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

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

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Dynamical tunneling in molecules: Quantum routes to energy flow

Dynamical tunneling, introduced in the molecular context, is more than two decades old and refers to phenomena that are classically forbidden but allowed by quantum mechanics. On the other hand the phenomenon of intramolecular vibrational energy redistribution (IVR) has occupied a central place in the field of chemical physics for a much longer period of time. Although the two phenomena seem to be unrelated several studies indicate that dynamical tunneling, in terms of its mechanism and timescales, can have important implications for IVR. Examples include the observation of local mode doublets, clustering of rotational energy levels, and extremely narrow vibrational features in high resolution molecular spectra. Both the phenomena are strongly influenced by the nature of the underlying classical phase space. This work reviews the current state of understanding of dynamical tunneling from the phase space perspective and the consequences for intramolecular vibrational energy flow in polyatomic molecules.Comment: 37 pages and 23 figures (low resolution); Int. Rev. Phys. Chem. (Review to appear in Oct. 2007

Remineralization of initial carious lesions in deciduous enamel after application of dentifrices of different fluoride concentrations

The aim of the present study was to evaluate the remineralization potential of five dentifrices with different fluoride concentrations. Initial caries lesions were created in 72 cylindrical enamel blocks from deciduous teeth. The specimens were randomly distributed among six experimental groups corresponding to six experimental periods. Each of the six volunteers carried two deciduous enamel specimens fixed in an intraoral appliance for a period of 4 weeks. They brushed their teeth and the enamel blocks at least two times a day with dentifrices containing 0 ppm (period 1), 250 ppm (period 2), and 500 ppm fluoride (period 3), respectively. A second group of volunteers (n = 6) used dentifrices with a fluoride content of 0 ppm (period 4), 1,000 ppm (period 5), or 1,500 ppm (period 6). At the end of the respective period, the mineral content was determined by transversal microradiography (TMR). The use of dentifrices containing 500 ppm fluoride (38% MR), 1,000 ppm fluoride (42% MR), and 1,500 ppm fluoride (42% MR) resulted in a statistically significant higher mineral recovery compared to the control group (0 ppm fluoride). Mineral recovery was similar after use of dentifrices containing 0 and 250 ppm fluoride (24%; 25%). It is concluded that it is possible to remineralize initial carious lesions in deciduous enamel in a similar way as it has been described for enamel of permanent teeth

Mapping Patent Classifications: Portfolio and Statistical Analysis, and the Comparison of Strengths and Weaknesses

The Cooperative Patent Classifications (CPC) jointly developed by the European and US Patent Offices provide a new basis for mapping and portfolio analysis. This update provides an occasion for rethinking the parameter choices. The new maps are significantly different from previous ones, although this may not always be obvious on visual inspection. Since these maps are statistical constructs based on index terms, their quality--as different from utility--can only be controlled discursively. We provide nested maps online and a routine for portfolio overlays and further statistical analysis. We add a new tool for "difference maps" which is illustrated by comparing the portfolios of patents granted to Novartis and MSD in 2016.Comment: Scientometrics 112(3) (2017) 1573-1591; http://link.springer.com/article/10.1007/s11192-017-2449-

Identification and analysis of seven effector protein families with different adaptive and evolutionary histories in plant-associated members of the Xanthomonadaceae.

The Xanthomonadaceae family consists of species of non-pathogenic and pathogenic γ-proteobacteria that infect different hosts, including humans and plants. In this study, we performed a comparative analysis using 69 fully sequenced genomes belonging to this family, with a focus on identifying proteins enriched in phytopathogens that could explain the lifestyle and the ability to infect plants. Using a computational approach, we identified seven phytopathogen-enriched protein families putatively secreted by type II secretory system: PheA (CM-sec), LipA/LesA, VirK, and four families involved in N-glycan degradation, NixE, NixF, NixL, and FucA1. In silico and phylogenetic analyses of these protein families revealed they all have orthologs in other phytopathogenic or symbiotic bacteria, and are involved in the modulation and evasion of the immune system. As a proof of concept, we performed a biochemical characterization of LipA from Xac306 and verified that the mutant strain lost most of its lipase and esterase activities and displayed reduced virulence in citrus. Since this study includes closely related organisms with distinct lifestyles and highlights proteins directly related to adaptation inside plant tissues, novel approaches might use these proteins as biotechnological targets for disease control, and contribute to our understanding of the coevolution of plant-associated bacteria

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

Transcription of toll-like receptors 2, 3, 4 and 9, FoxP3 and Th17 cytokines in a susceptible experimental model of canine Leishmania infantum infection

Canine leishmaniosis (CanL) due to Leishmania infantum is a chronic zoonotic systemic disease resulting from complex interactions between protozoa and the canine immune system. Toll-like receptors (TLRs) are essential components of the innate immune system and facilitate the early detection of many infections. However, the role of TLRs in CanL remains unknown and information describing TLR transcription during infection is extremely scarce. The aim of this research project was to investigate the impact of L. infantum infection on canine TLR transcription using a susceptible model. The objectives of this study were to evaluate transcription of TLRs 2, 3, 4 and 9 by means of quantitative reverse transcription polymerase chain reaction (qRT-PCR) in skin, spleen, lymph node and liver in the presence or absence of experimental L. infantum infection in Beagle dogs. These findings were compared with clinical and serological data, parasite densities in infected tissues and transcription of IL-17, IL-22 and FoxP3 in different tissues in non-infected dogs (n = 10), and at six months (n = 24) and 15 months (n = 7) post infection. Results revealed significant down regulation of transcription with disease progression in lymph node samples for TLR3, TLR4, TLR9, IL-17, IL-22 and FoxP3. In spleen samples, significant down regulation of transcription was seen in TLR4 and IL-22 when both infected groups were compared with controls. In liver samples, down regulation of transcription was evident with disease progression for IL-22. In the skin, upregulation was seen only for TLR9 and FoxP3 in the early stages of infection. Subtle changes or down regulation in TLR transcription, Th17 cytokines and FoxP3 are indicative of the silent establishment of infection that Leishmania is renowned for. These observations provide new insights about TLR transcription, Th17 cytokines and Foxp3 in the liver, spleen, lymph node and skin in CanL and highlight possible markers of disease susceptibility in this model