Modeling Gas Chromatographic Retention Indices of Oxygen-containing Compounds by Novel Atom-type Topological Indices

为包含酉同类和酉旨的 39 包含氧的混合物的保留索引(RI ) 的评价的量的结构保留关系(QSRR ) 模型被我们的最新介绍的基于距离的原子类型索引奶妈建立。新奇奶妈索引的有用应用程序被为煤气的色析法的保留索引开发精确预兆的方程演示了。为最后的模型的多重线性回归的统计结果是 r=0.9973 和 s=8.23。而且， 10 含氧包含的混合物的一个外部测试集合能精确地与给下列统计结果的最后的方程被预言：r pred =0.9966 和 s pred =8.56。

On ev and ve-Degree Based Topological Indices of Silicon Carbides

In quantitative structure-property relationship(QSPR)and quantitative structure-activity relationship(QSAR)studies,computation of topological indices is a vital tool to predict biochemical and physio-chemical properties of chemical structures.Numerous topological indices have been inaugurated to describe different topological features.The ev and ve-degree are recently introduced novelties,having stronger prediction ability.In this article,we derive formulae of the ev-degree and ve-degree based topological indices for chemical structure of Si_(2)C_(3)−I[a,b].

Topological Aspects of Dendrimers via Connection-Based Descriptors

Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,nanotubes and neural networks with respect to their certain properties such as solubility,chemical stability and low cytotoxicity.Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core.A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches,including numerical graph invariants.Among topological descriptors,Zagreb connection indices(ZCIs)have much importance.This manuscript involves the establishment of general results to calculate ZCIs,namely first ZCI(FZCI),second ZCI(SZCI),third ZCI(TZCI),modified FZCI,modified SZCI and modified TZCI of two special types of dendrimers nanostars,namely,poly propylene imine octamin(PPIO)dendrimer and poly(propyl)ether imine(PPEtIm)dendrimer.Furthermore,we provide the numerical and graphical comparative analysis of our calculated results for both types of dendrimers with each other.

On Some Ev-Degree and Ve-Degree Dependent Indices of Benes Network and Its Derived Classes

One of the most recent developments in the field of graph theory is the analysis of networks such as Butterfly networks,Benes networks,Interconnection networks,and David-derived networks using graph theoretic parameters.The topological indices(TIs)have been widely used as graph invariants among various graph theoretic tools.Quantitative structure activity relationships(QSAR)and quantitative structure property relationships(QSPR)need the use of TIs.Different structure-based parameters,such as the degree and distance of vertices in graphs,contribute to the determination of the values of TIs.Among other recently introduced novelties,the classes of ev-degree and ve-degree dependent TIs have been extensively explored for various graph families.The current research focuses on the development of formulae for different ev-degree and ve-degree dependent TIs for s−dimensional Benes network and certain networks derived from it.In the end,a comparison between the values of the TIs for these networks has been presented through graphical tools.

Some Topological Values of Supramolecular Chain of Different Complexes of N-Salicylidene-L-Valine

L-valine is a glycogen-type amino acid regarded among the necessary mammalian amino acids.This is an amino acid that is essential for protein synthesis.N-salicylidene-L-valine is gaining a lot of attention because of its unique structure and increased catalytic and cytotoxic activity.We explore the chain of supramolecular dialkyltin N-salicylidene-L-valine complexes 2,3,and 4 to learn more about this structure and its features regarding topological indices.We computed the first and second Randi′c index,harmonic index,sum-connectivity index,atom-bond-connectivity index,geometric arithmetic index and reduced reciprocal Randi′c index of Supramolecular Chain of Different Complexes of N-Salicylidene-L-Valine.Furthermore,we present an analysis of such structures using specific examples,as well as a comparison of topological indices.

A Study of Cellular Neural Networks with Vertex-Edge Topological Descriptors

The CellularNeuralNetwork(CNN)has various parallel processing applications,image processing,non-linear processing,geometric maps,highspeed computations.It is an analog paradigm,consists of an array of cells that are interconnected locally.Cells can be arranged in different configurations.Each cell has an input,a state,and an output.The cellular neural network allows cells to communicate with the neighbor cells only.It can be represented graphically;cells will represent by vertices and their interconnections will represent by edges.In chemical graph theory,topological descriptors are used to study graph structure and their biological activities.It is a single value that characterizes the whole graph.In this article,the vertex-edge topological descriptors have been calculated for cellular neural network.Results can be used for cellular neural network of any size.This will enhance the applications of cellular neural network in image processing,solving partial differential equations,analyzing 3D surfaces,sensory-motor organs,and modeling biological vision.

