A General Backwards Calculus of Variations via Duality

We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010; accepted for publication 08-July-201

Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl. 145 (2010), no. 3. In Pres

Medieval and Ottoman period (14th–17th c.) Archaeology in the Drava River region, Hungary

The paper is a short summary of the main archaeological outcomes of an interdisciplinary project in a section of the Drava river crossing the territory of Somogy county, in Hungary. One of the study areas is the vicinity of Berzence where medieval settlement patterns, land use and economy have been reconstructed on the basis of historical sources and an archaeological field survey. A comprehensive review of architectural history and material culture of the Ottoman Period stronghold in Barcs was the other area under investigation. Research there was based on written sources and the archaeological assemblage recovered from the palisaded fort. Zooarchaeological research at this site revealed some significant culture historical aspects of this stronghold. Underwater archaeological investigations carried out in the Drava river itself and aerial exploration of the study areas also supplied valuable archaeological results

Transversality Conditions for Infinite Horizon Variational Problems on Time Scales

We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for publication in "Optimization Letters"

Euler-Lagrange equations for composition functionals in calculus of variations on time scales

In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form $H(\int_{a}^{b}f(t,x^{\sigma}(t),x^{\Delta}(t))\Delta t)$. Euler-Lagrange equations, natural boundary conditions for such problems as well as a necessary optimality condition for isoperimetric problems, on a general time scale, are given. A number of corollaries are obtained, and several examples illustrating the new results are discussed in detail.Comment: Submitted 10-May-2009 to Discrete and Continuous Dynamical Systems (DCDS-B); revised 10-March-2010; accepted 04-July-201

Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay

We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations and optimal control with delays.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

Evidence for Concurrent Effects of Exposure to Environmental Cadmium and Lead on Hepatic CYP2A6 Phenotype and Renal Function Biomarkers in Nonsmokers

We examined the interrelationships between phenotype of hepatic cytochrome P450 2A6 (CYP2A6), nephropathy, and exposure to cadmium and lead in a group of 118 healthy Thai men and women who had never smoked. Their urinary Cd excretion ranged from 0.05 to 2.36 μg/g creatinine, whereas their urinary Pb excretion ranged from 0.1 to 12 μg/g creatinine. Average age and Cd burden of women and men did not differ. Women, however, on average showed a 46% higher urinary Pb excretion (p < 0.001) and lower zinc status, suggested by lower average serum Zn and urinary Zn excretion compared with those in men. Cd-linked nephropathy was detected in both men and women. However, Pb-linked nephropathy was seen only in women, possibly because of higher Pb burden coupled with lower protective factors, notably of Zn (p < 0.001), in women compared with men. In men, Pb burden showed a negative association with CYP2A6 activity (adjusted β= −0.29, p = 0.003), whereas Cd burden showed a positive association with CYP2A6 activity (adjusted β= 0.38, p = 0.001), suggesting opposing effects of Cd and Pb on hepatic CYP2A6 phenotype. The weaker correlation between Cd burden CYP2A6 activity in women despite similarity in Cd burden between men and women is consistent with opposing effects of Pb and Cd on hepatic CYP2A6 phenotypic expression. A positive correlation between Cd-linked nephropathy (urinary N-acetyl-β-d-glucosaminidase excretion) and CYP2A6 activity in men (r = 0.39, p = 0.002) and women (r = 0.37, p = 0.001) suggests that Cd induction of hepatic CYP2A6 expression and Cd-linked nephropathy occurred simultaneously

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201