In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.
Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the ...Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence c (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where c = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+= 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of c against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, c - 25, and for plate flow, c - 151.5. These findings suggest that a certain combination of c and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.展开更多
Effective atomic numbers for photon energy absorption(ZPEA_(eff)) and their corresponding electron numbers (NPEA_(eff)), and effective macroscopic removal cross sections of fast neutrons(RR) were calculated for 27 dif...Effective atomic numbers for photon energy absorption(ZPEA_(eff)) and their corresponding electron numbers (NPEA_(eff)), and effective macroscopic removal cross sections of fast neutrons(RR) were calculated for 27 different types of three-dimensional dosimeters, four types of phantom materials, and water. The values of ZPEA_(eff) and NPEA_(eff) were obtained using the direct method for energies ranging from 10 keV to 20 MeV. Results are presented relative to water, for direct comparison over the range of examined energies. The effect of monomers that are used in polymer gel dosimeters on the water equivalence is discussed. The relation between Σ_R and hydrogen content was studied. Micelle gel dosimeters are highly promising because our results demonstrate perfect matching between the effective atomic number, electron density number, and fast neutron attenuation coefficient of water.展开更多
In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the a...In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.展开更多
To investigate the problem of ethylene jet mixing and combustion in the scramjet at high Mach number(Ma = 8), numerical simulations were carried out for different equivalent ratios at cold and combustion conditions, i...To investigate the problem of ethylene jet mixing and combustion in the scramjet at high Mach number(Ma = 8), numerical simulations were carried out for different equivalent ratios at cold and combustion conditions, in which three-dimensional steady compressible RANS and k-ω SST turbulence model were adopted. It demonstrates that as the equivalence ratio increases from 0.42 to 1.08, the combustion becomes more intensified, and the higher backpressure pushes flame to propagate upstream. The supersonic combustion region in the combustor decreases from 92% to 85% with the increase of equivalence ratio from 0.42 to 1.08, resulting in the transition of the combustor from scram-mode to dual-mode. Both mixing and combustion efficiencies decrease by 35% and 16% respectively when the equivalence ratio increases from 0.42 to 1.08, indicating that the high equivalence ratio is unfavorable to the mixing and combustion processes. Combustion mode analysis reveals that the flame in the cavity under the high Mach number is dominated by non-premixed flames, i.e., more than 95% behaves as non-premixed mode, and the heat release is also mainly contributed by non-premixed flame. Increasing the equivalence ratio is beneficial to the thrust performance. Although the viscous force hardly changes with equivalence ratio, the percentage of pressure force used to balance the viscous force increases gradually,which limits the engine performance.展开更多
地震土体液化一直是岩土动力学中前沿、热点和难点课题。超孔隙水压力(简称超孔压)增长是衡量土体液化进程的重要指标,而超孔压比为1.0常作为饱和砂土液化的参数标志,所以孔压增长模型是模拟饱和砂土液化进程的一个重要要素。以Seed等[1...地震土体液化一直是岩土动力学中前沿、热点和难点课题。超孔隙水压力(简称超孔压)增长是衡量土体液化进程的重要指标,而超孔压比为1.0常作为饱和砂土液化的参数标志,所以孔压增长模型是模拟饱和砂土液化进程的一个重要要素。以Seed等[1]简化孔压增长模型为基础,采用时域非线性方法和“逐循环”累积方法改进孔压增长模型中的土体剪应变和不规则荷载等效循环次数的确定方法。通过算例分析,对比了国内外4种饱和砂土孔压增长模型预测的孔压增长时程曲线,分析结果显示,除了FLAC3D,其他3种模型得到的孔压比增长曲线变化趋势基本一致,且改进模型与近期提出的A.Chiaradonna et al[2]的孔压增长模型计算结果吻合较好,验证了改进模型的可靠性。提出的孔压增长模型可为考虑孔压增长的场地地震反应分析提供支撑。展开更多
In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extende...In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory.展开更多
Under very weak condition 0 × r(f) ↑ ∞, t→ ∞, we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for ...Under very weak condition 0 × r(f) ↑ ∞, t→ ∞, we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.展开更多
文摘In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.
