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.

A servicing strategy for items sold under warranty

When repairable items sold under warranty fail, the rectification action taken by the manufacturer can be either a repair or a replacement, In this paper a new repair-replacement strategy is proposed for the manufacturer when the items are sold with a non-renewing free replacement warranty policy. The strategy involves splitting the warranty period into two intervals where only repairs are carried out, separated by a third interval with at most one replacement.

Breaking the deadlock over an Australian trial of injectable opioid maintenance

INJECTABLE HEROIN MAINTENANCE has been advocated as a form of treatment for opioid dependence that would attract, and retain in treatment, addicts who have either not sought treatment or who have failed at other forms of treatment, including methadone maintenance. Advocates of heroin maintenance argue that it would increase the proportion of addicts in treatment and reduce heroin use, drug related crime, and deaths due to overdose.

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

GH treatment in adults with chronic liver disease: A randomized, double-blind, placebo-controlled, cross-over study

Patients with chronic liver disease (CLD) are catabolic and GH-resistant. The effects of supraphysiological recombinant human GH (rhGH; 0.2 IU.kg(-1).d(-1)) treatment in adults with CLD were assessed in a randomized, double-blind, placebo-controlled cross-over trial (4-wk dietary run-in, 4-wk treatment, and 2-wk wash-out phases). Nine adults with mild- to moderate-severity CLD participated (median age, 49 yr; three males and six females; Child's classification A in six and B in three). Biopsy-proven etiologies were: alcohol (four patients), primary biliary cirrhosis (three patients), non-A, non-B, non-C hepatitis (one patient), and cryptogenic (one patient). Treatment with rhGH increased serum IGF-I (median increase over placebo, +93 mug.liter(-1); P = 0.004), IGF-binding protein-3 (+0.9 mg.liter(-1): P = 0.004), and acid labile subunit (+10.7 nM; P = 0.004). Total body potassium (+8.0 g; P = 0.023), body weight (+1.6 kg; P = 0.008), and total body water (by bioelectrical impedance; +4.9 kg; P = 0.004) increased. Resting metabolic rate (+313 ml.kg(-1).min(-1); P = 0.004) and lipid oxidation (+1072.0 kcal.d(-1); P = 0.032) increased. Metabolic changes included increased fasting plasma glucose (+1.2 mm; P = 0.008), insulin (+33.8 mU.liter(-1); P = 0.004), C-peptide (+0.7 nM; P = 0.004), and free-fatty acids (+0.1 mEq.liter(-1); P = 0.04). Clinical side effects included worsening edema and ascites. Hepatocellular function did not change. Therefore, rbGH treatment in CLD: 1) overcame hepatic GH resistance; 2) may have improved whole-body protein catabolism; 3) increased lipolysis and lipid oxidation; 4) increased insulin resistance; and 5) had potent antinatriuretic effects. Long-term safety and efficacy require further assessment.

Benefits, harms and costs of screening mammography in women 70 years and over: a systematic review

Objective: To assess the (i) benefits, (ii) harms and (iii) costs of continuing mammographic screening for women 70 years and over. Data sources and synthesis: (i) We conducted a MEDLINE search (1966 - July 2000) for decision-analytic models estimating life-expectancy gains from screening in older women. The five studies meeting the inclusion criteria were critically appraised using standard criteria. We estimated relative benefit from each model's estimate of effectiveness of screening in older women relative to that in women aged 50-69 years using the same model. (ii) With data from BreastScreen Queensland, we constructed balance sheets of the consequences of screening for women in 10-year age groups (40-49 to 80-89 years), and (iii) we used a validated model to estimate the marginal cost-effectiveness of extending screening to women 70 years and over. Results: For women aged 70-79 years, the relative benefit was estimated as 40%-72%, and 18%-62% with adjustment for the impact of screening on quality of life. For women over 80 years the relative benefit was about a third, and with quality-of-life adjustment only 14%, that in women aged 50-69 years. (ii) Of 10 000 Australian women participating in ongoing screening, about 400 are recalled for further testing, and, depending on age, about 70-112 undergo biopsy and about 19-80 cancers are detected. (iii) Cost-effectiveness estimates for extending the upper age limit for mammographic screening from 69 to 79 years range from $8119 to $27 751 per quality-adjusted life-year saved, which compares favourably with extending screening to women aged 40-49 years (estimated at between $24 000 and $65 000 per life-year saved). Conclusions: Women 70 years and over, in consultation with their healthcare providers, may want to decide for themselves whether to continue mammographic screening. Decision-support materials are needed for women in this age group.

