(chemistry) In polymer chemistry, a simple empirical formula that relates molecular weight to the glass transition temperature of a polymer system.

(mathematics) The equation that defines the Legendre polynomials: d/dx[(1-x²)d/dxP_n(x)]+n(n+1)P_n(x)=0.

(mechanics, analytical mechanics) A differential equation which describes a function mathbf q(t) which describes a stationary point of a functional, S( mathbf q)=∫L(t, mathbf q(t), mathbf ̇q(t)),dt, which represents the action of mathbf q(t), with L representing the Lagrangian. The said equation (found through the calculus of variations) is ∂L/∂ mathbf q=d/dt∂L/∂ mathbf ̇q and its solution for mathbf q(t) represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action.

(physics) An equation that attempts to meld the ideas of quantum mechanics and general relativity. It describes the quantum version of the Hamiltonian constraint using metric variables.

plural of Cauchy-Riemann equation

(mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.

(chemistry) An equation describing the derivation of pH as a measure of acidity (using pKa, the negative log of the acid dissociation constant) in biological and chemical systems.

(mathematics) A special kind of integral equation, having applications in demography, the study of viscoelastic materials, and actuarial science.

plural of Lotka-Volterra equation

plural of Volterra integral equation