We study the problem of fitting a two-joint orthogonal polygonal chain to a set S of n points in the plane, where the objective function is to minimize the maximum orthogonal distance from S to the chain. We show that this problem can be solved in Θ(n) time if the orientation of the chain is fixed, and in Θ(n log n) time when the orientation is not a priori known. We also consider some variatio...

We prove that if V = L then there is a Π11 maximal orthogonal (i.e. mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known Theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.

We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial ensemble. Introduction This note is about a certain duality of orthogonal polynomials defined on a finite set. If the weights of two systems of orthogonal p...

We present near infra-red (NIR) adaptive optics assisted spectroscopic observations of the CO (∆μ = 2) absorption bands towards the centre of the giant elliptical galaxy NGC 1399. The observations were made with NAOS-CONICA (ESO VLT) and have a FWHM resolution of 0. 15 (14pc). Kinematic analysis of the observations reveals a decoupled core and strongly non-Gaussian line-of-sight velocity profil...

A set of multipartite orthogonal quantum states is strongly nonlocal if it locally irreducible for every bipartition the subsystems [S. Halder, M. Banik, S. Agrawal, and Bandyopadhyay, Phys. Rev. Lett. 122, 040403 (2019)]. Although this property has been shown in three-, four-, five-partite systems, existence sets $N$-partite systems remains unknown when $N\ensuremath{\ge}6$. In paper, we succe...

The Searchlight Scheduling Problem was first studied in 2D polygons, where the goal is for point guards in fixed positions to rotate searchlights to catch an evasive intruder. Here the problem is extended to 3D polyhedra, with the guards now boundary segments who rotate half-planes of illumination. After carefully detailing the 3D model, several results are established. The first is a nearly di...

introduction: orthogonal radial fields are those in which the central axes are perpendicular to each other. an example of these orthogonal fields is the set of craniospinal orthogonal fields that are used for radiotherapy of medulloblastoma. craniospinal radial fields consist of two parallel-opposed fields for brain exposure and one or two posterior spinal fields for spinal cord exposure. the m...

A 2-directional orthogonal ray graph is an intersection graph of rightward rays (half-lines) and downward rays in the plane. We show a dynamic programming algorithm that solves the weighted dominating set problem in O(n3) time for 2-directional orthogonal ray graphs, where n is the number of vertices of a graph. key words: Boolean-width, dominating set, dynamic programming, twodirectional ortho...