130,597 research outputs found
Some geometric properties of hypersurfaces with constant r-mean curvature in euclidean space
No full textLet f : M -> R(m+1) be an isometrically immersed hypersurface. In this paper, we exploit recent results due to the authors to analyze the stability of the differential operator L(r) associated with the rth Newton tensor of f. This appears in the Jacobi operator for the variational problem of minimizing the r-mean curvature H(r). Two natural applications are found. The first one ensures that under a mild condition on the integral of H(r) over geodesic spheres, the Gauss map meets each equator of S(m) infinitely many times. The second one deals with hypersurfaces with zero (r + 1)-mean curvature. Under similar growth assumptions, we prove that the affine tangent spaces f(*)T(p)M, p is an element of M, fill the whole R(m+1)
Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson-Walker spacetimes
No full textn this paper we analyse the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes. We consider first the case of compact spacelike hypersurfaces, completing some previous results given in [2]. We next extend these results to the complete noncompact case. In that case, our approach is based on the use of a generalized version of the Omori-Yau maximum principle for trace type differential operators, recently given by the authors in [3]
ON THE GEOMETRY OF NEWTON OPERATORS
No full textWe studied the geometry of hypersurfaces of complete constant higher order mean curvature, both in the Riemannian and in the Lorentzian setting. In particular, in the Riemannian setting, we focused on uniqueness results for hypersurfaces in warped products. An analytic approach based on a general version of the Omori-Yau maximum principle for trace-type semi-elliptic operators and on the parabolicity for elliptic operators in divergence form, combined with suitable geometric conditions on the geometry of the ambient manifold, allowed to characterize the slices as the only hypersurfaces of constant higher order mean curvature in warped products. Later on, we studied how to extend, using the same technique, uniqueness results to spacelike hypersurfaces of constant higher order mean curvature in Lorentzian warped products. Finally, we focused on comparison geometry in the Lorentzian setting proving, under suitable bounds on the Ricci or the sectional curvature of a Lorentzian manifold, hessian and laplacian comparison theorems for the Lorentzian distance function. Jointly with the Omori-Yau maximum principle, these theorems, applied to the distance function restricted to spacelike hypersurfaces, allowed to obtain higher order mean curvature estimates for spacelike hypersurfaces bounded by a level set of the distance function and Bernstein-type theorems
MeSH term explosion and author rank improve expert recommendations
No full textInformation overload is an often-cited phenomenon that reduces the productivity, efficiency and efficacy of scientists. One challenge for scientists is to find appropriate collaborators in their research. The literature describes various solutions to the problem of expertise location, but most current approaches do not appear to be very suitable for expert recommendations in biomedical research. In this study, we present the development and initial evaluation of a vector space model-based algorithm to calculate researcher similarity using four inputs: 1) MeSH terms of publications; 2) MeSH terms and author rank; 3) exploded MeSH terms; and 4) exploded MeSH terms and author rank. We developed and evaluated the algorithm using a data set of 17,525 authors and their 22,542 papers. On average, our algorithms correctly predicted 2.5 of the top 5/10 coauthors of individual scientists. Exploded MeSH and author rank outperformed all other algorithms in accuracy, followed closely by MeSH and author rank. Our results show that the accuracy of MeSH term-based matching can be enhanced with other metadata such as author rank
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
"Closing the R&D Gap, Evaluating the Sources of R&D Spending"
No full textBoth spending and tax policies have been implemented in the United States with the goal of stimulating private sector research and development (R&D). Karier questions whether current R&D policy, especially the research and experimentation tax credit, can contribute to closing the gap between nondefense expenditures on R&D in the United States and such expenditures in other countries, such as Japan and Germany. He also explores possible changes to our current R&D policy to make it more effective.
A complex rearrangement involving cryptic deletion of ETV6 and CDKN1B genes in a case of childhood acute lymphoblastic leukemia
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