Extended energy and its dependence on molecular structure

2017 ◽  
Vol 95 (5) ◽  
pp. 526-529 ◽  
Author(s):  
Ivan Gutman ◽  
Boris Furtula ◽  
Kinkar Ch. Das
Keyword(s):  
Molecular Structure ◽  
Electron Energy ◽  
Topological Index ◽  
Molecular Properties ◽  
Vertex Degree ◽  
Energy Formula ◽  
The Difference ◽  
Basic Characteristics ◽  
Ga Index ◽  
Structure Descriptor

The extended energy ([Formula: see text]) is a vertex degree based and spectrum-based molecular structure descriptor, shown to be well correlated with a variety of physicochemical molecular properties. We investigate the dependence of [Formula: see text] on molecular structure and establish its basic characteristics. In particular, we show how [Formula: see text] is related with the geometric–arithmetic (GA) topological index. Our main finding is that the difference between [Formula: see text] and the total π-electron energy is linearly proportional to the difference between the number of edges and the GA index.

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 The Bounds of Vertex Padmakar–Ivan Index on k-Trees

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 324 ◽  
Author(s):  
Shaohui Wang ◽  
Zehui Shao ◽  
Jia-Bao Liu ◽  
Bing Wei
Keyword(s):  
Molecular Structure ◽  
Topological Index ◽  
Upper Bounds ◽  
Extremal Graphs ◽  
Structure Descriptor

The Padmakar–Ivan ( P I ) index is a distance-based topological index and a molecular structure descriptor, which is the sum of the number of vertices over all edges u v of a graph such that these vertices are not equidistant from u and v. In this paper, we explore the results of P I -indices from trees to recursively clustered trees, the k-trees. Exact sharp upper bounds of PI indices on k-trees are obtained by the recursive relationships, and the corresponding extremal graphs are given. In addition, we determine the P I -values on some classes of k-trees and compare them, and our results extend and enrich some known conclusions.

scholarly journals Relating Estrada index with spectral radius

2007 ◽  
Vol 72 (12) ◽  
pp. 1321-1327 ◽  
Author(s):  
Ivan Gutman ◽  
Slavko Radenkovic ◽  
Boris Furtula ◽  
Toufik Mansour ◽  
Matthias Schork
Keyword(s):  
Molecular Structure ◽  
Spectral Radius ◽  
Organic Molecules ◽  
Molecular Graph ◽  
3D Structure ◽  
Estrada Index ◽  
Basic Characteristics ◽  
Structure Descriptor ◽  
Long Chain

The Estrada index EE is a recently proposed molecular structure-descriptor, used in the modeling of certain features of the 3D structure of organic molecules, in particular of the degree of folding of proteins and other long-chain biopolymers. The Estrada index is computed from the spectrum of the molecular graph. Therefore, finding its relation with the spectral radius r (= the greatest graph eigenvalue) is of interest, especially because the structure-dependency of r is relatively well understood. In this work, the basic characteristics of the relation between EE and r, which turned out to be much more complicated than initially anticipated, was determined.

scholarly journals On atom-bond connectivity molecule structure descriptors

2016 ◽  
Vol 81 (3) ◽  
pp. 271-276 ◽  
Author(s):  
Boris Furtula ◽  
Ivan Gutman ◽  
Kinkar Das
Keyword(s):  
Molecular Structure ◽  
Connectivity Index ◽  
Benzenoid Hydrocarbons ◽  
Molecule Structure ◽  
New Variant ◽  
Basic Characteristics ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity index (ABC) is a degree-based molecular structure descriptor with well-documented chemical applications. In 2010 a distance-based new variant of this index (ABCGG) has been proposed. Until now, the relation between ABC and ABCGG has not been analyzed. In this paper, we establish the basic characteristics of this relation. In particular, ABC and ABCGG are not correlated and both cases ABC > ABCGG and ABC < ABCGG may occur in the case of (structurally similar) molecules. However, in the case of benzenoid hydrocarbons, ABC always exceeds ABCGG.

