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The implicit function theorem of more than two real variables deals with the continuity and differentiability of the function, as follows. [4] Let ϕ ( x 1 , x 2 , …, x n ) be a continuous function with continuous first order partial derivatives, and let ϕ evaluated at a point ( a , b ) = ( a 1 , a 2 , …, a n , b ) be zero:
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In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable or defined over a multi-dimensional domain. [1] A common special case is bivariate interpolation or two-dimensional interpolation, based on two variables or two dimensions.
Fractionation at total reflux. The Fenske equation in continuous fractional distillation is an equation used for calculating the minimum number of theoretical plates required for the separation of a binary feed stream by a fractionation column that is being operated at total reflux (i.e., which means that no overhead product distillate is being withdrawn from the column).
A heat recovery steam generator (HRSG) is an energy recovery heat exchanger that recovers heat from a hot gas stream, such as a combustion turbine or other waste gas stream. It produces steam that can be used in a process ( cogeneration ) or used to drive a steam turbine ( combined cycle ).
Sweave is a function in the statistical programming language R that enables integration of R code into LaTeX or LyX documents. It was introduced by Friedrich Leisch in 2002. [1] The purpose is "to create dynamic reports, which can be updated automatically if data or analysis change". [2]
To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions and linear algebra.
The steam so produced is injected into the gas turbine's combustion chamber to increase power output. [3] The process can be thought of as a parallel combination of the gas turbine Brayton cycle and a steam turbine Rankine cycle. [4] [5] The cycle was invented by Prof. Dah Yu Cheng of the University of Santa Clara who patented it in 1976. [6] [1]