L'Empordà de Joan Maragall i Enric Morera

S’exposa en aquestes notes la gènesi de la sardana L’Empordà, amb lletra de Joan Maragall i música d’Enric Morera, a través d’un manuscrit autògraf de Maragall adreçat a Morera –darrerament adquirit per la Biblioteca de Catalunya– i de correspondència conservada a l’Arxiu Joan Maragall. La col·laboració entre poeta i músic, que s’eixampla a d’altres obres, permet d’entreveure com s’esdevé el procés de creació –literària i musical– dels dos autors

Morera Theorems for Complex Manifolds

AbstractWe prove Morera theorems for the Radon transform integrating on geodesic spheres on complex analytic manifolds of arbitrary dimension. To avoid pathologies, we assume that the radius of each sphere of integration is less than the injectivity radius at its center. The proofs of the main results are local, and they involve the microlocal properties of associated Radon transforms and a theorem of Hörmander, Kawai, and Kashiwara on microlocal singularities. We consider Morera theorems for spheres of fixed radius and spheres of arbitrary radius

Jean-Claude Morera, Huit siècles de poésie catalane. Anthologie

Obra ressenyada: Jean-Claude MORERA, Huit siècles de poésie catalane. Anthologie. París: L'Harmattan, 2010

Airy, Beltrami, Maxwell, Morera, Einstein and Lanczos potentials revisited

The main purpose of this paper is to revisit the well known potentials, called stress functions, needed in order to study the parametrizations of the stress equations, respectively provided by G.B. Airy (1863) for 2-dimensional elasticity, then by E. Beltrami (1892), J.C. Maxwell (1870) and G. Morera (1892) for 3-dimensional elasticity, finally by A. Einstein (1915) for 4-dimensional elasticity, both with a variational procedure introduced by C. Lanczos (1949,1962) in order to relate potentials to Lagrange multipliers. Using the methods of Algebraic Analysis, namely mixing differential geometry with homological algebra and combining the double duality test involved with the Spencer cohomology, we shall be able to extend these results to an arbitrary situation with an arbitrary dimension n. We shall also explain why double duality is perfectly adapted to variational calculus with differential constraints as a way to eliminate the corresponding Lagrange multipliers. For example, the canonical parametrization of the stress equations is just described by the formal adjoint of the n2(n2 -- 1)/12 components of the linearized Riemann tensor considered as a linear second order differential operator but the minimum number of potentials needed in elasticity theory is equal to n(n -- 1)/2 for any minimal parametrization. Meanwhile, we can provide all the above results without even using indices for writing down explicit formulas in the way it is done in any textbook today. The example of relativistic continuum mechanics with n = 4 is provided in order to prove that it could be strictly impossible to obtain such results without using the above methods. We also revisit the possibility (Maxwell equations of electromag- netism) or the impossibility (Einstein equations of gravitation) to obtain canonical or minimal parametrizations for various other equations of physics. It is nevertheless important to notice that, when n and the algorithms presented are known, most of the calculations can be achieved by using computers for the corresponding symbolic computations. Finally, though the paper is mathematically oriented as it aims providing new insights towards the mathematical foundations of elasticity theory and mathematical physics, it is written in a rather self-contained way

Extremal discs and the holomorphic extension from convex hypersurfaces

Let D be a convex domain with smooth boundary in complex space and let f be a continuous function on the boundary of D. Suppose that f holomorphically extends to the extremal discs tangent to a convex subdomain of D. We prove that f holomorphically extends to D. The result partially answers a conjecture by Globevnik and Stout of 1991