Search results for "Computational Mathematic"
showing 10 items of 987 documents
Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation
2019
International audience; The inverse scattering approach for the defocusing Davey–Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We treat the D-bar problem as a complex linear second order integral equation which is solved with discrete Fourier transforms complemented by a regularization of the singular parts by explicit analytic computation. The resulting algebraic equation is solved either by fixed point iterations or GMRES. Several examples for small values of the semi-classical parameter in the system are discussed.
Computation of Yvon-Villarceau circles on Dupin cyclides and construction of circular edge right triangles on tori and Dupin cyclides
2014
Ring Dupin cyclides are non-spherical algebraic surfaces of degree four that can be defined as the image by inversion of a ring torus. They are interesting in geometric modeling because: (1) they have several families of circles embedded on them: parallel, meridian, and Yvon-Villarceau circles, and (2) they are characterized by one parametric equation and two equivalent implicit ones, allowing for better flexibility and easiness of use by adopting one representation or the other, according to the best suitability for a particular application. These facts motivate the construction of circular edge triangles lying on Dupin cyclides and exhibiting the aforementioned properties. Our first contr…
Approximation of functions over manifolds : A Moving Least-Squares approach
2021
We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any knowledge regarding the manifold other than its dimension $d$. We use the Manifold Moving Least-Squares approach of (Sober and Levin 2016) to reconstruct the atlas of charts and the approximation is built on-top of those charts. The resulting approximant is shown to be a function defined over a neighborhood of a manifold, approximating the originally sampled manifold. In other words, given a new point, located near the manifold, the approximation can be evaluated…
Topology-based goodness-of-fit tests for sliced spatial data
2023
In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. In the present paper, we illustrate how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, we devise goodness-of-fit tests that become asymptotically exact in large sampling windows. We illustrate the test…
Correction of cavity-induced errors in polarization charges of continuum solvation models
1998
MINDO/3 Study of the Rearrangement of 1-Methylcyclohexyl Cation to 1,2-Dimethylcyclopentyl Cation
1986
The rearrangement of the 1-methylcyclohexyl cation to the 1,2-dimethylcyclopentyl cation has been studied by MINDO/3 calculations, as an application of the branching mechanism model for cycloalkanes. Possible intermediates and transition states have been characterized by diagonalization of their Hessian matrixes. Two nonequivalent pathways, α and β scissions, are relatively close in energy. The calculated transition states are almost equivalent in energy to those found for cyclohexyl cation. Hence, the energy barriers are higher for the rearrangement of the 1-methyl than for cyclohexyl cation, because the former is less stable than the latter.
On the ultradistributions of Beurling type
2009
Sea un conjunto abierto no vac´ýo del espacio euclideo . En este articulo se demuestra que si S es una ultradistribucion en , perteneciente a una clase de tipo Beurling que sea estable frente a operadores diferenciales, entonces S se puede representar en la formaP 2Nk0 D f , donde f es una funcion compleja definida en que es Lebesgue medible y esencialmente acotada en cada subconjunto compacto de . Tambi´en se obtienen otros resultados de estructura de ciertas ultradistribuciones.
Una variante del metodo di Aparo per la determinazione degli zeri complessi di un polinomio
1968
Si espone un metodo per il calcolo degli zeri complessi di un polinomio che si presenta con caratteristiche intermedie tra quelli tradizionali del tipo «paper and pencil» e quelli sviluppati per l’impiego sui grandi calcolatori automatici. Il metodo e fondato su un principio analogo a quello di Aparo, ma utilizza una retta di inclinazione variabile passante per l’origine del piano complesso. Il passaggio di questa retta per gli zeri del polinomio viene individnato ricorrendo ad una opportuna variante del criterio di Routh, adattato allo studio della stabilita condizionata dei sistemi lineari.
Identification of small inhomogeneities: Asymptotic factorization
2007
We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymptotic expansions have already been used to design direct (i.e. noniterative) reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary, e.g. MUSIC-type methods. Our derivation of the asymptotic formulas is based on integral …