Logarithms of the values of all vulgar fractions, with numerator and denominator not exceeding 100, arranged in order of magnitude.

"Excerpt Minutes of proceedings of the Institution of Civil Engineers, vol. lxv. Session 1880-81. Part iii."

Sur le developpement des fonctions elliptiques en fractions continues.

Thesis (doctoral)--Universite de Zurich.

A Review of surface-water sediment fractions and their interactions with presistent manmade organic compounds /

Mode of access: Internet.

Randomized trial of 8 Gy in 1 versus 20 Gy in 5 fractions of radiotherapy for neuropathic pain due to bone metastases (Trans-Tasman Radiation Oncology Group, TROG 96.05)

Background and purpose: Despite numerous randomized trials investigating radiotherapy (RT) fractionation schedules for painful bone metastases, there are very few data on RT for bone metastases causing pain with a neuropathic component. The Trans-Tasman Radiation Oncology Group undertook a randomized trial comparing the efficacy of a single 8 Gy (8/1) with 20 Gy in 5 fractions (20/5) for this type of pain. Materials and methods: Eligible patients had radiological evidence of bone metastases from a known malignancy with no change in systemic therapy within 6 weeks before or anticipated within 4 weeks after RT, no other metastases along the distribution of the neuropathic pain and no clinical or radiological evidence of cord/cauda equina compression. All patients gave written informed consent. Primary endpoints were pain response within 2 months of commencement of RT and time to treatment failure (TTF). The hypothesis was that 8/1 is at least as effective as 20/5 and the planned sample size was 270 patients. Results: Between February 1996 and December 2002, 272 patients were randomized (8/1:20/5 = 137:135) from 15 centres (Australia 11, New Zealand 3, UK 1). The commonest primary cancers were lung (31%), prostate (29%) and breast (8%); index sites were spine (89%), rib (9%), other (2%); 72% of patients were males and the median age was 67 (range 2989). The median overall survival (95% CI) for all randomized patients was 4.8 mo (4.2-5.7 mo). The intention-to-treat overall response rates (95% Cl) for 8/1 vs 20/5 were 53% (45-62%) vs 61% (53-70%), P = 0.18. Corresponding figures for complete response were 26% (18-34%) vs 27% (19-35%), P = 0.89. The estimated median TTFs (95% CI) were 2.4 mo (2.0-3.3 mo) vs 3.7 mo (3.1-5.9 mo) respectively. The hazard ratio (95% Cl) for the comparison of TTF curves was 1.35 (0.99-1.85), log-rank P = 0.056. There were no statistically significant differences in the rates of re-treatment, cord compression or pathological fracture by arm. Conclusions: 8/1 was not shown to be as effective as 20/5, nor was it statistically significantly worse. Outcomes were generally poorer for 8/1, although the quantitative differences were relatively small. (c) 2004 Elsevier Ireland Ltd. All rights reserved.

Dissipation of acetochlor and its distribution in surface and sub-surface soil fractions during laboratory incubations

