Fixed-orientation equilateral triangle matching of point sets

Given a point set P and a class C of geometric objects, G(C)(P) is a geometric graph with vertex set P such that any two vertices p and q are adjacent if and only if there is some C is an element of C containing both p and q but no other points from P. We study G(del)(P) graphs where del is the class of downward equilateral triangles (i.e., equilateral triangles with one of their sides parallel to the x-axis and the corner opposite to this side below that side). For point sets in general position, these graphs have been shown to be equivalent to half-Theta(6) graphs and TD-Delaunay graphs. The main result in our paper is that for point sets P in general position, G(del)(P) always contains a matching of size at least vertical bar P vertical bar-1/3] and this bound is tight. We also give some structural properties of G(star)(P) graphs, where is the class which contains both upward and downward equilateral triangles. We show that for point sets in general position, the block cut point graph of G(star)(P) is simply a path. Through the equivalence of G(star)(P) graphs with Theta(6) graphs, we also derive that any Theta(6) graph can have at most 5n-11 edges, for point sets in general position. (C) 2013 Elsevier B.V. All rights reserved.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 mu m and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 mu m. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 mu m. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor. (C) 2009 Optical Society of America

Assessment of insect occurrence in boreal forests based on satellite imagery and field measurements.

The presence/absence data of twenty-seven forest insect taxa (e.g. Retinia resinella, Formica spp., Pissodes spp., several scolytids) and recorded environmental variation were used to investigate the applicability of modelling insect occurrence based on satellite imagery. The sampling was based on 1800 sample plots (25 m by 25 m) placed along the sides of 30 equilateral triangles (side 1 km) in a fragmented forest area (approximately 100 km2) in Evo, S Finland. The triangles were overlaid on land use maps interpreted from satellite images (Landsat TM 30 m multispectral scanner imagery 1991) and digitized geological maps. Insect occurrence was explained using either environmental variables measured in the field or those interpreted from the land use and geological maps. The fit of logistic regression models varied between species, possibly because some species may be associated with the characteristics of single trees while other species with stand characteristics. The occurrence of certain insect species at least, especially those associated with Scots pine, could be relatively accurately assessed indirectly on the basis of satellite imagery and geological maps. Models based on both remotely sensed and geological data better predicted the distribution of forest insects except in the case of Xylechinus pilosus, Dryocoetes sp. and Trypodendron lineatum, where the differences were relatively small in favour of the models based on field measurements. The number of species was related to habitat compartment size and distance from the habitat edge calculated from the land use maps, but logistic regressions suggested that other environmental variables in general masked the effect of these variables in species occurrence at the present scale.

Acto-myosin contractility rotates the cell nucleus

The nucleus of the eukaryotic cell functions amidst active cytoskeletal �laments, but its response to the stresses carried by these �laments is largely unexplored. We report here the results of studies of the translational and rotational dynamics of the nuclei of single �broblast cells, with the e�ects of cell migration suppressed by plating onto �bronectin-coated micro-fabricated patterns. Patterns of the same area but di�erent shapes and/or aspect ratio were used to study the e�ect of cell geometry on the dynamics. On circles, squares and equilateral triangles, the nucleus undergoes persistent rotational motion, while on high-aspect-ratio rectangles of the same area it moves only back and forth. The circle and the triangle showed respectively the largest and the smallest angular speed. We show that our observations can be understood through a hydrodynamic approach in which the nucleus is treated as a highly viscous inclusion residing in a less viscous uid of orientable �laments endowed with active stresses. Lowering actin contractility selectively by introducing blebbistatin at low concentrations drastically reduced the speed and persistence time of the angular motion of the nucleus. Time-lapse imaging of actin revealed a correlated hydrodynamic ow around the nucleus, with pro�le and magnitude consistent with the results of our theoretical approach. Coherent intracellular ows and consequent nuclear rotation thus appear to be a generic property that cells must balance by speci�c mechanisms in order to maintain nuclear homeostasis

Fabrication and characterization of uniform Fe3O4 octahedral micro-crystals

Uniform Fe3O4 octahedral microcrystals with perfect appearance have been successfully synthesized by a Triton X100-assisted polyol process. During the polyols process for the preparation of Fe3O4 octahedra. the introduction of Triton X100 decreases significantly the needed concentration of NaOH. The results show that Fe3O4 octahedra are composed of eight triangular sheets, which are equilateral triangles. The edge size of Fe3O4 octahedron is about 4 mu m. The magnetic properties of Fe3O4 octahedral particles were evaluated on a SQUID magnetometer at room temperature.

