Maximal orthogonality and pseudo-orthogonality with applications to generalized inverses

Pseudo-Hermiticity, weak pseudo-Hermiticity and η-orthogonality condition

We discuss certain features of pseudo-Hermiticity and weak pseudo-Hermiticity conditions and point out that, contrary to a recent claim, there is no inconsistency if the correct orthogonality condition is used for the class of pseudo-Hermitian, PTsymmetric Hamiltonians of the type Hβ = [p + iβν(x)] 2/2m + V (x). PACS: 03.65.Ca

Multiple Orthogonality and Applications in Numerical Integration

In this paper a brief survey of multiple orthogonal polynomials defined using orthogonality conditions spread out over r different measures are given. We consider multiple orthogonal polynomials on the real line, as well as on the unit semicircle in the complex plane. Such polynomials satisfy a linear recurrence relation of order r+1, which is a generalization of the well known three-term recur...

Enhancing Fuzzy Controllers Using Generalized Orthogonality Principle

Generalized BackPropagation, Étude De Cas: Orthogonality

This paper introduces an extension of the backpropagation algorithm that enables us to have layers with constrained weights in a deep network. In particular, we make use of the Riemannian geometry and optimization techniques on matrix manifolds to step outside of normal practice in training deep networks, equipping the network with structures such as orthogonality or positive definiteness. Base...

Global Orthogonality Implies Local Almost-orthogonality

We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums. 0. Introduction. First, an apology. The title, though correct, is somewhat misleading. It should be “Global almostorthogonality implies...