Search results for "singular"

About the Reliability of Extrapolation of Nuclear Structure Data for r-process Calculations

2002

Gross decay properties are the nuclear part of the input for calculations of elemental abundances. They depend, sometimes very sensitively, on details of nuclear structure. Models for predictions of nuclear masses and shapes have to be used for isotopes very far from stability. The reliability of extrapolations far from experimentally reachable nuclei is, however, not always granted due to singularities in the nuclear landscape. We review data on the region of the neutron-rich isotopes near A = 100, which is a region of especially dramatic changes.

Computational aspects in 2D SBEM analysis with domain inelastic actions

2009

The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals. In the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed, and by means of a limiting operation, this traction is evaluated on the boundary. First the weakly singular domain integral in the Somigliana Identity (S.I.) of the displacements is regularized and the singular integral is transformed into a boundary one using the Radial Integration Method; subsequently, using the differential operator applied to the displacement field, the S.I. of the tractions inside the body is obtained and through…

Inversion Formulas for the Discretized Hilbert Transform on the Unit Circle

1998

A discrete version of the Hilbert transform on the unit circle is considered. Its Moore--Penrose inverse with respect to suitable scalar products is derived for different side conditions. Furthermore, stability of the pseudo-inverse is studied. These results allow the efficient computation of approximate solutions of singular integral equations with Hilbert kernel. Furthermore, the stability analysis of such methods becomes much easier even for graded meshes which are useful for weakly singular solutions.

Exponential convergence andH-c multiquadric collocation method for partial differential equations

2003

The radial basis function (RBF) collocation method uses global shape functions to interpolate and collocatethe approximate solution of PDEs. It is a truly meshless method as compared to some of the so-calledmeshless or element-free finite element methods. For the multiquadric and Gaussian RBFs, there are twoways to make the solution converge—either by refining the mesh size

Reflection and Refraction of Singularities for Wave Equations with Interface Conditions given by Fourier Integral Operators

1992

Cauchy problems for hyperbolic operators often have the property, that the singularities of the initial data propagate along the bicharacteristic strips of the operator (cf. e.g. [13]). We consider, in the linear case, the situation where the bicharacteristics hit transversally a spacelike interface, which is ‘active’ in the sense that the interface condition is given via certain Fourier integral operators. Taking the identity, we obtain classical transmission conditions. A suitable functional analytic setting is furnished by the interaction concept [3], [6], [7], which covers very general mutual influences of evolution phenomena on different domains.

On a singular boundary value problem for a second order ordinary differential equation

2000

Parallel Schwarz methods for convection-dominated semilinear diffusion problems

2002

AbstractParallel two-level Schwarz methods are proposed for the numerical solution of convection-diffusion problems, with the emphasis on convection-dominated problems. Two variants of the methodology are investigated. They differ from each other by the type of boundary conditions (Dirichlet- or Neumann-type) posed on a part of the second-level subdomain interfaces. Convergence properties of the two-level Schwarz methods are experimentally compared with those of a variant of the standard multi-domain Schwarz alternating method. Numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods.

Combining Mendonça-Cipolla self-calibration and scene constraints

2011

International audience; In this paper, we propose a method that combines plane parallelism and the Mendonça/Cipolla self-calibration constraints. In our method each pair of images is treated independently and can therefore use a different pair of parallel planes not necessarily visible in the other views. While, for each pair of images, constraints on the singular values of the essential matrix provide two algebraic constraints on the intrinsic parameters, those we derive from plane parallelism have the advantage of providing two additional ones making the calibration of a no-skew camera possible from two images only.

Singular integrals, analytic capacity and rectifiability

1997

In this survey we study some interplay between classical complex analysis (removable sets for bounded analytic functions), harmonic analysis (singular integrals), and geometric measure theory (rectifiability).

A note on the analytic solutions of the Camassa-Holm equation

2005

Abstract In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using the Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic, belongs to H s ( R ) with s > 3 / 2 , ‖ u 0 ‖ L 1 ∞ and u 0 − u 0 x x does not change sign, we prove that the solution stays analytic globally in time. To cite this article: M.C. Lombardo et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).