scholarly journals Upgrading the Wiener index

2002 ◽  
Vol 67 (10) ◽  
pp. 647-651 ◽  
Author(s):  
Eduardo Castro ◽  
Ivan Gutman ◽  
Damian Marino ◽  
Pablo Peruzzo
Keyword(s):  
Shortest Path ◽  
Linear Correlation ◽  
Euclidean Distance ◽  
Topological Index ◽  
Molecular Graph ◽  
Wiener Index ◽  
Bond Lengths ◽  
Good Linear ◽  
Structure Descriptor ◽  
Good Linear Correlation

The Wiener index Wis the oldest molecular-graph-based structure-descriptor. It is defined as the sum of the distances of all pairs of vertices of the molecular graph G, where the distance is the number of edges in the shortest path connecting the respective vertices, and where G is the hydrogen-depleted molecular graph. This seemingly very simple topological index could be "upgraded" (a) by using as the distance the sum of the bond lengths along the shortest path, or (b) by using the Euclidean distance between the respective pairs of atoms. Each of these "upgraded" Wiener indices could be computed either (?) for the hydrogen- depleted or (?) for the hydrogen-filled molecular graph. We provide examples showing that none of the modifications (a?), (a?), (b?), (b?) yields better results than the ordinary Wiener index, and that there is a very good linear correlation between W and its "upgraded" variants.

scholarly journals Wiener-type indices and internal molecular energy

2003 ◽  
Vol 68 (4-5) ◽  
pp. 401-408 ◽  
Author(s):  
Ivan Gutman ◽  
Dusica Vidovic ◽  
Boris Furtula ◽  
Igor Zenkevich
Keyword(s):  
Linear Correlation ◽  
Molecular Graph ◽  
Wiener Index ◽  
Single Line ◽  
Good Linear ◽  
Wiener Type ◽  
Structure Descriptor ◽  
Good Linear Correlation

In earlier studies it was established that internal molecular energies (Eint) of alkanes can be reproduced, in an approximate yet reliable manner by means of a molecular-graph-based structure-descriptor U. It was also established that U is linearly correlated with the Wiener index W. We now show that the correlation between U and W is more complicated than earlier expected, and that it cannot be represented by a single line. We also show that a very good linear correlation exists between U and a modified version Wm(?) of the Wiener index, which is thus more suitable for modeling Eint than the ordinary Wiener index. .

scholarly journals Total π-electron energy and Laplacian energy: How far the analogy goes?

2007 ◽  
Vol 72 (12) ◽  
pp. 1343-1350 ◽  
Author(s):  
Slavko Radenkovic ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Linear Correlation ◽  
Molecular Graph ◽  
Total Electron ◽  
Good Linear ◽  
Molecular Graphs ◽  
Acyclic Graphs ◽  
Laplacian Energy ◽  
Total Electron Energy ◽  
Good Linear Correlation

The Laplacian energy LE is a newly introduced molecular-graph-based analog of the total ?-electron energy E. It is shown that LE and E have a similar structure-dependency only when molecules of different sizes are compared, when a good linear correlation between them exists. Within classes of isomers, LE and E are either not correlated at all or (as in the case of acyclic systems) are inversely proportional. The acyclic graphs and molecular graphs having the greatest and smallest LE values (determined in this work) differ significantly from those (previously known) having the greatest and smallest E values.

scholarly journals Quantifying Mold Biomass on Gypsum Board: Comparison of Ergosterol and Beta-N-Acetylhexosaminidase as Mold Biomass Parameters

2003 ◽  
Vol 69 (7) ◽  
pp. 3996-3998 ◽  
Author(s):  
M. Reeslev ◽  
M. Miller ◽  
K. F. Nielsen
Keyword(s):  
Stationary Phase ◽  
Linear Correlation ◽  
Stachybotrys Chartarum ◽  
Gypsum Board ◽  
Biomass Density ◽  
Activity Data ◽  
Good Linear ◽  
Ergosterol Content ◽  
Good Linear Correlation

ABSTRACT Two mold species, Stachybotrys chartarum and Aspergillus versicolor, were inoculated onto agar overlaid with cellophane, allowing determination of a direct measurement of biomass density by weighing. Biomass density, ergosterol content, and beta-N-acetylhexosaminidase (3.2.1.52) activity were monitored from inoculation to stationary phase. Regression analysis showed a good linear correlation to biomass density for both ergosterol content and beta-N-acetylhexosaminidase activity. The same two mold species were inoculated onto wallpapered gypsum board, from which a direct biomass measurement was not possible. Growth was measured as an increase in ergosterol content and beta-N-acetylhexosaminidase activity. A good linear correlation was seen between ergosterol content and beta-N-acetylhexosaminidase activity. From the experiments performed on agar medium, conversion factors (CFs) for estimating biomass density from ergosterol content and beta-N-acetylhexosaminidase activity were determined. The CFs were used to estimate the biomass density of the molds grown on gypsum board. The biomass densities estimated from ergosterol content and beta-N-acetylhexosaminidase activity data gave similar results, showing significantly slower growth and lower stationary-phase biomass density on gypsum board than on agar.

