The weak convergence of orthogonal polynomials is given under conditions on the asymptotic behaviour of the coefficients in the three-term recurrence relation. The results generalize known results and are applied to several systems of orthogonal polynomials, including orthogonal polynomials on a finite set of points.

A (symmetric) nested orthogonal array is a symmetric orthogonal array OA(N, k, s, g) which contains an OA(M,k, r, g) as a subarray, where M < N and r < s. In this communication, some methods of construction of nested symmetric orthogonal arrays are given. Asymmetric nested orthogonal arrays are defined and a few methods of their construction are described.

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...

We introduce a new family of Space-Time Trellis Codes which extends the powerful characteristics of SuperOrthogonal Space-Time Trellis Codes to four transmit antennas. We consider a family of quasi-orthogonal space-time block codes as building blocks in our new trellis codes. These codes combine set-partitioning and a super set of quasi-orthogonal space-time block codes in a systematic way to p...

We introduce a new class of space-time codes called super-orthogonal space-time trellis codes. These codes combine set partitioning and a super set of orthogonal space–time block codes in a systematic way to provide full diversity and improved coding gain over earlier space–time trellis code constructions. We also study the optimality of our set partitioning and provide coding gain analysis. Co...

The aim of this paper is to prove that if a planar set A has a difference set ∆(A) satisfying ∆(A) ⊂ Z + s for suitable s than A has at most 3 elements. This result is motivated by the conjecture that the disk has not more than 3 orthogonal exponentials. Further, we prove that if A is a set of exponentials mutually orthogonal with respect to any symmetric convex set K in the plane with a smooth...

In this paper, using both an analytic and algorithmic approach, we derive the coefficients Dm(n, a) of the multiplication formula pn(ax) = n ∑ m=0 Dm(n, a)pm(x) or the translation formula pn(x +a) = n ∑ m=0 Dm(n, a)pm(x), where {pn}n≥0 is an orthogonal polynomial set, including the classical continuous orthogonal polynomials, the classical discrete orthogonal polynomials, the q-classical orthog...