On comparing two sequences of numbers and its applications to clustering analysis

A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall`s indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index. (C) 2008 Elsevier Inc. All rights reserved.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Understanding the Effect of Adsorption Geometry over Substrate Selectivity in the Surface-Enhanced Raman Scattering Spectra of Simazine and Atrazine

This paper studies the selectivity of Well-defined Au and Ag nanostructures as substrates for the SERS, (surface-enhanced Raman scattering) detection of simazine (6-chloro-N,N`-diethyl-1,3,5-triazine-2,4-diamine) and atrazine (6-chloro-N-ethyl-N`-isopropyl-1,3,5-triazine-2,4-diamine). Our data showed that simazine and atrazine displayed similar SERS spectra when the Au was employed as substrate. Conversely, distinct SERS signatures were obtained upon the utilization of Ag substrates. Density functional theory (DFT) calculations and vibrational assignments suggested that, while simazine and atrazine adsorbed on Au via the N3 position of the triazine ring, simazine adsorbed on Ag via N3 and atrazine via N5. The results presented herein demonstrated that the adsorption geometry of analyte molecules can play a central role over substrate selectivity in SERS, which is particularly important in applications involving ultrasensitive analysis of mixtures containing structurally similar molecules.

Gas streaming motions towards the nucleus of M81

We present two-dimensional stellar and gaseous kinematics of the inner 120 x 250 pc2 of the LINER/Seyfert 1 galaxy M81, from optical spectra obtained with the Gemini Multi-Object Spectrograph (GMOS) integral field spectrograph on the Gemini-North telescope at a spatial resolution of approximate to 10 pc. The stellar velocity field shows circular rotation and, overall, is very similar to the published large-scale velocity field, but deviations are observed close to the minor axis which can be attributed to stellar motions possibly associated with a nuclear bar. The stellar velocity dispersion of the bulge is 162 +/- 15 km s-1, in good agreement with previous measurements and leading to a black hole mass of M(BH) = 5.5+3.6(-2.0) x 107 M(circle dot) based on the M(BH)-Sigma relationship. The gas kinematics is dominated by non-circular motions and the subtraction of the stellar velocity field reveals blueshifts of approximate to-100 km s-1 on the far side of the galaxy and a few redshifts on the near side. These characteristics can be interpreted in terms of streaming towards the centre if the gas is in the plane. On the basis of the observed velocities and geometry of the flow, we estimate a mass inflow rate in ionized gas of approximate to 4.0 x 10-3 M(circle dot) yr-1, which is of the order of the accretion rate necessary to power the LINER nucleus of M81. We have also applied the technique of principal component analysis (PCA) to our data, which reveals the presence of a rotating nuclear gas disc within approximate to 50 pc from the nucleus and a compact outflow, approximately perpendicular to the disc. The PCA combined with the observed gas velocity field shows that the nuclear disc is being fed by gas circulating in the galaxy plane. The presence of the outflow is supported by a compact jet seen in radio observations at a similar orientation, as well as by an enhancement of the [O i]/H alpha line ratio, probably resulting from shock excitation of the circumnuclear gas by the radio jet. With these observations we are thus resolving both the feeding - via the nuclear disc and observed gas inflow, and the feedback - via the outflow, around the low-luminosity active nucleus of M81.

