Strong Grobner bases for polynomials over a principal ideal ring

Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.

Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

An evaluation of the changes in malocclusion index scores over a 25-year period

Background: The measured values of specific traits of occlusion may be subject to significant change due to growth and maturation of the dentofacial structures. Some traits may show improvement while others may show deterioration. Rarely is there an opportunity to examine a sample of occlusions 25 years after the acquisition of the original set of records. This study examines the changes in traits of occlusion in a sample of 46 subjects who were originally examined between 1971-1973 and for whom records were again obtained in 1998. Methods: The 46 patients were a sub-group of a previously selected randomised school-based sample and study models obtained in 1971-1973 were still available. New models for each patient were obtained in 1998. Of the 46 subjects, only eight had received orthodontic treatment. Results: Assessments of the changes in specific traits were made using the methods proposed in the Harry L Draker, California Modification (HLD Cal Mod) index. This simple index was chosen because the main component traits were well defined and, when analysed separately, reflected changes with time. The total index score gave a broad indication of the global changes in the individual's occlusion. The five basic traits of the HLD index include overjet, overbite, openbite, mandibular protrusion and labio-lingual spread. Three additional traits (ectopic eruption, anterior crowding and posterior crossbite) are used in the HLD Cal Mod index. These traits provided a useful reflection of occlusal changes with time. Measurements were made with reference to specifications and the details outlined in the HLD Cal Mod protocol. The results revealed an increase in total index scores over time with a significant increase in lower labio-lingual spread associated with an increased score in anterior crowding. Overjet and overbite, however, displayed a significant decrease with time. Conclusions: These findings are in keeping with previous studies and highlight the importance of time as a significant issue in the assessment of occlusion.

Historical PCDD Inputs and Their Source Implications from Dated Sediment Cores in Queensland (Australia)

Recent investigations have demonstrated the presence of an unidentified source of polychlorinated dibenzo-p-dioxins (PCDDs) in the coastal zone of Queensland (Australia). The present study provides new information on the possible PCDD sources and their temporal input to this environment. Two estuarine sediment cores were collected in northern Queensland for which radiochemical chronologies were established. Core sections from different depositional ages, up to three centuries, have been analyzed for 2,3,7,8-substituted PCDDs and polychlorinated dibenzofurans (PCDFs). Variations of PCDD concentrations in the sediment cores over several centuries of depositional history were relatively small, and elevated PCDD levels were still present in sediment slices from the early 17th century. PCDD/F isomer patterns and congener profiles in sediments deposited during the last 350 years were almost identical and correlated well to the characteristic profiles observed in surface sediments and soils from the entire Queensland coastline. Profiles were dominated by higher chlorinated PCDDs, in particular octachlorodibenzodioxin (OCDD), whereas PCDF concentrations were below or near the limit of detection. These results indicate the presence of a PCDD source prior to industrialization and production of commercial organochlorine products. Further, the present study demonstrates that PCDD input patterns have been similar along an extensive but localized area over at least several centuries, contributing relatively high concentrations of PCDDs to the coastal system of Queensland.

Evidence for the presence of a widespread PCDD source in coastal sediments and soils from Queensland, Australia

Recent studies have demonstrated the occurrence of elevated levels of higher chlorinated PCDDs in the coastal environment of Queensland, Australia. This study presents new data for OCDD contamination and full PCDD/F profile analysis in the environment of Queensland. Marine sediments, irrigation drain sediments and topsoil were collected from sites that were expected to be influenced by specific land-use types. High OCDD concentrations were associated mainly with sediments collected near the mouth of rivers which drain into large catchments in the tropical and subtropical regions. Further, analysis of sediments from irrigation drains could be clearly differentiated on the basis of OCDD contamination, with high concentrations in samples from sugarcane drains collected from coastal regions, and low concentrations in drain sediments from drier inland cotton growing areas. PCDD/F congener-specific analysis demonstrated almost identical congener profiles in all samples collected along the coastline. This indicates the source to be widespread. Profiles were dominated by higher chlorinated PCDDs, in particular OCDD whereas 2,3,7,8-substituted PCDFs were below the limit of quantification in the majority of samples. The full PCDD/F profile analysis of samples strongly resemble those reported for lake sediments from Mississippi and kaolinite samples from Germany, Strong similarities to these samples with respect to congener profiles and isomer patterns may indicate the presence of a similar source and/or formation process that is yet unidentified. (C) 2001 Elsevier Science Ltd. All rights reserved.

Responses of sugarcane, maize, and soybean to phosphorus and vesicular-arbuscular mycorrhizal fungi

The presence of vesicular-arbuscular mycorrhizal (VAM) fungi in long-term cane-growing fields associated with yield decline led to the supposition that VAM fungi may be responsible for the poor yields. A glasshouse trial was established to test the effectiveness of a species of VAM fungi, Glomus clarum, extracted from one of these North Queensland fields on the growth of sugarcane (Saccharum interspecific hybrid), maize (Zea mays), and soybean (Glycine max) for 6 phosphorus (P) rates (0, 2.7, 8.2, 25, 74, 222 mg/kg). For maize and soybean plants that received VAM (+ VAM), root colonisation was associated with enhanced P uptake, improved dry weight (DW) production, and higher index tissue-P concentrations than those without VAM (-VAM). By comparing DW responses of maize and soybean for different P rates, savings in fertiliser P of up to 160 and 213 kg/ha, respectively, were realised. Sugarcane plants were generally less responsive. Apart from a 30% DW increase with VAM when 2.7 mg P/kg was added, DW of +VAM plants was equivalent to, or worse than in the case of 222 mg P/kg, DW of -VAM plants. For all 3 host species, colonisation was least at the highest P application, presumably from excessive P within the plant tissue. Critical P concentrations for the 3 host species were below those reported elsewhere, and for soybean and sugarcane, the critical concentration for +VAM plants was lower than that of -VAM plants. There are 3 implications that arise from this study. First, VAM fungi present in cane-growing soils can promote the growth of maize and soybean, which are potential rotation crops, over a range of P levels. Second, the mycorrhizal strain taken from this site did not generally contribute to a yield decline in sugarcane plants. Third, application of P fertiliser is not necessary for sugarcane when acid-extractable P is