Tillering in grain sorghum over a wide range of population densities: Identification of a common hierarchy for tiller emergence, leaf area development and fertility

Most studies of tiller development have not related the physiological and morphological features of each calm to its subsequent fertility. This introduced problems when trying to account for the effects of tillering on yield in crop models. The objective of this study was to detect the most likely early determinants of tiller fertility in sorghum by identifying hierarchies for emergence, fertility and grain number of tillers over a wide range of assimilate availabilities. Emergence, phenology, leaf area development and dry weight partitioning were quantified weekly for individual tillers and main culms of tillering and uniculm plants grown at one of four densities, from two to 16 plants m(-2). For a given plant in any given density, the same tiller hierarchy applied for emergence of tillers, fertility of the emerged tillers and their subsequent grain number. These results were observed over a range of tiller fertility rates (from 7 to 91%), fertile tiller number per plant at maturity (from 0.2 to 4.7), and tiller contribution to grain yield (from 5 to 78%). Tiller emergence was most probably related to assimilate supply and light quality. Development, fertility and contribution to yield of a specific tiller were highly dependent on growing conditions at the time of tiller emergence, particularly via early leaf area development of the tiller, which affected its subsequent leaf area accumulation. Assimilate availability in the main culm at the time of tiller emergence was the most likely early determinant of subsequent tiller fertility in this study. (C) 2002 Annals of Botany Company.

Tillering in grain sorghum over a wide range of population densities: Modelling dynamics of tiller fertility

The prediction of tillering is poor or absent in existing sorghum crop models even though fertile tillers contribute significantly to grain yield. The objective of this study was to identify general quantitative relationships underpinning tiller dynamics of sorghum for a broad range of assimilate availabilities. Emergence, phenology, leaf area development and fertility of individual main calms and tillers were quantified weekly in plants grown at one of four plant densities ranging from two to 16 plants m(-2). On any given day, a tiller was considered potentially fertile (a posteriori) if its number of leaves continued to increase thereafter. The dynamics of potentially fertile tiller number per plant varied greatly with plant density, but could generally be described by three determinants, stable across plant densities: tiller emergence rate aligned with leaf ligule appearance rate; cessation of tiller emergence occurred at a stable leaf area index; and rate of decrease in potentially fertile tillers was linearly related to the ratio of realized to potential leaf area growth. Realized leaf area growth is the measured increase in leaf area, whereas potential leaf area growth is the estimated increase in leaf area if all potentially fertile tillers were to continue to develop. Procedures to predict this ratio, by estimating realized leaf area per plant from intercepted radiation and potential leaf area per plant from the number and type of developing axes, are presented. While it is suitable for modelling tiller dynamics in grain sorghum, this general framework needs to be validated by testing it in different environments and for other cultivars. (C) 2002 Annals of Botany Company.

Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state

A thermodynamic approach based on the Bender equation of state is suggested for the analysis of supercritical gas adsorption on activated carbons at high pressure. The approach accounts for the equality of the chemical potential in the adsorbed phase and that in the corresponding bulk phase and the distribution of elements of the adsorption volume (EAV) over the potential energy for gas-solid interaction. This scheme is extended to subcritical fluid adsorption and takes into account the phase transition in EAV The method is adapted to gravimetric measurements of mass excess adsorption and has been applied to the adsorption of argon, nitrogen, methane, ethane, carbon dioxide, and helium on activated carbon Norit R I in the temperature range from 25 to 70 C. The distribution function of adsorption volume elements over potentials exhibits overlapping peaks and is consistently reproduced for different gases. It was found that the distribution function changes weakly with temperature, which was confirmed by its comparison with the distribution function obtained by the same method using nitrogen adsorption isotherm at 77 K. It was shown that parameters such as pore volume and skeleton density can be determined directly from adsorption measurements, while the conventional approach of helium expansion at room temperature can lead to erroneous results due to the adsorption of helium in small pores of activated carbon. The approach is a convenient tool for analysis and correlation of excess adsorption isotherms over a wide range of pressure and temperature. This approach can be readily extended to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).