scholarly journals The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

2021 ◽  
Author(s):  
Xiaona Fang ◽  
Lihua You ◽  
Hechao Liu
Keyword(s):  
Chemical Graphs ◽  
Expected Values

scholarly journals The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

2021 ◽  
Author(s):  
Xiaona Fang ◽  
Lihua You ◽  
Hechao Liu
Keyword(s):  
Graph Theory ◽  
Aromatic Compounds ◽  
Polycyclic Aromatic Compounds ◽  
Carbon Nanocones ◽  
Chemical Graph ◽  
Benzenoid System ◽  
Chemical Graph Theory ◽  
Chemical Graphs ◽  
Polycyclic Aromatic ◽  
Expected Values

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene chains are a class of polycyclic aromatic compounds. Recently, A family of Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these indices may be successfully applied on modeling thermodynamic properties of compounds. In this paper, we study the expected values of the Sombor indices in random hexagonal chains, phenylene chains, and consider the Sombor indices of some chemical graphs such as graphene, coronoid systems and carbon nanocones.

Quantitative Diameter Measurements of Chromatin and TMV Fibers in the Freeze-Dried State

1988 ◽  
Vol 46 ◽  
pp. 170-171
Author(s):  
B. D. Athey ◽  
A. L. Stout ◽  
M. F. Smith ◽  
J. P. Langmore
Keyword(s):  
Reliable Method ◽  
Fiber Diameter ◽  
Quantitative Agreement ◽  
One Dimension ◽  
Fiber Axis ◽  
Two Dimensional ◽  
Fiber Density ◽  
Variable Diameter ◽  
Freeze Dried ◽  
Expected Values

Although there is general agreement that Inactive chromosome fibers consist of helically packed nucleosomes, the pattern of packing is still undetermined. Only one of the proposed models, the crossed-linker model, predicts a variable diameter dependent on the length of DNA between nucleosomes. Measurements of the fiber diameter of negatively-stained and frozen- hydrated- chromatin from Thyone sperm (87bp linker) and Necturus erythrocytes (48bp linker) have been previously reported from this laboratory. We now introduce a more reliable method of measuring the diameters of electron images of fibrous objects. The procedure uses a modified version of the computer program TOTAL, which takes a two-dimensional projection of the fiber density (represented by the micrograph itself) and projects it down the fiber axis onto one dimension. We illustrate this method using high contrast, in-focus STEM images of TMV and chromatin from Thyone and Necturus. The measured diameters are in quantitative agreement with the expected values for the crossed-linker model for chromatin structure

scholarly journals M-polynomial and topological indices of zigzag edge coronoid fused by starphene

2020 ◽  
Vol 18 (1) ◽  
pp. 1362-1369
Author(s):  
Farkhanda Afzal ◽  
Sabir Hussain ◽  
Deeba Afzal ◽  
Saira Hameed
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Zigzag Edge ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Chemical Graphs

AbstractChemical graph theory is a subfield of graph theory that studies the topological indices for chemical graphs that have a good correlation with chemical properties of a chemical molecule. In this study, we have computed M-polynomial of zigzag edge coronoid fused by starphene. We also investigate various topological indices related to this graph by using their M-polynomial.

scholarly journals A hierarchical clustering method for random intervals based on a similarity measure

2021 ◽  
Author(s):  
Ana Belén Ramos-Guajardo
Keyword(s):  
Hierarchical Clustering ◽  
Similarity Measure ◽  
Clustering Algorithm ◽  
Real Life ◽  
Stopping Criterion ◽  
Clustering Method ◽  
Bootstrap Test ◽  
Empirical Performance ◽  
Random Intervals ◽  
Expected Values

AbstractA new clustering method for random intervals that are measured in the same units over the same group of individuals is provided. It takes into account the similarity degree between the expected values of the random intervals that can be analyzed by means of a two-sample similarity bootstrap test. Thus, the expectations of each pair of random intervals are compared through that test and a p-value matrix is finally obtained. The suggested clustering algorithm considers such a matrix where each p-value can be seen at the same time as a kind of similarity between the random intervals. The algorithm is iterative and includes an objective stopping criterion that leads to statistically similar clusters that are different from each other. Some simulations to show the empirical performance of the proposal are developed and the approach is applied to two real-life situations.

