Oscillation and nonoscillation of Hill's equation with periodic damping

We prove new results on the oscillation and nonoscillation of the Hill's equation with periodic damping:

y″+p(t)y′+q(t)y=0,t?0,     

Compact 21-W 2-mum intracavity optical parametric oscillator

We report on an intracavity optical parametric oscillator (OPO) placed within a compact diode-pumped Nd:YALO laser cavity. This OPO utilizes a pair of KTP crystals, which are diffusion bonded together in a walk-off-compensated configuration. We have generated up to 21.4 W of 2-mum radiation, operating in a few-kilohertz range.     

Superhydrophobicity of polytetrafluoroethylene thin film fabricated by pulsed laser deposition

Superhydrophobic polytetrafluoroethylene (PTFE) thin films were obtained by pulsed laser deposition (PLD) technique carried out with KrF excimer laser (λ = 248 nm) of about 1 J/cm² at a pressure of 1.33 Pa. The samples exhibit high water contact angle of about 170° and the sliding angle smaller than 2°. From studying the surface morphology of the prepared films, it is believed that the nano-scale surface roughness has enhanced the hydrophobic property of the PTFE. The increase of trapping air and reducing liquid-solid contact area due to the rough surface, as suggested by the Cassie-Baxter's model, should be responsible for superhydrophobicity of the PLD prepared films. This study thus provides a convenient one-step method without using wet-process to produce a superhydrophobic surface with good self-cleaning properties.     

Integrated scheduling of handling equipment at automated container terminals

To improve the productivities of an automated container terminal, it is important to schedule different types of handling equipment in an integrated way. A mixed-integer programming model, which considers various constraints related to the integrated operations between different types of handling equipment, is formulated. A heuristic algorithm, called multi-layer genetic algorithm (MLGA) is developed with a view to overcome the computation difficulty for solving the mathematical model. A numerical experimentation is carried out in order to evaluate the performance of the algorithm.     

Self-Affine Sets and Graph-Directed Systems

   Abstract. A self-affine set in R ⁿ is a compact set T with A(T)= ∪ _{d∈ D} (T+d) where A is an expanding n× n matrix with integer entries and D ={d ₁ , d ₂ ,···, d _N } ⊂ Z ⁿ is an N -digit set. For the case N = | det(A)| the set T has been studied in great detail in the context of self-affine tiles. Our main interest in this paper is to consider the case N > | det(A)| , but the theorems and proofs apply to all the N . The self-affine sets arise naturally in fractal geometry and, moreover, they are the support of the scaling functions in wavelet theory. The main difficulty in studying such sets is that the pieces T+d, d∈ D, overlap and it is harder to trace the iteration. For this we construct a new graph-directed system to determine whether such a set T will have a nonvoid interior, and to use the system to calculate the dimension of T or its boundary (if T ^o ≠  ). By using this setup we also show that the Lebesgue measure of such T is a rational number, in contrast to the case where, for a self-affine tile, it is an integer.     

Contractive projections on Banach algebras

In this paper, we explore the properties of projections of norm one on general Banach algebras, in particular the relation with conditional expectations for algebras which arise in harmonic analysis.     

Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces

In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results.