Skewincidence

We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinate i for which x_i=y_{i+1}=1 or vice versa. We give rather sharp bounds on the maximum number of binary sequences of length n any pair of which has a skewincidence

Sperner's problem for G-independent families

Given a graph G, let Q(G) denote the collection of all independent (edge-free) sets of vertices in G. We consider the problem of determining the size of a largest antichain in Q(G). When G is the edge-less graph, this problem is resolved by Sperner's Theorem. In this paper, we focus on the case where G is the path of length n-1, proving the size of a maximal antichain is of the same order as the size of a largest layer of Q(G).Comment: 26 page

Zero-error capacity of binary channels with memory

We begin a systematic study of the problem of the zero--error capacity of noisy binary channels with memory and solve some of the non--trivial cases.Comment: 10 pages. This paper is the revised version of our previous paper having the same title, published on ArXiV on February 3, 2014. We complete Theorem 2 of the previous version by showing here that our previous construction is asymptotically optimal. This proves that the isometric triangles yield different capacities. The new manuscript differs from the old one by the addition of one more pag

Reflective Toraldo pupil for high-resolution millimeter-wave astronomy

A novel, to the best of our knowledge, beam-shaping reflective surface for high-resolution millimeter/ submillimeter-wave astronomy instruments is presented. The reflector design is based on Toraldo’s superresolution principle and implemented with annulated binary-phase coronae structure inspired by the achromatic magnetic mirror approach. A thin, less than half a free-space wavelength, reflective Toraldo pupil device operated in the W-band has been fabricated using mesh-filter technology developed at Cardiff University. The device has been characterized on a quasi-optical test bench and demonstrated expected reduction of the beam width upon reflection at oblique incidence, while featuring a sidelobe level lower than −10 dB. The proposed reflective Toraldo pupil structure can be easily scaled for upper millimeter and infrared frequency bands as well as designed to transform a Gaussian beam into a flat-top beam with extremely low sidelobe level

Wiener-Hopf solution for impenetrable wedges at skew incidence

A new Wiener–Hopf approach for the solution of impenetrable wedges at skew incidence is presented. Mathematical aspects are described in a unified and consistent theory for angular region problems. Solutions are obtained using analytical and numerical-analytical approaches. Several numerical tests from the scientific literature validate the new technique, and new solutions for anisotropic surface impedance wedges are solved at skew incidence. The solutions are presented considering the geometrical and uniform theory of diffraction coefficients, total fields, and possible surface wave contributions

The generalized Wiener-Hopf equations for wave motion in angular regions: Electromagnetic application

In this work, we introduce a general method to deduce spectral functional equations and, thus, the generalized Wiener-Hopf equations (GWHEs) for wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity with application to electromagnetics. The functional equations are obtained by solving vector differential equations of first order that model the problem. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper shows the general theory and the validity of GWHEs in the context of electromagnetic applications with respect to the current literature. Extension to scattering problems by wedges in arbitrarily linear media in different physics will be presented in future works

Skewincidence

We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinatei for which x(i) = y(i+1) = 1 or vice versa. We give relatively close bounds on the maximum number of binary sequences of length n any pair of which has a skewincidence. A systematic study of these problems helps to understand the mathematical difficulties to solve zero-error problems in information theory