On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

A class of permutation quadrinomials

In this paper, we investigate the permutation behavior of a class of quadrinomials. Each term of these quadrinomials has a Niho-type exponent, and two sets of coefficient triples making the quadrinomials to be permutations are obtained. We use a substitution to transform the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations.     

电磁场作用下菜籽油的摩擦学性能研究

使用改进后的四球摩擦磨损试验机考察了不同电磁场强度和不同载荷条件下菜籽油的摩擦学性能,结合扫描电子显微镜(SEM)、X射线能谱仪(EDS)和X射线光电子能谱仪(XPS)分析了磨斑的表面形貌及表面典型元素的化学状态,并对摩擦学机理进行了初步探讨.结果表明:在所考察的工况下,电磁场有利于改善菜籽油的抗磨减摩性能,其强度越大,对菜籽油抗磨减摩性能的改善效果越好;电磁场通过促进吸附膜的吸附作用和O元素与金属表面作用,有利于在磨斑表面生成更厚、更致密的摩擦化学反应膜,从而增强了菜籽油的抗磨减摩性能;不同强度的电磁场可能会改变长链菜籽油分子在摩擦界面的吸附形态而影响其减摩性能.     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

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 .     

水产品中11种海洋生物毒素的高效液相色谱-四极杆/静电场轨道阱高分辨质谱检测方法研究

建立了水产品中11种海洋生物毒素的高效液相色谱-四极杆/静电场轨道阱高分辨质谱(HPLC-Q-Orbitrap HRMS)检测方法。该方法采用分级提取原理,结合分散固相萃取技术(dSPE)和载体辅助液液萃取技术(SLLE),建立了对亲水性及亲脂性海洋生物毒素的"一站式"提取净化体系。在优化条件下,11种毒素在一定质量浓度范围内具有良好的线性关系,相关系数(r)均大于0.99。该方法对11种毒素的检出限为1～10μg/kg,定量下限为2～20μg/kg,加标回收率为55.6%～122%,相对标准偏差为5.4%～16%。方法快速高效,可操作性强,解决了不同理化性质的海洋生物毒素的通用性检测问题,可满足水产品中海洋生物毒素的快速筛查要求。     

Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in ${\mathbb{R}}^d$ 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.     

Semi-concurrent vector fields in Finsler geometry

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 $(M,F)$, admitting a non-constant smooth function f on M such that $\frac{\partial f}{\partial x^i}\frac{\partial g^{ij}}{\partial y^k}=0$?”. 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.