Evaluation of Natural Rubber from Clones of Hevea Brasiliensis

2002 ◽  
Vol 75 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Mariselma Ferreira ◽  
Rogério M. B. Moreno ◽  
Paulo S. Gonçalves ◽  
Luiz H. C. Mattoso
Keyword(s):  
Natural Rubber ◽  
Linear Correlation ◽  
Hevea Brasiliensis ◽  
Cold Season ◽  
The State ◽  
Rubber Content ◽  
Good Linear ◽  
Mooney Viscosity ◽  
In The Beginning ◽  
Good Linear Correlation

Abstract The latex and natural rubber from rubber trees [Hevea brasiliensis (Willd. exAdr. de Juss.) Muell. Arg.] from clones (RRIM 600, IAN 873, GT 1 and PB 252) recommended to the state of São Paulo, Brazil, were studied in three different tapping systems. The parameters studied were dry rubber content (DRC), percentages of ash and of nitrogen, Wallace Plasticity (P0) and Mooney Viscosity (VR). The rubber properties vary considerably as a function of clone type, tapping method and season of the year. DRC tends to decrease in the beginning of the dry, cold season (May and June), whereas both nitrogen % and ash % increase in the same period. A good linear correlation was obtained for P0 and VR. The highest P0 and VR were obtained for RRIM 600.

Effect of Limestone Powder on Autogenous Shrinkage of Concrete

2011 ◽  
Vol 88-89 ◽  
pp. 767-771
Author(s):  
Bin Wang ◽  
You Ping Ding ◽  
Jing Gao ◽  
Jin Fang Sun ◽  
Miao Miao Cui ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Linear Correlation ◽  
Autogenous Shrinkage ◽  
Limestone Powder ◽  
Subsequent Reduction ◽  
Reduction Stage ◽  
Good Linear ◽  
Good Linear Correlation

The effect law and mechanism of limestone powder on autogenous shrinkage of concrete was studied. The results indicate that limestone powder accelerates autogenous shrinkage speed of concrete on which effect of fineness is little, and limestone powder reduces autogenous shrinkage which decreases with the increase of fineness. The change law of autogenous shrinkage of concrete is consistent with that of chemically combined water of paste. Autogenous shrinkage of concrete is also divided into 2 stages according to the initial vapor saturated stage and subsequent reduction stage of interior relative humidity, with both showing a good linear correlation at each stage.

scholarly journals Relating the ABC and harmonic indices

2014 ◽  
Vol 79 (5) ◽  
pp. 557-563 ◽  
Author(s):  
Ivan Gutman ◽  
Lingping Zhong ◽  
Kexiang Xu
Keyword(s):  
Molecular Structure ◽  
Topological Index ◽  
Molecular Graph ◽  
Vertex Degree ◽  
Harmonic Index ◽  
Abc Index ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

scholarly journals Linear correlation between Debye temperature and lattice thermal conductivity in II-VI and III-V semiconductors

2015 ◽  
Vol 3 (2) ◽  
pp. 216 ◽  
Author(s):  
Salah Daoud
Keyword(s):  
Thermal Conductivity ◽  
Simple Model ◽  
Debye Temperature ◽  
Rock Salt ◽  
Linear Correlation ◽  
Lattice Thermal Conductivity ◽  
Empirical Relationship ◽  
Average Percentage ◽  
Good Linear ◽  
Good Linear Correlation

<p>A simple linear empirical relationship between high intrinsic lattice thermal conductivity K, and Debye temperature θ<em><sub>a</sub></em> is suggested from data on high intrinsic lattice thermal conductivity K, and Debye temperature θ<em><sub>a</sub></em> for some selected II-VI and III-V cubic zincblende type, and I-VII and II-VI rock-salt type binary semiconductors. A good linear correlation between Debye temperature and the high intrinsic lattice thermal conductivity was obtained. The minimum average percentage deviations in the present approach reveal that our simple model prove its identity and soundness compared to those of other author relations.</p>

Determination of Imidacloprid Residues in Chinese Cabbage by UPLC-MS/MS

2014 ◽  
Vol 852 ◽  
pp. 274-277
Author(s):  
Yu Bing Zha ◽  
Mao Fang Huang ◽  
Chun Liang Yang ◽  
Ming Yue Wang ◽  
Xiao Fang Wang ◽  
...  
Keyword(s):  
Chinese Cabbage ◽  
Linear Correlation ◽  
Good Linear ◽  
Calibration Curves ◽  
Relative Standard ◽  
External Standard ◽  
Standard Calibration ◽  
Standard Deviations ◽  
Good Linear Correlation

A method for determination of imidacloprid in Chinese Cabbage was established by using UPLCMS/MS. and the samples are extracted with acetontrile,and the extract is cleaned up by Florisil SPE cartridges and evaporated.Choromatographic separation was performed on a C18 column,and determined by UPLC-MS/MS.The external standard calibration curves were used for quantification. The results showed that a good linear correlation was obtained in the range of 0.005-0.1ug/mL. The limit of quantif icat ion w as 0. 008 mg/ kg .The average recoveries and the relative standard deviations were in the range of 84.9 %~92.7 % and 0.9 %~6.2 %, respectively. It is applicable to the determination of imidacloprid redidue in Chinese cabbage.

scholarly journals Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Bo Bi ◽  
Muhammad Kamran Jamil ◽  
Khawaja Muhammad Fahd ◽  
Tian-Le Sun ◽  
Imran Ahmad ◽  
...  
Keyword(s):  
Physical Properties ◽  
Topological Index ◽  
Linear Time ◽  
Molecular Graph ◽  
Wiener Index ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Unicyclic Graphs ◽  
Polarity Index ◽  
Acyclic Graphs

Let G = V G , E G be a molecular graph, where V G and E G are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity, and the terminal Wiener indices are the distance-based topological indices. In this paper, we described a linear time algorithm (LTA) that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener polarity index. All these algorithms compute the indices in time O n .

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