Search results for "singular"

A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics

2011

International audience; We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always comp…

Lenses on very curved zones of a singular line field of ${\mathbb C}^2$ or of a singular plane field of ${\mathbb C}^3$

2020

We renormalize, using suitable lenses, small domains of a singular holomorphic line field of ${\mathbb C}^2$ or plane field of ${\mathbb C}^3$ where the curvature of a plane-field is concentrated. At a proper scale the field is almost invariant by translations. When the field is integrable, the leaves are locally almost translates of a surface that we will call {\it profile}. When the singular rays of the tangent cone (a generalization to a plane-field of the tangent cone of a singular surface is defined) are isolated, we obtain more precise results. We also generalize a result of Merle (\cite{Me}) concerning the contact order of generic polar curves with the singular level $f=0$ when $\ome…

Four-dimensional representation of scattering amplitudes and physical observables through the application of the Loop-Tree Duality theorem

2019

Las últimas dos décadas han sido testigo de un tremendo progreso en la física teórica de alta precisión. Muchos avances han sido hechos, en particular, en la evaluación de diagramas multi-loop, pero el principal desafío yace en el tratamiento de las divergencias IR a través de eficientes esquemas de substracción. Con la complejidad del procedimiento incrementándose exponencialmente con el número de escalas, se ha hecho necesario tratar la cuestión desde un ángulo diferente, invocando así al desarrollo de nuevas técnicas. La Dualidad Lazo-Árbol (LTD, por sus siglas en inglés) provee de un nuevo marco para el cómputo de amplitudes con loops. A través de la modificación de la prescripción está…

Lebesgue-type decomposition for sesquilinear forms via differences

2022

Definitions of regularity and singularity are proposed for sesquilinear forms with respect to a non-negative one and a correspondent Lebesgue-type decomposition is proved. In contrast to other Lebesgue-type decompositions established in the literature for sesquilinear forms with generic sign, the underlying idea in this paper is to write symmetric forms as the difference of non-negative sesquilinear forms.

Higher order matrix differential equations with singular coefficient matrices

2014

In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

EXISTENCE RESULTS FOR SINGULAR CONVECTIVE ELLIPTIC PROBLEMS

2021

On the scientific work of Victor Isakov

2022

Singular (p, q)-equations with superlinear reaction and concave boundary condition

2020

We consider a parametric nonlinear elliptic problem driven by the sum of a p-Laplacian and of a q-Laplacian (a (Formula presented.) -equation) with a singular and (Formula presented.) -superlinear reaction and a Robin boundary condition with (Formula presented.) -sublinear boundary term (Formula presented.). So, the problem has the combined effects of singular, concave and convex terms. We look for positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.

Some recent results on singular $ p $-Laplacian systems

2022

Some recent existence, multiplicity, and uniqueness results for singular p-Laplacian systems either in bounded domains or in the whole space are presented, with a special attention to the case of convective reactions. A extensive bibliography is also provided.

Some recent results on a singular p-laplacian equations

2022

Abstract A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided.