On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.     

An analysis of seismic attenuation in random porous media

The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency.     

Theoretical study on the dislocations in the bubble rafts

The core structure of the dislocation in a bubble raft has been evaluated by using the improved P–N equation. The dislocation profile has been obtained explicitly for the bubble radius R=0.296, 0.592, 0.650, 0.888 mm. The results show that the core width of dislocation will increase rapidly when the bubble radius decreases, especially, this trend will become more significant as the radius is more smaller. Our calculated results agree well with the experimental data, and our method can be used to predict the core structure of the dislocation in a bubble raft where bubble-radius is given arbitrarily.     

The Pullback Asymptotic Behavior of the Solutions for 2D Nonautonomous G-Navier-Stokes Equations

The pullback asymptotic behavior of the solutions for 2D Nonautonomous G-Navier-Stokes equations is studied, and the existence of its $L^2$-pullback attractors on some bounded domains with Dirichlet boundary conditions is investigated by using the measure of noncompactness. Then the estimation of the fractal dimensions for the 2D G-Navier-Stokes equations is given.     

Search for νμ and ντ supernova neutrinos with massive liquid-scintillation detectors

Summary In this paper we have estimated the sensitivity of a large-mass liquid-scintillation detector to search for supernova neutrinos of different flavours. Events produced by ν_μ and ν_τ interactions can be identified by looking at the distorsion in the neutrino energy spectrum. We have shown here that, overlapped to the main energy distribution produced by interactions with protons a peak at 15.11 MeV (due to the de-excitation of¹²C^* nuclei excited by neutral-current neutrino interactions) gives a possible signature of these neutrino flavours. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

Spin-adapted wave functions of the serber type and time reversal

A procedure is proposed for generating Serber-type spin eigenfunctions withM _s = 0. The procedure uses the time-reversal invariance of these functions to increase the efficiency and to reduce the storage requirements. Simplifications in calculating the matrix elements of an observable operator which follow from the use of the time-reversal symmetry are briefly discussed.     

The Mitsunobu 1-O-esterification of 1-hydroxy-3-phenyl-1H-quinoxalin-2-one 4-oxide

1-Hydroxy-2-oxo-3-phenyl-1,2-dihydroquinoxaline 4-oxide under conditions of the Mitsunobu reaction reacts with alcohols giving the corresponding esters at the hydroxy group in position 1. Other representatives of hydroxamic acids such as 1,4-dihydroxyperhydroquinoxaline-2,3-dione and 1,4-dihydroxy-3,3,6,6-tetramethylpiperazine-2,5-dione undergo destruction under these conditions. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1240–1243, June, 2008.     

高效液相色谱溶剂系统四面体优化法

改进了Ｇｌａｊｃｈ的三角形法,建立了适合于高效液相色谱（ＨＰＬＣ）的四面体优化法。将７个溶剂系统的实验结果输入计算机,由计算机模拟２３１个溶剂系统的色谱行为,优选出最佳溶剂系统。将此法用于１２种磺胺药物的分离,得到了满意的结果。