Vertex Operator Algebras Associated to Type G Affine Lie Algebras II

We continue the study of the vertex operator algebra $L(k,0)$ associated to a type $G_2^{(1)}$ affine Lie algebra at admissible one-third integer levels, $k = -2 + m + \tfrac{i}{3}\ (m\in \mathbb{Z}_{\ge 0}, i = 1,2)$, initiated in \cite{AL}. Our main result is that there is a finite number of irreducible $L(k,0)$-modules from the category $\mathcal{O}$. The proof relies on the knowledge of an explicit formula for the singular vectors. After obtaining this formula, we are able to show that there are only finitely many irreducible $A(L(k,0))$-modules form the category $\mathcal{O}$. The main result then follows from the bijective correspondence in $A(V)$-theory.Comment: 28 pages, 1 tabl

A clever elimination strategy for efficient minimal solvers

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.Comment: 13 pages, 7 figure

Higgs induced FCNC as a source of new physics in b→sb\to s transitions

The observations in the $B_{s}$ sector suggest the existence of some new physics contribution to the $B_S-\bar{B}_s$ mixing. We study the implications of a hypothesis that this contribution is generated by the Higgs induced flavour changing neutral currents. We concentrate on the specific $b\to s$ transition which is described by two complex FCNC parameters $F_{23}$ and $F_{32}$ and parameters in the Higgs sector. Model independent constraints on these parameters are derived from the $B_S-\bar{B}_s$ mixing and are used to predict the branching ratios for $\bar{B}_s\to \mu^+\mu^-$ and $\bar{B}_d\to \bar{K}\mu^+\mu^-$ numerically by considering general variations in the Higgs parameters assuming that Higgs sector conserves CP. Taking the results on $B_{s}^0-\bar{B}_{s}^0$ mixing derived by the global analysis of UTfit group as a guide we present the general constraints on $F_{23}^*F_{32}$ in terms of the pseudo-scalar mass $M_A$. The former is required to be in the range $\sim (1-5) \times 10^{-11} M_A^2 {\rm GeV}^{-2}$ if the Higgs induced FCNC represent the dominant source of new physics. The phases of these couplings can account for the large CP violating phase in the $B_{s}^0-\bar{B}_{s}^0$ mixing except when $F_{23}=F_{32}$. The Higgs contribution to $\bar{B}_s\to \mu^+\mu^-$ branching ratio can be large, close to the present limit while it remains close to the standard model value in case of the process $\bar{B}_d\to \bar{K}\mu^+\mu^-$ for all the models under study. We identify and discuss various specific examples which can naturally lead to suppressed FCNC in the $K^0-\bar{K}^0$ mixing allowing at the same time the required values for $F_{23}^*$ and $F_{32}$.Comment: 19 pages;six figure

Double-slit and electromagnetic models to complete quantum mechanics

We analyze a realistic microscopic model for electronic scattering with the neutral differential delay equations of motion of point charges of the Wheeler-Feynman electrodynamics. We propose a microscopic model according to the electrodynamics of point charges, complex enough to describe the essential physics. Our microscopic model reaches a simple qualitative agreement with the experimental results as regards interference in double-slit scattering and in electronic scattering by crystals. We discuss our model in the light of existing experimental results, including a qualitative disagreement found for the double-slit experiment. We discuss an approximation for the complex neutral differential delay equations of our model using piecewise-defined (discontinuous) velocities for all charges and piecewise-constant-velocities for the scattered charge. Our approximation predicts the De Broglie wavelength as an inverse function of the incoming velocity and in the correct order of magnitude. We explain the scattering by crystals in the light of the same simplified modeling with Einstein-local interactions. We include a discussion of the qualitative properties of the neutral-delay-equations of electrodynamics to stimulate future experimental tests on the possibility to complete quantum mechanics with electromagnetic models.Comment: 4 figures, the same post-publication typos over the published version of Journal of Computational and Theoretical Nanoscience, only that these correction are not marked in red as in V7, this one is for a recollectio