On Consecutive Triples Of Powerful Numbers

A powerful number is a positive integer such that every prime that appears in its prime factorization appears there at least twice. Erdős, Mollin and Walsh conjectured that three consecutive powerful numbers do not exist. This paper shows that if they do exist, the smallest of the three numbers must have remainder 7, 27, or 35 when divided by 36

Using Cox's Proportional Hazard Models to Implement Optimal Strategies: An Example from Behavioural Ecology

Simple behavioural rules, or "rules of thumb", which lead to behaviour that closely approximates an optimal strategy, have generated a lot of recent interest in the field of foraging behaviour. In this paper, we derive rules of thumb from a stochastic simulation model in which the foragers behave optimally. We use a particular biological system: the patch leaving behaviour of a parasitoid. We simulate parasitoids whose patch leaving behaviour is determined by a stochastic dynamic programming (SDP) model, while allowing parasitoids to make mistakes in their estimation of host density when arriving in a patch. We use Cox's proportional hazards models to obtain statistical rules of thumb from the simulated behaviour. This represents the first use of a proportional hazard approximation to generate rules of thumb from a complex optimal strategy

First description of a fossil chamaeleonid from Greece and its relevance for the European biogeographic history of the group

The fossil record of Chamaeleonidae is very scarce and any new specimen is therefore considered important for our understanding of the evolutionary and biogeographic history of the group. New specimens from the early Miocene of Aliveri (Evia Island), Greece constitute the only fossils of these lizards from southeastern Europe. Skull roofing material is tentatively attributed to the Czech species Chamaeleo cf. andrusovi, revealing a range extension for this taxon, whereas tooth-bearing elements are described as indeterminate chamaeleonids. The Aliveri fossils rank well among the oldest known reptiles from Greece, provide evidence for the dispersal routes of chameleons out of Africa towards the European continent and, additionally, imply strong affinities with coeval chamaeleonids from Central Europe

Effect Threshold for Selenium Toxicity in Juvenile Splittail, Pogonichthys macrolepidotus A

In fish, selenium can bioaccumulate and cause adverse impacts. One of the fish species potentially at risk from selenium in the San Francisco Bay (California, USA) is the splittail (Pogonichthys macrolepidotus). Previous studies have derived a whole body NOAEL and LOAEL of 9.0 and 12.9 mg/kg-dw, respectively, for selenium in juveniles. However, the NOAEL/LOAEL approach leaves some uncertainty regarding the threshold of toxicity. Therefore, the raw data from the original experiment was re-analyzed using a logistic regression to derive EC10 values of 0.9 mg/kg-dw in feed, 7.9 mg/kg-dw in muscle, 18.6 mg/kg-dw in liver for juvenile splittail. Selenium concentrations in the dietary items of wild splittail exceed the EC10 values derived here. Thus, deformities previously reported in wild splittail may have resulted from selenium exposures via the food chain

Texture in Louis Andriessen's "Contra Tempus" and "De Staat"

210 p.Thesis (A.Mus.D.)--University of Illinois at Urbana-Champaign, 2002.This a study of the musical texture of two works, Contra Tempus and De Staat, by composer Louis Andriessen. After an introduction and brief biography of the composer, definitions and methods of analysis in regard to the study of musical texture are established. Following this is a look at the musical texture of Andriessen's Contra Tempus and De Staat. Special attention is given to clarity and ambiguity in Andriessen's textures and how he handles qualitative and quantitative stasis and progression of textural components. Besides an overview of the texture, there is also a detailed look at the final sections of each piece. Finally, there is a comparison of the two pieces, an overview of their salient features, and an examination of their place in his musical career.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Fantasy for Piano and Orchestra. (Original Composition).

Fantasy for Piano and Orchestra is scored for large orchestra with woodwinds in twos, four horns, two trumpets, two trombones, tuba, percussion, harp, strings and solo piano. More rhapsodic in style and form than a concerto, the Fantasy strives to evoke several moods, often in a dream-like manner. There are two movements, each with similar motivic elements; these ideas occur rhythmically as well as melodically, becoming increasingly assertive in the last section of the first movement. The piano solo projects the main motives, taking them from their original contexts into contrasting material and bringing about a development. The first movement, in three sections, begins with an improvisatory introduction, followed by a quiet first section. The piano enters for the first time in this quiet passage with material similar to the improvisatory music of the introduction. The primary theme enters and recurs in variation. The second section consists of a fast playful texture and a contrasting rhythmic motive. This motive, chaotically tossed about, surprisingly leads to a dream-like cadenza. The cadenza is followed by the third major section, containing quiet material similar to that of the first. The ending music evolves into the throbbing rhythmic idea that opens the second movement. The second movement, like the first, is also in three sections. There is a short introduction consisting of the throbbing rhythmic idea mentioned above, a feature which continues into the first section, where the piano presents the main theme. A dream-like passage follows, producing a light, delicate, dance-like texture. The third section touches slightly on ideas from the second, but is prolonged by developmental material. A new and contrasting theme occurs in agitated fashion and within a dense texture. The piano makes a final statement of the dance-like theme, carrying it to its climactic height. The piece ends with a coda consisting of fragments drawn from throughout the work.Ph.D.MusicUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/159490/1/8324121.pd

A General Approach to Modeling Biphasic Relationships

Biphasic relationships can be found throughout the sciences, especially in the dose-response relationships of pharmacology, toxicology, agriculture, and nutrition. Accurate modeling of biphasic dose-response is an essential step in establishing effective guidelines for the protection of human and ecosystem health, yet currently-used biphasic mathematical models lack biological rationale and fit only limited sets of biphasic data. To model biphasic relationships more closely over wider ranges of exposures, we suggest a simple, general, biologically reasonable modeling approach leading to a family of mathematical models that combine log-logistic functions: at least one for the upslope and one for the downslope of the biphasic relationship. All parameters employed are meaningfully interpretable. These models can be used to test for the presence of biphasic effects, and they simplify to a standard log-logistic model in the special case where no biphasic effect can be detected. They offer the promise of improvement in assessment of the safety and efficacy of pharmaceuticals and nutrients as well as in determination of the toxicity of contaminants. Additionally, they may be useful in modeling nonmonotonic cause-effect relationships in other scientific disciplines