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In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

Combinatorics · Mathematics 2016-11-01 Franck Gabriel

In this paper, we consider the inverse shape problem of recovering small and extended isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. We will…

Analysis of PDEs · Mathematics 2023-10-13 Rafael Ceja Ayala , Isaac Harris

We consider the broken ray transform on Riemann surfaces in the presence of an obstacle, following earlier work of Mukhometov. If the surface has nonpositive curvature and the obstacle is strictly convex, we show that a function is…

Differential Geometry · Mathematics 2016-06-21 Joonas Ilmavirta , Mikko Salo

Given a polarized complex manifold, projection of a torus-equivariant test configuration to holomorphic vector fields was introduced by G. Sz\'ekelyhidi, as the limit of the associated $\mathbb{C}^*$-actions. We show that there actually…

Differential Geometry · Mathematics 2017-01-13 Tomoyuki Hisamoto

In this paper, we study the relation between geodesic and harmonic mappings. Harmonic mappings are defined between Riemannian manifolds as critical points of the energy functional, on the other hand, geodesic mappings are defined in a more…

Differential Geometry · Mathematics 2019-11-01 Stanislav Hronek

In the present notes we introduce and study the twisted gamma-filtration on K_0(G), where G is a split simple linear algebraic group over a field of characteristic prime to the order of the center of G. We apply this filtration to construct…

Algebraic Geometry · Mathematics 2019-02-20 Kirill Zainoulline

This work deals with two real scalar fields in two-dimensional spacetime, with the fields coupled to allow the study of localized configurations. We consider models constructed to engender geometric constrictions, and use them to…

High Energy Physics - Theory · Physics 2025-01-08 D. Bazeia , I. Bezerra , R. Menezes

We study boundary effects in a linear wave equation with Dirichlet type conditions in a weakly curved pipe. The coordinates in our pipe are prescribed by a given small curvature with finite range, while the pipe's cross section being…

Pattern Formation and Solitons · Physics 2015-05-14 Shin-itiro Goto

We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…

Analysis of PDEs · Mathematics 2014-05-13 David Dos Santos Ferreira , Yaroslav Kurylev , Matti Lassas , Mikko Salo

It is shown that the geodesic rays constructed as limits of Bergman geodesics from a test configuration are always of class $C^{1,\alpha}, 0<\alpha<1$. An essential step is to establish that the rays can be extended as solutions of a…

Differential Geometry · Mathematics 2009-08-06 D. H. Phong , Jacob Sturm

We propose here a first-principles, parameter free, real space method for the study of disordered extended defects in solids. We shall illustrate the power of the technique with an application to graphene sheets with randomly placed…

We consider the imaging of cosmic strings by using Cosmic Microwave Background (CMB) data. Mathematically, we study the inversion of an X-ray transform in Lorentzian geometry, called the light ray transform. The inverse problem is highly…

Numerical Analysis · Mathematics 2024-05-06 Julianne Chung , Lucas Onisk , Yiran Wang

We present a concept study on weak lensing map reconstruction through the cosmic magnification effect in galaxy number density distribution. We propose a minimal variance linear estimator to minimize both the dominant systematical and…

Cosmology and Nongalactic Astrophysics · Physics 2012-02-16 Xinjuan Yang , Pengjie Zhang

Inspired by the results obtained in \cite{SR}, in this work, we develop techniques to handle the contraction property for weak normalization and Lipschitz saturation of algebras for the following types of algebras: universally injective,…

Commutative Algebra · Mathematics 2025-03-26 Thiago da Silva

We present the geodesics on homogeneous and isotropic negatively curved spaces in a simple form suitable for application to cosmological problems. We discuss how the patterns in the microwave sky of anisotropic homogeneous universes can be…

Astrophysics · Physics 2009-10-30 John D. Barrow , Janna Levin

In this article, the ray tracing method is studied beyond the classical geometrical theory. The trajectories are here regarded as geodesics in a Riemannian manifold, whose metric and topological properties are those induced by the…

Mathematical Physics · Physics 2013-07-24 Enrico De Micheli , Giovanni Alberto Viano

Motivated by flat lensing effects, now commonplace utilising negative refraction with finite slabs, we create negative refraction upon a graded line-array. We do so in the setting of flexural waves on a structured Kirchhoff--Love elastic…

Classical Physics · Physics 2019-07-03 Gregory J. Chaplain , Richard V. Craster

Given a complex projective surface with an ADE singularity and p_{g}=0, we construct ADE bundles over it and its minimal resolution. Furthermore, we descibe their minuscule representation bundles in terms of configurations of (reducible)…

Algebraic Geometry · Mathematics 2013-01-04 Yunxia Chen , Naichung Conan Leung

The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…

Numerical Analysis · Mathematics 2021-05-26 Long Li , Jiansheng Yang , Bo Zhang , Haiwen Zhang

We consider a basis of square integrable functions on a rectangle, contained in $R^2$, constructed with Legendre polynomials, suitable, for instance, for the analogical description of images on the plane or in other fields of application of…

Mathematical Physics · Physics 2024-10-16 Enrico Celeghini , Manuel Gadella , Mariano A. del Olmo