A possible etymology is a derivation from the Greek word – aiges = " waves " ( Hesychius of Alexandria ; metaphorical use of ( aix ) " goat "), hence " wavy sea ", cf.

* Hanging With Galileo – mathematical derivation of formula for suspended and free-hanging chains ; interactive graphical demo of parabolic versus hyperbolic suspensions.

* Cable Sag Error Calculator – Calculates the deviation from a straight line of a catenary curve and provides derivation of the calculator and references.

Nearly simultaneously David Hilbert published " The Foundations of Physics ", an axiomatic derivation of the field equations ( see Einstein – Hilbert action ).

* 1684 – Isaac Newton's derivation of Kepler's laws from his theory of gravity, contained in the paper De motu corporum in gyrum, is read to the Royal Society by Edmund Halley.

* 1900 – Quantum Mechanics: Max Planck presents a theoretical derivation of his black-body radiation law.

The arbitrary assumptions made by Fresnel to arrive at the Huygens – Fresnel equation emerge automatically from the mathematics in this derivation.

* December 10 – Isaac Newton's derivation of Kepler's laws from his theory of gravity, contained in the paper De motu corporum in gyrum, is read to the Royal Society by Edmund Halley.

The derivation of the Navier – Stokes equations begins with an application of Newton's second law: conservation of momentum ( often alongside mass and energy conservation ) being written for an arbitrary portion of the fluid.

* Simplified derivation of the Navier – Stokes equations

* A further derivation has been given by Peter R. Holland, on which he bases the entire work presented in his quantum physics textbook The Quantum Theory of Motion, a main reference book on the de Broglie – Bohm theory.

Around this time Erwin Madelung also developed a hydrodynamic version of Schrödinger's equation which is incorrectly considered as a basis for the density current derivation of the de Broglie – Bohm theory.

* 1939 – Nikolay Krylov and Nikolay Bogolyubov give the first consistent microscopic derivation of the Fokker-Planck equation in the single scheme of classical and quantum mechanics.

* 1945 – 1946 – Nikolay Bogoliubov develops a general method for a microscopic derivation of kinetic equations for classical statistical systems using BBGKY hierarchy.

* 1947 – Nikolay Bogoliubov and Kirill Gurov extend this method for a microscopic derivation of kinetic equations for quantum statistical systems.

In computer science, Augmented Backus – Naur Form ( ABNF ) is a metalanguage based on Backus – Naur Form ( BNF ), but consisting of its own syntax and derivation rules.

The purpose of these notes is to clarify some aspects of the derivation of the Bose – Einstein ( B – E )

The lemma is widely employed in mathematical finance, and its best known application is in the derivation of the Black – Scholes equation for option values.

The term " ultraviolet catastrophe " was first used in 1911 by Paul Ehrenfest, although the concept goes back to 1900 with the first derivation of the dependence of the Rayleigh – Jeans law ; the word " ultraviolet " refers to the fact that the problem appears in the short wavelength region of the electromagnetic spectrum.

* Wiseman, Howard, 2000 ' The derivation of the date of Badon in the Annales Cambriae from Bede and Gildas ' Parergon 17. 2, pp. 1 – 10.

460 – 370 BC ) and Epicurus ( 341 – 270 BC ); from which academic speculation proposes is the derivation of the logical architecture of Capital: Critique of Political Economy, because exchange value, the " syllogisms " ( C-M-C ' and M-C-M ') for simple commodity circulation, and the circulation of value as capital, derive from the Politics and the Nicomachean Ethics, by Aristotle.

The Poincaré recurrence theorem was used by Zermelo to object to Boltzmann's derivation of the increase in entropy in a dynamical system of colliding atoms.

The series of formulas which is constructed within such a system is called a derivation and the last formula of the series is a theorem, whose derivation may be interpreted as a proof of the truth of the proposition represented by the theorem.

The derivation of a theorem is often interpreted as a proof of the truth of the resulting expression, but different deductive systems can yield other interpretations, depending on the meanings of the derivation rules.

Different sets of derivation rules give rise to different interpretations of what it means for an expression to be a theorem.

