An analytic solution to Wahbaʼs problem

AN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM

In this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. This system is solved iteratively, where the applicationof the infinite stiffness matrix, that is sufficiently compressible,is r...

An analytic solution for the perspective 4-point problem

An Analytic Solution to the Busemann-Petty Problem on Sections of Convex Bodies

We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in Rn with the Fourier transform of powers of the radial function of the body. A parallel section function (or (n − 1)dimensional X-ray) gives the ((n − 1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characteri...

An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

On the Analytic Solution of the Cauchy Problem

Derivatives of a solution of an ODE Cauchy problem can be computed inductively using the Faà di Bruno formula. In this paper, we exhibit a noninductive formula for these derivatives. At the heart of this formula is a combinatorial problem, which is solved in this paper. We also give a more tractable form of the Magnus expansion for the solution of a homogeneous linear ODE.