On the k-restricted structure ratio in planar and outerplanar graphs

A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1/2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.

Angular-planar CMB power spectrum

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum C(l), this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual C(l)'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales l = 7 and l = 8. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.

Absorption of planar waves in a draining bathtub

We present an analysis of the absorption of acoustic waves by a black hole analogue in (2 + 1) dimensions generated by a fluid flow in a draining bathtub. We show that the low-frequency absorption length is equal to the acoustic hole circumference and that the high-frequency absorption length is 4 times the ergoregion radius. For intermediate values of the wave frequency, we compute the absorption length numerically and show that our results are in excellent agreement with the low-and high-frequency limits. We analyze the occurrence of superradiance, manifested as negative partial absorption lengths for corotating modes at low frequencies.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

Er(3+) doped phosphoniobate glasses and planar waveguides: structural and optical properties

Phosphoniobate glasses with composition (mol%) (100-x) NaPO(3)-xNb(2)O(5) ( x varying from 11 to 33) were prepared and characterized by means of thermal analysis, Fourier transform infrared spectroscopy, Raman scattering and (31)P nuclear magnetic resonance. The addition of Nb(2)O(5) to the polyphosphate base glass leads to depolymerization of the metaphosphate structure. Different colors were observed and assigned as indicating the presence of Nb(4+) ions, as confirmed by electron paramagnetic resonance measurements. The color was observed to depend on the glass composition and melting temperature as well. Er(3+) containing samples were also prepared. Strong emission in the 1550 nm region was observed. The Er(3+4)I(15/2) emission quantum efficiency was observed to be 90% and the quenching concentration was observed to be 1.1 mol%( 1.45 x 10(20) ions cm(-3)). Planar waveguides were prepared by Na(+)-K(+)-Ag(+) ion exchange with Er(3+) containing samples. Optical parameters of the waveguides were measured at 632.8, 543.5 and 1550 nm by the prism coupling technique as a function of the ion exchange time and Ag(+) concentration. The optimized planar waveguides show a diffusion depth of 5.9 mu m and one propagating mode at 1550 nm.

Erbium-activated silica-zirconia planar waveguides prepared by sol-gel route

Er(3+) doped (100-x)SiO(2)-xZrO(2) planar waveguides were prepared by the sol-gel route, with x ranging from 10 up to 30 mol%. Multilayer films doped with 0.3 mol% Er(3+) ions were deposited on fused quartz substrates by the dip-coating technique. The thickness and refractive index were measured by m-line spectroscopy at different wavelengths. The fabrication protocol was optimized in order to confine one propagating mode at 1.5 mu m. Photoluminescence in the near and visible region indicated a crystalline local environment for the Er(3+) ion. (c) 2007 Elsevier B.V. All rights reserved.

Proton flux induced by free fatty acids across phospholipid bilayers: New evidences based on short-circuit measurements in planar lipid membranes

Free fatty acids (FFA) are important mediators of proton transport across membranes. However, information concerning the influence of the Structural features of both FFA and the membrane environment on the proton translocation mechanisms across phospholipid membranes is relatively scant. The effects of FFA chain length, unsaturation and membrane composition on proton transport have been addressed in this study by means of electrical measurements in planar lipid bilayers. Proton conductance (G(H)(+)) was calculated from open-circuit voltage and short-circuit current density measurements. We found that cis-unsaturated FFA caused a more pronounced effect on proton transport as compared to Saturated and trans-unsaturated FFA. Cholesterol and cardiolipin decreased membrane leak conductance. Cardiolipin also decreased proton conductance. These effects indicate a dual modulation of protein-independent proton transport by FFA: through a flip-flop mechanism and by modifying a proton diffusional pathway. Moreover the membrane phospholipid composition was shown to importantly affect both processes. (C) 2009 Elsevier Inc. All rights reserved.

Effects of the cationic antimicrobial peptide eumenitin from the venom of solitary wasp Eumenes rubronotatus in planar lipid bilayers: Surface charge and pore formation activity

Eumenitin, a novel cationic antimicrobial peptide from the venom of solitary wasp Eumenes rubronotatus, was characterized by its effects on black lipid membranes of negatively charged (azolectin) and zwitterionic (1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPhPC) or DPhPC-cholesterol) phospholipids: surface potential changes, single-channel activity, ion selectivity, and pore size were studied. We found that eumenitin binds preferentially to charged lipid membranes as compared with zwitterionic ones. Eumenitin is able to form pores in azolectin (G(1) = 118.00 +/- 3.67 pS or G(2) = 160.00 +/- 7.07 pS) and DPhPC membranes (G = 61.13 +/- 7.57 pS). Moreover, cholesterol addition to zwitterionic DPhPC membranes inhibits pore formation activity but does not interfere with the binding of peptide. Open pores presented higher cation (K (+)) over anion (Cl-) selectivity. The pore diameter was estimated at between 8.5and 9.8 angstrom in azolectin membranes and about 4.3 angstrom in DPhPC membranes. The results are discussed based on the toroidal pore model for membrane pore-forming activity and ion selectivity. (c) 2007 Elsevier Ltd. All rights reserved.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

