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Graphical representations of classical Friedmanns models are often misleading when one considers the age of the universe. Most textbooks disregard conceptual differences in the representations, as far as ages are concerned. We discuss the details of the scale-factor versus time function for Friedmanns solutions in the time range that includes the ages of model universes.
begin{abstract} We show that if the initial profile $qleft( xright) $ for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and $int^{infty }x^{5/2}leftvert qleft( xright) rightvert dx<infty,$ (no decay at $-infty$ is require
This paper deals with necessary and sufficient condition for consistency of the matrix equation $AXB = C$. We will be concerned with the minimal number of free parameters in Penroses formula $X = A^(1)CB^(1) + Y - A^(1)AYBB^(1)$ for obtaining the gen
In this paper, we study the existence of global classical solutions to the generalized surface quasi-geostrophic equation. By using the variational method, we provide some new families of global classical solutions for to the generalized surface quas
We study the 7x7 Hagen-Hurley equations describing spin 1 particles. We split these equations, in the interacting case, into two Dirac equations with non-standard solutions. It is argued that these solutions describe decay of a virtual W boson in beta decay.
We define a new class of unitary solutions to the classical Yang-Baxter equation (CYBE). These ``boundary solutions are those which lie in the closure of the space of unitary solutions to the modified classical Yang-Baxter equation (MCYBE). Using the