Packing triangles in low degree graphs and indifference graphs

We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation ratio known so far for these problems has ratio 3/2 + epsilon, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver [On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM J. Discrete Math. 2(1) (1989) 68-72]. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs. (C) 2007 Elsevier B.V. All rights reserved.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Leishmania amazonensis: Biosynthesis of polyprenols of 9 isoprene units by amastigotes

The isoprenoid metabolic pathway in protozoa of the Leishmania genus exhibits distinctive characteristics. These parasites, as well as other members of the Trypanosomatidae family, synthesize ergosterol, instead of cholesterol, as the main membrane sterol lipid. Leishmania has been shown to utilize leucine, instead of acetate as the main precursor for sterol biosynthesis. While mammalian dolichols are molecules containing 15-23 isoprene units, Leishmania amazonensis promastigotes synthesize dolichol of 11 and 12 units. In this paper, we show that the intracellular stages of L. amazonensis, amastigotes, synthesize mainly polyprenols of 9 isoprene units, instead of dolichol. (c) 2007 Elsevier Inc. All rights reserved.

Use of Information Visualization Methods Eliminating Cross Talk in Multiple Sensing Units Investigated for a Light-Addressable Potentiometric Sensor

The integration of nanostructured films containing biomolecules and silicon-based technologies is a promising direction for reaching miniaturized biosensors that exhibit high sensitivity and selectivity. A challenge, however, is to avoid cross talk among sensing units in an array with multiple sensors located on a small area. In this letter, we describe an array of 16 sensing units, of a light-addressable potentiometric sensor (LAPS), which was made with layer-by-Layer (LbL) films of a poly(amidomine) dendrimer (PAMAM) and single-walled carbon nanotubes (SWNTs), coated with a layer of the enzyme penicillinase. A visual inspection of the data from constant-current measurements with liquid samples containing distinct concentrations of penicillin, glucose, or a buffer indicated a possible cross talk between units that contained penicillinase and those that did not. With the use of multidimensional data projection techniques, normally employed in information Visualization methods, we managed to distinguish the results from the modified LAPS, even in cases where the units were adjacent to each other. Furthermore, the plots generated with the interactive document map (IDMAP) projection technique enabled the distinction of the different concentrations of penicillin, from 5 mmol L(-1) down to 0.5 mmol L(-1). Data visualization also confirmed the enhanced performance of the sensing units containing carbon nanotubes, consistent with the analysis of results for LAPS sensors. The use of visual analytics, as with projection methods, may be essential to handle a large amount of data generated in multiple sensor arrays to achieve high performance in miniaturized systems.

Effect of Pre-Heating Resin Composite and Light-Curing Units on Monomer Conversion

The purpose of this study was to evaluate the effect of pre-heating resin composite photo-cured with light-curing units (LCU) by FT-IR. Twenty specimens were made in a metallic mold (4 mm diameter x 2 mm thick) from composite resin-Tetric Ceram (R) (Ivoclar/Vivadent) at room temperature (25 degrees C) and pre heated to 37, 54, and 60 degrees C. The specimens were cured with halogen curing light (QTH) and light emitted by diodes (LED) during 40 s. Then, the specimens were pulverized, pressed with KBr and analyzed with FT-IR. The data were submitted to statistical analysis of variance and Kruskal-Wallis test. Study data showed no statistically significant difference to the degree of conversion for the different light curing units (QTH and LED) (p > 0.05). With the increase of temperature there was significant increase in the degree of conversion (p < 0.05). In this study were not found evidence that the light curing unit and temperature influenced the degree of conversion.

Degree of Conversion and Temperature Increase of a Composite Resin Light Cured with an Argon Laser and Blue LED

Different light sources and power densities used on the photoactivation process may provide changes in the degree of conversion (DC%) and temperature ( T) of the composite resins. Thus, the purpose of this study was to evaluate the DC (%) and T (degrees C) of the microhybrid composite resin (Filtek (TM) Z-250, 3M/ESPE) photoactivated with one argon laser and one LED (light-emitting diode) with different power densities. For the KBr pellet technique, the composite resin was placed into a metallic mould (2-mm thickness, 4-mm diameter) and photoactivated as follows: a continuous argon laser (CW) and LED LCUs with power density values of 100, 400, 700, and 1000 mW/cm(2) for 20 s. The measurements for DC (%) were made in a FTIR spectrometer Bomen ( model MB 102, Quebec, Canada). Spectroscopy ( FTIR) spectra for both uncured and cured samples were analyzed using an accessory of the reflectance diffusion. The measurements were recorded in absorbance operating under the following conditions: 32 scans, 4 cm(-1) resolution, 300 to 4000-cm(-1) wavelength. The percentage of unreacted carbon double bonds (% C=C) was determined from the ratio of absorbance intensities of aliphatic C=C (peak at 1638 cm(-1)) against an internal standard before and after the curing of the specimen: aromatic C-C (peak at 1608 cm(-1)). For T (degrees C), the samples were created in a metallic mould (2-mm thickness, 4-mm diameter) and photoactivated for 20 s. The thermocouple was attached to the multimeter allowing temperature readings. The DC (%) and T (degrees C) were submitted to ANOVA and Tukey`s test (p < 0.05). The degree of conversion values varied from 35.0 to 50.0% ( 100 to 1000 mW/cm(2)) for an argon laser and from 41.0 to 49% (100 to 1000 mW/cm(2)) for an LED. The temperature change values varied from 1.1 to 13.1 degrees C (100 to 1000 mW/cm(2)) for an argon laser and from 1.9 to 15.0 degrees C (100 to 1000 mW/cm(2)) for an LED. The power densities showed a significant effect on the degree of conversion and changes the temperature for both light-curing units.

