Reflected backward doubly stochastic differential equations with discontinuous coefficients

In this paper, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous (left or right continuous) generator. We obtain an existence theorem and a comparison theorem for solutions of the class of RBDSDEs.     

Traveling Waves for Nonlocal and Non-monotone Delayed Reaction-difusion Equations

We study the existence of traveling wave solutions for a nonlocal and non-monotone delayed reaction-difusion equation.Based on the construction of two associated auxiliary reaction difusion equations with monotonicity and by using the traveling wavefronts of the auxiliary equations,the existence of the positive traveling wave solutions for c≥c is obtained.Also,the exponential asymptotic behavior in the negative infnity was established.Moreover,we apply our results to some reactiondifusion equations with spatio-temporal delay to obtain the existence of traveling waves.These results cover,complement and/or improve some existing ones in the literature.     

研究型教学柔性评分方案研究

研究型教学的本质是培养学生创新的精神与能力,而现行的学生成绩评分体系差异度较小,不能全面反映出学生的真实掌握情况,不能适应研究型教学模式的开展.借鉴"开根乘十"的经典处理案例,提出了一种将贡献值反映到幂次上的适合研究型教学的柔性评分系统,对其进行方案设计,并推导扩展了其评分计算公式.结合升级模式,对其进行自动实现,以所见即所得的方式进行展示,活跃了课堂气氛,也充分调动了学生课后进行研究探索活动的积极性.     

关于Diophantine方程(20n)x+(21n)y=(29n)z

设a,b,c是满足条件a2+ b2=c2的两两互素的正整数.Jesmanowicz于1956年猜想对于任意给定的正整数n,方程(an)x+(bn)y=(cn)z仅有解(x,y,z)=(2,2,2).本文证明了方程(20n)x+(21n)y=(29n)z有唯一解(x,y,z)=(2,2,2).     

Recent development of studies on the mechanism of resistive memories in several metal oxides

Resistive switching random access memories(RRAM)have been considered to be promising for future information technology with applications for non-volatile memory,logic circuits and neuromorphic computing.Key performances of those resistive devices are approaching the realistic levels for production.In this paper,we review the progress of valence change type memories,including relevant work reported by our group.Both electrode engineering and in-situ transmission electron microscopy(TEM)high-resolution observation have been implemented to reveal the influence of migration of oxygen anions/vacancies on the resistive switching effect.The understanding of resistive memory mechanism is significantly important for device applications.     

Formation of hydrophobic coating on PMMA surface using unipolar nanosecond-pulse DBD in atmospheric air

Dielectric barrier discharge (DBD) can modify the material surface and result in complicated physical and chemical reactions to improve the surface hydrophilicity, which is proved to be an effective method for surface modification. Compared with the traditional ac-excitation DBD, the DBD using unipolar pulses can avoid local overheat of microdischarges and can improve discharge efficiency under some conditions. In this paper, DBD excited by repetitive unipolar nanosecond generator was used to improve the hydrophobicity of Plexiglass (PMMA) surface by means of the interaction between air plasma and silicone oil. The output voltage had a rise time of 40 ns and a full width at half maximum of about 70 ns. The surface hydrophobicity of the PMMA, before and after the surface modification, was evaluated via the contact angle measurement under different experimental conditions. The values of the contact angle shown in this paper were the average of eight measured values, and the standard deviations were also calculated. The surface energy including polar and dispersion components was calculated using the measured average contact angles of distilled water and polyethyleneglycol. The results showed that, as the increase of the discharge voltage, the contact angle increased but the surface energy decreased. With the increase of treatment time, the water contact angle of the modified surface increased at the beginning, and it would reach to a maximum at 7.5 min treatment, and then decreased. The effect of pulse frequency on the modification results was different at various treatment times. In addition, the possible physical and chemical reaction among the DBD plasma, silicone oil and the PMMA surface was discussed.     

Calculation on the CO2 influences on the structure,stability of (MgO)m (m = 1–6) clusters

ABSTRACT

The concentration of carbon dioxide (CO₂) has a significant influence on the morphology of thermal decomposition products of magnesite. So, structures, stabilities and adsorption mechanisms of (MgO)_m (m?=?1–6) clusters by one or two CO₂ molecules were calculated by the GGA-PW91 method. The results show that the stability of the considered clusters is (MgO)_m(CO₂)₂ clusters > (MgO)_m(CO₂) clusters > (MgO)_m clusters by the average binding energy. Certain low-lying isomers of (MgO)_m(CO₂) and (MgO)_m(CO₂)₂ clusters which have an isolated O atom are deviating from the cluster center which possess higher kinetic activity. (MgO)_m clusters prefer to adsorb a CO₂ molecule, while (MgO)₃(CO₂) clusters prefer to adsorb a CO₂ molecule rather than the neighbors. Magnesite is difficult to transit to (MgCO₃)₂ clusters at room temperature. However, magnesite will spontaneously transit to (MgO)₂ clusters and further transit to MgO crystal which need to adsorb more energy at 700?K.     

Numerical investigations of supercavitation around blunt bodies of submarine shape

Cavitation occurs when liquid is subjected to rapid changes of pressure. If the local pressure is lower than the liquid saturation pressure, the liquid changes its phase into vapor. A fast moving solid body underwater will reduce the local pressure around the body. Under certain conditions, the local pressure can be lower than the water saturation pressure, accordingly causing cavitation. If the velocity of the moving body increases further, a supercavitation will occur. In this paper, the cavitation and supercavitation were studied by the SST k–ω turbulence model combined with a finite-rate mass transfer modeling under the mixture assumption. The validations of these models were performed through comparisons between numerical simulations and experiments. After the validations, the supercavitation generated by a high speed moving body, which can be described as a large bubble, was studied. The studies were on several blunt bodies, such as a submarine hull shape, a submarine hull shape with appendages and a full submarine shape with sail and appendages. It was found that the naked submarine hull is difficult to have the supercavitation covering the whole body. The sail and appendages can help supercavitation occurs earlier. Furthermore the effects of the supercavitation on the submarine and generation mechanism of the supercavitation is discussed based on the simulations.