{"title":"LOSSY TRANSMISSION LINES TERMINATED BY PARALLEL CONNECTED RLC-ELEMENTS WITHOUT THE HEAVISIDE’S CONDITION","authors":"V. Angelov","doi":"10.37516/adv.math.sci.2019.0063","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0063","url":null,"abstract":"The paper deals with analysis of propagation of transverse electromagnetic waves along\u0000lossy transmission lines terminated by a circuit consisting of parallel connected RLCelements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the\u0000mixed problem for hyperbolic system describing the lossy transmission line. Without the\u0000Heaviside's condition, we cannot guarantee the distortionless propagation of waves and\u0000hence we cannot apply the known methods. That is why we apply a different method and\u0000obtain conditions for existence-uniqueness of generalized solution. We change variables\u0000and formulate a mixed problem for the hyperbolic system with respect to the new\u0000variables. The nonlinear characteristics of the RLC-elements generate nonlinearity in the\u0000equations of neutral type on the boundary. We propose an operator presentation of the\u0000mixed problem for transmission line system and by means of fixed point technique we\u0000prove existence-uniqueness of a generalized solution.","PeriodicalId":187230,"journal":{"name":"Global Journal of Applied Engineering Mathematics","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132151931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rachanna R Kanabur, S. K. Giregol, Anand Jirli, Iranna M. Chanal
{"title":"ON COMPUTATION OF NEW DEGREE-BASED TOPOLOGICAL INDICES OF SILICATE CHAIN GRAPH","authors":"Rachanna R Kanabur, S. K. Giregol, Anand Jirli, Iranna M. Chanal","doi":"10.37516/GLOBAL.J.APPL.ENG.MATH.2019.0073","DOIUrl":"https://doi.org/10.37516/GLOBAL.J.APPL.ENG.MATH.2019.0073","url":null,"abstract":"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.","PeriodicalId":187230,"journal":{"name":"Global Journal of Applied Engineering Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125589469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}