We first define a kind of new function space, called the space of twice conormal distributions. With some estimates on these function spaces, we can prove that if there exist two characteristic hypersurfaces bearing s...We first define a kind of new function space, called the space of twice conormal distributions. With some estimates on these function spaces, we can prove that if there exist two characteristic hypersurfaces bearing strong and weak singularities respectively intersect transversally, then some new singularities will take place anti their strength will be no more than the original weak one.展开更多
An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aero...An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.展开更多
According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surf...According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant＇s theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.展开更多
The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for ...The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for corresponding prime number, proved that the conjecture of twin prime numbers and obtain the corresponding prime distribution equation. According to the distribution rate of corresponding prime numbers, the distribution pattern of twin prime numbers was proved the distribution rate theorem. This is the distribution rate of prime numbers corresponding to composite numbers, which approaches the distribution rate of prime numbers corresponding to integers. Based on the corresponding prime distribution equation, obtain the twin prime inequality function. Then, the formula for calculating twin prime numbers was discussed. There is also the Hardy Littlewood conjecture. This provides a practical and feasible approach for studying the distribution of twin prime numbers.展开更多
By simplifying the characters in the air reverse circulation bit interior fluid field, the authors used air dynamics and fluid mechanics to calculate the air distribution in the bit and obtained an equation of flow di...By simplifying the characters in the air reverse circulation bit interior fluid field, the authors used air dynamics and fluid mechanics to calculate the air distribution in the bit and obtained an equation of flow distribution with a unique resolution. This study will provide help for making certain the bit parameters of the bit structure effectively and study the air reverse circulation bit interior fluid field character deeply.展开更多
This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian ...This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.展开更多
On the basis of analyzing some limitations in the existing algorithm, a modified Monte Carlo methodwas proposed to simulate two-dimensional normal grain growth. With the modified method. the simulated time exponent of...On the basis of analyzing some limitations in the existing algorithm, a modified Monte Carlo methodwas proposed to simulate two-dimensional normal grain growth. With the modified method. the simulated time exponent of grain growth attained n=0.49±0.01, which is very close to the theoretical value of the steady graingrowth n=0.5, indicating the possibility to investigate the total process of normal grain growth. The relationbetween the Hillert and the von Neumann equations were studied and identified, the Hillert's basic equation hasbeen found to hold during the normal grain growth. The grain size distribution was found to van continuouslyand slowly with the simulated time in the total growth process, the lognormal and the Hillert functions may betwo types of the expression forms during its transition, and the later seemingly corresponds at the distribution ofthe steady stage were n≈0.50.展开更多
We find an upper viscosity solution and give a proof of the existence-uniqueness in the space C^∞（t∈（0,∞）;H2^s＋2（R^n））∩C^0（t∈[0,∞）;H^s（R^n））,s∈R,to the nonlinear time fractional equation of distribu...We find an upper viscosity solution and give a proof of the existence-uniqueness in the space C^∞（t∈（0,∞）;H2^s＋2（R^n））∩C^0（t∈[0,∞）;H^s（R^n））,s∈R,to the nonlinear time fractional equation of distributed order with spatial Laplace operator subject to the Cauchy conditions ∫0^2p（β）D＊^βu（x,t）dβ=△xu（x,t）＋f（t,u（t,x））,t≥0,x∈R^n,u（0,x）=φ（x）,ut（0,x）=ψ（x）,（0.1） where △xis the spatial Laplace operator,D＊^β is the operator of fractional differentiation in the Caputo sense and the force term F satisfies the Assumption 1 on the regularity and growth. For the weight function we take a positive-linear combination of delta distributions concentrated at points of interval （0, 2）, i.e., p（β） =m∑k=1bkδ（β-βk）,0〈βk〈2,bk〉0,k=1,2,…,m.The regularity of the solution is established in the framework of the space C^∞（t∈（0,∞）;C^∞（R^n））∩C^0（t∈[0,∞）;C^∞（R^n））when the initial data belong to the Sobolev space H2^8（R^n）,s∈R.展开更多
Through the comparison of calcination conditions between cement preclinkering technology and cement precalcining technology,we studied the characteristics of temperature field distribution of cement preclinkering tech...Through the comparison of calcination conditions between cement preclinkering technology and cement precalcining technology,we studied the characteristics of temperature field distribution of cement preclinkering technology systems including cyclone preheater,preclinkering furnace,and rotary kiln.We used numericalsimulation method to obtain data of temperature field distribution.Some results are found by system study.The ratio of tailcoalof cement preclinkering technology is about 70%,and raw mealtemperature can reach 1070 ℃.Shorter L/D kiln type of preclinkering technology can obtain more stable calcining zone temperature.The highest solid temperature of cement preclinkering technology is higher than 80 ℃,and high temperature region（〉1450 ℃）length is 2 times,which is beneficialfor calcining clinker and higher clinker quality.So cement preclinkering technology can obtain more performance temperature filed,which improves both the solid-phase reaction and liquid-phase reaction.展开更多
