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A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
We present the numerical solution of two-point boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary…
We numerically integrate finite two- and three-loop scalar integrals using the threshold subtraction method. This represents a first step towards extending our calculation of the $N_f$-part to the full NNLO virtual corrections for the…
We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}{D^{2n+1}}$, for large $g$ and $n$, up to approximately degree $n$. The…
In our previous work, numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
Let U denote the open subset formed by deleting the unique line from the singular cubic surface x_1x_2^2+x_2x_0^2+x_3^3=0. In this paper an asymptotic formula is obtained for the number of rational points on U of bounded height, which…
This paper describes a numerical formulation for calculating wave propagation with high precision in a three-dimensional system. Yee's discretization scheme is used to formulate a frequency domain method that is compatible with the…
We find $n(n-3)/2$-dimensional regions of the space of kinematic invariants, where all the solutions to the scattering equations (the core of the CHY formulation of amplitudes) for $n$ massless particles are real. On these regions, the…
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
The soft and collinear singularities of general scalar and tensor one-loop N-point integrals are worked out explicitly. As a result a simple explicit formula is given that expresses the singular part in terms of 3-point integrals. Apart…
In this work we design a new domain decomposition method for the Euler equations in 2 dimensions. The basis is the equivalence via the Smith factorization with a third order scalar equation to whom we can apply an algorithm inspired from…
We propose a method for computing numerically integrals defined via $i \epsilon$ deformations acting on single-pole singularities. We achieve this without an explicit analytic contour deformation. Our solution is then used to produce…
Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and…
In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation…
We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equation - equation that makes manifest the symmetries of a model in local form. We construct a…
Simulation of many-particle system evolution by molecular dynamics takes to decrease integration step to provide numerical scheme stability on the sufficiently large time interval. It leads to a significant increase of the volume of…
The direct method is one of the most important algorithms for solving linear systems of equations, with LU decomposition comprising a significant portion of its computation time. This study explores strategies to accelerate complex LU…