The influence of edge detection algorithms on the estimation of the fractal dimension of binary digital images

The boundary of a fractal object, represented in a two-dimensional space, is theoretically a line with an infinitely small width. In digital images this boundary or contour is limited to the pixel resolution of the image and the width of the line commonly depends on the edge detection algorithm used. The Minkowski dimension was evaluated by using three different edge detection algorithms (Sobel, Roberts, and Laplace operator). These three operators were investigated because they are very widely used and because their edge detection result is very distinct concerning the line width. Very common fractals (Sierpinski carpet and Koch islands) were investigated as well as the binary images from a cancer invasion assay taken with a confocal laser scanning microscope. The fractal dimension is directly proportional to the width of the contour line and the fact, that in practice very often the investigated objects are fractals only within a limited resolution range is considered too.     

Studies of translational diffusion in the smectic A phase of a Gay-Berne mesogen using molecular dynamics computer simulation

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.     

Studies on pyridazine azide cyclisation reactions

Reaction of sodium azide with 4-methyl-3,5,6-tribromopyridazine results in the formation of 3,5,6-triazide intermediate which could cyclise to give two possible bicyclic products while ab initio calculations show that the formation of a tricyclic compound is extremely energetically unfavourable. However, experimentally, only one major product is isolated. The structure of this unstable product has been conclusively established by X-ray crystallography as 3,5-diazido-4-methyl[1,5-b]tetrazolopyridazine confirming theoretical predictions.     

Investigation of modified basal plane pyrolytic graphite electrodes: definitive evidence for the electrocatalytic properties of the ends of carbon nanotubes

The basis of the electrocatalytic nature of multi-wall carbon nanotubes is suggested to reside in electron transfer from the ends of nanotubes, which structurally resemble the behaviour of edge plane (as opposed to basal plane) graphite, and is demonstrated via the comparison of the electrochemical oxidation of epinephrine and the electrochemical reduction of ferricyanide at nanotube-modified electrodes using different types of graphite electrodes and with C(60)-modified electrodes.     

XAFS studies of anti-inflammatory dinuclear and mononuclear Zn(II) complexes of indomethacin

Zinc K-edge X-ray absorption fine structure (XAFS) experiments were performed in the solid and solution states at low temperature (10 K), on dimeric and monomeric anti-inflammatory Zn(II) complexes of indomethacin [1-(4-chlorobenzoyl)-5-methoxy-2-methyl-1H-indole-3-acetic acid=IndoH] of the formula [Zn2(Indo)4L2] [L=pyridine (Py), N,N-dimethylacetamide (DMA)], [Zn(Indo)2L2] [L=ethanol (EtOH), methanol (MeOH)], and Zn(II) acetate dihydrate [Zn(OAc)2(OH2)2]. The bond distances and angles obtained from multiple-scattering fits to the XAFS data of the Zn(II) dimeric complexes in the solid and solution states exhibit excellent correspondence with those obtained from single crystal diffraction studies. The Zn...Zn separations of 2.97 and 2.96 A and carboxylate group O-C-O angles of 125 degrees for powdered [Zn2(Indo)4(Py)2] and [Zn2(Indo)4(DMA)2] agree well with the XRD values of 2.969(1) and 2.9686(6) A and 125.8(4) degrees and 126.1(2) degrees, respectively. The calculated Zn-O(RCOO) and Zn-L bond distances of 2.03 and 2.04 A, or 2.02 and 1.98 A for Py or DMA complexes, respectively, also agree well with crystallographic data. The X-ray powder diffraction data on samples of the monomers exhibited additional reflections apart from those due to the crystallographically characterized cis-[Zn(eta2-O,O'-Indo)2L2], but microanalyses were consistent with this formulation. Therefore, mixed models that contained the cis complex and a second component consisting of a trans-six-coordinate complex, a five-coordinate complex, or a four-coordinate complex were used to model the XAFS. The best fits to the XAFS data were obtained with a mixture of the cis-six-coordinate complex and a four-coordinate complex containing two monodentate Indo ligands. The bond lengths for the six-coordinate structure were consistent with those determined on a single crystal, and those for the four-coordinate complexes were consistent with related four-coordinate structures with two monodentate carboxylate ligands. Dissolution of the dimer (DMA adduct) in DMF resulted in a mixture of dimer and monomer species as shown by MS XAFS fitting. This is the first time that solution structures have been determined for anti-inflammatory Zn(II) complexes, and this is an important first step in understanding the pharmacology of the complexes.     

Invariant foliations near normally hyperbolic invariant manifolds for semiflows

Let be a compact manifold which is invariant and normally hyperbolic with respect to a semiflow in a Banach space. Then in an -neighborhood of there exist local center-stable and center-unstable manifolds and , respectively. Here we show that and may each be decomposed into the disjoint union of submanifolds (leaves) in such a way that the semiflow takes leaves into leaves of the same collection. Furthermore, each leaf intersects in a single point which determines the asymptotic behavior of all points of that leaf in either forward or backward time.

     

Trends in microdisk laser research and linear optical modelling

Research into microdisk lasers demonstrates new achievements both in the technology and in the associated physical effects and applications. Melting and rounding of the disk edge boosts the Q-factors due to improved surface smoothness. In-plane cavity shape is widely used as a design instrument. Optimal shaping of pumped area lowers the threshold power. Photonic molecules made of several microdisks as “photonic atoms” show lasing at several closely spaced frequencies. A microdisk with a single quantum dot as an active region is considered as the most promising system for realisation of a single photon emitter necessary for quantum computing. These new effects and devices can be simulated with accurate numerical techniques, developed recently for “warm-cavity” linear modelling, that are able to bring a new vision of the physics of lasing.     

An extension of the Dirac theory of constraints

Constructions introduced by Dirac for singular Lagrangians are extended and reinterpreted to cover cases when kernel distributions are either nonintegrable or of nonconstant rank, and constraint sets need not be closed.     

A bi-logistic growth model for conference registration with an early bird deadline

The recent interest in human dynamics has led researchers to investigate the processes that explain human behaviour within different contexts. Here we are concerned in modelling the human response to a deadline, and in particular we look at the process of conference registration with an early bird deadline. We provide empirical evidence from a six-year conference registration data set that the bi-logistic growth function, with the interpretation as registration with an early bird deadline, can be viewed as a social mechanism.