Comparative Study of Valency-Based Topological Descriptor for Hexagon Star Network

A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism.There are various uses of graph theory in the field of basic science.The main notable utilization of a topological descriptor in science was by Wiener in the investigation of paraffin breaking points.In this paper we study the topological descriptor of a newly design hexagon star network.More preciously,we have computed variation of the Randic0 R0,fourth Zagreb M4,fifth Zagreb M5,geometric-arithmetic GA;atom-bond connectivity ABC;harmonic H;symmetric division degree SDD;first redefined Zagreb,second redefined Zagreb,third redefined Zagreb,augmented Zagreb AZI,Albertson A;Irregularity measures,Reformulated Zagreb,and forgotten topological descriptors for hexagon star network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.We also gave the numerical and graphical representations comparisons of our different results.

Topological Quantization of Linear Defects

Using Ф-mapping method and topological current theory,we get the topological structure and the topological quantization of topological linear defects and point out that the topological quantum numbers of the linear defects are described by the Winding numbers of Ф-mapping which are determined in terms of the Hopf indices and the Brouwer degrees.All the topological linear defects are generated from the zero points of the Ф-mapping.

On Harmonic and Ev-Degree Molecular Topological Properties of DOX,RTOX and DSL Networks

Topological indices enable to gather information for the underlying topology of chemical structures and networks.Novel harmonic indices have been defined recently.All degree based topological indices are defined by using the classical degree concept.Recently two novel degree concept have been defined in graph theory:ve-degree and evdegree.Ve-degree Zagreb indices have been defined by using ve-degree concept.The prediction power of the ve-degree Zagreb indices is stronger than the classical Zagreb indices.Dominating oxide,silicate and oxygen networks are important network models in view of chemistry,physics and information science.Physical and mathematical properties of dominating oxide,silicate and oxygen networks have been considerably studied in graph theory and network theory.Topological properties of the dominating oxide,silicate and oxygen networks have been intensively investigated for the last few years period.In this study we examined,the first,the fifth harmonic and ev-degree topological indices of dominating oxide(DOX),regular triangulene oxide network(RTOX)and dominating silicate network(DSL).

On Vertex-Edge-Degree Topological Descriptors for Certain Crystal Networks

Due to the combinatorial nature of graphs they are used easily in pure sciences and social sciences.The dynamical arrangement of vertices and their associated edges make them flexible(like liquid)to attain the shape of any physical structure or phenomenon easily.In the field of ICT they are used to reflect distributed component and communication among them.Mathematical chemistry is another interesting domain of applied mathematics that endeavors to display the structure of compounds that are formed in result of chemical reactions.This area attracts the researchers due to its applications in theoretical and organic chemistry.It also inspires the mathematicians due to involvement of mathematical structures.Regular or irregular bonding ability of molecules and their formation of chemical compounds can be analyzed using atomic valences(vertex degrees).Pictorial representation of these compounds helps in identifying their properties by computing different graph invariants that is really considered as an application of graph theory.This paper reflects the work on topological indices such as ev-degree Zagreb index,the first ve-degree Zagrebindex,the first ve-degree Zagrebindex,the second ve-degree Zagreb index,ve-degree Randic index,the ev-degree Randic index,the ve-degree atom-bond connectivity index,the ve-degree geometric-arithmetic index,the ve-degree harmonic index and the ve-degree sum-connectivity index for crystal structural networks namely,bismuth tri-iodide and lead chloride.In this article we have determine the exact values of ve-degree and ev-degree based topological descriptors for crystal networks.

Vertex-Edge Degree Based Indices of Honey Comb Derived Network

Chemical graph theory is a branch of mathematics which combines graph theory and chemistry.Chemical reaction network theory is a territory of applied mathematics that endeavors to display the conduct of genuine compound frameworks.It pulled the research community due to its applications in theoretical and organic chemistry since 1960.Additionally,it also increases the interest the mathematicians due to the interesting mathematical structures and problems are involved.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.In this paper,we determined the newly introduced topological indices namely,first ve-degree Zagreb?index,first ve-degree Zagreb?index,second ve-degree Zagreb index,ve-degree Randic index,ve-degree atom-bond connectivity index,ve-degree geometric-arithmetic index,ve-degree harmonic index and ve-degree sum-connectivity index for honey comb derived network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure-activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.Also,we give the numerical and graphical representation of our outcomes.

