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The Smith chart (sometimes also called Smith diagram, Mizuhashi chart (水橋チャート), Mizuhashi–Smith chart (水橋スミスチャート), [1] [2] [3] Volpert–Smith chart (Диаграмма Вольперта—Смита) [4] [5] or Mizuhashi–Volpert–Smith chart), is a graphical calculator or nomogram designed for electrical and electronics engineers specializing in radio ...
The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949.
If a gaseous emission sample is analyzed and found to contain water vapor and a pollutant concentration of say 40 ppmv, then 40 ppmv should be designated as the "wet basis" pollutant concentration. The following equation can be used to correct the measured "wet basis" concentration to a "dry basis" concentration: [3]
For example, 50 g of zinc will react with oxygen to produce 62.24 g of zinc oxide, implying that the zinc has reacted with 12.24 g of oxygen (from the Law of conservation of mass): the equivalent weight of zinc is the mass which will react with eight grams of oxygen, hence 50 g × 8 g/12.24 g = 32.7 g.
For instance, triolein, a triglyceride occurring in many fats and oils, has three oleic acid residues esterified to a molecule of glycerol with a total MW of 885.4 (g / mol). Therefore, its SV equals 190 mg KOH / g sample. [9] In comparison, trilaurin with three shorter fatty acid residues (lauric acid) has a MW of 639 and an SV of 263.
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
The same calculation performed on the orthogonal complement of gives the next largest eigenvalue and so on. The complex Hermitian case is similar; there f ( x ) = x ∗ M x {\displaystyle f(\mathbf {x} )=\mathbf {x} ^{*}\mathbf {M} \mathbf {x} } is a real-valued function of 2 n {\displaystyle 2n} real variables.
The theorem also leads to a formula for perfectly reconstructing the original continuous-time function from the samples. Perfect reconstruction may still be possible when the sample-rate criterion is not satisfied, provided other constraints on the signal are known (see § Sampling of non-baseband signals below and compressed sensing). In some ...