A high-frequency,high-resolution shore-based video monitoring system(VMS)was installed on a macrotidal(tidal amplitude>4 m)beach with multiple cusps along the Quanzhou coast,China.Herein,we propose a video imagery-...A high-frequency,high-resolution shore-based video monitoring system(VMS)was installed on a macrotidal(tidal amplitude>4 m)beach with multiple cusps along the Quanzhou coast,China.Herein,we propose a video imagery-based method that is coupled with waterline and water level observations to reconstruct the terrain of the intertidal zone over one tidal cycle.Furthermore,the beach cusp system(BCS)was precisely processed and embedded into the digital elevation model(DEM)to more effectively express the microrelief and detailed characteristics of the intertidal zone.During a field experiment conducted in January 2022,the reconstructed DEM was deemed satisfactory.The DEM was verified by RTK-GPS and had an average vertical root mean square error along corresponding RTK-GPS-derived intertidal profiles and corresponding BCS points of 0.134 m and 0.065 m,respectively.The results suggest that VMSs are an effective tool for investigating coastal geomorphic processes.展开更多
Hypomelanosis of Ito (HI) is a rare neurocutaneous disorder most likely caused by chromosomal mosaicism. HI patients may suffer from numerous clinical manifestations, but the expression of the disease is highly variab...Hypomelanosis of Ito (HI) is a rare neurocutaneous disorder most likely caused by chromosomal mosaicism. HI patients may suffer from numerous clinical manifestations, but the expression of the disease is highly variable. Ophthalmologic, musculoskeletal, neurologic, and dental anomalies may be associated with the syndrome. The dental abnormalities found in HI include talon cusps, a single maxillary central in-cisor, enamel defects, hypodontia, and irregularly spaced teeth. The aim of this case report is to present multiple talon cusps, dens in dente and concrescence of maxillary permanent incisors in an 8-year-old boy affected with hypomelanosis of Ito. This unusual dental anomaly has been described in two previous reports of this neurocutaneous syndrome. HI can be difficult to diagnose, these dental findings may help to identify the syndrome in cases where other findings are minimal or atypical.展开更多
Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause,the magnetosheath and the polar cusps by remote sensing tech...Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause,the magnetosheath and the polar cusps by remote sensing techniques.The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)and Lunar Environment heliospheric X-ray Imager(LEXI)missions aim to obtain soft Xray images of near-Earth space thanks to their Soft X-ray Imager(SXI)instruments.While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission,the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma.To investigate the possible signatures of ion-kinetic-scale processes in soft Xray images,we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model.The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field.We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations,providing meridional and equatorial views.We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirrormode wave structures in the magnetosheath and flux transfer events(FTEs)at the magnetopause.Our results suggest that,although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers,mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images.For instance,a local increase by 30%in the proton density at the dayside magnetopause resulting from the transit of multiple FTEs leads to a 12%enhancement in the line-of-sight-and time-integrated soft X-ray emissivity originating from this region.Likewise,a proton density increase by 14%in the magnetosheath associated with mirror-mode structures can result in an enhancement in the soft X-ray signal by 4%.These are likely conservative estimates,given that the solar wind conditions used in the Vlasiator run can be expected to generate weaker soft X-ray emissions than the more common denser solar wind.These results will contribute to the preparatory work for the SMILE and LEXI missions by providing the community with quantitative estimates of the effects of small-scale,transient phenomena occurring on the dayside.展开更多
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ...For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.展开更多
Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficien...Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of Rankin-Selberg L-function L(f×f,s).This paper combines Kühleitner and Nowak′s Omega theorem and the analytic properties of Rankin-Selberg L-functions to study Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences,and establishes the asymptotic formula for Σ_(n≤x)λf×f(n^(m))(m=2,3).展开更多
