Related papers: On locating the zeros and poles of a meromorphic f…
Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved…
In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code,…
The usual methods for root finding of polynomials are based on the iteration of a numerical formula for improvement of successive estimations. The unpredictable nature of the iterations prevents to search roots inside a pre-specified region…
This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the…
Multivariate renormalisation techniques are implemented in order to build, study and then renormalise at the poles, branched zeta functions associated with trees. For this purpose, we first prove algebraic results and develop analytic…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
We study vanishing cycles naturally attached to a meromorphic function with isolated singularities, in both local and global settings.
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
We study the distribution of zeros of general solutions of the Airy and Bessel equations in the complex plane. Our results characterize the patterns followed by the zeros for any solution, in such a way that if one zero is known it is…
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. But, in the case of general ($C^{\infty}$) smooth functions, the meromorphic…
We prove a topological decomposition of the space of meromorphic germs at zero in several variables with prescribed linear poles as a sum of spaces of holomorphic and polar germs. Evaluating the resulting holomorphic projection at zero…
In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…
We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…
A new computational method to solve the hyperbolic (Vlasov) equation and the elliptic (Poisson-like) equation at the polar axis is proposed. It is shown that the value of a scalar function at the polar axis can be predicted by its…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…