Euler angles determining rotations of a system as a whole are conveniently separated in three–particle basis functions. Analytic integration of matrix elements over Euler angles is done in a general form. Results for the Euler angle integrated matrix elements of a realistic NN interaction are listed. The partial wave decomposition of correlated three–body states is considered.

We calculate the universal Euler characteristic and universal dimension function on semilinear and semibounded sets and obtain some criteria for definable equivalence of semilinear and semibounded sets in terms of these invariants.

In [12], Stark formulated his far-reaching refined conjecture on the first derivative of abelian (imprimitive) L–functions of order of vanishing r = 1 at s = 0. In [10], Rubin extended Stark’s refined conjecture to describe the r-th derivative of abelian (imprimitive) L-functions of order of vanishing r at s = 0, for arbitrary values r. However, in both Stark’s and Rubin’s setups, the order of ...

Let p(n) denote the number of partitions of an integer n. Recently the author has shown that in any arithmetic progression r (mod t), there exist infinitely many N for which p(N) is even, and there are infinitely many M for which p(M) is odd, provided there is at least one such M. Here we construct finite sets of integers Mi for which p(Mi) is odd for an odd number of i. Whereas Euler’s recurre...

In this paper we extend, and Poincaré dualize, the concept of Euler structures, introduced by Turaev for manifolds with vanishing Euler– Poincaré characteristic, to arbitrary manifolds. We use the Poincaré dual concept, co-Euler structures, to remove all geometric ambiguities from the Ray–Singer torsion by providing a slightly modified object which is a topological invariant. We show that the m...

This paper, first, we consider the Volterra integral equation for remainder term in asymptotic formula associated Euler totient function. Secondly, solve and split error function into two summands called arithmetic analytic part respectively.

In this paper we extend, and Poincaré dualize, the concept of Euler structures, introduced by Turaev for manifolds with vanishing Euler–Poincaré characteristic, to arbitrary manifolds. We use the Poincaré dual concept, coEuler structures, to remove all geometric ambiguities from the Ray–Singer torsion by providing a slightly modified object which is a topological invariant. We show that when th...

Let X ⊂ R be a closed semialgebraic set and let f P(X) be the ring obtained from the characteristic function of X by the operations +, −, ∗, the half link operator and by the polynomial operations with rational coefficients which preserve finite formal sum of signs. McCrory and Parusiński proved that necessary conditions for X to be semialgebraically homeomorphic to a real algebraic set is that...

Many interesting problems in computer vision can be formulated as a minimization problem for an energy functional. If this functional is given as an integral of a scalar-valued weight function over an unknown hypersurface, then the minimal surface we are looking for can be determined as a solution of the functional’s Euler-Lagrange equation. This paper deals with a general class of weight funct...

in this research optimal reconfiguration strategy of the improved srr reconfigurable mobile robot based on force-angle stability measure has been designed using genetic algorithm. path tracking nonlinear controller which keeps robot’s maximum stability has been designed and simulated in matlab. motion equations of the robot have been derived in parametric form by means of newton- euler, lagrang...