INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

Integral group ring of the Suzuki sporadic simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle`s conjecture on prime graphs.

Determination of vertebral range of motion using inertial measurement units in 27 Franches-Montagnes stallions and comparison between conditions and with a mixed population

REASONS FOR PERFORMING STUDY: The diagnosis of equine back disorders is challenging. Objectively determining movement of the vertebral column may therefore be of value in a clinical setting. OBJECTIVES: To establish whether surface-mounted inertial measurement units (IMUs) can be used to establish normal values for range of motion (ROM) of the vertebral column in a uniform population of horses trotting under different conditions. STUDY DESIGN: Vertebral ROM was established in Franches-Montagnes stallions and a general population of horses and the variability in measurements compared between the two groups. Repeatability and the influence of specific exercise condition (on ROM) were assessed. Finally, attempts were made to explain the findings of the study through the evaluation of factors that might influence ROM. METHODS: Dorsoventral (DV) and mediolateral (ML) vertebral ROM was measured at a trot under different exercise conditions in 27 Franches-Montagnes stallions and six general population horses using IMUs distributed over the vertebral column. RESULTS: Variability in the ROM measurements was significantly higher for general population horses than for Franches-Montagnes stallions (both DV and ML ROM). Repeatability was strong to very strong for DV measurements and moderate for ML measurements. Trotting under saddle significantly reduced the ROM, with sitting trot resulting in a significantly lower ROM than rising trot. Age is unlikely to explain the low variability in vertebral ROM recorded in the Franches-Montagnes horses, while this may be associated with conformational factors. CONCLUSIONS: It was possible to establish a normal vertebral ROM for a group of Franches-Montagnes stallions. While within-breed variation was low in this population, further studies are necessary to determine variation in vertebral ROM for other breeds and to assess their utility for diagnosis of equine back disorders.

Assessment of groups in a network organization based on the Shapley group value.

The focus of this paper is the assessment of groups of agents or units in a network organization. Given a social network, the relations between agents are modeled by means of a graph, and its functionality will be codified by means of a cooperative game. Building on previous work of Gomez et al. (2003) for the individual case, we propose a Myerson group value to evaluate the ability of each group of agents inside the social network to achieve the organization's goals. We analyze this centrality measure, and in particular we offer several decompositions that facilitate obtaining a precise interpretation of it.

Isomorphism of Commutative Modular Group Algebras

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.

Units of F5kD10

2000 Mathematics Subject Classification: 20C05, 16U60, 16S84, 15A33.

Writing together, learning together : the value and effectiveness of a research writing group for doctoral students

The high level of scholarly writing required for a doctoral thesis is a challenge for many research students. However, formal academic writing training is not a core component of many doctoral programs. Informal writing groups for doctoral students may be one method of contributing to the improvement of scholarly writing. In this paper, we report on a writing group that was initiated by an experienced writer and higher degree research supervisor to support and improve her doctoral students’ writing capabilities. Over time, this group developed a workable model to suit their varying needs and circumstances. The model comprised group sessions, an email group, and individual writing. Here, we use a narrative approach to explore the effectiveness and value of our research writing group model in improving scholarly writing. The data consisted of doctoral students’ reflections to stimulus questions about their writing progress and experiences. The stimulus questions sought to probe individual concerns about their own writing, what they had learned in the research writing group, the benefits of the group, and the disadvantages and challenges to participation. These reflections were analysed using thematic analysis. Following this analysis, the supervisor provided her perspective on the key themes that emerged. Results revealed that, through the writing group, members learned technical elements (e.g., paragraph structure), non-technical elements (e.g., working within limited timeframes), conceptual elements (e.g., constructing a cohesive arguments), collaborative writing processes, and how to edit and respond to feedback. In addition to improved writing quality, other benefits were opportunities for shared writing experiences, peer support, and increased confidence and motivation. The writing group provides a unique social learning environment with opportunities for: professional dialogue about writing, peer learning and review, and developing a supportive peer network. Thus our research writing group has proved an effective avenue for building doctoral students’ capability in scholarly writing. The proposed model for a research writing group could be applicable to any context, regardless of the type and location of the university, university faculty, doctoral program structure, or number of postgraduate students. It could also be used within a group of students with diverse research abilities, needs, topics and methodologies. However, it requires a group facilitator with sufficient expertise in scholarly writing and experience in doctoral supervision who can both engage the group in planned writing activities and also capitalise on fruitful lines of discussion related to students’ concerns as they arise. The research writing group is not intended to replace traditional supervision processes nor existing training. However it has clear benefits for improving scholarly writing in doctoral research programs particularly in an era of rapidly increasing student load.

Emergency department surge capacity : Recommendations of the Australasian surge strategy working group

Background For more than a decade emergency medicine organizations have produced guidelines, training and leadership for disaster management. However to date, there have been limited guidelines for emergency physicians needing to provide a rapid response to a surge in demand. The aim of this study is to identify strategies which may guide surge management in the Emergency Department. Method A working group of individuals experienced in disaster medicine from the Australasian College for Emergency Medicine Disaster Medicine Subcommittee (the Australasian Surge Strategy Working Group) was established to undertake this work. The Working Group used a modified Delphi technique to examine response actions in surge situations. The Working Group identified underlying assumptions from epidemiological and empirical understanding and then identified remedial strategies from literature and from personal experience and collated these within domains of space, staff, supplies, and system operation. Findings These recommendations detail 22 potential actions available to an emergency physician working in the context of surge. The Working Group also provides detailed guidance on surge recognition, triage, patient flow through the emergency department and clinical goals and practices. Discussion These strategies provide guidance to emergency physicians confronting the challenges of a surge in demand. The paper also identifies areas that merit future research including the measurement of surge capacity, constraints to strategy implementation, validation of surge strategies and measurement of strategy impacts on throughput, cost, and quality of care.

