In this paper, we consider an enriched orthogonality for classes of spaces, with respect to groupoids, simplicial sets and spaces themselves. This point of view allows one to characterize homotopy equivalences, shape and strong shape equivalences. We show that there exists a class of spaces, properly containing ANR-spaces, for which shape and strong shape equivalences coincide. For such a class...

The family of general Jacobi polynomials P (α,β) n where α, β ∈ C can be characterised by complex (nonhermitian) orthogonality relations (cf. [15]). The special subclass of Jacobi polynomials P (α,β) n where α, β ∈ R are classical and the real orthogonality, quasi-orthogonality as well as related properties, such as the behaviour of the n real zeros, have been well studied. There is another spe...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

In a semiorthogonal Lanczos algorithm, the orthogonality of the Lanczos vectors is allowed to deteriorate to roughly the square root of the rounding unit, after which the current vectors are reorthogonalized. A theorem of Simon 4] shows that the Rayleigh quotient | i.e., the tridiagonal matrix produced by the Lanczos recursion | contains fully accurate approximations to the Ritz values in spite...

Zernike polynomials are an orthogonal set over a unit circle and are often used to represent surface distortions from FEA analyses. There are several reasons why these coefficients may lose their orthogonality in an FEA analysis. The effects, their importance, and techniques for identifying and improving orthogonality are discussed. Alternative representations are presented.

We generalize the array orthogonality property for perfect autocorrelation sequences to n-dimensional arrays. The generalized array orthogonality property is used to derive a number of ndimensional perfect array constructions.

We establish the orthogonality of the range and the kernel of a normal derivation with respect to the unitarily invariant norms associated with norm ideals of operators. Related orthogonality results for certain nonnormal derivations are also given.

The present study focuses on the development of a general framework for propagating the effects of parametric uncertainty, modeled as random fields, from input to output for complex engineering systems via Stochastic Finite Element techniques. These techniques are similar in concept to deterministic finite element approaches in that they approximate both input and output quantities in terms of ...