THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

On automorphisms of split metacyclic groups

Let D( m, n; k) be the semi-direct product of two finite cyclic groups Z/m = < x > and Z/n = < y >, where the action is given by yxy(-1) = x(k). In particular, this includes the dihedral groups D(2m). We calculate the automorphism group Aut (D(m, n; k)).

On cohomologies and extensions of cyclic groups

Cohomology groups H(s)(Z(n), Z(m)) are studied to describe all groups up to isomorphism which are (central) extensions of the cyclic group Z(n) by the Z(n)-module Z(m). Further, for each such a group the number of non-equivalent extensions is determined. (C) 2011 Elsevier B.V. All rights reserved.

Automorphism Groups of Generalized (Binary) Icosahedral, Tetrahedral and Octahedral Groups

Let G be any of the (binary) icosahedral, generalized octahedral (tetrahedral) groups or their quotients by the center. We calculate the automorphism group Aut(G).

On automorphisms of finite abelian p-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A(p). For a finite abelian p-group A of type (k(1),..., k(n)), simple necessary and sufficient conditions for an n x n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k(1), k(2)) is analyzed. (C) 2008 Mathematical Institute Slovak Academy of Sciences.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Carcass quality of feedlot finished steers fed yeast, monensin, and the association of both additives

To evaluate the effects of the supplementation of feed additives on carcass quality in beef cattle, 72 Nellore steers (339.5kg, 20-month old) were feedlot finished and fed for 91 days one of the following diets: 1) control with no additives; or added of 2) live yeast culture; 3) monensin; or 4) the association of both additives. After slaughter, renal, pelvic, and inguinal fat and hot carcass weights were recorded and carcass was split into muscle, bone, and trimmable fat. Carcass Longissimus muscle area and subcutaneous fat thickness at the 12th rib were measured and steaks of Longisimus muscle were taken to determine meat color, shear force, drip, and cooking losses. Yeast increased carcass dressing percentage but there were no effects on hot carcass weight, Longissimus area, subcutaneous fat thickness, percentage and weight of retail cut yield and trimmings. Feed additives had no effect on carcass pH, meat color, fat content, shear force, and drip losses. Supplementation of yeast, monensin or the association of both additives had no important effects on carcass traits and on meat quality of feedlot finished steers.

Evaluation of two semi-selective media to detect Curtobacterium flaccumfaciens pv. flaccumfaciens in bean seeds

Evaluation of two semi-selective media to detect Curtobacterium flaccumfaciens pv. flaccumfaciens in bean seeds This study aimed to compare the effectiveness of the semi-selective MSCFF and modified CNS culture media in detecting Curtobacterium flaccumfaciens pv. flaccumfaciens (Cff) in bean seeds, using the streak and spread plate techniques. Four 500 g subsamples, obtained from two samples of bean seeds, were immersed in 600 mL of sterile distilled water for 18 h at 5 degrees C. Suspensions were picked and transferred to plates with both culture media. Plates were then incubated at 28 degrees C, and bacterial growth on both media was evaluated 72 and 144 hours later, compared to the growth of a Cff reference strain. Both media revealed the presence of Cff colonies. Typical colonies were isolated for PCR analyses and pathogenicity tests on tobacco leaves. A characteristic Cff growth on MSCFF medium was observed for the seed samples, for the two plate techniques used, in both evaluations. On the modified CNS culture medium, the bacterial growth was only detected in seed samples after 144 hours of incubation, regardless of the plate technique used. The results showed Cff grew faster on the MSCFF semi-selective culture medium. Bacterial isolates tested were identified as Cff by both PCR analyses and a positive tobacco hypersensitivity reaction.

Tree-ring formation, radial increment periodicity, and phenology of tree species from a seasonal semi-deciduous forest in southeast Brazil

Many tropical tree species produce growth rings in response to seasonal environmental factors that influence the activity of the vascular cambium. We applied the following methods to analyze the annual nature of treering formation of 24 tree species from a seasonal semi-deciduous forest of southeast Brazil: describing wood anatomy and phenology, counting tree rings after cambium markings, and using permanent dendrometer bands. After 7 years of systematic observations and measurements, we found the following: the trees lost their leaves during the dry season and grew new leaves at the end of the same season; trunk increment dynamics corresponded to seasonal changes in precipitation, with higher increment (active period) during the rainy season (October-April) and lower increment (dormant period) during the dry season (May-September); the number of tree rings formed after injuries to the cambium coincided with the number of years since the extraction of the wood samples. As a result of these observations, it was concluded that most study trees formed one growth ring per year. This suggests that tree species from the seasonal semi-deciduous forests of Brazil have an annual cycle of wood formation. Therefore, these trees have potential for use in future studies of tree age and radial growth rates, as well as to infer ecological and regional climatic conditions. These future studies can provide important information for the management and conservation of these endangered forests.

