Generalized Fractional Evolution Equation

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.

Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary

Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Clifford-Hermite polynomials in fractional Clifford analysis

In this paper we generalize radial and standard Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven.

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

Boundary integral technique for the numerical modelling of the air flow for the Aaberg exhaust system

A boundary integral technique has been developed for the numerical simulation of the air flow for the Aaberg exhaust system. For the steady, ideal, irrotational air flow induced by a jet, the air velocity is an analytical function. The solution of the problem is formulated in the form of a boundary integral equation by seeking the solution of a mixed boundary-value problem of an analytical function based on the Riemann-Hilbert technique. The boundary integral equation is numerically solved by converting it into a system of linear algebraic equations, which are solved by the process of the Gaussian elimination. The air velocity vector at any point in the solution domain is then computed from the air velocity on the boundary of the solution domains.

Las trayectorias de los estudiantes universitarios : un modelo integral = Les trajectoires des étudiants universitaires : un modèle intégré

Nous avons développé un modèle qui cherche à identifier les déterminants des trajectoires scolaires des élèves universitaires en articulant deux perspectives théoriques et en utilisant une approche méthodologique mixte en deux phases : quantitative et qualitative. La première phase est basée sur le modèle de Tinto (1992) avec l'incorporation d'autres variables de Crespo et Houle (1995). Cette étape a atteint deux objectifs. Dans le premier, on a identifié les différences entre les variables exogènes (indice économique, l'éducation parentale, moyen au lycée et moyenne dans l’examen d'entrée) et trois types de trajectoires: la persévérante, de décalage et d’abandon. Cette phase était basée sur les données d'un sondage administré à 800 étudiants à l'Université de Sonora (Mexique). Les résultats montrent que ceux qui ont quitté l'institution ont obtenu des scores significativement plus bas sur les variables exogènes. Le deuxième objectif a été atteint pour les trajectoires persévérantes et de décalage, en établissant que les étudiants ont une plus grande chance d’être persévérants lorsqu’ils présentent de meilleurs scores dans deux variables exogènes (l'examen d'entrée et être de genre féminin) et quatre viable endogènes (haute intégration académique, de meilleures perspectives d'emploi, ont une bourse). Dans la deuxième phase nous avons approfondi la compréhension (Verstehen) des processus d'articulation entre l'intégration scolaire et sociale à travers de trois registres proposés par Dubet (2005): l'intégration, le projet et la vocation. Cette phase a consisté dans 30 interviews avec étudiantes appartenant aux trois types de trajectoire. À partir du travail de Bourdages (1994) et Guzman (2004), nous avons cherché le sens de l'expérience attribuée par les étudiants au processus éducatif. Les résultats révèlent cinq groupes d’étudiantes avec des expériences universitaires identifiables : ceux qui ont une intégration académique et sociale plus grande, les femmes travailleuses intégrées académiquement, ceux qui ont les plus grandes désavantages économiques et d’intégration scolaire, ceux qui ont cherché leur vocation dans un autre établissement et ceux qui n'ont pas poursuivi leurs études. L'utilisation de différents outils statistiques (analyse de corrélation, analyse de régression logistique et analyse des conglomérats) dans la première phase a permis d’identifier des variables clés dans chaque type de trajectoire, lesquelles ont été validées avec les résultats de la phase qualitative. Cette thèse, en plus de montrer l'utilité d'une approche méthodologique mixte, étend le modèle de Tinto (1987) et confirme l'importance de l'intégration scolaire pour la persévérance à l'université.

Una alternativa a la integral de Riemann

Se trata de un análisis del proceso de aprendizaje matemático desde puntos de vista interdisciplinares donde se pretende que el alumno tenga un desarrollo del proceso matemático de forma paulatina y no se vea forzado a absorber los diversos conceptos de forma simultanea. Finalmente se concluye con la importancia de encontrar una alternativa al sistema de aprendizaje de la integral de Riemann, como el cálculo de superficies a partir de áreas planas o la integral definida.

La integral de Riemann.

La obra trata sobre el estudio de la Integral de Riemann, intentando compatibilizar la sencillez del planteamiento clásico usado en el Bachillerato con las directrices emanadas de la Universidad, que obligan a un planteamiento opuesto al anterior. La estrategia didáctica se ha experimentado en el Instituto de Bachillerato San Juan de la Cruz de Caravaca de la Cruz durante los cursos 1987-88 y 1988-89, tanto en tercero de BUP como en COU. El tema ha sido desarrollado para su lectura directa por los alumnos, por lo que se ha procurado detallar al máximo la exposición.

