Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

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).

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)).

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Crystalline particles from self-assembled divinyl oligomers

Ethylene glycol dimethacrylate (EGDMA) and/or triethylene glycol dimethacrylate (TEGDMA) oligomers formation was catalyzed in aqueous medium by horseradish peroxidase (HRP) in the presence of H(2)O(2) at room temperature. EGDMA and/or TEGDMA oligomers were characterized by means of gel permeation chromatography, infrared vibrational spectroscopy and (1)H NMR spectroscopy. Self-assembling of oligomers led to right-angled crystalline particles, as evidenced by scanning electron microscopy and differential scanning calorimetry. EGDMA, TEGDMA and EGDMA-co-TEGDMA oligomers synthesized in the presence of HRP-H(2)O(2) system presented pendant vinyl groups along the chains. good solubility in chloroform, and well-defined melting point. These features evidenced few cross-linking or cyclization and revealed that the catalytic properties of HRP led to oligomeric materials with new characteristics. (C) 2008 Elsevier B.V. All rights reserved.

Use of self-organizing maps and molecular descriptors to predict the cytotoxic activity of sesquiterpene lactones

Some sesquiterpene lactones (SLs) are the active compounds of a great number of traditionally medicinal plants from the Asteraceae family and possess considerable cytotoxic activity. Several studies in vitro have shown the inhibitory activity against cells derived from human carcinoma of the nasopharynx (KB). Chemical studies showed that the cytotoxic activity is due to the reaction of alpha,beta-unsaturated carbonyl structures of the SLs with thiols, such as cysteine. These studies support the view that SLs inhibit tumour growth by selective alkylation of growth-regulatory biological macromolecules, such as key enzymes, which control cell division, thereby inhibiting a variety of cellular functions, which directs the cells into apoptosis. In this study we investigated a set of 55 different sesquiterpene lactones, represented by 5 skeletons (22 germacranolides, 6 elemanolides, 2 eudesmanolides, 16 guaianolides and nor-derivatives and 9 pseudoguaianolides), in respect to their cytotoxic properties. The experimental results and 3D molecular descriptors were submitted to Kohonen self-organizing map (SOM) to classify (training set) and predict (test set) the cytotoxic activity. From the obtained results, it was concluded that only the geometrical descriptors showed satisfactory values. The Kohonen map obtained after training set using 25 geometrical descriptors shows a very significant match, mainly among the inactive compounds (similar to 84%). Analyzing both groups, the percentage seen is high (83%). The test set shows the highest match, where 89% of the substances had their cytotoxic activity correctly predicted. From these results, important properties for the inhibition potency are discussed for the whole dataset and for subsets of the different structural skeletons. (C) 2008 Elsevier Masson SAS. All rights reserved.

Self-reinforced composites obtained by the partial oxypropylation of cellulose fibers. 1. Characterization of the materials obtained with different types of fibers

The in-depth oxypropylation of different types of cellulose fibers, namely Avicel, Rayon, Kraft, and Filter Paper, was investigated. New biphasic mono-component materials were obtained, which could be hot-pressed to form films of cellulose fibers dispersed into a thermoplastic matrix. The success of this chemical modification was assessed by FTIR spectroscopy, X-ray diffraction, scanning electron microscopy. differential scanning calorimetry, thermogravimetric analysis and contact angle measurements. The optimization of this process led to the establishment of the optimal molar ratio between the cellulose CH groups and propylene oxide, which varied as a function of the specific morphology of the fibers. (C) 2008 Elsevier Ltd. All rights reserved.

