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Producer surplus, or producers' surplus, is the amount that producers benefit by selling at a market price that is higher than the least that they would be willing to sell for; this is roughly equal to profit (since producers are not normally willing to sell at a loss and are normally indifferent to selling at a break-even price).
This equation is a special form of the more general weakly singular Volterra integral equation of the first kind, called Abel's integral equation: [7] = Strongly singular: An integral equation is called strongly singular if the integral is defined by a special regularisation, for example, by the Cauchy principal value.
The finite element method (FEM) is used to find approximate solution of partial differential equations (PDE) and integral equations. The solution approach is based either on eliminating the time derivatives completely (steady state problems), or rendering the PDE into an equivalent ordinary differential equation , which is then solved using ...
The following bound on the L 2 → L 2 action of oscillatory integral operators (or L 2 → L 2 operator norm) was obtained by Lars Hörmander in his paper on Fourier integral operators: [2] Assume that x,y ∈ R n, n ≥ 1. Let S(x,y) be real-valued and smooth, and let a(x,y) be smooth and compactly supported.
A Sommerfeld expansion is an approximation method developed by Arnold Sommerfeld for a certain class of integrals which are common in condensed matter and statistical physics. Physically, the integrals represent statistical averages using the Fermi–Dirac distribution.
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics.It asserts that the phase-space distribution function is constant along the trajectories of the system—that is that the density of system points in the vicinity of a given system point traveling through phase-space is constant with time.
In 1911, Lalescu wrote the first book ever on integral equations. Volterra integral equations find application in demography as Lotka's integral equation, [2] the study of viscoelastic materials, in actuarial science through the renewal equation, [3] and in fluid mechanics to describe the flow behavior near finite-sized boundaries. [4] [5]
The Feynman checkerboard, or relativistic chessboard model, was Richard Feynman's sum-over-paths formulation of the kernel for a free spin- 1 / 2 particle moving in one spatial dimension. It provides a representation of solutions of the Dirac equation in (1+1)-dimensional spacetime as discrete sums.