Specifically, a formal theorem is always the last formula of a derivation in some formal system each formula of which is a logical consequence of the formulas which came before it in the derivation.

The initially accepted formulas in the derivation are called its axioms, and are the basis on which the theorem is derived.

The notion of a theorem is very closely connected to its formal proof ( also called a " derivation ").

Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates.

He also claims to have proven a derivation of Bayes ' theorem from the concept of fuzzy subsethood.

The Poynting vector appears in Poynting's theorem ( see this article for the derivation of the theorem and vector ), an energy-conservation law,

A similar derivation applies for conditioning on multiple events, using the appropriate extension of Bayes ' theorem

The direct computation of this integral is quite difficult, but we can simplify the derivation of the result using the divergence theorem:

The generic, statistical physical derivation of this noise is called the fluctuation-dissipation theorem, where generalized impedance or generalized susceptibility is used to characterize the medium.

In 1938 he published a simpler derivation of Van Cittert's 1934 theorem on the coherence of radiation from distant sources, now known as the Van Cittert-Zernike theorem.

A derivation of the MLE uses the spectral theorem.

Boltzmann defended the derivation of his equipartition theorem as correct, but suggested that gases might not be in thermal equilibrium because of their interactions with the aether.

A chief characteristic of experience in the mode of causal efficacy is one of derivation from the past.

With this derivation, the name would have a double meaning in the poem: When the hero is functioning rightly, his men bring grief to the enemy, but when wrongly, his men get the grief of war.

The character of Miss Marple is based on Christie's grandmother and her cronies, but there is no definitive source for the derivation of the name ' Marple '.

The derivation of the name ( Latin Aprilis ) is uncertain.

To show the derivation clearly, we propose that the stress should be on the penultimate syllable, the second half of the word being pronounced like " ptosis " ( with the " p " silent ), which comes from the same root " to fall ", and is already used to describe the drooping of the upper eyelid.

In between lies Strathmore, a derivation of the Gaelic for the Great Valley, which is a fertile agricultural area noted for the growing of potatoes, soft fruit and the raising of Angus cattle.

The exact derivation is unclear, with the Old English fiæll or feallan and the Old Norse fall all being possible candidates.

Its derivation is uncertain.

A bishop ( English derivation from the New Testament Greek ἐπίσκοπος, epískopos, " overseer ", " guardian ") is an ordained or consecrated member of the Christian clergy who is generally entrusted with a position of authority and oversight.

One possible derivation is from the proto-Germanic word * bastjan ( from Proto-Indo-European root word * b < sup > h </ sup > as ) means " binding " or " tie ".< ref > Köbler * b < sup > h </ sup > as </ ref > In this case, Bastarnae may have had the original meaning of an alliance or bund of tribes.

This name is possibly of Celtic derivation ( cf.

Notice that both expressions for are proportional to, reflecting how the derivation is independent of the type of forces considered.

where is the numerical integration step size of the trapezoidal rule used in the bilinear transform derivation.

( The symbol ∈ is a derivation from the Greek letter epsilon, " ε ", introduced by Peano in 1888.

Justice Holmes cautioned that “ the proper derivation of general principals in both common and constitutional law ... arise gradually, in the emergence of a consensus from a multitude of particularized prior decisions .” Justice Cardozo noted the “ common law does not work from pre-established truths of universal and inflexible validity to conclusions derived from them deductively ,” but “ ts method is inductive, and it draws its generalizations from particulars .”

Despite the failure of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the van't Hoff equation.

A sequence of rule applications is called a derivation.

The most common derivation provided in English dictionaries is from the Alpine French dialect pronunciation of the word Chrétien ("( a ) Christian "), which was a greeting there.

where X < sub > x </ sub > is a tangent vector at x, thought of as a derivation.

A typical derivation in this grammar is

The exact derivation of the term is unknown, but it has been thought that in early Canadian football, the scoring of a single was signalled with a red flag.

Because derivation is a slower and less productive word formation process than the more overtly syntactical morphological methods, there are fewer collectives formed this way.