The Riemann–Hilbert analysis to the Pollaczek–Jacobi type orthogonal polynomials

In this paper, we study polynomials orthogonal with respect to a Pollaczek–Jacobi type weight The uniform asymptotic expansions for the monic orthogonal polynomials on the interval (0,1) and outside this interval are obtained. Moreover, near , the uniform asymptotic expansion involves Airy function as , and Bessel function of order α as in the neighborhood of , the uniform asymptotic expansion is associated with Bessel function of order β as . The recurrence coefficients and leading coefficient of the orthogonal polynomials are expressed in terms of a particular Painlevé III transcendent. We also obtain the limit of the kernel in the bulk of the spectrum. The double scaled logarithmic derivative of the Hankel determinant satisfies a σ‐form Painlevé III equation. The asymptotic analysis is based on the Deift and Zhou's steepest descent method.     

Critical Behaviors in a Stochastic One-Dimensional Sand-Pile Model

A one-dimensional sand-pile model (Manna model), which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A detailed analysis of the probability distribution of the avalanche size and duration is numerically investigated. Interestingly,contrary to the deterministic one-dimensional sand-pile model, where multifractal analysis works well, the analysis based on simple finite-size scaling is suited to fitting the data on the distribution of the avalanche size and duration. The exponents characterizing these probability distributions are measured. Scaling relations of these scaling exponents and their universality class are discussed.     

The structure and optical properties of AlN nanocrystals prepared by Schlenk techniques at atmospheric pressure and low temperature

AlN nanocrystals were prepared in organic solvent at atmospheric pressure and low temperature by the Schlenk technique. Both hexagonal and cubic AlN nanocrystals were obtained. The hexagonal nano-AlN powder possessed a wurtzite structure with a=3.124 Å, c=5.024 Å, the average grain size was about 2 nm. The lattice constant of the cubic nano-AlN was a=9.171 Å, the average grain size was about 4 nm. The structural and optical properties of the obtained AlN were analyzed. The emission related to deep-level defects was investigated by using temperature-dependent photoluminescence.     

Textbook research in mathematics education: development status and directions

This paper presents a survey study aiming to systematically examine, analyse and review relevant research focusing on mathematics textbooks and hence identify future directions in this field of research. The literature surveyed is selected from different data sources, including mainly journal articles, research theses and conference proceedings. The survey revealed that important progress has been made over the last few decades in mathematics textbook research, though the major achievement has been concentrated in the areas of textbook analysis (including textbook comparison), and the use of textbooks in teaching and learning. It is overall no longer true that the textbook research in mathematics is “scattered, inconclusive, and often trivial” as described six decades ago; however, the development of research on mathematics textbooks has been unbalanced in different areas. Following the review and discussion, the paper proposes five needed directions for advancing the research in this field.     

Wavelength beam combining of ytterbium fiber lasers

Wavelength beam combining of five ytterbium fiber lasers is demonstrated in a master-oscillator power-amplifier configuration at combined powers up to 6 W. The combined beam profile has an M2 value of 1.14, which is equal to that of an individual fiber. Beam steering in one dimension over 140 resolvable spots is also demonstrated.     

Fabrication and magnetic properties of Ni-Zn nanowire arrays

Ni-Zn nanowire arrays, with diameters of approximately 60 nm and lengths of around 40 μm, were fabricated by electrodeposition in porous anodic aluminum oxide templates at different electric potentials. X-ray diffraction observations demonstrated that the isolated nanowires had polycrystalline structure and that their phases changed with the deposition potential. The amount of deposited zinc in the nanowires increased with the deposition potential, whereas the amount of nickel decreased. Magnetic measurements showed that there was a gradual change of magnetism from isotropic to anistropic with increasing potential amplitude and that the coercivity reached a maximum value in the nanowire deposited at −1.35 V.     

New equation for deriving pure state density operators by Weyl correspondence and Wigner operator

By virtue of the completeness of Wigner operator and Weyl correspondence we construct a general equation for deriving pure state density operators. Several important examples are considered as the applications of this equation, which shows that our approach is effective and convenient for deducing these entangled state representations.     

Evaluation of natural recharge of Chingshui geothermal reservoir using tritium as a tracer

Naturally existing tritium in groundwater was applied as a tracer to evaluate the natural recharge of the Chingshui geothermal reservoir. The residence time (or, age) of Chingshui geothermal water was first determined with tritium data at 15.2 and 11.3 year using the plug flow and dispersive model, respectively. The annual natural recharge was then estimated by combining the use of the residence time and the fluid-in-place of the Chingshui geothermal reservoir. The natural recharge for Chingshui geothermal reservoir was estimated at 5.0 × 10⁵ and 6.7 × 10⁵ m³ year^?1 using the plug flow and dispersive model, respectively. Chingshui geothermal water is largely from a fractured zone in the Jentse Member of the Miocene Lushan Formation. The dispersive model more adequately represents the fracture flow system than the simple plug flow model.     

Observation of a red-blue detuning asymmetry in matter-wave superradiance

We report the first experimental observation of strong suppression of matter-wave superradiance using blue-detuned pump light and demonstrate a pump-laser detuning asymmetry in the collective atomic recoil motion. In contrast to all previous theoretical frameworks, which predict that the process should be symmetric with respect to the sign of the detuning of the pump laser from the one-photon resonance, we find that for condensates the symmetry is broken. With high condensate densities and red-detuned pump light the distinctive multiorder, matter-wave scattering pattern is clearly visible, whereas with blue-detuned pump light superradiance is strongly suppressed. However, in the limit of a dilute atomic gas symmetry is restored.