Performance analysis of blockchain for civil aviation business data based on M/G/1 queuing theory

An Ethereum blockchain based on proof of stake ( PoS) consensus mechanism is used to achieve the data sharing within the civil aviation service platform for both airport group management and passengers. Considering the Gas consumption of Ethereum, the dynamic batch-service capacity constraint by the Block Gas Limit and the priority mechanism depending on the different Gas Price of transactions, M/ G/1 queuing theory with batch-service is used to construct the service model of transactions confirmation process in the proposed blockchain system, where the effects of transactions arrival rate, block capacity, service rate and number of nodes on the average confirmation time of transactions with different priority are analyzed, and eventually a performance analysis model of blockchain for civil aviation business data is proposed. The simulation results prove the usability and accuracy of the model, which can provide both theoretical basis for data sharing of civil aviation using Ethereum blockchain and the further optimization of transactions confirmation time.

Mechanistic Investigation on Rhodium(III)-Catalyzed Cycloaddition of 2-Vinylphenol Derivatives with Ethyne or Carbon Monoxide by DFT Study

Rhodium-catalyzed cycloaddition reaction was calculated by density functional theory M06-2X method to directly synthesize benzoxepine and coumarin derivatives.In this work,we conducted a computational study of two competitive mechanisms in which the carbon atom of acetylene or carbon monoxide attacked and inserted from two different directions of the six-membered ring reactant to clarify the principle characteristics of this transformation.The calculation results reveal that:(i)the insertion process of alkyne or carbon monoxide is the key step of the reaction;(ii)for the(5+2)cycloaddition reaction of acetylene,higher energy is required to break the Rh−O bond of the reactant,and the reaction tends to complete the insertion from the side of the Rh−C bond;(iii)for the(5+1)cycloaddition of carbon monoxide,both reaction paths have lower activation free energy,and the two will generate a competition mechanism.

Non-Commutative Fock-Darwin System and Magnetic Field Limits

A Fock-Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of ω/ωe and certain algebra realization （SU（2）and SU（1,1））, and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.

ON THE SPECTRUM OF SINGULAR HAMILTONIAN DIFFERENTIAL SYSTEMS

In this paper, we study a bounded-below singular Hamiltonian system. Sufficient and necessary conditions are obtained for the existence and the number of eigenvalues on the left-axis. The main results of this paper are the extension and improvement of Weyl spectral theorem for singular sccond order differential equations.