Bayesian inference and life testing plans for generalized exponential distribution

Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters cannot be obtained in the closed form. Lindley’s approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process. And we have recommended to use the sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes. This work was partially supported by a grant from the Department of Science and Technology, Government of India     

Enhancing the precision of phase estimation by weak measurement and quantum measurement reversal

The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.     

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.

     

3-取代芳基-2-吲哚基膦酸酯的合成

本文根据Fischer吲哚合成法制备了一系列的3-取代芳基-2-吲哚基膦酸酯. 盐酸苯肼与o,o-二异丙基-4-氯-苯乙酰基膦酸酯在无水酒精中反应, O,O-二异丙基-(4'-氯苯-3H-吲哚-2-膦酸酯能被分离出来, 而且它的异构化最终产物能被观察到.     

A structural approach to investigate halogen substituted MAO-B inhibitors using QSAR modeling,molecular dynamics,and conceptual DFT analysis

Halogenated inhibitors showed robust, reversible, and selective monoamine oxidase-B (MAO-B) inhibitory efficacy in candidates that were derived from them. Our team has previously synthesized and assessed a panel of halogenated chalcones and coumarin for the study on MAO-B inhibition. The aim of this study was to build GA-MLR based QSAR models and predictive 3D Pharmacophore models, as well as to investigate the relationship between halogenated derivatives and MAO-B inhibitory activity. The robust statistical significance in the parameter (R² = 0.78 and Q² = 0.69) was demonstrated. Best Hypo1 contains one hydrophobic and two aromatic rings. The lead molecule for quantum mechanics was performed, and it was revealed that it would bind to proteins and provide stability. To determine the stability of the ligand-enzyme complex, a thorough molecular dynamics analysis of the lead compounds was accomplished.