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*[[George Boole|Boole, G]]. (1860/1970), ''Calculus of finite differences''. *{{Citation | last1=Jordan | first1=Charles | title=Calculus of Finite Differences | url=https://books.google.com/books?id=3RfZOsDAyQsC | publisher=Hungarian ...

...[Imre Ruzsa]] (1996),<ref>{{cite journal|last=Ruzsa|first=I.|title=Sums of finite sets|journal=Number Theory: New York Seminar 1991-1995|date=1996|pages=281– ...math_statement = If <math>A</math>, <math>B</math>, and <math>C</math> are finite subsets of a group, then ...

=== Group of differences === ...fically, there is a unique group <math>gp(M)</math>, called ''the group of differences'', in which <math>M</math> can be embedded. ...

Generally speaking, treatment levels may be finite or infinite as well as ordinal or cardinal, which leads to a large collecti Assume there exists a finite collection of multi-valued treatment status <math>T=\{0,1,2,\ldots,J,\}</ma ...

...e [[monoid]]s, varieties of finite [[ordered semigroup]]s and varieties of finite [[ordered monoid]]s are defined similarly. A variety ''V'' of finite (ordered) semigroups is a class of finite (ordered) semigroups that: ...

...oint method uses standard numerical approaches such as finite differences, finite element or spectral methods in order to solve the embedding partial differe ...ur interpolation polynomials for the interpolations. Second-order centered differences are used for the spatial discretization. The CPM results in the expected se ...

...nd use an [[interpolation formula]] using second-order [[finite difference|differences]].<ref>{{cite book|last=Van Brummelen|first=Glen|authorlink=Glen Van Brumme |&nbsp; Differences ||&nbsp; {{math|''D''₁}} ||&nbsp; ... ||&nbsp; {{math|''D''<sub> ...

...ary order of accuracy, it is possible to use the [[finite difference]]. A finite difference can be '''central''', '''forward''' or '''backward'''. ==Central finite difference== ...

...vative-free optimization, algorithms that do not use derivatives or finite differences are called '''derivative-free algorithms'''.<ref name="CSV" >{{cite book|la ...

{{Short description|Julian Date (JD) corrected for differences in the Earth's position with respect to the Sun}} ...n]]. When timing events that occur beyond the [[Solar System]], due to the finite [[speed of light]], the time the event is observed depends on the changing ...

* For the "sum of squared differences", see [[Mean squared error]] * The sum of squared dimensions of a finite group's pairwise nonequivalent complex representations is equal to cardinal ...

==Finite case== ...necessarily identically distributed, and <math> \epsilon_{ij} </math> has finite fourth moment. ...

...ence]], a '''signal automaton''' is a [[finite automaton]] extended with a finite set of real-valued clocks. During a run of a signal automaton, clock values ...ons and double circle represents accepting locations. However, contrary to finite automata, letters occurs in locations and not in transition. This is becaus ...

...spect to the [[Barycenter|barycentre]] of the [[Solar System]]. Due to the finite [[speed of light]], the time an astronomical event is observed depends on t ...ernational Atomic Time|TAI]], [[Barycentric Dynamical Time|TDB]], etc. The differences between these time standards are of the order of a minute, so for better th ...

...calculi and quantum differential calculi on finite sets and finite groups (finite group [[Lie algebra]] theory). ...m d}f={f(x+\lambda)-f(x)\over\lambda}{\rm d}x</math> This shows how finite differences arise naturally in quantum geometry. Only the limit <math>\lambda\to 0</mat ...

...56-0 |url=https://archive.org/details/optionsfuturesot00hull_1 }}</ref> [[Finite difference method]]s were first applied to [[Valuation of options|option pr ...ple [[Black–Scholes equation|the Black–Scholes PDE]]. Once in this form, a finite difference model can be derived, and the valuation obtained.<ref name="Schw ...

...Mullainathan|date=2004-02-01|title=How Much Should We Trust Differences-In-Differences Estimates?|url=https://academic.oup.com/qje/article/119/1/249/1876068|journ ...any panel data settings (such as [[Difference in differences|difference-in-differences]]) clustering often offers a simple and effective way to account for non-in ...

...erywhere and for all times, we will be satisfied with its calculation at a finite number of locations and at specified time intervals. The [[partial differen ...our purposes are: [[finite difference methods]], finite volume methods, [[finite element methods]], and [[spectral methods]]. ...

...sp;&minus;&nbsp;''y''&nbsp;|&nbsp;''x'',&nbsp;''y''&nbsp;in&nbsp;''X''} of differences of pairs of elements of ''X''.<ref>Moody gives different definitions for re ...Delone,<ref name="moody"/> or a Delone set ''X'' for which there exists a finite set ''F'' with ''X''&nbsp;&minus;&nbsp;''X''&nbsp;&sub;&nbsp;''X''&nbsp;+&n ...

...aterial relations; and that its convergence rate is faster than some other finite differencing methods, such as forward and backward differencing. The right *[[Finite difference method]] ...