H H math , where H is the hyperbolic eccentric anomaly. This equation is derived by multiplying Kepler s equation ... to obtain math M i left E epsilon sin E right math Radial Kepler equation The Radial Kepler equation is math t x sin 1 sqrt x sqrt x 1 x math , where t is time, and x is the distance along an x axis. This equation is derived by multiplying Kepler s equation by 1 2 making the replacment math E 2 sin ... more challenging. Kepler s equation can be solved for E analytic function analytically by Lagrange inversion theorem Lagrange inversion . The solution of Kepler s equation given by two Taylor series below. Confusion over the solvability of Kepler s equation has persisted in the literature for four centuries ref It is often erroneously claimed that Kepler s equation cannot be solved analytically ... s equation cannot be solved a priori, on account of the different nature of the arc and the sine. But if I ... of Mathematics ref Inverse Kepler equation The inverse Kepler equation is the solution of Kepler ... more details
whether a given equation could be solved by radicals which gave rise to the field of Galois theory . ref name Mathworld Sextic Equation It follows from Galois theory that a sextic equation is solvable ... subsets of three roots. There are formulas to test either case, and, if the equation is solvable ... sextic equations , J. Algebra 233 2000 , 704 757 ref The general sextic equation can be solved in terms of Kamp de F riet function s. ref name Mathworld Sextic Equation http mathworld.wolfram.com SexticEquation.html Mathworld Sextic Equation ref A more restricted class of sextics can be solved in terms ... s approach to solving the quintic equation . ref name Mathworld Sextic Equation See also Cubic function Septic equation Quintic function References references Polynomials DEFAULTSORT Sextic Equation ... more details
odds is little different from the pre test probability, and as such is used primarily for diagnostic ... that an individual has a disorder or condition prior to the use of a diagnostic test. It allows the clinician to better interpret the results of the diagnostic test and helps to predict the likelihood ... controlled trial compared how well physicians interpreted diagnostic tests that were presented ... 1 Pretest probability Posttest odds Pretest odds Likelihood ratio In equation above, positive ... more details
Unreferenced stub auto yes date December 2009 The SCSI Send Diagnostic command is used to instruct a target device to perform a self test on a specific Logical Unit Number LUN . The SCSI CDB CDB structure is class wikitable bit br byte width 50 7 width 50 6 width 50 5 width 50 4 width 50 3 width 50 2 width 50 1 width 50 0 0 colspan 8 align center Operation code 1Dh 1 colspan 3 align center SELF TEST CODE align center PF align center Reserved align center SelfTest align center DevOfl align center UnitOfl 2 colspan 8 align center Reserved 3 4 colspan 8 align center Parameter list length 5 colspan 8 align center Control The special parameter fields in the CDB have the following meaning PF Page Format 0 SCSI 1 compliant vendor specific 1 SCSI 2 compliant addresses a particular SCSI SCSI diagnostic pages diagnostic page as defined in the parameter list. In this case the Send Diagnostic command is usually followed by a SCSI Receive Diagnostic Results Command Receive Diagnostic Results command. SelfTest if this bit is one then the device runs its default self test. The device will then return either good status or a check condition. This version of the command is usually followed by a Receive Diagnostic Results command. If the SelfTest bit is zero then the device performs a special diagnostic operation as specified in the parameter list. DevOfL Device Off Line used in high availability applications if this is one then the target is allowed to perform diagnostic operations that could cause it to fail read write operations to the same from other initiators. UnitOfL Unit Off Line similar to DevofL but refers to all LUNs DEFAULTSORT Scsi Send Diagnostic Command Category SCSI Compu hardware stub ... more details
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