Co3(SO4)3(OH)2[enH2]: a newS= 3/2 Kagome-type layered sulfate with a unique connectivity

The Kagome lattice, comprising a two-dimensional array of corner-sharing equilateral triangles, is central to the exploration of magnetic frustration. In such a lattice, antiferromagnetic coupling between ions in triangular plaquettes prevents all of the exchange interactions being simultaneously satisfied and a variety of novel magnetic ground states may result at low temperature. Experimental realization of a Kagome lattice remains difficult. The jarosite family of materials of nominal composition AM3(SO4)2(OH)6 (A = monovalent cation; M= Fe3+, Cr3+), offers perhaps one of the most promising manifestations of the phenomenon of magnetic frustration in two dimensions. The magnetic properties of jarosites are however extremely sensitive to the degree of coverage of magnetic sites. Consequently, there is considerable interest in the use of soft chemical techniques for the design and synthesis of novel materials in which to explore the effects of spin, degree of site coverage and connectivity on magnetic frustration.

Optimal low cost transfer to L4 and L5 lagrangian points

Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. Because of their distance electromagnetic radiations from the Earth arrive on them substantially attenuated. As so, these Lagrangian points represent remarkable positions to host astronomical observatories. However, this same distance characteristic may be a challenge for periodic servicing mission. In this work, we introduce a new low-cost orbital transfer strategy that opportunistically combine chaotic and swing-by transfers to get a very efficient strategy that can be used for servicing mission on astronomical mission placed on Lagrangian points L4 or L5. This strategy is not only efficient with respect to thrust requirement, but also its time transfer is comparable to others known transfer techniques based on time optimization. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

Fractais no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Rod-shaped plasmonic sensors

Plasmonic nanoparticles exhibit strong light scattering efficiency due to the oscillations of their conductive electrons (plasmon), which are excited by light. For rod-shaped nanoparticles, the resonance position is highly tunable by the aspect ratio (length/width) and the sensitivity to changes in the refractive index in the local environment depends on their diameter, hence, their volume. Therefore, rod-shaped nanoparticles are highly suitable as plasmonic sensors.rnWithin this thesis, I study the formation of gold nanorods and nanorods from a gold-copper alloy using a combination of small-angle X-ray scattering and optical extinction spectroscopy. The latter represents one of the first metal alloy nanoparticle synthesis protocols for producing rod-shaped single crystalline gold-copper (AuxCu(1-x)) alloyed nanoparticles. I find that both length and width independently follow an exponential growth behavior with different time-constants, which intrinsically leads to a switch between positive and negative aspect ratio growth during the course of the synthesis. In a parameter study, I find linear relations for the rate constants as a function of [HAuCl4]/[CTAB] ratio and [HAuCl4]/[seed] ratio. Furthermore, I find a correlation of final aspect ratio and ratio of rate constants for length and width growth rate for different [AgNO3]/[HAuCl4] ratios. I identify ascorbic acid as the yield limiting species in the reaction by the use of spectroscopic monitoring and TEM. Finally, I present the use of plasmonic nanorods that absorb light at 1064nm as contrast agents for photoacoustic imaging (BMBF project Polysound). rnIn the physics part, I present my automated dark-field microscope that is capable of collecting spectra in the range of 450nm to 1750 nm. I show the characteristics of that setup for the spectra acquisition in the UV-VIS range and how I use this information to simulate measurements. I show the major noise sources of the measurements and ways to reduce the noise and how the combination of setup charactersitics and simulations of sensitivity and sensing volume can be used to select appropriate gold rods for single unlabeled protein detection. Using my setup, I show how to estimate the size of gold nano-rods directly from the plasmon linewidth measured from optical single particle spectra. Then, I use this information to reduce the distribution (between particles) of the measured plasmonic sensitivity S by 30% by correcting for the systematic error introduced from the variation in particle size. I investigate the single particle scattering of bowtie structures — structures consisting of two (mostly) equilateral triangles pointing one tip at each other. I simulate the spectra of the structures considering the oblique illumination angle in my setup, which leads to additional plasmon modes in the spectra. The simulations agree well with the measurements form a qualitative point of view.rn

