Let ([M.sup.2], g) be an oriented Riemannian surface and E an oriented and

spin vector bundle of rank 2 over M with scalar product (*,*)E and compatible connection [[nabla].sup.E].

spin vector out of the intended x-y plane accompanied by a usually small

The winner of the 'Best S Pen Apps' category's grand prize is From Cheese developed by an Italian company

Spin Vector. The application allows users to play with the S Pen to lure a mouse to the cheese by drawing a scented trail on the screen.

At this point, we may note that the

spin vector ' is always orthogonal to the world-velocity vector as

This is a Pauli current; S is a

spin vector and [??] = [psi] [chi] where [chi] (and [??]) is a 2-component spinor.

Suppose that a

spin vector in a spatial region of ordered

spin vectors in the ground state with SBS happens to deviate slightly from the aligned direction of all the other

spin vectors.

In a general coordinate system the

spin vector in parallel obeys the equation:

The most important features of neutron decay are described by the formula of Jackson, Treiman, and Wyld [1], which gives the neutron decay probability as a function of the emitted ([p.sub.e]) and antineutrino ([p.sub.v]) momenta, and the direction of the initial neutron's

spin vector ([sigma]):

where [[sigma].sup.[mu]] are the components of the non-integrable four-dimensional macroscopic displacement field vector, [[phi].sup.[mu]] are the components of the four-dimensional microscopic (micropolar) intrinsic

spin vector, [bar.e] is a constant proportional to the electric charge, and [[phi].sup.[mu] are the components of the electromagnetic four-potential vector.

A propagating neutron experiences a transverse rotation of its

spin vector about its momentum axis--an effect which manifestly violates parity.

An axial magnetic field will rotate a transverse

spin vector about the momentum axis.

In the AF phase the symmetry generator is given by the

spin vector S = ([S.sub.x], [S.sub.y], [S.sub.z]) (6a).