In the planar N-body problem, N point masses move in the plane under their mutual gravitational attraction. It is classical that the dynamics of this motion conserves the intgrals of motion: center of mass, linear momentum, angular momentum c, and energy h. Further, the motion has a rotational symmetry. The dynamics thus takes place on a (4N?7)-dimensional open manifold, known as the reduced in...

In the spatial three body problem, the topology of the integral manifolds M(c; h) (i.e. the level sets of energy h and angular momentum c, as well as center of mass and linear mo-mementum) and the Hill's regions H(c; h) (the projection of the integral manifold onto position coordinates) depends only on the quantity = hjcj 2 : In 1] and 3], it was established that, for h < 0 and c 6 = 0, there a...

modeling and simulation of processing plants are widely used in industry. construction of a mathematical model for a plant is a time-consuming and error-prone task. in light of extensive advancements in computer science (both hardware and software), computers are becoming a necessary instrument in industrial activities. many software tools for modeling, simulation and optimization of processing...

Geometry constrains but does not dictate the topology of the three-dimensional space. In a locally spatially homogeneous and isotropic universe, however, the topology of its spatial section dictates its geometry. We show that, besides determining the geometry, the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of setting constraints on the density param...

Let M be a big o-minimal structure and G a type-definable group in Mn. We show that G is a type-definable subset of a definable manifold in Mn that induces on G a group topology. If M is an o-minimal expansion of a real closed field, then G with this group topology is even definably isomorphic to a type-definable group in some Mk with the topology induced by Mk. Part of this result holds for th...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

Let M be a smooth closed manifold. We will denote the group of all self-diffeomorphisms of M, with the smooth topology, by DIF F (M).

Solvothermal reactions of mixed ligands H(3)BTC and macrocyclic oxamide complexes (ML, M = Cu, Ni) with M(ClO(4))(2)·6H(2)O (M = Co, Zn, Ni and Cd) afford six new complexes, including [M'(4)(BTC)(2)(ML)(2)(OH)(2)(H(2)O)(2)]·2H(2)O (M' = Co, M = Ni, for (1); M' = Zn, M = Ni, for (2); M' = Zn, M = Cu, for (3)), [Ni(3)(BTC)(2)(NiL)(2)(H(2)O)(6)]·2CH(3)OH·2H(2)O (4), [Cd(4)(BTC)(2)(HBTC)(NiL)(4)(H(...