一类没有单调性假设的渐近线性波方程的多解

本文借助文[1]除去零空间的技巧,利用L—S度数理论讨论了一类浙近线性波方程。在对非线性项不做单调性假设的前提下,给出了一个新的多解定理。     

A generalization of biorthogonal systems based on Drazin inverse

In this paper, the transformations of generating systems of Euclidean space are examined in connection with the Drazin inverse of their Gram matrices and the notion of biorthogonal systems is generalized. The results obtained in this paper can be considered as the extension of some recent results concerning Moore-Penrose biorthogonal systems and reflexiveg-inverse systems in Euclidean spaces.     

DESIGN OF A NOVEL 2-D UNIPLANAR CRLH-TL STRUCTURE

A novel uniplanar 2-D composite right/left-handed transmission line (CRLH-TL) structure is proposed based on a general transmission line theory and the way to increase the relative operating bandwidth in the left-handed (LH) region and lower the LH operating frequency is illustrated. In addition, a new method to extract parameters and calculate the Bloch impedance of the structure is presented. Numerical results of the dispersion as well as the extracted parameters are given, which are calculated based on full-wave simulation. The present 2-D uniplanar CRLH-TL structure is applicable to 2-D left-handed materials in lower and wider LH frequency range. Supported by the National Natural Science Foundation of China (No. 60371010) (No. 60471037) (No. 63531020)     

神经网络在工程爆破应力波规律探讨中的应用

采用BP（Back Propagation)前馈人工神经网络模型，对工程爆破中柱状震源的自由场应力波传播规律进行了探讨。结果表明：利用人神经网络模型的非线性映射功能，可以较好地给出工程爆破引起的近区自由场力学规律，对于同类型问题的研究，也有着很重要的意义。     

用离子速度影象技术研究n-C4H9Br的光解

利用离子速度影象技术研究了正一溴丁烷(n-C4H9Br)在231~267 nm波段的光解,得出了如下结论:正一溴丁烷(n-C4H9Br)在231~267 nm波段的吸收源于基态到三个最低激发态的跃迁,这三个激发态标识为1A″、2A′和3A′;发生在这三个排斥态的势能面(PES)上的光解最终导致C4H9 Br(2P3/2)或C4H9 Br*(2P1/2)的产生;2A′和3A′态之间存在避免交叉(Avoided crossing)会影响最终的光解产物;从基态1A′到激发态1A″的跃迁矩垂直于对称面,也就垂直于C-Br键;从基态1A′到激发态3A′的跃迁矩平行于对称面,同时平行于C-Br键;从基态1A′到激发态2A′的跃迁矩在对称面内,且与C-Br键成53.1°夹角.我们也讨论了正一溴丁烷(n-C4H9Br)在234 nm和267 nm附近光解时的避免交叉几率(Avoided crossingprobability),以及它对单通道相对产额(Relative fraction of the individual pathways)的影响.     

Structural studies of Cr-doped mullite derived from single-phase precursors

Cr-doped mullites were prepared from single-phase precursors containing up to 9.60 wt% Cr₂O₃ using a sol-gel technique followed by thermal treatment. Particle induced X-ray emission spectroscopy and X-ray powder diffraction were used to characterize the samples. Mullites were orthorhombic, space group Pbam. Cr doping caused the increase of unit-cell parameters. Strongest expansion was noticed along c-axis followed by a and b (Δc/c=0.089, Δa/a=0.061, Δb/b=0.045% per mole Cr₂O₃). A second phase, namely θ-(Al,Cr)₂O₃, was revealed by XRD in the sample containing 9.60 wt% Cr₂O₃. The structure of mullites was refined by the Rietveld method, location of Cr³⁺ was performed by the EPR spectroscopy. At low chromium doping level (Cr₂O₃ content less than ∼5 wt%) Cr³⁺ ions were substituted for Al³⁺ in the AlO₆ octahedra of the mullite structure (M1 site). For higher doping level, Cr³⁺ ions were additionally substituted for Al³⁺ in the AlO₆ octahedra of the second phase [θ-(Al,Cr)₂O₃ at 1400 °C, or α-(Al,Cr)₂O₃ at 1600 °C] which segregated in the system. Substitution of Cr³⁺ for Al³⁺ on M1 site in the mullite structure resulted in increase of average distances in (M1)O₆ octahedron and decrease of average distances in T*O₄ tetrahedron, while average distances in TO₄ tetrahedron stayed almost constant.     

