A Thomson's Principle for Infinite, Nonlinear Resistive Networks
نویسندگان
چکیده
Suppose T is an infinite resistive electrical network with resistors of the form (2). We prove an existence and uniqueness theorem for the current generated by external current sources by establishing the analogue of Thomson's principle in suitable modular sequence spaces.
منابع مشابه
Transfinite Graphs and Electrical Networks
All prior theories of infinite electrical networks assume that such networks are finitely connected, that is, between any two nodes of the network there is a finite path. This work establishes a theory for transfinite electrical networks wherein some nodes are not connected by finite paths but are connected by transfinite paths. Moreover, the voltages at those nodes may influence each other. Th...
متن کاملNumerical treatment for nonlinear steady flow of a third grade fluid in a porous half space by neural networks optimized
In this paper, steady flow of a third-grade fluid in a porous half space has been considered. This problem is a nonlinear two-point boundary value problem (BVP) on semi-infinite interval. The solution for this problem is given by a numerical method based on the feed-forward artificial neural network model using radial basis activation functions trained with an interior point method. ...
متن کاملSolving nonlinear Lane-Emden type equations with unsupervised combined artificial neural networks
In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks cont...
متن کاملOperating Points in Infinite Nonlinear Networks Approximated by Finite Networks
Given a nonlinear infinite resistive network, an operating point can be determined by approximating the network by finite networks obtained by shorting together various infinite sets of nodes, and then taking a limit of the nodal potential functions of the finite networks. Initially, by taking a completion of the node set of the infinite network under a metric given by the resistances, limit po...
متن کاملCoarse Image Region Segmentation Using Resistive-fuse Networks Implemented in FPGA
Two digital LSI implementation methods for nonlinear resistive networks are proposed; one is for pixel-parallel operation and the other is for pixel-serial operation. we have designed digital circuits that emulate the operation of analog nonlinear resistive networks by discrete-time dynamics based on clock operation. The steady state of the networks is obtained by repeating the updating sequenc...
متن کامل