A parametric family of quintic Thue equations

For an integral parameter we investigate the family of Thue equations

originating from Emma Lehmer's family of quintic fields, and show that for the only solutions are the trivial ones with or . Our arguments contain some new ideas in comparison with the standard methods for Thue families, which gives this family a special interest.

     

Parametric fluorescence in semiconductor waveguides

We report on semiconductor waveguides for room-temperature parametric fluorescence in the near infrared. Two phase-matching schemes are presented: form birefringence and counter-propagating phase matching. The characteristics and performances of these solutions are discussed and compared for different kinds of applications. The emergence of these devices opens new perspectives toward guided-wave parametric amplifiers, oscillators, and sources for quantum information. To cite this article: M. Ravaro et al., C. R. Physique 8 (2007).     

Boundary penalty finite element methods for blending surfaces, . Superconvergence and stability and examples

This paper is Part III of the study on blending surfaces by partial differential equations (PDEs). The blending surfaces in three dimensions (3D) are taken into account by three parametric functions, x(r,t),y(r,t) and z(r,t). The boundary penalty techniques are well suited to the complicated tangent (i.e., normal derivative) boundary conditions in engineering blending. By following the previous papers, Parts I and II in Li (J. Comput. Math. 16 (1998) 457–480; J. Comput. Appl. Math. 110 (1999) 155–176) the corresponding theoretical analysis is made to discover that when the penalty power σ=2, σ=3 (or 3.5) and 0<σ1.5 in the boundary penalty finite element methods (BP-FEMs), optimal convergence rates, superconvergence and optimal numerical stability can be achieved, respectively. Several interesting samples of 3D blending surfaces are provided, to display the remarkable advantages of the proposed approaches in this paper: unique solutions of blending surfaces, optimal blending surfaces in minimum energy, ease in handling the complicated boundary constraint conditions, and less CPU time and computer storage needed. This paper and Li (J. Comput. Math. 16 (1998) 457–480; J. Comput. Appl. Math.) provide a foundation of blending surfaces by PDE solutions, a new trend of computer geometric design.     

On Nash Equilibrium Strategy of Two-person Zero-sum Games with Trapezoidal Fuzzy Payoffs

In this paper, we investigate Nash equilibrium strategy of two-person zero-sum games with fuzzy payoffs. Based on fuzzy max order, Maeda and Cunlin constructed several models in symmetric triangular and asymmetric triangular fuzzy environment, respectively. We extended their models in trapezoidal fuzzy environment and proposed the existence of equilibrium strategies for these models. We also established the relation between Pareto Nash equilibrium strategy and parametric bi-matrix game. In addition, numerical examples are presented to find Pareto Nash equilibrium strategy and weak Pareto Nash equilibrium strategy from bi-matrix game.     

Parametric study of acoustically-driven microbubble cavitations in a sonochemical reactor

The bubble cavitation along a solid wall is investigated with a three-dimensional model based on the indirect boundary element method. Kinetic energy and Kelvin impulse are calculated in order to quantify the strength of cavitation. The influences of acoustic wave amplitude and frequency and liquid properties on the strength of cavitation are investigated. This study was carried out in order to better understand the relation between microscale processes and macroscale parameters in a sonochemical reactor used for impregnation of fabrics with nanoparticles.     

Wave Generation in a Warm Magnetized Multi‐Component Plasma

The resonant interaction between three waves propagating perpendicularly to an external magnetic field in a plasma is considered. We present the explicit expressions for the three wave coupling coefficients of a warm multi‐component plasma. The results of previous work on the generation of THz radiation by laser plasma interaction are significantly improved. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Noncascading THz-wave parametric oscillator synchronously pumped by mode-locked picosecond Ti:sapphire laser in doubly-resonant external cavity

A noncascading terahertz (THz) wave parametric oscillator synchronously pumped by a mode-locked picosecond Ti:sapphire laser whose average power was less than 1 W was demonstrated with a noncollinear phase-matching MgO:LiNbO₃ crystal in an external enhancement cavity doubly resonant for both pump (780 nm) and signal (781-784 nm) waves. In the external cavity, in which the pump wave enhanced so as to reduce the pumping threshold of parametric processes, the signal wave could also resonate and thus be enhanced simultaneously, resulting in a THz wave output at approximately 0.9 THz as the idler wave. The novel dual enhancement of pump and signal waves reduced the threshold pumping intensity to approximately 50 MW/cm², which was much lower than that of a conventional externally pumped THz wave parametric oscillator with a crystal.     

Parametric option pricing: A divide-and-conquer approach

Non-parametric option pricing models, such as artificial neural networks, are often found to outperform their parametric counterparts in empirical option pricing exercises. In this context, non-parametric models are viewed as more flexible and amenable to adaptive learning. However, the main drawback of non-parametric approaches is their lack of stability, which is detrimental to out-of-sample performance. This is the key reason why one may prefer a parsimonious parametric model. This paper proposes a parametric Takagi-Sugeno-Kang (TSK) fuzzy rule-based option pricing model that requires only a small number of rules to describe highly complex non-linear functions. The findings for this data-driven approach indicate that the TSK model presents a robust option pricing tool that is superior to an array of well-known parametric models from the literature. In addition, its predictive performance is consistently no worse than that of a non-parametric feedforward neural network model.     

A tunable fiber parametric oscillator for the 2 μm wavelength range employing an intra-cavity thulium doped fiber active filter

We report an efficient fiber parametric oscillator operating in the wavelengths range of 1.97 μm to 2.14 μm. The oscillator is based on narrow band parametric amplification and employs a thulium doped fiber placed at the loops end as an intra-cavity active filter. The filter eliminates any signal generated by stimulated Raman scattering which inherently accompanies the parametric process. Short wavelength parametric oscillations and the pump signal are also absorbed. Only the long wavelength parametric oscillations can build up in the resonantly pumped system which emits 4 ns pulses at ~ 1 MHz with a maximum peak pulse power of 20 W.     

Observation of parametric X-rays produced by 400 GeV/c protons in bent crystals

Spectral maxima of parametric X-ray radiation (PXR) produced by 400 GeV/c protons in bent silicon crystals aligned with the beam have been observed in an experiment at the H8 external beam of the CERN SPS. The total yield of PXR photons was about 10⁻⁶ per proton. Agreement between calculations and the experimental data shows that the PXR kinematic theory is valid for bent crystals with sufficiently small curvature as used in the experiment. The intensity of PXR emitted from halo protons in a bent crystal used as a primary collimator in a circular accelerator may be considered as a possible tool to control its crystal structure, which is slowly damaged because of irradiation. The intensity distribution of PXR peaks depends on the crystal thickness intersected by the beam, which changes for different orientations of a crystal collimator. This dependence may be used to control crystal collimator alignment by analyzing PXR spectra produced by halo protons.