SURFACE ALFVEN WAVE DAMPING IN A THREE-DIMENSIONAL SIMULATION OF THE SOLAR WIND

Here we investigate the contribution of surface Alfven wave damping to the heating of the solar wind in minima conditions. These waves are present in the regions of strong inhomogeneities in density or magnetic field (e.g., the border between open and closed magnetic field lines). Using a three-dimensional (3D) magnetohydrodynamics (MHD) model, we calculate the surface Alfven wave damping contribution between 1 and 4 R(circle dot) (solar radii), the region of interest for both acceleration and coronal heating. We consider waves with frequencies lower than those that are damped in the chromosphere and on the order of those dominating the heliosphere: 3 x 10(-6) to 10(-1) Hz. In the region between open and closed field lines, within a few R(circle dot) of the surface, no other major source of damping has been suggested for the low frequency waves we consider here. This work is the first to study surface Alfven waves in a 3D environment without assuming a priori a geometry of field lines or magnetic and density profiles. We demonstrate that projection effects from the plane of the sky to 3D are significant in the calculation of field line expansion. We determine that waves with frequencies >2.8 x 10(-4) Hz are damped between 1 and 4 R(circle dot). In quiet-Sun regions, surface Alfven waves are damped at further distances compared to active regions, thus carrying additional wave energy into the corona. We compare the surface Alfven wave contribution to the heating by a variable polytropic index and find it as an order of magnitude larger than needed for quiet-Sun regions. For active regions, the contribution to the heating is 20%. As it has been argued that a variable gamma acts as turbulence, our results indicate that surface Alfven wave damping is comparable to turbulence in the lower corona. This damping mechanism should be included self-consistently as an energy driver for the wind in global MHD models.

Geoelectric evidence for centripetal resurge of impact melt and breccias over central uplift of Araguainha impact structure

We present five profiles from electrical resistivity tomography (ERT), with surface constraints and gravity data, in the central uplift of the Araguainha impact structure in central Brazil. The central uplift, the overlying polymict breccias, and decameter-scale impact melt rocks are characterized by contrasting ranges of electrical resistivity. Our resistivity model provides empirical evidence that supports the existing model in which impact melt and breccias resurged toward the crater center in the final stages of the cratering process. On the basis of our results from the first use of ERT in impact cratering studies, we conclude that the deposition and flow of impact melt and breccias over the central uplift were influenced by the geometry of the lithologic boundaries in the central uplift.

Geophysical investigation using resistivity and GPR methods: a case study of a lubricant oil waste disposal area in the city of Ribeiro Preto, So Paulo, Brazil

Geophysics has been shown to be effective in identifying areas contaminated by waste disposal, contributing to the greater efficiency of soundings programs and the installation of monitoring wells. In the study area, four trenches were constructed with a total volume of about 25,000 m(3). They were almost totally filled with re-refined lubricating oil waste for approximately 25 years. No protection liners were used in the bottoms and laterals of the disposal trenches. The purpose of this work is to evaluate the potential of the resistivity and ground penetrating radar (GPR) methods in characterizing the contamination of this lubricant oil waste disposal area in Ribeiro Preto, SP, situated on the geological domain of the basalt spills of the Serra Geral Formation and the sandstones of the Botucatu Formation. Geophysical results were shown in 2D profiles. The geophysical methods used enabled the identification of geophysical anomalies, which characterized the contamination produced by the trenches filled with lubricant oil waste. Conductive anomalies (smaller than 185 Omega m) immediately below the trenches suggest the action of bacteria in the hydrocarbons, as has been observed in several sites contaminated by hydrocarbons in previously reported cases in the literature. It was also possible to define the geometry of the trenches, as evidenced by the GPR method. Direct sampling (chemical analysis of the soil and the water in the monitoring well) confirmed the contamination. In the soil analysis, low concentrations of several polycyclic aromatic hydrocarbons (PAHs) were found, mainly naphthalene and phenanthrene. In the water samples, an analysis verified contamination of the groundwater by lead (Pb). The geophysical methods used in the investigation provided an excellent tool for environmental characterization in this study of a lubricant oil waste disposal area, and could be applied in the study of similar areas.

