Monitoring of the atmospheric conditions is very important for fluorescence observations. Particularly, the presence of clouds can drastically distort the signal from the extensive air shower. Infra-red (IR) sensors, measuring sky temperature, can help to distinguish clouds, which are usually significantly warmer than clear skies. Array of such sensors, covering the detector’s field of view, wa...

A t-covering array is a set of k binary vectors of length n with the property that, in any t coordinate positions, all 2t possibilities occur at least once. Such arrays are used for example in circuit testing, and one wishes to minimize k for given values of n and t. The case t = 2 was solved by Rknyi, Katona, and Kleitman and Spencer. The present article is concerned with the case t = 3, where...

This paper introduces a new similarity measure, the covering similarity, that we formally define for evaluating the similarity between a symbolic sequence and a set of symbolic sequences. A pair-wise similarity can also be directly derived from the covering similarity to compare two symbolic sequences. An efficient implementation to compute the covering similarity is proposed that uses a suffix...

A Covering Array denoted by CA(N ; t, k, v) is a matrix of size N × k, in which each of the v combinations appears at least once in every t columns. Covering Arrays (CAs) are combinatorial objects used in software testing. There are different methods to construct CAs, but as it is a highly combinatorial problem, few complete algorithms to construct CAs have been reported. In this paper a new ba...

A novel 1-to-64 (6-bit (2 6 )) optical true-time delay module that can provide linear time delays ranging from 0 to 443.03 picoseconds is presented. The bandwidth of the fully packaged module is determined to be as high as 539 GHz. This true-time delay module is employed to control an eight-element K-band phased array antenna system. Far field patterns covering 18 GHz to 26.5 GHz are measured a...

We investigate the covering problem in RT spaces induced by the RosenbloomTsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen an...

In 1914 Lebesgue defined a ‘universal covering’ to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pál, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before. However, Hansen’...

Our main observation concerns closed geodesics on surfaces M with a smooth Finsler metric, i.e. a function F : TM → [0,∞) which is a norm on each tangent space TpM , p ∈ M , which is smooth outside of the zero section in TM , and which is strictly convex in the sense that Hess(F ) is positive definite on TpM \ {0}. One calls a Finsler metric F symmetric if F (p,−v) = F (p, v) for all v ∈ TpM . ...