The numerical descriptor gathers the data from the molecular graphs and helps to know the characteristics of the chemical structure known as topological index. The QSAR/QSPR/QSTR studies are benefited with the significant role played by topological indices in the drug design. Topological indices provide the information about the physical/chemical/biological properties of chemical compounds. The Zagreb indices are widely studied because of their extensive usage in chemical graph theory. Inspired by the earlier work on inverse sum indeg index (ISI index), novel topological index known as SS index is introduced and computed for four dendrimer structures. Also, the strong correlation coefficient between SS index and 5 physico-chemical characteristics such as boiling point (bp), molar volume (mv), molar refraction (mr), heats of vaporization (hv), and critical pressure (cp) of 67 alkane isomers have been determined. It is found that newly introduced index has shown good correlation in comparison with three most popular existing indices (ISI index and first and second Zagreb indices). In the last part, the mathematical properties of SS index are discussed.
The spontaneous breaking of topological symmetry induced by a vanishingly small symmetry breaking term is investigated. It is shown that, in the presence of Gribov zero modes, topological theories without smearing terms, which are inequivalent to theories with smearing terms, permit spontaneous symmetry breaking. The relation with reducible configurations is briefly discussed. PACS numbers: 1 UO.Qc, 02.40.+m One of the motivations for developing topological field theories [1] is the hope that these models can describe the highly symmetrical phases of some realistic, less symmetric, field theories. The main obstacle to this approach is the difficulty in finding a way to break topological symmetry [1]. Hitherto, the models that have been investigated on this issue all contain gauge "smearing" terms that smear the gauge-fixing 8 function (these models correspond to the Feynman gauge in gauge theories), and no spontaneous breaking of topological symmetries has yet been found [2]. (An exception might be the symmetry breaking attributed to an instanton in a noncompact base manifold [3]; we will only consider compact manifolds in which such instantons do not exist.) Meanwhile, on other issues, models without smearing terms (corresponding to the Landau gauge), owing to their simplicity, have been extensively studied as substitutes to models with smearing terms [2-6]. The presumed interchangeability of the two classes of models is based on the argument that the only difference between them-a gauge smearing term which is BRST (Becchi-Rouet-Stora-Tyutin) exact -does not affect any of the properties of the theories [1], However, this is not unconditionally true. In fact, if Gribov zero modes [7] occur, a model in the Landau gauge may well not be connected to a model in the Feynman gauge by a smooth gauge transformation [7,8]. To see this [8], let F(X) be the gauge-fixing function in theLandau gauge. Its presence in the action picks out a configuration X that is a solution of FiX) =0. We now try to transfer to the Feynman gauge by replacing the F(X) =0 by F(X) = P, where P is arbitrary and depends locally on the coordinates of the base space in which X lives. If the path integration does not depend on P, the Feynman gauge is arrived at by averaging over the gauge function with weight exp( -aP 2 ). However, such P independence is contingent upon the existence, for every pair (P,8P), of an associated infinitesimal gauge transformation v that will transform the solution to F(X)=P to the solution to F{X)=P + SF SX SX 8v V = P + SP.
With the development of mobile network and communication technology, traditional supply chain management is gradually updating to mobile supply chain management, and multi-agent technology has been considered as a very efficient method for supply chain management in mobile environment. After considering the characteristics and limitations of mobile supply chain, and according to the requirements in the manufacturing domain, this paper designs a multi-agent middleware for mobile supply chain management, aiming to solve integration problems and shield off network and terminal heterogeneity in mobile environment, which can achieve mobile supply chain dynamic integration and then improve the efficiency of supply chain management. Its feasibility and efficiency was demonstrated by experiments
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