Universal families and quantum control in infinite dimensions

In a topological space, a family of continuous mappings is called universal if its action, in at least one element of the space, is dense. If the mappings are unitary or trace-preserving completely positive, the notion of universality is closely related to the notion of controllability in either closed or open quantum systems. Quantum controllability in infinite dimensions is discussed in this setting and minimal generators are found for full control universal families. Some of the requirements of the operators needed for control in infinite dimensions follow from the properties of the infinite unitary group. Hence, a brief discussion of this group and the appropriate mathematical spaces is also included.     

Robust pair‐copula based forecasts of realized volatility

A useful application for copula functions is modeling the dynamics in the conditional moments of a time series. Using copulas, one can go beyond the traditional linear ARMA (p,q) modeling, which is solely based on the behavior of the autocorrelation function, and capture the entire dependence structure linking consecutive observations. This type of serial dependence is best represented by a canonical vine decomposition, and we illustrate this idea in the context of emerging stock markets, modeling linear and nonlinear temporal dependences of Brazilian series of realized volatilities. However, the analysis of intraday data collected from e‐markets poses some specific challenges. The large amount of real‐time information calls for heavy data manipulation, which may result in gross errors. Atypical points in high‐frequency intraday transaction prices may contaminate the series of daily realized volatilities, thus affecting classical statistical inference and leading to poor predictions. Therefore, in this paper, we propose to robustly estimate pair‐copula models using the weighted minimum distance and the weighted maximum likelihood estimates (WMLE). The excellent performance of these robust estimates for pair‐copula models are assessed through a comprehensive set of simulations, from which the WMLE emerged as the best option for members of the elliptical copula family. We evaluate and compare alternative volatility forecasts and show that the robustly estimated canonical vine‐based forecasts outperform the competitors. Copyright © 2013 John Wiley & Sons, Ltd.     

The Asymptotic and Numerical Inversion of the Marcum Q‐Function

The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi‐squared cumulative distribution functions. In this paper, we describe a new asymptotic method for inverting the generalized Marcum Q‐function and for the complementary Marcum P‐function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant methods to invert the function. We present details of numerical computations that show the reliability of the asymptotic approximations.     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing’s oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.     

Kidney exchange simulation and optimization

One of the challenges in a kidney exchange program (KEP) is to choose policies that ensure an effective and fair management of all participating patients. In order to understand the implications of different policies of patient allocation and pool management, decision makers should be supported by a simulation tool capable of tackling realistic exchange pools and modeling their dynamic behavior. In this paper, we propose a KEP simulator that takes into consideration the wide typology of actors found in practice (incompatible pairs, altruistic donors, and compatible pairs) and handles different matching policies. Additionally, it includes the possibility of evaluating the impact of positive crossmatch of a selected transplant, and of dropouts, in a dynamic environment. Results are compared to those obtained with a complete information model, with knowledge of future events, which provides an upper bound to the objective values. Final results show that shorter time intervals between matches lead to higher number of effective transplants and to shorter waiting times for patients. Furthermore, the inclusion of compatible pairs is essential to match pairs of specific patient–donor blood type. In particular, O-blood type patients benefit greatly from this inclusion.     

A laboratory scale fundamental time?

In the Regge kinematics the amplitude for gluon production off three scattering centers is found in the Lipatov effective action technique. The vertex for gluon emission with the reggeon splitting in three reggeons is calculated and its transversality is demonstrated. It is shown that in the sum of all contributions terms containing principal value singularities are canceled and substituted by the standard Feynman poles. These results may be used for calculation of the inclusive cross section for gluon production on two nucleons in the nucleus.     

Structural and Spectral Study of Nickel(II) Complexes of Pyridyl bis{3‐piperidyl‐, bis{hexamethyleneiminyl‐, bis{N(4)‐diethyl‐, and bis{N(4)‐dipropylthiosemicarbazones}

Pyridyl bis(N(4)‐substituted thiosemicarbazones), in which the substituents replacing the NH₂ group on the thiosemicarbazone moieties are piperidyl, H₂Plpip; hexamethyleneiminyl, H₂Plhexim; diethylamino, H₂Pl4DE; and dipropylamino, H₂Pl4DP, have been synthesized. These bis(thiosemicarbazones) and their nickel(II) complexes have been characterized with IR, electronic, mass, and ¹H and ¹³C NMR spectra. Crystal structures have been solved for H₂Plpip and all four nickel(II) complexes. H₂Plpip does not possess hydrogen bonding between the thiosemicarbazone moieties, but is in the Z isomeric form with intramolecular hydrogen bonding from both thiosemicarbazone moieties to pyridine nitrogen atoms. The nickel(II) complexes possess square‐planar N₂S₂ (i. e., imine nitrogen and thiolato sulfur atoms) centers and the two pyridine ring nitrogen atoms are not coordinated.     

Cloud point extraction for cobalt preconcentration with on-line phase separation in a knotted reactor followed by ETAAS determination in drinking waters

A novel method for cobalt preconcentration by cloud point extraction with on-line phase separation in a PTFE knotted reactor and further determination by electrothermal atomic absorption spectrometry (ETAAS) is proposed. The cloud point system was formed in the presence of non-ionic micelles of polyethyleneglycolmono-p-nonylphenylether (PONPE 7.5) and it was retained on the inner walls of a knotted reactor (KR). The surfactant rich-phase was removed from the knotted reactor with 75 microL of methanol acidified with 0.8 mol L(-1) nitric acid, directly into the dosing hole of the L'Vov graphite tube. An enrichment factor of 15 was obtained with a preconcentration time of 60 s, with respect to the direct determination of cobalt by ETAAS in aqueous solutions. The value of the detection limit for the preconcentration of 5 mL of sample solution was 10 ng L(-1). The precision, expressed as the relative standard deviation (R.S.D.), for 10 replicate determinations at 0.5 microg L(-1) Co level was 4.5%. Verification of the accuracy was carried out by analysis of a standard reference material (NIST SRM 1640e "Trace elements in natural water"). The method was successfully applied to the determination of cobalt in drinking water samples.