Coincidences in generalized Lucas sequences

For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)}$ in nonnegative integers $n,k,m,\ell$ with $k, \ell\geq 2$. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method. This paper is a continuation of the earlier work [4].Comment: 14 page

Effcient M-estimators with auxiliary information

This paper introduces a new class of M-estimators based on generalised empirical likelihood estimation with some auxiliary information available in the sample. The resulting class of estimators is efficient in the sense that it achieves the same asymptotic lower bound as that of the efficient generalised method of moment-based M-estimator with the same auxiliary information. The results of the paper are quite general and apply to M-estimators defined by both smooth and nonsmooth estimating equations. Simulations show that the proposed estimators perform well in finite samples, and can be less biased and more precise than standard M-estimators within China.Asymptotic efficiency. Generalised empirical likelihood. Generalised method of moments. M-estimators. Generalised method of moments, M-estimators.

Interval model predictive control

6TH INTERNATIONAL WORKSHOP ON ALGORITHMS AND ARCHITECTURES FOR REAL TIME CONTROL (6) (6.2000.PALMA DE MALLORCA. ESPAÑA)Model Predictive Control is one of the most popular control strategy in the process industry. One of the reason for this success can be attributed to the fact that constraints and uncertainties can be handled. There are many techniques based on interval mathematics that are used in a wide range of applications. These interval techniques can mean an important contribution to Model Predictive Control giving algorithms to achieve global optimization and constraint satisfaction

Wavelength de-multiplexing properties of a single aperture flanked by periodic arrays of indentations

In this paper we explore the transmission properties of single subwavelength apertures perforated in thin metallic films flanked by asymmetric configurations of periodic arrays of indentations. It is shown how the corrugation in the input side can be used to transmit selectively only two different wavelengths. Also, by tuning the geometrical parameters defining the corrugation of the output side, these two chosen wavelengths can emerge from the structure as two very narrow beams propagating at well-defined directions. This new ability of structured metals can be used as a base to build micron-sized wavelength de-multiplexers.Comment: Accepted for publication in Photonics and Nanostructure

Robust MPC of constrained nonlinear systems based on interval arithmetic

A robust MPC for constrained discrete-time nonlinear systems with additive uncertainties is presented. The proposed controller is based on the concept of reachable sets, that is, the sets that contain the predicted evolution of the uncertain system for all possible uncertainties. If processes are nonlinear these sets are very difficult to compute. A conservative approximation based on interval arithmetic is proposed for the online computation of these sets. This technique provides good results with a computational effort only slightly greater than the one corresponding to the nominal prediction. These sets are incorporated into the MPC formulation to achieve robust stability. By choosing a robust positively invariant set as a terminal constraint, a robustly stabilising controller is obtained. Stability is guaranteed in the case of suboptimality of the computed solution. The proposed controller is applied to a continuous stirred tank reactor with an exothermic reaction.Ministerio de Ciencia y Tecnología DPI-2001-2380-03- 01Ministerio de Ciencia y Tecnología DPI-2002-4375-C02-0

Bounded Error Identification of Systems With Time-Varying Parameters

This note presents a new approach to guaranteed system identification for time-varying parameterized discrete-time systems. A bounded description of noise in the measurement is considered. The main result is an algorithm to compute a set that contains the parameters consistent with the measured output and the given bound of the noise. This set is represented by a zonotope, that is, an affine map of a unitary hypercube. A recursive procedure minimizes the size of the zonotope with each noise corrupted measurement. The zonotopes take into account the time-varying nature of the parameters in a nonconservative way. An example has been provided to clarify the algorithm

Observations on Longidorus africanus Merny from Portual with description of L. vinearum n.sp. (Nematoda : Longidoridae)

Une enquête conduite au Portugal a révélé la présence de deux espèces de #Longidorus. L'une, décrite ici sous le nom de #L. vinearum sp. n., est une espèce bisexuée, caractérisée par une région labiale arrondie et presque continue avec le reste du corps, des poches amphidiennes bilobées - le lobe ventral étant allongé et atteignant presque le niveau du guide - une queue courte, arrondie et, chez le juvénile premier stade, une queue pourvue d'un mucron terminal. L'autre espèce est identifiée à #L. africanus$ Merny, 1966 ; les données morphométriques relatives à cette espèce sont fournies, ainsi que des observations sur leurs différences avec celles de la population type et de populations provenant d'autres parties du monde. (Résumé d'auteur

Exit, Punishment and Rewards in Commons Dilemmas: An Experimental Study

Commons dilemmas are interaction situations where a common good is provided or exploited by a group of individuals so that optimal collective outcomes clash with private interests. Although in these situations, social norms and institutions exist that might help individuals to cooperate, little is known about the interaction effects between positive and negative incentives and exit options by individuals. We performed a modified public good game experiment to examine the effect of exit, rewards and punishment, as well as the interplay between exit and rewards and punishment. We found that punishment had a stronger effect than rewards on cooperation if considered by itself, whereas rewards had a stronger effect when combined with voluntary participation. This can be explained in terms of the ‘framing effect’, i.e., as the combination of exit and rewards might induce people to attach higher expected payoffs to cooperative strategies and expect better behaviour from others