We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential–density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to r and r at large radii where l is the latitudinal quantum number of spherical harmonics. The lowest order term ...

We present a new methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design. Complete information about the freespace and goal is encoded in the form of a special artificial potential function a navigation function that connects the kinematic planning problem with the dynamic execution problem i...

Different potential energy functions have predominated in protein dynamics simulations, protein design calculations, and protein structure prediction. Clearly, the same physics applies in all three cases. The differences in potential energy functions reflect differences in how the calculations are performed. With improvements in computer power and algorithms, the same potential energy function ...

The problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. Using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations...

For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size N , in term of a determinant; this determinant is function of four kernels constructed from the orthogonal polynomials corresponding to the potential and from their Cauchy transform. The correlation functions ...