Bulk universality for Wigner matrices

We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e^?U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson sine kernel provided that U ∈ C⁶( \input amssym $\Bbb R$ ) with at most polynomially growing derivatives and ν(x) ≥ Ce^?C|x| for x large. The proof is based upon an approximate time reversal of the Dyson Brownian motion combined with the convergence of the eigenvalue density to the Wigner semicircle law on short scales. © 2010 Wiley Periodicals, Inc.     

Generation of hyperchaos from the Chen–Lee system via sinusoidal perturbation

A system with more than one positive Lyapunov exponent can be classified as a hyperchaotic system. In this study, a sinusoidal perturbation was designed for generating hyperchaos from the Chen–Lee chaotic system. The hyperchaos was identified by the existence of two positive Lyapunov exponents and bifurcation diagrams. The system is hyperchaotic in several different regions of the parameters c, ε, and ω. It was found that this method not only can enhance or suppress chaotic behavior, but also induces chaos in non-chaotic parameter ranges. In addition, two interesting dynamical behaviors, Hopf bifurcation and intermittency, were also found in this study.     

Thermomagnetic effect in ferrofluids with weakly coupled particles

Thermomagnetic curves for water based ferrofluid with large magnetic latex particles are analyzed. The particles are found to have extremely low barrier height of thermal relaxation (≤1200 K at temperatures below 100 K) whose field dependence is deduced. Work sponsored by the National Science Council of the R.O.C. under Grant No. NSC85-2112-M-001-020.     

Synthesis and optical and electrochemical properties of copolymers consisting of 9,9‐dihexylfluorene and aromatic triazole chromophores

Aromatic triazole chromophores were incorporated into polyfluorene in an attempt to increase electron affinity, to promote emission efficiency, and to diminish excimer formation. Poly(9,9‐dihexylfluorene) ( P1 ) and new copolymers with aromatic triazoles ( P2 – P4 ) were prepared by Suzuki coupling polymerization. In P2 , the aromatic triazole (3.8 mol %) was attached exclusively as terminal groups, whereas P3 and P4 were main‐chain copolymers containing 3.9 and 10.3 mol % aromatic triazole chromophores, respectively. The copolymers were soluble in common organic solvents and showed high decomposition temperatures (437–458 °C). The twisted structure between the triazole and fluorene increased the emission efficiency and effectively prevented excimer formation in P2 – P4 . After the introduction of the triazole units, the absorption spectra showed a blueshift (from 388 to 381 nm in chloroform) due to confined conjugation, but the photoluminescence spectra remained almost the same (417–418 nm); this was attributed to oligofluorene segments. No emission of triazole fluorophores was observed because of efficient energy transfer from the triazole to oligofluorene segments. However, incomplete energy transfer was observed in CH₃COOH. The optical stability upon thermal annealing was also improved by the incorporation of aromatic triazole segments. From cyclic voltammetry results, P2 – P4 , containing triazole groups, showed greater electron affinity (lowest unoccupied molecular orbital level = ?2.67 to ?2.71 eV) than P1 (?2.52 eV). Electroluminescence devices of P1 – P4 all exhibited excimer emissions (483–521 nm), which could also be diminished by the introduction of aromatic triazole chromophores. © 2006Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 136–146, 2007     

Optical and electrochemical properties of copoly(aryl ether)s consisting of alternate 2,5‐distyrylbenzene and electron‐transporting oxadiazole or triazole derivatives

