Given an ergodic probability measure preserving dynamical system Γ y (X,μ), where Γ is a finitely generated countable group, we show that the asymptotic growth of the number of finite models for the dynamics, in the sense of sofic approximation, is an invariant of orbit equivalence. We then prove an additivity formula for free products of orbit structures with amenable (possibly trivial) amalga...

We consider the action of a semigroup S on a standard space E. An orbit coupling of two probability measures on E is a coupling of these measures giving the largest possible weight to the event that the orbits of the two coordinates meet each other. We establish the existence of such orbit couplings for a large class of semigroups S. We also discuss some applications.

ENVISAT ASAR Wide Swath data from ascending and descending orbit have been normalized and combined in the eastern Alps in order to increase the covered area from 60-70% to up to 78%. Band rationing was applied for the identification of wet snow surface. Although that probability maps of thawing snow can be derived, combinations of morning and evening orbits are difficult to interpret in late sp...

If the Moon’s spin evolved from faster prograde rates, it could have been captured into a higher spin–orbit resonance than the current 1:1 resonance. At the current value of orbital eccentricity, the probability of capture into the 3:2 resonance is as high as 0.6, but it strongly depends on the temperature and average viscosity of the Moon’s interior. A warmer, less viscous Moon on a higher ecc...

In this paper, we study an M/G/1 queue with two phases of heterogeneous service. A first essential service is provided to all arriving customers. Upon completion of this service, a customer can either opt for a second phase of service or can leave the system. A customer, who finds the server busy, either leaves the system with probability (1-α) or joins an orbit with probability α. From the orb...

This paper presents the application of polynomial chaos (PC) to estimating the probability of collision between two spacecraft. Common methods of quantifying this probability for conjunction assessment use either Monte Carlo analyses or include simplifying assumptions to improve tractability. A PC expansion, or PCE, provides a means for approximating the solution to a large set of stochastic or...

Integration of the orbit of asteroid (29075) 1950 DA, which is based on radar and optical measurements spanning 51 years, reveals a 20-minute interval in March 2880 when there could be a nonnegligible probability of the 1-kilometer object colliding with Earth. Trajectory knowledge remains accurate until then because of extensive astrometric data, an inclined orbit geometry that reduces in-plane...

Abstract. A batch arrival retrial queue with general retrial times, state dependent admission, modified vacation policy and feed back is analysed in this paper. Arrivals are controlled according to the state of the server. If the orbit is empty, the server takes at most J vacations until at least one customer is received in the orbit when the server returns from the vacation. At the service com...