Expansive soils shrink and swell with drying wetting cycles. The shrink-swell capacity of expansive can result in differential movement beneath foundations which is a very common cause foundation problems. Ribbed slab, often called waffle one the efficient inexpensive solutions for use under light structures resting on soils. This paper presents numerical analysis that used to calculate displac...

For two dimensional Schrr odinger operators with a nonzero constant magnetic eld perturbed by an innnite number of periodically disposed, long range magnetic and electric wells, it is proven that when the inter-well distance (R) grows to innnity, the essential spectrum near the eigenvalues of the \one well Hamiltonian" is located in mini-bands whose width shrink faster than any exponential with...