Kelvin Functions For Determination Of Magnetic Susceptibility In Nonmagnetic Metals

A method to calculate the real and imaginary parts of the magnetic permeability and susceptibility of nonmagnetic metals by using Kelvin functions is presented. The exact treatment is shown for the massive cylindrical geometry. An expression for a hollow circular cylinder is discussed and expanded to the thin-shell limit.65124505450

Eddy Current Decay Method Applied To A New Geometry

The eddy current decay method for determination of metallic samples resistivities is presented for the case of a hollow circular cylindrical geometry. The theory is developed for two kinds of experimental arrangements: the primary coil is driven by a voltage source or by a current source. The measurements made for several metals (Al, Cu, Nb, brass, and bronze) at room temperature and at the temperature of liquid nitrogen analyzed by the theory give accurate results compared with the four terminal method.61125237524

The Phase Angle Method For Electrical Resistivity Applied To The Hollow Circular Cylinder Geometry

The phase-angle method to measure electrical resistivity in nonmagnetic metals is calculated for samples presenting the hollow circular geometry. The phase angle versus the operating frequency for a general hollow circular cylinder geometry shows a similar qualitative behavior when compared with the massive cylinder geometry. A discussion of a procedure for a desirable experimental condition related to the geometrical parameters and exciting signal is presented. UFaipxr.6731167116

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time, and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space. While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes, vast areas of the tropics remain understudied. In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity, but it remains among the least known forests in America and is often underrepresented in biodiversity databases. To worsen this situation, human-induced modifications may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge, it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost

On The Spectrum Of The Twisted Dolbeault Laplacian Over Kähler Manifolds

We use Dirac operator techniques to a establish sharp lower bound for the first eigenvalue of the Dolbeault Laplacian twisted by Hermitian-Einstein connections on vector bundles of negative degree over compact Kähler manifolds. © 2008 Elsevier B.V. All rights reserved.273412419Alexandrov, B., Grantcharov, G., Ivanov, S., The Dolbeault operator on Hermitian spin surfaces (2001) Ann. Inst. Fourier, 51, pp. 221-235Almorox, A.L., Tejero Prieto, C., Holomorphic spectrum of twisted Dirac operators on compact Riemann surfaces (2006) J. Geom. Phys., 56, pp. 2069-2091Atiyah, M., Eigenvalues of the Dirac operator (1985) Lecture Notes in Math., 1111, pp. 251-260. , Workshop. Bonn, 1984, Springer, BerlinBaum, H., Eigenvalues estimates for Dirac operators coupled to instantons (1994) Ann. Global Anal. Geom., 12, pp. 193-209Bourguignon, J.P., Li, P., Yau, S.T., Upper bound for the first eigenvalue of algebraic submanifolds (1994) Comment. Math. Helv., 69, pp. 199-207Colbois, B., El Soufi, A., Eigenvalues of the Laplacian acting on p-forms and metric conformal deformations (2006) Proc. Amer. Math. Soc., 134, pp. 715-721Donaldson, S.K., Kronheimer, P.B., (1990) The Geometry of Four-Manifolds, , Oxford University Press, New YorkFriedrich, T., (2000) Dirac Operator in Riemannian Geometry, , American Mathematical Society, Providence, RIHitchin, N., Harmonic spinors (1974) Adv. Math., 14, pp. 1-55Kirchberg, K.D., An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature (1986) Ann. Global Anal. Geom., 4, pp. 291-325Kirchberg, K.D., The first eigenvalue of the Dirac operator on Kähler manifolds (1991) J. Geom. Phys., 7, pp. 449-468Lawson, H.B., Michelsohn, M.L., Spin Geometry Princeton Mathematical Series, 38. , Princeton University PressTejero Prieto, C., Holomorphic spectral geometry of magnetic Schrödinger operators on Riemann surfaces (2006) Differential Geom. Appl., 24, pp. 288-31