Abstract. Let Rk(n) be the number of representations of an integer n as the sum of a prime and a k-th power for k ≥ 2. Furthermore, set Ek(X) = |{n ≤ X, n ∈ Ik, n not a sum of a prime and a k-th power}|. In the present paper we use sieve techniques to obtain a strong upper bound on Rk(n) for n ≤ X with no exceptions, and we improve upon the results of A. Zaccagnini to prove Ek(X) ≪k X 1−181 log...

A complete proof of the quark Reggeization hypothesis in the leading logarithmic approximation for any quark–gluon inelastic process in the multi–Regge kinematics in all orders of α s is given. First, we show that the multi–Regge form of QCD amplitudes is guarantied if a set of conditions on the Reggeon vertices and the trajectories is fulfilled. Then, we examine these conditions and show that ...

Some rigorous results can be derived using a very simple approach to hadron spectroscopy, in which a static potential is associated with non-relativistic kinematics. Several regularities of the experimental spectrum are explained by such models. It is underlined that certain methods developed for hadronic physics have found applications in other fields, in particular atomic physics. A few resul...

Inverse kinematics computation using an artificial neural network that learns the inverse kinematics of a robot arm has been employed by many researchers. However, conventional learning methodologies do not p a y enough attention to the discontinuity of the inverse kinematics system of typical robot arms with joint limits. The inverse kinematics system of the robot arms, including a human arm w...

The information required for solving the inverse kinematic problem associated with any single-loop spatial mechanism is essentially stored in the inverse kinematic solution set of the orthogonal spherical mechanism (SS ÿ 3 for short). The ®rst part of this paper is devoted to the characterization of SS ÿ 3 in terms of its connectivity, singularities and symmetries. The second one focuses on ®nd...

Inverse kinematics computation using an arti cial neural network that learns the inverse kinematics of a robot arm has been employed by many researchers. However, conventional learning methodologies do not pay enough attention to the discontinuity of the inverse kinematics system of typical robot arms with joint limits. The inverse kinematics system of the robot arms is a multi-valued and disco...

In this paper we call an FK space X containing φ Cesàro semiconservative space if X ⊂ σs holds. Therefore we give some characterizations of these spaces.

We consider a Stewart platform and show that it forward kinematics has at most 12 solutions. A first geometrical demonstration is provided which uses the concept of circularity and in a second proof we show that this problem is equivalent to find a system of two planar parallel manipulators with each 6 solutions to the forward kinematic problem. A geometrical construction is provided to constru...