We consider n-body problems given by potentials of the form α r + β r with a, b, α, β constants, 0 ≤ a < b. To analyze the dynamics of the problem, we first prove some properties related to central configurations, including a generalization of Moulton’s theorem. Then we obtain several qualitative properties for collision and near-collision orbits in the Manev-type case a = 1. At the end we poin...

A large class of Type II fluid solutions to Einstein field equations in Ndimensional spherical spacetimes is found, wich includes most of the known solutions. A family of the generalized collapsing Vaidya solutions with homothetic self-similarity, parametrized by a constant λ, is studied, and found that when λ > λc(N), the collapse always forms black holes, and when λ < λc(N), it always forms n...

We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algebraic numbers. One motivation is to explain the method’s good performance in practice. We derive an expected complexity bound of ÕB(d + d4τ2), where d is the polynomial degree and τ bounds the coefficient bit size, usin...

DETECTION OF LINEAR ALGEBRA OPERATIONS IN POLYHEDRAL PROGRAMS Writing a code which uses an architecture at its full capability has become an increasingly difficult problem over the last years. For some key operations, a dedicated accelerator or a finely tuned implementation exists and delivers the best performance. Thus, when compiling a code, identifying these operations and issuing calls to t...

We prove that if the outer billiard map around a plane oval is algebraically integrable in a certain non-degenerate sense then the oval is an ellipse. In this note, an outer billiard table is a compact convex domain in the plane bounded by an oval (closed smooth strictly convex curve) C. Pick a point x outside of C. There are two tangent lines from x to C; choose one of them, say, the right one...

The traditional economic approach to index number theory is based on a ratio concept. The Konüs true cost of living index is a ratio of cost functions evaluated at the same utility level but with the prices of the current period in the cost function that appears in the numerator and the prices of the base period in the denominator cost function. The Allen quantity index is also a ratio of cost ...

Wide field interferometry has become a subject of increasing interest in the recent years. New methods have been suggested in order to avoid the drawbacks of the standard wide field method (homothetic mapping) which is not applicable when the aperture is highly diluted; for this reason imaging with non-homothetic arrays is being extensively studied1,2. The field of view of a pupil plane interfe...