Cusp spot,High Latitude Dayside aurora(HiLDA),‘space hurricane’,and 15MLT-PCA(Polar Cap Arc observed around 15:00 Magnetic Local Time)are mesoscale auroral structures observed in the polar cap region.They share many...Cusp spot,High Latitude Dayside aurora(HiLDA),‘space hurricane’,and 15MLT-PCA(Polar Cap Arc observed around 15:00 Magnetic Local Time)are mesoscale auroral structures observed in the polar cap region.They share many common properties and,at the same time,have notable differences.A 15MLT-PCA is a polar cap arc connected to the auroral oval,but the others are auroral spots detached from the oval.A cusp spot differs from a HiLDA in local time location.A space hurricane differs from a HiLDA in having spiral-arm structures.Until now,relationships among these auroras have not been depicted clearly.Here we propose a unified model,based on lobe reconnection,that encompasses their similarities and differences.We then provide critical supporting evidence for the model.The model suggests that different reconnection sites under different IMF conditions result in these differently-appearing auroral forms.The model explains all the characteristic features of these auroras and has implications for understanding the dawn/dusk and inter-hemispheric asymmetries observed in their occurrence patterns.We anticipate confirmation of the model by observations to be made during the Solar wind-Magnetosphere-Ionosphere Link Explorer(SMILE)mission.Moreover,since the model indicates that these auroras appear on the footprint of the poleward cusp boundary,we expect data from the SMILE mission to make it possible to estimate the approximate shape of the cusp.展开更多
Stabilization of the axisymmetric magnetic mirror relies on the pressure-weighted magnetic field curvature.We report a new experiment by configuring a magnetic cusp structure to stabilize m=1 interchange mode in the K...Stabilization of the axisymmetric magnetic mirror relies on the pressure-weighted magnetic field curvature.We report a new experiment by configuring a magnetic cusp structure to stabilize m=1 interchange mode in the KMAX tandem mirror.The cusp configuration is formed by reversing currents in the two side cell coils,and a stronger cusp can lead to a more stable plasma once the null point of the cusp is less than 35–40 cm away from the device axis.The density fluctuations measured by four axial Langmuir probes are mitigated by 70%–80%.The stabilization effect is consistent with the prediction of a theoretical calculation.展开更多
The driving forces behind cryptoassets’price dynamics are often perceived as being dominated by speculative factors and inherent bubble-bust episodes.Fundamental components are believed to have a weak,if any,role in ...The driving forces behind cryptoassets’price dynamics are often perceived as being dominated by speculative factors and inherent bubble-bust episodes.Fundamental components are believed to have a weak,if any,role in the price-formation process.This study examines five cryptoassets with different backgrounds,namely Bitcoin,Ethereum,Litecoin,XRP,and Dogecoin between 2016 and 2022.It utilizes the cusp catastrophe model to connect the fundamental and speculative drivers with possible price bifurcation characteristics of market collapse events.The findings show that the price and return dynamics of all the studied assets,except for Dogecoin,emerge from complex interactions between fundamental and speculative components,includ-ing episodes of price bifurcations.Bitcoin shows the strongest fundamentals,with on-chain activity and economic factors driving the fundamental part of the dynam-ics.Investor attention and off-chain activity drive the speculative component for all studied assets.Among the fundamental drivers,the analyzed cryptoassets present their coin-specific factors,which can be tracked to their protocol specifics and are economi-cally sound.展开更多
The microwave discharge cusped field thruster is a novel concept of electric micropropulsion device,which operatesμN level thrust in low mass flow rate conditions,making use of a coaxial transmission line resonator.W...The microwave discharge cusped field thruster is a novel concept of electric micropropulsion device,which operatesμN level thrust in low mass flow rate conditions,making use of a coaxial transmission line resonator.With its advantages of low thrust noise and high thrust resolution over a wide range of thrust,the thruster has emerged as a candidate thruster for the space-borne gravitational wave detection mission.The cathode effects commonly exist in many kinds of electric propulsion,and they are typically significant in micropropulsions.In order to find out the cathode position effects on a microwave discharge cusped field thruster,a thermionic cathode is mounted on a cross-slider for coupling.Under different cathode positions,the plume is analyzed by a Faraday probe and a retarding potential analyzer to analyze the performance and discharge characteristics.The results show that the magnetic mirror effect leads to significant degradation of anode current and an increase in low-energy ion ratio as the cathode moves away from the thruster exit.The electron conduction route also significantly impacts anode current efficiency,related to the cathode-exit distance and the thruster magnetic topology.展开更多
