Recursion Relations for Unitary Integrals,Combinatorics and the Toeplitz Lattice

 In a discussion in spring 2001, Alexei Borodin showed us recursion relations for the Toeplitz determinants going with the symbols e ^{t(z + z−1)} and \!. Borodin obtained these relations using Riemann-Hilbert methods; see the recent work of Borodin B and Baik Baik. The nature of Borodin's recursion relations pointed towards the Toeplitz lattice and its Virasoro algebra, introduced by us in AvM1. In this paper, we take the Toeplitz lattice and Virasoro algebra approach for a fairly large class of symbols, leading to a systematic way of generating recursion relations. The latter are very naturally expressed in terms of the L-matrices appearing in the Toeplitz lattice equations. As a surprise, we find, compared to Borodin's, a different set of relations, except for the 3-step relations associated with the symbol e ^{t(z + z−1)} . The Painlevé analysis of the Toeplitz lattice enables us to show the ``singularity confinement' for these recursion relations. Received: 30 January 2002 / Accepted: 6 January 2003 Published online: 19 May 2003 RID="⋆" ID="⋆" The support of a National Science Foundation grant DMS-01-00782 is gratefully acknowledged. RID="⋆⋆" ID="⋆⋆" The support of a National Science Foundation grant DMS-01-00782, a Nato, a FNRS and a Francqui Foundation grant is gratefully acknowledged. Communicated by L. Takhtajan     

Elliptic flow of identified hadrons in Au+Au collisions at sqrt sNN =200 GeV

The anisotropy parameter (v(2)), the second harmonic of the azimuthal particle distribution, has been measured with the PHENIX detector in Au+Au collisions at sqrt[s(NN)]=200 GeV for identified and inclusive charged particle production at central rapidities (|eta|<0.35) with respect to the reaction plane defined at high rapidities (|eta|=3-4 ). We observe that the v(2) of mesons falls below that of (anti)baryons for p(T)>2 GeV/c, in marked contrast to the predictions of a hydrodynamical model. A quark-coalescence model is also investigated.     

Scaling properties of proton and antiproton production in sqrt[s(NN)]=200 GeV Au+Au collisions

We report on the yield of protons and antiprotons, as a function of centrality and transverse momentum, in Au+Au collisions at sqrt[s(NN)]=200 GeV measured at midrapidity by the PHENIX experiment at the BNL Relativistic Heavy Ion Collider. In central collisions at intermediate transverse momenta (1.5相似文献   

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de     

Leaky wave detection at air-solid interfaces by laser interferometry

A recently developed optical heterodyne interferometer is proved to be sensitive to detect ultrasonic waves leaking out from metals (and from non-metals as well) several centimeters away from the metal surface in air. This measurement is based on the detection of the optical index variation in air due to the leaky wave. Experiments were carried out using both ultrasonic leaky Rayleigh and leaky Lamb waves in the low-megahertz region. Optical measurements of these leaky wave velocities in semi-infinite materials and plates, which are related to elastic constants of the materials, showed a good correlation to the predicted values. Optical measurements of the amplitude of the leaky waves were used to obtain attenuation coefficients, which correlate to the structural integrity of the materials. Surface and near-surface defects were also detected. This optical method can be used for metals with low-reflectivity surfaces. Thus, it can be used for non-polished surfaces and can be extended for non-contact, non-destructive evaluation applications.     

Sum frequency generation of continuously tunable blue pulses from a two-branch femtosecond fiber source

We report on the generation of femtosecond blue pulses from a two-branch mode-locked erbium-doped fiber source. This is achieved by sum-frequency mixing in β-barium borate between the frequency doubled laser radiation at 770 nm and a tunable near-infrared component generated inside a highly nonlinear fiber. Small angle tuning of the nonlinear crystal leads to a continuously variable output wavelength in the visible band between 460 nm and 500 nm. Average power levels exceeding 1.5 mW were collected throughout the entire tuning range of our device, which delivered sub-300-fs pulses at a repetition rate of 98 MHz. These values indicate that the input near-infrared radiation is up-converted with a photon efficiency of 20%.     

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Synthesis and characterization of pH sensitive poly(glycidol)‐b‐poly(4‐vinylpyridine) block copolymers

Block copolymers of poly(glycidol)‐b‐poly(4‐vinylpyridine) were obtained by ATRP of 4‐vinylpyridine initiated by ω‐(2‐chloropropionyl) poly(glycidol) macroinitiators. By changing the monomer/macroinitiator ratio in the synthesis polymers with varied P4VP/PGl molar ratio were obtained. The obtained block copolymers showed pH sensitive solubility. It was found that the linkage of a hydrophilic poly(glycidol) block to a P4VP influenced the pK_a value of P4VP. DLS measurements showed the formation of fully collapsed aggregates exceeding pH 4.7. Above this pH values the collapsed P4VP core of the aggregates was stabilized by a surrounding hydrophilic poly(glycidol) corona. The size of the aggregates depended significantly upon the composition of the block copolymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1782–1794, 2009