The PDE-preserving operators on nuclearly entire functions of bounded type

The PDE-preserving operators O on the space of nuclearly entire functions of bounded type H_Nb(E) on a Banach space E are characterized. An operator is PDE-preserving when it preserves homogenous solutions to homogeneous convolution equations. We establish a one to one correspondence between O and a set Σ of sequences of entire functionals, i.e. exponential type functions. In this way, algebraic structures on Σ, such as ring structures, can be carried over to O and vice versa. In particular, it follows that O is a non-commutative ring (algebra) with unity with respect to composition and the convolution operators form a commutative subring (subalgebra). We discuss range and kernel properties, for the operators in O, and characterize the projectors (onto polynomial spaces) in O by determining the corresponding elements in Σ. This revised version was published online in June 2006 with corrections to the Cover Date.     

静压下半导体微腔内激子与光子行为的研究

由于腔模与激子对压力的依赖关系不同,所以可以选择不同的压力使激子和光场处于不同的耦合状态,从而实现对耦合的调谐。利用这种办法,我们观测到了代表激子与光场强耦合作用的Rabi分裂。由于在我们现有样品结构中压力对激子本征行为的影响很小,与以前报道的温度、电场等调谐方式相比,这种调谐方法不仅可以有效地调谐半导体微腔内激子与腔模的耦合程度,而且能够保持激子的本征性质在整个调谐过程中基本不变。这有助于研究在强耦合过程中激子极化激元的本征性质。将实验结果与压力下激子与腔模耦合理论进行拟合,得出了正确的Rabi分裂值。     

An approximation property of harmonic functions in Lipschitz domains and some of its consequences

An extension of an inequality of J. B. Garnett (1979), with improvements by B. E. J. Dahlberg (1980), on an approximation property of harmonic functions is proved. The weighted inequality proved here was suggested by the work of J. Pipher (1993) and it implies an extension of a result of S. Y. A. Chang, J. Wilson and T. Wolff (1985) and C. Sweezy (1991) on exponential square integrability of the boundary values of solutions to second-order linear differential equations in divergence form. This implies a solution of a problem left open by R. Bañuelos and C. N. Moore (1989) on sharp estimates for the area integral of harmonic functions in Lipschitz domains.

     

一个素变数丢番图不等式

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指数型寿命数据中异常值的检验

本文讨论了在指数型寿命数据中,对同时存在的异常大数据和异常小数据的检验方法,给出了一个明确的判别标准,并以一例说明其应用。     

Diffusion via splitting and remeshing via merging in vortex methods

The technique of splitting a fat vortex element (with a core width larger than some threshold) into some thin ones in order to fix the convergence problem of the core‐spreading vortex methods is convenient and efficient. In particular, it keeps the method purely Lagrangian. In the present investigation, the splitting process is further viewed as part of the physical diffusion process. A new splitting method in which several weaker child vortices surround a thinned but still strong parent vortex is proposed. It is found that because of the survival of the parent vortex, the error arising from the splitting events can be largely reduced. The computational amount on the other hand is kept reasonably large by merging similar and close‐by vortices. The merging scheme designed herein not only involves fewer restrictions but also allows merging vortices of opposite rotations through the viewpoint of remeshing. The validity and accuracy of these techniques, proposed particularly for simulations undergoing lots of splitting and merging events, are verified by successfully simulating the interactions between two Burgers vortices under an external straining field. Copyright © 2005 John Wiley & Sons, Ltd.     

指数分布卷积形式参数的估计

本文研究指数分布卷积形式参数的点估计，区间估计以及经验分布函数与分布函数最大偏差的概率估计．     

On characterizing the bivariate exponential and geometric distributions

In this note, a characterization of the Gumbel's bivariate exponential distribution based on the properities of the conditional moments is discussed. The result forms a sort of bivariate analogue of the characterization of the univariate exponential distribution given by Sahobov and Geshev (1974) (cited in Lau and Rao ((1982), Sankhy Ser. A, 44, 87)). A discrete version of the property provides a similar conclusion relating to a bivariate geometric distribution.     

Ab initio calculations of vibronic activity in phosphorescence microwave double resonance spectra of p-dichlorobenzene

The phosphorescence spectrum of p-dichlorobenzene has been calculated using multiconfiguration self-consistent-field wave functions and the quadratic response technique. Attention has been paid to the intensity distribution of the singlet–triplet (³B_1u¹A_g) transition through a number of vibronic subbands. The second order spin–orbit coupling (SOC) contribution to the spin splitting of the ³B_1u (^3*) state is found to be almost negligible, and the calculations therefore provide a good estimate for the zero-field splitting (ZFS) parameters based only on the electron spin–spin coupling expectation values. Nuclear quadrupole resonance constants for the different Cl isotopes are also calculated to accomplish the ZFS assignment. The electric dipole activity of the spin sublevels in the triplet–singlet transitions to the ground-state vibrational levels is estimated by calculations of derivatives using distorted geometries which are shifted from the equilibrium position along different vibrational modes. A vibrational analysis of the phosphorescence spectrum, based on the SOC-induced mixing of the singlet and triplet states calculated along different vibrational modes, provides reasonable agreement with experimental data.Acknowledgment O. R.-P. would like to thank the European MOLPROP network for support. The authors thank Alexander Baev for fruitful discussions. This work was supported by the Swedish Royal Academy of Science (KVA).     

Simultaneous hydrogen and peroxide production by photocatalytic water splitting

Photocatalytic oxidation of water is a promising method to realize large-scale H₂O₂ production without a hazardous and energy-intensive process. In this study, we introduce a Pt/TiO₂(anatase) photocatalyst to construct a simple and environmentally friendly system to achieve simultaneous H₂ and H₂O₂ production. Both H₂ and H₂O₂ are high-value chemicals, and their separation is automatic. Even without the assistance of a sacrificial agent, the system can reach an efficiency of 7410 and 5096 μmol g^–1 h^–1 (first 1 h) for H₂ and H₂O₂, respectively, which is much higher than that of a commercial Pt/TiO₂(anatase) system that has a similar morphology. This exceptional activity is attributed to the more favorable two-electron oxidation of water to H₂O₂, compared with the four-electron oxidation of water to O₂.