GENERATION OF FORESTS ON TERRAIN WITH DYNAMIC LIGHTING AND SHADOWING

The purpose of this research project is to exhibit an efficient method of creating dynamic lighting and shadowing for the generation of forests on terrain. In this research project, I use textures which contain images of trees from a bird’s eye view in order to create a high scale forest. Furthermore, by manipulating the transparency and color of the textures according to the algorithmic calculations of light and shadow on terrain, I provide the functionality of dynamic lighting and shadowing. Finally, by analyzing the OpenGL pipeline, I design my code in order to allow efficient rendering of the forest

On the spectrum of shear flows and uniform ergodic theorems

The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a purely singular continuous spectrum is provided. For flows admitting more regular spectra the density of states is analyzed, and spaces on which it is uniformly bounded are identified. As an application, an ergodic theorem with uniform convergence is proved.Comment: 18 pages, no figure

Lack of Finite Characterizations for the Distance-based Revision

Lehmann, Magidor, and Schlechta developed an approach to belief revision based on distances between any two valuations. Suppose we are given such a distance D. This defines an operator |D, called a distance operator, which transforms any two sets of valuations V and W into the set V |D W of all elements of W that are closest to V. This operator |D defines naturally the revision of K by A as the set of all formulas satisfied in M(K) |D M(A) (i.e. those models of A that are closest to the models of K). This constitutes a distance-based revision operator. Lehmann et al. characterized families of them using a loop condition of arbitrarily big size. An interesting question is whether this loop condition can be replaced by a finite one. Extending the results of Schlechta, we will provide elements of negative answer. In fact, we will show that for families of distance operators, there is no "normal" characterization. Approximatively, a normal characterization contains only finite and universally quantified conditions. These results have an interest of their own for they help to understand the limits of what is possible in this area. Now, we are quite confident that this work can be continued to show similar impossibility results for distance-based revision operators, which suggests that the big loop condition cannot be simplified

Preferential and Preferential-discriminative Consequence relations

The present paper investigates consequence relations that are both non-monotonic and paraconsistent. More precisely, we put the focus on preferential consequence relations, i.e. those relations that can be defined by a binary preference relation on states labelled by valuations. We worked with a general notion of valuation that covers e.g. the classical valuations as well as certain kinds of many-valued valuations. In the many-valued cases, preferential consequence relations are paraconsistant (in addition to be non-monotonic), i.e. they are capable of drawing reasonable conclusions which contain contradictions. The first purpose of this paper is to provide in our general framework syntactic characterizations of several families of preferential relations. The second and main purpose is to provide, again in our general framework, characterizations of several families of preferential discriminative consequence relations. They are defined exactly as the plain version, but any conclusion such that its negation is also a conclusion is rejected (these relations bring something new essentially in the many-valued cases).Comment: team Logic and Complexity, written in 2004-200

Instability of Nonmonotone Magnetic Equilibria of the Relativistic Vlasov-Maxwell System

We consider the question of linear instability of an equilibrium of the Relativistic Vlasov-Maxwell (RVM) System that has a strong magnetic field. Standard instability results deal with systems where there are fewer particles with higher energies. In this paper we extend those results to the class of equilibria for which the number of particles does not depend monotonically on the energy. Without the standard sign assumptions, the analysis becomes significantly more involved.Comment: 46 page

Assessment of Pelagic Food Webs in Mendums Pond, NH

This study focused on the relationship between plankton in Mendums Pond, NH. A grazing experiment was conducted to determine the effect of zooplankton on the phytoplankton population. The phytoplankton were largely composed of net plankton (75 %) and this fraction was dominated by cyanobacteria (84.5 %) even though this was a slightly acidic system. Data indicated that the mean body length of zooplankton increased with depth. The average body length of Daphnia ranged from 1.4 mm in the epilimnion to 1.9 mm in the hypolimnion. Copepods followed a similar trend increasing in average body length from 0.85 mm to 0.95 mm. The high numbers of cyanobacteria and copepods resulted in a 17.92 % day-1 grazing rate indicating that almost 18 % of the total lake water was filtered every day by the zooplankton. This also suggests that the phytoplankton are reproducing at a higher rate than they are being consumed by grazers. This may raise concerns about the future diversity of the food web as cyanobacteria reproduce and become more dominant in this system

Approximations of strongly continuous families of unbounded self-adjoint operators

The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approximations is constructed. An important feature of these approximations is that they are valid for the entire family uniformly. An application of this result to the study of plasma instabilities is illustrated.Comment: 22 pages, final version to appear in Commun. Math. Phy