Marital Deduction Formulae—A Planner’s Guide

The marital deduction formula bequest exists principally as a means of minimizing federal estate taxes. Considerations apart from the estate tax, however, have had a substantial effect upon the form of such clauses, and a 1964 pronouncement by the Internal Revenue Service has circumscribed their continued utility. The author examines the basic formula clauses, setting out the characteristics of each, the respects in which they differ, the objectives each is designed to secure, and the factors to be weighed by the draftsman who wishes to utilize a formula bequest to achieve a maximum federal estate tax marital deduction

Assessing the Early Holocene Environment of Northwestern Guyana: An Isotopic Analysis of Human and Faunal Remains

This study used stable carbon δ13C and oxygen δ18O isotope compositions data to assess the extent to which diet breadths of northwestern Guyana changed during the Holocene. We analyzed human bone and enamel remains from seven shell mound sites dating between 7500 and 2600 BP. Our analyses demonstrate some degree of constancy in the availability of C3 plants during the past several thousand years—though we note an increasing reliance on such plants beginning in the Early Holocene. We also document warming intervals during the Early Holocene (Early Archaic), which appear to correlate with dry periods known elsewhere in the central Amazon during this period

Output Mode Switching for Parallel Five-bar Manipulators Using a Graph-based Path Planner

The configuration manifolds of parallel manipulators exhibit more nonlinearity than serial manipulators. Qualitatively, they can be seen to possess extra folds. By projecting such manifolds onto spaces of engineering relevance, such as an output workspace or an input actuator space, these folds cast edges that exhibit nonsmooth behavior. For example, inside the global workspace bounds of a five-bar linkage appear several local workspace bounds that only constrain certain output modes of the mechanism. The presence of such boundaries, which manifest in both input and output projections, serve as a source of confusion when these projections are studied exclusively instead of the configuration manifold itself. Particularly, the design of nonsymmetric parallel manipulators has been confounded by the presence of exotic projections in their input and output spaces. In this paper, we represent the configuration space with a radius graph, then weight each edge by solving an optimization problem using homotopy continuation to quantify transmission quality. We then employ a graph path planner to approximate geodesics between configuration points that avoid regions of low transmission quality. Our methodology automatically generates paths capable of transitioning between non-neighboring output modes, a motion which involves osculating multiple workspace boundaries (local, global, or both). We apply our technique to two nonsymmetric five-bar examples that demonstrate how transmission properties and other characteristics of the workspace can be selected by switching output modes.Comment: 7 pages, 6 figure

Excitation spectrum and instability of a two-species Bose-Einstein condensate

We numerically calculate the density profile and excitation spectrum of a two-species Bose-Einstein condensate for the parameters of recent experiments. We find that the ground state density profile of this system becomes unstable in certain parameter regimes, which leads to a phase transition to a new stable state. This state displays spontaneously broken cylindrical symmetry. This behavior is reflected in the excitation spectrum: as we approach the phase transition point, the lowest excitation frequency goes to zero, indicating the onset of instability in the density profile. Following the phase transition, this frequency rises again.Comment: 8 pages, 5 figures, uses REVTe

Coherence properties of an atom laser

We study the coherence properties of an atom laser, which operates by extracting atoms from a gaseous Bose-Einstein condensate via a two-photon Raman process, by analyzing a recent experiment. We obtain good agreement with the experimental data by solving the time-dependent Gross-Pitaevskii equation in three dimensions both numerically and with a Thomas-Fermi model. The coherence length is strongly affected by the space-dependent phase developed by the condensate when the trapping potential is turned off.Comment: 11 pages, 2 Postscript figure

Force distributions in a triangular lattice of rigid bars

We study the uniformly weighted ensemble of force balanced configurations on a triangular network of nontensile contact forces. For periodic boundary conditions corresponding to isotropic compressive stress, we find that the probability distribution for single-contact forces decays faster than exponentially. This super-exponential decay persists in lattices diluted to the rigidity percolation threshold. On the other hand, for anisotropic imposed stresses, a broader tail emerges in the force distribution, becoming a pure exponential in the limit of infinite lattice size and infinitely strong anisotropy.Comment: 11 pages, 17 figures Minor text revisions; added references and acknowledgmen