BACKGROUND Pulp revascularization is a novel way to treat immature teeth with periapical disease,and the technique has become increasingly well established in recent years.By puncturing the periapical tissue,bleeding ...BACKGROUND Pulp revascularization is a novel way to treat immature teeth with periapical disease,and the technique has become increasingly well established in recent years.By puncturing the periapical tissue,bleeding is induced,and a blood clot is formed in the root canal.The blood clot acts as a natural bioscaffold onto which mesenchymal stem cells from periapical tissue can be seeded and restore pulp vascularity,thus promoting root development as well as apical closure.Although the effect of pulp revascularization is ideal,there are certain requirements for the apical condition of the teeth.The apical barrier technique and apexification are still indispensable for teeth that cannot achieve ideal blood clot formation.In addition,a meta-analysis of several clinical studies concluded that pulp revascu-larization has no significant advantages over other treatments.CASE SUMMARY A 10-year-old girl complained of pain in the right upper and lower posterior teeth for 2 d.Clinical and radiological examinations revealed that both the right maxillary and mandibular second premolars were immature with periapical radiolucency.The right maxillary second premolar was treated by pulp revascu-larization,while the right mandibular second premolar was treated by conven-tional apical barrier surgery after revascularization failed.The purpose of this report is to compare the different root maturation processes induced by the pulp revascularization and apical barrier techniques in the same patient in homonymous teeth from different jaws.Twelve months of follow-up showed that the apical foramen of both teeth presented a clear tendency to close;however,the tooth treated with pulp revascularization showed a significant increase in root length as well as root canal wall thickness.CONCLUSION For the treatment of nonvital immature teeth,pulp revascularization showed a superior therapeutic effect in comparison with the apical barrier technique.展开更多
We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we w...We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation,extended from an earlier resultonaspecial case.展开更多
A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects ...A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects three curve segments. This paper is the succession and development of reference of Tang Yuehong. We analyze the geometric features like cusps and inflection points in the curve and calculate the cusps and inflection points, then give a necessary and sufficient condition to the inflection points in the curve when it is non degenerative, and finally show that the curves have no cusps in the interval (0,1). In many applications, it is desirable to analyze the parametric curves for undesirable features like cusps and inflection points展开更多
基金The National Key Research and Development Program of China under contract No.2022YFC3106100the Key Program of National Natural Science Foundation of China under contract No.41930538.
文摘A high-frequency,high-resolution shore-based video monitoring system(VMS)was installed on a macrotidal(tidal amplitude>4 m)beach with multiple cusps along the Quanzhou coast,China.Herein,we propose a video imagery-based method that is coupled with waterline and water level observations to reconstruct the terrain of the intertidal zone over one tidal cycle.Furthermore,the beach cusp system(BCS)was precisely processed and embedded into the digital elevation model(DEM)to more effectively express the microrelief and detailed characteristics of the intertidal zone.During a field experiment conducted in January 2022,the reconstructed DEM was deemed satisfactory.The DEM was verified by RTK-GPS and had an average vertical root mean square error along corresponding RTK-GPS-derived intertidal profiles and corresponding BCS points of 0.134 m and 0.065 m,respectively.The results suggest that VMSs are an effective tool for investigating coastal geomorphic processes.
文摘Hypomelanosis of Ito (HI) is a rare neurocutaneous disorder most likely caused by chromosomal mosaicism. HI patients may suffer from numerous clinical manifestations, but the expression of the disease is highly variable. Ophthalmologic, musculoskeletal, neurologic, and dental anomalies may be associated with the syndrome. The dental abnormalities found in HI include talon cusps, a single maxillary central in-cisor, enamel defects, hypodontia, and irregularly spaced teeth. The aim of this case report is to present multiple talon cusps, dens in dente and concrescence of maxillary permanent incisors in an 8-year-old boy affected with hypomelanosis of Ito. This unusual dental anomaly has been described in two previous reports of this neurocutaneous syndrome. HI can be difficult to diagnose, these dental findings may help to identify the syndrome in cases where other findings are minimal or atypical.
