BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras

2000 Mathematics Subject Classification: 16R10, 16R30.

Experimenting with infinite groups, I

A group is termed parafree if it is residually nilpotent and has the same nilpotent quotients as a given free group. Since free groups are residually nilpotent, they are parafree. Nonfree parafree groups abound and they all have many properties in common with free groups. Finitely presented parafree groups have solvable word problems, but little is known about the conjugacy and isomorphism problems. The conjugacy problem plays an important part in determining whether an automorphism is inner, which we term the inner automorphism problem. We will attack these and other problems about parafree groups experimentally, in a series of papers, of which this is the first and which is concerned with the isomorphism problem. The approach that we take here is to distinguish some parafree groups by computing the number of epimorphisms onto selected finite groups. It turns out, rather unexpectedly, that an understanding of the quotients of certain groups leads to some new results about equations in free and relatively free groups. We touch on this only lightly here but will discuss this in more depth in a future paper.

Molecular structures of cytidine-5-diphosphate and cytidine-5-diphospho-choline, and their role in intermediary metabolism

The nucleotide coenzyme cytidine-5-diphospho-choline is highly folded. The CMP-5 parts of the molecules in the crystal structure are strongly linked by metal ligation and hydrogen bonds leaving the phosphoryl-choline residues relatively free. Cytidine-5-diphosphoric acid exists as a zwitterion with N31 protonated. The P−O bond lengths from the anhydride bridging oxygen in the pyrophosphate are significantly different.

Splittings of free groups, normal forms and partitions of ends

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x S (1). These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in pi (2)(M) can be represented by an embedded sphere.

Development of zona-free hamster ova to blastocysts in vitro

The zona pellucida (ZP) enclosing the mammalian ovum is important for its protection and for initial stages of fertilization, but the role of the ZP during embryo development is less clear. This study was designed to investigate if the hamster ZP is needed for embryo development from 1-cell to blastocyst in vitro, and to compare methods for removing the ZP. A total of 395 hamster pronucleate ova were collected 10 h post activation from superovulated, mated female hamsters. The ZP was removed from some ova using either 0.05% pronase, 0.05% trypsin or acid Tyrode's solution. To prevent ZP-free ova from sticking together, they were cultured singly in 30-50 muL drops of HECM-6 culture medium together with ZP-intact ova as controls. There was no significant difference among treatment groups in embryo development to blastocyst: 36/87 (42%) in the ZP intact group; 35/75 (47%) in the pronase-treated ZP-free group; 37/74 (50%) in the trypsin-treated ZP-free group; and 37/71 (52%) in the acid-treated ZP-free group. These results indicate that 1) the ZP is unnecessary for hamster embryo development in vitro from the pronucleate ovum stage to blastocyst; 2) none of the three ZP-removal methods was detrimental to embryo development; 3) embryos do not need to be cultured in groups during in vitro development from 1-cell to blastocyst. (C) 2000 by Elsevier Science Inc.

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

TMD and GOHAI indices of Brazilian institutionalised and community-dwelling elderly

Considering the controversy in the literature regarding several aspects of temporomandibular dysfunction (TMD) in elderly populations and the absence of reliable data on elderly Brazilians in this field, this study consisted of an evaluation of TMD prevalence and the self-perception of oral health among institutionalised and community-dwelling elderly in Sao JosE dos Campos, Brazil.Two hundred and fifteen community-dwelling and 185 institutionalised elderly people were evaluated by the Helkimo anamnestic (Ai) and clinical dysfunction (Di) indices and answered a questionnaire using the Geriatric Oral Health Assessment Index (GOHAI).The major prevalence of TMD symptoms was for the Ai0 (symptom-free) group (69.5%), while the major prevalence of clinical signs was for the DiI (mild) group (56%). Women presented a higher AiII classification than men (chi(2) test, p = 0.049). Community-dwelling elderly presented a significantly lower Ai0 classification than the institutionalised ones (Two ratios equality test, p < 0.001). There was no relationship between the institutionalised status and the clinical dysfunction index for Di0 and DiIII classification (Two ratios equality test, p = 0.194 and 0.535 respectively). The institutionalised elderly presented greater (One-way anova = 0.005) self-perception of oral health (33.45) than did the community-dwelling group (32.66). There were only weak Pearson's correlations among the anamnestic (-33.0%) or clinical (-14.7%) findings by the TMD and GOHAI indices. Symptom-free (Ai0) institutionalised elderly presented better scores in all GOHAI dimensions and elderly representing an absence of clinical TMD signs (Di0) presented higher GOHAI physical dimension scores in both groups.The prevalence of TMD symptoms among this sample of elderly individuals was relatively low, self-perception of oral health was reasonable and a weak, inverse correlation was found between TMD signs and symptoms and elderly self-perception of oral health measured by the GOHAI index.