ANALISA KANDUNGAN BETA-GLUKAN LARUT AIR DAN LARUT ALKALI DARI TUBUH BUAH JAMUR TIRAM (Pleurotus ostreatus) DAN SHIITAKE (Lentinus edodes)

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Netty Widyastuti ◽  
Teguh Baruji ◽  
Henky Isnawan ◽  
Priyo Wahyudi ◽  
Donowati Donowati
Keyword(s):  
Molecular Structure ◽  
Molecular Weight ◽  
Immune System ◽  
Pleurotus Ostreatus ◽  
Water Soluble ◽  
Low Molecular Weight ◽  
Lentinus Edodes ◽  
Beta Glucan ◽  
Oyster Mushrooms ◽  
The Difference

Beta glucan is a polysaccharide compound, generally not soluble inwater and resistant to acid. Beta glucan is used as an immunomodulator (enhancing the immune system) in mammals is usually a beta-glucan soluble in water, easily absorbed and has a low molecular weight. Several example of beta-glucan such as cellulose (β-1 ,4-glucan), lentinan (β-1 0.6-glucan) and (β-1 ,3-glucan), pleuran (β-1, 6 and β-1 ,3-glucan) are isolated from species of fungi Basidiomycota include mushrooms (Pleurotus ostreatus) and shiitake (Lentinus edodes).The purpose of thisresearch activity is to obtain beta-glucan compound that can be dissolved in water and in alkali derived from fungi Basidiomycota, i.e, Oyster mushrooms (Pleurotus ostreatus) and shiitake (Lentinus edodes). The result of beta-glucan compared to characterize the resulting beta glucan that is molecular structure . The difference of beta glucan extraction is based on the differences in solubility of beta-glucan. Beta glucan could be water soluble and insoluble water.

scholarly journals СПОЉНОТРГОВИНСКА РАЗМЕНА СРБИЈЕ И ЗНАЧАЈ АГРАРНОГ СЕКТОРА

TEME ◽  
2017 ◽  
pp. 711
Author(s):  
Драгица Божић ◽  
Марија Николић
Keyword(s):  
Foreign Trade ◽  
Comparative Advantage ◽  
Trade Balance ◽  
Total Trade ◽  
Agrarian Sector ◽  
Primary Products ◽  
The World ◽  
The Difference ◽  
Basic Characteristics ◽  
Large Deficit

The foreign trade of the Serbian economy is characterized by a large deficit and unfavourable structure. The importance of the agrarian sector in total trade is reflected in the constant positive trade balance and increasing participation, particularly in export. The aim of the paper is to analyze the basic characteristics of foreign trade of Serbia, as well as to point out the importance of the agrarian sector in the period 2005-2014. In the first part of the paper are analyzed trends of export, import, and the level of openness of Serbian economy. In the following part the structure of export and import is discussed, and the concentration index presented, or the Herfindahl-Hirschmann index, as well as the diversification index which indicates the difference between the structure of Serbian export and import and the international average. In addition to these indicators, the revealed comparative advantage index was calculated. The analysis of foreign trade of Serbian overall economy indicates a significant presence of agricultural and food products in its structure, particularly in export, and confirms that the agrarian sector is one of few sectors with a constant surplus. Determined indicators show that the comparative advantage in the overall economy trade of Serbia with the world is achieved in primary products and products of lower processing phase, of which a significant part is from the agrarian sector. Therefore, in the final part of the paper the participation of the agrarian sector in the total foreign trade of Serbia is shown.

scholarly journals Computing Fifth Geometric-Arithmetic Index for Circumcoronene series of benzenoid Hk

2007 ◽  
Vol 3 (1) ◽  
pp. 143-148 ◽  
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Connected Graph ◽  
Topological Index ◽  
Degree Of Vertex ◽  
Simple Connected Graph ◽  
Ga Index

Let G=(V; E) be a simple connected graph. The sets of vertices and edges of G are denoted by V=V(G) and E=E (G), respectively. The geometric-arithmetic index is a topological index was introduced by Vukicevic and Furtula in 2009 and defined as  in which degree of vertex u denoted by dG(u) (or du for short). In 2011, A. Graovac et al defined a new version of GA index as  where  The goal of this paper is to compute the fifth geometric-arithmetic index for "Circumcoronene series of benzenoid Hk (k≥1)".

scholarly journals Hakikat Ilmu Pengetahuan dalam Perspektif Modern dan Islam

2017 ◽  
Vol 7 (1) ◽  
pp. 81
Author(s):  
Via Linda Siswati
Keyword(s):  
Correspondence Theory ◽  
Human Experience ◽  
Coherence Theory ◽  
Natural Phenomena ◽  
Human Knowledge ◽  
Truth Theory ◽  
Sources Of Knowledge ◽  
The Difference ◽  
Basic Characteristics ◽  
Structure Of Knowledge

