On Statistics of Graph Energy

2001 ◽  
Vol 56 (3-4) ◽  
pp. 307-311 ◽  
Author(s):  
Ante Graovac ◽  
Ivan Gutman ◽  
Peter E. John ◽  
Dušica Vidović ◽  
Ivana Vlah
Keyword(s):  
Electron Energy ◽  
Molecular Graph ◽  
Molecular Graphs ◽  
Average Value ◽  
Graph Energy ◽  
The Absolute ◽  
The Difference ◽  
Conjugated Molecule

Abstract The energy EG of a graph G is the sum of the absolute values of the eigenvalues of G. In the case whene G is a molecular graph, EG is closely related to the total π-electron energy of the corresponding conjugated molecule. We determine the average value of the difference between the energy of two graphs, randomly chosen from the set of all graphs with n vertices and m edges. This result provides a criterion for deciding when two (molecular) graphs are almost coeneigetic.

scholarly journals Estimating the total π-electron energy

2013 ◽  
Vol 78 (12) ◽  
pp. 1925-1933 ◽  
Author(s):  
Ivan Gutman ◽  
Kinkar Das
Keyword(s):  
Electron Energy ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Total Electron ◽  
Molecular Graphs ◽  
Conjugated Hydrocarbons ◽  
Short Survey ◽  
Total Electron Energy ◽  
Graph Energy

The paper gives a short survey of the most important lower and upper bounds for total ?-electron energy, i.e., graph energy (E). In addition, a new lower and a new upper bound for E are deduced, valid for general molecular graphs. The strengthened versions of these estimates, valid for alternant conjugated hydrocarbons, are also reported.

scholarly journals Comparing energy and Randic energy

2013 ◽  
Vol 32 (1) ◽  
pp. 117 ◽  
Author(s):  
Boris Furtula ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Linear Correlation ◽  
Connected Graph ◽  
Fixed Number ◽  
Molecular Graphs ◽  
Average Value ◽  
Underlying Graph

The recently conceived Randić energy (RE) is examined, and its relation to the (earlier much studied) total π-electron energy (E) is investigated. Within classes of molecular graphs, there exists a relatively good (increasing) linear correlation between RE and E. However, several significant differences between the structure-dependencies of RE and E have been discovered, the most striking of which is their dependence on the number m of edges of the underlying graph. Whereas, with increasing m, the average value of E increases, reaches a maximum and then decreases, the average value of RE monotonically decreases. The structure of the connected graph with a fixed number of vertices and maximal RE value was established.

scholarly journals Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Jia Bao Liu ◽  
Sana Akram ◽  
Muhammad Javaid ◽  
Abdul Raheem ◽  
Roslan Hasni
Keyword(s):  
Structural Properties ◽  
Electron Energy ◽  
Boiling Point ◽  
Molecular Descriptors ◽  
Molecular Descriptor ◽  
Molecular Graph ◽  
Topological Indices ◽  
Real Numbers ◽  
Molecular Graphs

A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjastic and Gutman (1972) used molecular descriptors to find the boiling point of paraffin and total π -electron energy of the molecules, respectively. For molecular graphs, the general sum-connectivity and general Randić are well-studied fundamental topological indices (TIs) which are considered as degree-based molecular descriptors. In this paper, we obtain the bounds of the aforesaid TIs for the generalized F -sum graphs. The foresaid TIs are also obtained for some particular classes of the generalized F -sum graphs as the consequences of the obtained results. At the end, 3   D -graphical presentations are also included to illustrate the results for better understanding.

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.

Translocation Relative to Range

Methodology ◽  
2008 ◽  
Vol 4 (3) ◽  
pp. 132-138 ◽  
Author(s):  
Michael Höfler
Keyword(s):  
Risk Difference ◽  
Binary Outcomes ◽  
Number Needed To Treat ◽  
Likert Scales ◽  
Psychological Science ◽  
The Absolute ◽  
The Difference ◽  
Variance Parameters ◽  
Standardized Index ◽  
Maximum Possible Magnitude

A standardized index for effect intensity, the translocation relative to range (TRR), is discussed. TRR is defined as the difference between the expectations of an outcome under two conditions (the absolute increment) divided by the maximum possible amount for that difference. TRR measures the shift caused by a factor relative to the maximum possible magnitude of that shift. For binary outcomes, TRR simply equals the risk difference, also known as the inverse number needed to treat. TRR ranges from –1 to 1 but is – unlike a correlation coefficient – a measure for effect intensity, because it does not rely on variance parameters in a certain population as do effect size measures (e.g., correlations, Cohen’s d). However, the use of TRR is restricted on outcomes with fixed and meaningful endpoints given, for instance, for meaningful psychological questionnaires or Likert scales. The use of TRR vs. Cohen’s d is illustrated with three examples from Psychological Science 2006 (issues 5 through 8). It is argued that, whenever TRR applies, it should complement Cohen’s d to avoid the problems related to the latter. In any case, the absolute increment should complement d.

