Browsing by Subject "Linearity"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Publication
    Open Access
    On a linear refinement of the Prékopa-Leindler inequality
    (Cambridge University Press, 2018-11-20) Colesanti, Andrea ; Saorín Gómez, Eugenia; Yepes Nicolás, Jesús; Matemáticas; Facultades de la UMU::Facultad de Matemáticas
    If f; g : R^n -> R>=0 are non-negative measurable functions, then the Prékopa-Leindler inequality asserts that the integral of the Asplund sum (provided that it is measurable) is greater or equal than the 0-mean of the integrals of f and g. In this paper we prove that under the sole assumption that f and g have a common projection onto a hyperplane, the Prékopa-Leindler inequality admits a linear refinement. Moreover, the same inequality can be obtained when assuming that both projections (not necessarily equal as functions) have the same integral. An analogous approach may be also carried out for the so-called Borell-Brascamp-Lieb inequality.
  • Thumbnail Image
    Publication
    Open Access
    Students’ errors in L1 Spanish grammar from the perspective of formal linguistics
    (John Benjamins, 2021-05-25) Bravo, Ana; Lengua Española y Lingüística General
    This paper studies the role that knowledge about formal linguistics can play in teacher education. In order to do so, this contribution focuses on specific secondary students’ errors and misconceptions when confronted with L1 explicit grammar instruction. Errors are measured with respect to a formal theory of grammar. The rationale for developing this research is that certain aspects of formal theories, such as constituency, recursion, dependency and compositionality function not only are the building blocks of the utterances, but are also needed for speech processing. If this is the case, acquiring them correctly might be helpful for enhancing literacy, since the very same notions are at the core of both the construction and the understanding of any text. As a second issue, the present paper addresses the question of how the absence of such knowledge models the perspective from which students’ errors are evaluated by the teachers. Errors are described following the theories for analyzing errors in mathematics. A side effect of this approach is that the parallelism between errors made in learning mathematics and in learning the grammatical concepts just mentioned allows broadening the perspective from which the latter is approached.