Philosophy of science is a branch of philosophy that reflects, radically and integral about the nature of knowledge itself. This writing aims to understand: (1) understanding of knowledge and science in etymology and terminology. (2) the difference of science, knowledge and religion in epistimology. (3) the extent of science in Islam. (4) the basic characteristics of science. (5) truth theory. (6) sources of knowledge. (7) the boundaries of science (8) the structure of knowledge. The results of this paper are: (1) science is from Arabic, 'alima. The meaning of this word is knowledge. And science in terminology is the whole conscious effort to investigate, find, and improve human understanding from various aspects of reality in human nature and we know (2) The location of the difference is the science is a summary of a collection of knowledge or the result of knowledge and facts, The order of faith or order of belief in the existence of something absolute outside man, in accordance and in line with the order of faith and order of worship. (3) The principal features of science are as follows: (a) Systematic, (b) Authenticity, (c) Rationality, (d) Objectivity, (e) Verifiability, (f) Communality. (4) The theory in a theory of truth there are 3 namely: Correspondence Theory, Coherence Theory, Theory of Pragmatism. (4) The source of human knowledge uses two ways of obtaining correct knowledge, first through rationality and secondly through experience. (5) Science limits its exploration to human experience, hence science begins on exploration of human experience and ceases to human experience, and that is the limit of knowledge. (6) Science is essentially a collection of knowledge that explains the various natural phenomena that allow humans to perform a series of actions to master these symptoms based on existing explanations.

scholarly journals On relations between Kirchhoff index, Laplacian energy, Laplacian-energy-like invariant and degree deviation of graphs

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 1025-1033
Author(s):  
Predrag Milosevic ◽  
Emina Milovanovic ◽  
Marjan Matejic ◽  
Igor Milovanovic
Keyword(s):  
Topological Index ◽  
Degree Sequence ◽  
Laplacian Matrix ◽  
Vertex Degree ◽  
Graph Invariants ◽  
Kirchhoff Index ◽  
Laplacian Eigenvalues ◽  
Laplacian Energy ◽  
Degree Deviation ◽  
Simple Connected Graph

Let G be a simple connected graph of order n and size m, vertex degree sequence d1 ? d2 ?...? dn > 0, and let ?1 ? ? 2 ? ... ? ?n-1 > ?n = 0 be the eigenvalues of its Laplacian matrix. Laplacian energy LE, Laplacian-energy-like invariant LEL and Kirchhoff index Kf, are graph invariants defined in terms of Laplacian eigenvalues. These are, respectively, defined as LE(G) = ?n,i=1 |?i-2m/n|, LEL(G) = ?n-1 i=1 ??i and Kf (G) = n ?n-1,i=1 1/?i. A vertex-degree-based topological index referred to as degree deviation is defined as S(G) = ?n,i=1 |di- 2m/n|. Relations between Kf and LE, Kf and LEL, as well as Kf and S are obtained.

Synthesis and Characterization of Some Functional Luminol Derivatives with Aromatic Substituted Groups

2011 ◽  
Vol 197-198 ◽  
pp. 606-609 ◽  
Author(s):  
Ti Feng Jiao ◽  
Yuan Yuan Xing ◽  
Jing Xin Zhou ◽  
Wei Wang
Keyword(s):  
Molecular Structure ◽  
Thermal Stability ◽  
Molecular Structures ◽  
Synthesis And Characterization ◽  
Functional Material ◽  
Aromatic Substituent ◽  
The Difference ◽  
Imide Group ◽  
Thermal Stability Of

Some functional luminol derivatives with aromatic substituted groups have been designed and synthesized from the reaction of the corresponding aromatic acyl chloride precursors with luminol. It has been found that depending on the size of aromatic groups, the formed luminol derivatives showed different properties, indicating distinct regulation of molecular skeletons. UV and IR data confirmed commonly the formation of imide group as well as aromatic segment in molecular structures. Thermal analysis showed that the thermal stability of luminol derivatives with p-phthaloyl segment was the highest in those derivatives. The difference of thermal stability is mainly attributed to the formation of imide group and aromatic substituent groups in molecular structure. The present results have demonstrated that the special properties of luminol derivatives can be turned by modifying molecular structures of objective compounds with proper substituted groups, which show potential application in functional material field and ECL sensor.

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