Comments on “Modeling of chaotic motion of gyrostats in resistant environment on the base of dynamical systems with strange attractors” (Commun Nonlinear Sci Numer Simul 2011;16:3188-3202)

Extensive prior literature (not referenced in the paper) on links between mechanical gyrostats and nonlinear dynamical systems with strange attractors is called to the readers’ attention.     

Electrochemically-Switched 2nd Order Non-Linear Optical Response in an Arylimido-Polyoxometalate with High Contrast and Cyclability

Electrochemically switched 2^nd order non-linear optical responses have been demonstrated for the first time in polyoxometalates (POMs), with an arylimido-derivative showing a leading combination of high on/off contrast (94 %), high visible transparency, and cyclability. Spectro-electrochemical and TD-DFT studies indicate that the switch-off results from weakened charge transfer (CT) character of the electronic transitions in the reduced state. This represents the first study of an imido-POM reduced state, and demonstrates the potential of POM hybrids as electrochemically activated molecular switches.     

Ultrashort Phase-Matching Wavelength and Strong Second-Harmonic Generation in Deep-UV-Transparent Oxyfluorides by Covalency Reduction

The development of urgently-needed ultraviolet (UV)/deep-UV nonlinear optical (NLO) materials has been hindered by contradictory requirements of the microstructure, in particular the need for a strong second-harmonic generation (SHG) response as well as a short phase-matching (PM) wavelength. We herein employ a “de-covalency” band gap engineering strategy to adjust the optical linearity and nonlinearity. This has been achieved by assembling two types of transition-metal (TM) polyhedra ([TaO₂F₄] and [TaF₇]), affording the first tantalum-based deep-UV-transparent NLO materials, A₅Ta₃OF₁₈ (A = K (KTOF), Rb (RTOF)). Experimental and theoretical studies reveal that the highly ionic bonds and strong electropositivity of tantalum in the two oxyfluorides induce record short PM wavelengths (238 (KTOF) and 240 (RTOF) nm) for d⁰-TM-centered oxides, in addition to strong SHG responses (2.8 × KH₂PO₄ (KTOF) and 2.6 × KH₂PO₄ (RTOF)), and sufficient birefringences (0.092 (KTOF) and 0.085 (RTOF) at 546 nm). These results not only broaden the available strategies for achieving deep-UV NLO materials by exploiting the currently neglected d⁰-TMs, but also push the shortest PM wavelength into the short-wavelength UV region.     

Solving nonlinear equations with the convex combination of two positive spectral coefficients

We present a spectral algorithm based on the convex combination of two modified spectral coefficients for solving systems of nonlinear equations. The proposed algorithm does not require the exact or approximated directional derivative for its implementation. By employing a derivative-free line search, the global convergence of the sequence generated by the algorithm is supported. Numerical experiments are given to demonstrate the performance of the algorithm compared with a similar algorithm in the literature for solving nonlinear equations problems.     

Semiclassical limit of the nonlinear Schrödinger equation in small time

We study the semi-classical limit of the nonlinear Schrödinger equation for initial data with Sobolev regularity, before shocks appear in the limit system, and in particular the validity of the WKB method.

     

The modified propagation equation for TM polarized subwavelength spatial solitons in a nonlinear planar waveguide

The wave equation of TM polarized subwavelength beam propagations in a nonlinear planar waveguide is derived beyond the paraxial approximation. This modified equation contains more higher-order linear and nonlinear terms than the nonlinear Schrödinger equation. The propagation of fundamental subwavelength spatial solitons is numerically studied. It is shown that the effect of the higher nonlinear terms is significant. That is, for the propagation of narrower beam the modified nonlinear Schrödinger equation is more suitable than the nonlinear Schrödinger equation.     

多分子生化反应模型在正平衡点的二阶近似摄动解

对一类多分子生化反应系统进行定性研究,运用摄动方法求出该模型在正平衡点当(A/C)pq+Cq(CA)q-q1=B(p-1)的二阶近似摄动解.     

Regularizing properties of a truncated newton-cg algorithm for nonlinear inverse problems

This paper develops truncated Newton methods as an appropriate tool for nonlinear inverse problems which are ill-posed in the sense of Hadamard. In each Newton step an approximate solution for the linearized problem is computed with the conjugate gradient method as an inner iteration. The conjugate gradient iteration is terminated when the residual has been reduced to a prescribed percentage. Under certain assumptions on the nonlinear operator it is shown that the algorithm converges and is stable if the discrepancy principle is used to terminate the outer iteration. These assumptions are fulfilled, e.g., for the inverse problem of identifying the diffusion coefficient in a parabolic differential equation from distributed data.     

Positive solution of singularly perturbed Dirichlet problem with singularities

A class of singularly perturbed boundary value problem with singularities is considered. Introducing the stretched variables, the boundary layer corrective terms near x = 0 and x = 1 are constructed. Under suitable conditions, by using the theory of differential inequalities the existence and asymptotic behavior of solution for boundary value problem are proved, uniformly valid asymptotic expansion of solution with boundary layers are obtained,