Differential resultant formulas for linear od-polynomials.

Ponencia

Linear Sparse Differential Resultant Formulas

Let P be a system of n linear nonhomogeneous ordinary differential polynomials in a set U of n-1 differential indeterminates. Differential resultant formulas are presented to eliminate the differential indeterminates in U from P. These formulas are determinants of coefficient matrices of appropriate sets of derivatives of the differential polynomials in P, or in a linear perturbation Pe of P. In particular, the formula dfres(P) is the determinant of a matrix M(P) having no zero columns if the system P is ``super essential". As an application, if the system PP is sparse generic, such formulas can be used to compute the differential resultant dres(PP) introduced by Li, Gao and Yuan.

Sparse differential resultant formulas: between the linear and the nonlinear case

A matrix representation of the sparse differential resultant is the basis for efficient computation algorithms, whose study promises a great contribution to the development and applicability of differential elimination techniques. It is shown how sparse linear differential resultant formulas provide bounds for the order of derivation, even in the nonlinear case, and they also provide (in many cases) the bridge with results in the nonlinear algebraic case.

Determinación de los periodos propios de presas bóveda simétricas mediante formulas empíricas

El artículo presenta una formulación sencilla que permite obtener los seis primeros períodos propios de vibración de una presa bóveda simétrica diseñada según las recomendaciones del U.S. Bureau of Reclamation. Se indican las expresiones polinómicas aproximadas de estos períodos, tanto para embalse vacío como para embalse lleno. El efecto del embalse se modeliza mediante la técnica de Westergaard modificada. Asimismo se indica una expresión que intenta tener en cuenta, de modo tentativo, el efecto de la flexibilidad del terreno

Checking existing formulas for estimating overtopping rates in harbour breakwaters

The purpose of the research work resulting from various studies undertaken in the CEDEX, as summarized in this article, is to make a comparative analysis of methods for calculating overtopping rates developed by different authors. To this effect, in the first place, existing formulas for estimating the overtopping rate on rubble mound and vertical breakwaters were summarised and analysed. Later, the above mentioned formulas were compared using the results obtained in a series of hydraulic model tests at the CEDEX. The results obtained in the Ferrol outer harbour breakwater and Melilla harbour breakwater tests are presented here. A calculation method based on the neural network theory, developed in the European CLASH Project, was applied to a series of sloping breakwater tests in order to complete this research and the results obtained in the Ferrol outer harbour breakwater test are presented in this article. A series of additional tests was also carried out in a physical model on the standard cross section of the Bilbao harbour sloping breakwater’s cross section, the results of which are under study using the empirical formulas applicable to the cross section, as well as the NN-OVERTOPPING neural network