二阶Volterra系统对平稳正态激励的统计响应的表示定理的数学证明

1974年,Neal根据Kac和Siegert的思想,给出了一个在电子工程、海洋工程、建筑工程、航空工程、自动控制的随机振动中有重要应用的二阶Volterra非线性系统对平稳正态输入的统计响应的表示定理.1984年,Naess对此定理又给出了一个数学证明.经过研究后发现,他们对定理条件的叙述都是模糊的,而且其数学证明都是有问题的.本文重新讨论了这个表示定理,给出了明确的定理条件及严格的数学证明,为它的广泛应用奠定了理论基础.     

Bipyridinophane‐containing conjugated polymers modulated with an intramolecular aromatic C?H/π interaction

Bipyridinophane–fluorene conjugated copolymers have been synthesized via Suzuki and Heck coupling reactions from 5,8‐dibromo‐2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane and suitable fluorene precursors. Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P7 ) exhibits large absorption and emission redshifts of 20 and 34 nm, respectively, with respect to its planar reference polymer Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐1,4‐(2,5‐dimethylbenzene)] ( P11 ), which bears the same polymer backbone as P7 . These spectral shifts originate from intramolecular aromatic C? H/π interactions, which are evidenced by ultraviolet–visible and ¹H NMR spectra as well as X‐ray single‐crystal structural analysis. However, the effect of the intramolecular aromatic C? H/π interactions on the spectral shift in poly[9,9‐dihexylfluorene‐2,7‐yleneethynylene‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P10 ) is much weaker. Most interestingly, the quenching behaviors of these two conjugated polymers are largely dependent on the polymer backbone. For example, the fluorescence of P7 is efficiently quenched by Cu²⁺, Co²⁺, Ni²⁺, Zn²⁺, Mn²⁺, and Ag⁺ ions. In contrast, only Cu²⁺, Co²⁺, and Ni²⁺ ions can partially quench the fluorescence of P10 , but much less efficiently than the fluorescence of P7 . The static Stern–Volmer quenching constants of Cu²⁺, Co²⁺, and Ni²⁺ ions toward P7 are of the order of 10⁶ M^?1, being 1300, 2500, and 37,300 times larger than those of P10 , respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4154–4164, 2006     

VUV-UV excited luminescent properties of LnCa4O(BO3)3:RE (Ln=Y, La, Gd; Re=Eu, Tb, Dy, Ce)

Calcium lanthanide oxyborate doped with rare-earth ions LnCa₄O(BO₃)₃:RE³⁺ (LnCOB:RE, Ln=Y, La, Gd, RE=Eu, Tb, Dy, Ce) was synthesized by the method of solid-state reaction at high temperature. Their fluorescent spectra were measured from vacuum ultraviolet (VUV) to visible region at room temperature. Their excitation spectra all have a broadband center at about 188 nm, which is ascribed to host absorption. Using Dorenbos’ and Jφrgensen's work [P. Dorenbos, J. Lumin. 91 (2000) 91, R. Resfeld, C.K. Jφrgensen, Lasers and Excite States of Rare Earth [M], Springer, Berlin, 1977, p. 45], the position of the lowest 5d levels E(Ln,A) and charge transfer band E_ct were calculated and compared with their excitation spectra.Eu³⁺ and Tb³⁺ ions doped into LnCOB show efficient luminescence under VUV and UV irradiation. In this system, Ce³⁺ ions do not show efficient luminescence and quench the luminescence of Tb³⁺ ions when Tb³⁺ and Ce³⁺ ions are co-doped into LnCOB. GdCOB doped with Dy³⁺ shows yellowish white light under irradiation of 254 nm light for the reason that Gd³⁺ ions transfer the energy from itself to Dy³⁺. Because of the existence of Gd³⁺, the samples of GdCOB:RE³⁺ show higher excitation efficiency than LaCOB:RE³⁺ and YCOB:RE³⁺, around 188 nm, which indicates that the Gd³⁺ ions have an effect on the host absorption and can transfer the excitation energy to the luminescent center such as Tb³⁺, Dy³⁺ and Eu³⁺.