Dissipative Nonlinear Evolution Equations and Chaos

In this article we have studied the nonlinear interaction between ellipticity and dissipation in a set of model equations (1.1) and established the relation between this interaction and chaos. In addition to theoretical investigations, extensive numerical simulations with these equations have been made, and different routes to chaos have been found. The numerical studies have revealed the chaotic nature of the solutions.     

EXISTENCE OF PERIODIC SOLUTION OF A NEURONIC EQUATION

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The reaction pattern of norbornene with excited state carbonyl compounds: Photochemical preparations of norbornene derivatives

We established that acetylacetone and acetone photolytically sensitize norbornene to undergo an efficient radical addition of solvent (ranging from hexane, cyclic ethers, haloalkanes, acetone, alcohols and acetonitrile) across the double bond. In view of its synthetic applicability, sensitized photoreactions of norbornene were reviewed and their mechanisms were compared. Photolysis of acetylacetone in the presence of norbornene in hexane induced i) acetylacetone to cycloadd to norbornene giving the expected 1,5-diketone, and ii) sensitization by triplet excited acetylacetone to generate reactive norbornene, which underwent dimerization as well as the addition of a solvent molecule by radical chain processes. In other solvents, the radical chain addition of solvent dominated the photoreaction, and superseded the cycloaddition, to give excellent to good yields of adducts to norbornene. While the excited species of acetylacetone for the sensitization was deduced to be its spectroscopic triplet excited state, that for the cycloaddition should involve a different one which may be a twisted triplet acetylacetone; sensitization experiments showed that the cycloaddition did not occur from the spectroscopic triplet state. Triplet excited acetone sensitized norbornene to undergo the same solvent addition more efficiently and cleanly than acetylacetone did. In view of various conflicts existing in the proposed energy transfer mechanism, the sensitized norbornene reactions were rationalized with electron transfer and a cation radical chain mechanism.     

Experimental study of a plasma-filled backward wave oscillator

Experimental studies of a plasma-filled X-band backward-wave oscillator (BWO) are presented. Depending on the background gas pressure, microwave frequency upshifts of up to 1 GHz appeared along with an enhancement by a factor of 7 in the total microwave power emission. The bandwidth of the microwave emission increased from ⩽0.5 GHz to 2 GHz when the BWO was working at the RF power enhancement pressure region. The RF power enhancement appeared over a much wider pressure range in a high beam current case (10-100 mT for 3 kA) than in a lower beam case (80-115 mT for 1.6 kA). The plasma-filled BWO has higher power output than the vacuum BWO over a broader region of magnetic guide field strength. Trivelpiece-Gould modes (T-G modes) are observed with frequencies up to the background plasma frequency in a plasma-filled BWO. Mode competition between the T-G modes and the X-band Tm₀₁ mode prevailed when the background plasma density was below 6×10¹¹ cm^-3 . At a critical background plasma density of ≃8×10¹¹ cm^-3 power enhancement appeared in both X-band and the T-G modes. Power enhancement of the S-band in this mode collaboration region reached up to 8 dB. Electric fields measured by the Stark-effect method were as high as 34 kV/cm while the BWO power level was 80 MW. These electric fields lasted throughout the high-power microwave pulse     

苯基取代聚乙炔中的元激发

苯环取代聚乙炔是一类具有简并基态的发光聚合物.利用扩展的SuSchriefferHeeger模型,研究了这类聚合物链中的孤子、极化子等元激发特性.结果表明:由于苯环与聚乙炔主链间的强π电子耦合,苯环取代抑制了聚乙炔主链的二聚化,减小了导带与价带之间的能隙;因此取代聚乙炔中的元激发具有较小的激发能,同时具有更大的相干长度.尽管苯基取代对元激发有很大的影响,但是非取代聚乙炔中元激发的基本物理规律依然成立,表明这些元激发的基本特性不受取代基团的影响 关键词： 孤子 极化子 苯基取代聚乙炔     

Dielectric effect on the rf characteristics of a helical groove travelling wave tube

A new type of partial-dielectric-loaded helical groove slow-wave structure (SWS) for millimetre wave travelling wave tube (TWT） is presented in this paper.The radio-frequency characteristics including the dispersion properties,the longitudinal electric field distribution and the beam-wave coupling impedance of this structure are analysed.The results show that the dispersion of the helical groove circuit is weakened,the phase velocity is reduced and the position of the maximum Ez is moved from the mouth to the inside of the groove after partially filling the dielectric materials in the helical groove SWS.Therefore,the dielectric-loaded helical groove SWS is suitable for a multi-beam TWT with broad band and high gain.     

The standard model on non-commutative space-time

We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter . No new particles are introduced; the structure group is . We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. Received: 29 November 2001 / Published online: 25 January 2002     

Determination of the portfolio selection for a property-liability insurance company

This paper presents an analysis of a portfolio model which can be used to assist a property-liability insurance company in determining the optimal composition of the insurance and investment portfolios. By introducing insurer's threshold risk and relaxing some non-realistic assumptions made in traditional chance constraint insurance and investment portfolio models, we propose a method for an insurer to maximize his return threshold for a given threshold risk level. This proposed model can be used to optimize the composition of underwriting and investment portfolios regarding the insurer's threshold risk level, as well as to generate the efficient frontier by adjusting insurer's threshold risk levels. A numerical example is given based on the industry's aggregated data for a sixteen year period.     

The optical properties of planar waveguides in LiB3O5 crystals formed by Cu implantation

A planar optical waveguide has been formed in a LiB₃O₅ crystal using 6.0 MeV Cu⁺-ions with a dose of 1 × 10¹⁵ ions/cm² at room temperature. Possible propagating modes were measured at a wavelength of 633 nm using the prism-coupling method. The refractive index profiles of the waveguide were reconstructed by an effective refractive index method and the beam propagation method was used to investigate the properties of the propagation modes in the formed waveguide. The results suggest that the fundamental TE₀ and TM₀ modes may be well-confined and propagate a longer distance inside the waveguide. The implantation process was also simulated using the transport of ions in matter code (TRIM), which indicates that the nuclear energy deposition may be the main factor for the refractive index change.