In this Letter, we introduce an analytic procedure for designing diffractive lenses using the combination of wavefronts aberrated by Zernike polynomials. We show how to design amplitude-only, phase-only, continuous, and binary lenses providing equivalent results. As an example we apply it to the design of a multiple-axis, multifocal lens. The number of foci and their positions can be easily con...

Phonological ganging is a type of cumulativity in constraint interaction where one strong constraint C1 can be overtaken by two weaker constraints C2 and C3 together but not by C2 or C3 independently (e.g., Jäger and Rosenbach 2006). In strict-ranking Optimality Theory (OT), phonological ganging is achieved via (local) constraint conjunction (e.g., Smolensky 1993, 2006; Baković 2000; Ito and Me...

The analytic signal of a real signal is a standard concept in 1D signal processing. However, the deenition of an analytic signal for real 2D signals is not possible by a straightforward extension of the 1D deenition. There rather occur several diierent approaches in the literature. We review the main approaches and propose a new deenition which is based on the recently introduced quaternionic F...

We consider a labelled tableau presentation of constant domain rst-order S5 and prove a strong cut-elimination theorem.

In this paper, we derive an analytic representation of the eigenvectors and coefficients for in-plane rotated images. This, on the one hand, allows an efficient PCA-basis calculation in the learning stage and on the other hand a direct computation of the rotation angle in the recognition stage. In the experimental section, we demonstrate that the new method is feasible and the recognition and o...

abstract: An analytical method validation represents a complete investigation of the materials’ properties, following certain steps, being necessary for “proving the fit for purpose of an analytical method”. The validation procedure demonstrate that a defined validation protocol for an analytical method applied to a specified testing material and a defined concentration of the analyt – named an...

In this paper we investigate tableau proof procedures for reasoning about actions and plans. Our framework is a multimodal language close to that of propositional dynamic logic, wherein we solve the frame problem by introducing the notion of dependence as a weak causal connection between actions and atoms. The tableau procedure is sound and complete for an important fragment of our language, wi...

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained re...