On the number of trees with n terminal nodes

Number of trees with arbitrary number of terminal node

Spin Dynamics of a Canted Antiferromagnet in a Magnetic Field

The spin dynamics of a canted antiferromagnet with a quadratic spin-wave dispersion near \vq =0 is shown to possess a unique signature. When the anisotropy gap is negligible, the spin-wave stiffness \dsw (\vq, B) = (\omega_{\vq}-B)/q^2 depends on whether the limit of zero field or zero wavevector is taken first. Consequently, \dsw is a strong function of magnetic field at a fixed wavevector. Even in the presence of a sizeable anisotropy gap, the field dependence of both \dsw and the gap energy distinguishes a canted antiferromagnet from a phase-separated mixture containing both ferromagnetic and antiferromagnetic regions.Comment: 10 pages, 3 figure

Outline bibliography, and KWIC index on mechanical theorem proving and its applications

Bibliography and KWIC index on mechanical theorem proving and its application

The value of improved (ERS) information based on domestic distribution effects of U.S. agriculture crops

The value of improving information for forecasting future crop harvests was investigated. Emphasis was placed upon establishing practical evaluation procedures firmly based in economic theory. The analysis was applied to the case of U.S. domestic wheat consumption. Estimates for a cost of storage function and a demand function for wheat were calculated. A model of market determinations of wheat inventories was developed for inventory adjustment. The carry-over horizon is computed by the solution of a nonlinear programming problem, and related variables such as spot and future price at each stage are determined. The model is adaptable to other markets. Results are shown to depend critically on the accuracy of current and proposed measurement techniques. The quantitative results are presented parametrically, in terms of various possible values of current and future accuracies

EXIST's Gamma-Ray Burst Sensitivity

We use semi-analytic techniques to evaluate the burst sensitivity of designs for the EXIST hard X-ray survey mission. Applying these techniques to the mission design proposed for the Beyond Einstein program, we find that with its very large field-of-view and faint gamma-ray burst detection threshold, EXIST will detect and localize approximately two bursts per day, a large fraction of which may be at high redshift. We estimate that EXIST's maximum sensitivity will be ~4 times greater than that of Swift's Burst Alert Telescope. Bursts will be localized to better than 40 arcsec at threshold, with a burst position as good as a few arcsec for strong bursts. EXIST's combination of three different detector systems will provide spectra from 3 keV to more than 10 MeV. Thus, EXIST will enable a major leap in the understanding of bursts, their evolution, environment, and utility as cosmological probes.Comment: 25 pages, 10 figures, accepted by Ap

Proposed Next Generation GRB Mission: EXIST

A next generation Gamma Ray Burst (GRB) mission to follow the upcoming Swift mission is described. The proposed Energetic X-ray Imaging Survey Telescope, EXIST, would yield the limiting (practical) GRB trigger sensitivity, broad-band spectral and temporal response, and spatial resolution over a wide field. It would provide high resolution spectra and locations for GRBs detected at GeV energies with GLAST. Together with the next generation missions Constellation-X, NGST and LISA and optical-survey (LSST) telescopes, EXIST would enable GRBs to be used as probes of the early universe and the first generation of stars. EXIST alone would give ~10-50" positions (long or short GRBs), approximate redshifts from lags, and constrain physics of jets, orphan afterglows, neutrinos and SGRs.Comment: 4 pages, 4 figures. Presented at Woods Hole GRB Conf. (2001); to appear in AIP Conf. Pro

Destruction of first-order phase transition in a random-field Ising model

The phase transitions that occur in an infinite-range-interaction Ising ferromagnet in the presence of a double-Gaussian random magnetic field are analyzed. Such random fields are defined as a superposition of two Gaussian distributions, presenting the same width $\sigma$. Is is argued that this distribution is more appropriate for a theoretical description of real systems than its simpler particular cases, i.e., the bimodal ($\sigma=0$) and the single Gaussian distributions. It is shown that a low-temperature first-order phase transition may be destructed for increasing values of $\sigma$, similarly to what happens in the compound $Fe_{x}Mg_{1-x}Cl_{2}$, whose finite-temperature first-order phase transition is presumably destructed by an increase in the field randomness.Comment: 13 pages, 3 figure

LOTIS Upper Limits and the Prompt OT from GRB 990123

GRB 990123 established the existence of prompt optical emission from gamma-ray bursts (GRBs). The Livermore Optical Transient Imaging System (LOTIS) has been conducting a fully automated search for this kind of simultaneous low energy emission from GRBs since October 1996. Although LOTIS has obtained simultaneous, or near simultaneous, coverage of the error boxes obtained with BATSE, IPN, XTE, and BeppoSAX for several GRBs, image analysis resulted in only upper limits. The unique gamma-ray properties of GRB 990123, such as very large fluence (top 0.4%) and hard spectrum, complicate comparisons with more typical bursts. We scale and compare gamma-ray properties, and in some cases afterglow properties, from the best LOTIS events to those of GRB 990123 in an attempt to determine whether the prompt optical emission of this event is representative of all GRBs. Furthermore, using LOTIS upper limits in conjunction with the relativistic blast wave model, we weakly constrain the GRB and afterglow parameters such as density of the circumburster medium and bulk Lorentz factor of the ejecta.Comment: 5 pages, 2 figures, To appear in Proceedings of the 5th Huntsville Gamma-Ray Burst Symposiu