Periodic orbits from Δ-modulation of stable linear systems

The �-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by cTx where c �Rn/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study the relationship between certain polyhedra and the periodicity of the �-modulated orbit

Zero polyhedral cones

AbstractProperties of zero polyhedral cones are studied by making use of Fourier-Motzkin eliminations. Algorithms are presented for the characterization of zero polyhedral cones

Interlacing Log-concavity of the Boros-Moll Polynomials

We introduce the notion of interlacing log-concavity of a polynomial sequence $\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$ interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\geq 0$. Interlacing log-concavity is stronger than the log-concavity. We show that the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a sufficient condition for interlacing log-concavity which implies that some classical combinatorial polynomials are interlacing log-concave.Comment: 10 page

Computational modelling study of yttria-stabilized zirconia

Interatomic potential and quantum mechanical simulation techniques have been applied to both the bulk and surfaces of yttrium-stabilized cubic zirconia (YSZ) with special reference to its role in partial oxidation reaction at high temperature. The stabilities of pure ZrO2 phases and surfaces have been examined. The bulk structures of low pressure phases are reproduced with the observed order of stability: monoclinic > tetragonal > cubic zirconia. The relative stability of plane cubic ZrO2 surfaces is predicted to be (111)c > (110)c > (100)c > (310)c. In addition, the stability of topological surfaces is found to be reduced with the coordination number of Zr ions at the topological sites in the order: plane > step > kink > corner. The dispersion of defects in YSZ systems has been studied, considering both the dopant content and surface segregation. In the bulk, the yttrium dopants tend to form a pair with two yttrium atoms close to each other and preferentially occupying the 1st or 2nd nearest neighbour (NN) sites to the compensating oxygen vacancy. At the surface, yttrium segregates to the top layers (up to 4-5 Å) of the dominant (111) surface of YSZ. The composition of the outermost surface of YSZ is predicted to be independent of Y bulk concentration and reach a maximum Y/Zr ratio of 1:1. In relation to catalytic oxidation, the interaction between oxygen molecules and the (111) surfaces of pure c-ZrO2 and YSZ have been investigated using quantum-mechanical DFT-GGA methods. The adsorption states of oxygen and the pathways for dissociation have been indentified on the plane and stepped (111) surfaces. In general, the creation of oxygen vacancies by yttrium doping provides an active site for oxygen adsorption. In addition, the low-coordinated Zr cations on the YSZ surfaces can attract strongly reduced oxygen species and the most stable adsorption state of oxygen is adopted to achieve a higher bond saturation of the neighbouring Zr site