In the paper [3] we have given a rigorous mathematical model and a general method for solving special problems in connection with secondary processes generated by a random point distribution of Poisson type. A random point distribution is a random selection of a finite or countably infinite number of points of an abstract set T where a σ-algebra ST is given. It is supposed that if ξ(A) denotes ...

Let A be a Noetherian commutative ring with identity, let A[x] = A[x1, . . . , xn] be a polynomial ring over A, and let I ⊂ A[x] be an ideal. Geometrically, I defines a family of schemes over the base scheme SpecA; the fiber over each point p ∈ SpecA is a subscheme of the affine space Ank(p) = Speck(p)[x], where k(p) = Ap/pp is the residue field of p. Let > be a total order on the monomials of ...

Let A be a Noetherian commutative ring with identity, let A[x] = A[x1, . . . , xn] be a polynomial ring over A, and let I ⊂ A[x] be an ideal. Geometrically, I defines a family of schemes over the base scheme Spec A; the fiber over each point p ∈ Spec A is a subscheme of the affine space Ak(p) = Spec k(p)[x], where k(p) = Ap/pp is the residue field of p. Let > be a total order on the monomials o...

Quadrupole ion traps are reviewed, emphasizing recent developments, especially the investigation of new geometries, guided by multiple particle simulations such as the ITSIM program. These geometries include linear ion traps (LITs) and the simplified rectilinear ion trap (RIT). Various methods of fabrication are described, including the use of rapid prototyping apparatus (RPA), in which 3D obje...

ABSTRACT Cosmic rays (CRs) are thought to escape their sources streaming along the local magnetic field lines. We show that this phenomenon generally leads excitation of both resonant and non-resonant instabilities. The self-generated fluctuations induce particle diffusion in extended regions around source, so CRs build up a large pressure gradient. By means two-dimensional (2D) three-dimension...