Near-to-Far Field Transformation in FDTD: A Comparative Study of Different Interpolation Approaches

Equivalence theorems in electromagnetic field theory stipulate that farfield radiation pattern/scattering profile of a source/scatterer can be evaluated from fictitious electric and magnetic surface currents on an equivalent imaginary surface enclosing the source/scatterer. These surface currents are in turn calculated from tangential (to the equivalent surface) magnetic and electric fields, respectively. However, due to the staggered-in-space placement of electric and magnetic fields in FDTD Yee cell, selection of a single equivalent surface harboring both tangential electric and magnetic fields is not feasible. The work-around is to select a closed surface with tangential electric (or magnetic) fields and interpolate the neighboring magnetic (or electric) fields to bring approximate magnetic (or electric) fields onto the same surface. Interpolation schemes available in the literature include averaging, geometric mean and the mixed-surface approach. In this work, we compare FDTD farfield scattering profiles of a dielectric cube calculated from surface currents that are obtained using various interpolation techniques. The results are benchmarked with those obtained from integral equation solvers available in the commercial packages FEKO and HFSS.

On the Riemann Hypothesis for the Zeta Function

In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.

On the Riemann Hypothesis for the Zeta Function

In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.

The optimality principle for second-order discrete and discrete-approximate inclusions

This paper deals with the necessary and sufficient conditions of optimality for the Mayer problem of second-order discrete and discrete-approximate inclusions. The main problem is to establish the approximation of second-order viability problems for differential inclusions with endpoint constraints. Thus, as a supplementary problem, we study the discrete approximation problem and give the optimality conditions incorporating the Euler-Lagrange inclusions and distinctive transversality conditions. Locally adjoint mappings (LAM) and equivalence theorems are the fundamental principles of achieving these optimal conditions, one of the most characteristic properties of such approaches with second-order differential inclusions that are specific to the existence of LAMs equivalence relations. Also, a discrete linear model and an example of second-order discrete inclusions in which a set-valued mapping is described by a nonlinear inequality show the applications of these results.

On the Riemann hypothesis for the zeta function

In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.

Absence of Envy among “Neighbors” Can Be Enough

We assume that the set of agents is decomposed into several classes containing individuals related each other in some way, for example groups of neighbors. We propose a new definition of fairness by requiring efficiency and envy-freeness only within each group. We identify conditions under which absence of envy among “neighbors” is enough to ensure fairness in the entire society. We also show that equal-income Walrasian equilibria are the only fair allocations according to our notion, deriving as corollaries the equivalence theorems of Zhou (1992) and Cato (2010). The analysis is conducted in atomless economies as well as in mixed markets.

An Optimal Design Criterion for Within-Individual Covariance Matrices Discrimination and Parameter Estimation in Nonlinear Mixed Effects Models

In this paper, we consider the problem of nding optimal populationdesigns for within-individual covariance matrices discrimination andparameter estimation in nonlinear mixed eects models. A compound optimality criterion is provided, which combines an estimation criterion and a discrimination criterion. We used the D-optimality criterion for parameter estimation, which maximizes the determinant of the Fisher information matrix. For discrimination, we propose a generalization of the T-optimality criterion for xed-eects models. Equivalence theorems are provided for these criteria. We illustrated the application of compound criteria with an example in a pharmacokinetic experiment.