Randomly transitional phenomena in the system governed by Duffing's equation

This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon.     

Time-resolved spectroscopy of soantaneous luminescence of CdSSe1−x quantum dots

Picosecond time-resolved spectroscopy of the edge luminescence band of CdS _x Se_1–x quantum dots with crystallite diameters as small as a few nanometers under band-to-band excitation reveals strong enhancement of the radiative recombination rate compared to bulk CdS owing to quantum confinement. The splitting of the luminescence band into two lines originates from near-band-gap absorption. Analysis of the temperature as well as the spectral dependence of the decay time (leading to a red shift of the luminescence with increasing time) and of the total-light-decay law result in a new model for the dominant radiative recombination channel: donor-acceptor pair recombination instead of an excitonic mechanism as claimed in previous publications.Dedicated to H.-J. Queisser on the occasion of his 60th birthday     

Hyperbolic mean growth of bounded holomorphic functions in the ball

We consider the hyperbolic Hardy class , . It consists of holomorphic in the unit complex ball for which and

p _{0

where denotes the hyperbolic distance of the unit disc. The hyperbolic version of the Littlewood-Paley type -function and the area function are defined in terms of the invariant gradient of , and membership of is expressed by the property of the functions. As an application, we can characterize the boundedness and the compactness of the composition operator , defined by , from the Bloch space into the Hardy space .

     

Flow Compactifications of Nondiscrete Monoids, Idempotents and Hindman's Theorem

We describe the extension of the multiplication on a not-necessarily-discrete topological monoid to its flow compactification. We offer two applications. The first is a nondiscrete version of Hindman's Theorem, and the second is a characterization of the projective minimal and elementary flows in terms of idempotents of the flow compactification of the monoid.     

Induced product representations of extended Cuntz algebras

Let _H be the extended Cuntz algebra over the Hilbert space H. Since its zero grade part _H⁰ is the C^*-inductive limit of B(H^r), we look for some family of representations on an inductive limit of H^r as r. When such construction is shaped according to the structure of _H⁰, von Neumanns notion of a reference sequence of unit vectors for Hilbert infinite tensor products emerges; after a further Rieffel induction step, a class IPR[H] of representations of _H arises. For any two such representations, we describe explicitly their associated intertwiners. Any two representations in IPR[H] are either disjoint or unitarily equivalent. Actions of the group by translation on sequences of unit vectors are involved, as well as the ideals of .     

p(x)-Laplace方程的强极大值原理

本文给出了如下形式的p(x)-Laplace方程 -div(|u|~(p(x)-2)u)+d(x)|u|~q(x)-2)u=0,x∈Ω的一个强极大值原理,其中p(x),q(x),d(x)满足一定的条件。     

A NEW FORMULA WITHOUT BOUNDARY INTEGRALS ON A STEIN MANIFOLD

A new Koppelman-Leray-Norguet formula of (p-1,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of (?)-equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.     

Pulsed power modeling of very-large-aperture,transverse-discharge CO2 lasers

Discharge behavior of large-aperture (10–70 cm) CO₂ lasers is computed using a coupled particle kinetics-equivalent circuit model. Pulsed power systems that produce a single excitation pulse are only able to satisfy the preionization, ignition, and impedance matching conditions for interelectrode gaps 40–50 cm. Double-pulse systems are required for larger gaps, not only to optimize electrical efficiency, but to avoid oscillatory behavior which can lead to arc formation during the second cycle.     

On invexity-type nonlinear programming problems

In this paper, we propose a new class of nonlinear programing, called SFJ-invex programming. The optimality characterization shows that a problem is SFJ-invex if and only if a Fritz John point together with its multiplier, is a Fritz John saddle point of the problem. Under any constraint qualification assumption, a problem is SFJ-invex if and only if a Kuhn-Tucker point together with its multiplier is a Kuhn-Tucker saddle point of the problem. Furthermore, a generalization of the SFJ-invex, class is developed; the applications to (h, )-convex programming, particularly geometric programming, and to generalized fractional programming provide a relaxation in constraint qualification for differentiable problems to get saddle-point type optimality criteria.The author wishes to thank the referee for helpful comments.     

Modelling the formation of nanostructures on metal surface induced by femtosecond laser ablation

We employ the particle-in-cell method to simulate the mechanisms of femtosecond (fs) laser interactions with a metallic target. The theoretical approach considers the solid as a gas of free electrons in a lattice of immobile ions and the laser fluences close to the ablation threshold. At first moments of the interaction, our simulations mapped out different nanostructures. We carefully characterized the rippling phase and found that its morphology is dependent on the distribution of the electron density and the period of the ripples depends on the laser intensity. The simulation method provides new insights into the mechanisms that are responsible for surface grating formation.