Implications of innovation for inclusive growth: a study of Medellín, Colombia's metro system and integral urban projects

Medellín, Colombia continues to attract global recognition for its evolution from a crimesaturated and desegregated city to an award-winning paragon of innovation. Two innovations in particular, the Metro System & the Integral Urban Projects, have fostered and contributed to Medellín’s inclusive growth, as indicated by a corresponding increase in both social and economic capital. Through a mixed methodology analysis of these two experiences, including participant observation, in-depth interviews with different industry leaders, and household surveys, this thesis explores the extent to which inclusive innovation has contributed to inclusive growth in Medellín. The surveys were distributed to three sensitive neighborhoods of Medellín and apply a Synthesized Framework for measuring inclusive growth, one that includes five indicators for social capital and five indicators for economic capital, emphasizing the importance of progression in both dimensions. By drawing on concepts of inclusivity surfacing more frequently in business lexicon and the emergence of a newly branded Medellín, the findings of this thesis indicates that the implementation of innovations in association with a unified city vision practiced by the local government, corporate and non-profit sector has contributed to achieving inclusive growth, and has left civilians hungry for more.

Absence or weak correlation between chewing side preference and lateralities in primary, mixed and permanent dentition

Objectives: To determine whether chewing side preference (CSP) is correlated to lateralities (handedness, footedness, eyedness and earedness) in primary, mixed and permanent dentitions.Design: Three-hundred subjects were divided into 3 groups: Group 1-100 children 3-5 years old, primary dentition; Group 2-100 children 6-12 years old, mixed dentition; Group 3 - 100 subjects 18-47 years old, permanent dentition. CSP was determined using a method developed by Mc Donnell et al.(9) Subjects were given a piece of gum and the position of the chewing gum was recorded 7 times as right or left. Subjects were classified as 'observed preferred chewing side' (OPCS) when they performed 5/7, 6/7 or 7/7 strokes on the same side. OPCS corresponded to the CSP. Laterality tests were performed for handedness, footedness, eyedness and earedness tasks. The Chi-square (chi(2)) and phi correlation (r) tests were used to investigate significant correlations between CSP and sidedness.Results: There was a significant correlation between chewing and earedness (p = 0.00), although there was weak positive correlation (r = 0.30) for primary dentition. There were significant correlations between chewing and handedness (p = 0.02; r = 0.25) and chewing and footedness (p = 0.02; r = 0.26), however, there were weak positive correlations for mixed dentition; there were significant correlations between chewing and handedness (p = 0.02; r = 0.26); chewing and footedness (p = 0.00; r = 0.33) and chewing and earedness (p = 0.01; r = 0.29); however, there were weak positive correlations for permanent dentition.Conclusion: It may be concluded that CSP can be significantly correlated with: earedness for primary dentition; handedness and footedness for mixed dentition; handedness, footedness and earedness for permanent dentition, but these are weak positive relationships. Future work on larger samples of left- and right-sided individuals is required to validate the findings. (C) 2012 Elsevier Ltd. All rights reserved.

A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL

It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem.

An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

The significance of endogeneity problems in crash models: An examination of left-turn lanes in intersection crash models

Crash prediction models are used for a variety of purposes including forecasting the expected future performance of various transportation system segments with similar traits. The influence of intersection features on safety have been examined extensively because intersections experience a relatively large proportion of motor vehicle conflicts and crashes compared to other segments in the transportation system. The effects of left-turn lanes at intersections in particular have seen mixed results in the literature. Some researchers have found that left-turn lanes are beneficial to safety while others have reported detrimental effects on safety. This inconsistency is not surprising given that the installation of left-turn lanes is often endogenous, that is, influenced by crash counts and/or traffic volumes. Endogeneity creates problems in econometric and statistical models and is likely to account for the inconsistencies reported in the literature. This paper reports on a limited-information maximum likelihood (LIML) estimation approach to compensate for endogeneity between left-turn lane presence and angle crashes. The effects of endogeneity are mitigated using the approach, revealing the unbiased effect of left-turn lanes on crash frequency for a dataset of Georgia intersections. The research shows that without accounting for endogeneity, left-turn lanes ‘appear’ to contribute to crashes; however, when endogeneity is accounted for in the model, left-turn lanes reduce angle crash frequencies as expected by engineering judgment. Other endogenous variables may lurk in crash models as well, suggesting that the method may be used to correct simultaneity problems with other variables and in other transportation modeling contexts.