Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation

The convergent iterative procedure for solving the groundstate Schroedinger equation is extended to derive the excitation energy and the wave function of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling $g$ is not too small.Comment: 14 pages, 4 figure

Deviations of the Lepton Mapping Matrix from the Harrison-Perkins-Scott Form

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott (HPS) form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary (thus maximally $T$-violating) and to have a strength in energy scale no greater (but perhaps smaller) than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than $O((m_\mu/m_\tau)^2) \simeq 3.5 \times 10^{-3}$ from their HPS values. Assuming that $(m_\mu/m_\tau)^2$ can be neglected, we derive two simple constraints on the four parameters $\theta_{12}$, $\theta_{23}$, $\theta_{31}$, and $\delta$ of the mapping matrix. These constraints are independent of the details of the imaginary $T$-violating perturbation of the charged lepton mass matrix. We also show that the $e$ and $\mu$ parts of the mapping matrix have a definite form governed by two parameters $\alpha$ and $\beta$; any deviation of order $m_\mu/m_\tau$ can be accommodated by adjusting these two parameters.Comment: 31 pages, 2 figure

Jarlskog Invariant of the Neutrino Mapping Matrix

The Jarlskog Invariant $J_{\nu-map}$ of the neutrino mapping matrix is calculated based on a phenomenological model which relates the smallness of light lepton masses $m_e$ and $m_1$ (of $\nu_1$) with the smallness of $T$ violation. For small $T$ violating phase $\chi_l$ in the lepton sector, $J_{\nu-map}$ is proportional to $\chi_l$, but $m_e$ and $m_1$ are proportional to $\chi_l^2$. This leads to $J_{\nu-map} \cong {1/6}\sqrt{\frac{m_e}{m_\mu}}+O \bigg(\sqrt{\frac{m_em_\mu}{m_\tau^2}}\bigg)+O \bigg(\sqrt{\frac{m_1m_2}{m_3^2}}\bigg)$. Assuming $\sqrt{\frac{m_1m_2}{m_3^2}}<<\sqrt{\frac{m_e}{m_\mu}}$, we find $J_{\nu-map}\cong 1.16\times 10^{-2}$, consistent with the present experimental data.Comment: 19 page

Noncompact Lattice Formulation of Gauge Theories

We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation $\,n\,$ and a wave number $\,\vec K\,$ restricted to the Brillouin zone. A noncompact formulation of lattice QCD (or QED) can be derived by restricting the expansion only to the $\,0^{th}$-band ($\,n = 0\,$) functions, which are simple continuum interpolations of discrete values associated with sites or links on a lattice. The exact continuum theory can be reached through the inclusion of all $\,n = 0\,$ and $\,n \ne 0\,$ bands, without requiring the lattice size $\,\ell \to 0\,$. This makes it possible, at a nonzero $\,\ell\,$, for the lattice coupling $\,g_\ell\,$ to act as the renormalized continuum coupling. All physical results in the continuum are, of course, independent of $\,\ell\,$.Comment: 72 pages, 3 Postscript figure

A large scale prediction of bacteriocin gene blocks suggests a wide functional spectrum for bacteriocins

Bacteriocins are peptide-derived molecules produced by bacteria, whose recently-discovered functions include virulence factors and signalling molecules as well as their better known roles as antibiotics. To date, close to five hundred bacteriocins have been identified and classified. Recent discoveries have shown that bacteriocins are highly diverse and widely distributed among bacterial species. Given the heterogeneity of bacteriocin compounds, many tools struggle with identifying novel bacteriocins due to their vast sequence and structural diversity. Many bacteriocins undergo post-translational processing or modifications necessary for the biosynthesis of the final mature form. Enzymatic modification of bacteriocins as well as their export is achieved by proteins whose genes are often located in a discrete gene cluster proximal to the bacteriocin precursor gene, referred to as \textit{context genes} in this study. Although bacteriocins themselves are structurally diverse, context genes have been shown to be largely conserved across unrelated species. Using this knowledge, we set out to identify new candidates for context genes which may clarify how bacteriocins are synthesized, and identify new candidates for bacteriocins that bear no sequence similarity to known toxins. To achieve these goals, we have developed a software tool, Bacteriocin Operon and gene block Associator (BOA) that can identify homologous bacteriocin associated gene clusters and predict novel ones. We discover that several phyla have a strong preference for bactericon genes, suggesting distinct functions for this group of molecules. Availability: https://github.com/idoerg/BOAComment: Accepted for publication in BMC Bioinformatic