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11.
Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac’s symbols (ket versus bra, e.g., |q〉〈q| of continuous parameter q) in quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |〉〈| cannot be directly performed by Newton-Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac’s symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented. 相似文献
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13.
Weidong Gao Meiqiong Zhan Shuhai Fan Janda Shao Zheng-Xiu Fan 《Applied Surface Science》2005,250(1-4):195-202
The laser-induced damage (LID) behavior of narrow-band interference filters was investigated with a Nd:YAG laser at 1064 nm under single-pulse mode and free-running mode. The absorption measurement of such coatings was performed with surface thermal lensing (STL) technique. The damage morphologies under the two different laser modes were also studied in detail. It was found that all the filters exhibited a pass-band-center-dependent absorption and laser-induced damage threshold (LIDT) behavior, but the damage morphologies were diverse. The explanation was given with the analysis of the electric field distribution and the operational behavior of the irradiation laser. 相似文献
14.
A graph G is N2‐locally connected if for every vertex ν in G, the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjá?ek conjectured that every 3‐connected N2‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005 相似文献
15.
The first α‐diimine nickel(I) complex having a chloro bridge is reported. The centrosymmetric dinuclear structure of {[ArN?C(Me)C(Me)?NAr]NiCl}2[Ar?2,6?C6H3(i‐Pr)2] features two chelating α‐diimine ligands and two bridged chlorine atoms, so that a distorted tetrahedral N2Cl2 coordination geometry for nickel results. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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17.
Generation of UV laser light by stimulated Raman scattering in D2, D2/Ar and D2/He using a pulsed Nd:YAG laser at 355nm
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A pulsed Nd:YAG laser at 355nm is used to pump Raman cell filled with D_2, D_2/Ar and D_2/He. With adequately adjusted parameters, the maximum photon conversion efficiency of the first-order Stokes light (S_1, 396.796nm) reaches 33.33% in D_2/Ar and the stability of S_1 in pure D_2 is fairly high, the energy drift being less than 10% when the pump energy drifts in the range of 5%. The conversion efficiency and stability, which are functions of the composition and pressure of the Raman medium and the energy of pump laser, are investigated. The result has been used to optimize the laser transmitter system for a differential absorption lidar system to measure NO_2 concentration profiles. 相似文献
18.
We present the procedure of exactly solving the Izergin–Korepin model with open boundary conditions by using the algebraic Bethe ansatz, which include constructing the multi-particle state and achieving the eigenvalue of the transfer matrix and corresponding Bethe equations. We give a proof about our conclusions on the multi-particle state based on an assumption. When the model is Uq(su(2)) quantum invariant, our results agree with that obtained by analytic Bethe ansatz method. 相似文献
19.
In this Note, we shall consider the Riemannian distance on loop groups, which will be identified to one introduced by Hino and Ramirez [M. Hino, J.A. Ramirez, Small-time Gaussian behavior of symmetric diffusion semigroups, Ann. Probab. 31 (2003) 1254–1295]. A transportation cost inequality is established. To cite this article: S. Fang, J. Shao, C. R. Acad. Sci. Paris, Ser. I 341 (2005). 相似文献
20.
Yu‐Hsiang Hu Chuh‐Yung Chen Chen‐Chien Wang Yao‐Hui Huang Shao‐Ping Wang 《Journal of polymer science. Part A, Polymer chemistry》2004,42(19):4976-4993
The bulk polymerization of styrene initiated by ?‐caprolactam (CL) and n‐dodecyl mercaptan (RSH) has been explored. This novel polymerization system shows living characteristics. For example, the molecular weight of the resulting polymers increases with conversion, and the system has the ability to form diblock copolymers and so forth. The polymer chain end contains thiol and lactam structures, which we have investigated with Fourier transform infrared, 1H NMR, and 13C NMR techniques. Electron spin resonance spectra and theoretical calculations by the Hartree–Fock methods have been used to examine the mechanism. The results reveal that the initial polymerization starts from thiol via a chain‐transfer reaction, and the propagation proceeds by the insertion of a monomer between the terminal group and the intermediate structure of lactam. Finally, the polymerization kinetics have been examined. The polymerization rate varies linearly with the concentration of CL and RSH, and this confirms the mechanism. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4976–4993, 2004 相似文献