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.

Solution behavior and surface properties of carboxymethylcellulose acetate butyrate

Solution behavior of carboxymethylcellulose acetate butyrate (CMCAB) in acetone and ethyl acetate has been investigated by small-angle X-ray scattering (SAXS) and capillary viscometry and correlated with the characteristics of CMCAB films. Viscosity and SAXS measurements showed that ethyl acetate is a better solvent than acetone for CMCAB. Thin films of CMCAB were deposited onto silicon wafers (Si/SiO(2)) by spin coating. AFM images revealed that CMCAB spin coated films from solutions prepared in ethyl acetate were homogeneous and flat. However, films obtained from solutions in acetone were very rough. Contact angle measurements with polar and apolar test liquids characterized CMCAB surfaces as hydrophobic and allowed estimating the surface energy of CMCAB. Sum frequency generation vibrational spectroscopy was used to understand the role played by solvents and to gain insight about molecular orientation at Si/SiO(2)/CMCAB interface.

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.

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.

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.

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.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

Spacelike Surfaces in L(4) with Degenerate Gauss Map

In this paper we study and present a complete classification of spacelike surfaces with degenerate Gauss map in the Lorentz-Minkowski space L(4).

Triply periodic minimal surfaces which converge to the Hoffman-Wohlgemuth example

We get a continuous one-parameter new family of embedded minimal surfaces, of which the period problems are two-dimensional. Moreover, one proves that it has Scherk`s second surface and Hoffman-Wohlgemuth`s example as limit-members.

Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

A characterisation of the Hoffman-Wohlgemuth surfaces in terms of their symmetries

For an embedded singly periodic minimal surface (M) over tilde with genus rho >= 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the Hoffman-Wohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces.

Structure-Activity Relationship for Quaternary Ammonium Compounds Hybridized with Poly(methyl methacrylate)

Hybrid films from poly (methylmethacrylate) (PMMA) and dioctadecyldimethylammonium bromide (DODAB), cetyltrimethylammonium bromide (CTAB), or tetrapropylammonium bromide (TPAB) were characterized by determination of wettability, ellipsometry, atomic force microscopy, active compounds diffusion to water, X-ray photoelectron spectroscopy (XPS) with determination of atomic composition on the films surface, and biocidal activity against Pseudomonas aeruginosa or Staphylococcus aureus. QAC mobility in the films increased from DODAB to CTAB to TPAB. Diffusion and optimal hydrophobic hydrophilic balance imparted the highest bioactivity to CTAB. DODAB sustained immobilization at the film surface killed bacteria upon contact. TPAB ability to diffuse was useless because of its unfavorable hydrophobic hydrophilic balance for bioactivity.

Protein Adsorption onto Polyelectrolyte Layers: Effects of Protein Hydrophobicity and Charge Anisotropy

Ellipsometry was used to investigate the influence of ionic strength (I) and pH on the adsorption of bovine serum albumin (BSA) or beta-lactoglobulin (BLG) onto preabsorbed layers of two polycations: poly(diallyldimethylammonium chloride) (PDADMAC) or poly(4-vinylpyridine bromide) quaternized with linear aliphatic chains of two (QPVP-C2) or five (QPVP-C5) carbons. Comparisons among results for the three polycations reveal hydrophobic interactions, while comparisons between BSA and BLG-proteins of very similar isoelectric points (pI)-indicate the importance of protein charge anisotropy. At pH close to pI, the ionic strength dependence of the adsorbed amount of protein (Gamma) displayed maxima in the range 10 < I < 25 mM corresponding to Debye lengths close to the protein radii. Visualization of protein charge by Delphi suggested that these ionic strength conditions corresponded to suppression of long-range repulsion between polycations and protein positive domains, without diminution of short-range attraction between polycation segments and locally negative protein domains, in a manner similar to the behavior of PE-protein complexes in solution.(1-4) This description was consistent with the disappearance of the maxima at pH either above or below pI. In the former case, Gamma values decrease exponentially with I(1/2), due to screening of attractions, while in the latter case adsorption of both proteins decreased at low I due to strong repulsion. Close to or below pI both proteins adsorbed more strongly onto QPVP-C5 than onto QPVP-C2 or PDADMAC due to hydrophobic interactions with the longer alkyl group. Above pI, the adsorption was more pronounced with PDADMAC because these chains may assume more loosely bound layers due to lower linear charge density.