We study a critical case of coagulation-fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel. Our method is based on the viscosity solutions to new singular Hamilton-Jacobi equation, which results from applying Bernstein transform original equation. include well-posedness, regularity, long-time behaviors equation in certain regimes, have implications ...

This paper presents the details of flux-ordered thinning algorithm, which we refer to as Hamilton-Jacobi Skeleton (HJS). It computes skeleton any binary 2D shape. is based on observation that points have low average outward flux gradient distance transform. The algorithm starts by computing function and approximating values for all pixels inside Then a procedure called homotopy preserving itera...

A new method for interpolation by rational functions of prescribed numerator and denominator degrees is presented. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm is particularly simple and relies on discrete Fourier transform matrices, which results in a fast implementation using the Fast Fourier Transform. The method is generalised for arbitrary grids, which...

Computational Convex Analysis algorithms have been rediscovered several times in the past by researchers from different fields. To further communications between practitioners, we review the field of computational convex analysis, which focuses on the numerical computation of fundamental transforms arising from convex analysis. Current models use symbolic, numeric, and hybrid symbolic-numeric a...

The spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomial...

The evolution of a Bose–Einstein condensate (BEC) with an internal degree of freedom, i.e., spinor BEC, is governed by a system of three coupled mean-field equations. The system admits the application of the inverse scattering transform and Hirota bilinear method under appropriate conditions, which makes it possible to generate exact analytical solutions relevant to physical applications. Here,...