In this paper,we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds.As an example of application,we study the dependence of the four-dimensional quantum Yang–Mills effective ac...In this paper,we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds.As an example of application,we study the dependence of the four-dimensional quantum Yang–Mills effective action on the special gauge transformation with respect to the background field.Also,we formulate some open questions about a structure of divergences for a special type of regularization in the presence of the background field formalism.展开更多
This study presents an order exponential model for estimating road traffic safety in city clusters.The proposed model introduces the traffic flow intrinsic properties and uses the characteristics and regular patterns ...This study presents an order exponential model for estimating road traffic safety in city clusters.The proposed model introduces the traffic flow intrinsic properties and uses the characteristics and regular patterns of traffic development to identify road traffic safety levels in city clusters.Additionally,an evaluation index system of city cluster road traffic safety was constructed based on the spatial and temporal distribution.Then Order Exponential Evaluation Model(OEEM),a comprehensive model using order exponent function for road traffic safety evaluation,was put forward,which considers the main characteristics and the generation process of traffic accidents.The model effectively controlled the unsafe behavior of the traffic system.It could define the levels of city cluster road traffic safety and dynamically detect road safety risk.The proposed model was verified with statistical data from three Chinese city clusters by comparing the common model for road traffic safety with an ideal model.The results indicate that the order exponent approach undertaken in this study can be extended and applied to other research topics and fields.展开更多
In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential s...In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential stability. Finally, we use one numerical simulation example to illustrate the correctness and effectiveness of our results.展开更多
This study explores the effects of heat transfer on the Williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the Williamson fluid model for two dimensional flow with heat tr...This study explores the effects of heat transfer on the Williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the Williamson fluid model for two dimensional flow with heat transfer are presented. Two cases of heat transfer are considered, i.e., the prescribed exponential order surface temperature （PEST） case and the prescribed exponential order heat flux （PEHF） case. The highly nonlinear partial differential equations are simplified with suitable similar and non-similar variables, and finally are solved analytically with the help of the optimal homotopy analysis method （OHAM）. The optimal convergence control parameters are obtained, and the physical fea- tures of the flow parameters are analyzed through graphs and tables. The skin friction and wall temperature gradient are calculated.展开更多
In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between t...In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.展开更多
The bullwhip effect in a multistage supply chain was analyzed using sophisticated stationary forecasts (third order moving average and third order exponential smoothing forecasts). The third order exponential smoothin...The bullwhip effect in a multistage supply chain was analyzed using sophisticated stationary forecasts (third order moving average and third order exponential smoothing forecasts). The third order exponential smoothing and third order moving average forecasts sometimes have a variance reducing effect on the supply chain.In a supply chain with positively correlated or independent and identically distributed (i.i.d) demands, the order variance based on simple moving average forecast (or simple exponential smoothing forecast) is larger than the order variance based on second order moving average forecast (or second order exponential smoothing forecast),and the order variance based on second order moving average forecast( or second order exponential smoothing forecast) is larger than the order variance based on third order moving average forecast( or third order exponential smoothing forecast). In addition, for i.i.d demands, third order exponential smoothing forecast leads to a larger variation than third order moving average forecast.展开更多
GH4169 superalloy stress relaxation test was investigated to study its characteristics of stress relaxation curves at various temperatures( 550,650,and 750 ℃). These curves presented jointly two distinct stages,the s...GH4169 superalloy stress relaxation test was investigated to study its characteristics of stress relaxation curves at various temperatures( 550,650,and 750 ℃). These curves presented jointly two distinct stages,the stage of inner stress relaxing quickly,and the stage of inner stress relaxing slowly and closing to the stress relaxation limit. And these curves obtained could be fitted by second order exponential decay function well. Based on the experimental stress relaxation curves,the relationship between stress relaxation rate and time were derived, which showed that the higher relaxation temperature and the greater initial rate of stress relaxation. The whole process presented two different stages,the stage of stress relaxation rate falling rapidly and the stage of stress relaxation rate slowing down and tending to be constant. The relation curve between creep strain rate and stress of GH4169 superalloy can be divided into three stages,low stress stage,transition stage,and high stress stage.Both the high stage and the low stage present linear correlation.展开更多
The nonlinear two-point boundary value problem(TPBVP)is converted to a new form of the problem including integral terms.Then the combination of weak-form integral equation method(WFIEM)and special functions create a r...The nonlinear two-point boundary value problem(TPBVP)is converted to a new form of the problem including integral terms.Then the combination of weak-form integral equation method(WFIEM)and special functions create a robust and applicable numerical scheme to solve the problem.To display the accuracy of our method,some examples are investigated.Also,the fractional Boussinesq-like equation involving the β-derivative has been considered that describes the propagation of small amplitude long capillary-gravity waves on the surface of shallow water.展开更多
In the present paper,we present some important properties of N-transform,which is the Laplace transform for the nabla derivative on the time scale of integers(Bohner and Peterson in Dynamic equations on time scales,Bi...In the present paper,we present some important properties of N-transform,which is the Laplace transform for the nabla derivative on the time scale of integers(Bohner and Peterson in Dynamic equations on time scales,Birkhauser,Boston,2001;Advances in dynamic equations on time scales,Birkhauser,Boston,2002).We obtain the N-transform of nabla fractional sums and differences and then apply this transform to solve some nabla fractional difference equations with initial value problems.Finally,usingN-transforms,we prove that discrete Mittag-Leffler function is the eigen function of Caputo type nabla fractional difference operator∇α.展开更多
基金supported by the Ministry of Science and Higher Education of the Russian Federation,agreement 07515-2022-289supported in parts by the Foundation for the Advancement of Theoretical Physics and Mathematics‘BASIS’,grant‘Young Russian Mathematics’。
文摘In this paper,we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds.As an example of application,we study the dependence of the four-dimensional quantum Yang–Mills effective action on the special gauge transformation with respect to the background field.Also,we formulate some open questions about a structure of divergences for a special type of regularization in the presence of the background field formalism.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51178157)the High-level Project of the Top Six Talents in Jiangsu Province(Grant No.JXQC-021)+1 种基金the Key Science and Technology Program in Henan Province(Grant No.182102310004)the Humanities and Social Science Research Programs Foundation of Ministry of Education of China(Grant No.18YJAZH028).
