Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

A note on finite determinacy for corank 2 map germs from surfaces to 3-space

We study properties of finitely determined corank 2 quasihomogeneous map germs f: (C(2), 0) -> (C(3), 0). Examples and counter examples of such map germs are presented.

Rotation effect on geodesic and zonal flow modes in tokamak plasmas with isothermal magnetic surfaces

The electrostatic geodesic mode oscillations are investigated in rotating large aspect ratio tokamak plasmas with circular isothermal magnetic surfaces. The analysis is carried out within the magnetohydrodynamic model including heat flux to compensate for the non-adiabatic pressure distribution along the magnetic surfaces in plasmas with poloidal rotation. Instead of two standard geodesic modes, three geodesic continua are found. The two higher branches of the geodesic modes have a small frequency up-shift from ordinary geodesic acoustic and sonic modes due to rotation. The lower geodesic continuum is a newzonal flowmode (geodesic Doppler mode) in plasmas with mainly poloidal rotation. Limits to standard geodesic modes are found. Bifurcation of Alfven continuum by geodesic modes at the rational surfaces is also discussed. Due to that, the frequency of combined geodesic continuum extends from the poloidal rotation frequency to the ion-sound band that can have an important role in suppressing plasma turbulence.

Termination of diamond surfaces with hydrogen, oxygen and fluorine using a small, simple plasma gun

We have formed and characterized polycrystalline diamond films with surfaces having hydrogen terminations, oxygen terminations, or fluorine terminations, using a small, simple and novel plasma gun to bombard the diamond surface, formed by plasma assisted CVD in a prior step, with ions of the wanted terminating species. The potential differences between surface regions with different terminations were measured by Kelvin Force Microscopy (KFM). The highest potential occurred for oxygen termination regions and the lowest for fluorine. The potential difference between regions with oxygen terminations and hydrogen terminations was about 80 mV, and between regions with hydrogen terminations and fluorine terminations about 150 mV. Regions with different terminations were identified and imaged using the secondary electron signal provided by scanning electron microscopy (SEM). since this signal presents contrast for surfaces with different electrical properties. The wettability of the surfaces with different terminations was evaluated, measuring contact angles. The sample with oxygen termination was the most hydrophilic, with a contact angle of 75 degrees. hydrogen-terminated regions with 83 degrees, and fluorine regions 93 degrees, the most hydrophobic sample. (C) 2010 Elsevier B.V. All rights reserved.

Probing the functionalization of gold surfaces and protein adsorption by PM-IRRAS

The control of morphology and coating of metal surfaces is essential for a number of organic electronic devices including photovoltaic cells and sensors. In this study, we monitor the functionalization of gold surfaces with 11-mercaptoundecanoic acid (MUA, HS(CH(2))(10)CO(2)H) and cysteamine, aiming at passivating the surfaces for application in surface plasmon resonance (SPR) biosensors. Using polarization-modulated infrared reflection-absorption spectroscopy (PM-IRRAS), cyclic voltammetry, atomic force microscopy and quartz crystal microbalance, we observed a time-dependent organization process of the adsorbed MUA monolayer with alkyl chains perpendicular to the gold surface. Such optimized condition for surface passivation was obtained with a systematic search for experimental parameters leading to the lowest electrochemical signal of the functionalized gold electrode. The ability to build supramolecular architectures was also confirmed by detecting with PM-IRRAS the adsorption of streptavidin on the MUA-functionalized gold. As the approaches used for surface functionalization and its verification with PM-IRRAS are generic, one may now envisage monitoring the fabrication of tailored electrodes for a variety of applications.

Laser microstructuring for fabricating superhydrophobic polymeric surfaces

In this paper we show the fabrication of hydrophobic polymeric surfaces through laser microstructuring. By using 70-ps pulses from a Q-switched and mode-locked Nd:YAG laser at 532 nm, we were able to produce grooves with different width and separation, resulting in square-shaped pillar patterns. We investigate the dependence of the morphology on the surface static contact angle for water, showing that it is in agreement with the Cassie-Baxter model. We demonstrate the fabrication of a superhydrophobic polymeric surface, presenting a water contact angle of 157 degrees. The surface structuring method presented here seems to be an interesting option to control the wetting properties of polymeric surfaces. (C) 2010 Elsevier B.V. All rights reserved.

Neopaleozoic striated surfaces in the granitic basement and clast pavement remains of Salto, SP

Near Guarau Ceramic, localized southwest of Salto city in the State of Sao Paulo, two granite outcrops, distant some tens of meters from each other, display Neopaleozoic striated surfaces. These surfaces are in contact with diamictites from the Itarare Subgroup. The striae correspond to sub parallel grooves with millimetric spacing and depth, oriented about N48E and dipping 12 degrees to 42 degrees towards SE. Observed features and association with diamictites indicate an origin by glacial abrasion due to ice movement from southeast towards northwest. About 1.8 km east of Salto, unconsolidated material containing flat-iron-shaped and striated clasts was found on top of granite outcrops, interpreted as clasts pavement remains.

ON AMINO ACID AND CODON ASSIGNMENT IN ALGEBRAIC MODELS FOR THE GENETIC CODE

We give a list of all possible schemes for performing amino acid and codon assignments in algebraic models for the genetic code, which are consistent with a few simple symmetry principles, in accordance with the spirit of the algebraic approach to the evolution of the genetic code proposed by Hornos and Hornos. Our results are complete in the sense of covering all the algebraic models that arise within this approach, whether based on Lie groups/Lie algebras, on Lie superalgebras or on finite groups.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space. (C) 2010 Elsevier Inc. All rights reserved.

Algebraic Bol loops

In this paper, we study the category of algebraic Bol loops over an algebraically closed field of definition. On the one hand, we apply techniques from the theory of algebraic groups in order to prove structural theorems for this category. On the other hand, we present some examples showing that these loops lack some nice properties of algebraic groups; for example, we construct local algebraic Bol loops which are not birationally equivalent to global algebraic loops.