Matrix fractional systems

This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole–Cole, Davidson–Cole, and Havriliak–Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.

Fractional state space analysis of economic systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Factores Críticos del Desarrollo Local y Regional Integrado zona serrana y Norte de la Provincia de Córdoba-. Validación causal estadística de Modelos de Ecuaciones Estructurales. Identificación de problemas normativos de las OSC.Critical Factors of Local and Regional Development in north of the Province of Córdoba. Causal validation with Structural Equation Modeling. Legal regulations of civil society.

En la investigación anterior -en la zona pampeana de la Provincia de Córdoba- se demostró teórica y empíricamente, que el desarrollo de la Sociedad Civil muchas veces libradas a su suerte y con limitaciones legales apoyan decididamente el desarrollo local, sin embargo han logrado solo parcialmente sus objetivos, por lo que es necesario comenzar un camino de fortalecimiento en los nuevos roles que deben asumir. Los gobiernos locales, a la vez, intentan trabajosamente con contados éxitos detener el procesos de descapitalización social -financiera y humana- de sus comunidades locales y regionales, peregrinando con escaso éxito a los centros concentrados del poder político y económico, para procurar los recursos financieros y humanos necesarios que no alcanzan a reponer los que se fugan desde hace décadas de sus localidades. Las empresas, con ciclos recurrentes de crecimiento y decrecimiento vinculados a los mercados en que colocan sus productos, también se debaten en la búsqueda de los escasos recursos, financieros y humanos, que les permitan consolidar un desarrollo a mediano y largo plazo. El desarrollo alcanzado en Sistemas de información, instrumentos de relevamiento, análisis y elaboración de propuestas para el Desarrollo Local, nos permite avanzar en: 1. La confirmación empírica de las hipótesis iniciales - factores exógenos y endógenos - en la zona Norte y Serrana de la provincia 2. La validación científica -mediante el Análisis de ecuaciones estructurales. de tales supuestos, para el conjunto de las poblaciones analizadas en ambas etapas. 3. La identificación de los problemas normativos que afectan el desarrollo de las Organizaciones de la Sociedad Civil (OSC). METODOLOGÍA Respecto la validación empírica en la zona norte y serrana 1. Selección de las 4 localidades a relevar de acuerdo a las categorías definidas 2. Elaboración de acuerdos con autoridades e instituciones locales. 3. Relevamiento cualitativo con líderes locales y fuentes de datos secundarias. 4. Adaptación de instrumentos de relevamiento a las realidades locales y estudios previos 5. Relevamiento cuantitativo de campo, capacitación de encuestadores y supervisores. 6. Procesamiento y elaboración de informes finales locales. Respecto de la construcción de modelos de desarrollo 1. Desarrollar las dimensiones especificas y las variables (items) de cada factor crítico. 2. Revisar el instrumento con expertos de cada una de las dimensiones. 3. Validar a nivel exploratorio por medio de un Análisis de Componentes Principales 4. Someter a los expertos la evaluación de una serie de localidades que representan cada uno. Respecto de la identificación de las normas legales que afectan a la Sociedad Civil 1.Relevamiento documental de normas 2. Relevamiento con líderes de instituciones de la Sociedad Civil 3. Análisis de las normas vigentes 4. Elaboración de Informes Finales y Transferencia a líderes e instituciones

An Equation for the Prediction of Oxygen Consumption in a Brazilian Population

Background: The equations predicting maximal oxygen uptake (VO2max or peak) presently in use in cardiopulmonary exercise testing (CPET) softwares in Brazil have not been adequately validated. These equations are very important for the diagnostic capacity of this method. Objective: Build and validate a Brazilian Equation (BE) for prediction of VO2peak in comparison to the equation cited by Jones (JE) and the Wasserman algorithm (WA). Methods: Treadmill evaluation was performed on 3119 individuals with CPET (breath by breath). The construction group (CG) of the equation consisted of 2495 healthy participants. The other 624 individuals were allocated to the external validation group (EVG). At the BE (derived from a multivariate regression model), age, gender, body mass index (BMI) and physical activity level were considered. The same equation was also tested in the EVG. Dispersion graphs and Bland-Altman analyses were built. Results: In the CG, the mean age was 42.6 years, 51.5% were male, the average BMI was 27.2, and the physical activity distribution level was: 51.3% sedentary, 44.4% active and 4.3% athletes. An optimal correlation between the BE and the CPET measured VO2peak was observed (0.807). On the other hand, difference came up between the average VO2peak expected by the JE and WA and the CPET measured VO2peak, as well as the one gotten from the BE (p = 0.001). Conclusion: BE presents VO2peak values close to those directly measured by CPET, while Jones and Wasserman differ significantly from the real VO2peak.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Periodic orbits in complex Abel equation

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Hopf bifurcation of a delay differential equation with two delays

We consider a delay differential equation with two delays. The Hopf bifurcation of this equation is investigated together with the stability of the bifurcated periodic solution, its period and the bifurcation direction. Finally, three applications are given.

Dynamics of the third order Lyness' difference equation

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The equation xpyq=zr and groups that act freely on Λ-trees

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On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Analysing the impact of public capital stock using the NEG wage equation: a panel data approach

This paper examines the relationship between the level of public infrastructure and the level of productivity using panel data for the Spanish provinces over the period 1984-2004, a period which is particularly relevant due to the substantial changes occurring in the Spanish economy at that time. The underlying model used for the data analysis is based on the wage equation, which is one of a handful of simultaneous equations which when satisfied correspond to the short-run equilibrium of New Economic Geography theory. This is estimated using a spatial panel model with fixed time and province effects, so that unmodelled space and time constant sources of heterogeneity are eliminated. The model assumes that productivity depends on the level of educational attainment and the public capital stock endowment of each province. The results show that although changes in productivity are positively associated with changes in public investment within the same province, there is a negative relationship between productivity changes and changes in public investment in other regions.