The Effect of Jigsaw Methode and Motivation on Students’ of Learning Outcomes

2020 ◽  
Vol 3 (1) ◽  
pp. 20-30
Author(s):  
Yunita Yunita ◽  
Hidayat Hidayat ◽  
Harun Sitompul
Keyword(s):  
Cooperative Learning ◽  
Student Learning ◽  
Learning Outcomes ◽  
Student Learning Outcomes ◽  
Learning Motivation ◽  
Learning Approaches ◽  
High Learning ◽  
Average Value ◽  
The Difference ◽  
Low Motivation

This study aims to: (1) investigate the effect of Jigsaw cooperative learning on students learning outcomes; (2) find the difference in learning outcomes between high and low learning motivation and (3) find the interaction between learning approaches and learning motivation towards learning outcomes. The population of the study is students of grade IVa, IVb, IVc at SD Kasih Ibu Patumbak and the sample in this study is grade IVa with 35 students and grade IVb with 35 students. The results show that: (1) the average student learning outcomes of jigsaw cooperative learning is 28.40 while conventional is 24.14. Thus, students learning outcomes that get cooperative learning of jigsaw type are higher than conventional learning, (2) Students who have high motivation get an average value = 30.74, while low motivation is 22.72. Thus, it can be concluded that there are differences in student learning outcomes having high learning motivation and low learning motivation, and (3) students learning outcomes  taught by jigsaw cooperative learning are high learning motivation groups (32.94), and low learning motivation groups (24.58), while students taught with conventional learning are high learning motivation groups (28.40 ), and low motivation groups (20,95). Thus, there is no interaction between learning approaches and learning motivation towards learning outcomes.

The Issue of Sustainability in Third World Food Production (The Distinguishedl Lecture)

1992 ◽  
Vol 31 (4I) ◽  
pp. 511-534
Author(s):  
Winfried Von Urff
Keyword(s):  
Developing Countries ◽  
Population Growth ◽  
Food Production ◽  
Third World ◽  
Total Population ◽  
Absolute Number ◽  
Comprehensive Analysis ◽  
World Food ◽  
The Absolute ◽  
The Difference

In spite of the fact that food production in developing countries doubled over the last 25 years undernutrition is still widely spread. At the beginning of the eighties, according to FAO, 335 to 494 million people in developing countries suffered from serious undernutrition the difference being due to different concepts to determine undernutrition on which scientist were unable to find a consensus.) Unfortunately there is no recent comprehensive analysis of the food situation comparable to those of previous World Food Surveys but it can be taken for sure that the absolute number of undernourished has increased. According to unofficial FAO sources a figure of 870 million was estimated for 1990 (22 percent of the total population in developing countries) using the same concept that led to the figure of 494 million in 1979-81 (23 percent of the total population in developing countries) which means that most probably the number of undernourished increased at a rate slightly less than population growth.

Pengaruh Jumlah Pencucian Beras dengan Kadar Klorin

2017 ◽  
Vol 1 (1) ◽  
pp. 89
Author(s):  
Indah Purwaningsih ◽  
Supriyanto Supriyanto
Keyword(s):  
Mucous Membrane ◽  
Confidence Level ◽  
Iodometric Titration ◽  
Titration Method ◽  
Anova Test ◽  
Average Value ◽  
Significant Difference ◽  
The Difference