Self-reinforced composites obtained by the partial oxypropylation of cellulose fibers. 2. Effect of catalyst on the mechanical and dynamic mechanical properties

This work describes the partial oxypropylation of filter paper cellulose fibers, employing two different basic catalyst, viz., potassium hydroxide and 1,4-diazabicyclo [2.2.2] octane, to activate the hydroxyl groups of the polysaccharide and thus provide the anionic initiation sites for the ""grafting-from"" polymerization of propylene oxide. The success of this chemical modification was assessed by FTIR spectroscopy, X-ray diffraction, scanning electron microscopy, differential scanning calorimetry, thermogravimetric analysis and contact angle measurements. The study of the role of the catalyst employed on the extent of the modification and on the mechanical properties of the ensuing composites, after hot pressing, showed that both the Bronsted and the Lewis base gave satisfactory results, without any marked difference.

Influência da largura do septo inter-radicular sobre a estabilidade dos mini-implantes

OBJETIVO: este estudo teve como objetivo avaliar a influência da largura do septo inter-radicular no local de inserção de mini-implantes autoperfurantes sobre o grau de estabilidade desses dispositivos de ancoragem. MÉTODOS: a amostra consistiu de 40 mini-implantes inseridos entre as raízes do primeiro molar e segundo pré-molar superiores de 21 pacientes, com o intuito de fornecer ancoragem para retração anterior. A largura do septo no local de inserção (LSI) foi mensurada nas radiografias pós-cirúrgicas e, sob esse aspecto, os mini-implantes foram divididos em dois grupos: grupo 1 (áreas críticas, LSI<3mm) e grupo 2 (áreas não críticas, LSI>3mm). A estabilidade dos mini-implantes foi avaliada mensalmente pela quantificação do grau de mobilidade e a partir dessa variável foi calculada a proporção de sucesso. Avaliou-se também: a quantidade de placa, altura de inserção, grau de sensibilidade e período de observação. RESULTADOS: os resultados obtidos demonstraram que não houve diferença estatisticamente significativa para o grau de mobilidade e proporção de sucesso entre os mini-implantes inseridos em septos de largura mesiodistal crítica e não crítica. A proporção de sucesso total encontrada foi de 90% e nenhuma variável demonstrou estar relacionada ao insucesso dos mini-implantes. No entanto, observou-se maior sensibilidade nos pacientes cujos mini-implantes apresentavam mobilidade, e que a falha desses dispositivos de ancoragem ocorria logo após sua inserção. CONCLUSÃO: a largura do septo inter-radicular no local de inserção não interferiu na estabilidade dos mini-implantes autoperfurantes avaliados neste estudo.

Effect of different ferrule designs on the fracture resistance and failure pattern of endodontically treated teeth restored with fiber posts and all-ceramic crowns

OBJECTIVE: This study investigated the effect of different ferrule heights on endodontically treated premolars. MATERIAL AND METHODS: Fifty sound mandibular first premolars were endodontically treated and then restored with 7-mm fiber post (FRC Postec Plus #1 Ivoclar-Vivadent) luted with self-polymerized resin cement (Multilink, Ivoclar Vivadent) while the coronal section was restored with hybrid composite core build-up material (Tetric Ceram, Ivoclar-Vivadent), which received all-ceramic crown. Different ferrule heights were investigated: 1-mm circumferential ferrule without post and core (group 1 used as control), a circumferential 1-mm ferrule (group 2), non-uniform ferrule 2-mm buccally and 1-mm lingually (group 3), non-uniform ferrule 3-mm buccally and 2-mm lingually (group 4), and finally no ferrule preparation (group 5). The fracture load and failure pattern of the tested groups were investigated by applying axial load to the ceramic crowns (n=10). Data were analyzed statistically by one-way ANOVA and Tukey's post-hoc test was used for pair-wise comparisons (α=0.05). RESULTS: There were no significant differences among the failure load of all tested groups (P<0.780). The control group had the lowest fracture resistance (891.43±202.22 N) and the highest catastrophic failure rate (P<0.05). Compared to the control group, the use of fiber post reduced the percentage of catastrophic failure while increasing the ferrule height did not influence the fracture resistance of the restored specimens. CONCLUSIONS: Within the limitations of this study, increasing the ferrule length did not influence the fracture resistance of endodontically treated teeth restored with glass ceramic crowns. Insertion of a fiber post could reduce the percentage of catastrophic failure of these restorations under function.

