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A 1,2-rearrangement is an organic reaction where a substituent moves from one atom to another atom in a chemical compound. In a 1,2 shift the movement involves two adjacent atoms but moves over larger distances are possible. Skeletal isomerization is not normally encountered in the laboratory, but is the basis of large applications in oil ...
For example, many asymptotic expansions are derived from the formula, and Faulhaber's formula for the sum of powers is an immediate consequence. The formula was discovered independently by Leonhard Euler and Colin Maclaurin around 1735. Euler needed it to compute slowly converging infinite series while Maclaurin used it to calculate integrals.
On the continuum level, the second-order velocity term demonstrates that the Ergun equation also includes the pressure drop due to inertia, as described by the Darcy–Forchheimer equation. Specifically, the Ergun equation gives the following permeability k {\displaystyle k} and inertial permeability k 1 {\displaystyle k_{1}} from the Darcy ...
Randles–Sevcik equation. In electrochemistry, the Randles–Ševčík equation describes the effect of scan rate on the peak current ip for a cyclic voltammetry experiment. For simple redox events such as the ferrocene / ferrocenium couple, ip depends not only on the concentration and diffusional properties of the electroactive species but ...
Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has. where e is the base of the natural logarithm, i is the imaginary unit, and ...
Ramberg–Osgood relationship. The Ramberg–Osgood equation was created to describe the nonlinear relationship between stress and strain —that is, the stress–strain curve —in materials near their yield points. It is especially applicable to metals that harden with plastic deformation (see work hardening ), showing a smooth elastic ...
In physics and thermodynamics, the Redlich–Kwong equation of state is an empirical, algebraic equation that relates temperature, pressure, and volume of gases. It is generally more accurate than the van der Waals equation and the ideal gas equation at temperatures above the critical temperature. It was formulated by Otto Redlich and Joseph ...
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