plural of Cauchy problem

(mathematics, mathematical analysis) For a given m-order partial differential equation, the problem of finding a solution function u on ℝⁿ that satisfies the boundary conditions that, for a smooth manifold S⊂ℝⁿ, u(x)=f_0(x) and (∂ᵏu(x))/(∂nᵏ)=f_k(x), ∀x∈S, k=1…m-1, given specified functions f_k defined on, and vector n normal to, the manifold.

plural of Cauchy horizon

(physics) A light-like boundary of the domain of validity of a Cauchy problem. One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics.

(linear algebra, mathematical analysis) A theorem which states that the absolute value of the dot product between two vectors is less than or equal to the product of the magnitudes of the two vectors.

plural of Cauchy-Schwarz inequality

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.