We show that the general Levy process can be embedded in a suitable Fock space, classified by cocycles of the real line regarded as a group. The formula of de Finetti corresponds to coboundaries. Kolmogorov’s processes correspond to cocycles of which the derivative is a cocycle of the Lie algebra of R. The Lévy formula gives the general cocycle. 1 Cyclic representations of groups Let G be a gro...

This paper proposes design techniques for the efficient VLSI implementation of bit-serial multiplication over a modulus. These techniques reduce multiplication into simple cyclic shifts, where the number representation of the data is chosen appropriately. This representation will, in general, be highly redundant, implying a relatively poor throughput for the multiplier. It is then shown how, by...

We develop an algebraic representation for (1, 1)-knots using the mapping class group of the twice punctured torus MCG2(T ). We prove that every (1, 1)-knot in a lens space L(p, q) can be represented by the composition of an element of a certain rank two free subgroup of MCG2(T ) with a standard element only depending on the ambient space. As notable examples, we obtain a representation of this...

We address the problem of repeated coverage of a target area, of any polygonal shape, by a team of robots having a limited visual range. Three distributed Clusterbased algorithms, and a method called Cyclic Coverage are introduced for the problem. The goal is to evaluate the performance of the repeated coverage algorithms under the effects of the variables: Environment Representation, and the R...

We develop an algebraic representation for (1, 1)-knots using the mapping class group of the twice punctured torus MCG2(T ). We prove that every (1, 1)-knot in a lens space L(p, q) can be represented by the composition of an element of a certain rank two free subgroup of MCG2(T ) with a standard element only depending on the ambient space. As a notable examples, we obtain a representation of th...

A multivariate interpolation formula (MVIF) over finite fields is presented by using the proposed Kronecker delta function. The MVIF can be applied to yield polynomial relations over the base field among homogeneous symmetric rational functions. Besides the property that all the coefficients are coming from the base field, there is also a significant one on the degrees of the obtained polynomia...

Abstract. The cyclic mechanism is one of the basic automatic machines components. It mechanisms that define performance and reliability limits these machines. methods for assessing are based on data dynamic forces acting mechanism's links, leading to their deformation possible destruction under certain operating conditions. Simulation modeling processes in its representation form interconnected...

An N2 dimensional representation of the periodic Temperley-Lieb algebra TLL(x) is presented. It is also a representation of the cyclic group ZN . We choose x = 1 and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamilto...

We describe an interprocedural shape analysis that makes use of spatial locality (i.e. the fact that most procedures modify only a small subset of the heap) in its representation of abstract states. Instead of tracking reachability information directly and aliasing information indirectly, our representation tracks reachability indirectly and aliasing directly. Computing the effect of procedure ...

Let [Formula: see text]. In this paper, we show that for any abelian subgroup text] of the crystallographic group has Bieberbach subgroups with holonomy Using approach, obtain an explicit description representation As application, when is cyclic odd order, study and determine existence Anosov diffeomorphisms Kähler geometry flat manifold fundamental