We present a numerical method which accurately computes the discrete spectrum and associated bound states of semi-infinite Hamiltonians model electronic “edge” localized at boundaries one- two-dimensional crystalline materials. The problem is nontrivial since arbitrarily large finite “hard” (Dirichlet) truncations Hamiltonian in infinite bulk direction tend to produce spurious partially support...

The role of the operator-product expansion in QCD calculations is discussed. Approximating the two-point correlation function by several terms and assuming an upper bound on the truncation error along the euclidean ray, we consider two model situations to examine how the bound develops with increasing deflection from the euclidean ray towards the cut. We obtain explicit bounds on the truncation...

We generalize the theory of sheaves to chamber systems. We prove that, given a chamber system C and a family R of proper residues of C containing all residues of rank c1, every sheaf defined over R admits a completion which extends C. We also prove that, under suitable hypotheses, a sheaf defined over a truncation of C can be extended to a sheaf for C. In the last section of this paper, we appl...

Previous studies find that small stocks have higher average returns than large stocks, and the difference between the returns can not be accounted for by the systematic risk, b. In my analysis of Compustat and CRSP data from 1976 to 1995, and simulation experiments based on the data, I find the size effect can be largely explained by data truncation that is caused by survival. Small stocks’ ret...

The a-posteriori error evaluation based on differential approximation of a finite-difference scheme and adjoint equations is addressed. The differential approximation is composed of primal equations and a local truncation error determined by a Taylor series in Largange form. This approach provides the feasibility of both refining the solution and using the Holder inequality for asymptotic bound...