New copoly(aryl ether) P1 consisting of alternate electron‐transporting 2‐(3‐(trifluoromethyl)phenyl)‐5‐(4‐(5‐(3‐(trifluoromethyl)phenyl)‐1,3,4‐oxadiazol‐2‐yl)‐2,5‐bis(hexyloxy)phenyl)‐1,3,4‐oxadiazole and hole‐transporting 2,5‐distyrylbenzene (DSB) was synthesized via nucleophilic substitution polymerization. We investigated the optical and electrochemical properties of alternate copoly(aryl ether)s P1 – P6 , which contain the same hole‐transporting DSB segments, but with different electron transporting segments. The effect of trifluoromethyl groups in electron transporting segments is also discussed. Referencing to the spectra of their model compounds M1 – M4 , the emissions of P1 – P3 are dominated exclusively by the hole‐transporting fluorophores with longer emissive wavelength about 452–453 nm via efficient excitation energy transfer. Furthermore, P1 – P3 also exhibit unique variations in energy transfer in acidic media and solvatochromism in organic solvents. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of P1 – P4 , estimated from electrochemical data, are ?5.12, ?5.15, ?5.18, ?5.00 eV and ?2.93, ?3.39, ?3.49, ?2.76 eV, respectively. The electron and hole affinity of P1 – P6 can be enhanced simultaneously by introducing isolated hole‐ and electron‐transporting segments in backbone. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5083–5096, 2005     

Cheating in Visual Cryptography

A secret sharing scheme allows a secret to be shared among a set of participants, P, such that only authorized subsets of P can recover the secret, but any unauthorized subset cannot recover the secret. In 1995, Naor and Shamir proposed a variant of secret sharing, called visual cryptography, where the shares given to participants are xeroxed onto transparencies. If X is an authorized subset of P, then the participants in X can visually recover the secret image by stacking their transparencies together without performing any computation. In this paper, we address the issue of cheating by dishonest participants, called cheaters, in visual cryptography. The experimental results demonstrate that cheating is possible when the cheaters form a coalition in order to deceive honest participants. We also propose two simple cheating prevention visual cryptographic schemes.     

Aryne‐Induced Novel Tandem 1,2‐Addition/(3+2) Cycloaddition to Generate Imidazolidines and Pyrrolidines

A new “single‐flask” method was developed for the synthesis of imidazolidines and pyrrolidines with high stereoselectivity. First, a Schiff base was arylated with an aryne. Second, an intramolecular proton transfer took place from the methylene position to the anionic aryne ring. Third, the resultant ylide reacted with a second equivalent of the same Schiff base in situ or an electron‐deficient alkene through a (3+2) cycloaddition. These sequential tandem 1,2‐addition/(3+2) cycloaddition reactions led to the desired heterocycles in 63–88 % yields.     

Local Semicircle Law for Random Regular Graphs

We consider random d‐regular graphs on N vertices, with degree d at least (log N)⁴. We prove that the Green's function of the adjacency matrix and the Stieltjes transform of its empirical spectral measure are well approximated by Wigner's semicircle law, down to the optimal scale given by the typical eigenvalue spacing (up to a logarithmic correction). Aside from well‐known consequences for the local eigenvalue distribution, this result implies the complete (isotropic) delocalization of all eigenvectors and a probabilistic version of quantum unique ergodicity.© 2017 Wiley Periodicals, Inc.     

Study of temperature distribution of sliding block with asperity surface

In this study, a numerical thermal model is developed for sliding block contact under various loads, sliding velocities and surface roughness. The temperature distributions are shown for perfectly insulated thermal conditions along noncontact surfaces. For a particular five‐peaks contact model, the maximum temperature at the central peak is slightly lhigher than the others. The temperature profile decreases as the distance to the symmetry axis increases, and then decreases dramatically at the noncontact area. It is clear to see that the maximum temperature locates at the symmetry central peak of the asperity contact area instead of the leading head of the smooth surface. The maximum temperature rise parameter increases as the pressure, sliding velocity and asperity roughness increased or conductivity decreased. This phenomenon becomes obvious for cases at high pressure, velocity and roughness and low conductivity. Particularly, the influence of roughness is not significant for low velocity. Similar results are found for the maximum temperature rise parameter difference between peaks or peaks/valleys. The simulation results of this asperity surface sliding block contact model are able to provide essential information for the components of microelectro—mechanical systems (MEMS) and biochemical reaction mechanism. Copyright © 2011 John Wiley & Sons, Ltd.