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Consequently, the adjunction formula says that the restriction of (d − 3)H to C equals the canonical class of C. This restriction is the same as the intersection product (d − 3)H ⋅ dH restricted to C, and so the degree of the canonical class of C is d(d−3). By the Riemann–Roch theorem, g − 1 = (d−3)d − g + 1, which implies the ...
The 30th edition (1996) was renamed CRC Standard Mathematical Tables and Formulae, with Daniel Ian Zwillinger as the editor-in-chief. [2] The 33rd edition (2018) was renamed CRC Standard Mathematical Tables and Formulas. [3]
Hydroxyproline is a major component of the protein collagen, [3] comprising roughly 13.5% of mammalian collagen. Hydroxyproline and proline play key roles for collagen stability. [4]
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field.
In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [1] [2] It is occasionally known as adjunct matrix, [3] [4] or "adjoint", [5] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
More compact collections can be found in e.g. Brychkov, Marichev, Prudnikov's Tables of Indefinite Integrals, or as chapters in Zwillinger's CRC Standard Mathematical Tables and Formulae or Bronshtein and Semendyayev's Guide Book to Mathematics, Handbook of Mathematics or Users' Guide to Mathematics, and other mathematical handbooks.
A formulae booklet was available to all candidates for all examinations up to and including those in 2018. As of 2019, candidates are no longer be issued with a formulae booklet; instead they will be expected to recall, or know how to derive quickly, standard formulae.
Hexafluoroisopropanol, commonly abbreviated HFIP, is the organic compound with the formula (CF 3) 2 CHOH. This fluoroalcohol finds use as solvent in organic chemistry. [1] Hexafluoro-2-propanol is transparent to UV light with high density, low viscosity and low refractive index. It is a colorless, volatile liquid with a pungent odor.