The hierarchy consists of sets k = NPPlog k n] NP. Unlike collapses in the polynomial hierarchy and the Boolean hierarchy, collapses in the hierarchy do not seem to translate up, nor does closure under complement seem to cause the hierarchy to collapse. For any consistent set of collapses and separations of levels of the hierarchy that respects P = 1 2 NP, we can construct an oracle relative to...

Via competing provers, we show that if a language A is self-reducible and has polynomial-size circuits then S2 = S2. Building on this, we strengthen the Kämper– AFK Theorem, namely, we prove that if NP ⊆ (NP ∩ coNP)/poly then the polynomial hierarchy collapses to SNP∩coNP 2 . We also strengthen Yap’s Theorem, namely, we prove that if NP ⊆ coNP/poly then the polynomial hierarchy collapses to SNP...

The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...

The dynamic response of a transversely isotropic, linearly elastic layer bonded to the surface of a half-space of a different transversely isotropic material under arbitrary shape surface loads is considered. With the help of displacements and stresses Green’s functions, an analytical formulation is presented for the determination of the displacements and stresses at any point in both surface l...