On embeddings of CAT(0) cube complexes into products of trees via colouring their hyperplanes

We prove that the contact graph of a 2-dimensional CAT(0) cube complex X of maximum degree Δ can be coloured with at most ?(Δ)=MΔ²⁶$?(\mathrm{\Delta })=M{\mathrm{\Delta }}^{26}$ colours, for a fixed constant M. This implies that X (and the associated median graph) isometrically embeds in the Cartesian product of at most ?(Δ)$?(\mathrm{\Delta })$ trees, and that the event structure whose domain is X admits a nice labelling with ?(Δ)$?(\mathrm{\Delta })$ labels. On the other hand, we present an example of a 5-dimensional CAT(0) cube complex with uniformly bounded degrees of 0-cubes which cannot be embedded into a Cartesian product of a finite number of trees. This answers in the negative a question raised independently by F. Haglund, G. Niblo, M. Sageev, and the first author of this paper.     

Gray codes for signed involutions

In this paper we present two cyclic Gray codes for signed involutions. The first one has a natural construction, implemented by a CAT algorithm, based in the recursive formula for the number of signed involutions. The second code, although with a higher computational cost, has the smallest possible Hamming distance for this family of objects.     

基于LabVIEW的电液伺服阀测试系统设计与实现

为了解决电液伺服阀测试中手动测试效率低下、误差率高的现状,开发了一种基于LabVIEW图形编程语言的自动测试系统;系统结合NI PCI-6232板卡,用LabVIEW软件实现了电液伺服阀的静态及动态特性的自动测试,系统具有数据采集、处理及实时显示、数据保存等功能;对空载流量特性、零位泄漏特性、压力特性等进行了实验测试,并对测试结果进行了分析,各测试数据在伺服阀允许的误差范围内;实验结果表明测试系统运行良好、数据采集及处理可靠有效。     

The diffusion of complex securities: The case of CAT bonds

Complex securities generally do not diffuse smoothly but by fits and starts in response to sudden shifts in demand, occurring as investors learn about the intrinsic value of the securities from their noisy performance. We use CAT bonds, a capital market-based alternative to CAT risk reinsurance, to illustrate the diffusion of a complex security that competes against a legacy financial product offered by financial intermediaries. We find that the diffusion of the security is highly path-dependent with the capricious ups and downs of its actual performance plus the competitive response of CAT reinsurers jointly determining its ultimate success or failure.     

Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces

In this paper, for a commuting pair consisting of a point-valued nonexpansive self-mapping t and a set-valued nonexpansive self-mapping T of a hyperconvex metric space (or a CAT(0) space) X, we look for a solution to the problem of existence of z∈E⊂X such that

     

模拟污水中氮、磷对水稻幼苗过氧化氢酶和乙醇酸氧化酶的影响

以水稻为材料，研究了不同浓度的模拟污水中Ｎ、Ｐ对幼苗过氧化氢酶（Ｃａｔａｌａｓｅ，ＣＡＴ，ＥＣ１．１１．１．６）、乙醇酸氧化酶（Ｇｌｅｃｏｌａｔｅｏｘｉｄａｓｅ，ＧＯ，ＥＣ１．３．３．１）、过氧化物酶（Ｐｅｒｏｘｉｄａｓｅ，ＰＯＤ，ＥＣ１．１１．１．７）和叶绿素含量的影响．结果表明：低浓度Ｎ、Ｐ（分别；在０～４．２８ｍｍｏｌ·Ｌ－１、０～０．２ｍｍｏｌ·Ｌ－１范围）可诱导ＣＡＴ活性增大，而后下降，Ｎ、Ｐ浓度分别超过８．５６ｍｍｏｌ·Ｌ－１和０．４ｍｍｏｌ·Ｌ－１后，活性又升高；ＰＯＤ的活性变化与ＣＡＴ变化很相似．Ｎ、Ｐ浓度分别在０～６．４２ｍｍｏｌ·Ｌ－１、０～０．３ｍｍｏｌ·Ｌ－１范围，ＧＯ活性随Ｎ、Ｐ浓度增高而活性下降，超过６．４２ｍｍｏｌ·Ｌ－１、０．３ｍｍｏｌ·Ｌ－１后，则随Ｎ、Ｐ浓度增大而增大．这可能是高浓度Ｎ、Ｐ可提高水稻的光呼吸的结果．另外，污水中Ｎ、Ｐ抑制叶绿素的合成，使叶绿素的含量降低；低浓度污水Ｎ、Ｐ促进根生长，高浓度Ｎ、Ｐ抑制根生长     

CAT(-1) Structures for Free-by-Free Groups

We give a procedure for constructing CAT(-1) free-by-free groups which uses tree valued Morse theory and branched coverings of 2-complexes.     

Group actions and Helly's theorem

We describe a connection between the combinatorics of generators for certain groups and the combinatorics of Helly's 1913 theorem on convex sets. We use this connection to prove fixed point theorems for actions of these groups on nonpositively curved metric spaces. These results are encoded in a property that we introduce called “property FAr”, which reduces to Serre's property FA when r=1. The method applies to S-arithmetic groups in higher Q-rank, to simplex reflection groups (including some nonarithmetic ones), and to higher rank Chevalley groups over polynomial and other rings (for example SLn(Z[x₁,…,xd]), n>2).     

Singularities of Solution Surfaces for Quasilinear First-Order Partial Differential Equations

For a closed curve in a CAT(K) space with given circumradius and upper bound on curvature, a basic lower bound on the length is established. The inequality is sharp, assumed only when the curve is the boundary of an isometric copy of a racetrack (the convex hull of two congruent circles) from a plane of constant curvature K. Previously such a theorem was proved for Euclidean plane curves by G.D.Chakerian, H.H. Johnson, and A. Vogt, and for curves in higher dimensional Euclidean spaces by A.D. Milka. A similar theorem is proved for nonclosed curves, with a notion of breadth replacing circumradius. Thus we illustrate how singular methods can extend classical Euclidean theorems to a large class of new spaces (including Riemannian manifolds of curvature bounded above) and also give significant strengthenings even in Euclidean space.     

A Bo?ejko-Picardello type inequality for finite-dimensional CAT(0) cube complexes

We prove a Bo?ejko-Picardello type inequality for finite-dimensional CAT(0) cube complexes and as a consequence we obtain that a group acting properly on a finite-dimensional CAT(0) cube complex is weakly amenable with the Cowling-Haagerup constant 1.