Global analysis of piecewise linear systems using impact maps and surface Lyapunov functions

This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be "unfriendly" maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS

Spectrophotometric determination of the deltamethrin

In the province of Corrientes is found highest production of indoor plants from all Argentina, specially in the northeast of this province. This is because the low frequency orthelack of frosts, allowing a lower cost in the production, since heating is not needed. In this type of cultive is commonly used thedeltamethrin, as the result of this, the validation of a simple method comparable with the gas chromatography for the determination of this Pesticide on both, irrigation and consumption water, was studied. In this work, a spectrophotometric method is proposed for the determination of deltamethrin inirrigation water from the area of flower crops located in the Department of Concepción in the province of Corrientes. Deltamethrin solutions in a range from 0,025 to 1 mg/L on irrigation water were prepared. The absorbance spectrum was scanned between 200 and 400 nm. The maximum absorbance was found at 220 nm. A calibration curve in the range from 0.025 to 1 mg/L, responded to A = (0.3246± 0.0224) C + (0.0096 ± 0.0068) with R2 = 0.998. The % RSD was 0.961 indicating good repeatability for the analytical procedure. The accuracy in the recovery experience was 99.0 - 109.6%. The statistical comparison using the t-test and the F-test indicates that there are no significant differences between GC and spectrophotometric methods, with a confidence level of 95%. The specificity and intermediate accuracy tests were satisfactory.Fil: Gimenez, L. I.. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Departamento de Química; ArgentinaFil: Michellod, A. M. M.. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Departamento de Química; ArgentinaFil: Jorge, M. J.. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Departamento de Química; ArgentinaFil: Pila, Andrea Natalia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; ArgentinaFil: Bordón, Alexander Germán. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Departamento de Química; ArgentinaFil: Profeta, Mariela Inés. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Departamento de Química; ArgentinaFil: Romero, Jorge Marcelo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Departamento de Química; ArgentinaFil: Jorge, Nelly Lidia. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Departamento de Química; Argentin

Analysis domain model for shared virtual environments

The field of shared virtual environments, which also encompasses online games and social 3D environments, has a system landscape consisting of multiple solutions that share great functional overlap. However, there is little system interoperability between the different solutions. A shared virtual environment has an associated problem domain that is highly complex raising difficult challenges to the development process, starting with the architectural design of the underlying system. This paper has two main contributions. The first contribution is a broad domain analysis of shared virtual environments, which enables developers to have a better understanding of the whole rather than the part(s). The second contribution is a reference domain model for discussing and describing solutions - the Analysis Domain Model

The self-consistent general relativistic solution for a system of degenerate neutrons, protons and electrons in beta-equilibrium

We present the self-consistent treatment of the simplest, nontrivial, self-gravitating system of degenerate neutrons, protons and electrons in $\beta$-equilibrium within relativistic quantum statistics and the Einstein-Maxwell equations. The impossibility of imposing the condition of local charge neutrality on such systems is proved, consequently overcoming the traditional Tolman-Oppenheimer-Volkoff treatment. We emphasize the crucial role of imposing the constancy of the generalized Fermi energies. A new approach based on the coupled system of the general relativistic Thomas-Fermi-Einstein-Maxwell equations is presented and solved. We obtain an explicit solution fulfilling global and not local charge neutrality by solving a sophisticated eigenvalue problem of the general relativistic Thomas-Fermi equation. The value of the Coulomb potential at the center of the configuration is $eV(0)\simeq m_\pi c^2$ and the system is intrinsically stable against Coulomb repulsion in the proton component. This approach is necessary, but not sufficient, when strong interactions are introduced.Comment: Letter in press, Physics Letters B (2011