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Padmakar–Ivan Index
In chemical graph theory, the Padmakar–Ivan (PI) index is a topological index of a molecule, used in biochemistry. The Padmakar–Ivan index is a generalization introduced by Padmakar V. Khadikar and Iván Gutman of the concept of the Wiener index, introduced by Harry Wiener. The Padmakar–Ivan index of a graph ''G'' is the sum over all edges ''uv'' of ''G'' of number of edges which are not equidistant from ''u'' and ''v''. Let ''G'' be a graph and ''e'' = ''uv'' an edge of ''G''. Here n_(e\mid G) denotes the number of edges lying closer to the vertex ''u'' than the vertex ''v'', and n_(e\mid G) is the number of edges lying closer to the vertex ''v'' than the vertex ''u''. The Padmakar–Ivan index of a graph ''G'' is defined as : \operatorname(G)=\sum_ _(e\mid G) + n_(e\mid G) The PI index is very important in the study of quantitative structure–activity relationship for the classification models used in the chemical, biological sciences, engineering, and nano ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Graph Theory
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena. The pioneers of chemical graph theory are Alexandru Balaban, Ante Graovac, Iván Gutman, Haruo Hosoya, Milan Randić and Nenad Trinajstić (also Harry Wiener and others). In 1988, it was reported that several hundred researchers worked in this area, producing about 500 articles annually. A number of monographs have been written in the area, including the two-volume comprehensive text by Trinajstić, ''Chemical Graph Theory'', that summarized the field up to mid-1980s. The adherents of the theory maintain that the properties of a chemical graph (i.e., a graph-theoretical representation of a molecule) give valuable insights into the chemical phenomena. Others contend that graphs play only a fringe role in chemical research.D.H. Rouvray, "Combinatorics in Chemistry", pp. 1955-1982, in: Ronald Graham, Martin Grötschel, László Lovász (E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Index
In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. Calculation Topological descriptors are derived from hydrogen-suppressed molecular graphs, in which the atoms are represented by vertices and the bonds by edges. The connections between the atoms can be described by various types of topological matrices (e.g., distance or adjacency matrices), which can be mathematically manipulated so as to derive a single number, usually known as grap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and ''molecule'' is often used when referring to polyatomic ions. A molecule may be homonuclear, that is, it consists of atoms of one chemical element, e.g. two atoms in the oxygen molecule (O2); or it may be heteronuclear, a chemical compound composed of more than one element, e.g. water (two hydrogen atoms and one oxygen atom; H2O). In the kinetic theory of gases, the term ''molecule'' is often used for any gaseous particle regardless of its composition. This relaxes the requirement that a molecule contains two or more atoms, since the noble gases are individual atoms. Atoms and complexes connected by non-covalent interactions, such as hydrogen bonds or ionic bonds, are typically not consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and metabolism. Over the last decades of the 20th century, biochemistry has become successful at explaining living processes through these three disciplines. Almost all areas of the life sciences are being uncovered and developed through biochemical methodology and research. Voet (2005), p. 3. Biochemistry focuses on understanding the chemical basis which allows biological molecules to give rise to the processes that occur within living cells and between cells,Karp (2009), p. 2. in turn relating greatly to the understanding of tissues and organs, as well as organism structure and function.Miller (2012). p. 62. Biochemistry is closely related to molecular biology, which is the study of the molecular mechanisms of biological phenomena.As ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iván Gutman
Iván Gutman (born in 1947) is a Serbian chemist and mathematician. Life and work Gutman was born in Sombor, Yugoslavia in a Bunjevac family. In 1970 he graduated chemistry from the University of Belgrade where he worked a short time as an assistant at the Chemistry Department. From 1971 until 1976 he worked as Research Assistant and Senior Research Assistant at Ruđer Bošković Institute in Zagreb, Department of Physical Chemistry. In 1973 he received M.Sc. degree from the University of Zagreb, in the area of theoretical organic chemistry. In the same year he received a doctorate degree in chemistry from the University of Zagreb. His supervisor was Nenad Trinajstić. From 1977 he worked at the University of Kragujevac, eventually becoming a full research professor in 1982. In 1981 he received a doctorate degree in mathematics from the University of Belgrade. From 2012 he is a professor emeritus at the University of Kragujevac. His research interests are theoretical organic c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener Index
