Towards a standard methodology to evaluate internal cluster validity indices

The evaluation and comparison of internal cluster validity indices is a critical problem in the clustering area. The methodology used in most of the evaluations assumes that the clustering algorithms work correctly. We propose an alternative methodology that does not make this often false assumption. We compared 7 internal cluster validity indices with both methodologies and concluded that the results obtained with the proposed methodology are more representative of the actual capabilities of the compared indices.

Anomalous electric dipole internal conversion

Electric dipole internal conversion has been experimentally studied for several nuclei in the rare earth region. Anomalies in the conversion process have been interpreted in terms of nuclear structure effects. It was found that all the experimental results could be interpreted in terms of the j ∙ r type of penetration matrix element; the j ∙ ∇ type of penetration matrix element was not important. The ratio λ of the El j ∙ r penetration matrix element to the El gamma-ray matrix element was determined from the experiments to be:

Lu¹⁷⁵,396 keV, λ = - 1000 ± 100;

282 keV, λ = 500 ± 100;

144 keV, λ = 500 ± 250;

Hf¹⁷⁷, 321 keV λ = - 1400 ± 200;

208 keV λ = - 90 ± 40;

72 keV |λ| ≤ 650;

Gd¹⁵⁵, 86 keV λ = - 150 ± 100;

Tm¹⁶⁹, 63 keV λ = - 100 ± 100;

W¹⁸², 152 keV, λ = - 160 ±80;

67 keV, λ = - 100 ± 100.

Predictions for λ are made using the unified nuclear model.

Nuclear structure effects in internal conversion

Experimental studies of nuclear effects in internal conversion in Ta¹⁸¹ and Lu¹⁷⁵ have been performed. Nuclear structure effects (“penetration” effects), in internal conversion are described in general. Calculation of theoretical conversion coefficients are outlined. Comparisons with the theoretical conversion coefficient tables of Rose and Sliv and Band are made. Discrepancies between our results and those of Rose and Sliv are noted. The theoretical conversion coefficients of Sliv and Band are in substantially better agreement with our results than are those of Rose. The ratio of the M1 penetration matrix element to the M1 gamma-ray matrix element, called λ, is equal to + 175 ± 25 for the 482 keV transition in Ta¹⁸¹ . The results for the 343 keV transition in Lu¹⁷⁵ indicate that λ may be as large as – 8 ± 5. These transitions are discussed in terms of the unified collective model. Precision L subshell measurements in Tm¹⁶⁹ (130keV), W¹⁸² (100 keV), and Ta¹⁸¹ (133 keV) show definite systematic deviations from the theoretical conversion coefficients. The possibility of explaining these deviations by penetration effects is investigated and is shown to be excluded. Other explanations of these anomalies are discussed.

I. Nuclear spin-internal-rotation-coupling. II. Fluorine spin-rotation interaction and magnetic shielding in fluorobenzene

Part I.

The interaction of a nuclear magnetic moment situated on an internal top with the magnetic fields produced by the internal as well as overall molecular rotation has been derived following the method of Van Vleck for the spin-rotation interaction in rigid molecules. It is shown that the Hamiltonian for this problem may be written

H_SR = Ῑ · M · Ĵ + Ῑ · M” · Ĵ”

Where the first term is the ordinary spin-rotation interaction and the second term arises from the spin-internal-rotation coupling.

The F¹⁹ nuclear spin-lattice relaxation time (T₁) of benzotrifluoride and several chemically substituted benzotrifluorides, have been measured both neat and in solution, at room temperature by pulsed nuclear magnetic resonance. From these experimental results it is concluded that in benzotrifluoride the internal rotation is crucial to the spin relaxation of the fluorines and that the dominant relaxation mechanism is the fluctuating spin-internal-rotation interaction.

Part II.

The radiofrequency spectrum corresponding to the reorientation of the F¹⁹ nuclear moment in flurobenzene has been studied by the molecular beam magnetic resonance method. A molecular beam apparatus with an electron bombardment detector was used in the experiments. The F¹⁹ resonance is a composite spectrum with contributions from many rotational states and is not resolved. A detailed analysis of the resonance line shape and width by the method of moments led to the following diagonal components of the fluorine spin-rotational tensor in the principal inertial axis system of the molecule:

F/Caa = -1.0 ± 0.5 kHz

F/Cbb = -2.7 ± 0.2 kHz

F/Ccc = -1.9 ± 0.1 kHz

From these interaction constants, the paramagnetic contribution to the F¹⁹ nuclear shielding in C₆H₅F was determined to be -284 ± ppm. It was further concluded that the F¹⁹ nucleus in this molecule is more shielded when the applied magnetic field is directed along the C-F bond axis. The anisotropy of the magnetic shielding tensor, σ_” - σ_⊥, is +160 ± 30 ppm.

