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For convenience in avoiding conversions in the imperial (or US customary units), some engineers adopted the pound-mole (notation lb-mol or lbmol), which is defined as the number of entities in 12 lb of 12 C. One lb-mol is equal to 453.592 37 g‑mol, [6] which is the same numerical value as the number of grams in an international avoirdupois pound.
The Avogadro constant, commonly denoted N A [1] or L, [2] is an SI defining constant with an exact value of 6.022 140 76 × 10 23 mol −1 (reciprocal moles). [3] [4] It is this defined number of constituent particles (usually molecules, atoms, ions, or ion pairs—in general, entities) per mole and used as a normalization factor in relating the amount of substance, n(X), in a sample of a ...
V m = 10.7316 × 519.67 / 14.696 = 379.48 ft 3 /lbmol at 60 °F and 14.696 psi (or about 0.8366 ft 3 /gram mole) V m = 10.7316 × 519.67 / 14.730 = 378.61 ft 3 /lbmol at 60 °F and 14.73 psi; Technical literature can be confusing because many authors fail to explain whether they are using the ideal gas constant R, or the specific gas constant R s.
The proof of the Brunn–Minkowski inequality predates modern measure theory; the development of measure theory and Lebesgue integration allowed connections to be made between geometry and analysis, to the extent that in an integral form of the Brunn–Minkowski inequality known as the Prékopa–Leindler inequality the geometry seems almost ...
One of the important developments arising from the geometric approach to mechanics is the incorporation of the geometry into numerical methods. In particular symplectic and variational integrators are proving particularly accurate for long-term integration of Hamiltonian and Lagrangian systems.
In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity. As the name implies, the fundamental meaning of monodromy comes from "running round singly".
Symplectic manifolds arise from classical mechanics; in particular, they are a generalization of the phase space of a closed system. [1] In the same way the Hamilton equations allow one to derive the time evolution of a system from a set of differential equations, the symplectic form should allow one to obtain a vector field describing the flow of the system from the differential of a ...
A Kähler manifold is a Riemannian manifold of even dimension whose holonomy group is contained in the unitary group (). [3] Equivalently, there is a complex structure on the tangent space of at each point (that is, a real linear map from to itself with =) such that preserves the metric (meaning that (,) = (,)) and is preserved by parallel transport.
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