304 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
A complex rearrangement involving cryptic deletion of ETV6 and CDKN1B genes in a case of childhood acute lymphoblastic leukemia
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Novel chromosomal translocation (17;22)(q12;q12) in a case of myelodisplastic syndrome characterized with signs of hemolytic anemia at presentation.
No full textMyelodysplastic syndromes (MDS) are clonal stem cell diseases that can result in cytopenias, dysplasia in one or more cell lineages, infective hematopoiesis, and increase the risk of progression to acute myeloid leukemia (AML). MDSs are characterized by several recurrent cytogenetic defects, which can affect diagnosis, prognosis, and treatment. Some of that chromosomal alterations are associated with very poor prognosis. Conventional cytogenetics cannot accurately define the rearranged karyotype. Instead, molecular cytogenetics analyses can provide important diagnostic and prognostic information for patients affected by MDS, allowing the characterization of the whole mutational spectrum and, mainly, novel chromosomal lesions. In this paper, we report a MDS case with a novel chromosomal translocation [t(17;22)(q12;q22)], described for the first time here. Following Giemsa-banding karyotyping, fluorescent in situ hybridization analyses, by using chromosome-specific probes, displayed the breakpoint regions at chromosomes 17 and 22, within which intra and inter-chromosomal segmental duplications (SD) are present. Because of the occurrence of SDs in breakpoint region, it was not possible to finely define the genomic regions where breaks fell. Further investigations could be required to better understand the molecular basis of the novel translocation t(17;22)(q12;q12) acting in MDS context and to explain if SDs could contribute to the pathogenesis of MDS
Molecular characterization of a complex karyotype revealed cryptic dletion of the ETV6 and CDKN1B genes on 12p in the case of childood B-ALL.
No full textSimilar mechanisms formed ring markers containing chromosome 12 pericentromeric region in two patients with therapy-related acute myeloid leukemia
No full textTwo cases of therapy-related acute myeloid leukemia showed complex karyotypes, including a small ring and a larger D-chromosome. Multicolor fluorescence in situ hybridization and bacterial artificial chromosome and fosmid clones showed that both ring chromosomes were composed entirely of material excised from chromosome 12. The deleted segment of 12 was found fused to the short arm of a D-group chromosome. We hypothesized that similar mechanisms were involved in both rearrangements. A fusion at the short arms of chromosome 12 and a D-group chromosome was accompanied by excision and ligation of the chromosome 12 pericentromeric region to form a small ring chromosome
Devide Et Impera: The United Arab Emirates’ Strategic Policy In Yemen
No full textThe United Arab Emirates (UAE) may have withdrawn its troops from Yemen, but its influence remains substantial and significant. From the first stage of the war, Saudi Arabia focused on the north of Yemen, while the UAE actively engaged in the north\u27s south and coastal areas. Not only trains fighters, but the UAE also provides them with financial and political support. This is a descriptive-analytical article, using qualitative methods with data and works of literature, collected various books, journals, and online resources related to the topic. Furthermore, the author uses the devide et impera theory to elaborate, examine, and investigate the UAE\u27s policy, as well as its strategy, in Yemen. This article found that UAE\u27s divide and rule strategy is applied to achieve several interests in Yemen, such as countering terrorism, extremism, and Houthi. Nevertheless, the UAE is also ambitious to dispel al-Islah, a group affiliated to the Islamic Brotherhood
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