Pub Date : 2019-07-01DOI: 10.37516/adv.math.sci.2019.0063
V. Angelov
The paper deals with analysis of propagation of transverse electromagnetic waves along lossy transmission lines terminated by a circuit consisting of parallel connected RLCelements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the mixed problem for hyperbolic system describing the lossy transmission line. Without the Heaviside's condition, we cannot guarantee the distortionless propagation of waves and hence we cannot apply the known methods. That is why we apply a different method and obtain conditions for existence-uniqueness of generalized solution. We change variables and formulate a mixed problem for the hyperbolic system with respect to the new variables. The nonlinear characteristics of the RLC-elements generate nonlinearity in the equations of neutral type on the boundary. We propose an operator presentation of the mixed problem for transmission line system and by means of fixed point technique we prove existence-uniqueness of a generalized solution.
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Pub Date : 2019-07-01DOI: 10.37516/GLOBAL.J.APPL.ENG.MATH.2019.0073
Rachanna R Kanabur, S. K. Giregol, Anand Jirli, Iranna M. Chanal
The Arithmetic-Geometric index (AG1 index), SK index, SK1 index, SK2 indices of a graph G was introduced by V. S. Shigehalli and R. R. Kanabur. These topological indices explain the modeling of various physico-chemical, biological and pharmacological properties of organic molecules in chemistry and explains studies of various results on Silicate Chain Graph.
V. S. Shigehalli和R. R. Kanabur提出了图G的算术几何指数(AG1指数)、SK指数、SK1指数和SK2指数。这些拓扑指数解释了化学中有机分子的各种物理化学、生物和药理学性质的建模，并解释了硅酸盐链图上各种结果的研究。
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