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.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

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.

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.

Paleomagnetism at DSDP Leg 85 Holes

On Leg 85, 16 holes were cored at five sites. Thirteen of the holes were cored with the hydraulic piston corer (HPC) or the variable-length hydraulic piston corer (VLHPC) or both; the remainder were rotary drilled. Partially duplicating stratigraphic sections were successfully recovered by hydraulic piston coring at Sites 572 to 575. Sub-bottom penetration was deepest (about 210 m) at HPC Hole 575A, which bottomed in lower Miocene sediments. Penetration by hydraulic piston coring was limited at all sites not by the failure of the corer to stroke out but by the excessive force (overpull) necessary to retrieve the core barrel from the hole. The sediments recovered are relatively uniform siliceous-calcareous oozes to calcareous ooze-chalks. Paleomagnetic measurements were made at all stratigraphic levels, but magnetostratigraphic sequences could be resolved only for the Pleistocene-Pliocene and for brief upper, middle, and lower Miocene sections. In the younger and less consolidated sediments, the declination often shows large-scale azimuthal rotations downcore. These smooth trends vary from core to core, indicating either rotation between the sediment and the core liner or the rotation of the core barrel during the coring or retrieval process. Thus, azimuthal orientation of the samples was impossible even though a Kuster azimuthal orientation tool was used during the hydraulic piston coring. At all sites, the downhole shift from mainly siliceous to mainly calcareous ooze-chalk coincided with a decrease in NRM intensity of at least one order of magnitude, to 1.0*10**-8 G. Diagenesis is the probable reason for this behavior, although the dilution of magnetic carriers as the result of higher accumulation rates may also be a factor. A tectonic analysis using data from samples with stable remanence indicates a northward plate motion of about 0.3 deg/m.y. during the last 18 m.y., a rate that agrees with most previous reconstructions of Pacific Plate motion.

Jurassic microfossils of DSDP Hole 79-547B

The first marine incursion of the incipient North Atlantic Ocean is recorded in the uppermost Triassic to Lower Jurassic sequence of DSDP Site 547 off central Morocco. A lithologic change from continental red beds below to slope breccias and hemipelagic carbonates above indicates that a carbonate ramp was probably established by Sinemurian time along the Moroccan continental margin and that subsidence in the adjacent basin was rapid in the early phases of continental rift. Foraminifers recovered from the Liassic (Sinemurian-Pliensbachian) basinal deposits are diverse and well preserved. The faunas are compositionally similar to contemporaneous neritic assemblages of Europe and the Grand Banks of Newfoundland. The Middle Jurassic in Hole 547B is characterized by regressive deposits that are poor in foraminifers. The major Late Jurassic "Atlantic" transgression is again represented by basinal deposits consisting of limestone breccias and pelagic carbonates. Foraminifers recovered from this interval are transitional between Late Jurassic assemblages reported from deep-sea deposits in the North Atlantic and typical Late Jurassic neritic assemblages of Europe. The Late Jurassic assemblages of Hole 547B are primarily dominated by nodosariids and spirillinids with moderate abundances of simple arenaceous forms. Nonreticulate epistominids occur very rarely in the Upper Jurassic of Hole 547B. It is tentatively suggested that these represent upper bathyal assemblages.

Lower Cretaceous dinoflagellate cysts of Exmouth Plateau, Nortwest Australia

Cores from Leg 122, Sites 762 and 763, were sampled at intervals of one sample per 1.5-m section in the Lower Cretaceous sequences. More than 400 samples were studied, most of which contained dinoflagellate cysts, spores, pollen, and various types of palynoclasts. From the entire palynomorph assemblage mainly dinoflagellate cysts were studied to give a stratigraphic outline for the Lower Cretaceous. Stratigraphic units were interpreted in terms of zones in use for the Jurassic and Cretaceous of Australia. At both sites a condensed Valanginian to Aptian sequence and an expanded middle to late Berriasian sequence containing a rich microplankton assemblage were recovered. Sites 762 and 763 can be correlated with each other and with the wells Eendracht-1 and Vinck-1.

Lack of Spontaneous Venous Pulsation: Possible Risk Indicator in Normal Tension Glaucoma?

PURPOSE: Recently, the absence of spontaneous venous pulsation (SVP) has been suggested as a vascular risk factor for primary open-angle glaucoma (POAG). As the mechanism behind this phenomenon is still unknown, the authors have studied this vascular component using colour Doppler imaging (CDI). METHODS: A total of 236 patients were divided into three diagnostic groups: healthy controls (81), POAG (86) and normal tension glaucoma (NTG; 69). All subjects were submitted to CDI studies of the retrobulbar circulation, intraocular pressure measurements and assessment of SVP existence. Mann-Whitney, chi-square contingency tables and Spearman correlations were used to explore differences and correlations between variables in the diagnostic groups. RESULTS: Eighty-two percent of healthy controls had SVP (66/81), while a smaller numbers were registered in both glaucoma groups: POAG - 50% (43/86); NTG - 51% (35/69). In NTG patients, but not in POAG patients, the prevalence of the SVP phenomenon decreases with increased glaucoma damage (p = 0.04; p = 0.55, respectively). Overall glaucoma patients from both groups had lower central retinal vein (CRV) velocities than the healthy controls (p < 0.05). NTG patients with SVP had less severe visual field defects (mean defect -6.92 versus -11.1, p < 0.05), higher [correction added after online publication 21 September 2012; the word 'higher' has been inserted to replace the word 'lower'] peak systolic and mean flow velocities in the central retinal artery (p < 0.01; p < 0.05, respectively) as well as higher [correction added after online publication 21 September 2012; the word higher has been inserted to replace the word lower] maximal velocities and RI of the CRV (p < 0.02; p < 0.05, respectively). CONCLUSIONS: Glaucoma patients have a decrease in CRV velocities. SVP is less prevalent in glaucoma patients than in healthy individuals. This phenomenon apparently reflects different hemodynamic patterns in the central retinal vessels. This variable may be of particular importance in NTG patients, where it may be associated with more advanced functional damage.

The classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).

Treatment of a severe dental lateral luxation associated with extrusion in an 8-month-old baby: a conservative approach

This case report documents the trauma and follow-up care of lateral luxation associated with extrusion of the lower central incisors in an 8-month-old patient. The teeth were repositioned by digital pressure and stabilized using proximal sutures. Clinical and radiographic follow-up 40 months after the injury showed alterations in both incisors, but both remained functional and free of pathology.

Extracellular matrix of porcine pericardium: Biochemistry and collagen architecture

Pericardial tissue has been used to construct bioprostheses employed in the repair of different kinds of injuries, mostly cardiac. However, calcification and mechanical failure have been the main causes of the limited durability of cardiac bioprostheses constructed with bovine pericardium. In the course of this work, a study was conducted on porcine fibrous pericardium, its microscopic structure and biochemical nature. The general morphology and architecture of collagen were studied under conventional light and polarized light microscopy. The biochemical study of the pericardial matrix was conducted according to the following procedures: swelling test, hydroxyproline and collagen dosage, quantification of amino acids in soluble collagen, component extraction of the extracellular matrix of the right and left ventral regions of pericardium with different molarities of guanidine chloride, protein and glycosaminoglycan (GAG) dosage, sodium dodecyl sulfate-polyacrylamide gel electrophoresis and total GAG analysis. Microscopic analysis showed collagen fibers arranged in multidirectionally oriented layers forming a closely knit web, with a larger number of fibers obliquely oriented, initiating at the lower central region toward the upper left lateral relative to the heart. No qualitative differences were found between proteins extracted from the right and left regions. Likewise, no differences were found between fresh and frozen material. Protein dosages from left frontal and right frontal pericardium regions showed no significant differences. The quantities of extracted GAGs were too small for detection by the method used. Enzymatic digestion and electrophoretic analysis showed that the GAG found is possibly dermatan sulfate. The proteoglycan showed a running standard very similar to the small proteoglycan decorin.

Análise da influência dos sistemas de retenção para overdentures implanto-retidas e da espessura e resiliência da fibromucosa na distribuição interna das tensões, através do método de elementos finitos bidimensional

Pós-graduação em Odontologia - FOA

Estimativa da altura por dimensões dentárias: uma revisão da literatura

The knowledge of Forensic Anthropology is very importance in cases of identification of human remains. One phase of this process is the study of human height, which can be accomplished with relative ease when intact corpses, complete skeletons or long bones are available. However, the experience of Forensic Dentistry is essential in situations in which there is only information of the skull or of the teeth. The objective of this study was to review in the literature and evaluate works concerning the estimate of the height calculated from dental dimensions. Carrea, in 1920, proposed the estimation of the probable height of an individual by developing formulas for maximum and minimum heights from measurements of the lower central and lateral incisors and canines. The method was used in the case "Josef Mengele", to complement estimates. Tested in the Brazilian population, 70% of match between the actual and the estimated stature were obtained. Using more precise instruments, in the modified method, 96% of correct matching were verified. Recently, a new formula was introduced to estimate height, from measurements of upper teeth, because the technique cannot be used when jaw is not available. The correlation between height and dental dimensions is demonstrated. However, there is still a lack in scientific literature in this field, and further studies are necessary. The estimate of height from dental dimensions can be very useful and important, especially in situations where the complete skeleton it not found, and long bones are not available.

Natale und neonatale Zähne

Natal teeth have been defined as teeth which are present at birth, while neonatal teeth erupt during the first 30 days. Their occurrence is rare, the prevalence ranges from 1:2000 to 1:3000 with a higher frequency in the lip and palate clefts and syndroms. In about 85% natal or neonatal teeth are lower central incisors (60% in pairs), rare are upper teeth, molars and multiple teeth. In almost 90% they are part of the deciduous dentition. A lot of possible causes of early eruption are discussed, but only the relation to hereditary factors seems to be evident. An autosomal dominant trait is often described. The appearance of these teeth is dependent on the degree of maturity, but most of the time it is loose, small, discoloured and hypoplastic. Histologically, enamel hypoplasia with normal prism structure is apparent. No significant disturbances of the dentin structures are observed, only cervically dentin becomes atubular with spaces and enclosed cells. A large vascular pulp and failure of root formation are further investigations. Our microhardness measurements showed values from 24.3-32.4 KHN for enamel and 48.3-62.2 KHN for dentin, while normal deciduous teeth have an enamel hardness of 322.0 +/- 17.5 KHN. The thickness of enamel was never more than 280 microm compared to up to 1200 microm in normal teeth. This shows the retarded development of natal and neonatal teeth, because mineralization has not finished at the time of birth. In accordance with developmental age tooth structure and appearence are normal. In consideration of complications as Riga-Fede-disease, feeding problems, possibility of infection and hypermobility most of the time extraction is the treatment of choice, but in the interest of protecting the child this decision should be made carefully.