基金the European Research Council for starting grant 200141-QuESpace,with which the Vlasiator model was developedconsolidator grant 682068-PRESTISSIMO awarded for further development of Vlasiator and its use in scientific investigations+4 种基金Academy of Finland grant numbers 338629-AERGELC’H,339756-KIMCHI,336805-FORESAIL,and 335554-ICT-SUNVACThe Academy of Finland also supported this work through the PROFI4 grant(grant number 3189131)support from the NASA grants,80NSSC20K1670 and 80MSFC20C0019the NASA GSFC FY23 IRADHIF funds。
文摘Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause,the magnetosheath and the polar cusps by remote sensing techniques.The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)and Lunar Environment heliospheric X-ray Imager(LEXI)missions aim to obtain soft Xray images of near-Earth space thanks to their Soft X-ray Imager(SXI)instruments.While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission,the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma.To investigate the possible signatures of ion-kinetic-scale processes in soft Xray images,we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model.The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field.We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations,providing meridional and equatorial views.We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirrormode wave structures in the magnetosheath and flux transfer events(FTEs)at the magnetopause.Our results suggest that,although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers,mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images.For instance,a local increase by 30%in the proton density at the dayside magnetopause resulting from the transit of multiple FTEs leads to a 12%enhancement in the line-of-sight-and time-integrated soft X-ray emissivity originating from this region.Likewise,a proton density increase by 14%in the magnetosheath associated with mirror-mode structures can result in an enhancement in the soft X-ray signal by 4%.These are likely conservative estimates,given that the solar wind conditions used in the Vlasiator run can be expected to generate weaker soft X-ray emissions than the more common denser solar wind.These results will contribute to the preparatory work for the SMILE and LEXI missions by providing the community with quantitative estimates of the effects of small-scale,transient phenomena occurring on the dayside.
文摘For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.
文摘Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of Rankin-Selberg L-function L(f×f,s).This paper combines Kühleitner and Nowak′s Omega theorem and the analytic properties of Rankin-Selberg L-functions to study Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences,and establishes the asymptotic formula for Σ_(n≤x)λf×f(n^(m))(m=2,3).
基金the National Natural Science Foundation of China(42030101,41974185,41774174)the Shanghai Science and Technology Innovation Action Plan(No.21DZ1206102).
文摘Cusp spot,High Latitude Dayside aurora(HiLDA),‘space hurricane’,and 15MLT-PCA(Polar Cap Arc observed around 15:00 Magnetic Local Time)are mesoscale auroral structures observed in the polar cap region.They share many common properties and,at the same time,have notable differences.A 15MLT-PCA is a polar cap arc connected to the auroral oval,but the others are auroral spots detached from the oval.A cusp spot differs from a HiLDA in local time location.A space hurricane differs from a HiLDA in having spiral-arm structures.Until now,relationships among these auroras have not been depicted clearly.Here we propose a unified model,based on lobe reconnection,that encompasses their similarities and differences.We then provide critical supporting evidence for the model.The model suggests that different reconnection sites under different IMF conditions result in these differently-appearing auroral forms.The model explains all the characteristic features of these auroras and has implications for understanding the dawn/dusk and inter-hemispheric asymmetries observed in their occurrence patterns.We anticipate confirmation of the model by observations to be made during the Solar wind-Magnetosphere-Ionosphere Link Explorer(SMILE)mission.Moreover,since the model indicates that these auroras appear on the footprint of the poleward cusp boundary,we expect data from the SMILE mission to make it possible to estimate the approximate shape of the cusp.
基金the National Key R&D Program of China(No.2017YFE0301802)National Natural Science Foundation of China(No.12175226).
文摘Stabilization of the axisymmetric magnetic mirror relies on the pressure-weighted magnetic field curvature.We report a new experiment by configuring a magnetic cusp structure to stabilize m=1 interchange mode in the KMAX tandem mirror.The cusp configuration is formed by reversing currents in the two side cell coils,and a stronger cusp can lead to a more stable plasma once the null point of the cusp is less than 35–40 cm away from the device axis.The density fluctuations measured by four axial Langmuir probes are mitigated by 70%–80%.The stabilization effect is consistent with the prediction of a theoretical calculation.
基金financial support from the Czech Science Foundation under the 20-17295S“Cryptoassets:Pricing,Interconnectedness,Mining,and their Interactions”project and from the Charles University PRIMUS program(project PRIMUS/19/HUM/17)Jiri Kukacka gratefully acknowledges financial support from the Charles University UNCE program(project UNCE/HUM/035)supported by the Cooperatio Program at Charles University,research area Economics.
