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《Journal of Pure and Applied Algebra》2022,226(8):106948
Let be a Henselian discrete valued field with residue field of characteristic , and be the Brauer p-dimension of K. This paper shows that if , for some . It proves that if and only if . 相似文献
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Theo Steininger Jait Dixit Philipp Frank Maksim Greiner Sebastian Hutschenreuter Jakob Knollmüller Reimar Leike Natalia Porqueres Daniel Pumpe Martin Reinecke Matev raml Csongor Varady Torsten Enßlin 《Annalen der Physik》2019,531(3)
NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy 3, a major upgrade to the original NIFTy framework. NIFTy 3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy 3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy 3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 . 相似文献
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J. Chevallier A. Duarte E. Löcherbach G. Ost 《Stochastic Processes and their Applications》2019,129(1):1-27
We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis. 相似文献
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In the present paper, we give an answer to a question which is closely related to doubly warped product of Finsler metrics: ‘‘For each n, is there an n-dimensional Finsler manifold , admitting a non-constant smooth function f on M such that ?”. We relate the preceding mentioned condition to different concepts appeared and studied in Finsler geometry. We introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization of Finsler manifolds admitting a concurrent vector field leads to Riemannian metrics. Various examples for conic Finsler spaces that admit semi-concurrent vector field are presented. 相似文献
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量子力学中很少有系统能够精确地计算传播子, 特别是在考虑了自旋轨道耦合效应的情况下. 利用相空间的群论方法, 首先导出了有原子自旋轨道耦合的各向异性量子点传播子的精确解析表达式. 随后利用传播子来计算自旋高斯波包的演化与相应的概率密度, 并研究了原子自旋轨道耦合效应和磁场强度对距离期望值的影响. 相似文献