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Your search keyword '"Abreu Blaya, Ricardo"' showing total 263 results
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263 results on '"Abreu Blaya, Ricardo"'

19. Looking for structures in the solutions of a generalized lamé-navier system

Author

Alfonso Santiesteban, Daniel, Abreu Blaya, Ricardo, Árciga Alejandre, Martín Patricio, Alfonso Santiesteban, Daniel, Abreu Blaya, Ricardo, and Árciga Alejandre, Martín Patricio

Abstract

This research is devoted to a fundamental system of equations in Linear Elasticity Theory: the Lamé-Navier system. The Clifford algebras language allows us to rewrite this system in terms of the Euclidean Dirac operator, which at the same time suggests a very natural generalization involving the so-called structural sets. We are interested in finding some structures in the solutions of these generalized Lamé-Navier systems. The flexibility involved in the consideration of arbitrary structural sets suggests that this system leads to a wide range of systems of partial differential equations that could be of mathematical interest as well as in the context of Physics., Esta investigación está dedicada a un sistema fundamental de ecuaciones en la Teoría de la Elasticidad Lineal: el sistema de Lamé-Navier. El lenguaje de las álgebras de Clifford posibilita reescribir este sistema en términos del clásico operador de Dirac Euclidiano, lo cual sugiere al mismo tiempo considerar una generalización natural a través de los llamados conjuntos estructurales. El objetivo principal de este trabajo es describir la estructura de las soluciones de estos sistemas. El alto grado de flexibilidad que supone la consideración de conjuntos estructurales arbitrarios, sugiere que dichos sistemas generalizados conducen a una amplia gama de sistemas de ecuaciones en derivadas parciales que podrían tener un interés no solo matemático sino también dentro de la Física.

Published
2023

22. Boundary value problems for a second‐order elliptic partial differential equation system in Euclidean space.

Author

Alfonso Santiesteban, Daniel, Abreu Blaya, Ricardo, and Bory Reyes, Juan

Subjects
*BOUNDARY value problems, *DIRAC operators, *DIFFERENTIAL forms, *CLIFFORD algebras, *ELLIPTIC operators, *QUADRATIC forms
Abstract

Let Ω⊂ℝm$$ \Omega \subset {\mathrm{\mathbb{R}}}^m $$ be a bounded regular domain, let ∂x_$$ {\partial}_{\underset{\_}{x}} $$ be the standard Dirac operator in ℝm$$ {\mathrm{\mathbb{R}}}^m $$, and let ℝ0,m$$ {\mathrm{\mathbb{R}}}_{0,m} $$ be the Clifford algebra constructed over the quadratic space ℝ0,m$$ {\mathrm{\mathbb{R}}}^{0,m} $$. For k∈{1,...,m}$$ k\in \left\{1,\dots, m\right\} $$ fixed, ℝ0,m(k)$$ {\mathrm{\mathbb{R}}}_{0,m}^{(k)} $$ denotes the space of k$$ k $$‐vectors in ℝ0,m$$ {\mathrm{\mathbb{R}}}_{0,m} $$. In the framework of Clifford analysis, we consider two boundary value problems for a second‐order elliptic system of partial differential equations of the form ∂x_Fk∂x_=fk$$ {\partial}_{\underset{\_}{x}}{F}_k{\partial}_{\underset{\_}{x}}={f}_k $$ in Ω$$ \Omega $$, where fk$$ {f}_k $$ is a smooth k$$ k $$‐vector valued function. The boundary conditions of the problems contain the inner and outer products of the k$$ k $$‐vector solution Fk$$ {F}_k $$ with both the Dirac operator and the normal vector to ∂Ω$$ \mathrm{\partial \Omega } $$, ensuring the well‐posedness for the problems. Investigation of the spectral properties of the sandwich operator ∂x_(.)∂x_$$ {\partial}_{\underset{\_}{x}}(.){\partial}_{\underset{\_}{x}} $$ is considered by using the Fredholm theory. Finally, it is shown that satisfactory problem‐solving properties, in general, fail when we replace the standard Dirac operator by those, obtained via unusual orthogonal bases of ℝm$$ {\mathrm{\mathbb{R}}}^m $$. [ABSTRACT FROM AUTHOR]

Published
2023
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33. Teodorescu Transform Decomposition of Multivector Fields on Fractal Hypersurfaces

Author

Abreu-Blaya, Ricardo, Bory-Reyes, Juan, Moreno-García, Tania, Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Coburn, L. A., editor, Curto, R. E., editor, Davidson, K. R., editor, Douglas, R. G., editor, Dijksma, A., editor, Dym, H., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Helton, J. A., editor, Kaashoek, M. A., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lancaster, P., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevsky, V., editor, Putinar, M., editor, Rodman, L., editor, Rovnyak, J., editor, Sarason, D. E., editor, Spitkovsky, I. M., editor, Treil, S., editor, Upmeier, H., editor, Lunel, S. M. Verduyn, editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, Alpay, Daniel, editor, Luger, Annemarie, editor, and Woracek, Harald, editor

Published
2006
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36. Complex and quaternionic Cauchy formulas in Koch snowflakes

Author

Marisel Avila Alfaro and Abreu Blaya Ricardo

Subjects
Numerical Analysis, Pure mathematics, Mathematics::Dynamical Systems, Mathematics::Complex Variables, Applied Mathematics, Mathematics::Analysis of PDEs, Holomorphic function, Mathematics::General Topology, Cauchy distribution, Computer Science::Computational Geometry, Koch snowflake, Computational Mathematics, Fractal, Bounded function, Snowflake, Quaternion, Analysis, Cauchy's integral formula, Mathematics
Abstract

In this paper we derive a Cauchy integral formula for holomorphic and hyperholomorphic functions in domains bounded by a Koch snowflake in two- and three-dimensional setting.

Published
2021

46. Riemann problem for bianalytic functions on h-summable curves.

Author

Abreu Blaya, Ricardo, De la Cruz, Martha Paola Cruz, Sánchez Santiesteban, José Luis, and Sigarreta Almira, José María

Subjects
*RIEMANN-Hilbert problems
Abstract

This paper is concerned with the Riemann problem for bianalytic functions on a closed Jordan curve with a certain degree of fractality. We derive a solvability condition under which an explicit solution of this problem is obtained. [ABSTRACT FROM AUTHOR]

Published
2022
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