Assembly and Photophysics of Ternary Luminescent Lanthanide Molecular Complex Systems

In this paper, according to the molecular fragment principle, a series of eight ternary luminescent lanthanide complex systems were assembled, and whose compositions were determined with elemental analysis and infrared spectrum: Ln(MA)₃(L)·H₂O, where Ln = Sm, Eu, Tb, Dy; HMA = α‐methylacrylic acid; L = 1,10‐phenanthroline (phen), 2,2′‐bipyridine (bipy). The photophysical properties of these functional molecular systems were studied with ultraviolet‐visible absorption spectrum, and fluorescence excitation and emission spectrum. It was found that the heterocylic compounds (phen and bipy) act as the main energy donor and luminescence sensitizer for their suitable energy match and effective energy transfer to the emission energy level of Ln³⁺ ions. MMA ligand was only used as the terminal structural ligand to influence the luminescence. Especially terbium complex systems show the strongest luminescence for the optimum energy match and transfer between phen (bipy) and Tb³⁺ ion.     

Invex-convexlike functions and duality

We define a class of invex-convexlike functions, which contains all convex, pseudoconvex, invex, and convexlike functions, and prove that the Kuhn-Tucker sufficient optimality condition and the Wolfe duality hold for problems involving such functions. Applications in control theory are given.The author is grateful to Professor W. Stadler and the referees for many valuable remarks and suggestions, which have enabled him to improve considerably the paper.     

Lipschitz estimates for generalized commutators of fractional integrals with rough kernel

Let (0 < α < n) be the generalized commutator generated by fractional integral with rough kernel and the m–th order remainder of the Taylor formula of a function A. In this paper, the (L^p, L^r) (r > 1) boundedness, the weak (L¹, L^{n/(n–α–β)}) boundedness and the (L^p, ?^{β, ∞}_p) boundedness of are discussed, when D^γA belongs to the Lipschitz function spaces.     

Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs

We introduce the concept of partially strictly monotone functions and apply it to construct a class of nonlinear penalty functions for a constrained optimization problem. This class of nonlinear penalty functions includes some (nonlinear) penalty functions currently used in the literature as special cases. Assuming that the perturbation function is lower semi-continuous, we prove that the sequence of optimal values of nonlinear penalty problems converges to that of the original constrained optimization problem. First-order and second-order necessary optimality conditions of nonlinear penalty problems are derived by converting the optimality of penalty problems into that of a smooth constrained vector optimization problem. This approach allows for a concise derivation of optimality conditions of nonlinear penalty problems. Finally, we prove that each limit point of the second-order stationary points of the nonlinear penalty problems is a second-order stationary point of the original constrained optimization problem.     

Low-threshold interband cascade lasers operating above room temperature

Mid-IR type-II interband cascade lasers were demonstrated in pulsed mode at temperatures up to 325 K and in continuous mode up to 200 K. At 80 K, the threshold current density was 8.9 A/cm² and a continuous wave output power of 140 mW/facet was obtained.     

Non-elliptic deformation field near the tip of a mixed-mode crack in a compressible hyperelastic material

This paper gives an asymptotic analysis of the deformation field near the tip of an arbitrary mixed-mode crack in a compressible hyperelastic harmonic material which loses ellipticity at sufficiently large deformations. It is found that the near-tip deformation field is characterized by a localized non-elliptic deformation band issuing from the crack-tip and bounded by two curves of discontinuous deformation gradient. Explicit expression for the near-tip deformation field is obtained both inside and outside the localized deformation band. In particular, a simple relation is derived that determines the orientation of the deformation band in terms of two complex governing parameters of the near-tip fields inside and outside the deformation band, respectively.     

Optical investigation of cavitation erosion by laser-induced bubble collapse

By means of a new force sensor based on optical beam deflection (OBD), the mechanical effects of laser-matter interaction underwater at different incident laser energy are investigated in detail. The experimental results show that a target underwater is impacted in turn by laser-plasma ablation force and high-speed liquid-jet impulse induced by bubbles collapse in the vicinity of a solid boundary. Furthermore, the amplitudes of the two forces increase monotonously with laser energy. According to the ablation force detected by the experiment and the theoretical relationship between laser intensity and ablation pressure, the value of liquid-jet impact against a solid boundary can be easily obtained. In addition, based on the model of a collapsing bubble, some characteristic parameters, such as the liquid-jet impact velocity, the maximum bubble radius, the bubble energy can also be obtained at different laser energy, which are valuable in the corresponding research fields.     

Optimal control of the obstacle in a quasilinear elliptic variational inequality

In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle. The state is chosen to be close to the desire profile while the H² norms of the obstacle is not too large. Existence and necessary conditions for the optimal control are established.     

Regular Approximations of Singular Sturm-Liouville Problems with Limit-Circle Endpoints

For any self-adjoint realization S of a singular Sturm-Liouville equation on an interval (a,b) with limit-circle endpoints, we construct a family of self-adjoint realizations S _r ,r ∈ (0,∞), of this equation on subintervals (a _r ,b _r ) of (a,b) such that every eigenvalue of S is the limit of a continuous eigenvalue branch of this family. Of particular interest are the cases when at least one endpoint is oscillatory or the leading coefficient function changes sign. In these cases, we show that the index determining each continuous eigenvalue branch has an infinite number of jump discontinuities and give an explicit characterization of these discontinuities.     

Evolution of Spiral Waves under Modulated Electric Fields

Spirals generated from the excitable media within the Barkley model is investigated under the gradient electric fields by a numerical simulation. The spiral drift and spiral break up are observed when the amplitude of the electric fields is modulated by a constant signal or a chaotic signal. It is also verified that, even in the presence of the white noise, the whole system can reach homogeneous states after the spiral breakup, by using an adaptive strategy.