Abelianisation of logarithmic $$\mathfrak {sl}_2$$-connections

We prove a functorial correspondence between a category of logarithmic $$\mathfrak {sl}_2$$ sl 2 -connections on a curve $${\mathsf {X}}$$ X with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover "Equation missing". The proof is by constructing a pair of inverse functors $$\pi ^\text {ab}, \pi _\text {ab}$$ π ab , π ab , and the key is the construction of a certain canonical cocycle valued in the automorphisms of the direct image functor $$\pi _*$$ π ∗ .

The asymptotic of curvature of direct image bundle associated with higher powers of a relatively ample line bundle

Let $$\pi :\mathcal {X}\rightarrow M$$ π : X → M be a holomorphic fibration with compact fibers and L a relatively ample line bundle over $$\mathcal {X}$$ X . We obtain the asymptotic of the curvature of $$L^2$$ L 2 -metric and Qullien metric on the direct image bundle $$\pi _*(L^k\otimes K_{\mathcal {X}/M})$$ π ∗ ( L k ⊗ K X / M ) up to the lower order terms than $$k^{n-1}$$ k n - 1 , for large k. As an application we prove that the analytic torsion $$\tau _k(\bar{\partial })$$ τ k ( ∂ ¯ ) satisfies $$\partial \bar{\partial }\log (\tau _k(\bar{\partial }))^2=o(k^{n-1})$$ ∂ ∂ ¯ log ( τ k ( ∂ ¯ ) ) 2 = o ( k n - 1 ) , where n is the dimension of fibers.

Frontal sinuses as tools for human identification: a systematic review of imaging methods

The frontal sinuses are potential evidences for human identification because of the inherent distinctiveness of their morphology. Over the last decades, several techniques emerged to enable the visualization and analysis of the frontal sinuses via bi- and three-dimensional imaging. This systematic review aimed to compile different methodological approaches found in the scientific literature to contribute to human identification. Three examiners revisited the scientific literature in order to find imaging techniques for the visualization of the frontal sinuses applied to human identification. The standard search strings built-up from a PICO question identified 404 unique articles in the following databases Medline/Pubmed, Web of Science, Scopus, Lilacs and Scielo. Based on eligibility criteria applied during title, abstract and full-text reading, the sample reduced to 19 articles. The articles were published between 1987 and 2019 by research groups from 10 different countries. Computed tomography was used in 37% of the techniques, while the remaining (63%) techniques used skull radiographs. The techniques were highly heterogeneous and varied between metric analysis, direct image superimposition and morphology code-based systems. The authors considered their techniques useful for human identification and reported accuracy rates from 13 to 100%. Most of the studies revealed low risk of bias. More advantages were related with the techniques based on direct image superimpositions and three-dimensional visualization. Forensic experts must be aware of the use of frontal sinuses for human identification, especially when three-dimensional images are available as ante-mortem and post-mortem evidences for superimposition and comparison.

On the Menger and almost Menger properties in locales

<p>The Menger and the almost Menger properties are extended to locales. Regarding the former, the extension is conservative (meaning that a space is Menger if and only if it is Menger as a locale), and the latter is conservative for sober T_D-spaces. Non-spatial Menger (and hence almost Menger) locales do exist, so that the extensions genuinely transcend the topological notions. We also consider projectively Menger locales, and show that, as in spaces, a locale is Menger precisely when it is Lindelöf and projectively Menger. Transference of these properties along localic maps (via direct image or pullback) is considered.</p>

Representation Theory of Groups and D -Modules

In this paper, we study a decomposition D -module structure of the polynomial ring. Then, we illustrate a geometric interpretation of the Specht polynomials. Using Brauer’s characterization, we give a partial generalization of the fact that factors of the discriminant of a finite map π : spec B ⟶ spec A generate the irreducible factors of the direct image of B under the map π .