Symbolic Computations and Exact and Explicit Solutions of Some Nonlinear Evolution Equations in Mathematical Physics

With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher＇s equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G′/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered.     

Symmetries and solutions for a Fisher equation with a proliferation term involving tumor development

We consider a generalized Fisher equation involving tumor development from the point of view of the theory of symmetry reductions in partial differential equations. The study of this equation is relevant as it includes generalizations within the proliferation rate, being interpreted in terms of the total mass of the tumor. Classical Lie point symmetries admitted by the equation are determined. Finally, we obtain some biologically meaningful solutions in terms of a hyperbolic tangent function, which describes the tumor dynamics.     

Fisher Information and Complexity Measure of Generalized Morse Potential Model

The spreading of the quantum-mechanical probability distribution density of the three-dimensional system is quantitatively determined by means of the local information-theoretic quantity of the Shannon information and information energy in both position and momentum spaces. The complexity measure which is equivalent to Cramer-Rao uncertainty product is determined. We have obtained the information content stored, the concentration of quantum system and complexity measure numerically for n=0, 1, 2 and 3 respectively.     

Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors

Sensor placement is an important factor that may significantly affect the localization performance of a sensor network. This paper investigates the sensor placement optimization problem in three-dimensional (3D) space for angle of arrival (AOA) target localization with Gaussian priors. We first show that under the A-optimality criterion, the optimization problem can be transferred to be a diagonalizing process on the AOA-based Fisher information matrix (FIM). Secondly, we prove that the FIM follows the invariance property of the 3D rotation, and the Gaussian covariance matrix of the FIM can be diagonalized via 3D rotation. Based on this finding, an optimal sensor placement method using 3D rotation was created for when prior information exists as to the target location. Finally, several simulations were carried out to demonstrate the effectiveness of the proposed method. Compared with the existing methods, the mean squared error (MSE) of the maximum a posteriori (MAP) estimation using the proposed method is lower by at least 25% when the number of sensors is between 3 and 6, while the estimation bias remains very close to zero (smaller than 0.15 m).     

Exact Solutions of Fisher and Generalized Fisher Equations with Variable Coefficients

In this work,we consider a Fisher and generalized Fisher equations with variable coefficients.Usingtruncated Painlevé expansions of these equations,we obtain exact solutions of these equations with a constrainton the coefficients a(t)and b(t).     

LBVW分布的Fisher信息矩阵

文本考察由Larry Lee提出的其生存函数为 F(x_1,x_2)=exp{-[(x_1/θ_1)~(1/αδ)]~δ} (x_i>0,θ_i>0,i=1,2;0<δ≤1,α>0)的LBVW(θ_1,θ_2,δ,α)分布的统计性质,该分布的Fisher信息矩阵被导出。     

Heisenberg Limit Phase Sensitivity in the Presence of Decoherence Channels

In the present study, time evolution of quantum Cramer–Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as decoherence approach is characterized by quantum fisher information flow and entanglement amount in order to distinguish between Markovian and Non-Markovian process. The comparison between quantum fisher information and quantum fisher information flow assists to comprehend the phase sensitivity evolution corresponding to Non-Markovian and Markovian process. Furthermore, as result of backflow of information from the environment to system, the phase sensitivity corresponding memory effect of environment are revived after complete decay and increase in the few times.     

Information Measure in Terms of the Hazard Function and Its Estimate

It is well-known that some information measures, including Fisher information and entropy, can be represented in terms of the hazard function. In this paper, we provide the representations of more information measures, including quantal Fisher information and quantal Kullback-leibler information, in terms of the hazard function and reverse hazard function. We provide some estimators of the quantal KL information, which include the Anderson-Darling test statistic, and compare their performances.     

Information entropic measures of a quantum harmonic oscillator in symmetric and asymmetric confinement within an impenetrable box

Information‐based uncertainty measures like Shannon entropy, Onicescu energy and Fisher information (in position and momentum space) are employed to understand the effect of symmetric and asymmetric confinement in a quantum harmonic oscillator. Also, the transformation of the Hamiltonian into a dimensionless form gives an idea of the composite effect of force constant and confinement length (x_c). In the symmetric case, a wide range of x_c has been taken up, whereas asymmetric confinement is dealt with by shifting the minimum of the potential from the origin keeping box length and boundary fixed. Eigenvalues and eigenvectors for these systems are obtained quite accurately via an imaginary‐time propagation scheme. For asymmetric confinement, a variation‐induced exact diagonalization procedure is also introduced, which produces very high quality results. One finds that, in symmetric confinement, after a certain characteristic x_c, all these properties converge to respective values of a free harmonic oscillator. In the asymmetric situation, excited‐state energies always pass through a maximum. For this potential, the classical turning point decreases, whereas well depth increases with the strength of asymmetry. A study of these uncertainty measures reveals that localization increases with an increase of the asymmetry parameter.