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31.
For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 相似文献
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This paper gives a critical review on the applications of ToF SIMS in the areas of polymer additive characterization and in the study of polymer blends and interfaces. Polymer additives can readily be identified by ToF SIMS using their parent molecular ions or characteristic fragments. This analytical capability has been successfully applied to monitor the migration or segregation of additives during polymer processing. ToF SIMS is an ideal analytical tool for the study of polymer blends and interfaces because it is able to provide information on both surface composition and morphology. In combination with other analytical techniques such as AFM and XPS, ToF SIMS chemical imaging capability has opened up new horizons in the investigation of complex polymer blend systems. Finally the main advantages and limitations of ToF SIMS in these application areas are also discussed. 相似文献
34.
Canonical correlation analysis based on information theory 总被引:2,自引:0,他引:2
In this article, we propose a new canonical correlation method based on information theory. This method examines potential nonlinear relationships between p×1 vector Y-set and q×1 vector X-set. It finds canonical coefficient vectors a and b by maximizing a more general measure, the mutual information, between aTX and bTY. We use a permutation test to determine the pairs of the new canonical correlation variates, which requires no specific distributions for X and Y as long as one can estimate the densities of aTX and bTY nonparametrically. Examples illustrating the new method are presented. 相似文献
35.
We examine the ferroelectric-relaxor behavior of (Ba0.65Sr0.35)(Zr0.35Ti0.65)O3 (BSZT) ceramics in the temperature range from 80 to 380 K. A broad dielectric maximum, which shifts to higher temperature with increasing frequency, signifies the relaxor-type behavior of these ceramics. The value of the relaxation parameter γ∼2 estimated from the linear fit of the modified Curie-Weiss law, indicates the relaxor nature of the BSZT ceramics. The dielectric relaxation rate follows the Vogel-Fulcher relation with TVF=107 K, Ea=0.121 eV, and ν0=6.83×1014 Hz, further supports such relaxor nature. The slim P-E hysteresis loop and ‘butterfly’ shape dc bias field dependence of permittivity at T>Tm (Tm, the temperature of permittivity maximum) clearly signifies the occurrence of nanopolar clusters, which is the typical characteristic of ferroelectric relaxor. At 300 K and 10 kHz, the dielectric constant and loss tan δ are ∼1100 and 0.0015, respectively. The high tunability (∼25%) and figure of merit (∼130) at room temperature show that the BSZT ceramics could be a promising candidate for tunable capacitor applications. 相似文献
36.
This work is devoted to near-optimal controls of large-scale discrete-time nonlinear dynamic systems driven by Markov chains; the underlying problem is to minimize an expected cost function. Our main goal is to reduce the complexity of the underlying systems. To achieve this goal, discrete-time control models under singularly-perturbed Markov chains are introduced. Using a relaxed control representation, our effort is devoted to finding near-optimal controls. Lumping the states in each irreducible class into a single state gives rise to a limit system. Applying near-optimal controls of the limit system to the original system, near-optimal controls of the original system are derived. 相似文献
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38.
A new method of using time-averaged digital speckle pattern interferometry for the quantitative measurement of vibration amplitude was developed. Signal processing techniques especially the Hilbert transformation for quantitative evaluation of the Bessel fringes obtained in time-averaged digital speckle pattern interferometry were explored. The quadrature signal after Hilbert transformation is equivalent to a 90° phase-shifted interferogram for a monotonically increasing or decreasing phase function. An algorithm was developed for Bessel fringe contrast enhancement and phase extraction. The techniques were tested numerically and experimentally. Sub-fringe quantification of the time-averaged vibration fringes is realised with the proposed method. Compared with the commonly used phase shift method which requires a minimum of two images for image processing, this method requires only one fringe pattern for data extraction. 相似文献
39.
In this paper,the concept of the infinitesimal realization factor is extended to the parameter-dependent performance functions in closed queueing networks. Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed. This provides a united framework for both IPA and non IPA approaches. Finally,another physical meaning of the service rate is given. 相似文献