Twisted Surfaces with Null Rotation Axis in Minkowski 3-Space

We examine curvature properties of twisted surfaces with null rotation axis in Minkowski 3-space. That is, we study surfaces that arise when a planar curve is subject to two synchronized rotations, possibly at different speeds, one in its supporting plane and one of this supporting plane about an axis in the plane. Moreover, at least one of the two rotation axes is a null axis. As is clear from its construction, a twisted surface generalizes the concept of a surface of revolution. We classify flat, constant Gaussian curvature, minimal and constant mean curvature twisted surfaces with a null rotation axis. Aside from pseudospheres, pseudohyperbolic spaces and cones, we encounter B-scrolls in these classifications. The appearance of B-scrolls in these classifications is of course the result of the rotation about a null axis. As for the cones in the classification of flat twisted surfaces, introducing proper coordinates, we prove that they are determined by so-called Clelia curves. With a Clelia curve we mean a curve that has linear dependent spherical coordinates.     

A domain decomposition method for linear exterior boundary value problems

In this paper, we present a domain decomposition method, based on the general theory of Steklov-Poincaré operators, for a class of linear exterior boundary value problems arising in potential theory and heat conductivity. We first use a Dirichlet-to-Neumann mapping, derived from boundary integral equation methods, to transform the exterior problem into an equivalent mixed boundary value problem on a bounded domain. This domain is decomposed into a finite number of annular subregions, and the Dirichlet data on the interfaces is introduced as the unknown of the associated Steklov-Poincaré problem. This problem is solved with the Richardson method by introducing a Dirichlet-Robin-type preconditioner, which yields an iteration-by-subdomains algorithm well suited for parallel computations. The corresponding analysis for the finite element approximations and some numerical experiments are also provided.     

Stopping Time Convergence for Processes Associated with Dirichlet Forms

Potential Analysis - Convergence is proved for solutions un of Dirichlet problems in regions with many small excluded sets (holes), as the holes become smaller and more numerous. The problem is...     

Banach-stone theorems and separating maps

LetC(X,E) andC(Y,F) denote the spaces of continuous functions on the Tihonov spacesX andY, taking values in the Banach spacesE andF, respectively. A linear mapH:C(X,E)→C(Y,F) isseparating iff(x)g(x)=0 for allx inX impliesHf(y)Hg(y)=0 for ally inY. Some automatic continuity properties and Banach-Stone type theorems (i.e., asserting that isometries must be of a certain form) for separating mapsH between spaces of real- and complex-valued functions have already been developed. The extension of such results to spaces of vector-valued functions is the general subject of this paper. We prove in Theorem 4.1, for example, for compactX andY, that a linear isometryH betweenC(X,E) andC(Y,F) is a “Banach-Stone” map if and only ifH is “biseparating (i.e,H andH ⁻¹ are separating). The Banach-Stone theorems of Jerison and Lau for vector-valued functions are then deduced in Corollaries 4.3 and 4.4 for the cases whenE andF or their topological duals, respectively, are strictly convex. Research supported by the Fundació Caixa Castelló, MI/25.043/92     

Tuning the gas sensing performance of single PEDOT nanowire devices

This paper reports the synthesis and dopant dependent electrical and sensing properties of single poly(ethylenedioxythiophene) (PEDOT) nanowire sensors. Dopant type (i.e. polystyrenesulfonate (PSS(-)) and perchlorate (ClO(4)(-))) and solvent (i.e. acetonitrile and 1 : 1 water-acetonitrile mixture) were adjusted to change the conjugation length and hydrophilicity of nanowires which resulted in change of the electrical properties and sensing performance. Temperature dependent coefficient of resistance (TCR) indicated that the electrical properties are greatly dependent on dopants and electrolyte where greater disorder was found in PSS(-) doped PEDOT nanowires compared to ClO(4)(-) doped nanowires. Upon exposure to different analytes including water vapor and volatile organic compounds, these nanowire devices displayed substantially different sensing characteristics. ClO(4)(-) doped PEDOT nanowires from an acetonitrile bath show superior sensing responses toward less electronegative analytes and followed a power law dependence on the analyte concentration at high partial pressures. These tunable sensing properties were attributed to variation in the conjugation lengths, dopant type and concentration of the wires which may be attributed to two distinct sensing mechanisms: swelling within the bulk of the nanowire and work function modulation of Schottky barrier junction between nanowire and electrodes.     

Complete solution of the problem of one-dimensional non-covalent non-cooperative self-assembly in two-component systems

Equations for the mass conservation law and the molecular parameters observed in spectroscopic experiments have been derived for non-covalent, non-cooperative, one-dimensional self-assembly in systems containing two types of interacting molecules (hetero-association), taking into account "reflected" complexes and "edge effects."     

Spectroscopic and theoretical study of the weakly bound H2-HCCCN dimer

Rotational spectra of the H(2)-HCCCN complex were studied using a pulsed-nozzle Fourier transform microwave spectrometer. Complexes containing the main and several minor isotopologues of cyanoacetylene (HCCC(15)N, DCCCN, and various (13)C containing isotopologues) and the two spin isomers of the H(2) molecule (paraH(2) and orthoH(2)) were investigated. Transitions of complexes with (14)N and D containing isotopologues have nuclear quadrupole hyperfine structures, which were measured and analyzed. Transitions of orthoH(2) molecule containing complexes show additional hyperfine structures due to nuclear magnetic proton spin-proton spin coupling of the hydrogen nuclei in the H(2) molecule. For orthoH(2)-HCCCN, both strong a- and weaker b-type transitions were measured and analyzed using a semirigid asymmetric rotor model. For the paraH(2)-HCCCN complex, only a-type transitions could be observed. The dimer complexes are floppy and have near T-shaped structures. Intermolecular interaction potential energy surfaces were calculated for H(2)-HCCCN using the coupled-cluster method with single and double excitations and noniterative inclusion of triple excitations [CCSD(T)]. Three orientations of the hydrogen molecule within the complex were considered. Equal weighting of the surfaces corresponding to the three hydrogen orientations provided an averaged potential energy surface. Bound-state rotational energy levels supported by the surfaces were determined for the different hydrogen orientations, as well as for the averaged surface. Simple scaling of the surfaces improved the agreement with the experimental results and produced surfaces with near spectroscopic accuracy.