In chemical graph theory, the Wiener index (also Wiener number) introduced by Harry Wiener, is a topological index of a molecule, defined as the sum of the lengths of the shortest paths between all pairs of vertices in the chemical graph representing the non-hydrogen atoms in the molecule.. Wiener index can be used for the representation of computer networks and enhancing lattice hardware security. History The Wiener index is named after Harry Wiener, who introduced it in 1947; at the time, Wiener called it the "path number".. It is the oldest topological index related to molecular branching. Based on its success, many other topological indexes of chemical graphs, based on information in the distance matrix of the graph, have been developed subsequently to Wiener's work. The same quantity has also been studied in pure mathematics, under various names including the gross status, the distance of a graph,. and the transmission. The Wiener index is also closely related to the cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harry Wiener
Harry Wiener (Oct. 29, 1924 in Vienna, Austria – Nov. 8, 1998 in New York City, USA) was an Austrian-American chemist, physician and psychologist, a pioneer in cheminformatics and chemical graph theory, and a long-time employee at Pfizer. Education and career Wiener was born in Vienna in 1924 to Jewish parents Joseph Wiener and Beile Wiener. His family emigrated to New York City, USA in 1941 by way of France and Portugal. Wiener attended Brooklyn College and received a BS in chemistry in 1945. Wiener attended Long Island College of Medicine and obtained an MD in 1949. Wiener was appointed to the management team at Pfizer in 1958 and remained at the company until 1995, when he retired. Achievements Wiener made important and fundamental contributions to the study of topological indices and established a correlation between the Wiener index and boiling points (hence viscosity and surface tension) of the paraffins. He laid the foundation of chemical graph theory, and built ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantitative Structure–activity Relationship
Quantitative structure–activity relationship models (QSAR models) are regression or classification models used in the chemical and biological sciences and engineering. Like other regression models, QSAR regression models relate a set of "predictor" variables (X) to the potency of the response variable (Y), while classification QSAR models relate the predictor variables to a categorical value of the response variable. In QSAR modeling, the predictors consist of physico-chemical properties or theoretical molecular descriptors of chemicals; the QSAR response-variable could be a biological activity of the chemicals. QSAR models first summarize a supposed relationship between chemical structures and biological activity in a data-set of chemicals. Second, QSAR models predict the activities of new chemicals. Related terms include ''quantitative structure–property relationships'' (''QSPR'') when a chemical property is modeled as the response variable. "Different properties or behav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical
A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., without breaking chemical bonds. Chemical substances can be simple substances (substances consisting of a single chemical element), chemical compounds, or alloys. Chemical substances are often called 'pure' to set them apart from mixtures. A common example of a chemical substance is pure water; it has the same properties and the same ratio of hydrogen to oxygen whether it is isolated from a river or made in a laboratory. Other chemical substances commonly encountered in pure form are diamond (carbon), gold, table salt (sodium chloride) and refined sugar (sucrose). However, in practice, no substance is entirely pure, and chemical purity is specified according to the intended use of the chemical. Chemical substances exist as solids, liquids, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biological Sciences
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary information encoded in genes, which can be transmitted to future generations. Another major theme is evolution, which explains the unity and diversity of life. Energy processing is also important to life as it allows organisms to move, grow, and reproduce. Finally, all organisms are able to regulate their own internal environments. Biologists are able to study life at multiple levels of organization, from the molecular biology of a cell to the anatomy and physiology of plants and animals, and evolution of populations.Based on definition from: Hence, there are multiple subdisciplines within biology, each defined by the nature of their research questions and the tools that they use. Like other scientists, biologists use the scientific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specialized List of engineering branches, fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application. See glossary of engineering. The term ''engineering'' is derived from the Latin ''ingenium'', meaning "cleverness" and ''ingeniare'', meaning "to contrive, devise". Definition The American Engineers' Council for Professional Development (ECPD, the predecessor of Accreditation Board for Engineering and Technology, ABET) has defined "engineering" as: The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
