A 12.5 GHz-Spaced Optical Frequency Comb Spanning >400 nm for near-Infrared Astronomical Spectrograph Calibration

A 12.5 GHz-spaced optical frequency comb locked to a Global Positioning disciplined oscillator for near-IR spectrograph calibration is presented. The comb is generated via filtering a 250 MHz-spaced comb. Subsequency nonlinear broadening of the 12.5 GHz comb extends the wavelength range to cover 1380 nm to 1820 nm, providing complete coverage over the H-band transmission widow of Earth's atmosphere. Finite suppression of spurious sidemodes, optical linewidth and instability of the comb have been examined to estmiate potential wavelength biases in spectrograph calibration. Sidemode suppression varies between 20 db and 45 dB, and the optical linewidth is ~350 kHz at 1550 nm. The comb frequency uncertainty is bounded by +/- 30 kHz (corresponding to a radial velocity of +/- 5 cm/s), limited by the Global Positioning System disciplined oscillator reference. These results indicate this comb can readily support radial velocity measurements below 1 m/s in the near-IR.Comment: 16 pages, 12 figures, new file fixes some readability problems on Mac

An improved method of computing geometrical potential force (GPF) employed in the segmentation of 3D and 4D medical images

The geometric potential force (GPF) used in segmentation of medical images is in general a robustmethod. However, calculation of the GPF is often time consuming and slow. In the present work, wepropose several methods for improving the GPF calculation and evaluate their efficiency against theoriginal method. Among different methods investigated, the procedure that combines Riesz transformand integration by part provides the fastest solution. Both static and dynamic images have been employedto demonstrate the efficacy of the proposed methods

Point massive particle in General Relativity

It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle. Nevertheless, what is the exact solution of Einstein's equations with $\delta$-type source corresponding to a point particle is not known. In the present paper, we prove that the Schwarzschild solution in isotropic coordinates is the asymptotically flat static spherically symmetric solution of Einstein's equations with $\delta$-type energy-momentum tensor corresponding to a point particle. Solution of Einstein's equations is understood in the generalized sense after integration with a test function. Metric components are locally integrable functions for which nonlinear Einstein's equations are mathematically defined. The Schwarzschild solution in isotropic coordinates is locally isometric to the Schwarzschild solution in Schwarzschild coordinates but differs essentially globally. It is topologically trivial neglecting the world line of a point particle. Gravity attraction at large distances is replaced by repulsion at the particle neighbourhood.Comment: 15 pages, references added, 1 figur

On the asymptotic expansion of certain plane singular integral operators

We discuss the problem of the asymptotic expansion for some operators in a general theory of pseudo-differential equations on manifolds with border

Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and diffeomorphisms relative to which they are generalized Lie groups or topological groups. Among such topologies pairwise incomparable are found as well. Topological perfectness of the diffeomorphism group relative to certain topologies is studied. There are proved theorems about projective limit decompositions of these groups and their compactifications for compact manifolds. Moreover, an existence of one-parameter local subgroups of diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad

Distributions, non-smooth manifolds, transmutations and boundary value problems

One discusses the problem of constructing the theory of pseudo differential equations on manifoldswith a non-smooth boundary.Using special factorization principle and transmutation operators we consider some general boundary value problems for elliptic pseudo-differential equations in canonical non-smooth manifold