179 research outputs found
Numerical solution of systems of Cauchy singular integral equations with constant coefficients
No full textThis paper deals with the numerical solution of a class of systems of Cauchy singular integral equations with constant coefficients. The proposed procedure consists of two basic steps: the first one is to consider a modified problem equivalent to the original one under suitable conditions, the second one is to approximate its solution by means of a vector of polynomial functions. Such array is constructed by applying a quadrature type method,
based on Gaussian rules, that leads to solve a determined and well conditioned linear system.
The convergence and stability of the method are proved in weighted L2 spaces. Some numerical tests are also shown
A quadrature method for systems of Cauchy Singular Integral Equations
No full textThis talk deals with the numerical treatment of systems of Cauchy Singular integral equations with constant coefficients.
A quadrature type method is proposed and its stability and convergence are proved in weighted spaces.
Moreover it is shown that the procedure leads to solve a determined and well conditioned linear system
A modified Nystrom method for integral equations with Mellin type kernels
No full textThe aim of this paper is to propose a new modified Nyström method for the approximation of the solutions of second kind integral equations with fixed singularities of Mellin convolution type. The stability and the convergence are proved in L^2 spaces and error estimates in L^2 norm are given. Finally, numerical tests showing the effectiveness of the method are presented
The numerical solution of Cauchy singular integral equations with additional fixed singularities
No full textIn this paper we propose a quadrature method for the numerical solution of Cauchy singular integral
equations with additional fixed singularities. The unknown function is approximated by a weighted
polynomial which is the solution of a finite dimensional equation obtained discretizing the involved
integral operators by means of a Gauss-Jacobi quadrature rule. Stability and convergence results for the
proposed procedure are proved. Moreover, we prove that the linear systems one has to solve, in order to
determine the unknown coefficients of the approximate solutions, are well conditioned. The efficiency of
the proposed method is shown through some numerical examples
A quadrature method for systems of Cauchy Singular Integral Equations
No full textThe aim of this paper is to propose a numerical method approximating the solutions of a system of CSIE.
The stability and the convergence of the method are proved in weighted spaces. An application to the numerical resolution of CSIE on curves is also given. Finally some numerical tests confirming the error estimates are shown
A Nyström method for integral equations with fixed singularities of Mellin type in weighted Lp spaces
No full textWe consider integral equations of the second kind with fixed singularities of Mellin type. According to the behavior of the Mellin kernel, we first determine suitable weighted Lp spaces where we look for the solution. Then, for its approximation, we propose a numerical method of Nyström type based on a Gauss–Jacobi quadratura formula. Actually, a slight modification of the classical procedure is introduced in order to prove convergence results in weighted Lp spaces. Moreover, a preconditioning technique allows us to solve well conditioned linear systems. We show the efficiency of the proposed method through some numerical tests
Nyström method for Cauchy Singular Integral Equations with negative index
No full textIn this paper, the authors propose a Nyström method to approximate the solutions of Cauchy singular integral equations with constant coefficients having a negative index. They
consider the equations in spaces of continuous functions with weighted uniform norm. They prove the stability and the convergence of the method and show some numerical tests that confirm the error estimates
Numerical treatment of second kind Fredholm integral equations systems on bounded intervals
No full textIn this paper the authors propose numerical methods to approximate the solutions of systems of second kind Fredholm integral equations. They prove that such methods are stable and convergent. Error estimates in weighted norm, , are given and some numerical tests are shown
Mustelictis olivieri Bonis 1997
No full text<i>Mustelictis</i> aff. <i>olivieri</i> Bonis, 1997 <p>(Figs 4 C-E, G; 5F)</p> <p>TYPE SPECIMEN. — Holotype: skull, UP MGB60, by author designation; paratype: hemi-mandible, UP MGB 7.</p> <p>NEW MATERIAL. — Left m1, LPL11; left fragment of hemi-mandible, UP LPL12; right m1, UM VBOA 3-4; fragment of right hemi-mandible p2-p4, UM VD 12; left P4, VBO 494.</p> <p>REMARKS</p> <p>The holotype and paratype of the species come from Mas de Got (MP 22). A skull and a hemi-mandible (paratype) were figured by Bonis (1997: figs 1, 2). New research has recovered additional specimens in other localities.</p> <p>DESCRIPTION</p> <p>The premolars are present in UP LPL12 and UM VD12 and all of them have cutting mesial and distal edges. The p2 is dissymmetric, the mesial part being smaller than the distal</p> <p> one and having a more sloping mesial edge, the distal one finishing by a small upturned spur at its base. The p3, less dissymmetric than p2, displays a mesial spur; distally there is a small talonid with a small fovea surrounded by a low cristid; there is also a small pacd at mid-height on the distal edge (Fig. 4G 1, G 2). The p4 is similar to p3 but is larger. The carnassial is very similar to that of the type of <i>M</i>. <i>olivieri</i> but the talonid is less narrow. The m2 is larger than in the type in both absolute size and relative to m1; it has a complete trigonid with high protoconid and metaconid and small but clear paraconid, and a narrow talonid (Fig. 4B). The isolated P4 (VBO 494) figured by Peigné <i>et al.</i> (2014: fig. 22a) is close to that of the type specimen from Mas de Got, with a mesio-lingually elongate protocone finishing by a conic cusp, a buccal cingulum and a small mesial bulging representing a parastyle (Fig. 5F). These remains are close to the material of <i>M</i>. <i>olivieri</i> (Fig. 4F 1, F 2) but the small differences lead us to be cautious about the identification. They could be due to a small difference in the geological age between two localities of MP 22.</p>Published as part of <i>Bonis, Louis de, Gardin, Axelle & Blondel, Cécile, 2019, Carnivora from the early Oligocene of the ' Phosphorites du Quercy' in southwestern France, pp. 601-621 in Geodiversitas 41 (15)</i> on pages 614-615, DOI: 10.5252/geodiversitas2019v41a15, <a href="http://zenodo.org/record/3694209">http://zenodo.org/record/3694209</a>
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