Nonsmooth stabilizability and feedback linearization of discrete-time nonlinear systems

We consider the problem of stabilizing a discrete-time nonlinear system using a feedback which is not necessarily smooth. A sufficient condition for global dynamical stabilizability of single-input triangular systems is given. We obtain conditions expressed in terms of distributions for the nonsmooth feedback triangularization and linearization of discrete-time systems. Relations between stabilization and linearization of discrete-time systems are given

Fermion masses in a model for spontaneous parity breaking

In this paper we discuss a left-right symmetric model for elementary particles and their connection with the mass spectrum of elementary fermions. The model is based on the group $SU(2)_L\otimes SU(2)_R\otimes U(1)$. New mirror fermions and a minimal set of Higgs particles that breaks the symmetry down to $U(1)_{em}$ are proposed. The model can accommodate a consistent pattern for charged and neutral fermion masses as well as neutrino oscillations. An important consequence of the model is that the connection between the left and right sectors can be done by the neutral vector gauge bosons Z and a new heavy Z'.Comment: 7 pages, 3 figures. Accepted in Eur. Phys. J.

On the possibility of calibrating urban storm-water drainage models using gauge-based adjusted radar rainfall estimates

Traditionally, urban storm water drainage models have been calibrated using only raingauge data, which may result in overly conservative models due to the lack of spatial description of rainfall. With the advent of weather radars, radar rainfall estimates with higher temporal and spatial resolution have become increasingly available and have started to be used operationally for urban storm water model calibration and real time operation. Nonetheless, the insufficient accuracy of radar rainfall estimates has proven problematic and has hindered its widespread practical use. This work explores the possibility of improving the applicability of radar rainfall estimates to the calibration of urban storm-water drainage models by employing gauge-based radar rainfall adjustment techniques. Four different types of rainfall estimates were used as input to the recently verified urban storm water drainage models of the Beddington catchment in South London; these included: raingauge, block-kriged raingauge, radar (UK Met Office Nimrod) and the adjusted (or merged) radar rainfall estimates. The performance of the simulated flow and water depths was assessed using measurements from 78 gauges. Results suggest that a better calibration could be achieved by using the block-kriged raingauge and the adjusted radar estimates as input, as compared to using only radar or raingauge estimates

Minimal anomaly-free chiral fermion sets and gauge coupling unification

We look for minimal chiral sets of fermions beyond the standard model that are anomaly free and, simultaneously, vectorlike particles with respect to colour SU(3) and electromagnetic U(1). We then study whether the addition of such particles to the standard model particle content allows for the unification of gauge couplings at a high energy scale, above $5.0 \times 10^{15}$ GeV so as to be safely consistent with proton decay bounds. The possibility to have unification at the string scale is also considered. Inspired in grand unified theories, we also search for minimal chiral fermion sets that belong to SU(5) multiplets. Restricting to representations up to dimension 50, we show that some of these sets can lead to gauge unification at the GUT and/or string scales.Comment: 13 pages, 5 figures, 8 tables; Comments and references added, final version to appear in Phys. Rev.

Reconstruction of Quark Mass Matrices with Weak Basis Texture Zeroes from Experimental Input

All quark mass matrices with texture zeroes obtained through weak basis transformations are confronted with the experimental data. The reconstruction of the quark mass matrices M_u and M_d at the electroweak scale is performed in a weak basis where the matrices are Hermitian and have a maximum of three vanishing elements. The same procedure is also accomplished for the Yukawa coupling matrices at the grand unification scale in the context of the Standard Model and its minimal supersymmetric extension as well as of the two Higgs doublet model. The analysis of all viable power structures on the quark Yukawa coupling matrices that could naturally appear from a Froggatt-Nielsen mechanism is also presented.Comment: RevTeX4, 3 tables, 21 pages; misprints corrected and one reference adde