Abstract: Chlorine is a green halogen-shaped halogen gas at normal temperature and serves as bleach, stain remover and disinfectant. Chlorine is now widely used for bleaching rice so that less quality rice looks like quality rice. Chlorine is very toxic and causes mucous membrane irritation, highly reactive and very powerful oxidizer. The purpose of this research was to determine the difference of chlorine level in chlorinated rice washed once, twice and 3 times. The sample in this study amounted to 11 samples calculated by replication formula. Each sample was treated 3 times, ie 1 washed once, 2 washed twice and washed 3 times. The samples then examined by iodometric titration method. Based on the results of the study using ANOVA test, 11 samples obtained the average value of chlorine after washed once amount of 0.0176%, after washed twice amount of 0.0111%, and after washed 3 times amount of 0.0052% with the value significance p = 0.03 (p <0.05) at 95% confidence level which means there was a significant difference between chlorine levels in chlorinated rice washed once, twice and 3 times.Abstrak: Klorin merupakan unsur halogen berbentuk gas berwarna kuning kehijauan pada suhu normal danberfungsi sebagai pemutih, penghilang noda maupun desinfektan. Klorin sekarang banyak digunakan untuk bahan pemutih beras agar beras yang kurang berkualitas tampak seperti beras berkualitas. Klorin sangat toksik dan menyebabkan iritasi membran mukosa, sangat reaktif dan merupakan oksidator yang sangat kuat. Tujuan dari penelitian ini ialah untuk mengetahui perbedaan kadar klorin pada beras berklorin yang dicuci sebanyak 1 kali, 2 kali dan 3 kali. Sampel dalam penelitian ini berjumlah 11 sampel yang dihitung dengan rumus replikasi. Setiap sampel diberi perlakuan sebanyak 3 kali, yaitu 1 kali pencucian, 2 kali pencucian dan 3 kali pencucian. Sampel penelitian kemudian diperiksa dengan metode titrasi iodometri. Berdasarkan hasil penelitian menggunakan uji Anova secara komputerisasi terhadap 11 sampel diperoleh nilai rata-rata kadar klorin setelah 1 kali pencucian sebesar 0,0176 %, setelah 2 kali pencucian sebesar 0,0111 %, dan setelah 3 kali pencucian sebesar 0,0052 % dengan nilai signifkansi p = 0,03 (p<0,05) pada tingkat kepercayaan 95% yang artinya ada perbedaan yang bermakna antara kadar klorin pada beras berklorin yang dicuci sebanyak 1 kali, 2 kali dan 3 kali.

Results of studying the dimensional accuracy of the bases of complete removable prostheses made using 3D printing and traditional technologies

2020 ◽  
pp. 34-39
Author(s):  
Vokulova Yu.A. Vokulova ◽  
E.N. Zhulev
Keyword(s):  
3D Printing ◽  
Traditional Method ◽  
Laser Scanning ◽  
Laser Scanner ◽  
Digital Technologies ◽  
Dimensional Accuracy ◽  
3D Printer ◽  
Significance Level ◽  
Average Value ◽  
The Difference

This article presents the results of studying the dimensional accuracy of the bases of complete removable prostheses made using a 3D printer and the traditional method. Bases of complete removable prostheses were made using an intraoral laser scanner iTero Cadent (USA) and a 3D printer Asiga Max UV (Australia). To study the dimensional accuracy of the bases of complete removable prostheses, we used the DentalCAD 2.2 Valletta software. The Nonparametric Wilcoxon W-test was used for statistical analysis of the obtained data. We found that the average value of the difference with the standard for bases made using digital technologies is 0.08744±0.0484 mm. The average value of the difference with the standard for bases made by the traditional method is 0.5654±0.1611 mm. Based on these data, we concluded that the bases of complete removable prostheses made using modern digital technologies (intraoral laser scanning and 3D printer) have a higher dimensional accuracy compared to the bases of complete removable prostheses made using the traditional method with a significance level of p<0.05 (Wilcoxon's W-test=0, p=0.031). Keywords: digital technologies in dentistry, digital impressions, intraoral scanner, 3D printing, ExoCAD, complete removable dentures.

scholarly journals II. On the electro-chemical equivalent of silver, and on the absolute electromotive force of clark cells

1883 ◽  
Vol 36 (228-231) ◽  
pp. 448-450
Keyword(s):  
Electromotive Force ◽  
British Association ◽  
General Character ◽  
Daily Work ◽  
The Absolute ◽  
The Difference

The investigations upon this subject which have been carried on by Mrs. Sidgwick and myself during the last year and a half, though not yet quite finished, are so far advanced that no doubt remains as to the general character of the results; and as these results have application in the daily work of practical electricians, it is thought desirable to communicate them without further delay. The currents are measured by balancing the attraction and repulsion of coaxal coils against known weights, as described before the British Association in 1882, a method which has fully answered the favourable expectations then expressed. To what was said on that occasion it will be sufficient for the present to add that the readings are taken by reversal of the current in the fixed coils, and the difference of weights thus found (about 1 gram) represents the double force of attraction, free from errors depending upon the connections of the suspended coil, and other sources of disturbance.

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