文摘Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence c (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where c = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+= 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of c against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, c - 25, and for plate flow, c - 151.5. These findings suggest that a certain combination of c and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.
文摘Effective atomic numbers for photon energy absorption(ZPEA_(eff)) and their corresponding electron numbers (NPEA_(eff)), and effective macroscopic removal cross sections of fast neutrons(RR) were calculated for 27 different types of three-dimensional dosimeters, four types of phantom materials, and water. The values of ZPEA_(eff) and NPEA_(eff) were obtained using the direct method for energies ranging from 10 keV to 20 MeV. Results are presented relative to water, for direct comparison over the range of examined energies. The effect of monomers that are used in polymer gel dosimeters on the water equivalence is discussed. The relation between Σ_R and hydrogen content was studied. Micelle gel dosimeters are highly promising because our results demonstrate perfect matching between the effective atomic number, electron density number, and fast neutron attenuation coefficient of water.
基金the National Natural Science Foundation of China(11671271)the Natural Science Foundation of Beijing Municipality(1172004).
文摘In this article,we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a={a j}j≥1 and b={b j}j≥1 of positive numbers.We obtain strong equivalences of the approximation numbers,and necessary and sufficient conditions on a,b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.
文摘To investigate the problem of ethylene jet mixing and combustion in the scramjet at high Mach number(Ma = 8), numerical simulations were carried out for different equivalent ratios at cold and combustion conditions, in which three-dimensional steady compressible RANS and k-ω SST turbulence model were adopted. It demonstrates that as the equivalence ratio increases from 0.42 to 1.08, the combustion becomes more intensified, and the higher backpressure pushes flame to propagate upstream. The supersonic combustion region in the combustor decreases from 92% to 85% with the increase of equivalence ratio from 0.42 to 1.08, resulting in the transition of the combustor from scram-mode to dual-mode. Both mixing and combustion efficiencies decrease by 35% and 16% respectively when the equivalence ratio increases from 0.42 to 1.08, indicating that the high equivalence ratio is unfavorable to the mixing and combustion processes. Combustion mode analysis reveals that the flame in the cavity under the high Mach number is dominated by non-premixed flames, i.e., more than 95% behaves as non-premixed mode, and the heat release is also mainly contributed by non-premixed flame. Increasing the equivalence ratio is beneficial to the thrust performance. Although the viscous force hardly changes with equivalence ratio, the percentage of pressure force used to balance the viscous force increases gradually,which limits the engine performance.
文摘地震土体液化一直是岩土动力学中前沿、热点和难点课题。超孔隙水压力(简称超孔压)增长是衡量土体液化进程的重要指标,而超孔压比为1.0常作为饱和砂土液化的参数标志,所以孔压增长模型是模拟饱和砂土液化进程的一个重要要素。以Seed等[1]简化孔压增长模型为基础,采用时域非线性方法和“逐循环”累积方法改进孔压增长模型中的土体剪应变和不规则荷载等效循环次数的确定方法。通过算例分析,对比了国内外4种饱和砂土孔压增长模型预测的孔压增长时程曲线,分析结果显示,除了FLAC3D,其他3种模型得到的孔压比增长曲线变化趋势基本一致,且改进模型与近期提出的A.Chiaradonna et al[2]的孔压增长模型计算结果吻合较好,验证了改进模型的可靠性。提出的孔压增长模型可为考虑孔压增长的场地地震反应分析提供支撑。
基金supported in part by the National Natural Science Foundation of China(Grant No.12061033)by the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grants No.NJZY20119)by the Natural Science Foundation of Inner Mongolia(Grant No.2019MS01007),China.
文摘In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory.
文摘Under very weak condition 0 × r(f) ↑ ∞, t→ ∞, we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.