This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,...This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,we construct a kind of oneparameter finite difference(OPFD)method.It is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and space.In implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method.For 2D problems,we develop another kind of OPFD method.For such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG scheme.In particular,we prove that ADI scheme can arrive at second-order accuracy in time and space.With some numerical experiments,the computational effectiveness and accuracy of the methods are further verified.Moreover,for the suggested methods,a numerical comparison in computational efficiency is presented.展开更多
The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equatio...The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.展开更多
To characterize the Neumann problem for nonlinear Fokker-Planck equations,we investigate distribution dependent reflecting stochastic differential equations(DDRSDEs)in a domain.We first prove the well-posedness and es...To characterize the Neumann problem for nonlinear Fokker-Planck equations,we investigate distribution dependent reflecting stochastic differential equations(DDRSDEs)in a domain.We first prove the well-posedness and establish functional inequalities for reflecting stochastic differential equations with singular drifts,and then extend these results to DDRSDEs with singular or monotone coefficients,for which a general criterion deducing the well-posedness of DDRSDEs from that of reflecting stochastic differential equations is established.展开更多
Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications,distribution dependent stochastic differential equations(DDSDEs)have been intensively investigated.In this paper,we summar...Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications,distribution dependent stochastic differential equations(DDSDEs)have been intensively investigated.In this paper,we summarize some recent progresses in the study of DDSDEs,which include the correspondence of weak solutions and nonlinear Fokker-Planck equations,the well-posedness,regularity estimates,exponential ergodicity,long time large deviations,and comparison theorems.展开更多
This paper addresses overall performance analysis of coal-fired power unit. From the point of view of system engineering, a general steam-water distribution equation of the thermal plant system is presented. This syst...This paper addresses overall performance analysis of coal-fired power unit. From the point of view of system engineering, a general steam-water distribution equation of the thermal plant system is presented. This system state equation is an exact expression combining system topological structure and system properties. Through proper mathematic transform, the inner relationship and interaction between the main system and auxiliary system are revealed and its general form is given. An analytical formula for the heat consumption rote of thermal power plant is one direct fruit of the equation, which greatly facilitate the online analyzing and optimizing of complex thermal system. The new approach, with the aid of modem data acquiring technology, is a perfect extension of the traditional analysis method based on the First Law of Thermodynamics.展开更多
文摘We first define a kind of new function space, called the space of twice conormal distributions. With some estimates on these function spaces, we can prove that if there exist two characteristic hypersurfaces bearing strong and weak singularities respectively intersect transversally, then some new singularities will take place anti their strength will be no more than the original weak one.
基金The National Natural Science Foundation of China(No50475073,50775036)the High Technology Research Program of Jiangsu Province(NoBG2006035)
文摘An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.
文摘According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant＇s theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.
文摘The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for corresponding prime number, proved that the conjecture of twin prime numbers and obtain the corresponding prime distribution equation. According to the distribution rate of corresponding prime numbers, the distribution pattern of twin prime numbers was proved the distribution rate theorem. This is the distribution rate of prime numbers corresponding to composite numbers, which approaches the distribution rate of prime numbers corresponding to integers. Based on the corresponding prime distribution equation, obtain the twin prime inequality function. Then, the formula for calculating twin prime numbers was discussed. There is also the Hardy Littlewood conjecture. This provides a practical and feasible approach for studying the distribution of twin prime numbers.
基金Jilin Province Science and Technology Development Leading Project(No.200405033)
文摘By simplifying the characters in the air reverse circulation bit interior fluid field, the authors used air dynamics and fluid mechanics to calculate the air distribution in the bit and obtained an equation of flow distribution with a unique resolution. This study will provide help for making certain the bit parameters of the bit structure effectively and study the air reverse circulation bit interior fluid field character deeply.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10675088)
文摘This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.
文摘On the basis of analyzing some limitations in the existing algorithm, a modified Monte Carlo methodwas proposed to simulate two-dimensional normal grain growth. With the modified method. the simulated time exponent of grain growth attained n=0.49±0.01, which is very close to the theoretical value of the steady graingrowth n=0.5, indicating the possibility to investigate the total process of normal grain growth. The relationbetween the Hillert and the von Neumann equations were studied and identified, the Hillert's basic equation hasbeen found to hold during the normal grain growth. The grain size distribution was found to van continuouslyand slowly with the simulated time in the total growth process, the lognormal and the Hillert functions may betwo types of the expression forms during its transition, and the later seemingly corresponds at the distribution ofthe steady stage were n≈0.50.
