Recent work [12] has proposed that tracking phase differences through the resolutions of bandpass filtering created via Hilbert transform pairs can be used to obtain unrotated stereoscopic disparities both horizontally and vertically. These ideas are now extended to incorporate the deformation arising from a stereoscopic transformation. From an ordered arrangement of directionally selective qua...

Given a classical symmetric pair, (G, K), with g = Lie(G), we provide descriptions of the Hilbert series of the algebra of K-invariant vectors in the associated graded algebra of U(g) viewed as a K-representation under restriction of the adjoint representation. The description illuminates a certain stable behavior of the Hilbert series, which is investigated in a case-by-case basis. We note tha...

In the paper, we consider Hilbert spaces of functions on infinite graphs, and their compactifications. We arrive at a sampling formula in the spirit of Shannon; the idea is that we allow for sampling of functions f defined on a continuum completion of an infinite graph G, sampling the continuum by values of f at points in the graph G. Rather than the more traditional frequency analysis of band-...

EEG is widely used to record the electrical activity of the brain for detecting various kinds of diseases and disorders of the human brain. EEG signals are contaminated with several unwanted artifacts during EEG recording and these artifacts make the analysis of EEG signal difficult by hiding some valuable information. Time-frequency representation of electroencephalogram (EEG) signal provides ...

Hilbert C∗-modules are useful tools in AW ∗-algebra theory, theory of operator algbras, operator K-theory, group representation theory and theory of operator spaces. The theory of Hilbert C∗-modules is very interesting on its own. In this paper we give fundamentals of the theory of Hilbert C∗-modules and examine some ways in which Hilbert C∗-modules differ from Hilbert spaces.

We present a constructive algebraic integration theory. The theory is constructive in the sense of Bishop, however we avoid the axiom of countable, or dependent, choice. Thus our results can be interpreted in any topos. Since we avoid impredicative methods the results may also be interpreted in Martin-L type theory or in a predicative topos in the sense of Moerdijk and Palmgren. We outline how ...

Through numerical simulations, it is predicted that the gravitational waves (GWs) reflect characteristics of core-collapse supernova (CCSN) explosion mechanism. There are multiple GW excitation processes occur inside a star before its explosion, and suggested GWs originating from CCSN have mode for each process in terms time-frequency representation. Therefore, we propose an application Hilbert...

An algebraic extended bilinear Hilbert semispace H∓ is proposed as being the natural representation space for the algebras of von Neumann. This bilinear Hilbert semispace has a well defined structure given by the representation space Repsp(GLn(Lv ×Lv)) of an algebraic general bilinear semigroup GLn(Lv ×Lv) over the product of sets of completions characterized by increasing ranks. This represent...