‎‎‎In this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $S$-posets‎, ‎posets with a monotone action of a‎ pomonoid $S$ on them‎, ‎is studied‎. ‎We give a criterion‎, ‎like the Baer condition for injectivity of modules‎, ‎or Skornjakov criterion for injectivity of $S$-sets‎, ‎for the order dense injectivity‎. ‎Also‎, ‎we consider such injectivit...

We study the effects of laser phase noise on a phase diversity coherent optical frequency domain (C-OFD) technique that has been recently proposed to measure passive devices used in dense wavelength division multiplexing (DWDM) systems. Theoretical expressions are provided to calculate the laser phase-noise to intensity-noise conversion in this technique under simplified circumstances. Obtained...

Abstract Let F be an ordered topological vector space (over $$\mathbb {R}$$ R ) whose positive cone $$F_+$$ F + is weakly closed, and let $$E \subseteq F$$ E ⊆ a subspace. We prove that the set of...

An interesting feature of the finite-dimensional real spectral triple (A,H,D,J) Standard Model is that it satisfies a ``second-order'' condition: conjugation by J maps Clifford algebra Cl_D(A) into its commutant, which in fact isomorphic to itself (H self-Morita equivalence Cl_D(A)-bimodule). This resembles property canonical closed oriented Riemannian manifold: there dense subspace H Cl_D(A)-b...

The eigensystem realization algorithm (ERA) is a data-driven approach for subspace system identification and widely used in many areas of engineering. However, the computational cost ERA dominated by step that involves singular value decomposition (SVD) large, dense matrix with block Hankel structure. This paper develops computationally efficient algorithms reducing SVD using randomized iterati...

$C_{p}\left ( X\right )$ is distinguished $\Leftrightarrow$ the strong dual $L_{\beta }\left barrelled bidual $M\left ) =\mathbb {R}^{X}$. So one may judge how nearly by is, and also near dense subspace to Baire space $\mathbb Being Baire-like, always fairly close {R}^{X}$ in that sense. But if not distinguished, we show codimension of uncountable, i.e., algebraically far from {R}^{X}$, moreove...

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive C0-semigroups under topology uniform weak operator convergence on compact subsets R+. Eisner and Serény raised in [6] [3] open problem: Does this constitute a Baire space? Observing that subspace unitary semigroups is completely metrisable appealing to known density resul...

In this paper we describe a variational approach to computing dense optic flow in the case of non-rigid motion. We optimise a global energy to compute the optic flow between each image in a sequence and a reference frame simultaneously. Our approach is based on subspace constraints which allow to express the optic flow at each pixel in a compact way as a linear combination of a 2D motion basis ...