Search results for " math"
showing 10 items of 11183 documents
High precision numerical approach for Davey–Stewartson II type equations for Schwartz class initial data
2020
We present an efficient high-precision numerical approach for Davey–Stewartson (DS) II type equa- tions, treating initial data from the Schwartz class of smooth, rapidly decreasing functions. As with previous approaches, the presented code uses discrete Fourier transforms for the spatial dependence and Driscoll’s composite Runge–Kutta method for the time dependence. Since DS equations are non-local, nonlinear Schrödinger equations with a singular symbol for the non-locality, standard Fourier methods in practice only reach accuracy of the order of 10−6or less for typical examples. This was previously demonstrated for the defocusing integrable case by comparison with a numerical approach for …
Análisis de los antecedentes histórico-filosóficos de la "paradoja cognitiva de Duval"
2015
In a famous article published in 1993, Raymond Duval highlighted a simple fact: the student may confuse the mathematical object O he is trying to build cognitively with one of its semiotic representations R(O). Duval explained that this confusion was due to a sort of inevitable paradox: only someone who has already built O, can recognize R(O) as a representation of O and not as an object in itself. Thereafter, this thought has been extremely influential for researchers. However, even if in different terms, many scholars of semiotics have emphasized the same phenomenon. In this paper we propose to remind some of them. En un famoso artículo publicado en 1993, Raymond Duval evidenciaba el sigu…
Some Investigations on Similarity Measures Based on Absent Words
2019
In this paper we investigate similarity measures based on minimal absent words, introduced by Chairungsee and Crochemore in [1]. They make use of a length-weighted index on a sample set corresponding to the symmetric difference M(x)ΔM(y) of the minimal absent words M(x) and M(y) of two sequences x and y, respectively. We first propose a variant of this measure by choosing as a sample set a proper subset (x, y) of M(x)ΔM(y), which appears to be more appropriate for distinguishing x and y. From the algebraic point of view, we prove that (x, y) is the base of the ideal generated by M(x)ΔM(y). We then remark that such measures are able to recognize whether the sequences x and y share a common s…
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.
Shape identification in inverse medium scattering problems with a single far-field pattern
2016
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset {\mathbb R}^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be Holder continuous near the corners. If $D\subset {\mathbb R}^2$ is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions $N \geq 3$, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of nonscattering waven…
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.
Existence of two solutions for singular Φ-Laplacian problems
2022
AbstractExistence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by theΦ\Phi-Laplacian operator, and the reaction term can be nonmonotone. The main tools employed are the local minimum theorem and the Mountain pass theorem, together with the truncation technique. GlobalC1,τ{C}^{1,\tau }regularity of solutions is also investigated, chiefly viaa prioriestimates and perturbation techniques.
ETAT TOPOLOGIQUE DE L'ESPACE TEMPS A L'ECHELLE 0
2002
We propose in this research a new solution regarding the existence and the content of the initial spacetime singularity. In the context of topological field theory we consider that the initial singularity of space-time corresponds to a zero size singular gravitational instanton characterized by a Riemannian metric configuration (++++) in dimension D = 4. Connected with some unexpected topological data corresponding to the zero scale of space-time, the initial singularity is thus not considered in terms of divergences of physical fields but can be resolved in the frame of topological field theory. We get this result from the physical observation that the pre-spacetime is in a thermal equilib…