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.

In vitro antimalarial activity and cytotoxicity of some selected cuban medicinal plants

Terrestrial plants have been demonstrated to be sources of antimalarial compounds. In Cuba, little is known about antimalarial potentials of plant species used as medicinals. For that reason, we evaluated the antimalarial activity of 14 plant species used in Cuba as antimalarial, antipyretic and/or antiparasitic. Hydroalcoholic extracts were prepared and tested in vitro for the antimalarial activity against Plasmodium falciparum Ghana strain and over human cell line MRC-5 to determine cytotoxicity. Parasite multiplication was determined microscopically by the direct count of Giemsa stained parasites. A colorimetric assay was used to quantify cytotoxicity. Nine extracts showed IC50 values lower than 100 µg/mL against P. falciparum, four extracts were classified as marginally active (SI < 4), one as partially active (Parthenium hysterophorus) exhibiting SI equal to 6.2 and two extracts as active (Bambusa vulgaris and Punica granatum), showing SI > 10. B. vulgaris showed the most potent and specific antiplasmodial action (IC50 = 4.7 µg/mL, SI = 28.9). Phytochemical characterization of active extracts confirmed the presence of triterpenoids in B. vulgaris and polar compounds with phenol free groups and fluorescent metabolites in both extracts as major phytocompounds, by thin layer chromatography. In conclusion, antimalarial use of B. vulgaris and P. hysterophorus was validated. B. vulgaris and P. granatum extracts were selected for follow-up because of their strong antimalarial activity.

ROOT PROBLEM FOR CONVENIENT MAPS

In this paper we study when the minimal number of roots of the so-called convenient maps horn two-dimensional CW complexes into closed surfaces is zero We present several necessary and sufficient conditions for such a map to be root free Among these conditions we have the existence of specific fittings for the homomorphism induced by the map on the fundamental groups, existence of the so-called mutation of a specific homomorphism also induced by the map, and existence of particular solutions of specific systems of equations on free groups over specific subgroups

The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

Impacto da cárie precoce severa na infância na qualidade de vida relacionada à saúde bucal de pré-escolares sob privação social

Early childhood caries, especially in its severe form, which is characterized by an acute and aggressive nature, can have negative impacts on thequality of life of a child, due to effects such as difficulty in chewing, decreased appetite, weight loss, insomnia, changes in behavior and a decreased performance in school, among others. Moreover, the quality of life of the child`s family can also be affected, as the pain and discomfort caused by this type of caries result in loss of working days of parents, spending on dental treatments, changes in sleep patterns and stress. The aim of this study was to evaluate the impact of severe early childhood caries in the Oral Health-Related Quality of Life (OHRQoL) of public daycares`s preschool children through the Escala de Impacto da Saúde Bucal na Primeira Infância, a Brazilian version of the Early Childhood Oral Health Impact Scale (ECOHIS). A single calibrated examiner (kappa=1.0) evaluated, through the dmfs index, the oral health of 116 children aged between 3 and 5, which were included in one of three study groups: "caries-free", "not-severe early childhood caries" and "severe early childhood caries". The parents responded to ECOHIS, to assess their perception regarding the OHRQoL of their children, and a questionnaire on socioeconomic conditions. The OHRQoL was measured through the total scores and domains of ECOHIS. Descriptive analysis, Mann-Whitney test, Kruskal-Wallis test, chi-square test and Poisson multiple regression with robust variance were used. Among the children observed, 38.8% were caries-free, 27.6% showed not-severe early childhood caries and 33.6% showed severe early childhood caries. Regarding the total score of ECOHIS, severe early childhood caries had a greater negative impact on OHRQoL, compared to caries-free and not-severe early childhood caries groups (p <0.001). Regarding the child subscale, there was significant difference between the "severe early childhood caries" group and the other groups in all domains, except for theone of self-image / social interaction. In the family subscale domains, there was statistical significance between the severe early childhood caries and the caries-free groups in all domains (p <0.001), whereas between the "severe early childhood caries and not-severe early childhood caries groups there was a statistically significant difference only in the domain of parental anguish (p <0.001). Multivariate analysis showed that early childhood caries and the parent`s age were significantly associated to OHRQoL (p <0.05), independently of the other variables in the model. The presence of severe early childhood caries resulted in greater negative impact on OHRQoL (AdjPR= 6.016; 95%CI = 3.12 11.56; p<0.001), while older parents reported better OHRQoL (AdjPR = 0.603; 95%CI = 0.428 - 0.850; p = 0.004). The presence of severe early childhood caries had a negative impact on OHRQoL of preschool children and their families.

Presence of mutans streptococci and Candida spp. in dental plaque/dentine of carious teeth and early childhood caries

This study determined the presence of mutans streptococci and Candida spp. in supragingival. dental plaque and infected dentine of caries-free children, with early childhood caries and caries. Pooled samples of dental plaque and infected dentine were collected from 56 children aged 1-5 years, which were divided into 3 groups: early childhood caries (ECC); caries and caries-free. Infected dentine was collected in ECC and caries groups to compare the frequency of these microorganisms in the collected sites. The samples were inoculated in SB20 and SA medium, for mutans streptococci and Candida spp., respectively, and incubated at 37 degrees C for 48 h. Colony growth was verified and the identification was performed by biochemical tests and CHROMagar Candida. Fisher's test or chi-square (chi(2)) were applied (p = 0.05). The more prevalent species were S. mutans and Candida albicans in ECC (85.4% and 60.4%, respectively), independently of the sample site. S. mutans only was significantly associated with carious teeth, whether in early childhood caries or not. However, the frequency of C. albicans in ECC was higher when compared to caries and caries-free groups. There is a significant association between the presence of C. albicans and early childhood caries. (c) 2006 Elsevier Ltd. All rights reserved.

