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In [[mathematics]], the [[Complex dimension|''n''-dimensional]] '''complex coordinate space' The variables <math>z_i</math> are the (complex) coordinates on the complex ''n''-space. ...

...that the independence of the sum and difference of two independent random variables characterizes the [[normal distribution]] (the [[Gauss]] distribution). Thi ...<math>\xi</math>&nbsp; and <math>\eta</math>&nbsp; be independent random variables. If <math>\xi+\eta</math>&nbsp; and <math>\xi-\eta</math>&nbsp; are indepe ...

In [[mathematics]], an '''information source''' is a sequence of [[random variable]]s rangin is the sequence of random variables defining the information source, and ...

In mathematics, '''Osgood's lemma''', introduced by {{harvs|txt|authorlink=William Fogg Os There is no analogue of this result for real variables. If we assume that a function <math>f:\mathbb{R}^n\to\mathbb{R}</math> is g ...

...ion|If 2 linear forms on independent random variables are independent, the variables are normal}} ...tribution) by the independence of two linear forms from independent random variables. This theorem was proved independently by [[Georges Darmois|G. Darmois]] an ...

...Hydrodynamics and Continuum Mechanics, Society for Industrial and Applied Mathematics, Philadelphia, PA, 231-266.</ref> although [[Osborne Reynolds]] had also al ==Favre averaged variables== ...

...ath> This table has <math>K^3</math> cells. In general, for <math>M</math> variables <math>x_1,x_2,\ldots,x_M</math> with <math>K_i</math> states for each varia ...put into [[matrix (mathematics)|matrix]] form. As an example with only two variables, the values of <math>P(x_1=a_k\mid x_2=b_j)=T_{kj},</math> with ''k'' and ' ...

...ated]], integrable [[random variable]]s, each with finite second [[Moment (mathematics)|moment]].<ref name="loeve" /> This simplification gives: ...stimated variance of the cumulative sum of iid normally distributed random variables (which could represent a [[gaussian random walk]] approximating a [[Wiener ...

...eralization of the rule for the sum of [[variance]]s of independent random variables to moments of arbitrary order. It is a special case of the [[Burkholder-Dav ...X_{i}</math>, <math>\textstyle i=1,\ldots,n</math>, are independent random variables such that <math>\textstyle E\left( X_{i}\right) =0</math> and <math>\texts ...

...he process is operating far enough from the specification limit. Plans for variables may produce a similar OC curve to attribute plans with significantly less s A variables sampling plan can be designed so that the OC curve passes through two point ...

In mathematics, the '''Beck–Fiala theorem''' is a major theorem in [[discrepancy theory]] ...c argument. Start with <math> x_i = 0</math> for all elements and call all variables active in the beginning. ...

{{Short description|Function that is invariant under all permutations of its variables}} ...r variables|the generalization of symmetric polynomials to infinitely many variables (in algebraic combinatorics)|ring of symmetric functions|symmetric function ...

{{Short description|Theorem in mathematics about unions of domains of holomorphy}} ...matics, especially [[Function of several complex variables|several complex variables]], the '''Behnke–Stein theorem''' states that a union of an increasing sequ ...

...th fresh variables can be helpful as a way to avoid accidentally capturing variables that should be [[free variable|free]].<ref>{{cite book ...here it is sometimes useful to replace constants by newly introduced fresh variables.<ref>{{cite book ...

...from an initial series of [[independent and identically distributed random variables]] <math>X_1,\ldots,X_n</math>. The members of the variational series form [ ...rg/index.php?title=Variational_series&oldid=14157 |website=Encyclopedia of Mathematics |accessdate=14 February 2020 |date=7 February 2011}}</ref> The [[Range (sta ...

...k=Kiyoshi Oka|first=Kiyoshi|last=Oka|year=1950}}, states that the [[sheaf (mathematics)|sheaf]] <math>\mathcal{O}_{\mathbb{C}^n}</math> of [[holomorphic function * [[Function of several complex variables|Several complex variables]] ...

{{Short description|Uniform approximation theorem in mathematics}} ...ally the theory of [[Function of several complex variables|several complex variables]], the '''Oka–Weil theorem''' is a result about the [[uniform convergence]] ...

In [[mathematics]] a '''partial differential algebraic equation (PDAE)''' set is an incomple * '''x''' is a set of independent variables; ...

{{Expert needed|1=Mathematics|date=March 2011|talk=The page uses an overly-simplistic reading of the simp ...form. The "Big M" refers to a large number associated with the artificial variables, represented by the letter&nbsp;M. ...

...ry of probability, the '''Heyde theorem'''&nbsp;is the [[characterization (mathematics)|characterization]] theorem concerning the [[normal distribution]] (the [[G ...\alpha_1\xi_1 + \cdots + \alpha_n\xi_n</math> is symmetric then all random variables <math>\xi_j</math> have [[Normal distribution | normal distributions]] (Gau ...