Search results for "Computational Mathematic"
showing 10 items of 987 documents
Extended Natural Numbers and Counters
2020
Summary This article introduces extended natural numbers, i.e. the set ℕ ∪ {+∞}, in Mizar [4], [3] and formalizes a way to list a cardinal numbers of cardinals. Both concepts have applications in graph theory.
Ejection and collision orbits of the spatial restricted three-body problem
1985
We begin by describing the global flow of the spatial two body rotating problem, μ=0. The remainder of the work is devoted to study the ejection and collision orbits when μ>-0. We make use of the ‘blow up’ techniques to show that for any fixed value of the Jacobian constant the set of these orbits is diffeomorphic to S2×R. Also we find some particular collision-ejection orbits.
Closed form coefficients in the Symmetric Boundary Element Approach
2006
Abstract In the area of the structural analysis, the problems connected to the use of the symmetric Galerkin Boundary Element Method (SGBEM) must be investigated especially in the mathematical and computational difficulties that are present in computing the solving system coefficients. Indeed, any coefficient is made by double integrals including often fundamental solutions having a high degree of singularity. Therefore, the related computation proves to be difficult in the solution. This paper suggests a simple computation technique of the coefficients obtained in closed form. Using a particular matrix, called ‘progenitor’ matrix [Panzeca T, Cucco F, Terravecchia S. Symmetric boundary elem…
Adaptive rational interpolation for point values
2019
Abstract G. Ramponi et al. introduced in Carrato et al. (1997,1998), Castagno and Ramponi (1996) and Ramponi (1995) a non linear rational interpolator of order two. In this paper we extend this result to get order four. We observe the Gibbs phenomenon that is obtained near discontinuities with its weights. With the weights we propose we obtain approximations of order four in smooth regions and three near discontinuities. We also introduce a rational nonlinear extrapolation which is also of order four in the smooth region of the given function. In the experiments we calculate numerically approximation orders for the different methods described in this paper and see that they coincide with th…
A generalized Newton iteration for computing the solution of the inverse Henderson problem
2020
We develop a generalized Newton scheme IHNC for the construction of effective pair potentials for systems of interacting point-like particles.The construction is made in such a way that the distribution of the particles matches a given radial distribution function. The IHNC iteration uses the hypernetted-chain integral equation for an approximate evaluation of the inverse of the Jacobian of the forward operator. In contrast to the full Newton method realized in the Inverse Monte Carlo (IMC) scheme, the IHNC algorithm requires only a single molecular dynamics computation of the radial distribution function per iteration step, and no further expensive cross-correlations. Numerical experiments…
Approximation and quasicontinuity of Besov and Triebel–Lizorkin functions
2016
We show that, for $0<s<1$, $0<p<\infty$, $0<q<\infty$, Haj\l asz-Besov and Haj\l asz-Triebel-Lizorkin functions can be approximated in the norm by discrete median convolutions. This allows us to show that, for these functions, the limit of medians, \[ \lim_{r\to 0}m_u^\gamma(B(x,r))=u^*(x), \] exists quasieverywhere and defines a quasicontinuous representative of $u$. The above limit exists quasieverywhere also for Haj\l asz functions $u\in M^{s,p}$, $0<s\le 1$, $0<p<\infty$, but approximation of $u$ in $M^{s,p}$ by discrete (median) convolutions is not in general possible.
A boundary min-max principle as a tool for boundary element formulations
1991
Abstract A min-max principle for elastic solids, expressed in terms of the unknown boundary displacements and tractions, is presented. It is shown that its Euler-Lagrange equations coincide with the classical boundary integral equations for displacements and for tractions. This principle constitutes a suitable starting point for a symmetric sign-definite formulation of the boundary element method.
On a new proof of Moser's twist mapping theorem
1976
Based on a new idea of the author, a new proof of J. Moser's twist mapping theorem is presented.
Monotonicity-based inversion of the fractional Schr\"odinger equation II. General potentials and stability
2019
In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder\'on problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Sch…
On a global superconvergence of the gradient of linear triangular elements
1987
Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.