On h h -transforms of one-dimensional diffusions stopped upon hitting zero

For a one-dimensional diffusion on an interval for which 0 is the regular-reflecting left boundary, three kinds of conditionings to avoid zero are studied. The limit processes are $h$-transforms of the process stopped upon hitting zero, where $h$'s are the ground state, the scale function, and the renormalized zero-resolvent. Several properties of the $h$-transforms are investigated

Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations

In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower dimensional metric is independent of reduced dimensions the counterpart of the symmetric extrinsic curvature is proportional to the antisymmetric Kaluza-Klein gauge field strength. For isometry group of internal space, the SO(n) symmetry and SU(n) symmetry are discussed. And the Kaluza-Klein instanton is also enquired.Comment: 15 page

Towards the spatial resolution of metalloprotein charge states by detailed modeling of XFEL crystallographic diffraction.

Oxidation states of individual metal atoms within a metalloprotein can be assigned by examining X-ray absorption edges, which shift to higher energy for progressively more positive valence numbers. Indeed, X-ray crystallography is well suited for such a measurement, owing to its ability to spatially resolve the scattering contributions of individual metal atoms that have distinct electronic environments contributing to protein function. However, as the magnitude of the shift is quite small, about +2 eV per valence state for iron, it has only been possible to measure the effect when performed with monochromated X-ray sources at synchrotron facilities with energy resolutions in the range 2-3 × 10-4 (ΔE/E). This paper tests whether X-ray free-electron laser (XFEL) pulses, which have a broader bandpass (ΔE/E = 3 × 10-3) when used without a monochromator, might also be useful for such studies. The program nanoBragg is used to simulate serial femtosecond crystallography (SFX) diffraction images with sufficient granularity to model the XFEL spectrum, the crystal mosaicity and the wavelength-dependent anomalous scattering factors contributed by two differently charged iron centers in the 110-amino-acid protein, ferredoxin. Bayesian methods are then used to deduce, from the simulated data, the most likely X-ray absorption curves for each metal atom in the protein, which agree well with the curves chosen for the simulation. The data analysis relies critically on the ability to measure the incident spectrum for each pulse, and also on the nanoBragg simulator to predict the size, shape and intensity profile of Bragg spots based on an underlying physical model that includes the absorption curves, which are then modified to produce the best agreement with the simulated data. This inference methodology potentially enables the use of SFX diffraction for the study of metalloenzyme mechanisms and, in general, offers a more detailed approach to Bragg spot data reduction

N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models

We study N=2 nonlinear two dimensional sigma models with boundaries and their massive generalizations (the Landau-Ginzburg models). These models are defined over either Kahler or bihermitian target space manifolds. We determine the most general local N=2 superconformal boundary conditions (D-branes) for these sigma models. In the Kahler case we reproduce the known results in a systematic fashion including interesting results concerning the coisotropic A-type branes. We further analyse the N=2 superconformal boundary conditions for sigma models defined over a bihermitian manifold with torsion. We interpret the boundary conditions in terms of different types of submanifolds of the target space. We point out how the open sigma models correspond to new types of target space geometry. For the massive Landau-Ginzburg models (both Kahler and bihermitian) we discuss an important class of supersymmetric boundary conditions which admits a nice geometrical interpretation.Comment: 48 pages, latex, references and minor comments added, the version to appear in JHE