Preparation and characterization of the bacterial cellulose/polyurethane nanocomposites

New nanocomposites based on bacterial cellulose nanofibers (BCN) and polyurethane (PU) prepolymer were prepared and characterized by SEM, FT-IR, XRD, and TG/DTG analyses. An improvement of the interface reaction between the BCN and the PU prepolymer was obtained by a solvent exchange process. FT-IR results showed the main urethane band at 2,270 cm-1 to PU prepolymer; however, in nanocomposites new bands appear as disubstituted urea at 1,650 and 1,550 cm-1. In addition, the observed decrease in the intensity of the hydroxyl band (3,500 cm-1) suggests an interaction between BCN hydroxyls and NCO-free groups. The nanocomposites presented a non-crystalline character, significant thermal stability (up to 230 °C) and low water absorption when compared to pristine BCN. © 2013 Akadémiai Kiadó, Budapest, Hungary.

Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

Insular volume abnormalities associated with different transition probabilities to psychosis

Background Although individuals vulnerable to psychosis show brain volumetric abnormalities, structural alterations underlying different probabilities for later transition are unknown. The present study addresses this issue by means of voxel-based morphometry (VBM). Method We investigated grey matter volume (GMV) abnormalities by comparing four neuroleptic-free groups: individuals with first episode of psychosis (FEP) and with at-risk mental state (ARMS), with either long-term (ARMS-LT) or short-term ARMS (ARMS-ST), compared to the healthy control (HC) group. Using three-dimensional (3D) magnetic resonance imaging (MRI), we examined 16 FEP, 31 ARMS, clinically followed up for on average 3 months (ARMS-ST, n=18) and 4.5 years (ARMS-LT, n=13), and 19 HC. Results The ARMS-ST group showed less GMV in the right and left insula compared to the ARMS-LT (Cohen's d 1.67) and FEP groups (Cohen's d 1.81) respectively. These GMV differences were correlated positively with global functioning in the whole ARMS group. Insular alterations were associated with negative symptomatology in the whole ARMS group, and also with hallucinations in the ARMS-ST and ARMS-LT subgroups. We found a significant effect of previous antipsychotic medication use on GMV abnormalities in the FEP group. Conclusions GMV abnormalities in subjects at high clinical risk for psychosis are associated with negative and positive psychotic symptoms, and global functioning. Alterations in the right insula are associated with a higher risk for transition to psychosis, and thus may be related to different transition probabilities.

Genotype-specific risk factors for Staphylococcus aureus in Swiss dairy herds with an elevated yield-corrected herd somatic cell count

Bovine mastitis is a frequent problem in Swiss dairy herds. One of the main pathogens causing significant economic loss is Staphylococcus aureus. Various Staph. aureus genotypes with different biological properties have been described. Genotype B (GTB) of Staph. aureus was identified as the most contagious and one of the most prevalent strains in Switzerland. The aim of this study was to identify risk factors associated with the herd-level presence of Staph. aureus GTB and Staph. aureus non-GTB in Swiss dairy herds with an elevated yield-corrected herd somatic cell count (YCHSCC). One hundred dairy herds with a mean YCHSCC between 200,000 and 300,000cells/mL in 2010 were recruited and each farm was visited once during milking. A standardized protocol investigating demography, mastitis management, cow husbandry, milking system, and milking routine was completed during the visit. A bulk tank milk (BTM) sample was analyzed by real-time PCR for the presence of Staph. aureus GTB to classify the herds into 2 groups: Staph. aureus GTB-positive and Staph. aureus GTB-negative. Moreover, quarter milk samples were aseptically collected for bacteriological culture from cows with a somatic cell count ≥150,000cells/mL on the last test-day before the visit. The culture results allowed us to allocate the Staph. aureus GTB-negative farms to Staph. aureus non-GTB and Staph. aureus-free groups. Multivariable multinomial logistic regression models were built to identify risk factors associated with the herd-level presence of Staph. aureus GTB and Staph. aureus non-GTB. The prevalence of Staph. aureus GTB herds was 16% (n=16), whereas that of Staph. aureus non-GTB herds was 38% (n=38). Herds that sent lactating cows to seasonal communal pastures had significantly higher odds of being infected with Staph. aureus GTB (odds ratio: 10.2, 95% CI: 1.9-56.6), compared with herds without communal pasturing. Herds that purchased heifers had significantly higher odds of being infected with Staph. aureus GTB (rather than Staph. aureus non-GTB) compared with herds without purchase of heifers. Furthermore, herds that did not use udder ointment as supportive therapy for acute mastitis had significantly higher odds of being infected with Staph. aureus GTB (odds ratio: 8.5, 95% CI: 1.6-58.4) or Staph. aureus non-GTB (odds ratio: 6.1, 95% CI: 1.3-27.8) than herds that used udder ointment occasionally or regularly. Herds in which the milker performed unrelated activities during milking had significantly higher odds of being infected with Staph. aureus GTB (rather than Staph. aureus non-GTB) compared with herds in which the milker did not perform unrelated activities at milking. Awareness of 4 potential risk factors identified in this study guides implementation of intervention strategies to improve udder health in both Staph. aureus GTB and Staph. aureus non-GTB herds.

Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

Parabolic and quasiparabolic subgroups of free partially commutative groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

On the intersection of free subgroups in free products of groups

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On uniform conjugators in torsion-free hyperbolic groups

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