Identification tree based on fragmentation rules for structure elucidation of organophosphorus esters by electrospray mass spectrometry

Organophosphorus compounds have played important roles as pesticides, chemical warfare agents and extractors of radioactive material. Structural elucidation of phosphonates poses a particular challenge because their initial forms can be hydrolyzed, thus, degradation products may predominate in samples acquired in the field. The analysis of non‐volatile organophosphorus compounds and their degradation products is possible using electrospray tandem mass spectrometry ESI‐MS/MS. Here, we present a generic strategy that allows the unambiguous identification of substituents for two families of organophosphorus compounds: the phosphonates and phosphates. General fragmentation rules were deduced based on the study of decomposition pathways of 55 organophosphorus esters, including examples found in the literature. Multistage MS (MSⁿ) experiments at high resolution in a hybrid mass spectrometer provide accurate mass measurements, whereas collision‐induced dissociation experiments in a triple quadrupole give access to small fragment ions. The creation of a specific nomenclature for each possible structure of organophosphorus compound, depending on the alkyl side chain linked to the oxygen, was achieved by applying these fragmentation rules. This led to the creation of an ‘identification tree’ based upon the unique consecutive decomposition pathways uncovered for each individual compound. Hence, seven structural motifs were created that orient an unequivocal identification using the ‘identification tree’. Despite the similar structures of the ensemble of phosphate and phosphonate esters, distinct identifications based upon characteristic neutral losses and diagnostic fragment ions were possible in all cases. Copyright © 2013 John Wiley & Sons, Ltd.     

最大Randid指标的k悬挂点化学树的性质

化学分子图G的Randie指标为R（G）=∑wv（dG（u）dG（v））^2/1．其中uv是G的边,dG（u）表示的顶点u的度．本文刻画了具有最大Randie指标的k悬挂点化学树的一些性质．     

Scenario Reduction Algorithms in Stochastic Programming

We consider convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P, i.e., finitely many scenarios. The behaviour of such stochastic programs is stable with respect to perturbations of P measured in terms of a Fortet-Mourier probability metric. The problem of optimal scenario reduction consists in determining a probability measure that is supported by a subset of supp P of prescribed cardinality and is closest to P in terms of such a probability metric. Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately. Compared to earlier versions, the computational performance (accuracy, running time) of the new algorithms has been improved considerably. Numerical experience is reported for different instances of scenario trees with computable optimal lower bounds. The test examples also include a ternary scenario tree representing the weekly electrical load process in a power management model.     

一类T形树匹配唯一的充要条件

证明：若m∈Ze^ ,则T形树T(1,m,n）匹配唯一当且仅当n≠m,m 3,2m 5.     

出生率与年龄段有关的生灭分枝树

本文基于生灭过程的生灭演化机理, 将生物繁衍过程描述为有向随机图过程-随机分枝树, 建立了出生率与年龄段有关的生灭分枝树演化模型. 本文研究了任一节点在不同年龄及临死时刻的出度分布、虚出度分布和拟出度分布, 并证明了拟出度过程是随机时刻终止的Poisson过程, 讨论了首生年龄及相对出生年龄的分布, 给出了任一节点成为孤立节点的概率.     

树的Nordhaus-Gaddum类型谱半径的排序

给出了n阶树的Nordhaus-Gaddum类型谱半径即图及其补图的谱半径之和的可达上界:ρ(T) ρ(Tc)≤■ n-2,等号成立当且仅当T K1,n-1,其中Tc为T的补图,K1,n-1为n阶星图.同时证明了对于n阶双星图S(a,b)的Nordhaus-Gaddum类型谱半径随a的值单调上升,其中[n-1/2]≤a≤n-3.     

Addendum to: “Hamilton-laceable bi-powers of locally finite bipartite graphs” [Discrete Math. 345 (2022) 112777]

In this addendum we give a short and easy negative answer to the two questions raised in the original article.     

The effect of a market factor on information flow between stocks using the minimal spanning tree

We empirically investigated the effects of market factors on the information flow created from N(N−1)/2 linkage relationships among stocks. We also examined the possibility of employing the minimal spanning tree (MST) method, which is capable of reducing the number of links to N−1. We determined that market factors carry important information value regarding information flow among stocks. Moreover, the information flow among stocks showed time-varying properties according to the changes in market status. In particular, we noted that the information flow increased dramatically during periods of market crises. Finally, we confirmed, via the MST method, that the information flow among stocks could be assessed effectively with the reduced linkage relationships among all links among stocks from the perspective of the overall market.     

决策树分类模型在工程项目评标风险预警中的应用

本文将数据挖掘中的决策树分类方法运用到工程项目评标数据分析,从200多个天津市工程项目招投标打分数据中,随机抽取15个招投标项目中的67个承包商的评标专家打分数据进行分析,得到中标承包商技术和商务评分分界点,进而得到工程项目潜在风险的预警阈值,然后借助因子分析辨识出风险来源并进行预警。     

Eigenvalue estimates for Schrödinger operators on metric trees

We consider Schrödinger operators on radial metric trees and prove Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.