Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Hyperbolic unit groups and quaternion algebras

We classify the quadratic extensions K = Q[root d] and the finite groups G for which the group ring o(K)[G] of G over the ring o(K) of integers of K has the property that the group U(1)(o(K)[G]) of units of augmentation 1 is hyperbolic. We also construct units in the Z-order H(o(K)) of the quaternion algebra H(K) = (-1, -1/K), when it is a division algebra.

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.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

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.

Influence of specimens' design and manufacturing process on microtensile bond strength to enamel: laboratory and FEA comparison

This study evaluated the effect of specimens' design and manufacturing process on microtensile bond strength, internal stress distributions (Finite Element Analysis - FEA) and specimens' integrity by means of Scanning Electron Microscopy (SEM) and Laser Scanning Confocal Microscopy (LCM). Excite was applied to flat enamel surface and a resin composite build-ups were made incrementally with 1-mm increments of Tetric Ceram. Teeth were cut using a diamond disc or a diamond wire, obtaining 0.8 mm² stick-shaped specimens, or were shaped with a Micro Specimen Former, obtaining dumbbell-shaped specimens (n = 10). Samples were randomly selected for SEM and LCM analysis. Remaining samples underwent microtensile test, and results were analyzed with ANOVA and Tukey test. FEA dumbbell-shaped model resulted in a more homogeneous stress distribution. Nonetheless, they failed under lower bond strengths (21.83 ± 5.44 MPa)c than stick-shaped specimens (sectioned with wire: 42.93 ± 4.77 MPaª; sectioned with disc: 36.62 ± 3.63 MPa b), due to geometric irregularities related to manufacturing process, as noted in microscopic analyzes. It could be concluded that stick-shaped, nontrimmed specimens, sectioned with diamond wire, are preferred for enamel specimens as they can be prepared in a less destructive, easier, and more precise way.

Wing diagnostic characters for Culex quinquefasciatus and Culex nigripalpus (Diptera, Culicidae)

Wing diagnostic characters for Culex quinquefasciatus and Culex nigripalpus (Diptera, Culicidae). Culex quinquefasciatus and Culex nigripalpus are mosquitoes of public health interest, which can occur sympatrically in urban and semi-urban localities. Morphological identification of these species may be difficult when specimens are not perfectly preserved. In order to suggest an alternative taxonomical diagnosis, wings of these species were comparatively characterized using geometric morphometrics. Both species could be distinguished by wing shape with accuracy rates ranging from 85-100%. Present results indicate that one can identify these species relying only on wing characters when traditional taxonomical characters are not visible.

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.

Different coordination modes for disulfoxides towards diorganotin(IV) dichlorides. X-ray crystal structures of 1,2-cis-bis-(phenylsulfinyl)ethene (rac-,cis-cbpse) and adducts [{Ph2SnCl2(meso-bpse)}n] and [{n-Bu2SnCl2(pdtd)}2]

The reactions of meso-1,2-bis(phenylsulfinyl)ethane (meso-bpse) with Ph2SnCl2, 2-phenyl-1,3-dithiane trans-1-trans-3-dioxide (pdtd) with n-Bu2SnCl2 and 1,2-cis-bis-(phenylsulfinyl)ethene (rac-,cis-cbpse) with Ph2SnCl2, in 1:1 molar ratio, yielded [{Ph2SnCl2(meso-bpse)}n], [{n-Bu2SnCl2(pdtd)}2] and [{Ph2SnCl2(rac,cis-cbpse)}x] (x = 2 or n), respectively. All adducts were studied by IR, Mössbauer and 119Sn NMR spectroscopic methods, elemental analysis and single crystal X-ray diffractometry. The X-ray crystal structure of [{Ph2SnCl2(meso-bpse)}n] revealed the occurrence of infinite chains in which the tin(IV) atoms appear in a distorted octahedral geometry with Cl atoms in cis and Ph groups in trans positions. The X-ray crystal structure of [{n-Bu2SnCl2(pdtd)}2] revealed discrete centrosymmetric dimeric species in which the tin(IV) atoms possess a distorted octahedral geometry with bridging disulfoxides in cis and n-butyl moieties in trans positions. The spectroscopic data indicated that the adduct containing the rac,cis-cbpse ligand can be dimeric or polymeric. The X-ray structural analysis of the free rac-,cis-cbpse sulfoxide revealed that the crystals belong to the C2/c space group.

