DP curves, which possess the shape-preserving property and linear complexity evaluation algorithm, occupy a significantly important place in computer aided geometric design. Thus to do the research on the DP curves algorithms has a positive meaning. Aphirukmatakun et al. presented a degree elevation algorithm of DP curves based on the transformation between the DP basis and power basis. At the ...

Let A be a C∗-algebra. Let E and F be Hilbert A-modules with E being full. Suppose that θ : E → F is a linear map preserving orthogonality, i.e., 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We show in this article that if, in addition, A has real rank zero, and θ is an A-module map (not assumed to be bounded), then there exists a central positive multiplier u ∈M(A) such that 〈θ(x), θ(y)〉 = u〈x, y〉 (x...

We describe an algorithm that morphs between two planar orthogonal drawings ΓI and ΓO of a connected graph G, while preserving planarity and orthogonality. Necessarily ΓI and ΓO share the same combinatorial embedding. Our morph uses a linear number of linear morphs (linear interpolations between two drawings) and preserves linear complexity throughout the process, thereby answering an open ques...

The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Grünbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages]. In this study, a simple proof of the necessary and sufficient condition of orthogonality is given for a general case.

A new methodology to aid interpretation of a principal component analysis is presented. While preserving orthogonality, each eigenvector is replaced by a vector, close to it in angle terms, whose entries are small integers. We call such vectors simple. The approach is exploratory, a range of sets of pairwise orthogonal simple components being systematically obtained, from which the user may cho...

Visualization of medical organs and biological structures is a challenging task because of their complex geometry and the resultant occlusions. Global spherical and planar mapping techniques simplify the complex geometry and resolve the occlusions to aid in visualization. However, while resolving the occlusions these techniques do not preserve the geometric context, making them less suitable fo...

Engineering analysis often involves the accurate numerical solution of boundary value problems in discrete form. Hierarchical quadtree (or octree) grid generation offers an efficient method for the spatial discretisation of arbitrary-shaped two- (or three-) dimensional domains. It consists of recursive algebraic splitting of sub-domains into quadrants (or cubes), leading to an ordered hierarchi...

Orthogonality of polynomials in several variableswith respect to a positiveBorelmeasure supported on an algebraic set is themain theme of this paper.As a step towards this goal quasi-orthogonality with respect to a non-zero Hermitian linear functional is studied in detail; this occupies a substantial part of the paper. Therefore necessary and sufficient conditions for quasi-orthogonality in ter...

Abstract The orthogonality time is examined for different initial states settings interacting locally with types of spin interaction: XX , Ising and anisotropic models. It shown that the number increases, consequently decreases as environment qubits increase. shortest displayed chain model, while largest model. external field increases numbers orthogonality, Dzyaloshinsky–Moriya interaction ort...

A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect t...