On Multi-threaded Metrical Task Systems

Traditionally, on-line problems have been studied under the assumption that there is a unique sequence of requests that must be served. This approach is common to most general models of on-line computation, such as Metrical Task Systems. However, there exist on-line problems in which the requests are organized in more than one independent thread. In this more general framework, at every moment the first unserved request of each thread is available. Therefore, apart from deciding how to serve a request, at each stage it is necessary to decide which request to serve among several possibilities.In this paper we introduce Multi-threaded Metrical Task Systems, that is, the generalization of Metrical Task Systems to the case in which there are many threads of tasks. We study the problem from a competitive analysis point of view, proving lower and upper bounds on the competitiveness of on-line algorithms. We consider finite and infinite sequences of tasks, as well as deterministic and randomized algorithms. In this work we present the first steps towards a more general framework for on-line problems which is not restricted to a sequential flow of information.     

Variational characterization for eigenvalues of Dirac operators

In this paper we give two different variational characterizations for the eigenvalues of H+V where H denotes the free Dirac operator and V is a scalar potential. The first one is a min-max involving a Rayleigh quotient. The second one consists in minimizing an appropriate nonlinear functional. Both methods can be applied to potentials which have singularities as strong as the Coulomb potential. Received June 5, 1998 / Accepted June 11, 1999     

Hardy-type estimates for Dirac operators

We prove some Hardy type inequalities related to the Dirac operator by elementary methods, for a large class of potentials, which even includes measure valued potentials. Optimality is achieved by the Coulomb potential. When potentials are smooth enough, our estimates provide some spectral information on the operator.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Arduino-based chaotic secure communication system using multi-directional multi-scroll chaotic oscillators

The experimental realization of a chaotic secure communication system is introduced herein taking advantage of Arduino’s open source integrated development environment along with its preset functions that reduce development time and complexity. The system uses multi-directional multi-scroll chaotic oscillators that are based on piecewise-linear functions. Experimental results are given for chaos generators in 1-direction (1-D), 2-D and 3-D of up to 20, \(20\times 20\) and \(20\times 20\times 20\) scrolls, respectively. Using two chaos generators, a chaotic secure communication system is implemented in a master–slave topology by applying generalized Hamiltonian forms and observer approach. Finally, we detail experimental results for the synchronization of \(6\times 6\) and \(20\times 20\) scroll attractors, which are used for transmitting a monochromatic image through the Arduino-based chaotic secure communication system.     

Homogeneous diffusion in ℝ with power-like nonlinear diffusivity

We study the nonnegative solutions of the initial-value problem u_t=(u^r|u_x|^p-1u_x)_x,u(x, 0)L ¹(), where p>0, r+p>0. The local velocity of propagation of the solutions is identified as V = -v_x| v_x|^p-1 where v =cu (with r +p - 1)/p and c (r +p/(r +p- 1)) is the nonlinear potential. Our main result is the a priori estimate (v_x|v_x|^p-1)_x-

Numerical study of sliding wear caused by a loaded pin on a rotating disc

A computational approach is proposed to predict the sliding wear caused by a loaded spherical pin contacting a rotating disc, a condition typical of the so-called pin-on-disc test widely used in tribological studies. The proposed framework relies on the understanding that, when the pin contacts and slides on the disc, a predominantly plane strain region exists at the centre of the disc wear track. The wear rate in this plane strain region can therefore be determined from a two dimensional idealisation of the contact problem, reducing the need for computationally expensive three dimensional contact analyses. Periodic unit cell techniques are used in conjunction with a ratchetting-based failure criterion to predict the wear rate in the central plane strain region. The overall three dimensional wear rate of the disc is then determined by scaling the plane strain wear rate with a conversion factor related to the predicted shape of the wear track. The approach is used to predict pin-on-disc test data from an Al-Si coating using a tungsten carbide pin. The predicted results are found to be consistent with measured data.     

Simultaneous determination of a selected group of cytostatic drugs in water using high-performance liquid chromatography-triple-quadrupole mass spectrometry

In recent years, an increasing concern has risen about the presence of pharmaceuticals in the aquatic environment. Despite their toxicity, increasing consumption and release into the municipal sewage, only a few studies have been focused on cytostatic drugs, mainly due to the lack of methods for their simultaneous analysis. In this work, a method, based on solid-phase extraction prior to high-performance liquid chromatography-triple quadrupole mass spectrometry determination, was optimized and validated for the simultaneous determination of some (14) of the most widely used cytostatic drugs in river water, influent and effluent wastewater. Process efficiency was in the range between 41 and 99% in real samples, except for cytarabine (24%), docetaxel (17%) and methotrexate (30%), due to suppression effects; precision values were <11%, except for gemcitabine (up to 19%); and detection limits were in the range between 0.1 and 38 ng/L. Cytarabine, doxorubicin, etoposide, gemcitabine, iphosphamide and vinorelbine were found at concentration levels up to 14 ng/L in influent and effluent wastewater, showing an insignificant decrease during sewage treatment; cytarabine and gemcitabine were found in effluent wastewater and were also detected in river water associated with effluent discharges.     

Ni5, Ni8, and Ni10 clusters with 2,6-diacetylpyridine-dioxime as a ligand

In the present work, novel coordination possibilities for the system dapdoH(2)/Ni(II) (dapdoH(2) = 2,6-diacetylpyridine-dioxime) have been explored. Depending on the starting reagents and solution conditions, several clusters with nuclearities ranging from Ni(5) to Ni(10) were achieved and structurally characterized, namely, [Ni(5)(R-COO)(2)(dapdo)(2)(dapdoH)(2)(N(CN)(2))(2)(MeOH)(2)] in which R-COO(-) = benzoate (1) or 3-chlorobenzoate (2), [Ni(8)(dapdo)(4)(NO(3))(4)(OH)(4)(MeOH)(4)] (3), and [Ni(10)(dapdo)(8)(N(CN)(2))(2)(MeO)(MeOH)](NO(3)) (4). For the first time, pentadentate coordination for the dapdo(2-) ligand has been established. All compounds show a combination of square-planar and octahedrally coordinated nickel atoms. According to the Ni(2)(sp)Ni(3)(Oh) (1 and 2), Ni(4)(sp)Ni(4)(Oh) (3), and Ni(4)(sp)Ni(6)(Oh) (4) environments, these systems magnetically behave as trimer, tetramer, and hexanuclear clusters, respectively. dc magnetic measurements in the 2-300 K range of temperature reveal antiferromagnetic coupling for all compounds, and the correlation of the superexchange interaction with the torsion angles involving the oximato bridges is experimentally confirmed.