To formulate gravity in spacetimes bounded by a null boundary, an arbitrary hypothetical surface, boundary degrees of freedom (d.o.f) should be added to account for the d.o.f and dynamics spacetime regions excised behind boundary. In D dimensional example, are labelled charges defined at D-2 spacelike slices While modes can have their own dynamics, interaction with bulk is governed flux-balance...

The paper deals with the stability of control algorithms in extended operational space for redundant robots. We compare the performance of the control algorithm based on minimal-null space projection and pseudoinverse based projection into the Jacobian null space. We show how the null-space projection affects the stability of the null-space tracking algorithm. The results are verified with the ...