基金Partially supported by projects:MNTR:174024APV:114-451-3605/2013
文摘We find an upper viscosity solution and give a proof of the existence-uniqueness in the space C^∞（t∈（0,∞）;H2^s＋2（R^n））∩C^0（t∈[0,∞）;H^s（R^n））,s∈R,to the nonlinear time fractional equation of distributed order with spatial Laplace operator subject to the Cauchy conditions ∫0^2p（β）D＊^βu（x,t）dβ=△xu（x,t）＋f（t,u（t,x））,t≥0,x∈R^n,u（0,x）=φ（x）,ut（0,x）=ψ（x）,（0.1） where △xis the spatial Laplace operator,D＊^β is the operator of fractional differentiation in the Caputo sense and the force term F satisfies the Assumption 1 on the regularity and growth. For the weight function we take a positive-linear combination of delta distributions concentrated at points of interval （0, 2）, i.e., p（β） =m∑k=1bkδ（β-βk）,0〈βk〈2,bk〉0,k=1,2,…,m.The regularity of the solution is established in the framework of the space C^∞（t∈（0,∞）;C^∞（R^n））∩C^0（t∈[0,∞）;C^∞（R^n））when the initial data belong to the Sobolev space H2^8（R^n）,s∈R.
基金Funded by the Major State Basic Research Perelopment Program of China(973 Program)(No.2009CB623102)the Key Fund Project of Sichuan Provincial Department of Education(No.14ZA0086)the Key Fund Project of Professional Scientific Research Innovation Team of Southwest University of Science and Technology(No.14tdfk01)
文摘Through the comparison of calcination conditions between cement preclinkering technology and cement precalcining technology,we studied the characteristics of temperature field distribution of cement preclinkering technology systems including cyclone preheater,preclinkering furnace,and rotary kiln.We used numericalsimulation method to obtain data of temperature field distribution.Some results are found by system study.The ratio of tailcoalof cement preclinkering technology is about 70%,and raw mealtemperature can reach 1070 ℃.Shorter L/D kiln type of preclinkering technology can obtain more stable calcining zone temperature.The highest solid temperature of cement preclinkering technology is higher than 80 ℃,and high temperature region（〉1450 ℃）length is 2 times,which is beneficialfor calcining clinker and higher clinker quality.So cement preclinkering technology can obtain more performance temperature filed,which improves both the solid-phase reaction and liquid-phase reaction.
基金supported by the NSFC(Grant No.11971010)the Science and Technology Development Fund of Macao(Grant No.0122/2020/A3)MYRG2020-00224-FST from University of Macao,China.
文摘This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,we construct a kind of oneparameter finite difference(OPFD)method.It is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and space.In implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method.For 2D problems,we develop another kind of OPFD method.For such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG scheme.In particular,we prove that ADI scheme can arrive at second-order accuracy in time and space.With some numerical experiments,the computational effectiveness and accuracy of the methods are further verified.Moreover,for the suggested methods,a numerical comparison in computational efficiency is presented.
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.
基金supported by the National Key R&D Program of China(Grant No.2020YFA0712900)National Natural Science Foundation of China(Grant Nos.11831014 and 11921001)。
文摘To characterize the Neumann problem for nonlinear Fokker-Planck equations,we investigate distribution dependent reflecting stochastic differential equations(DDRSDEs)in a domain.We first prove the well-posedness and establish functional inequalities for reflecting stochastic differential equations with singular drifts,and then extend these results to DDRSDEs with singular or monotone coefficients,for which a general criterion deducing the well-posedness of DDRSDEs from that of reflecting stochastic differential equations is established.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11771326,11831014,11921001,11801406).
文摘Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications,distribution dependent stochastic differential equations(DDSDEs)have been intensively investigated.In this paper,we summarize some recent progresses in the study of DDSDEs,which include the correspondence of weak solutions and nonlinear Fokker-Planck equations,the well-posedness,regularity estimates,exponential ergodicity,long time large deviations,and comparison theorems.
文摘This paper addresses overall performance analysis of coal-fired power unit. From the point of view of system engineering, a general steam-water distribution equation of the thermal plant system is presented. This system state equation is an exact expression combining system topological structure and system properties. Through proper mathematic transform, the inner relationship and interaction between the main system and auxiliary system are revealed and its general form is given. An analytical formula for the heat consumption rote of thermal power plant is one direct fruit of the equation, which greatly facilitate the online analyzing and optimizing of complex thermal system. The new approach, with the aid of modem data acquiring technology, is a perfect extension of the traditional analysis method based on the First Law of Thermodynamics.