Raman spectroscopy of selected borate minerals of the pinakiolite group

The Raman spectra of a series of related minerals of the pinakiolite group of minerals have been collected and the spectra related to the mineral structure. These minerals are based upon an isolated BO33- ion. The site symmetry is reduced from D3h to C1. Intense Raman bands are observed for the minerals takeuchiite, pinakiolite, fredrikssonite and azoproite at 1084, 1086, 1086 and 1086 cm-1. These bands are assigned to the ν1 BO33- symmetric stretching mode. Low intensity Raman bands are observed for the minerals at 1345, 1748; 1435, 1748; 1435, 1750; 1436, 1749 cm-1. One probable assignment is to ν3 BO33- antisymmetric stretching mode. Intense Raman bands of takeuchiite, pinakiolite, fredrikssonite and azoproite at 712 cm-1 attributed to the ν2 out-of-plane bending mode. Importantly, through the comparison of the Raman spectra, the molecular structure of borate minerals with ill-defined structures can be obtained.

Vibrational spectroscopy of the multi anion mineral zykaite Fe4(AsO4)(SO4)(OH)•15H2O – implications for arsenate removal

Some minerals are colloidal and are poorly diffracting . Vibrational spectroscopy offers one of the few methods for the assessment of the structure of these types of minerals. Among this group of minerals is zykaite with formula Fe4(AsO4)(SO4)(OH)•15H2O. The objective of this research is to determine the molecular structure of the mineral zykaite using vibrational spectroscopy. Raman and infrared bands are attributed to the AsO43-, SO42- and water stretching vibrations. The sharp band at 3515 cm-1 is assigned to the stretching vibration of the OH units. This mineral offers a mechanism for the formation of more crystalline minerals such as scorodite and bukovskyite. Arsenate ions can be removed from aqueous systems through the addition of ferric compounds such as ferric chloride. This results in the formation of minerals such as zykaite and pitticite (Fe3+,AsO4,SO4,H2O).

Use of focus group technique to investigate infection control practice

Use of focus groups as a technique of inquiry is gaining attention in the area of health-care research. This paper will report on the technique of focus group interviewing to investigate the role of the infection control practitioner. Infection control is examined as a specialty area of health-care practice that has received little research attention to date. Additionally, it is an area of practice that is expanding in response to social, economic and microbiological forces. The focus group technique in this study helped a group of infection control practitioners from urban, regional and rural areas throughout Queensland identify and categorise their daily work activities. The outcomes of this process were then analysed to identify the growth in breadth and complexity of the role of the infection control practitioner in the contemporary health-care environment. Findings indicate that the role of the infection control practitioner in Australia has undergone changes consistent with and reflecting changing models of health-care delivery.

What’s in a name : Is there a right to terminate a contract for purchase of a unit if the name changes?

The significance of the proposed name of a building to buyers of units off the plan has received recent attention in Queensland and the ACT with differing results. In Gough v South Sky Investments Pty Ltd the Queensland Court of Appeal concluded that the name of the building was not an essential term of the contract and rejected a claim by a number of buyers to terminate their contracts because of the change of name from Oracle to Peppers. In contrast, Rares J in the Federal Court decision of Madison Constructions Pty Ltd v Empire Building Group (ACT) Pty Ltd considered that the name of the building in a proposed development could potentially form the basis of misleading conduct about the association of the seller with a particular development corporation.

Implementation Guide for Surveillance of Staphylococcus aureus Bacteraemia -- [Consultation Edition]

The Implementation Guide for the Hospital Surveillance of SAB has been produced by the Healthcare Associated Infection (HAI) Technical Working Group of the Australian Commission on Safety and Quality in Health Care (ACSQHC), and endorsed by the HAI Advisory Group. The Technical Working Group is made up of representatives invited from surveillance units and the ACSQHC, who have had input into the preparation of this Guide. The Guide has been developed to ensure consistency in reporting of SAB across public and private hospitals to enable accurate national reporting and benchmarking. It is intended to be used by Australian hospitals and organisations to support the implementation of healthcare associated Staphylococcus aureus bacteraemia(SAB) surveillance using the endorsed case definition1 in the box below and further detail in the Data Set Specification.

Implementation Guide for Surveillance of Central Line Associated Bloodstream Infection -- [Consultation Edition]

The implementation guide for the surveillance of CLABSI in intensive care units (ICU) was produced by the Healthcare Associated Infection (HAI) Technical Working Group of the Australian Commission on Safety and Quality in Health Care(ACSQHC), and endorsed by the ACSQHC HAI Advisory Committee. State surveillance units, the ACSQHC and the Australian and New Zealand Intensive Care Society (ANZICS) have representatives on the Technical Working Group, and have provided input into this document.