Pesticides in soil are subject to a number of processes that result in transformation and biodegradation, sorption to and desorption from soil components, and diffusion and leaching. Pesticides leaching through a soil profile will be exposed to changing environmental conditions as different horizons with distinct physical, chemical and biological properties are encountered. The many ways in which soil properties influence pesticide retention and degradation need to be addressed to allow accurate predictions of environmental fate and the potential for groundwater pollution. Degradation and sorption processes were investigated in a long-term (100 days) study of the chloroacetanilide herbicide, acetochlor. Soil cores were collected from a clay soil profile and samples taken from 0-30cm (surface), 1.0-1.3m (mid) and 2.7-3.0m (deep) and treated with acetochlor (2.5, 1.25, 0.67 mu g acetochlor g(-1) dry wt soil, respectively). In sterile and non-sterile conditions, acetochlor concentration in the aqueous phase declined rapidly from the surface and subsoil layers, predominantly through nonextractable residue (NER) formation on soil surfaces, but also through biodegradation and biotic transformation. Abiotic transformation was also evident in the sterile soils. Several metabolites were produced, including acetochlor-ethane sulphonic acid and acetochlor-oxanilic acid. Transformation was principally microbial in origin, as shown by the differences between non-sterile and sterile soils. NER formation increased rapidly over the first 21 days in all soils and was mainly associated with the macroaggregate (> 2000 mu m diameter) size fractions. It is likely that acetochlor is incorporated into the macroaggregates through oxidative coupling, as humification of particulate organic matter progresses. The dissipation (ie total loss of acetochlor) half-life values were 9.3 (surface), 12.3 (mid) and 12.6 days (deep) in the non-sterile soils, compared with 20.9 [surface], 23.5 [mid], and 24 days [deep] in the sterile soils, demonstrating the importance of microbially driven processes in the rapid dissipation of acetochlor in soil.

Optimization of Rational Approximations by Continued Fractions

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

Polynomials of Pellian Type and Continued Fractions

We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued fraction ex- pansion of √fk (X) is related to that of √C, where √fk (X) = ak*X^2 +bk*X + C. This continues work in [1]–[4].

Molecular characterization of Cladium peat from the Florida Everglades: biomarker associations with humic fractions

The accumulation and preservation of peat soils in Everglades freshwater marshes and mangrove swamps is an essential process in the ecological functioning of these ecosystems. Human intervention and climate change have modified nutrient dynamics and hydroperiod in the Everglades and peat loss due to such anthropogenic activities is evident. However, not much is known on the molecular level regarding the biogeochemical characteristics, which allow peat to be preserved in the Everglades. Lipid biomarkers trapped within or bound to humic-type structures can provide important geochemical information regarding the origin and microbial transformation of OM in peat. Four lipid fractions obtained from a Cladium peat, namely the freely extractable fraction and those associated with humin, humic acid, and fulvic acid fractions, showed clear differences in their molecular distribution suggesting different OM sources and structural and diagenetic states of the source material. Both, higher plant derived and microbial lipids were found in association with these humic-type substances. Most biomarker distributions suggest an increment in the microbial/terrestrial lipid ratio from the free to humin to humic to fulvic fractions. Microbial reworking of lipids, and the incorporation of microbial biomarkers into the humic-type fractions was evident, as well as the preservation of diagenetic byproducts. The lipid distribution associated with the fulvic acids suggests a high degree of microbial reworking for this fraction. Evidence for this 3D structure was obtained through the presence of the relatively high abundance of α,ω-dicarboxylic acids and phenolic and benzenecarboxylic compounds. The increment in structural complexity of the phenolic and benzencarboxylic compounds in combination with the reduction in the carbon chain length of the dicarboxylic acids from the free to fulvic fraction suggests the latter to be structurally the most stable, compacted and diagenetically altered substrate. This analytical approach can now be applied to peat samples from other areas within the Everglades ecosystem, affected differently by human intervention with the aim to assess changes in organic matter preservation.

What Teaching Strategies Can I Employ to Improve Student Achievement in the Addition of Fractions with Different Denominators?

The purpose of this action research was to determine what instructional strategies could be used to improve student achievement in fraction addition. An eighth grade intensive math class practiced multiplication facts and hands-on applications of fractions concepts for 2 months. Pretests/posttests were used to measure improvement in computation and understanding.

Analysis of Students’ Misconceptions and Error Patterns in Mathematics: The Case of Fractions

This study analyzed three fifth grade students’ misconceptions and error patterns when working with equivalence, addition and subtraction of fractions. The findings revealed that students used both conceptual and procedural knowledge to solve the problems. They used pictures, gave examples, and made connections to other mathematical concepts and to daily life topics. Error patterns found include using addition and subtraction of numerators and denominators, and finding the greatest common factor.