文摘This study presents an order exponential model for estimating road traffic safety in city clusters.The proposed model introduces the traffic flow intrinsic properties and uses the characteristics and regular patterns of traffic development to identify road traffic safety levels in city clusters.Additionally,an evaluation index system of city cluster road traffic safety was constructed based on the spatial and temporal distribution.Then Order Exponential Evaluation Model(OEEM),a comprehensive model using order exponent function for road traffic safety evaluation,was put forward,which considers the main characteristics and the generation process of traffic accidents.The model effectively controlled the unsafe behavior of the traffic system.It could define the levels of city cluster road traffic safety and dynamically detect road safety risk.The proposed model was verified with statistical data from three Chinese city clusters by comparing the common model for road traffic safety with an ideal model.The results indicate that the order exponent approach undertaken in this study can be extended and applied to other research topics and fields.
基金Supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2011FQ002)
文摘In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential stability. Finally, we use one numerical simulation example to illustrate the correctness and effectiveness of our results.
基金supported by the Ph.D.Indigenous Scheme of the Higher Education Commission of Pakistan(No.112-21674-2PS1-576)
文摘This study explores the effects of heat transfer on the Williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the Williamson fluid model for two dimensional flow with heat transfer are presented. Two cases of heat transfer are considered, i.e., the prescribed exponential order surface temperature （PEST） case and the prescribed exponential order heat flux （PEHF） case. The highly nonlinear partial differential equations are simplified with suitable similar and non-similar variables, and finally are solved analytically with the help of the optimal homotopy analysis method （OHAM）. The optimal convergence control parameters are obtained, and the physical fea- tures of the flow parameters are analyzed through graphs and tables. The skin friction and wall temperature gradient are calculated.
文摘In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.
基金The National Natural Science Foundation ofChina(No70573068)The Shanghai Education Com-mittee Foundation(No05FZ11)The Shanghai Lead-ing Academic Discipline(NoT0602)
文摘The bullwhip effect in a multistage supply chain was analyzed using sophisticated stationary forecasts (third order moving average and third order exponential smoothing forecasts). The third order exponential smoothing and third order moving average forecasts sometimes have a variance reducing effect on the supply chain.In a supply chain with positively correlated or independent and identically distributed (i.i.d) demands, the order variance based on simple moving average forecast (or simple exponential smoothing forecast) is larger than the order variance based on second order moving average forecast (or second order exponential smoothing forecast),and the order variance based on second order moving average forecast( or second order exponential smoothing forecast) is larger than the order variance based on third order moving average forecast( or third order exponential smoothing forecast). In addition, for i.i.d demands, third order exponential smoothing forecast leads to a larger variation than third order moving average forecast.
文摘GH4169 superalloy stress relaxation test was investigated to study its characteristics of stress relaxation curves at various temperatures( 550,650,and 750 ℃). These curves presented jointly two distinct stages,the stage of inner stress relaxing quickly,and the stage of inner stress relaxing slowly and closing to the stress relaxation limit. And these curves obtained could be fitted by second order exponential decay function well. Based on the experimental stress relaxation curves,the relationship between stress relaxation rate and time were derived, which showed that the higher relaxation temperature and the greater initial rate of stress relaxation. The whole process presented two different stages,the stage of stress relaxation rate falling rapidly and the stage of stress relaxation rate slowing down and tending to be constant. The relation curve between creep strain rate and stress of GH4169 superalloy can be divided into three stages,low stress stage,transition stage,and high stress stage.Both the high stage and the low stage present linear correlation.
文摘The nonlinear two-point boundary value problem(TPBVP)is converted to a new form of the problem including integral terms.Then the combination of weak-form integral equation method(WFIEM)and special functions create a robust and applicable numerical scheme to solve the problem.To display the accuracy of our method,some examples are investigated.Also,the fractional Boussinesq-like equation involving the β-derivative has been considered that describes the propagation of small amplitude long capillary-gravity waves on the surface of shallow water.
文摘In the present paper,we present some important properties of N-transform,which is the Laplace transform for the nabla derivative on the time scale of integers(Bohner and Peterson in Dynamic equations on time scales,Birkhauser,Boston,2001;Advances in dynamic equations on time scales,Birkhauser,Boston,2002).We obtain the N-transform of nabla fractional sums and differences and then apply this transform to solve some nabla fractional difference equations with initial value problems.Finally,usingN-transforms,we prove that discrete Mittag-Leffler function is the eigen function of Caputo type nabla fractional difference operator∇α.
