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

On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function

We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if both the density of states in rapidity space and the quadratic fluctuations around the saddle point solution to the TBA are properly taken into account. In relativistic boundary QFT the O(1) contributions are directly related to the exact g-function. In this paper we provide an all-orders proof of the previous results of P. Dorey et al. on the g-function in both massive and massless models. In addition, we derive a new result for the g-function which applies to massless theories with arbitrary diagonal scattering in the bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and references adde

Generalized transversality conditions for the Hahn quantum variational calculus

We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cannot be solved using the classical theory

Two New Dioecious Species of Symplocos (Symplocaceae) from Southern Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Two new dioecious species of Symplocos Jacquin from Southern Brazil are described and illustrated. Both species belong to section Barberina (Vellozo) A. DC. of subgenus Symplocos. Symplocos bidana Aranha is characterized by its cymose or racemose inflorescences (9.5-)11-34 mm long, corolla with five or six lobes 3.7-4.9 mm long, and fruits (10-)13-20 x 5-10 mm with the calyx lobes covering the fruiting disc. Symplocos incrassata Aranha is characterized by its reduced cymes, bracts caducous in fruit, and fruits 12-18 x (5-)6-8 mm. In addition, both species have thick endocarps (0.8-1.2 mm), a notable character among the Brazilian species of section Barberina.19116U.S. National Science Foundation [DEB-0126631]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)U.S. National Science Foundation [DEB-0126631

Twisted Bethe equations from a twisted S-matrix

All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld twist of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the boundary conditions, from which we derive these Bethe equations. Although the undeformed S-matrix factorizes into a product of two su(2|2) factors, the deformed S-matrix cannot be so factored. Diagonalization of the corresponding transfer matrix requires a generalization of the conventional algebraic Bethe ansatz approach, which we first illustrate for the simpler case of the twisted su(2) principal chiral model. We also demonstrate that the same twisted Bethe equations can alternatively be derived using instead untwisted S-matrices and boundary conditions with operatorial twists.Comment: 42 pages; v2: a new appendix on sl(2) grading, 2 additional references, and some minor changes; v3: improved Appendix D, additional references, and further minor changes, to appear in JHE

Moduli space coordinates and excited state g-functions

We consider the space of boundary conditions of Virasoro minimal models formed from the composition of a collection of flows generated by \phi_{1,3}. These have recently been shown to fall naturally into a sequence, each term having a coordinate on it in terms of a boundary parameter, but no global parameter has been proposed. Here we investigate the idea that the overlaps of particular bulk states with the boundary states give natural coordinates on the moduli space of boundary conditions. We find formulae for these overlaps using the known thermodynamic Bethe Ansatz descriptions of the ground and first excited state on the cylinder and show that they give a global coordinate on the space of boundary conditions, showing it is smooth and compact as expected.Comment: 10 pages, 4 figure

Health trajectories of Immigrant Children (CRIAS)-a prospective cohort study in the metropolitan area of Lisbon, Portugal

Funding Information: This research was financed by the Asylum, Integration and Migration Fund (ref.PT/2018/FAMI/350) under the Multianual Financial Framework 2014/20, by the Portuguese Foundation for Science and Technology (FCT) (ref.RESEARCH4COVID-19-065) and Global Health and Tropical Medicine (GHTM), Institute of Hygiene and Tropical Medicine (IHMT), NOVA University of Lisbon, Portugal (ref.UID/04413/2020). The extension of the cohort study is financed by the Portuguese Foundation for Science and Technology (FCT) (ref.PTDC/SAU-SER/4664/2020). Publisher Copyright: © 2022 BMJ Publishing Group. All rights reserved.Purpose The CRIAS (Health trajectories of Immigrant Children in Amadora) cohort study was created to explore whether children exposed to a migratory process experience different health risks over time, including physical health, cognitive, socioemotional and behavioural challenges and different healthcare utilisation patterns. Participants The original CRIAS was set up to include 604 children born in 2015, of whom 50% were immigrants, and their parents. Recruitment of 420 children took place between June 2019 and March 2020 at age 4/5 years, with follow-up carried out at age 5/6 years, at age 6/7 years currently under way. Findings to date Baseline data at age 4/5 years (2019-2020) suggested immigrant children to be more likely to belong to families with less income, compared with non-immigrant children. Being a first-generation immigrant child increased the odds of emotional and behavioural difficulties (adjusted OR 2.2; 95% CI: 1.06 to 4.76); more immigrant children required monitoring of items in the psychomotor development test (38.5% vs 28.3%). The prevalence of primary care utilisation was slightly higher among immigrant children (78.0% vs 73.8%), yet they received less health monitoring assessments for age 4 years. Utilisation of the hospital emergency department was higher among immigrants (53.2% vs 40.6%). Age 5 years follow-up (2020-2021) confirmed more immigrant children requiring monitoring of psychomotor development, compared with non-immigrant children (33.9% vs 21.6%). Economic inequalities exacerbated by post-COVID-19 pandemic confinement with parents of immigrant children 3.2 times more likely to have their household income decreased. Future plans Further follow-up will take place at 8, 10, 12/13 and 15 years of age. Funds awarded by the National Science Foundation will allow 900 more children from four other Lisbon area municipalities to be included in the cohort (cohort-sequential design).publishersversionpublishe

Evaluation of the effects of Quercetin and Kaempherol on the surface of MT-2 cells visualized by atomic force microscopy

AbstractThis study investigated the anti-viral effects of the polyphenolic compounds Quercetin and Kaempherol on the release of HTLV-1 from the surface of MT-2 cells. Atomic force microscopy (AFM) was used to scan the surface of the MT-2 cells. MT-2 cells were fixed with 100% methanol on round glass lamina or cleaved mica and dried under UV light and laminar flow. The images were captured on a Multimode equipment monitored by a NanoScope IIId controller from Veeco Instruments Inc operated in tapping mode and equipped with phase-imaging hardware. The images demonstrated viral budding structures 131±57nm in size, indicating profuse viral budding. Interestingly, cell-free viruses and budding structures visualized on the surface of cells were less common when MT-2 was incubated with Quercetin, and no particles were seen on the surface of cells incubated with Kaempherol. In summary, these data indicate that HTLV-1 is budding constantly from the MT-2 cell surface and that polyphenolic compounds were able to reduce this viral release. Biological samples were analyzed with crude cell preparations just after cultivation in the presence of Quercetin and Kaempherol, showing that the AFM technique is a rapid and powerful tool for analysis of antiviral activity of new biological compounds