Omega and Cluj-Ilmenau Indices of Hydrocarbon Molecules “Polycyclic Aromatic Hydrocarbons PAHk”

A topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. In this paper, we computed the Omega and Cluj-Ilumenau indices of a very famous hydrocarbon named as Polycyclic Aromatic Hydrocarbons PAHk for all integer number k.

萘乙酸对紫楠幼苗根系形态和内源激素的调节效应

为探究不同浓度萘乙酸(NAA)对紫楠幼苗根系形态和内源激素含量的影响,明确NAA在紫楠幼苗根系发育中的调节作用,以同一母树同一枝条上采集的成熟紫楠种子萌发的幼苗为研究对象,设置浓度为0、25、50和75 mg·L^(-1)NAA处理,分析NAA对紫楠幼苗根系形态和内源激素含量的调控作用。结果表明,NAA处理抑制了紫楠幼苗主根生长,主根直径和根系总表面积得到增加,同时显著提高根系总生物量(P<0.05)。当NAA浓度为75 mg·L^(-1)时,紫楠幼苗根系总表面积和根系总长度达到最大;1级侧根数目、1级侧根总长度增加且达到最大。外源激素NAA显著提高紫楠幼苗根系反式玉米素(TZ)含量(P<0.05);随着NAA浓度升高,根系拓扑指数显著增大(P<0.05),紫楠根系向鱼尾形分支类型进化。浓度为75 mg·L^(-1)NAA处理可以显著提高紫楠幼苗根系生物量和TZ含量(P<0.05),同时显著降低根系内源激素脱落酸含量(P<0.05),促进根系TZ的合成积累,促进根系的发育。

多情景洪水灾害对城市道路拓扑特征影响研究——以武汉市中心城区为例

以武汉市中心城区为研究区构建道路拓扑网络,通过水文过程模拟获取积水地图、通勤出行模拟获取道路车流量,选取3种中心性指标表征多降雨重现期下道路网络拓扑特征,通过描述性统计、分布规律拟合及空间可视化等方法分析道路网络拓扑特征变化规律。结果发现:①洪水事件对城市道路网络拓扑特征影响显著,50年一遇情景下,道路网络节点与连边数量分别减少20.29%和37.04%,超过80%的节点或连边的中心性指标值发生变化。②洪水情景下道路网络中介中心性最大值及99%分位数有所提高、邻近中心性值有所下降,表明洪水事件使关键节点或连边在道路网络中的影响更加凸显,但节点或连边之间的联通程度受到破坏;中心性累积分布函数的尾部分布也证实了这一结论。③中心城区内关键道路及节点的分布随洪水强度增大呈现出向城市内部收缩的态势,具体表现为由城市二环线附近转移至一环线内沿江大道区域。在未来灾害管理和城市规划过程中,应当重视对核心区域道路疏通管控工作,防止拥堵现象发生;同时,加强外围区域道路建设、提高道路排水性能及路网连通性也是降低洪涝灾害对城市道路网络影响的关键。

塔克拉玛干沙漠腹地3种植物根系构型及其生境适应策略

在塔克拉玛干沙漠腹地,采用挖掘法挖取塔克拉玛干柽柳(Tamarix taklamakanensis)、塔克拉玛干沙拐枣(Calligonum roborovskii)和罗布麻(Apocynum venetum)根系,对根系的拓扑结构特征进行了测定与分析。结果表明:1)3种植物根系均以水平分布占优势,根系浅层化。2)3种植物根系结构的适应性不同,表现为两种不同的根系分支模式,塔克拉玛干柽柳根系为叉状分支结构(qa=0.15、qb=0.09、TI=0.658),罗布麻(qa=0.43、qb=0.35、TI=0.83)和沙拐枣(qa=0.52、qb=0.38、TI=0.86)根系趋向于鱼尾形分支结构。3)3种植物根系的连接长度都较大,最小也达1.12m,说明在塔克拉玛干沙漠腹地,3种植物通过增加连接长度来扩大根系在土层中的分布范围,从而提高根系的有效营养空间,增加根系连接长度是根系对沙漠腹地贫瘠土壤环境的一个良好适应。4)研究验证了LeonardodaVinci法则,即根系分支前的横截面积等于根系分支后的横截面积之和,3种植物根系分支前后的横截面积符合LeonardodaVinci法则。研究表明沙漠腹地3种植物根系构型特征既有相似性又有差异性,在相似的沙漠环境中具有不同的根系适应策略。

