The Shannon entropy (S) and the Fisher Information (I) entropies are investigated for a generalized hyperbolic potential in position and momentum spaces. First, the Schrodinger equation is solved exactly using the Nikiforov-Uvarov-Functional Analysis method to obtain the energy spectra and the corresponding wave function. By Fourier transforming the position space wave function, the corresponding momentum wave function was obtained for the low-lying states corresponding to the ground and first excited states. The positions and momentum of Shannon entropy and Fisher Information entropies were calculated numerically. Finally, the Bialynicki-Birula and Mycielski and the Stam-Cramer-Rao inequalities for the Shannon entropy and Fisher Information entropies, respectively, were tested and were found to be satisfied for all cases considered. 相似文献
The goal of the paper is to automatize the construction and parameterization of kinetic reaction mechanisms that can describe a set of experimentally measured concentration versus time curves. Using the framework and theorems of formal reaction kinetics, first, we build a set of possible mechanisms with a given number of measured and unmeasured (real or fictitious) species and reaction steps that fulfill some chemically reasonable requirements. Then we fit all the corresponding mass-action kinetic models and offer the best one to the chemist to help explain the underlying chemical phenomenon or to use it for predictions. We demonstrate the use of the method via two simple examples: on an artificial, simulated set of data and on a small real-life data set. The method can also be used to do a kind of lumping to generate a model that can reproduce the simulation results of a detailed mechanism with less species and thereby can largely accelerate spatially inhomogeneous simulations. 相似文献
In order to further explore the detailed reaction mechanism of carbon dioxide activated by [Re(CO)2]+ complex, CCSD(T) methods was performed to determine related potential energy surface (PES). Crossing point is determined by using a partially optimized method. The result shows that larger spin-orbital coupling (155.37 cm−1) and intersystem crossing probabilities in spin-forbidden region causes the electron to spin flip at the minimum energy crossing point and access to the lower singlet PES. Nonadiabatic rate constant k is estimated to be quite rapid, so transition state (1TS1) is rate-controlled steps. In addition, the electronic structure of oxygen-atom transfer process is further analyzed by localized molecular orbital and Mayer bond order. The analysis finds that the form of main bonding orbital is the electron contribution from the p(O) in CO2 to the empty d(Re) orbital. 相似文献
The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.