Padé–Legendre approximants for uncertainty analysis with discontinuous response surfaces

A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Padé–Legendre (PL) formalism which does not require modifications to existing computational tools (non-intrusive approach) and it is a global method. The paper presents a novel PL method for problems in multiple dimensions, which is non-trivial in the Padé literature. In addition, a filtering procedure is developed in order to minimize the errors introduced in the approximation close to the discontinuities. The numerical examples include fluid dynamic problems characterized by shock waves: a simple dual throat nozzle problem with uncertain initial state, and the turbulent transonic flow over a transonic airfoil where the flight conditions are assumed to be uncertain. Results are presented in terms of statistics of both shock position and strength and are compared to Monte Carlo simulations.     

Effect of graded triple delta-doped sheets on the performance of GaAs based dual channel pseudomorphic high electron mobility transistors

The characteristics of InGaP/InGaAs/GaAs dual channel pseudomorphic high electron mobility transistors (DCPHEMTs) with different graded triple delta-doped sheets are investigated and experimentally demonstrated. Based on a two-dimensional simulator of ATLAS, the band diagrams, electron densities and DC characteristics of studied devices are comprehensively analyzed. Due to the use of properly graded triple delta-doped sheets, good pinch-off and saturation characteristics, improved transport properties and wide current swing are obtained. For comparison, a practical DCPHEMT with good device performances is fabricated as well. It is found that the simulated data are in good agreement with experimental results.     

A novel quasi-phase-matching frequency doubling technique

A new quasi-phase-matching technique for efficient second-harmonic generation is reported. It is based on the spatial periodic modulation of the light intensity along the propagation direction, rather than the conventional spatial periodic modulation of the nonlinear optical coefficients. It can be realized by using a novel dual-channel waveguide frequency doubler structure for the desired light intensity distribution. This dual-channel waveguide device has major advantages including very small beam size, high light intensity within long nonlinear-waveguide interaction length, highly efficient second-harmonic generation, ease in fabrication of the nonlinear channel waveguides without any spatially periodic poling, and low waveguide propagation losses. The new quasi-phase-matching technique can also be applied to third-harmonic generation and other nonlinear optics processes.     

Pairs of Dual Wavelet Frames from Any Two Refinable Functions

Starting from any two compactly supported refinable functions in L₂(R) with dilation factor d,we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L₂(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible. In particular, when we consider symmetric refinable functions, the constructed dual wavelets are also symmetric or antisymmetric. As a consequence, for any compactly supported refinable function in L₂(R), it is possible to construct, explicitly and easily, wavelets that are finite linear combinations of translates (d · – k), and that generate a wavelet frame with an arbitrarily preassigned number of vanishing moments.We illustrate the general theory by examples of such pairs of dual wavelet frames derived from B-spline functions.     

Widely tunable, high-repetition-rate, dual signal-wave optical parametric oscillator by using two periodically poled crystals

This paper reports on a high-repetition-rate dual signal-wave (DSW) optical parametric oscillator (OPO) operating at the 1.5 μm band with tunable wavelength intervals from 2.5 nm to 69.1 nm. Two periodically poled crystals, a periodically poled lithium niobate (PPLN) with multiple gratings and a single grating MgO-doped PPLN (PPMgOLN), are cascaded in the same OPO cavity to generate dual signal-waves by using quasi-phase-matched (QPM) technique. The pump source was a Q-switched diode-pumped Nd:YVO₄ laser operating at 50 kHz. At an incident pump power of 3 W, an average output power of 169.6 mW at 1489.2 nm and 1558.3 nm has been achieved.     

Simultaneous emissions from T2 and T1 states of naphthalene moiety in a specially designed naphthalene cryptand

We report here the photophysical properties of a naphthalene derivative of a specially designed cryptand system (L). The system exhibits the unusual phenomenon of emission from T₂ and T₁ states of naphthalene which has been attributed to the inherent rigidity of the system. The results obtained have been analysed by comparison with two other model systems where the flexibility of the fluorophore unit with respect to the receptor moiety have been varied.     

The dual bases for the Bézier-Said-Wang type generalized Ball polynomial bases and their applications

A unifying representation for the existing generalized Ball bases and the Bernstein bases are given. Then the dual bases for the Bézier-Said-Wang type generalized bases (BSWGB for short) are presented. The Marsden identity and the mutual transformation formulas between Bézier curve and Bézier-Said-Wang type generalized curve (BSWGB curve) are also given. These results are very useful for the applications of BSWGB curves and their popularization in CAGD. Numerical examples are also given to show the effectiveness of our methods.     

A novel synthetic approach towards N-phenylsuccinimides from γ-lactam-2-carboxylic acid derivatives by reaction with CAN-NaBrO3

N-Arylsuccinimides have been synthesized by decarboxylative oxidation of N-aryl-γ-lactam-2-carboxylic acids with the dual oxidant CAN/NaBrO₃ in refluxing acetonitrile-water.     

Gâteaux differentiability of the dual gap function of a variational inequality

In terms of the mapping involved in a variational inequality, we characterize the Gâteaux differentiability of the dual gap function G and present several sufficient conditions for its directional derivative expression, including one weaker than that of Danskin [J.M. Danskin, The theory of max–min, with applications, SIAM Journal on Applied Mathematics 14 (1966) 641–664]. When the solution set of a variational inequality problem is contained in that of its dual problem, the Gâteaux differentiability of G on the latter turns out to be equivalent to the conditions appearing in the authors’ recent results about the weakly sharp solutions of the variational inequality problem.     

Identities of arithmetic type between values of the theta function associated to a lattice in ℝ d and its derivatives

In this paper, we introduce a notion of similarly self dual lattice in a d-dimensional Euclidean space and a classical Jacobi theta function is associated to such a lattice. We establish identities of arithmetic type between values of this theta function and its successive derivatives. This work can be related to the spectral theory of the Landau operators.