The least-squares projection procedure appears frequently in mathematics, science, and engineering. It possesses the well-known property that a least-squares approximation (formed via orthogonal projection) to a given data set provides an optimal fit in the chosen norm. The orthogonal projection of the data onto a finite basis is typically approached by the inversion of a Gram matrix involving ...

Current orthogonal graph drawing algorithms produce drawings which are generally good. However, many times the readability of orthogonal drawings can be signiicantly improved with a postprocess-ing technique, called reenement, which improves aesthetic qualities of a drawing such as area, bends, crossings, and total edge length. Reene-ment is separate from layout and works by analyzing and then ...

A Room t-cube is standardized if it also satisfies (iv) the ith diagonal cell contains the pair of symbols {co, i}. There are several other equivalent forms that are taken by Room t-cubes, one in terms of graphs and one in terms of Latin squares. The first of these forms is as a set of orthogonal one-factorizations of K,,. Let G be a graph with an even number of vertices. A one-factor in G is a...

In this paper, the performance of quasi-synchronous direct-sequence CDMA communication systems based on diierent sets of orthogonal codes is investigated. We search for sets of sequences that minimize the probability of bit detection error, given that there is imperfect synchronization among the signals. Orthogonal sequences based on the Sylvester-type Hadamard matrices (Walsh functions) are sh...

For various quasisynchronous (QS) CDMA systems such as LAS-CDMA system which emerged recently, in order to reduce or eliminate the multiple access interference and multipath interference, it is required to design a set of spreading sequences which are mutually orthogonal within a designed shift zone, called orthogonal zone. For traditional orthogonal sequences, such as Walsh sequences and ortho...

The alternating sum of volumes (ASV) decomposition is a widely used technique for converting a b-rep into a CSG model, with all its implicit uses and advantages -like form feature recognition, among others. The obtained CSG tree has convex primitives at its leaf nodes, while the contents of its internal nodes alternate between the setunion and set-difference operators. This paper first shows th...

This paper presents a novel ECG signal measuring approach using compressive sensing method. The signal representing sparsity in any orthogonal basis can be well recovered using minimize L1 norm optimization, while satisfying the RIP condition for the measurement matrix  and orthogonal basis . First, based on this theorem, an analysis for evaluating the sparsity of ECG signal in orthogonal bas...

This paper shows that Cayley Transforms, which map Orthogonal and SkewSymmetric matrices, may be considered the extension to matrix field of the complex conformal mapping function f1(z) = 1− z 1 + x . Then, by using a set of real matrices which are, simultaneously, Orthogonal and Symmetric (the Ortho−Sym matrices), it similarly shows how to extend two complex conformal mapping functions (namely...

Let H be an infinite-dimensional complex Hilbert space and let L(H) be the logic formed by all closed subspaces of H. For every natural k we denote by Gk(H) the Grassmannian consisting of k-dimensional subspaces. An orthogonal apartment of Gk(H) is the set consisting of all k-dimensional subspaces spanned by subsets of a certain orthogonal base of H. Orthogonal apartments can be characterized a...

Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d+ 2 constraints for any d and any run size ...