Modelling the Self-similarity in Complex Networks Based on Coulomb's Law

Recently, self-similarity of complex networks have attracted much attention. Fractal dimension of complex network is an open issue. Hub repulsion plays an important role in fractal topologies. This paper models the repulsion among the nodes in the complex networks in calculation of the fractal dimension of the networks. The Coulomb's law is adopted to represent the repulse between two nodes of the network quantitatively. A new method to calculate the fractal dimension of complex networks is proposed. The Sierpinski triangle network and some real complex networks are investigated. The results are illustrated to show that the new model of self-similarity of complex networks is reasonable and efficient.Comment: 25 pages, 11 figure

Iron(III) bromide catalyzed bromination of 2-tert-butylpyrene and corresponding position-dependent aryl-functionalized pyrene derivatives

The present work probes the bromination mechanism of 2-tert-butylpyrene (1), which regioselectively affords mono-, di-, tri- and tetra-bromopyrenes, by theoretical calculation and detailed experimental methods. The bromine atom may be directed to the K-region (positions 5- and 9-) instead of the more reactive 6- and 8-positions in the presence of iron powder. In this process, FeBr₃ plays a significant role to release steric hindrance or lower the activation energy of the rearrangement. The intermediate bromopyrene derivatives were isolated and confirmed by ¹H NMR spectrometry, mass spectroscopy and elemental analysis. Further evidence on substitution position originated from a series of aryl substituted pyrene derivatives, which were obtained from the corresponding bromopyrenes on reaction with 4-methoxy-phenylboronic acid by a Suzuki–Miyaura cross-coupling reaction. All position-dependent aryl-functionalized pyrene derivatives are characterized by single X-ray diffraction, ¹H/¹³C NMR, FT-IR and MS, and offered straightforward evidence to support our conclusion. Furthermore, the photophysical properties of a series of compounds were confirmed by fluorescence and absorption, as well as by fluorescence lifetime measurements

Feasibility study on posterior laminar screw fixation techniques in the axis

AbstractObjectiveTo get morphologic parameters of Chinese adults through observation and measurement on axial laminas, to evaluate the feasibility of placing axial laminar screws and to introduce the technique.MethodsRelative parameters of 28 sets of fresh Chinese adults' axial specimens, including distance from the superior and inferior entry points of axial laminar screws to the superior margins of axial laminas, superior, middle, inferior thickness and height of the axial laminas, length and angle of the axial laminar screw trajectories, distance from the entry points of axial laminar screws to the transverse foramen and central points of the inferior articular process, were measured with a digital caliper and a goniometer. Data were statistically analyzed.ResultsAveragely, distance from the superior and inferior entry points of axial laminar screws to the superior margins of axial laminas was 5 mm and 9 mm, superior, middle, inferior thickness and the height of the axial laminas were 3.2 mm, 6.7 mm, 5.5 mm and 12.8 mm respectively, and the length of the superior and inferior axial laminar screw trajectories was 26.2 mm and 25.5 mm, respectively.ConclusionsIt is feasible and reliable to apply posterior laminar screw fixation techniques to the axes of Chinese adults. Also the C2 laminar screw fixation technique can be taken as a supplementary to conventional posterior screw fixations of C2

Effects of Symmetry Energy in the Reaction 40Ca+124Sn at 140 MeV/nucleon

The density-dependent symmetry energy is a hot topic in nuclear physics. Many laboratories over the world are planning to perform related experiments to probe the symmetry energy. Based on the semiclassical Boltzmann-Uehling-Uhlenbeck (BUU) transport model, we study the effects of nuclear symmetry energy in the central reaction 40Ca+124Sn at 140MeV/nucleon in the laboratory system. It is found that the rapidity distribution of free nucleon's neutron-to-proton ratio is sensitive to the symmetry energy, especially at large rapidities. The free neutron-to-proton ratios at small or large rapidities may reflect high or low density behavior of nuclear symmetry energy. To probe the density dependence of nuclear symmetry energy, it is better to give the kinetic distribution and the rapidity distribution of emitted nucleons at the same time.Comment: 4 pages, 6 figures. arXiv admin note: text overlap with arXiv:1204.085

Integrated photonic qubit quantum computing on a superconducting chip

We study a quantum computing system using microwave photons in transmission line resonators on a superconducting chip as qubits. We show that all control necessary for quantum computing can be implemented by coupling to Josephson devices on the same chip, and take advantage of their strong inherent nonlinearities to realize qubit interactions. We analyze the gate error rate to demonstrate that our scheme is realistic even for Josephson devices with limited decoherence times. A conceptually innovative solution based on existing technologies, our scheme provides an integrated and scalable approach to the next key milestone for photonic qubit quantum computing.Comment: 5 pages, 3 figure