scholarly journals Origin and Application of the Twinned Calcite Strain Gauge

Geosciences ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 296
Author(s):  
Richard H. Groshong
Keyword(s):  
Stress Analysis ◽  
Strain Gauge ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Constant Strain Rate ◽  
Axis Orientation ◽  
Order Of Magnitude ◽  
Rate Experiment ◽  
Strain Axis ◽  
Expected Values

This paper is a personal account of the origin and development of the twinned-calcite strain gauge, its experimental verification, and its relationship to stress analysis. The method allows the calculation of the three-dimensional deviatoric strain tensor based on five or more twin sets. A minimum of about 25 twin sets should provide a reasonably accurate result for the magnitude and orientation of the strain tensor. The opposite-signed strain axis orientation is the most accurately located. Where one strain axis is appreciably different from the other two, that axis is generally within about 10° of the correct value. Experiments confirm a magnitude accuracy of 1% strain over the range of 1–12% axial shortening and that samples with more than 40% negative expected values imply multiple or rotational deformations. If two deformations are at a high angle to one another, the strain calculated from the positive and negative expected values separately provides a good estimate of both deformations. Most stress analysis techniques do not provide useful magnitudes, although most provide a good estimate of the principal strain axis directions. Stress analysis based on the number of twin sets per grain provides a better than order-of-magnitude approximation to the differential stress magnitude in a constant strain rate experiment.

Sombor index of chemical graphs

2021 ◽  
Vol 399 ◽  
pp. 126018
Author(s):  
Roberto Cruz ◽  
Ivan Gutman ◽  
Juan Rada
Keyword(s):  
Chemical Graphs

A Phenomenological Theory of Socioeconomic Systems with Spatial Interactions

1982 ◽  
Vol 14 (7) ◽  
pp. 869-888 ◽  
Author(s):  
P F Lesse
Keyword(s):  
Lagrange Multipliers ◽  
Average Cost ◽  
Phenomenological Theory ◽  
Traffic Flows ◽  
Spatial Interactions ◽  
Practical Application ◽  
Density Distributions ◽  
Expected Values ◽  
Probability Density Distributions ◽  
The Relationship

This paper deals with a class of models which describe spatial interactions and are based on Jaynes's principle. The variables entering these models can be partitioned in four groups: (a) probability density distributions (for example, relative traffic flows), (b) expected values (average cost of travel), (c) their duals (Lagrange multipliers, traffic impedance coefficient), and (d) operators transforming probabilities into expected values. The paper presents several dual formulations replacing the problem of maximizing entropy in terms of the group of variables (a) by equivalent extreme problems involving groups (b)-(d). These problems form the basis of a phenomenological theory. The theory makes it possible to derive useful relationships among groups (b) and (c). There are two topics discussed: (1) practical application of the theory (with examples), (2) the relationship between socioeconomic modelling and statistical mechanics.

scholarly journals The epidemiology of the common cold IV. The effect of weather

1965 ◽  
Vol 63 (3) ◽  
pp. 427-439 ◽  
Author(s):  
O. M. Lidwell ◽  
R. W. Morgan ◽  
R. E. O. Williams
Keyword(s):  
Common Cold ◽  
Partial Correlation ◽  
Water Vapour Pressure ◽  
Outdoor Temperature ◽  
Weather Variables ◽  
Smooth Curves ◽  
Correlation Studies ◽  
The Common ◽  
Expected Values ◽  
Time Of Year

An investigation has been made of the association between weather and the numbers of colds reported on a given day. The seasonal trends were eliminated by working with the differences between the observed values on any day and the expected values derived from smooth curves fitted to the averages for the time of year.Examination of nine weather variables for the day on which the colds were reported and for each of the 29 preceding days showed that only two, mean day temperature and water-vapour pressure at 9 a.m., were significantly correlated with the numbers of colds. Partial correlation studies showed that the strongest association was with lowered mean day temperature between 2 and 4 days before the reported onset of symptoms.Regression analysis demonstrated that the magnitudes of the associations were sufficient to account for the greater part of the seasonal variation in the incidence of the common cold in both London and Newcastle. A small effect of atmospheric pollution appeared in this analysis.These results suggest that some effect of low outdoor temperature promotes transmission of the virus or the development of disease.

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