Investigation of effective internal field in congruent lithium niobate crystal by digital holographic interferometry

The phase contrast across the crystal thickness induced by the internal field is measured by the digital holographic interferometry just after the congruent lithium niobate crystal is partially poled. The direction of applied external field is antiparallel to that of internal field, and the measured phase contrast varies linearly with the applied external field. A new internal field is obtained by this method and named effective internal field. The distinct discrepancy between effective and equivalent internal fields is observed. The authors attribute this effect to the new macroscopic representation of elastic dipole components of defect complex in the crystal. (c) 2007 American Institute of Physics.

Super-resolution with a nonlinear thin film: Beam reshaping via internal multi-interference

In laser applications, the size of the focus spot can be reduced beyond the diffraction limit with a thin film of strong nonlinear optical Kerr effect. We present a concise theoretical simulation of the device. The origin of the super-resolution is found to be mainly from the reshaping effect due to the strongly nonlinear refraction mediated multi-interference inside the thin film. In addition, both diffraction and self-focusing effects have been explored and found negligible for highly refractive and ultrathin films in comparison with the reshaping effect. Finally, the theoretic model has been verified in experiments with single Ge2Sb2Te5 film and SiN/Si/SiN/Ge2Sb2Te2 multilayer structures. (c) 2006 American Institute of Physics.

A Câmara Municipal do Rio de Janeiro, das invasões corsárias ao governo de Luis Vahia Monteiro (1710 a 1732): uma história de conflitos pelo uso do território colonial.

As câmaras municipais constituíram-se em um dos mais notáveis mecanismos de manutenção do vasto império ultramarino português. Originavam-se dos antigos conselhos medievais, aglutinavam os interesses das elites coloniais ao serem compostas pelos homens bons da colônia, detinham considerável poder sobre a sociedade local além de terem a liberdade de representar ao rei de Portugal seus anseios ou dificuldades. Paralelo, ao poder do senado da câmara municipal, encontravam-se as autoridades nomeadas pelo rei de Portugal: governadores coloniais. Este compartilhamento do poder na colônia gerava, muitas vezes, conflitos entre a câmara municipal e os funcionários régios. No Rio de Janeiro, setecentista, vários fatores internos e externos à colônia deterioraram as relações entre os governadores coloniais e os membros do senado.Tal situação agrava-se com as incursões corsárias francesas de 1710 e 1711 que demonstraram a fragilidade do império português que há muito deixara de ter um poder naval significativo, perdendo espaços para potências como a França, Inglaterra e Holanda. Incapaz de conter os inimigos no vasto oceano, desprovido de meios navais capazes de patrulhar os litorais de suas colônias na África, Ásia e América, em especial o do Brasil, o império português dependia cada vez mais dos recursos humanos de suas colônias para a manutenção do seu território ultramarino. A corte portuguesa sofreu duro impacto com a conquista da cidade do Rio de Janeiro por Duguay-Trouin e, ao longo dos próximos anos, procurou fortalecer o sistema defensivo de sua colônia com o envio de tropas e navios além da construção de novas fortalezas e o reaparelhamento do sistema defensivo já existente.Todo este esforço para a guerra era bancado, em sua maior parte, com recursos da própria colônia do Rio de Janeiro. Obviamente este ônus não agradava a incipiente elite mercantil que florescia na colônia resultando no fato de que a política de enclausurar o Rio de Janeiro entre muralhas e fortificações, ás custas da economia colonial, colocou em campos opostos os funcionários do rei e os membros do senado por várias vezes nas primeiras décadas do século XVIII. Surgiram inevitáveis conflitos pelo uso e posse do território urbano do Rio de Janeiro cada vez mais pontilhado por fortalezas, sulcado por extensas valas e trincheiras a impedir-lhe o crescimento urbano. Além do conflito territorial, em função da expansão da atividade mercantil desenvolvida pelos colonos, as disputas comerciais envolveram as elites locais, ávidas por lucros e impulsionadas ao comércio devido à descoberta do ouro na região das Minas, e as autoridades e comerciantes lusos, uns querendo controlar a atividade comercial que crescia em acelerado ritmo, outros querendo lucrar e disputar espaços com as elites coloniais locais. No meio destes embates encontrava-se a Câmara Municipal do Rio de Janeiro, objetivo maior desta pesquisa, a defender os interesses das elites da colônia, pois delas era representante. Era uma disputa em que, muitas vezes, seus membros pagaram com a perda da liberdade e dos seus bens frente a governadores coloniais mais intolerantes