equilibrium (open distillation). Multiple residue curves for a single system are called residue curves map. Residue curves allow testing the feasibility of a...
5 KB (735 words) - 19:54, 10 June 2023
the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it...
13 KB (3,282 words) - 17:30, 14 October 2024
of batch distillation are based on analyses of the following maps: Residue curve map still path map distillate path map different column profile maps...
12 KB (1,384 words) - 22:24, 9 December 2023
Contour integration (redirect from Residue calculus)
complex-valued function along a curve in the complex plane; application of the Cauchy integral formula; and application of the residue theorem. One method can...
45 KB (9,663 words) - 18:18, 14 July 2024
Winding number (redirect from Index of the curve)
analysis (c.f. the statement of the residue theorem). In the context of complex analysis, the winding number of a closed curve γ {\displaystyle \gamma } in the...
16 KB (2,293 words) - 15:19, 15 September 2024
simple closed curve around a k {\displaystyle a_{k}} and not including any other singularities on or inside the curve. The definition of a residue can be generalized...
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when water is removed by azeotropic distillation. Azeotrope tables Residue curve Theoretical plate Vacuum distillation Kister, Henry Z. (1992). Distillation...
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Modular arithmetic (redirect from Residue class)
least residue system is a complete residue system, and a complete residue system is simply a set containing precisely one representative of each residue class...
29 KB (3,602 words) - 22:50, 24 September 2024
oxygen–hemoglobin dissociation curve, also called the oxyhemoglobin dissociation curve or oxygen dissociation curve (ODC), is a curve that plots the proportion...
23 KB (2,859 words) - 06:58, 17 August 2024
The runoff curve number (also called a curve number or simply CN) is an empirical parameter used in hydrology for predicting direct runoff or infiltration...
24 KB (1,494 words) - 02:10, 21 May 2024
Line integral (redirect from Curve integral)
where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour...
21 KB (3,181 words) - 19:21, 10 August 2024
mathematics, the residue field is a basic construction in commutative algebra. If R is a commutative ring and m is a maximal ideal, then the residue field is...
5 KB (625 words) - 22:59, 11 October 2024
Adjunction formula (section Poincaré residue)
\omega _{D}} is called the Poincaré residue. Suppose that X is a complex manifold. Then on sections, the Poincaré residue can be expressed as follows. Fix...
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invalid curve points for her key and Bob does not validate that Alice's points are part of the selected group, she can collect enough residues of Bob's...
13 KB (2,065 words) - 19:12, 14 October 2024
In mathematics, the Montgomery curve is a form of elliptic curve introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form...
15 KB (3,401 words) - 07:14, 29 September 2024
The Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer...
26 KB (4,508 words) - 23:04, 16 April 2024
Netherlands. In 2011 he coauthored the book Membrane Process Design Using Residue Curve Maps. He holds four patents, including patents for improving chemical...
11 KB (987 words) - 21:25, 17 January 2024
mathematics, the residue formula says that the sum of the residues of a meromorphic differential form on a smooth proper algebraic curve vanishes. In this...
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exist in the T4 lysozyme between aspartic acid (Asp) at residue 70 and a histidine (His) at residue 31 (Figure 3). Site-directed mutagenesis with asparagine...
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Semistable abelian variety (redirect from Semistable elliptic curve)
the group law. This is an open subgroup scheme of the Néron model. For a residue field k {\displaystyle k} , A k 0 {\displaystyle A_{k}^{0}} is a group...
5 KB (648 words) - 11:37, 19 December 2022
r)} . This sort of argument can be useful in locating residues when one applies Cauchy's residue theorem. Rouché's theorem can also be used to give a short...
11 KB (1,855 words) - 10:00, 18 April 2024
Amino acid (redirect from Residue (amino acid))
amino-acid residues form the second-largest component (water being the largest) of human muscles and other tissues. Beyond their role as residues in proteins...
98 KB (10,141 words) - 19:21, 21 September 2024
No-till farming (redirect from Residue management)
that vegetation). "Direct seeding" is when crops are sown through the residue of previous crop. "Surface seeding" or "direct seeding" is when seeds are...
42 KB (4,404 words) - 21:43, 29 September 2024
mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function...
8 KB (1,530 words) - 03:43, 6 January 2023
The resultant TGA curve plotted with the y-axis as a percentage of initial mass would show the residue at the final point of the curve. Oxidative mass losses...
17 KB (1,677 words) - 18:07, 4 October 2024
theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic varieties), for everywhere-regular differential...
4 KB (530 words) - 04:59, 21 May 2023
Logarithmic form (section Example of the residue)
D_{j}} . In this context, the residue may be called the Poincaré residue. For an explicit example, consider an elliptic curve D in the complex projective...
15 KB (2,984 words) - 02:01, 29 November 2023
Hemoglobin's oxygen binding affinity (see oxygen–haemoglobin dissociation curve) is inversely related both to acidity and to the concentration of carbon...
18 KB (2,334 words) - 10:18, 27 March 2023
In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods...
27 KB (4,792 words) - 19:45, 6 September 2024
that a curve is homotopic to a constant curve if there exists a smooth homotopy (within U {\displaystyle U} ) from the curve to the constant curve. Intuitively...
10 KB (1,635 words) - 21:31, 20 December 2022