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Anharmonic effective potential, Extended X-ray Absorption Fine Structure (EXAFS) and its parameters of hcp crystals have been theoretically and experimentally studied. Analytical expressions for the anharmonic effective potential, effective local force constant, three first cumulants, a novel anharmonic factor, thermal expansion coefficient and anhamonic contributions to EXAFS amplitude and phase have been derived. This anharmonic theory is applied to analyze the EXAFS of Zn and Cd at 77 K and 300 K, measured at HASYLAB (DESY, Germany). Numerical results are found to be in good agreement with experiment, where unnegligible anharmonic effects have been shown in the considered theoretical and experimental quantities.

This paper presents dipole moments, static isotropic polarizabilities and polarizability anisotropies of 20 molecules calculated in the framework of a new natural orbital functional method. All calculations have been performed using a finite field approach. Comparison with other correlated methods (CCSD(T), B3LYP) shows a reasonable agreement in the prediction of electric response properties by this new functional.

Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used. Examples of inequalities for qudit tomograms and a state-extended uncertainty relation are considered. Tomographic cumulant related to photon state tomographic probability distributions is introduced and it is used as parameter of the state non-Gaussianity.

Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the entries are taken from an i.i.d. sequence with finite variance, the LSD are tied together by a common thread — the $2k$th moment of the limit equals a weighted sum over different types of pair-partitions of the set $\{1,2,\dots ,2k\}$ and are universal. Some results are also known for the sparse case. In this paper, we generalize these results by relaxing significantly the i.i.d. assumption. For our models, the limits are defined via a larger class of partitions and are also not universal. Several existing and new results for patterned matrices, their band and sparse versions, as well as for matrices with continuous and discrete variance profile follow as special cases.

This paper proposes a transmission line overload assessment model and optimization control method based on transmission line overload risk. It uses probabilistic power flow (PPF) and cumulant method to analyze the uncertainty of system statuses and line flow, applies the severity function to describe the impact of transmission line load fluctuations and its result. Based on that, as an indicator of power system security, overload risk index is defined as the product of the probability and the severity of transmission line overload. A preventive control model was used to optimize the outputs of the system active and reactive resources, which based on optimal power flow (OPF) and primal dual interior point method. It reduces the system overload risks and increases the system security. By test, calculation on the IEEE-16 test system validates the method proposed above.

This paper proposes a transmission line overload assessment model and optimization control method based on transmission line overload risk. It uses probabilistic power flow (PPF) and cumulant method to analyze the uncertainty of system statuses and line flow, applies the severity function to describe the impact of transmission line load fluctuations and its result. Based on that, as an indicator of power system security, overload risk index is defined as the product of the probability and the severity of transmission line overload. A preventive control model was used to optimize the outputs of the system active and reactive resources, which based on optimal power flow (OPF) and primal dual interior point method. It reduces the system overload risks and increases the system security. By test, calculation on the IEEE-16 test system validates the method proposed above.

Mass wind power access to power system in steady state operation can't adopt traditional deterministic flow calculation method, probabilistic power flow calculation method can solve the power flow of random parameter equation effectively, has been widely applied. In this paper, it proposed power flow calculation in wind power based on the improved cumulant method, which introduced the Monte Carlo sampling method based on Latin hypercube sampling to deal with the correlation of input variables, to solve the difficult to use conventional numerical methods to solve the input variable of cumulant, and the Cornish - Fisher series expansion calculates the probability distribution of state variables. In addition, such IEEE 14 nodes system as example, proposed method verifies the validity and accuracy based on the results of Monte Carlo simulation.