Why Implementing History and Philosophy in School Science Education is a Challenge: An Analysis of Obstacles

Teaching and learning with history and philosophy of science (HPS) has been, and continues to be, supported by science educators. While science education standards documents in many countries also stress the importance of teaching and learning with HPS, the approach still suffers from ineffective implementation in school science teaching. In order to better understand this problem, an analysis of the obstacles of implementing HPS into classrooms was undertaken. The obstacles taken into account were structured in four groups: 1. culture of teaching physics, 2. teachers` skills, epistemological and didactical attitudes and beliefs, 3. institutional framework of science teaching, and 4. textbooks as fundamental didactical support. Implications for more effective implementation of HPS are presented, taking the social nature of educational systems into account.

Rhyacian (2.23-2.20 Ga) juvenile accretion in the southern Sao Francisco craton, Brazil: Geochemical and isotopic evidence from the Serrinha magmatic suite, Mineiro belt

The Serrinha magmatic suite (Mineiro belt) crops out in the southern edge of the Sao Francisco craton, comprising the Brito quartz-diorite, Brumado de Cima and Brumado de Baixo granodiorites, granophyres and felsic sub-volcanic and volcanic rocks, part of which intruded into the Nazareno greenstone belt. The suite rocks have petrographic features that are consistent with magma supercooling due to the low water content combined with volatile loss, leading to crystallization of quartz and alkaline feldspar at the rims of plagioclase phenocrysts (granophyric intergrowth). The investigated rocks are sub-alkaline, calc-alkaline and show low content in rare earth elements. The U-Pb zircon crystallization ages for the Brumado de Cima granodiorite [2227 +/- 22 (23) Ma] and a coeval granophyre [2211 +/- 22 (23) Ma], coupled with available single-zircon Pb evaporation ages for the Brito and Brumado de Baixo plutons, are significantly older than the ""Minas orogeny"" (ca. 2100-2050 Ga) of Quadrilatero Ferrifero area, eastward from the Serrinha suite. Our data establish an early Rhyacian event tectonically linked with the evolution of the Mineiro belt. The bulk Nd isotopic signature [low negative to positive epsilon(Nd(t)) values] of the Serrinha samples are consistent with the important role of Paleoproterozoic mantle components in the magma genesis. The integrated geologic, geochemical and isotopic information suggests that Paleoproterozoic evolution of the Mineiro belt initiated in a passive continental margin basin with deposition of the Minas Supergroup at ca. 2500 Ma. This stage was succeeded by outboard rupture of the oceanic lithosphere with development and coalescence of progressively younger magmatic arcs during Rhyacian time. One of the earliest arcs formed the Serrinha suite. The tectonic collage of the Serrinha and Ritapolis (2190-2120 Ma) arcs produced the NE-SW Lenheiro shear zone, resulting in mylonitization and recrystallization of both the granitoid intrusions and host rocks. As a matter of fact juxtaposition of distinct magmatic units in age and origin took place along the Lenheiros structure in this sector of the Mineiro belt. (C) 2009 Elsevier Ltd. All rights reserved.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

Flexural properties, microleakage, and degree of conversion of a resin polymerized with conventional light and argon laser

Objective: To evaluate the flexural strength, microleakage, and degree of conversion of a microhybrid resin polymerized with argon laser and halogen lamp. Method and Materials: For both flexural test and degree of conversion analysis, 5 bar samples of composite resin were prepared and polymerized according to ISO 4049. The halogen light-curing unit was used with 500 MW/cm(2) for 20 seconds and the argon laser with 250 mW for 10 and 20 seconds. Samples were stored in distilled water in a dark environment at 37 degrees C for 24 hours. The flexural property was quantified by a 3-point loading test. For the microleakage evaluation, 60 bovine incisors were used to prepare standardized Class 5 cavities, which were restored and polished. Specimens were stored in distilled water for 24 hours at 37 degrees C and thermocycled 500 times (6 degrees C to 60 degrees C). Specimens were then immersed in art aqueous solution of basic fuchsin for 24 hours. Longitudinal sections of each restoration were obtained and examined with a stereomicroscope for qualitative evaluation of microleakage. Fourier transform (FT)-Raman RFS 100/S spectrometer (Bruker) was used to analyze the degree of conversion. Results: ANOVA showed no statistically significant differences of flexural strength between the photoactivation types evaluated in the flexural study. Microleakage data were statistically analyzed by Mann-Whitney and Kruskal-Wallis tests. Enamel margins resulted in a statistically lower degree of leakage than dentin margins. No statistically significant difference was found among the 3 types of photocuring studied. ANOVA also showed no statistically significant difference in the degree of conversion among the studied groups. Conclusion: According to the methodology used in this research, the argon laser is a possible alternative for photocuring, providing the same quality of polymerization as the halogen lamp. None of the photocured units tested in this study completely eliminated microleakage.