Search results for "singular"

Cohomologie relative des applications polynomiales

2001

Let F be a polynomial dominating mapping from Cn to Cq with n>q. We study the de Rham cohomology of the fibres of F, and its relative cohomology groups. Let us fix a strictly positive weighted homogeneous degree on C[x1,…,xn]. With the leading terms of the coordinate functions of F, we construct a fibre of F that is said to be “at infinity”. We introduce the cohomology groups of F at infinity. These groups, denoted by Hk(F−1(∞)), enable us to study all the other cohomology groups of F. For instance, if the fibre at infinity has an isolated singularity at the origin, we prove that any quasi-homogeneous basis of Hn−q(F−1(∞)) provides a basis of all groups Hn−q(F−1(y)), as well as a basis of t…

Geometry of the projectivization of ideals and applications to problems of birationality

2018

In this thesis, we interpret geometrically the torsion of the symmetric algebra of the ideal sheaf I_Z of a scheme Z defined by n+1 equations in an n-dimensional variety. This is equivalent to study the geometry of the projectivization of I_Z. The applications of this point of view concern, in particular, the topic of birational maps of the projective space of dimension 3 for which we construct explicit birational maps that have the same algebraic degree as their inverse, free and nearly-free curves for which we generalise a characterization of free curves by extending the notion of Milnor and Tjurina numbers. We tackle also the topic of homaloidal hypersurfaces, our original motivation, fo…

Fourier integral operators and inhomogeneous Gevrey classes

1988

Fourier integral operators with inhomogeneous amplitude and phase junction are studied in the frame of Gevrey classes. Applications are given to propagation of singularities for a pseudodifferential equation.

A new hybrid method to improve the ultra-short-term prediction of LOD

2019

Accurate, short-term predictions of Earth orientation parameters (EOP) are needed for many real-time applications including precise tracking and navigation of interplanetary spacecraft, climate forecasting, and disaster prevention. Out of the EOP, the LOD (length of day), which represents the changes in the Earth’s rotation rate, is the most challenging to predict since it is largely affected by the torques associated with changes in atmospheric circulation. In this study, the combination of Copula-based analysis and singular spectrum analysis (SSA) method is introduced to improve the accuracy of the forecasted LOD. The procedure operates as follows: First, we derive the dependence structur…

Singular solutions to a quasilinear ODE

2005

In this paper, we prove the existence of infinitely many radial solutions having a singular behaviour at the origin for a superlinear problem of the form $-\Delta_pu=|u|^{\delta-1}u$ in $B(0,1)\setminus\{0\}\subset\mathbb R^N$,\, $u=0$ for $|x|=1$, where $N>p>1$ and $\delta>p-1$. Solutions are characterized by their nodal properties. The case $\delta+1 <\frac{Np}{N-p}$ is treated. The study of the singularity is based on some energy considerations and takes into account the classification of the behaviour of the possible solutions available in the literature. By following a shooting approach, we are able to deduce the main multiplicity result from some estimates on the rotation numbers asso…

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…

Singular integrals on regular curves in the Heisenberg group

2019

Let $\mathbb{H}$ be the first Heisenberg group, and let $k \in C^{\infty}(\mathbb{H} \, \setminus \, \{0\})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\nabla_{\mathbb{H}}^{n}k(p)| \leq C_{n}\|p\|^{-1 - n}, \qquad p \in \mathbb{H} \, \setminus \, \{0\}, \, n \geq 0.$$ The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the horizontally odd kernel $k(p) = \nabla_{\mathbb{H}} \log \|p\|$. We prove that convolution with $k$, as above, yields an $L^{2}$-bounded operator on regular curves in $\mathbb{H}$. This extends a theorem of G. David to the Heisenberg group. As a corollary of our main result, we infer that all …

On Weakly Singular Integral Equations of the Second Kind

1988

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.

Multiplicity of solutions for two-point boundary value problems with asymptotically asymmetric nonlinearities

1996