A note on kernel methods for multiscale systems with critical transitions

We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast‐slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near fast subsystem bifurcation points can be computed to leading order. This leading order approximation shows that the MMD depends intricately on the fast‐slow systems parameters, which can influence the detection of potential early‐warning signs before critical transitions. However, the MMD turns out to be an excellent binary classifier to detect the change‐point location induced by the critical transition. We cross‐validate our results by numerical simulations for a van der Pol‐type model.     

淮安板闸遗址受力性能的非线性有限元分析

为了解具有复杂形式和结构的淮安板闸遗址受力性能,采用FRANC 3D和ANSYS软件对淮安板闸遗址进行非线性有限元计算,研究存在初始裂缝的板闸遗址主体的受力及其周边土体的应力分布.研究结果表明:对于考虑含初始裂缝的板闸有限元模型,根据M积分法计算得到应力强度因子和J积分,并使用最大周向应力准则预测裂缝结果;在工况组合“自重+填土压力+水压力+0.75倍的设计附加堆载”作用下,淮安板闸主体结构曲率变化处的斜向裂缝,将会持续以下端开裂早于上端开裂的趋势,保持扭转撕裂的形式发展.对板闸遗址主体结构与周边土体进行参数分析,得出极限应力与板闸弹性参数、土体Drucker-Prager模型参数、板闸与土体间摩擦系数、附加荷载值之间的关系;同时,给出板闸遗址背部填土的较优Drucker-Prager模型参数区间,即粘聚力为12~20 kPa,内摩擦角为10°~20°,膨胀角/内摩擦角的比值为0~0.3,此时附加荷载增大对板闸遗址的应力提高效应较不敏感.     

Plane graphs of maximum degree Δ ≥ 7 are edge-face (Δ + 1)-colorable

A plane graph G is edge-face k-colorable if its edges and faces can be colored with k colors such that any two adjacent or incident elements receive different colors. It is known that every plane graph G of maximum degree Δ ≥ 8 is edge-face (Δ + 1)-colorable. The condition Δ ≥ 8 is improved to Δ ≥ 7 in this paper.     

Neighbor Sum Distinguishing Index of Sparse Graphs

A proper k-edge coloring of a graph G is an assignment of one of k colors to each edge of G such that there are no two edges with the same color incident to a common vertex. Let f(v) denote the sum of colors of the edges incident to v. A k-neighbor sum distinguishing edge coloring of G is a proper k-edge coloring of G such that for each edge uv∈E(G), f(u)≠f(v). By χ'_∑(G), we denote the smallest value k in such a coloring of G. Let mad(G) denote the maximum average degree of a graph G. In this paper, we prove that every normal graph with mad(G) ■ and Δ(G) ≥ 8 admits a(Δ(G) + 2)-neighbor sum distinguishing edge coloring. Our approach is based on the Combinatorial Nullstellensatz and discharging method.     

实二次代数整数环上的单位格的类数

用邻格方法及Siegelmass公式证明了实二次代数域Q(√d)上单位格种gen(In)n≥4)的类数h(In)=3当且仅当Q(√3):n=4;Q(√5);n=6;Q(√3);n=4;Q(√17):n=4.     

3,4跳图的平面性

For a graph G of size ε≥1 and its edge-induced subgraphs H1 and H2 of size r(1≤r≤ε), H1 is said to be obtained from H2 by an edge jump if there exist four distinct vertices u,v,w and x in G such that (u,v)∈E(H2), (w,x)∈ E(G)-E(H2) and H1=H2-(u,v)+(w,x). In this article, the r-jump graphs (r≥3) are discussed. A graph H is said to be an r-jump graph of G if its vertices correspond to the edge induced graph of size r in G and two vertices are adjacent if and only if one of the two corresponding subgraphs can be obtained from the other by an edge jump. For k≥2, the k-th iterated r-jump graph Jrk(G) is defined as Jr(Jrk-1(G)), where Jr1(G)=Jr(G).An infinite sequence{Gi} of graphs is planar if every graph Gi is planar. It is shown that there does not exist a graph G for which the sequence {J3k(G)} is planar, where k is any positive integer. Meanwhile,lim gen(J3k(G))=∞,where gen(G) denotes the genus of a graph G, if the sequencek→∞J3k(G) is defined for every positive integer k. As for the 4-jump gra     

刀具最大前角和最小后角及刃磨的调整计算

本文分析了最大前角剖面自主剖面起的旋向对刀具最大前角和最小后角公式的影响,导出了最大前角和最小后角的最简形式,并在此基础上推出了在Y—Z—Y配置的虎钳上刃磨车刀的计算公式。     

由非简并光学参量放大系统获得压缩态光所满足的Fokker-Planck方程及其解

通过解非简并光学参量放大的Fokker-Planck方程，得出压缩态光的腔内最大压缩的量子起伏为1/16（真空起伏为1/4）,与已知的简并光学参量放大情形腔内最大压缩为1/8相比，压缩度提高了一倍. 关键词： 非简并光学参量放大 Fokker-Planck方程 腔内最大压缩