We examined the fractional second-order singular Lagrangian systems. We wrote the action principal function and equations of motion as fractional total differential equations. Also, we constructed the set of Hamilton-...We examined the fractional second-order singular Lagrangian systems. We wrote the action principal function and equations of motion as fractional total differential equations. Also, we constructed the set of Hamilton-Jacobi partial differential equations (HJPDEs) within fractional calculus. We formulated the fractional path integral quantization for these systems. A mathematical example is examined with first- and second-class constraints.展开更多
As an appendix of [Gao et al. Sharp isolated toughness bound for fractional (k,m)-deleted graphs, Acta Mathematicae Applicatae Sinica, English Series, 2025, 41(1): 252-269], the detailed proof of Theorem 4.1 in this w...As an appendix of [Gao et al. Sharp isolated toughness bound for fractional (k,m)-deleted graphs, Acta Mathematicae Applicatae Sinica, English Series, 2025, 41(1): 252-269], the detailed proof of Theorem 4.1 in this work is presented.展开更多
Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control systems, signal processing, et...Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control systems, signal processing, etc. Therefore, it is of great significance to study fractional-order time-delay differential equations. In this paper, we discuss a finite volume element method for a class of fractional-order neutral time-delay differential equations. By introducing an intermediate variable, the fourth-order problem is transformed into a system of equations consisting of two second-order partial differential equations. The L1 formula is used to approximate the time fractional order derivative terms, and the finite volume element method is used in space. A fully discrete format of the equations is established, and we prove the existence, uniqueness, convergence and stability of the solution. Finally, the validity of the format is verified by numerical examples.展开更多
This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the ...This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.展开更多
In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order sp...In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.展开更多
Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensiona...Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.展开更多
Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlatio...Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.展开更多
In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogene...In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.展开更多
This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectio...This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.展开更多
Multi-phase machines are so attractive for electrical machine designers because of their valuable advantages such as high reliability and fault tolerant ability.Meanwhile,fractional slot concentrated windings(FSCW)are...Multi-phase machines are so attractive for electrical machine designers because of their valuable advantages such as high reliability and fault tolerant ability.Meanwhile,fractional slot concentrated windings(FSCW)are well known because of short end winding length,simple structure,field weakening sufficiency,fault tolerant capability and higher slot fill factor.The five-phase machines equipped with FSCW,are very good candidates for the purpose of designing motors for high reliable applications,like electric cars,major transporting buses,high speed trains and massive trucks.But,in comparison to the general distributed windings,the FSCWs contain high magnetomotive force(MMF)space harmonic contents,which cause unwanted effects on the machine ability,such as localized iron saturation and core losses.This manuscript introduces several new five-phase fractional slot winding layouts,by the means of slot shifting concept in order to design the new types of synchronous reluctance motors(SynRels).In order to examine the proposed winding’s performances,three sample machines are designed as case studies,and analytical study and finite element analysis(FEA)is used for validation.展开更多
Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper w...Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.展开更多
Dear Editor,Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method(ADM).Dynamics of the fractional-order Lorenz system with derivat...Dear Editor,Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method(ADM).Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents(LEs),bifurcation diagram.展开更多
BACKGROUND The recently introduced ultrasonic flow ratio(UFR),is a novel fast computational method to derive fractional flow reserve(FFR)from intravascular ultrasound(IVUS)images.In the present study,we evaluate the d...BACKGROUND The recently introduced ultrasonic flow ratio(UFR),is a novel fast computational method to derive fractional flow reserve(FFR)from intravascular ultrasound(IVUS)images.In the present study,we evaluate the diagnostic performance of UFR in patients with intermediate left main(LM)stenosis.METHODS This is a prospective,single center study enrolling consecutive patients with presence of intermediated LM lesions(diameter stenosis of 30%-80%by visual estimation)underwent IVUS and FFR measurement.An independent core laboratory assessed offline UFR and IVUS-derived minimal lumen area(MLA)in a blinded fashion.RESULTS Both UFR and FFR were successfully achieved in 41 LM patients(mean age,62.0±9.9 years,46.3%diabetes).An acceptable correlation between UFR and FFR was identified(r=0.688,P<0.0001),with an absolute numerical difference of 0.03(standard difference:0.01).The area under the curve(AUC)in diagnosis of physiologically significant coronary stenosis for UFR was 0.94(95%CI:0.87-1.01),which was significantly higher than angiographic identified stenosis>50%(AUC=0.66,P<0.001)and numerically higher than IVUS-derived MLA(AUC=0.82;P=0.09).Patient level diagnostic accuracy,sensitivity and specificity for UFR to identify FFR≤0.80 was 82.9%(95%CI:70.2-95.7),93.1%(95%CI:82.2-100.0),58.3%(95%CI:26.3-90.4),respectively.CONCLUSION In patients with intermediate LM diseases,UFR was proved to be associated with acceptable correlation and high accuracy with pressure wire-based FFR as standard reference.The present study supports the use of UFR for functional evaluation of intermediate LM stenosis.展开更多
In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home ...In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.展开更多
In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fracti...In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.展开更多
文摘We examined the fractional second-order singular Lagrangian systems. We wrote the action principal function and equations of motion as fractional total differential equations. Also, we constructed the set of Hamilton-Jacobi partial differential equations (HJPDEs) within fractional calculus. We formulated the fractional path integral quantization for these systems. A mathematical example is examined with first- and second-class constraints.
