arXiv subjects
Publications and source records attributed to Luiz C. L. Botelho.
We present a simple set-theoretic proof of the Banach-Stone Theorem .We thus apply this Topological classification theorem to the still unsolved problem of topological classification of euclidean manifolds through two conjectures and additionally we give a straightforward proof of the famous Brower theorem for Manifolds topologically classified by their euclidean dimensions.
We give a proof for the existence of a weak solution on the initial-value problem of a non-linear damped propagation
We present a complete study of the ergodic theorem for the difficult problem of non-linear wave propagations through cylindrical measures /path integrals and the famous Ruelle-Amrein-Geogerscu-Enss (R.A.G.E.) theorem on the caracterization of continuous spectrum of self-adjoint operators.
We present a new proof of an Ergodic theorem for Wide-Sense Stationary Random Processes added with a new canonical sampling theorem of mine for finite time duration signals in the frequency domain (periodograms) which is free from the Nyquist interval restriction.We point out the usefulness of such theorem in the context of a model of random vibrations transmission (pressure-explosive fluctuations).Replacement due to inadvertent and wrong acknowledgments
We present physical arguments based on loop space representations for Dirac/Klein gordon determinants that some suitable Fermionic String Ising models at the critical point and defined on the space-time base manifold are formal quantum states of the gravitational field when quantized in the Ashtekar-Sen connection canonical formalism .These results complements our previous Loop Space studies on the subject (Random surface representation for Einstein quantum gravity, Phys.Rev.D52,6941 (1995))
We propose a quantum surface wave functional describing the interaction between a colored membrane and a quantized Yang Mills. Additionally, we deduce its associated wave equation in the t'Hooft Nc-infinite limit. We show that it reproduces the Yang Mills Field Theory at a large rigid random surface scale.
We write a space-time Feynman path integral representation for scattered elastic wave fields from a weakly compact supported anisotropic non-homogeneity.Replacement by a new version where We (I!) propose a new tomographic inversion methodology based solely in the wave sampling of the Ray paths through Monte Carlo path integral sampling Holding thus great potentiality for Navy's advanced Sonar detection .