Transpressive dextral shear in the Italva-Itaperuna section, Northern State of Rio de Janeiro, Brazil

Structural analysis carried out on a segment of the Neoproterozoic Ribeira Belt, southeastern Brazil, show that it represents part of the transpressive dextral orogen related to the Central Mantiqueira Province. NNE-trending and steeply dipping regional mylonitic belts form anastomosed geometry, and describe a map-scale, S-C-like structure that is characterized by their deflection towards NE near the Além Paraíba Lineament. Lithological and structural control related to deformation partition were responsible for the formation of felsic mylonitic granulites with S-type granites lenses developed in ductile shear zones, alternated with less deformed intermediate to basic granulites associated with charnockites. The dextral shear sense indicators are consistent with transpressive deformation in the region and are common especially at the border of the main shear zones. The presence of S-type leucogranite may lead to variations of linear and planar relationships, which result in local extension zones. These elements are consistent with oblique continental collision considering the São Francisco Craton as a stable block.

Analysis of the effects of conical indentation variables on the indentation response of elastic-plastic materials through factorial design of experiment

In this work, the effects of conical indentation variables on the load-depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 2(6) was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/h(max), n, theta, E, and h(max). The dimensional variables E and h(max) were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/h(max) was obtained with two different h(max) values. A set of dimensionless functions was defined to analyze the effect of the input variables: Pi(1) = P(1)/Eh(2), Pi(2) = h(c)/h, Pi(3) = H/Y, Pi(4) = S/Eh(max), Pi(6) = h(max)/h(f) and Pi(7) = W(P)/W(T). These six functions were found to depend only on the dimensionless variables studied (Y/E, R/h(max), n, theta). Another dimension less function, Pi(5) = beta, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on beta was theta. However, beta showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that beta is especially Susceptible to the error in the Calculation of the initial unloading slope.

LOCAL HEAD LOSS OF NON-COAXIAL EMITTERS INSERTED IN POLYETHYLENE PIPE

The design of a lateral line for drip irrigation requires accurate evaluation of head losses in not only the pipe but in the emitters as well. A procedure was developed to determine localized head losses within the emitters by the formulation of a mathematical model that accounts for the obstruction caused by the insertion point. These localized losses can be significant when compared with tire total head losses within the system due to the large number of emitters typically installed along the lateral line. Air experiment was carried out by altering flow characteristics to create Reynolds numbers (R) from 7,480 to 32,597 to provide turbulent flow and a maximum velocity of 2.0 m s(-1). The geometry of the emitter was determined by an optical projector and sensor An equation was formulated to facilitate the localized head loss calculation using the geometric characteristics of the emitter (emitter length, obstruction ratio, and contraction coefficient). The mathematical model was tested using laboratory measurements on four emitters. The local head loss was accurately estimated for the Uniram (difference of +13.6%) and Drip Net (difference of +7.7%) emitters, while appreciable deviations were found for the Twin Plus (-21.8%) and Tiran (+50%) emitters. The head loss estimated by the model was sensitive to the variations in the obstruction area of the emitter However, the variations in the local head loss did not result in significant variations in the maximum length of the lateral lines. In general, for all the analyzed emitters, a 50% increase in the local head loss for the emitters resulted in less than an 8% reduction in the maximum lateral length.

Potassium trifluoro[(Z)-3-methoxyprop-1-enyl]borate

In the title salt, K(+)center dot C(4)H(7)BF(3)O(-), the K atom is surrounded by six anions making close contacts through seven F [K center dot center dot center dot F = 2.779 (1)-3.048 (1) angstrom] and two O [K center dot center dot center dot O = 2.953 (2) and 3.127 (2) angstrom] atoms in a trivacant fac-vIC-9 icosahedral coordination geometry.

1-[(Z)-1-Bromo-2-(butyldichloro-lambda(4)tellanyl)ethenyl]cyclohex-1-ene

The Te(IV) atom in the title compound, [Te(C(4)H(9))(C(8)H(10)Br)Cl(2)] or C(12)H(19)BrCl(2)Te, is in a distorted psi-trigonal-bipyramidal geometry, with the lone pair of electrons projected to occupy a position in the equatorial plane, and with the Cl atoms being mutually trans [172.48 (4)degrees]. Close intramolecular [Te center dot center dot center dot Br = 3.3444 (18) angstrom] and intermolecular [Te center dot center dot center dot Cl = 3.675 (3) angstrom] interactions are observed. The latter lead to centrosymmetric dimers which assemble into layers in the bc plane. The primary connections between layers are of the type C-H center dot center dot center dot Cl.