Curvature estimates for submanifolds in warped products

We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.Comment: 21 page

Foliations and Chern-Heinz inequalities

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially Salavessa's work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of 3-dimensional Riemannian manifolds by constant mean curvature surfaces. These Chern-Heinz inequalities for foliations can be applied to prove Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of bounded open subsets $\Omega \subset \mathbb{R}^{2}$ in terms of its inradius) for embedded tubular neighborhoods of simple curves of $\mathbb{R}^{n}$.Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz Inequalities. 8 Pages, Late

Structural analysis of Ti1−xSixNy nanocomposite films prepared by reactive magnetron sputtering

Nanocomposite thin films consisting of both nanosized solid solutions or nanosized polycrystalline materials embedded in various amorphous matrix materials thus provide a grate potential for future mechanical devices. In this paper we report on the preparation of films resulting from additions of Si to TiN matrix by r.f. reactive magnetron sputtering. Structural properties such as growing characteristics (type of matrix, texture and grain size) will be analysed in some detail. Conventional transmission electron microscopy (TEM) and High-resolution transmission electron microscopy (HRTEM), together with both symmetric and asymmetric mode X-ray diffraction (XRD) experiments were used for this characterisation. The atomic composition of the samples was obtained by Rutherford Backscattering Spectrometry (RBS). The analysis will be carried out as a function of the Si content in the Ti1-xSixNy matrix and several relations will be made regarding important parameters such as texture evolution, grain sizes, but most specially by the type of matrix developed. Regarding the results, all samples develop a double fcc phase with lattice parameters of 4.30 Å and 4.17 Å, corresponding to cubic TiN and most likely to a cubic lattice of SiNx, respectively. Although no significant changes in texture were observed till Si compositions up to 10.6 at. %, the arrangement in atoms planes seem to vary. Results show that an asymmetric arrangement is developed in samples of small Si additions. This arrangement becomes more isotropic with the increase of Si contents, which we attribute to the increase in the SiNx content. In fact this increase leads also to the development of a small amorphous tissue of Si3N4 for large Si additions.The authors gratefully acknowledge the financial support of the ‘Fundação para a Ciência e Tecnologia’ (FCT) during the course of this research under project n PBICT/P/CTM/1962/95 and also the French CNRS Institution and the Portugese ICCTI Institution through CNRS/ICCTI Programs (N: 5522-1998 and 7087-1999)

Prevalence, characteristics, and impact of spinal and lower limb recurrent pain at age 13

Objectives: To compare spinal and lower limb pain in adolescents regarding prevalence, characteristics, causes, and impact. Methods: A descriptive cross-sectional study was conducted in 13-year-old adolescents (female n=2210; male n=2353) from the Portuguese Generation XXI birth cohort. Data were collected between 2018 and 2020 through personal interviews by applying the Luebeck Pain Questionnaire. The pain features examined in each anatomical location (back and lower limb) were recurrence, duration, frequency, intensity, perceived causes, and impact on school and leisure activities. Frequencies and the Chi-square test were used. Results: Questionnaires from 4563 adolescents were analysed, 57.9% had pain in the last three months (main pain in the spine: 11.6%; main pain in the lower limb: 29.0%). Of those, 69.4% and 62.4% reported recurrent pain in the spine and lower limb, respectively. Recurrent pain was more frequent in girls than in boys (spine: 80.0%; 57.0%; lower limb: 70.4%; 58.1% respectively). Pain lasted more than three months in most adolescents (spine: about 60%; lower limb: above 50%); frequency was similarly high in both regions and both sexes (girls: 47.0%; boys: 45.7% in the spine; girls: 45.7%; boys: 40.3% in the lower limb); intensity was rated as high by girls (spine: 45.5%; lower limb: 47.3%) and moderate by boys (spine: 42.0%; lower limb: 41.0%). The leading causes of pain were daily living activities, both for the spine (girls: 65.9%; boys: 76.5%) and the lower limb (girls: 62.2%; boys: 72.1%). Psychosocial causes were the second most common cause of spinal pain (girls: 25.0%; boys: 21.0%). Other causes of lower limb pain were traumatic (girls: 25.5%; boys: 16.6%) and physical factors (girls: 20.7%; boys: 23.8%). Absences from school (girls: 11.7%; boys: 4.8%) and restrictions of leisure activities (girls: 20.7%; boys: 25.2%) were more related to pain in the lower limb. Conclusion: More than half of the adolescents reported spinal or lower limb recurrent pain, which presents a higher frequency, higher intensity, and longer duration in the spine. However, lower limb pain led to more concurrent limitations. © 2024, Sociedade Portuguesa de Reumatologia. All rights reserved

A differential method for bounding the ground state energy

For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a normalisation factor or a matrix element). It just requires the determination of the absolute minimum and maximum in the whole configuration space of the local energy associated with a normalisable trial function (the calculation of the norm is not needed). After a general introduction, the method is applied to three non-integrable systems: the asymmetric annular billiard, the many-body spinless Coulombian problem, the hydrogen atom in a constant and uniform magnetic field. Being more sensitive than the variational methods to any local perturbation of the trial function, this method can used to systematically improve the energy bounds with a local skilled analysis; an algorithm relying on this method can therefore be constructed and an explicit example for a one-dimensional problem is given.Comment: Accepted for publication in Journal of Physics

Resistance Curves in the Tensile and Compressive Longitudinal Failure of Composites

This paper presents a new methodology to measure the crack resistance curves associated with fiber-dominated failure modes in polymer-matrix composites. These crack resistance curves not only characterize the fracture toughness of the material, but are also the basis for the identification of the parameters of the softening laws used in the analytical and numerical simulation of fracture in composite materials. The method proposed is based on the identification of the crack tip location by the use of Digital Image Correlation and the calculation of the J-integral directly from the test data using a simple expression derived for cross-ply composite laminates. It is shown that the results obtained using the proposed methodology yield crack resistance curves similar to those obtained using FEM-based methods in compact tension carbon-epoxy specimens. However, it is also shown that the Digital Image Correlation based technique can be used to extract crack resistance curves in compact compression tests for which FEM-based techniques are inadequate

Biofortificação no Brasil (BioFort): Avaliação preliminar de clones de batata-doce ricos em betacaroteno.

Com o objetivo de disponibilizar aos agricultores e, por conseguinte aos consumidores, cultivares de batata-doce com melhores teores de betacaroteno, a Embrapa realiza seleçaõ de clones no âmbito do programa BioFORT: Biofortificação no Brasil - desenvolvendo produtos agricolas mais nutritivos, que tem por finalidade desenvolver alimentos naturais com quantidades de nutrientes capazes de suprir a necessidade nutricional do corpo humano. O objetivo deste trabalho é apresentar os resultados obtidos numa avaliação prelimar de 96 clones de batata-doce de polpa amarela e alaranjada, e identificar os promissores para avaliações subsequentes em difeentes regiões.CD-ROM. Suplemento. Trabalho apresentado no 51. Congresso Brasileiro de Olericultura, Viçosa, MG

Zero-mode analysis of quantum statistical physics

We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. We identify the stochastic variable of the effective statistical theory that we derive as a boundary configuration and a zero mode relevant to the discussion of infrared physics. We illustrate our formulation by computing the partition function of an interacting one-dimensional quantum mechanical system at finite temperature from the path-integral representation for the density matrix. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident endpoints, and includes non-vanishing boundary terms. An appropriately modified expansion into Matsubara modes provides a natural separation of the zero-mode physics. This feature may be useful in the treatment of infrared divergences that plague the perturbative approach in thermal field theory.Comment: 9 pages, 5 figure