Searching for planar signatures in WMAP

We search for planar deviations of statistical isotropy in the Wilkinson Microwave Anisotropy Probe (WMAP) data by applying a recently introduced angular-planar statistics both to full-sky and to masked temperature maps, including in our analysis the effect of the residual foreground contamination and systematics in the foreground removing process as sources of error. We confirm earlier findings that full-sky maps exhibit anomalies at the planar (l) and angular (l) scales (l; l) = (2; 5); (4; 7); and (6; 8), which seem to be due to unremoved foregrounds since this features are present in the full-sky map but not in the masked maps. On the other hand, our test detects slightly anomalous results at the scales (l; l) = (10; 8) and (2; 9) in the masked maps but not in the full-sky one, indicating that the foreground cleaning procedure (used to generate the full-sky map) could not only be creating false anomalies but also hiding existing ones. We also find a significant trace of an anomaly in the full-sky map at the scale (l; l) = (10; 5), which is still present when we consider galactic cuts of 18.3% and 28.4%. As regards the quadrupole (l = 2), we find a coherent over-modulation over the whole celestial sphere, for all full-sky and cut-sky maps. Overall, our results seem to indicate that current CMB maps derived from WMAP data do not show significant signs of anisotropies, as measured by our angular-planar estimator. However, we have detected a curious coherence of planar modulations at angular scales of the order of the galaxy`s plane, which may be an indication of residual contaminations in the full-and cut-sky maps.

Elaboration and optimization of (Y,Er)Al(3)(BO(3))(4) glassy planar waveguides through the sol-gel process

In this work, a sol-gel route was used to prepare Y(0.9)Er(0.1)Al(3)(BO(3))(4) glassy thin films by spin-coating technique looking for the preparation and optimization of planar waveguides for integrated optics. The films were deposited on silica and silicon substrates using stable sols synthesized by the sol-gel process. Deposits with thicknesses ranging between 520 and 720 nm were prepared by a multi-layer process involving heat treatments at different temperatures from glass transition to the film crystallization and using heating rates of 2 degrees C/min. The structural characterization of the layers was performed by using grazing incidence X-ray diffraction and Raman spectroscopy as a function of the heat treatment. Microstructural evolution in terms of annealing temperatures was followed by high resolution scanning electron microscopy and atomic force microscopy. Optical transmission spectra were used to determine the refractive index and the film thicknesses through the envelope method. The optical and guiding properties of the films were studied by m-line spectroscopy. The best films were monomode with 620 nm thickness and a refractive index around 1.664 at 980 nm wavelength. They showed good waveguiding properties with high light-coupling efficiency and low propagation loss at 632.8 and 1550 nm of about 0.88 dB/cm. (C) 2009 Elsevier B.V. All rights reserved.

Erbium and Ytterbium Codoped Titanoniobophosphate Glasses for Ion-Exchange-Based Planar Waveguides

This work presents the optical properties of erbium-doped and erbium/ytterbium codoped Na(2)O-Al(2)O(3)-TiO(2)-Nb(2)O(5)-P(2)O(5) glass systems and also the characterization of planar waveguides obtained by typical thermally assisted Ag+<-> Na+ ion-exchange process. The glass systems allow the preparation of single mode and multimode planar waveguides presenting a strong and relatively broad emission at 1536 nm. The emission signal in the infrared region is intensified for silver-containing samples when compared with free-silver samples. The emission signal intensification may be attributed to a nonplasmonic energy transfer from silver species to Er3+ ions as no bands related to surface plasmon resonance (SPR) of silver nanoparticles were observed.

Fabrication and integration of planar electrodes for contactless conductivity detection on polyester-toner electrophoresis microchips

In this report, we describe the microfabrication and integration of planar electrodes for contactless conductivity detection on polyester-toner (PT) electrophoresis microchips using toner masks. Planar electrodes were fabricated by three simple steps: (i) drawing and laser-printing the electrode geometry on polyester films, (ii) sputtering deposition onto substrates, and (iii) removal of toner layer by a lift-off process. The polyester film with anchored electrodes was integrated to PT electrophoresis microchannels by lamination at 120 degrees C in less than 1 min. The electrodes were designed in an antiparallel configuration with 750 mu m width and 750 gm gap between them. The best results were recorded with a frequency of 400 kHz and 10 V-PP using a sinusoidal wave. The analytical performance of the proposed microchip was evaluated by electrophoretic separation of potassium, sodium and lithium in 150 mu m wide x 6 mu m deep microchannels. Under an electric field of 250 V/cm the analytes were successfully separated in less than 90 s with efficiencies ranging from 7000 to 13 000 plates. The detection limits (S/N = 3) found for K+, Na+, and Li+ were 3.1, 4.3, and 7.2 mu mol/L, respectively. Besides the low-cost and instrumental simplicity, the integrated PT chip eliminates the problem of manual alignment and gluing of the electrodes, permitting more robustness and better reproducibility, therefore, more suitable for mass production of electrophoresis microchips.

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.