Isoperimetric problems of the calculus of variations with fractional derivatives

In this paper we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.Comment: Submitted 02-Oct-2009; revised 30-Jun-2010; accepted 10-May-2011; for publication in the journal Acta Mathematica Scienti

A formulation of the fractional Noether-type theorem for multidimensional Lagrangians

This paper presents the Euler-Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the Riemann-Liouville fractional derivative.Comment: Submitted 26-SEP-2011; accepted 3-MAR-2012; for publication in Applied Mathematics Letter

Leitmann's direct method for fractional optimization problems

Based on a method introduced by Leitmann [Internat. J. Non-Linear Mech. {\bf 2} (1967), 55--59], we exhibit exact solutions for some fractional optimization problems of the calculus of variations and optimal control.Comment: Submitted June 16, 2009 and accepted March 15, 2010 for publication in Applied Mathematics and Computation

Fractional variational calculus for nondifferentiable functions

We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free boundary conditions is considered, as well as problems with isoperimetric and holonomic constraints.Comment: Submitted 13-Aug-2010; revised 24-Nov-2010; accepted 28-March-2011; for publication in Computers and Mathematics with Application

Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

The Hanle Effect in 1D, 2D and 3D

This paper addresses the problem of scattering line polarization and the Hanle effect in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) media for the case of a two-level model atom without lower-level polarization and assuming complete frequency redistribution. The theoretical framework chosen for its formulation is the QED theory of Landi Degl'Innocenti (1983), which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. The self-consistent values of these density-matrix elements is to be determined by solving jointly the kinetic and radiative transfer equations for the Stokes parameters. We show how to achieve this by generalizing to Non-LTE polarization transfer the Jacobi-based ALI method of Olson et al. (1986) and the iterative schemes based on Gauss-Seidel iteration of Trujillo Bueno and Fabiani Bendicho (1995). These methods essentially maintain the simplicity of the Lambda-iteration method, but their convergence rate is extremely high. Finally, some 1D and 2D model calculations are presented that illustrate the effect of horizontal atmospheric inhomogeneities on magnetic and non-magnetic resonance line polarization signals.Comment: 14 pages and 5 figure

Projecting Tension in Virtual Environments through Lighting.

Interactive synthetic environments are currently used in a wide variety of applications, including video games, exposure therapy, education, and training. Their success in such domains relies on their immersive and engagement qualities. Filmmakers and theatre directors use many techniques to project tension in the hope of affecting audiences’ affective states. These techniques include narrative, sound effects, camera movements, and lighting. This paper focuses on temporal variation of lighting color and its use in evoking tension within interactive virtual worlds. Many game titles adopt some cinematic lighting effects to evoke certain moods, particularly saturated red colored lighting, flickering lights, and very dark lighting. Such effects may result in user frustration due to the lack of balance between the desire to project tension and the desire to use lighting for other goals, such as visibility and depth projection. In addition, many of the lighting effects used in game titles are very obvious and obtrusive. In this paper, the author will identify several lighting color patterns, both obtrusive and subtle, based on a qualitative study of several movies and lighting design theories. In addition to identifying these patterns, the author also presents a system that dynamically modulates the lighting within an interactive environment to project the desired tension while balancing other lighting goals, such as establishing visibility, projecting depth, and providing motivation for lighting direction. This work extends the author’s previous work on the Expressive Lighting Engine [1-3]. Results of incorporating this system within a game will be discussed

Organic farm conventionalisation and farmer practices in China, Brazil and Egypt.

Certified organic agriculture stipulates a range of principles and standards, which govern farmer practices. The recent global expansion of organic agriculture has raised new challenges for organic agriculture, particularly whether management practices in organic farms are subject to the forces of conventionalisation. We studied changes in agroecological practices in certified organic farms in China, Brazil and Egypt. The study takes departure in the conventionalisation hypothesis and the analysis is framed using organic and agroecological principles. The study focuses on agroecological design principles, inherent to organic agriculture, of diversity in crop production, pest, disease and weed management, and soil fertility management. The research design was as a multiple case study of five cases in China, Brazil and Egypt. We show that the adoption of organic agriculture has induced fundamental changes in organic farmer management practices, although agroecological practices of organic farmers do not fulfil organic principles. The forces of conventionalisation exert a strong influence on changes in organic farmer practices. Organic ‘niche’ market crops with a high-value influence organic farmers’ management decisions, particularly regarding the prioritisation of diversity in the cropping systems for agroecological purposes. The farming systems have therefore not undergone major changes of their cropping patterns. Furthermore, there was a general heavy reliance upon input substitution for pest and soil fertility management. This study thus presents new data and a novel analysis of the implications at the farm scale of the global expansion of organic agriculture, and the influence of conventionalisation on farmers practices

Variable exponent Triebel-Lizorkin-Morrey spaces

We introduce variable exponent versions of Morreyfied Triebel-Lizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the Hardy-Littlewood maximal inequality in the fully variable setting. Using it we obtain characterizations by means of Peetre maximal functions and use them to show the independence of the introduced spaces from the admissible system used.publishe

Generalized transversality conditions in fractional calculus of variations

Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the Bolza-type fractional variational problem, the fractional variational problem with a Lagrangian that may also depend on the unspecified end-point phi(b), where x = phi(t) is a given curve, and the infinite horizon fractional variational problem. (C) 2012 Elsevier B.V. All rights reserved