This paper introduces a new set of orthogonal moment Functions-franklin Moments (FMs). The kernel functions of FMs is Franklin set, which is a class of complete orthogonal spline function set of degree 1. The implementation of FMs does not involve any numerical approximation and has a rather low computation complexity, since the basis set has the advantages of lower order. These properties make...

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...

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...

To date very few results are known on the critical sets for a set of Mutually Orthogonal Latin Squares(MOLS). In this paper, we consider Orthogonal Array OA(n, k + 2, n, 2) constructed from k mutually orthogonal cyclic latin squares of order n and obtain bounds on the possible sizes of the minimal critical sets. In particular, for n = 7 we exhibit a critical set, thereby improving the bound rep...

In the paper, we study linear operators in complex Hilbert space C that are called real-orthogonal projections, which are a generalization of standard (complex) orthogonal projections but for which only the real part of the scalar product vanishes. We compare some partial order properties of orthogonal and of real-orthogonal projections. In particular, this leads to the observation that a natur...