Non-uniform Lossless Transmission Lines Terminated by L-Load in Series Connected to Parallel Connected GL-Loads | Chapter 1 | Recent Studies in Mathematics and Computer Science Vol. 1

The paper analyses non-uniform transmission lines terminated by nonlinear loads situated as follows: GC-loads are connected parallel and L-load is connected in series to them (Fig. 1). First, we formulate boundary conditions for a lossless transmission line system on the basis of the Kirchhoff’s law. Then, we reduce the mixed problem for the system in question to initial value problem for a neutral system on the boundary. We introduce an operator in a suitable function space whose fixed point is an оscillatory solution of the system on the boundary. The obtained conditions are easily verifiable. We demonstrate the advantages of our method in Numerical example.

Author(s) Details
Vasil G. Angelov 
Department of Mathematics, University of Mining and Geology “St. I. Rilski”, 1700 Sofia, Bulgaria.

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A New Definition of Limit of Periodic Function and Periodic g-Contractive Mapping at Infinity | Chapter 08 | Advances in Mathematics and Computer Science Vol. 1

Limit is a basic concept of calculus. However, according to the updated definition, the limit of periodic function at infinity is not in existence. This conclusion of description does not suit with the periodic phenomenon. For example, the temperature on earth is changed periodically every year since the birth of the earth (viewed as t=0). Today (viewed as t →∞) the temperature on earth is continuing. Continuation means that the limit exists. In this paper, a new definition of limit of periodic function and periodic g-contractive mapping at infinity is defined by the value of its initial point based on transformation of variables. Similar definition is made for g- contractive ratio of periodic g-contractive mapping with k-related fixed points. These definitions can be used to describe the k-polar problems and calculation the limit of combinations of periodic functions at infinity. Furthermore, the new definition on contractive ratio of periodic iterative g-contractive mapping at infinity can help us to find the constant G and improves the application of the periodic iterative g-contractive mapping theorem.

Author  Details:

Tian-Quan Yun

School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510641, P.R. China.

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View Volume: https://doi.org/10.9734/bpi/amacs/v1