Special invariance properties of the [ N +1/ N ] Padé approximants in Rayleigh-Schrödinger perturbation theory

Padé approximants to the electronic energy of atoms and molecules are investigated by using the expansion parameter of Rayleigh-Schrödinger perturbation theory as a formal variable. These problems are characterized by the fact that the exact Hamiltonian is known and, although the Hamiltonian is split into a zero order and a perturbing part, the exact Hamiltonian is recovered when the expansion parameter equals unity. The present study shows that for these problems the sequence of [ N +1/ N ] Padé approximants is special in that, when the expansion parameter is set equal to unity, the numerical value of each of these approximants is invariant to two modifications in the zero-order Hamiltonian; namely, a change of scale and a shift of origin in the zero-order energy spectrum. This suggests that it is the essence of the exact Hamiltonian which produces the final energy result, rather than the arbitrary scaling of the unperturbed Hamiltonian. This formalism is particularly appropriate for ab initio perturbative calculations, where the variational principle cannot be used to determine optimal values for the scale and shift parameters.

Lateral jaw muscles of Elachistodon westermanni Reinhardt (Reptilia: Serpentes)

Lateral jaw musculature of the very rare Elachistodon is described for the first time and compared with Dasypeltis. The enormous Harderian glands of both genera and their relationships with adjacent muscles are also described. Myological differences and similarities between Elachistodon, Dasypeltis, and some generalized colubrid snakes are tabulated. The primary myological differences are found in the adductor muscles of the lower jaw. Elachistodon and Dasypeltis have a single, major adductor muscle of the lower jaw, that attaches dorsally along the length of the quadrate and ventrally along the lower jaw. This muscle probably represents a fused medialis and profundus. Both species also have a small superficialis that may play a minor role in elevating the lower jaw. The reduction in size and shift of origin of the adductors is discussed in terms of functional demands associated with egg eating. Morphological similarities indicate that Elachistodon and Dasypeltis are probably related.

Origin shifts in divergent Feynman integrals

The surface terms arising from a shift of origin in divergent Feynman integrals are considered. Sum rules and recursion relations between these terms are derived for an arbitrary degree of divergence and tensor rank. These relations are explicitly solved for linear, quadratic, cubic, and quartic divergences.

Anisotropic Loading Functions for Combined Stresses in the Plastic Range

A loading function is a relation between combined stresses for which the beginning of plastic flow takes place. The loading function for a given material is different depending upon the initial plastic strains produced. That is, the initial stress or strain history influences the subsequent loading function. This paper gives the results of an experimental investigation to determine the validity of certain loading functions proposed for anisotropic materials. The study reported was conducted for an aluminum alloy 24S-T and the state of stress covered was biaxial tension. These stresses were produced in the usual way by subjecting thin-walled tubular specimens to axial tension and internal pressure. The test results showed that none of the existing loading functions is adequate for interpreting the plastic stress-strain relations obtained. Tests also were made to determine the change in the loading function with increase in plastic flow. It was found that the loading function did not remain symmetrical with respect to the original function, nor was the new loading function the same as the original except for a shift of origin. However, the test results support in a qualitative way the concept of the so-called “yield corner.”