塔克拉玛干沙漠腹地几种植物根系分形特征

在塔克拉玛干沙漠腹地采用全根挖掘法挖掘河西菊(Hexinia polydichotoma(Ostenf.)H. L.Yang)、沙拐枣(Calligonum roborovskii A.Los.)、罗布麻(Apocynum venetum L.)、阿克苏牛皮消(Cynanchum amplexicaule Hemsl)根系。运用分形理论对其分形特征进行研究,分析根系分支状况以及根系分形特征与拓扑特征之间的关系。研究发现:(1)在塔克拉玛干沙漠腹地,四种植物根系具有很好的分形特征,分形维数大小与拓扑参数连接总数、外部连接数之间具有较好的相关关系。(2)根丰度是描述根系在土层中扩展能力的有效指标,与根系长度、平均连接长度之间具有很好的指数关系分别可以用以下方程表示:y_1=2.7 694e^(1.5 496x),y_2=0.0 369e^(2.0 267x)(其中y_1、y_2分别为总根长、平均连接长度,R^2分别为:0.9 353、0.9 832),根丰度直接反映了根系空间占有能力与营养物质的吸收效率。通过对塔克拉玛干沙漠腹地四种植物根系分支状况与分形特征的研究表明,分形理论可以很好的反映根系空间占有能力与资源吸收效率,所以说分形理论是对根系几何、功能特征进行定量化研究的有效方法。

量子拓扑指数法预测多氯联苯醚的热力学性质

应用密度泛函理论(DFT),在B3LYP/6-31+G(d)基组上优化和振动分析计算了多氯联苯醚(PCDEs)所有209种可能的分子空间几何结构,得到其各原子之间空间拓扑距离,并建立拓扑空间距离矩阵。结合分子中各原子的支化度,应用原子的平衡电负性对分子图进行着色,得到量子拓扑指数PX1、PX2。采用多元线性回归技术建立联苯醚和209种可能结构的多氯联苯醚PCDEs 3种少见报道的热力学性质——标准生成热、标准生成自由能和相对自由能与PX1、PX2的定量关系拓扑模型,并用该模型分别对不同热力学性质进行预测与估算。结果表明,本方法的预测值、估算值与文献[3]的计算值均相吻合。同时,采用留一法(leave-one-out)和外检验方法测试模型的内部稳定性和外部预测能力,测试结果显示模型具有良好的稳定性和较强的预测能力。

黄河三角洲贝壳堤岛3种优势灌木的根系构型

根系构型决定了植物植株固定和资源吸收等很多重要功能,并通过资源的分配确定了植物的根冠比和净初级生产力。对黄河三角洲贝壳堤岛3种优势灌木柽柳、酸枣和杠柳的根系构型进行了研究,并验证了植物根系分支直径的尖细速率和根系分支前后的比例。结果表明:3种植物的根系构型不同,酸枣和杠柳根系主要分布在浅表层,水平根幅与垂直根幅的比值较大,而柽柳的垂直根深所占比例最大;杠柳和酸枣的拓扑指数分别为0.85和0.96,趋向于1,近似于鱼尾形分支,而柽柳的拓扑指数为0.65,接近于叉状分支。平均连接长度以酸枣最大,杠柳次之,柽柳最小。随连接长度增加,酸枣根系相比其他两种植物的尖细速率趋向于平缓。此外,3种植物的分支前后直径都符合Leonardo da Vinci法则。总之,根据根系构型,黄河三角洲贝壳堤岛3种灌木植物可以划分为2类,一类是以根系地表分布,扩大根幅,鱼尾形分支觅养的酸枣和杠柳,另一类则是根系深扎,充分利用地下资源的柽柳,体现了2种不同的生境适应对策。

胺类化合物气相色谱保留指数与结构的相关性研究

应用Am指数和引力指数C1对在3种体系下的胺类化合物的气相色谱保留指数和结构进行了相关性研究，并运用最佳子变量集算法和人工神经网法进行了计算分析，在非极性固定相OV-101和极性固定相OV-225和NGA下均获得了比较好的相关模型。

基于分子结构预测气相色谱程序升温保留指数

从拓扑指数出发,研究了分子结构与气相色谱程序升温保留指数之间的关系。对所选择的部分分子结构,利用主成分回归(PCR)的相关系数R=0.9998,标准偏差S=9.987,交互检验(leave one out cross-valida-tion)所得标准偏差S=11.17。同时,对同一柱型不同升温速率条件下的保留指数之间的关系、同一升温速率不同柱型条件下保留指数之间的关系进行了初步探讨,建立的模型线性关系明显。