文摘The driving forces behind cryptoassets’price dynamics are often perceived as being dominated by speculative factors and inherent bubble-bust episodes.Fundamental components are believed to have a weak,if any,role in the price-formation process.This study examines five cryptoassets with different backgrounds,namely Bitcoin,Ethereum,Litecoin,XRP,and Dogecoin between 2016 and 2022.It utilizes the cusp catastrophe model to connect the fundamental and speculative drivers with possible price bifurcation characteristics of market collapse events.The findings show that the price and return dynamics of all the studied assets,except for Dogecoin,emerge from complex interactions between fundamental and speculative components,includ-ing episodes of price bifurcations.Bitcoin shows the strongest fundamentals,with on-chain activity and economic factors driving the fundamental part of the dynam-ics.Investor attention and off-chain activity drive the speculative component for all studied assets.Among the fundamental drivers,the analyzed cryptoassets present their coin-specific factors,which can be tracked to their protocol specifics and are economi-cally sound.
基金supported by the National Key R&D Program of China(No.2020YFC2201000)National Natural Science Foundation of China(No.11927812)。
文摘The microwave discharge cusped field thruster is a novel concept of electric micropropulsion device,which operatesμN level thrust in low mass flow rate conditions,making use of a coaxial transmission line resonator.With its advantages of low thrust noise and high thrust resolution over a wide range of thrust,the thruster has emerged as a candidate thruster for the space-borne gravitational wave detection mission.The cathode effects commonly exist in many kinds of electric propulsion,and they are typically significant in micropropulsions.In order to find out the cathode position effects on a microwave discharge cusped field thruster,a thermionic cathode is mounted on a cross-slider for coupling.Under different cathode positions,the plume is analyzed by a Faraday probe and a retarding potential analyzer to analyze the performance and discharge characteristics.The results show that the magnetic mirror effect leads to significant degradation of anode current and an increase in low-energy ion ratio as the cathode moves away from the thruster exit.The electron conduction route also significantly impacts anode current efficiency,related to the cathode-exit distance and the thruster magnetic topology.
基金Supported by The Natural Science Foundation of Shaanxi Province,China,No.2022JM-447.
文摘BACKGROUND Pulp revascularization is a novel way to treat immature teeth with periapical disease,and the technique has become increasingly well established in recent years.By puncturing the periapical tissue,bleeding is induced,and a blood clot is formed in the root canal.The blood clot acts as a natural bioscaffold onto which mesenchymal stem cells from periapical tissue can be seeded and restore pulp vascularity,thus promoting root development as well as apical closure.Although the effect of pulp revascularization is ideal,there are certain requirements for the apical condition of the teeth.The apical barrier technique and apexification are still indispensable for teeth that cannot achieve ideal blood clot formation.In addition,a meta-analysis of several clinical studies concluded that pulp revascu-larization has no significant advantages over other treatments.CASE SUMMARY A 10-year-old girl complained of pain in the right upper and lower posterior teeth for 2 d.Clinical and radiological examinations revealed that both the right maxillary and mandibular second premolars were immature with periapical radiolucency.The right maxillary second premolar was treated by pulp revascu-larization,while the right mandibular second premolar was treated by conven-tional apical barrier surgery after revascularization failed.The purpose of this report is to compare the different root maturation processes induced by the pulp revascularization and apical barrier techniques in the same patient in homonymous teeth from different jaws.Twelve months of follow-up showed that the apical foramen of both teeth presented a clear tendency to close;however,the tooth treated with pulp revascularization showed a significant increase in root length as well as root canal wall thickness.CONCLUSION For the treatment of nonvital immature teeth,pulp revascularization showed a superior therapeutic effect in comparison with the apical barrier technique.
文摘We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation,extended from an earlier resultonaspecial case.
文摘A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects three curve segments. This paper is the succession and development of reference of Tang Yuehong. We analyze the geometric features like cusps and inflection points in the curve and calculate the cusps and inflection points, then give a necessary and sufficient condition to the inflection points in the curve when it is non degenerative, and finally show that the curves have no cusps in the interval (0,1). In many applications, it is desirable to analyze the parametric curves for undesirable features like cusps and inflection points