文摘As an appendix of [Gao et al. Sharp isolated toughness bound for fractional (k,m)-deleted graphs, Acta Mathematicae Applicatae Sinica, English Series, 2025, 41(1): 252-269], the detailed proof of Theorem 4.1 in this work is presented.
文摘Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control systems, signal processing, etc. Therefore, it is of great significance to study fractional-order time-delay differential equations. In this paper, we discuss a finite volume element method for a class of fractional-order neutral time-delay differential equations. By introducing an intermediate variable, the fourth-order problem is transformed into a system of equations consisting of two second-order partial differential equations. The L1 formula is used to approximate the time fractional order derivative terms, and the finite volume element method is used in space. A fully discrete format of the equations is established, and we prove the existence, uniqueness, convergence and stability of the solution. Finally, the validity of the format is verified by numerical examples.
文摘This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.
文摘In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.
基金the financial support from the National Natural Science Foundation of China(No.52109119)the Guangxi Natural Science Foundation(No.2021GXNSFBA075030)+2 种基金the Guangxi Science and Technology Project(No.Guike AD20325002)the Chinese Postdoctoral Science Fund Project(No.2022 M723408)the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin(China Institute of Water Resources and Hydropower Research)(No.IWHR-SKL-202202).
文摘Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.
基金support from the National Science Foundation of China(22078190)the National Key R&D Plan of China(2020YFB1505802).
文摘Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.
基金supported by Ministry of Education and Training(Vietnam),under grant number B2023-SPS-01。
文摘In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest.
文摘This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.
文摘Multi-phase machines are so attractive for electrical machine designers because of their valuable advantages such as high reliability and fault tolerant ability.Meanwhile,fractional slot concentrated windings(FSCW)are well known because of short end winding length,simple structure,field weakening sufficiency,fault tolerant capability and higher slot fill factor.The five-phase machines equipped with FSCW,are very good candidates for the purpose of designing motors for high reliable applications,like electric cars,major transporting buses,high speed trains and massive trucks.But,in comparison to the general distributed windings,the FSCWs contain high magnetomotive force(MMF)space harmonic contents,which cause unwanted effects on the machine ability,such as localized iron saturation and core losses.This manuscript introduces several new five-phase fractional slot winding layouts,by the means of slot shifting concept in order to design the new types of synchronous reluctance motors(SynRels).In order to examine the proposed winding’s performances,three sample machines are designed as case studies,and analytical study and finite element analysis(FEA)is used for validation.
基金financial support from the Energize Program between the University of Texas at Austin and Southwest Research InstituteHydraulic Fracturing and Sand Control Industrial Affiliates Program at the University of Texas at Austin for financially supporting this research。
文摘Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.
基金supported by the National Natural Science Foundation of China(62061008,62071496,61901530)。
文摘Dear Editor,Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method(ADM).Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents(LEs),bifurcation diagram.
基金supported by CAMS Innovation Fund for Medical Sciences(CIFMS)(2022–12M-C&TB-043).
文摘BACKGROUND The recently introduced ultrasonic flow ratio(UFR),is a novel fast computational method to derive fractional flow reserve(FFR)from intravascular ultrasound(IVUS)images.In the present study,we evaluate the diagnostic performance of UFR in patients with intermediate left main(LM)stenosis.METHODS This is a prospective,single center study enrolling consecutive patients with presence of intermediated LM lesions(diameter stenosis of 30%-80%by visual estimation)underwent IVUS and FFR measurement.An independent core laboratory assessed offline UFR and IVUS-derived minimal lumen area(MLA)in a blinded fashion.RESULTS Both UFR and FFR were successfully achieved in 41 LM patients(mean age,62.0±9.9 years,46.3%diabetes).An acceptable correlation between UFR and FFR was identified(r=0.688,P<0.0001),with an absolute numerical difference of 0.03(standard difference:0.01).The area under the curve(AUC)in diagnosis of physiologically significant coronary stenosis for UFR was 0.94(95%CI:0.87-1.01),which was significantly higher than angiographic identified stenosis>50%(AUC=0.66,P<0.001)and numerically higher than IVUS-derived MLA(AUC=0.82;P=0.09).Patient level diagnostic accuracy,sensitivity and specificity for UFR to identify FFR≤0.80 was 82.9%(95%CI:70.2-95.7),93.1%(95%CI:82.2-100.0),58.3%(95%CI:26.3-90.4),respectively.CONCLUSION In patients with intermediate LM diseases,UFR was proved to be associated with acceptable correlation and high accuracy with pressure wire-based FFR as standard reference.The present study supports the use of UFR for functional evaluation of intermediate LM stenosis.
文摘In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071496,61901530,and 62061008)the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ5767).
文摘In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.
