The Hartree-Fock Method Applied to Helium's Electrons

The difficulties of applying the Hartree-Fock method to many body problems is illustrated by treating Helium's electrons up to the point where tractability vanishes. Second, the problem of applying Hartree-Fock methods to the helium atom's electrons, when they are constrained to remain on a sphere, is revisited. The 6-dimensional total energy operator is reduced to a 2-dimensional one, and the application of that 2-dimensional operator in the Hartree-Fock mode is discussed.

Shadow Profit Maximization and a Generalized Measure of Inefficiency

Determining the profit maximizing input-output bundle of a firm requires data on prices. This paper shows how endogenously determined shadow prices can be used in place of actual prices to obtain the optimal input-output bundle where the firm.s shadow profit is maximized. This approach amounts to an application of the Weak Axiom of Profit Maximization (WAPM) formulated by Varian (1984) based on shadow prices rather than actual prices. At these prices the shadow profit of a firm is zero. Thus, the maximum profit that could have been attained at some other input-output bundle is a measure of the inefficiency of the firm. Because the benchmark input-output bundle is always an observed bundle from the data, it can be determined without having to solve any elaborate programming problem. An empirical application to U.S. airlines data illustrates the proposed methodology.

Labeling in the Classroom: Teacher Expectations and their Effects on Students' Academic Potential

The transition to high school can be challenging for some adolescents, resulting in drops of academic functioning (Barber & Olsen, 2004; Smith, 2006). While changes in academic demands and the disparity between adolescent needs and the environmental characteristics of high school have both been cited as possible contributors to this decrease in academic and personal functioning (Barber & Olsen, 2004), it is possible that teachers may play an even larger role in undermining these students’ functioning, specifically through labeling. Although labeling, and how it can lead to self-fulfilling prophesies, is a concept that has been thoroughly researched and applied to the field of criminology and deviant behavior, it is the goal of this current study to investigate if labeling also occurs in the classroom setting and how such labels ultimately effect the academic potential of high school students.