Física y Matemáticas
http://hdl.handle.net/10017/17964
FISMAT2022-09-25T09:20:16ZOn the base point locus of surface parametrizations: formulas and consequences
http://hdl.handle.net/10017/51737
On the base point locus of surface parametrizations: formulas and consequences
Cox, David A.; Pérez Díaz, Sonia; Sendra Pons, Juan Rafael
This paper shows that the multiplicity of the base point locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant. As a consequence, we get a new proof of the degree formula relating the degree of the surface, the degree of the parametrization, the base point multiplicity and the degree of the rational map induced by the parametrization. In addition, we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related. As an application of these results, we explore how the degree of a surface reparametrization is affected by the presence of base points.
2022-05-10T00:00:00ZAlgebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
http://hdl.handle.net/10017/51628
Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
Cano, José; Falkensteiner, Sebastian; Robertz, Daniel; Sendra Pons, Juan Rafael
In this paper we study systems of autonomous algebraic ODEs
in several differential indeterminates. We develop a notion of
algebraic dimension of such systems by considering them as
algebraic systems. Afterwards we apply differential elimination
and analyze the behavior of the dimension in the resulting
Thomas decomposition. For such systems of algebraic dimension
one, we show that all formal Puiseux series solutions can be
approximated up to an arbitrary order by convergent solutions. We
show that the existence of Puiseux series and algebraic solutions
can be decided algorithmically. Moreover, we present a symbolic
algorithm to compute all algebraic solutions. The output can
either be represented by triangular systems or by their minimal
polynomials.
2022-04-22T00:00:00ZComment on "Properties of the recovery phase of extreme storms" by Choraghe et al. (2021)
http://hdl.handle.net/10017/50725
Comment on "Properties of the recovery phase of extreme storms" by Choraghe et al. (2021)
Cid Tortuero, Consuelo; Saiz Villanueva, María Elena
Choraghe et al. (2021), based on a study of the recovery phase of the SYM-H index of 31 extreme
geomagnetic storms, have recently concluded that the hyperbolic decay function is only able to explain the
complete recovery phase of about one third of events and that both the exponential or the hyperbolic decay
functions fail to explain the late recovery phase of storms. Furthermore, they propose a linear function to model
the late recovery phase and claim that the proposed model could throw new light on the relative importance of
different physical processes involved during the complete recovery phase of extreme storms. We assert that the
Choraghe et al. (2021) conclusions regarding the recovery phase of extreme storms analysis are incorrect and
in particular are based on a misunderstanding of the nature of the evolution of the SYM-H index and the energy
balance of the ring current.
2021-12-20T00:00:00ZThe space weather station at the University of Alcala
http://hdl.handle.net/10017/50723
The space weather station at the University of Alcala
Guerrero Ortega, Antonio; Cid Tortuero, Consuelo; García, Alberto; Domínguez, Emilio; Montoya, Fernando; Saiz Villanueva, María Elena
The Space Weather station at the University of Alcala (UAH-STA) is a place for instrumentation that is able to produce useful products and services even in a worst case scenario (when power grid and/or communications have been compromised), assuring the access of critical data to decision-makers and consequently, increasing the confidence to take actions. The current development consists of an antenna to monitor ionospheric disturbances through the reception of very low frequency waves and a magnetometer to indicate the geomagnetic disturbances caused by sources external to the Earth. This work shows the development of both instruments and some examples of ionospheric and geomagnetic events recorded by both of them. This project serves also as a success story of using space weather as a teaching tool due to the involvement of undergraduate students at their final stage of industrial and telecommunication engineering.
2021-03-23T00:00:00Z