equilibrium (open distillation). Multiple residue curves for a single system are called residue curves map. Residue curves allow testing the feasibility of a...

the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it...

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...

of batch distillation are based on analyses of the following maps: Residue curve map still path map distillate path map different column profile maps...

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...

when water is removed by azeotropic distillation. Azeotrope tables Residue curve Theoretical plate Vacuum distillation Kister, Henry Z. (1992). Distillation...

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...

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...

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...

oxygen–hemoglobin dissociation curve, also called the oxyhemoglobin dissociation curve or oxygen dissociation curve (ODC), is a curve that plots the proportion...

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...

where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour...

\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...

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...

The Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer...

Netherlands. In 2011 he coauthored the book Membrane Process Design Using Residue Curve Maps. He holds four patents, including patents for improving chemical...

In mathematics, the Montgomery curve is a form of elliptic curve introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form...

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...

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...

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...

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...

theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic varieties), for everywhere-regular differential...

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...

that vegetation). "Direct seeding" is when crops are sown through the residue of previous crop. "Surface seeding" or "direct seeding" is when seeds are...

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...

In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods...

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...

globular protein via the N atoms of the imidazole ring of F8 histidine residue (also known as the proximal histidine) below the porphyrin ring. A sixth...

mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function...

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...