Let H be a complex Hilbert space. We study the geometry of the space of pairs (A,E), for A a (semidefinite bounded linear) positive operator on H and E a (bounded linear) projection on H such that AE = E∗A. Departamento de Matemática, Facultad de Ingenieŕıa,UBA, Buenos Aires(C1063ACV), Argentina; Instituto Argentino de Matemática CONICET, Saavedra 15, Buenos Aires (1083), Argentina. E-mail addr...

FFT and Multilayer neural networks (MLNN) have been applied to ‘Brain Computer Interface’ (BCI). In this paper, in order to extract features of mental tasks, individual feature of brain waves of each channel is emphasized. Since the brain wave in some interval can be regarded as a vector, Gram-Schmidt orthogonalization is applied for this purpose. There exists degree of freedom in the channel o...

Constrained orthogonal polynomials have been recently introduced in the study of the HohenbergKohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density. More generally, we define block orthogonal (BO) polynomials which are orthogonal, with respect to a first Euclidean scalar product, to a given i-dimensional subspace Ei of polyno...

A series of domino reactions in which the intramolecular Schmidt reaction is combined with either a Sakurai reaction, an aldol reaction, or both is reported. The Sakurai reaction of an allylsilane with an azido-containing enone under Lewis acidic conditions followed by protonation of the resulting titanium enolate species allowed for a subsequent intramolecular Schmidt reaction. Alternatively, ...

This paper is concerned with a technique for solving Fredholm integro-dierentialequations in the reproducing kernel Hilbert space. In contrast with the conventionalreproducing kernel method, the Gram-Schmidt process is omitted hereand satisfactory results are obtained. The analytical solution is represented inthe form of series. An iterative method is given to obtain the approximate solution.Th...

We study the effect of wave function orthogonality in the rela-tivistic treatment of the nucleon removal reactions (γ, p) and (e, e ′ p). The continuum wave function describing the outgoing nucleon is made orthogonal to the relevant bound states using the Gram-Schmidt procedure. This procedure has the advantage of preserving the asymp-totic character of the continuum wave function and hence the...

Model based analysis or explicit definition/listing of all models or assumptions used in the derivation of an image fusion method allows us to understand the rationale or properties of existing methods and shows a way for a proper usage or proposal/selection of new methods ‘better’ satisfying the needs of a particular application. Most existing pan-sharpening methods are based mainly on the two...

The partial least squares (PLS) method computes a sequence of approximate solutions xk ∈ Kk(AA,A b), k = 1, 2, . . . , to the least squares problem minx ‖Ax− b‖2. If carried out to completion, the method always terminates with the pseudoinverse solution x† = A†b. Two direct PLS algorithms are analyzed. The first uses the Golub–Kahan Householder algorithm for reducing A to upper bidiagonal form....

Sets of orthogonal basis functions over circular areas – pupils in optical applications – are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. Here, an orthogonal set is proposed if the area is two non-overlapping circles of equal size. The geometric master parameter is the ratio of the pupil radii over the distance between both circles. Increasingly ...

We study the algebraic aspects of equivariant quantum cohomology algebra of the flag manifold. We introduce and study the quantum double Schubert polynomials S̃w(x, y), which are the Lascoux– Schützenberger type representatives of the equivariant quantum cohomology classes. Our approach is based on the quantum Cauchy identity. We define also quantum Schubert polynomials S̃w(x) as the Gram–Schmidt...