By defining a prepotential function for the stationary Schrödinger equation we derive an inversion formula for the space variable x as a function of the wave–function ψ. The resulting equation is a Legendre transform that relates x, the prepotential F , and the probability density. We invert the Schrödinger equation to a third–order differential equation for F and observe that the inversion pro...

The problem of image reconstruction in thermoacoustic tomography requires inversion of a generalized Radon transform, which integrates the unknown function over circles in 2D or spheres in 3D. The paper investigates implementation of the recently discovered backprojection type inversion formulas for the case of spherical acquisition in 3D. A numerical simulation of the data acquisition with sub...

The use of Fourier transforms for deriving probability densities of sums and differences of random variables is well known. The use of Mellin transforms to derive densities for products and quotients of random variables is less well known. We present the relationship between the Fourier and Mellin transform, and discuss the use of these transforms in deriving densities for algebraic combination...

An asymptotic expression for the expected area of the union of n random rectangles is derived by Mellin transforms, where their two diagonal corners are independently and uniformly distributed over (0, 1). The general result for d-dimensional hyper-rectangles is also stated. COMPUTATIONAL GEOMETRY, CONVEX HULL, GEOMETRIC PROBABILITY, GEOMETRY OF RECTANGLES, MELLIN TRANSFORM, CALCULUS OF FINITE ...

The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is used to obtain estimates for

Using the Mellin transform a new method for solving the Black-Scholes equation is proposed. Our approach does not require either variable transformations or solving diffusion equations.