Oddness of residually reducible Galois representations

We show that suitable congruences between polarized automorphic forms over a CM field always produce elements in the Selmer group for exactly the ±-Asai (aka tensor induction) representation that is critical in the sense of Deligne. For this we relate the oddness of the associated polarized Galois representations (in the sense of the Bella ̈ıche-Chenevier sign being +1) to the parity condition for criticality. Under an assumption similar to Vandiver’s conjecture this also provides evidence for the Fontaine-Mazur conjecture for polarized Galois representations of any even dimension

The integral monodromy of hyperelliptic and trielliptic curves

We compute the \integ/\ell and \integ_\ell monodromy of every irreducible component of the moduli spaces of hyperelliptic and trielliptic curves. In particular, we provide a proof that the \integ/\ell monodromy of the moduli space of hyperelliptic curves of genus $g$ is the symplectic group \sp_{2g}(\integ/\ell). We prove that the \integ/\ell monodromy of the moduli space of trielliptic curves with signature $(r,s)$ is the special unitary group \su_{(r,s)}(\integ/\ell\tensor\integ[\zeta_3])

Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry

We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry

Critical slope p-adic L-functions of CM modular forms

For ordinary modular forms, there are two constructions of a p-adic L-function attached to the non-unit root of the Hecke polynomial, which are conjectured but not known to coincide. We prove this conjecture for modular forms of CM type, by calculating the the critical-slope L-function arising from Kato's Euler system and comparing this with results of Bellaiche on the critical-slope L-function defined using overconvergent modular symbols.Comment: 14 page

Comparative study of non-invasive force and stress inference methods in tissue

In the course of animal development, the shape of tissue emerges in part from mechanical and biochemical interactions between cells. Measuring stress in tissue is essential for studying morphogenesis and its physical constraints. Experimental measurements of stress reported thus far have been invasive, indirect, or local. One theoretical approach is force inference from cell shapes and connectivity, which is non-invasive, can provide a space-time map of stress and relies on prefactors. Here, to validate force- inference methods, we performed a comparative study of them. Three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces, were tested by using two artificial and two experimental data sets. Our results using different datasets consistently indicate that our Bayesian force inference, by which cell-junction tensions and cell pressures are simultaneously estimated, performs best in terms of accuracy and robustness. Moreover, by measuring the stress anisotropy and relaxation, we cross-validated the force inference and the global annular ablation of tissue, each of which relies on different prefactors. A practical choice of force-inference methods in distinct systems of interest is discussed.Comment: 12 pages, 8 figures, EPJ E: Topical issue on "Physical constraints on morphogenesis and evolution

Quantitative fractographic analysis of impact fracture surfaces of steel R73

Macroscopic images offracture surfaces of Charpy test specimens of steel R73 were studied, where bright spots in images represent cleavage facets or ductile dimples, respectively, both in special orientations. Within image analysis, they may be taken for the most significant textural element. Being the brightest patches in the image, they can be extracted by thresholding. Their counts and area distribution are closely related to temperature and impact energy.Выполнены исследования макроизображений поверхностей разрушений образцов Шарпи из стали R73. При специальных условиях ориентации поверхностей разрушения видны яркие участки на изображениях, соответствующие граням скола или ямкам вязкого разрушения. Эти участки могут быть использованы в качестве основного элемента текстуры для обработки изображения. Поскольку эти участки на изображениях являются наиболее яркими, их можно отсеять путем настройки порогового уровня освещенности. Результаты расчета относительной доли их площади тесно коррелируют с температурой и энергией ударного разрушения

The p-adic L-functions of evil Eisenstein series

We compute the p-adic L-functions of evil Eisenstein series, showing that they factor as products of two Kubota-Leopoldt p-adic L-functions times a logarithmic term. This proves in particular a conjecture of Glenn Stevens

The p-adic L-functions of evil Eisenstein series

We compute the p-adic L-functions of evil Eisenstein series, showing that they factor as products of two Kubota-Leopoldt p-adic L-functions times a logarithmic term. This proves in particular a conjecture of Glenn Stevens