The googly amplitudes in gauge theory are computed by using the off shell MHV vertices with the newly proposed rules of Cachazo, Svrcek and Witten. The result is in agreement with the previously well-known results. In particular we also obtain a simple result for the all negative but one positive helicity amplitude when one of the external line is off shell.

Starting from string field theory for 2d gravity coupled to c=1 matter we analyze the off-shell tree amplitudes of discrete states. The amplitudes exhibit the pole structure and we use the off-shell calculus to extract the residues and prove that just the residues are constrained by the Ward Identities. The residues generate a simple effective action.

Excitation energies for 3l-4l8 particle-hole states of Ni-like ions are determined to second order in relativistic many body perturbation theory. The calculations start from a closed-shell Dirac-Fock potential, and include second-order Coulomb and Breit-Coulomb interactions. Retarded electric-dipole matrix elements ~in length and velocity forms! are calculated in second order for transitions fr...

The present paper provides a semi-analytical solution to obtain the displacements and stresses in a functionally graded material (FGM) rotating thick cylindrical shell with clamped ends under non-uniform pressure. Material properties of cylinder are assumed to change along the axial direction according to a power law form. It is also assumed that the Poisson’s ratio is constant. Given the exist...

The aim of this paper is to determine the critical buckling load for simply supported thin shallow spherical shells made of functionally graded material (FGM) subjected to uniform external pressure. A metal-ceramic functionally graded (FG) shell with a power law distribution for volume fraction is considered, where its properties vary gradually through the shell thickness direction from pure me...

Matching biosolids application rates to crop phosphorus (P) needs requires quantifying the P fertilizer replacement value of biosolids. Neutral ammonium citrate (NAC) extraction of P, used for assessing available P in mineral fertilizers, was evaluated for 35 different biosolids. Biosolids NAC-P was not statistically different (p 1⁄4 0.05) from total P using strong acid digestion (EPA 3051-P). ...

Using ' Cut and Paste ' technique, we develop a thin shell wormhole in heterotic string theory. We determine the surface stresses, which are localized in the shell, by using Darmois-Israel formalism. The linearized stability of this thin wormhole is also analyzed.

The shell structure of magic nuclei far from stability is discussed in terms of the self-consistent spherical Hartree-Fock-Bogoliubov theory. In particular, the sensitivity of the shell-gap sizes and the two-neutron separation energies to the choice of particle-hole and particle-particle components of the effective interaction is investigated.

The spectral statistics of low–lying states of f p shell nuclei are studied by performing large shell–model calculations with a realistic nuclear interaction. For Ca isotopes, we find deviations from the predictions of the random–matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.

We give a framework to describe gauge theory in which a nonassociative Moufang loop takes the place of the structure group. The structure of such gauge theory has many formal similarities with that of Yang-Mills theory. We extend the gauge invariance to this theory and construct an on-shell version of N = 1 supersymmetric gauge theory.