This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specific...This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.展开更多
Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must ad...Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.展开更多
This research paper seeks to investigate the characteristics of almost Riemann solitons and almost gradient Riemann solitons within the framework of generalized Robertson–Walker(GRW)spacetimes that incorporate imperf...This research paper seeks to investigate the characteristics of almost Riemann solitons and almost gradient Riemann solitons within the framework of generalized Robertson–Walker(GRW)spacetimes that incorporate imperfect fluids.Our study begins by defining specific properties of the potential vector field linked to these solitons.We examine the potential vector field of an almost Riemann soliton on GRW imperfect fluid spacetimes,establishing that it aligns collinearly with a unit timelike torse-forming vector field.This leads us to express the scalar curvature in relation to the structures of soliton and spacetime.Furthermore,we explore the characteristics of an almost gradient Riemann soliton with a potential functionψacross a range of GRW imperfect fluid spacetimes,deriving a formula for the Laplacian ofψ.We also categorize almost Riemann solitons on GRW imperfect fluid spacetimes into three types:shrinking,steady,and expanding,when the potential vector field of the soliton is Killing.We prove that a GRW imperfect fluid spacetime with constant scalar curvature and a Killing vector field admits an almost Riemann soliton.Additionally,we demonstrate that if the potential vector field of the almost Riemann soliton is aν(Ric)-vector,or if the GRW imperfect fluid spacetime is W_2-flat or pseudo-projectively flat,the resulting spacetime is classified as a dark fluid.展开更多
文摘This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.
基金Project supported by the National Natural Science Foundation of China(No.12525202)。
文摘Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.
文摘This research paper seeks to investigate the characteristics of almost Riemann solitons and almost gradient Riemann solitons within the framework of generalized Robertson–Walker(GRW)spacetimes that incorporate imperfect fluids.Our study begins by defining specific properties of the potential vector field linked to these solitons.We examine the potential vector field of an almost Riemann soliton on GRW imperfect fluid spacetimes,establishing that it aligns collinearly with a unit timelike torse-forming vector field.This leads us to express the scalar curvature in relation to the structures of soliton and spacetime.Furthermore,we explore the characteristics of an almost gradient Riemann soliton with a potential functionψacross a range of GRW imperfect fluid spacetimes,deriving a formula for the Laplacian ofψ.We also categorize almost Riemann solitons on GRW imperfect fluid spacetimes into three types:shrinking,steady,and expanding,when the potential vector field of the soliton is Killing.We prove that a GRW imperfect fluid spacetime with constant scalar curvature and a Killing vector field admits an almost Riemann soliton.Additionally,we demonstrate that if the potential vector field of the almost Riemann soliton is aν(Ric)-vector,or if the GRW imperfect fluid spacetime is W_2-flat or pseudo-projectively flat,the resulting spacetime is classified as a dark fluid.
