We consider the semilinear subelliptic Laplace equation -Δ Hn u=u p+f(x,u) in Ω,u>0 in Ω,u=0 on Ω . Under suitable assumptions on f and p ,some existence and nonexistence results are obtained.
In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher t...In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level （higher than 4） equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth kd 〈 26. Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.展开更多
The structure and electronic properties of a series of biologically active dithiolethiones （1） have been calculated using semi-empirical. Multi-linear regression analysis suggests that there is a reasonable correlat...The structure and electronic properties of a series of biologically active dithiolethiones （1） have been calculated using semi-empirical. Multi-linear regression analysis suggests that there is a reasonable correlation between the experimental activity of the derivatives against chelation activity and calculated properties such as the HOMO energies, molar refractivity, dipole moments and experimental partition coefficient. From the derived QSAR equations the 3-Methylthio-4p-Tolyle-1,2-Dithiolylium accompanying ion （CH3SO4） and 4-para-tolyl-1,2-dithiole-3-thione （2b and 2） are predicted to show the highest activity against chelation activity, while 3-Methylthio-5p-methoxy phenyl-1,2-Dithiolylium accompanying ion （I-） （3a） is predicted to be the least active in line with the experimental results.展开更多
During the start-up and shut-down phase of reciprocating compressors, the loads on all components of driven train system are very high. In this paper a method for calculating the forces on coupling, e-motor, crank sha...During the start-up and shut-down phase of reciprocating compressors, the loads on all components of driven train system are very high. In this paper a method for calculating the forces on coupling, e-motor, crank shaft as well other components of the system will be described. The modelling of the electrical induction motor, coupling, crank shaft, damper as well as the compressor resistance torque are extremely important in simulating start-up and shut-down of reciprocating compressor. Furthermore the switching torque of the electrical motor and the instantaneous moment of inertia of the reciprocating compressor crank gear are important as well. The transient start-up and shut-down process under loaded and unloaded conditions is described using a non-linear differential equation for driven train system： E-motor--coupling--flywheel--reciprocating compressor--damper. Shaft torsional moments on the drive train and especially on the coupling, whether elastic or stiff, can then only be calculated using numerical simulation. This paper will describe some of the key elements in modelling, simulating and measurements of drive train start-up and shut-down carried out on already operational piston compressor units.展开更多
The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Re...The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal （Johansson＇s） propositional logics, the authors introduce the family of resolution systems with full substitution rule （SRC, SRI and SRM） and with e-restricted substitution rule （SeRC, SeRf and SeRM）, where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system （in tree form） is polynomially equivalent to Frege systems by size, but for every ~＇ 〉 0, Se＋lR-type has exponential speed-up over the SeR-type （in tree form）.展开更多
Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not ...Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacob/elliptic functions. The results also show that if the arbitrary constants are selected suitably, the approximate solutions may become the exact ones.展开更多
文摘We consider the semilinear subelliptic Laplace equation -Δ Hn u=u p+f(x,u) in Ω,u>0 in Ω,u=0 on Ω . Under suitable assumptions on f and p ,some existence and nonexistence results are obtained.
基金Supported by the Special Fund for Basic Scientific Research of Central Colleges Harbin Engineering University(Harbin)the National Natural Science Foundation of China+1 种基金Doctor Subject Foundation of the Ministry of Education of Chinathe"111"project(B07019)
文摘In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level （higher than 4） equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth kd 〈 26. Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.
文摘The structure and electronic properties of a series of biologically active dithiolethiones （1） have been calculated using semi-empirical. Multi-linear regression analysis suggests that there is a reasonable correlation between the experimental activity of the derivatives against chelation activity and calculated properties such as the HOMO energies, molar refractivity, dipole moments and experimental partition coefficient. From the derived QSAR equations the 3-Methylthio-4p-Tolyle-1,2-Dithiolylium accompanying ion （CH3SO4） and 4-para-tolyl-1,2-dithiole-3-thione （2b and 2） are predicted to show the highest activity against chelation activity, while 3-Methylthio-5p-methoxy phenyl-1,2-Dithiolylium accompanying ion （I-） （3a） is predicted to be the least active in line with the experimental results.
文摘During the start-up and shut-down phase of reciprocating compressors, the loads on all components of driven train system are very high. In this paper a method for calculating the forces on coupling, e-motor, crank shaft as well other components of the system will be described. The modelling of the electrical induction motor, coupling, crank shaft, damper as well as the compressor resistance torque are extremely important in simulating start-up and shut-down of reciprocating compressor. Furthermore the switching torque of the electrical motor and the instantaneous moment of inertia of the reciprocating compressor crank gear are important as well. The transient start-up and shut-down process under loaded and unloaded conditions is described using a non-linear differential equation for driven train system： E-motor--coupling--flywheel--reciprocating compressor--damper. Shaft torsional moments on the drive train and especially on the coupling, whether elastic or stiff, can then only be calculated using numerical simulation. This paper will describe some of the key elements in modelling, simulating and measurements of drive train start-up and shut-down carried out on already operational piston compressor units.
文摘The proof system, based on resolution method, has become quite popular in automatic theorem proving, because this method is simple to implement. At present many kinds of extensions for resolution method are known： Resolution with restricted number of variables in disjuncts, resolution over Linear Equations, Cutting planes, etc. For Classical, Intuitionistic and Minimal （Johansson＇s） propositional logics, the authors introduce the family of resolution systems with full substitution rule （SRC, SRI and SRM） and with e-restricted substitution rule （SeRC, SeRf and SeRM）, where the number of substituted formula connectives is bounded by . The authors show that for each of mentioned logic the SR-type system （in tree form） is polynomially equivalent to Frege systems by size, but for every ~＇ 〉 0, Se＋lR-type has exponential speed-up over the SeR-type （in tree form）.
基金Supported by National Natural Science Foundation of China under Grant No.11104248Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ12A01008Project of Education of Zhejiang Province under Grant No.Y201327716
文摘Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacob/elliptic functions. The results also show that if the arbitrary constants are selected suitably, the approximate solutions may become the exact ones.
