Analysis of EM scattering in Waveguide Filter using Neural Network
This paper discusses the application of Neural Network (NN) technique in the modeling of a typical electromagnetic (EM) field scattering problem in a waveguide filter structure [1]. The structure under consideration is a rectangular waveguide with four dielectric circular rod inserted symmetrically. The Neural Network takes into consideration the geometrical and material parameters of the EM model of the structure and the reflection coefficient values for different frequencies in the frequency band of interest. The Neural Network is trained off line using training data sets generated by the image theory. The work is to find out an acceptable Neural Network model of the waveguide structure having four dielectric post, verification using Method of moment by simulation and the corresponding filter structure practically implemented in hardware for verification.
Analysis of Electromagnetic Bandgap Based Filters in a Rectangular Waveguide
Electromagnetic crystals formed by vertical full posts stacked in a rectangular waveguide are analyzed using the image theory and the lattice sums technique. It is shown that the frequency response of the crystals consisting of circular posts can be obtained by a simpler matrix calculus based on the one-dimensional lattice sums, the T-matrix of a circular cylinder in free space, and the generalized reflection and transmission matrices.
Decidability of some intuitionistic predicate theories
Suppose T is a first order intuitionistic theory (more precisely, a theory of Heyting's predicate calculus, e.g., abelian groups, one unary function, dense linear order, etc.) presented to us by a set of axioms (denoted also by) T. Question. Is T decidable? One knows that if the classical counterpart of T (i.e., take the same axioms but with the classical predicate calculus as the underlying logic) is not decidable, then T cannot be decidable. The problem remains for theories whose classical counterpart is decidable. In [8], sufficient conditions for undecidability were given, and several intuitionistic theories such as abelian groups and unary functions (both with decidable equality) were shown to be undecidable. In this note we show decidability results (see Theorems 1 and 2 below), and compare these results with the undecidability results previously obtained. The method we use is the reduction-method, described fully in [12] and widely applied in [3], which is applied here roughly as follows: Let T be a given theory of Heyting's predicate calculus. We know that Heyting's predicate calculus is complete for the Kripke-model type of semantics. We choose a class M of Kripke models for which T is complete, i.e., all axioms of T are valid in any model of the class and whenever φ is not a theorem of T, φ is false in some model of M.