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A Comment about the existence of a weak solution for a nonlinear Wave Damped PropagationBotelho, Luiz C. L.-2008We give a proof for the existence of weak solutions on the initial-value problem of a non-linear wave damped propagation.
Some comments on rigorous quantum field path integrals in the analytical regularization schemeBotelho, Luiz C. L.-2008Through the systematic use of the Minlos theorem on the support of cylindrical measures on $R^\infty$, we produce several mathematically rigorous path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalized powers of the Laplacean operator.
Triviality - quantum decoherence of Fermionic quantum chromodynamics SU (Nc) in the presence of an external strong U([infinito]) flavored constant noise fieldBotelho, Luiz C. L.Centro Brasileiro de Pesquisas Físicas (CBPF)2008We analyze the triviality-quantum decoherence of Euclidean quantum chromodynamics in the gauge invariant quark current sector in the presence of an external flavor constant charged white noise reservoir.
On the Banach-Stone theorem and the manifold topological classificationBotelho, Luiz C. L.-2009We 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 additionaly we give a straightforward proof of the famous Brower theorem for manifolds topologically classified by their Euclidean dimensions. \noindent We start our comment announcing the:\noindent{\bf Banach-Stone Theorem} ([1]). Let $X$ and $Y$ be compact Hausdorff spaces, such that the associated function algebras of continuous functions $C(X,R)$ and $C(Y,R)$ separate points in $X$ and $Y$ respectively. We have thus \noindent a)\quad $X$ and $Y$ are homeomorphic $\Leftrightarrow$ \noindent b)\quad $C(X,R)$ and $C(Y,R)$ are isomorphic.