THE STRUCTURE OF FREE AUTOMORPHIC MOUFANG LOOPS

We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

Walter Lorenz – Wegbegleiter und Orientierungspunkt in der interkulturellen Sozialen Arbeit

First meeting, common interests and ways together The European Centre for Social Welfare, Training and Research situated in Vienna, was our first meeting place. W. Lorenz was interested in the international comparison of the different concepts and perspectives of social welfare problems in the European countries and the different developments in the training of social professions in Europe. The challenge of intercultural, antiracist social work in the context of Erasmus-Intensive Seminars To organize an intensive seminar with the aim to train students and colleagues for intercultural and antiracist competence in social professions, we formed an European network of European universities and schools of s.w. in Vienna (VIENNET), with the support of ECCE (European Centre of Community Education) in Koblenz. “The group discovered that working on these issues in an international context raises issues of ‘difference’ with renewed acuteness”(cit. W. Lorenz). We learned to cope with a variety of differences: biographical, language, theoretical and institutional backgrounds and discourse traditions. A Venue for an Intensive Seminar In choosing a venue for an Intensive Seminar we were relatively free. We locked for a place, “one dream about”, to support in the best way our seminar aims, to promote a base built on knowledge, skills and values particularly in the area of inner/outer borders, disadvantage, ignorance, minorities, majorities, vulnerable groups, racism and xenophobia. In a small village in Burgenland (Austria), very close to the Hungarian border, we thought to have found it. Future Prospect Are we only representatives of our background institutions or did we act and exposed ourselves as persons with a very specific biography and training experience. Can we sustain this created network, as a network of experts and friends in the field of intercultural, antiracist social work? This question is still open.

Mid-Pliocene diatom and palynological assemblages north-northeast of Cape Adare, Antarctica

Microfossil assemblages in Pliocene sediments from DSDP Site 274 (68°59.81'S, 173°2564'E) provide data on the age of the sediments and suggest the presence of Nothofagus (southern beach) in Antarctica during the Pliocene. A suite of 17 samples was collected in an interval from Samples 28-274-6R-1, 83-87 cm to 28-274-11R-4, 73-77 cm (48.33-100.29 mbsf). Biostratigraphic study of the abundant diatom assemblages combined with published radiolarian data indicates that the sample interval ranges in age from 5.0 to 2.2 Ma, with an apparent unconformity between about 3.8 and 3.2 Ma. Nothofagidites (the genus for fossil pollen referable to Nothofagus) occurs throughout the interval, as well as pollen and spores with known stratigraphic ranges that unequivocally indicate reworking from older rocks. Species of Nothofagidites recovered include N. asperus, N. brachyspinulosus, N. flemingii, N. senectus, and N. sp. cf. N. lachlaniae; the latter form is previously known from the Sirius Group in the Transantarctic Mountains. Abundant palynomorphs were recovered in only three of the samples from Site 274 (Samples 28-274-9R-2,15-19 cm; 28-274-9R-2,48-52 cm; and 28-274-9R-2,65-69 cm). Based on the diatom and radiolarian biostratigraphic data, the ages of these samples range from 3.00 to 3.01 Ma. The relative abundance of N. sp. cf. N. lachlaniae in the three samples is an order of magnitude higher than relative abundances for the other species of Nothofagidites in the same samples. The signiticantly higher relative abundance of N. sp. cf. N. luchlaniae suggests that this pollen was derived from trees of Nothofugus that were living in Antarctica during the mid Pliocene. Diatom assemblages from these three samples indicate that sediments in this interval were rapidly deposited as biogenic oozes in an open-ocean setting relatively free of sea ice, thus decreasing the possibility of reworking from a single source bed rich in N. sp. cf. N. lachlaniae. Clearly, more detailed work in additional well-dated cores from around Antarctica is needed before a clear picture of the Neogene history of Antarctic terrestrial vegetation emerges.

E-polynomial of the SL(3,C)-character variety of free groups.

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3,C). Expanding upon techniques of Logares, Muñoz and Newstead (Rev. Mat. Complut. 26:2 (2013), 635-703), we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give a new proof of results of Cavazos and Lawton (Int. J. Math. 25:6 (2014), 1450058).

Motivations for group membership: The role of subjective importance and uncertainty reduction

An experiment was conducted to investigate the idea that an important motive for identifying with social groups is to reduce subjective uncertainty, particularly uncertainty on subjectively important dimensions that have implications for the self-concept (e.g., Hogg, 1996; Hogg & Mullin, 1999). When people are uncertain on a dimension that is subjectively important, they self-categorize in terms of an available social categorization and, thus, exhibit group behaviors. To test this general hypothesis, group membership, task uncertainty, and task importance were manipulated in a 2 x 2 x 2 between-participants design (N = 128), under relatively minimal group conditions. Ingroup identification and desire for consensual validation of specific attitudes were the key dependent measures, but we also measured social awareness. All three predictions were supported. Participants identified with their group (H1), and desired to obtain consensual validation from ingroup members (H2) when they were uncertain about their judgments on important dimensions, indicating that uncertainty reduction motivated participants towards embracing group membership. In addition, identification mediated the interactive effect of the independent variables on consensual validation (H3), and the experimental results were not associated with an increased sense of social awareness and, therefore, were unlikely to represent only behavioral compliance with generic social norms. Some implications of this research in the study of cults and totalist groups and the explication of genocide and group violence are discussed.