Silver-based crystalline nanoparticles, microbially fabricated

One mechanism of silver resistance in microorganisms is accumulation of the metal ions in the cell. Here, we report on the phenomenon of biosynthesis of silver-based single crystals with well-defined compositions and shapes, such as equilateral triangles and hexagons, in Pseudomonas stutzeri AG259. The crystals were up to 200 nm in size and were often located at the cell poles. Transmission electron microscopy, quantitative energy-dispersive x-ray analysis, and electron diffraction established that the crystals comprise at least three different types, found both in whole cells and thin sections. These Ag-containing crystals are embedded in the organic matrix of the bacteria. Their possible potential as organic-metal composites in thin film and surface coating technology is discussed.

Axis-based grouping reduces visual extinction

We examined the effects on extinction of grouping by collinearity of edges and grouping by alignment of internal axes of shapes, in a patient (GK) with simultanagnosia following bilateral parietal brain damage. GK’s visual extinction was reduced when items (equilateral triangles and angles) could be grouped by base alignment (i.e., collinearity) or by axis alignment, relative to a condition in which items were ungrouped. These grouping effects disappeared when inter-item spacing was increased, though factors such as display symmetry remained constant. Overall, the results suggest that, under some conditions, grouping by alignment of axes of symmetry can have an equal beneficial effect on visual extinction as edge-based grouping; thus, in the extinguished field, there is derivation of axis-based representations from the contours present.

Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries

The influence of imperfect boundaries on the mode quality factor is investigated for equilateral-triangle-resonator (ETR) semiconductor microlasers by the finite difference time domain technique and the Pade approximation with Baker's algorithm. For 2-D ETR with a refractive index of 3.2 and side length of 5 mum, the confined modes can still have a quality factor of about 1000 as small triangles with side length of 1 mum are cut from the vertices of the ETR. For a deformed 5 mum ETR with round vertices and curve sides, the simulated mode quality factors are comparable to the measured results.

Synthesis and characterisation of heterometallic molecular triangles using ambidentate linker: self-selection of a single linkage isomer

The coordination driven self-assembly of discrete molecular triangles from a non-symmetric ambidentate linker 5-pyrimidinecarboxylate (5-pmc) and Pd(II)/Pt(II) based 90◦ acceptors is presented. Despite the possibility of formation of a mixture of isomeric macrocycles (linkage isomers) due to different connectivity of the ambidentate linker, formation of a single and symmetrical linkage somer in both the cases is an interesting observation. Moreover, the reported macrocycles represent the first example of discrete metallamacrocycles of bridging 5-pmc. While solution composition in both the cases was characterised by multinuclear NMR study and electrospray ionization mass spectrometry (ESI-MS), the identity of the assemblies in the solid state was established by X-ray single crystals structure analysis. Variable temperature NMR study clearly ruled out the formation of any other macrocycles by [4 + 4] or [2 + 2] self-assembly of the reacting components.

Method for measurement of the angles of an equilateral (60-deg) prism

A simple technique is devised io measure the angles of equilateral (60-deg) prisms, without using the expensive spectrometers, autocollimators, and angle gauges. The method can be extended to unpolished and opaque prisms made out of materials other than glass. (C) 1997 Society of Photo-Optical Instrumentation Engineers.