La aportación de W. von Humboldt a la gramática vasca

[EN] The aim of this paper is to introduce the main contributions of Humboldt to the study of the Basque grammar. His methodological innovations and the influence he had on european linguists are pointed out, the grammatical sources available to him are mentioned and his woks on Basque grammar are enumerated. Some of Humboldt's most interesting analysis are mentioned and are placed in the former and later tradition of the Basque grammar.

Carta enviada por W.I.B. Beveridge a Justo Garate en 1955

1 carta (mecanografiada) ; 190x250mm

Helmholtz Fermi surface harmonics: an efficient approach for treating anisotropic problems involving Fermi surface integrals

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface (FS) of metallic materials. The method introduces a set of numerically calculated generalized orthonormal functions which are the solutions of the Helmholtz equation defined on the FS. Noteworthy, many properties of our proposed basis set are also shared by the FS harmonics introduced by Philip B Allen (1976 Phys. Rev. B 13 1416), proposed to be constructed as polynomials of the cartesian components of the electronic velocity. The main motivation of both approaches is identical, to handle anisotropic problems efficiently. However, in our approach the basis set is defined as the eigenfunctions of a differential operator and several desirable properties are introduced by construction. The method is demonstrated to be very robust in handling problems with any crystal structure or topology of the FS, and the periodicity of the reciprocal space is treated as a boundary condition for our Helmholtz equation. We illustrate the method by analysing the free-electron-like lithium (Li), sodium (Na), copper (Cu), lead (Pb), tungsten (W) and magnesium diboride (MgB2)