In this paper we extend the continuum model for interdigital dielectrometry sensors and propose a new, direct technique for estimating material electrical properties from measurements. Interdigital sensors consist of alternating pairs of long, thin electrodes on a plane. An ideal model assumes that the periodic structure extends to infinity and the electrodes have no thickness. We extend this i...

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We consider unimodular random rooted trees (URTs) and invariant forests in Cayley graphs. We show that URTs of bounded degree are the same as the law of the component of the root in an invariant percolation on a regular tree. We use this to give a new proof that URTs are sofic, a result of Elek. We show that ends of invariant forests in the hyperbolic plane converge to ideal boundary points. We...

The paper presents a direct adaptive tracking control scheme for a class of matched SISO affine nonlinear uncertain systems with zero dynamic using neural network. Through neural network approximation, neural network is used as the emulator of the unknown ideal controller. A quadratic cost function of the error between the unknown ideal controller and the used neural network controller is minim...

We propose a method for the approximation of the solution of high-dimensional problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of an ideal minimal residual method with a residual norm corresponding to the error in a solution norm of interest. We introduce and analyze an algorithm for the approximation of the best approximation i...

In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Number Theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article we introduce the double sequence spaces     2 0 2...

This paper describes the cornerstones of a means-ends approach to the philosophy of inductive inference. I begin with a fallibilist ideal of convergence to the truth in the long run, or in the “limit of inquiry”. I determine which methods are optimal for attaining additional epistemic aims (notably fast and steady convergence to the truth). Means-ends vindications of (a version of) Occam’s Razo...

In weakly coupled plasmas, it is common to describe the microfield using a Debye model. We examine here an “artificial” ideal one-component plasma with an infinite Debye length, which has been used for the test of line shape codes. We show that the infinite Debye length assumption can lead to a misinterpretation of numerical simulations results, in particular regarding the convergence of calcul...