A possible signature of Lense-Thirring precession in dipping and eclipsing neutron-star low-mass X-ray binaries

Relativistic Lense-Thirring precession of a tilted inner accretion disk around a compact object has been proposed as a mechanism for low-frequency (~0.01-70 Hz) quasi-periodic oscillations (QPOs) in the light curves of X-ray binaries. A substantial misalignment angle (~15-20 degrees) between the inner-disk rotation axis and the compact-object spin axis is required for the effects of this precession to produce observable modulations in the X-ray light curve. A consequence of this misalignment is that in high-inclination X-ray binaries the precessing inner disk will quasi-periodically intercept our line of sight to the compact object. In the case of neutron-star systems this should have a significant observational effect, since a large fraction of the accretion energy is released on or near the neutron-star surface. In this Letter I suggest that this specific effect of Lense-Thirring precession may already have been observed as ~1 Hz QPOs in several dipping/eclipsing neutron-star X-ray binaries.Comment: Typo correcte

The Foundations of Mathematics in the Physical Reality

In this article we present an axiomatic definition of sets with individuals and a definition of natural numbers (finite ordinal numbers). We use the axioms pairs, union, regularity and separation of the standard set theory ZF. The equality of sets should be defined thus the axiom of extensionality is not used. And there are individuals thus there is no empty set. The principle of mathematical induction is proved for natural numbers. Then we define ordinal numbers and postulate the union set of all natural numbers and define transfinite ordinal numbers.Comment: 11 page

Developing Guidelines for Two-Dimensional Model Review and Acceptance

Two independent modelers ran two hydraulic models, SRH-2D and HEC-RAS 2D. The models were applied to the Lakina River (MP 44 McCarthy Road) and to Quartz Creek (MP 0.7 Quartz Creek Road), which approximately represent straight and bend flow conditions, respectively. We compared the results, including water depth, depth averaged velocity, and bed shear stress, from the two models for both modelers. We found that the extent and density of survey data were insufficient for Quartz Creek. Neither model was calibrated due to the lack of basic field data (i.e., discharge, water surface elevation, and sediment characteristics). Consequently, we were unable to draw any conclusion about the accuracy of the models. Concerning the time step and the equations used (simplified or full) to solve the momentum equation in the HEC-RAS 2D model, we found that the minimum time step allowed by the model must be used if the diffusion wave equation is used in the simulations. A greater time step can be used if the full momentum equation is used in the simulations. We developed a set of guidelines for reviewing model results, and developed and provided a two-day training workshop on the two models for ADOT&PF hydraulic engineers

Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems

We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0,1}. For a class F of boolean functions and a class G of graphs, an (F,G)-system is a boolean dynamical system with local transitions functions lying in F and graphs in G. We show that, if local transition functions are given by lookup tables, then the following complexity classification holds: Let F be a class of boolean functions closed under superposition and let G be a graph class closed under taking minors. If F contains all min-functions, all max-functions, or all self-dual and monotone functions, and G contains all planar graphs, then it is #P-complete to compute the number of fixed points in an (F,G)-system; otherwise it is computable in polynomial time. We also prove a dichotomy theorem for the case that local transition functions are given by formulas (over logical bases). This theorem has a significantly more complicated structure than the theorem for lookup tables. A corresponding theorem for boolean circuits coincides with the theorem for formulas.Comment: 16 pages, extended abstract presented at 10th Italian Conference on Theoretical Computer Science (ICTCS'2007