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151.
Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H2+ of the quantum numbers (n,m,Λ,±) with n=m=0 at Λ=0,1,2, with n=1, m=0 and n=0, m=1 at Λ=0 of both parities are explored for all interproton distances R. For all these states this approximation provides the relative accuracy ?10−5 (not less than 5 s.d.) locally, for any real coordinate x in eigenfunctions, when for total energy E(R) it gives 10-11 s.d. for R∈[0,50] a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1 is calculated with not less than 6 s.d. A dramatic dip in the E1 oscillator strength f1sσg−3pσu at R∼Req is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±) (or, equivalently, 1sσg and 2pσu states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσg and 2pσu potential curves is approximated with modified Pade Re−R[Pade(8/7)](R) with not less than 4-5 figures at R∈[0,40] a.u. Sum of potential curves E1sσg+E2pσu is approximated by Pade 1/R[Pade(5/8)](R) in R∈[0,40] a.u. with not less than 3-4 figures. 相似文献
152.
In this communication, we consider a p×n random matrix which is normally distributed with mean matrix M and covariance matrix Σ, where the multivariate observation xi=yi+?i with p dimensions on an object consists of two components, the signal yi with mean vector μ and covariance matrix Σs and noise with mean vector zero and covariance matrix Σ?, then the covariance matrix of xi and xj is given by Σ=Cov(xi,xj)=Γ⊗(B|i-j|Σs+C|i-j|Σ?), where Γ is a correlation matrix; B|i-j| and C|i-j| are diagonal constant matrices. The statistical objective is to consider the maximum likelihood estimate of the mean matrix M and various components of the covariance matrix Σ as well as their statistical properties, that is the point estimates of Σs,Σ? and Γ. More importantly, some properties of these estimators are investigated in slightly more general models. 相似文献
153.
154.
In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm. 相似文献
155.
In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations. 相似文献
156.
Finite <Emphasis Type="Italic">p</Emphasis>-groups with a class of complemented normal subgroups 下载免费PDF全文
Assume G is a finite group and H a subgroup of G. If there exists a subgroup K of G such that G = HK and H ∩ K = 1, then K is said to be a complement to H in G. A finite p-group G is called an NC-group if all its proper normal subgroups not contained in Φ(G) have complements. In this paper, some properties of NC-groups are investigated and some classes of NC-groups are classified. 相似文献
157.
Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions 下载免费PDF全文
Carlos A. Abanto‐Valle Roland Langrock Ming‐Hui Chen Michel V. Cardoso 《商业与工业应用随机模型》2017,33(4):394-408
In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
158.
Yang Qi 《数学研究通讯:英文版》2017,33(1)
In this article, we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values, which improves some earlier related results. 相似文献
159.
Nejal M. Bhatt Vijay D. Chavada Mallika Sanyal Pranav S. Shrivastav 《Biomedical chromatography : BMC》2019,33(10)
The present work describes novel methods using densitometry and indirect or off‐line high performance thin‐layer chromatography–mass spectrometry (HPTLC–MS) for the simultaneous detection and quantification of asenapine, propranolol and telmisartan and their phase II glucuronide metabolites. After chromatographic separation of the drugs and their metabolites the analytes were scraped, extracted in methanol and concentrated prior to mass spectrometric analysis. Different combinations of toluene and methanol–ethanol–n‐butanol–iso‐propanol were tested for analyte separation and the best results were obtained using toluene–methanol–ammonia (6.9:3.0:0.1, v/v/v) as the elution solvent. All of the drug–metabolite pairs were separated with a homologous retardation factor difference of ≥22. The conventional densitometric approach was also studied and the method performances were compared. Both of the approaches were validated following the International Conference on Harmonization guidelines, and applied to spiked human plasma samples. The major advantage of the TLC–MS approach is that it can provide much lower limits of detection (1.98–5.83 pg/band) and limit of quantitation (5.97–17.63 pg/band) with good precision (?3.0% coefficient of variation) compared with TLC–densitometry. The proposed indirect HPTLC–MS method is simple yet effective and has tremendous potential in the separation and quantitation of drugs and their metabolites from biological samples, especially for clinical studies. 相似文献
160.
S. N. Kreitmeier G. L. Liang D. W. Noid B. G. Sumpter 《Journal of Thermal Analysis and Calorimetry》1996,46(3-4):853-869
Thermal analysis by classical molecular dynamics simulations is discussed on hand of heat capacity of crystals of 9600 atoms. The differences between quantum mechanical and classical mechanical calculations are shown. Anharmonicity is proven to be an important factor. Finally, it is found that defects contribute to an increase in heat capacity before melting. The energy of conformational gauche defects within the crystal is only about 10% due to internal rotation. The other energy must be generated by cooperative strain. The conclusion is that the next generation of faster computers may permit wider use of molecular dynamics simulations in support of the interpretation of thermal analysis.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthday 相似文献