Cladistic analysis of the suborder Conulariina Miller and Gurley, 1896 (Cnidaria, Scyphozoa; Vendian-Triassic)

Results of a cladistic analysis of the suborder Conulariina Miller and Gurley, 1896, a major extinct (Vendian-Triassic) group of scyphozoan cnidarians, are presented. The analysis sought to test whether the three conulariid subfamilies (Conulariinae Walcott, 1886, Paraconulariinae Sinclair, 1952 and Ctenoconulariinae Sinclair, 1952) recognized in the Treatise on Invertebrate Paleontology ( TIP) are monophyletic. A total of 17 morphological characters were scored for 16 ingroup taxa, namely the genera Archaeoconularia, Baccaconularia, Climacoconus, Conularia, Conulariella, Conularina, Ctenoconularia, Eoconularia, Glyptoconularia, Metaconularia, Notoconularia, Paraconularia, Pseudoconularia, Reticulaconularia, Teresconularia and Vendoconularia. The extant medusozoan taxa Cubozoa, Stauromedusae, Coronatae and Semaeostomeae served as outgroups. Unweighted analysisof the data matrix yielded 1057 trees, and successive weighting analysis resulted in one of the 1057 original trees. The ingroup is monophyletic with two autapomorphies: (1) the quadrate geometry of the oral region; and (2) the presence of a mineralized (phosphatic) periderm. Within the ingroup, the clade (Vendoconularia, Teresconularia, Conularina, Eoconularia) is supported by the sinusoidal longitudinal geometry of the transverse ridges, and the much larger clade (Baccaconularia, Glyptoconularia, Metaconularia, Pseudoconularia, Conularia, Ctenoconularia, Archaeoconularia, Notoconularia, Climacoconus, Paraconularia, Reticulaconularia) is supported by the presence of external tubercles, which, however, were lost in the clade (Notoconularia, Climacoconus, Paraconularia, Reticulaconularia). As proposed by Van Iten et al. (2000), the clade (Notoconularia, Climacoconus, Paraconularia, Reticulaconularia) is supported by the termination and alternation of the transverse ribs in the corner sulcus. The previously recognized subfamilies Conulariinae, Paraconulariinae and Ctenoconulariinae were not recovered from this analysis. The diagnostic features of Conulariinae (continuation of the transverse ornament across the corner sulcus and lack of carinae) and Ctenoconulariinae ( presence of carinae) are symplesiomorphic or homoplastic, and Paraconulariinae is polyphyletic. The families Conulariellidae Kiderlen, 1937 and Conulariopsidae Sugiyama, 1942, also recognized in the TIP, are monogeneric, and since they provide no additional phylogenetic information, should be abandoned.

Total absolute horospherical curvature of submanifolds in hyperbolic space

We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of M, which implies, for the horospherical geometry, the analogues of classical inequalities of the Euclidean Geometry. We prove the horospherical Chern-Lashof inequality for surfaces in 3-space and the horospherical Fenchel and Fary-Milnor`s theorems.

INDEX OF AN IMPLICIT DIFFERENTIAL EQUATION

In this paper we introduce the concept of the index of an implicit differential equation F(x,y,p) = 0, where F is a smooth function, p = dy/dx, F(p) = 0 and F(pp) = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in R(5).

Femtosecond laser ablation on dental hard tissues-Analysis of ablated profile near an interface using local effective intensity

This study evaluated the process of ablation produced by a Ti:Sapphire femtosecond laser under different average powers taking place at the enamel/dentin interface. Based on the geometry of ablated microcavities the effective intensity for ablation was obtained. This study shows the validity for the local effective intensity analysis and allows a quantification of the variation in the ablation geometry taking place at the interface of two naturally different materials. It shows that the variation of the diameter of the ablated region as a function of the cavity depth comes essentially from a mechanism of effective intensity attenuation, as a result of a series of complex effects. Additionally, our data are sufficient to predict that a discontinuity on the ablation profile will occur on the interface between two biological media: enamel-dentin, showing a suddenly jump on the ablated cavity dimensions.