Permeability of different groups of maxillary teeth after 38% hydrogen peroxide internal bleaching

This study evaluated the influence of internal tooth bleaching with 38% hydrogen peroxide (H2O2) on the permeability of the coronal dentin in maxillary anterior teeth and premolars. Seventy teeth (14 per group) were used: central incisors (CI), lateral incisor (LI), canines (C), first premolars (1PM) and second premolars (2PM). Pulp chamber access and transversal sectioning at 2 mm from the cementoenamel junction were performed and the specimens were divided into 2 groups (n= 7): a) no treatment and b) bleaching with 38% H2O2. The bleaching agent was applied to the buccal surface and to the pulp chamber for 10 min. This procedure was repeated 3 times. The specimens were processed histochemically with copper sulfate and rubeanic acid, sectioned longitudinally, and digitalized in a scanner. The area of stained dentin was measured using Image Tool software. Data were analyzed statistically by ANOVA and Tukey's HSD test (?=0.05). There was statistically significant difference (p<0.001) among the untreated groups, CI (0.23 ± 0.26) having the lowest permeability and LI (10.14 ± 1.89) the highest permeability. Among the bleached groups, dentin permeability was increased in all groups of teeth except for 2PM. It may be concluded that bleaching with 38% H2O2 affected dentin permeability near the pulp chamber in maxillary anterior teeth and in first and second premolars.

Effect of temporary cements on the shear bond strength of luting cements

OBJECTIVE: The purpose of this study was to evaluate, by shear bond strength (SBS) testing, the influence of different types of temporary cements on the final cementation using conventional and self-etching resin-based luting cements. Material and Methods: Forty human teeth divided in two halves were assigned to 8 groups (n=10): I and V (no temporary cementation); II and VI: Ca(OH)2-based cement; III and VII: zinc oxide (ZO)-based cement; IV and VIII: ZO-eugenol (ZOE)-based cement. Final cementation was done with RelyX ARC cement (groups I to IV) and RelyX Unicem cement (groups V to VIII). Data were analyzed statistically by ANOVA and Tukey's test at 5% significance level. RESULTS: Means were (MPa): I - 3.80 (±1.481); II - 5.24 (±2.297); III - 6.98 (±1.885); IV - 6.54 (±1.459); V - 5.22 (±2.465); VI - 4.48 (±1.705); VII - 6.29 (±2.280); VIII - 2.47 (±2.076). Comparison of the groups that had the same temporary cementation (Groups II and VI; III and VII; IV and VIII) showed statistically significant difference (p<0.001) only between Groups IV and VIII, in which ZOE-based cements were used. The use of either Ca(OH)2-based (Groups II and VI) or ZO-based (Groups III and VII) cements showed no statistically significant difference (p>0.05) for the different luting cements (RelyX TM ARC and RelyX TM Unicem). The groups that had no temporary cementation (Groups I and V) did not differ significantly from each other either (p>0.05). CONCLUSION: When temporary cementation was done with ZO- or ZOE-based cements and final cementation was done with RelyX ARC, there was an increase in the SBS compared to the control. In the groups cemented with RelyX Unicem, however, the use of a ZOE-based temporary cement affected negatively the SBS of the luting agent used for final cementation.

