Groups whose word problems are not semilinear

Suppose that G is a finitely generated group and W is the formal language of words defining the identity in G. We prove that if G is a nilpotent group, the fundamental group of a finite volume hyperbolic three-manifold, or a right-angled Artin group whose graph lies in a certain infinite class, then W is not a multiple context free language

Granular Impact Model as an Energy-Depth Relation

Velocity-squared drag forces are common in describing an object moving through a granular material. The resulting force law is a nonlinear differential equation, and closed-form solutions of the dynamics are typically obtained by making simplifying assumptions. Here, we consider a generalized version of such a force law which has been used in many studies of granular impact. We show that recasting the force law into an equation for the kinetic energy versus depth, K(z), yields a linear differential equation, and thus general closed-form solutions for the velocity versus depth. This approach also has several advantages in fitting such models to experimental data, which we demonstrate by applying it to data from 2D impact experiments. We also present new experimental results for this model, including shape and depth dependence of the velocity-squared drag force

A project to evaluate moisture stress in corn and soybean areas of western and southwestern Minnesota

Remote sensing techniques, particularly LANDSAT data, were used to assess soil moisture stress through crop signature in southwestern Minnesota. Related objectives were: localization of droughty, well drained, and poorly drained soils; detection of stress from hail, wind, and disease damage; and the use of remote sensing data for agricultural management. Since the amount and distribution of precipitation were adequate during the 1977 and 1978 growing seasons, no significant stress occurred. Crop conditions were very favorable. As a result, crop signatures were too uniform to reflect soilscape variations and crop condition changes. In 1979 precipitation was again adequate to excess, particularly in June and August. In some cases, poorly drained sites especially, stress conditions developed as a result of excess of water and could be identified on color infrared photographs

Matrix Representation of Octonions and Generalizations

We define a special matrix multiplication among a special subset of 2N\x 2N matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative non-associative and when they become associative. In particular, these algebras yield special matrix representations of octonions and complex numbers; they naturally lead to the Cayley-Dickson doubling process. Our matrix representation of octonions also yields elegant insights into Dirac's equation for a free particle. A few other results and remarks arise as byproducts.Comment: 18 printed page

Diagnostic Efficacy of Morphological Characters of Larval \u3ci\u3eTramea Lacerata\u3c/i\u3e Hagen and \u3ci\u3eTramea Onusta\u3c/i\u3e Hagen (Odonata: Libellulidae) in the Prairie Region of Missouri

Distinguishing among species of larvae of the dragonfly genus Tramea historically has been problematic, largely due to conflicting characterizations of the larvae of T. lacerata Hagen and T. onusta Hagen (Odonata: Libellulidae) in the literature. The various systematic treatments usually focused on relative lengths of morphological characters to distinguish the species, but often contradicted one another and themselves as to what the diagnostic values actually were. We traced much of the confusion back to errors in the original larval description of T. onusta. We used morphometric analyses to determine the efficacy of previously published characterizations to distinguish between the larvae of T. lacerata and T. onusta. Previous characterizations, especially those involving relative lengths of the caudal appendages, were generally found to be inadequate for distinguishing larvae of the two species. The most reliable characteristic for distinguishing the two species was found to be the length of the epiproct relative to the length of the paraprocts

Quasilinear theory of the 2D Euler equation

We develop a quasilinear theory of the 2D Euler equation and derive an integro-differential equation for the evolution of the coarse-grained vorticity. This equation respects all the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive a H-theorem for the Fermi-Dirac entropy and make the connection with statistical theories of 2D turbulence.Comment: 4 page

Using parallel computation to improve Independent Metropolis--Hastings based estimation

In this paper, we consider the implications of the fact that parallel raw-power can be exploited by a generic Metropolis--Hastings algorithm if the proposed values are independent. In particular, we present improvements to the independent Metropolis--Hastings algorithm that significantly decrease the variance of any estimator derived from the MCMC output, for a null computing cost since those improvements are based on a fixed number of target density evaluations. Furthermore, the techniques developed in this paper do not jeopardize the Markovian convergence properties of the algorithm, since they are based on the Rao--Blackwell principles of Gelfand and Smith (1990), already exploited in Casella and Robert (1996), Atchade and Perron (2005) and Douc and Robert (2010). We illustrate those improvements both on a toy normal example and on a classical probit regression model, but stress the fact that they are applicable in any case where the independent Metropolis-Hastings is applicable.Comment: 19 pages, 8 figures, to appear in Journal of Computational and Graphical Statistic

Interstellar extinction at 10-20 microns

The IRAS low-resolution spectra (LRS) spectra of 117 stars of excellent signal/noise with optically thin silicate dust shells were analyzed. The stellar continua (assumed to be a cool black body) were subtracted, and the resulting dust shell spectra were fit with simple models F(sub lambda) assuming uniform mass loss and dust temperature as a function of distance from the star, calculated using the optical constants for silcates of Draine (1985). From the comparison of the spectra and the models, functions for the emissivity, kappa(sub lambda), were derived