Molecular conformation of the racemic indan derivative (+/-)-1-trans-3-(3,4-dichlorophenyl)-2,3-dihydro-1H-indene-1-carboxamide

This paper presents the structural characterization of the indan derivative (+/-)-1-trans-3-(3,4-dichlorophenyl)-2,3-dihydro-1H-indene-1-carboxamide, which was unambiguously determined by X-ray diffraction (XRD) to be a racemate (R/S: 50/50) crystallizing in an achiral crystal structure (P2(1)/c, a = 9.3180(1) , b = 7.9070(2) , c = 19.7550(4) , beta = 103.250(1)A degrees, V = 1416.75(5) (3) and Z = 4). The diastereomers are related by the inversion symmetry and linked by H bond forming a dimer. The crystal packing is stabilized by hydrogen bonds, including the classical one responsible for the formation of centrosymmetric dimers, and non-classical ones involving C-H center dot center dot center dot O and C-H center dot center dot center dot pi-aryl interactions. The intra and intermolecular geometry of the title compound is compared to the (+/-)-1-trans-3-(3,4-dichlorophenyl)-2,3-dihydro-1H-indene-1-carboxylic acid one, which also present an achiral crystal structure from racemates (R/S: 50/50). The two indan derivatives crystallize in a very similar unit cell.

Spectroscopic and theoretical studies of some N-methoxy-N-methyl-2-[(4 `-substituted) phenylthio]propanamides

The analysis of the IR carbonyl band of the N-methoxy-N-methyl-2-[(4`-substituted)phenylthio]propanamides Y-PhSCH(Me)C(O)N(OMe)Me (Y=OMe 1, Me 2, H 3, Cl 4, NO(2) 5), supported by B3LYP/cc-pVDZ calculations of 3, indicated the existence of two gauche conformers (g(1) and g(2)), the g(1) conformer being the more stable and the less polar one (in gas phase and in solution). Both conformers are present in solution of the polar solvents (CH(2)Cl(2) and CH(3)CN) for 1-5 and in solution of the less polar solvent (CHCl(3)) for 1-4, while only the g(1) conformer is present in solution of non polar solvents (n-C(6)H(14) and CCl(4)) and in solution of CHCl(3) for 5. NBO analysis shows that both the sigma(C-S) -> pi*(C=O) (hyperconjugative) and the pi(C=O) -> sigma*(C-S) orbital interactions contribute almost to the same extent for the stabilization of g(1) and g(2) conformers. The pi*(C=O) -> sigma*(C-S), n(S) -> pi*(C=O) and the n(S) -> pi*(C=O) orbital interactions stabilize more the g(1) conformer than the g(2) one. Moreover, the suitable geometry of the g(1) conformer leads to its stabilization through the LP(O2) -> sigma*(C8-H11) orbital interaction (hydrogen bond) along with the strong O([CO])(delta-) center dot center dot center dot H([O-Ph])(delta+) electrostatic interaction. On the other hand, the appropriate geometry of the g(2) conformer leads to its stabilization by the LP(O22) -> sigma*(C9-H13) orbital interaction (hydrogen bond) along with the weak O([OMe])(delta-) center dot center dot center dot H([o`-Ph])(delta+) electrostatic static interaction. As for the 4`-nitro derivative 5 the ortho-phenyl hydrogen atom becomes more acidic, leading to a stronger O([CO])(delta-) center dot center dot center dot H([o-Ph])(delta+) interaction and, thus, into a larger stabilization of the g(1) conformer in the whole series. This trend is responsible for the unique IR carbonyl band in CHCl(3) solution of 5. The larger occupancy of the pi*(C=O) orbital of the g(1) conformer relative to that of the g(2) conformer, along with the O([CO])(delta-) center dot center dot center dot H([o-Ph])(delta+) electrostatic interaction (hydrogen bond) justifies the lower carbonyl frequency of the g(1) conformer with respect to the g(2) one, in gas phase and in solution. (C) 2008 Elsevier B.V. All rights reserved.

3-manifolds in Euclidean space from a contact viewpoint

We study the geometry of 3-manifolds generically embedded in R(n) by means of the analysis of the singularities of the distance-squared and height functions on them. We describe the local structure of the discriminant (associated to the distribution of asymptotic directions), the ridges and the flat ridges.

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.