Triaxial projected shell model approach

The projected shell model analysis is carried out using the triaxial Nilsson+BCS basis. It is demonstrated that, for an accurate description of the moments of inertia in the transitional region, it is necessary to take the triaxiality into account and perform the three-dimensional angular-momentum projection from the triaxial Nilsson+BCS intrinsic wavefunction.Comment: 9 pages, 2 figure

A New Approach for Gay and Lesbian Domestic Partners: Legal Acceptance Through Relational Property Theory

In the past twenty years, the number of couples living together on a long-term basis without marrying has dramatically increased. 1 With the increase in domestic partnerships 2 has come new litigation in which one scorned domestic partner sues the other, claiming a right to property procured during the relationship. Often, one partner brought more present or future financial resources to the relationship than the other. The wealthier partner may have placed some or all of the property acquired during the relationship in her name only for a variety of seemingly innocuous reasons (e.g., business expertise, tax benefits, facilitation of financial management); nonetheless, the result is that one partner has title to the assets while the other partner has nothing. In fact, such a situation is similar to marriage, where one spouse typically enters the union with more assets, business expertise, or earning potential than the other. As this Note argues, the key difference between spouses and domestic partners, however, is that marital dissolution statutes protect spouses. Domestic partners must rely on scattered judicial decisions which often do not agree on the proper theory a domestic partner should advance in order to state a claim. The problems a domestic partner faces are compounded when the plaintiff making the property claim is gay or lesbian. Homosexuals are not a protected class, which means that they can be discriminated against as long as there is a rational basis for the statutory distinction and a legitimate government interest.

Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals

We consider nearest-neighbor self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on ${\mathbb{Z}}^d$. The two-point functions of these models are respectively the generating function for self-avoiding walks from the origin to $x\in{\mathbb{Z}}^d$, the probability of a connection from the origin to $x$, and the generating functions for lattice trees or lattice animals containing the origin and $x$. Using the lace expansion, we prove that the two-point function at the critical point is asymptotic to $\mathit{const.}|x|^{2-d}$ as $|x|\to\infty$, for $d\geq 5$ for self-avoiding walk, for $d\geq19$ for percolation, and for sufficiently large $d$ for lattice trees and animals. These results are complementary to those of [Ann. Probab. 31 (2003) 349--408], where spread-out models were considered. In the course of the proof, we also provide a sufficient (and rather sharp if $d>4$) condition under which the two-point function of a random walk on ${{\mathbb{Z}}^d}$ is asymptotic to $\mathit{const.}|x|^{2-d}$ as $|x|\to\infty$.Comment: Published in at http://dx.doi.org/10.1214/009117907000000231 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org