Dentin permeability of the apical third in different groups of teeth

This ex vivo study evaluated dentin permeability of the root canal in the apical third of different human groups of teeth. Eighty teeth were used, 8 from each dental group: maxillary and mandibular central incisors, lateral incisors and canines, maxillary first premolars (buccal and palatal roots), mandibular first premolars, and maxillary and mandibular second premolars, totalizing 88 roots that were distributed in 11 groups. The root canals were instrumented, irrigated with 1% NaOCl and 15% EDTA. Roots were immersed in 10% copper sulfate for 30 min and then in 1% rubeanic acid alcohol solution for the same period; this chemical reaction reveals dentin permeability by the formation of copper rubeanate, which is a dark-colored compound. Semi-serial 100-µm-thick cross-sections were obtained from the apical third of the roots. Five sections of each apical third were washed, dehydrated, cleared and mounted on glass slides for examination under optical microscopy. The percentage of copper ion infiltration and the amount of tubular dentin were quantified by morphometric analysis. The penetration of copper ions in the apical third ranged from 4.60 to 16.66%. The mandibular central and lateral incisors presented the highest dentin permeability (16.66%), while the maxillary canines and mandibular second and first premolars presented the lowest dentin permeability (4.60%, 4.80% and 5.71%, respectively; p<0.001). The other teeth presented intermediate permeability. In conclusion, dye penetration into dentin tubules at the apical region is strongly dependent on the group of teeth evaluated.

Microleakage in conservative cavities varying the preparation method and surface treatment

OBJECTIVE: To assess microleakage in conservative class V cavities prepared with aluminum-oxide air abrasion or turbine and restored with self-etching or etch-and-rinse adhesive systems. Materials and Methods: Forty premolars were randomly assigned to 4 groups (I and II: air abrasion; III and IV: turbine) and class V cavities were prepared on the buccal surfaces. Conditioning approaches were: groups I/III - 37% phosphoric acid; groups II/IV - self-priming etchant (Tyrian-SPE). Cavities were restored with One Step Plus/Filtek Z250. After finishing, specimens were thermocycled, immersed in 50% silver nitrate, and serially sectioned. Microleakage at the occlusal and cervical interfaces was measured in mm and calculated by a software. Data were subjected to ANOVA and Tukey's test (α=0.05). RESULTS: Marginal seal provided by air abrasion was similar to high-speed handpiece, except for group I. There was SIGNIFICANT difference between enamel and dentin/cementum margins for to group I and II: air abrasion. The etch-and-rinse adhesive system promoted a better marginal seal. At enamel and dentin/cementum margins, the highest microleakage values were found in cavities treated with the self-etching adhesive system. At dentin/cementum margins, high-speed handpiece preparations associated with etch-and-rinse system provided the least dye penetration. CONCLUSION: Marginal seal of cavities prepared with aluminum-oxide air abrasion was different from that of conventionally prepared cavities, and the etch-and-rinse system promoted higher marginal seal at both enamel and dentin margins.

Morphological analysis of glass, carbon and glass/carbon fiber posts and bonding to self or dual-cured resin luting agents

OBJECTIVE: The aim of this study was to evaluate the morphology of glass (GF), carbon (CF) and glass/carbon (G/CF) fiber posts and their bond strength to self or dual-cured resin luting agents. MATERIAL AND METHODS: Morphological analysis of each post type was conducted under scanning electron microscopy (SEM). Bond strength was evaluated by microtensile test after bisecting the posts and re-bonding the two halves with the luting agents. Data were subjected to two-way ANOVA and Tukey's test (α=0.05). Failure modes were evaluated under optical microscopy and SEM. RESULTS: GF presented wider fibers and higher amount of matrix than CF, and G/CF presented carbon fibers surrounded by glass fibers, and both involved by matrix. For CF and GF, the dual-cured material presented significantly higher (p<0.05) bond strength than the self-cured agent. For the dual agent, CF presented similar bond strength to GF (p>0.05), but higher than that of G/CF (p<0.05). For the self-cured agent, no significant differences (p>0.05) were detected, irrespective of the post type. For GF and G/CF, all failures were considered mixed, while a predominance of adhesive failures was detected for CF. CONCLUSION: The bonding between fiber posts and luting agents was affected by the type of fibers and polymerization mode of the cement. When no surface treatment of the post is performed, the bonding between glass fiber post and dual-cured agent seems to be more reliable.