Perspectives pour la linguistique : de la linguistique descriptive à la linguistique explicative

The text deals with one of the challenges of linguistics, which is to effectively combine description and explanation in linguistics.It is necessary that linguistic theories are not only capable of adequately describing their object of study within their framework, but they must also have a suitable explanatory power.Linguistics centred around the explanation of the why of the system is called here ‘explanatory’ or ‘non-autonomous’, in contrast to ‘descriptive’ or ‘autonomous’ linguistics, which is focused on the description of the system, the distinction being based on the difference in the objects of study, the goals and the descriptive and explanatory possibilities of the theories.From the point of view presented here, a comprehensive study of language has three main components: a general theory of what language is, a resulting theory and description, which is a function of this theory, of how language is organised, functions and has evolved in the human brain, and an explanation of the properties of language found.The explanatory value of a general linguistic theory is a function of various elements, among others, the quantity of the primitive elements of the theory adopted and the effectiveness of Ockham’s razor principle of simplicity. It is also a function of the quality of those elements which can be drawn not only from within the system, but also from outside the system becoming in this situation logically prior to the object under study.In science, in linguistics, one naturally needs two types of approach, two types of linguistics, descriptive/autonomous and explanatory/non-autonomous, one must first describe reality in order to explain it. But it is also certain that since the aim of science is to explain in order to reach that higher level of scientificity above pure description, it is necessary that this aim be realized in different linguistic theories within different research programs, uniting descriptivist and explanatory approaches.

Minimal degrees of algebraic numbers with respect to primitive elements

Given a number field [Formula: see text], we define the degree of an algebraic number [Formula: see text] with respect to a choice of a primitive element of [Formula: see text]. We propose the question of computing the minimal degrees of algebraic numbers in [Formula: see text], and examine these values in degree 4 Galois extensions over [Formula: see text] and triquadratic number fields. We show that computing minimal degrees of non-rational elements in triquadratic number fields is closely related to solving classical Diophantine problems such as congruent number problem as well as understanding various arithmetic properties of elliptic curves.

GENERATORS OF FINITE FIELDS WITH PRESCRIBED TRACES

This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the existence of such elements. We then derive concrete existence results for a special class of intermediate extensions.

Educational software tool for the generation of Quasi-Random urban scenarios applied to electromagnetic computer simulation

This document presents the development of a didactic software tool used as a platform for the generation of complex urban scenarios based on probabilistic user-defined parameters. An adaptive algorithm and a set of primitive elements have been developed in order to allow the user to define the complexity and main features of the scenario and obtain a script containing the geometric elements that conform the resulting geometry. This tool has been developed by undergraduate students and is the result of a number of multidisciplinary projects. It is used in undergraduate and graduate teaching programs in order to perform multipath ray tracing analyses, validate propagation models, analyze the multipath channel characteristics or study the performance of MIMO antennas, among others.