Evaluation of the role of environmental factors in the human gastrointestinal tract on the behaviour of probiotic cultures of Lactobacillus casei Shirota and Lactobacillus casei LC01 by the use of a semi-dynamic in vitro model

This study evaluated the influence of gastrointestinal environmental factors (pH, digestive enzymes, food components, medicaments) on the survival of Lactobacillus casei Shirota and Lactobacillus casei LC01, using a semi-dynamic in vitro model that simulates the transit of microorganisms through the human GIT. The strains were first exposed to different simulated gastric juices for different periods of time (0, 30, 60 and 120 min), and then to simulated intestinal fluids for zero, 120, 180 and 240 min, in a step-wise format. The number of viable cells was determined after each step. The influence of food residues (skim milk) in the fluids and resistance to medicaments commonly used for varied therapeutic purposes (analgesics, antiarrhythmics, antibiotics, antihistaminics, proton pump inhibitors, etc.) were also evaluated. Results indicated that survival of both cultures was pH and time dependent, and digestive enzymes had little influence. Milk components presented a protective effect, and medicaments, especially anti-inflammatory drugs, influenced markedly the viability of the probiotic cultures, indicating that the beneficial effects of the two probiotic cultures to health are dependent of environmental factors encountered in the human gastrointestinal tract.

The importance of dietary calcium consumption in two species of semi-terrestrial grapsoid crabs

Calcium (Ca) is essential for crustaceans, due to calcium carbonate (CaCO(3)) deposition in the new exoskeleton to harden it. The purpose of this work was to study short term Ca balance in terms of dietary Ca ingestion in two phylogenetically related crabs (Superfamily Grapsoidea) showing different degrees of terrestrial adaptations: Sesarma rectum Randall, 1840 and Neohelice granulata (Dana, 1851). Dietary Ca ingestion was studied using purified diets with different Ca concentrations (0, 2.2 and 6.66% Ca), together with measurements of Ca excretion and Ca hemolymph levels. The results showed that both crabs had the same response to foods containing different levels of Ca, with both species eating more of the high Ca diet. However, S. rectum consumed more per mg body mass at all Ca concentrations (6 mg.g(-1) for S. rectum against 3 mg.g(-1) for N. granulata). Both species excreted/egested Ca differently: S. rectum excreted Ca proportionally to ingestion, whereas N. granulata maintained constant faecal Ca output at all dietary Ca levels. Moreover, Ca hemolymph levels for crabs fed the different diets were independent of dietary Ca. In conclusion, both S. rectum and N. granulata seem to regulate the consumption of diets containing more Ca, which suggests a fine balance for Ca intake.

NEW CHARACTERIZATIONS OF COMPLETE SPACELIKE SUBMANIFOLDS IN SEMI-RIEMANNIAN SPACE FORMS

In this paper we study n-dimensional complete spacelike submanifolds with constant normalized scalar curvature immersed in semi-Riemannian space forms. By extending Cheng-Yau`s technique to these ambients, we obtain results to such submanifolds satisfying certain conditions on both the squared norm of the second fundamental form and the mean curvature. We also characterize compact non-negatively curved submanifolds in De Sitter space of index p.

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Conservação de filés de tilápia-do-nilo (Oreochromis niloticus) em salga seca e salga úmida

Acompanhou-se o desenvolvimento dos processos da salga em salmoura saturada (salga úmida) e salga seca de filés de tilápia-do-nilo (Oreochromis niloticus) e avaliaram-se algumas características indicativas de qualidade do produto durante a estocagem. Os processos foram acompanhados por 156 horas na salga úmida e por 96 horas na salga seca, e os filés salgados foram estocados, respectivamente, por 60 e 45 dias à temperatura ambiente. Os teores máximos de cloreto nos filés (14%) foram atingidos com 72 horas na salga úmida e com 36 horas na salga seca. Os filés de tilápia salgados em salmoura mantiveram as características próprias do produto por um período de 45 dias, e os submetidos à salga seca apresentaram baixo teor de umidade (6%) e alta concentração de extrato etéreo (4,6%). Recomenda-se somente o processo de salga em salmoura saturada como forma de conservação dos filés de tilápia-do-nilo.