Foliations by spacelike hypersurfaces on Lorentz manifolds

In this work we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and apply it to investigate conditions for the leaves being totally umbilical or geodesic. Using the Maximum principle with the mentioned equation we obtain an obstruction for the existence of totally geodesic spacelike foliations in a spacetime with positive Ricci curvature on the direction N

Exploring the low-mass regime of galaxy-scale strong lensing: Insights into the mass structure of cluster galaxies

We aim at a direct measurement of the compactness of three galaxy-scale lenses in massive clusters, testing the accuracy of the scaling laws that describe the members in strong lensing (SL) models of galaxy clusters. We selected the multiply imaged sources MACS J0416.1$-$2403 ID14 ($z=3.221$), MACS J0416.1$-$2403 ID16 ($z=2.095$), and MACS J1206.2$-$0847 ID14 ($z=3.753$). Eight images were observed for the first SL system, and six for the latter two. We focused on the main deflector of each galaxy-scale SL system (identified as members 8971, 8785, and 3910, respectively), and modelled its total mass distribution with a truncated isothermal sphere. We accounted for the lensing effects of the remaining cluster components, and included the uncertainty on the cluster-scale mass distribution through a bootstrapping procedure. We measured a truncation radius value of $6.1^{+2.3}_{-1.1} \, \mathrm{kpc}$, $4.0^{+0.6}_{-0.4} \, \mathrm{kpc}$, and $5.2^{+1.3}_{-1.1} \, \mathrm{kpc}$ for members 8971, 8785, and 3910, respectively. Alternative non-truncated models with a higher number of free parameters do not lead to an improved description of the SL system. We measured the stellar-to-total mass fraction within the effective radius $R_e$ for the three members, finding $0.51\pm0.21$, $1.0\pm0.4$, and $0.39\pm0.16$, respectively. We find that a parameterisation of the properties of cluster galaxies in SL models based on power-law scaling relations with respect to the total luminosity cannot accurately describe their compactness over their full total mass range. Our results agree with modelling of the cluster members based on the Fundamental Plane relation. Finally, we report good agreement between our values of the stellar-to-total mass fraction within $R_e$ and those of early-type galaxies from the SLACS Survey. Our work significantly extends the regime of the current samples of lens galaxies.Comment: Astronomy & Astrophysics, 679, A124 (2023), 15 pages, 12 figures, 8 table

Tanaka/Johnston : um método simplificado e efetivo para a predição de tamanho de dentes permanentes não erupcionados

Em um estudo feito em 52 pares de modelos de gesso de pacientes leucodermas, naturais de Porto Alegre, foi medido o diâmetro M-D de pré-molares e caninos permanentes com a finalidade de testar o método de Tanaka/Johnston ¹⁴. Neste estudo, não foram encontradas diferenças estatisticamente significantes entre os valores reais e os previstos por este método para as arcadas superior e inferior do sexo masculino e para a arcada superior do sexo feminino. Na arcada inferior do sexo feminino houve uma pequena diferença estatisticamente significante (p = 0,01).In a study mede in 52 pairs of cast models of white patients native to Porto Alegre, measures of the M-D diameters of permanent cuspids and bicuspids were taken, with the objective of testing Tanaka/Johnston's method14. In this study, no significant statiscal diference was found between the real values and the ones predicted by this method for both upper and lower arch for males and of upper arch for females. In the lower arch females, a small significant statistical diference (p = 0,01) was found

Avaliação de uma técnica de compactação do gesso odontológico como alternativa para a correta relação água/pó

The water-powder relationship is essential to achieve a proper performance of gypsum for prosthetic purposes. The ideal measure can be obtained with a balance, but this is clinically unavailable, once it is timeconsuming. A powder-compacting technique using a volume measurement is suggested in order to substitute the balance. The technique consists of using a gypsum meter within the gypsum bag. While the operator holds the gypsum meter with one hand, the palm of the other hand is pressed over the surface of the meter, supported by the ventral aspect of the fingers of the hand that is pressing. This procedure is based upon three compactation movements for each operator, then counting the average of compacting sample. Each of the ten operators repeated six times the procedure, and the final average was defined. The resulting samples for each procedure, of each operator, were weighted, and the statistical analysis showed significant differences (p = 0,006) among the operators.Para a obtenção do melhor desempenho do gesso odontológico é necessário que se obedeça uma relação água/pó adequada a fim manter suas propriedades ideais. A medida mais precisa do pó de gesso é tradicionalmente obtida através de uma balança, o que, clinicamente, acaba não sendo um método muito prático e rápido. Na tentativa de encontrar uma alternativa para substituir a balança foi proposta uma técnica de compactação do pó de gesso utilizando uma medida volumétrica. Essa técnica consiste em introduzir dentro do saco de gesso um medidor, o qual é segurado por uma das mãos, enquanto que a palma da outra pressiona a superfície do medidor, que é apoiado pela parte ventral dos dedos desta mão. Esse procedimento pressupõe três compactações para cada operador, obtendo-se daí uma média da massa compactada. Cada um dos dez operadores reproduziu por seis vezes o referido procedimento, obtendo-se então uma média final para cada operador. As massas resultantes de cada operação, de cada operador foram pesadas e os resultados comparados por testes estatísticos evidenciaram a existência de uma diferença estatisticamente significativa (p=0,006) entre os operadores