Background:One-legged pedaling is of interest to elite cyclists and clinicians.However,muscular usage in 1-legged vs.2-legged pedaling is not fully understood.Thus,the study was aimed to examine changes in leg muscle ...Background:One-legged pedaling is of interest to elite cyclists and clinicians.However,muscular usage in 1-legged vs.2-legged pedaling is not fully understood.Thus,the study was aimed to examine changes in leg muscle activation patterns between 2-legged and 1-legged pedaling.Methods:Fifteen healthy young recreational cyclists performed both 1-legged and 2-legged pedaling trials at about 30 Watt per leg.Surface electromyography electrodes were placed on 10 major muscles of the left leg.Linear envelope electromyography data were integrated to quantify muscle activities for each crank cycle quadrant to evaluate muscle activation changes.Results:Overall,the prescribed constant power requirements led to reduced downstroke crank torque and extension-related muscle activities(vastus lateralis,vastus medialis,and soleus)in 1-legged pedaling.Flexion-related muscle activities(biceps femoris long head,semitendinosus,lateral gastrocnemius,medial gastrocnemius,tensor fasciae latae,and tibialis anterior)in the upstroke phase increased to compensate for the absence of contralateral leg crank torque.During the upstroke,simultaneous increases were seen in the hamstrings and uni-articular knee extensors,and in the ankle plantarflexors and dorsiflexors.At the top of the crank cycle,greater hip flexor activity stabilized the pelvis.Conclusion:The observed changes in muscle activities are due to a variety of changes in mechanical aspects of the pedaling motion when pedaling with only 1 leg,including altered crank torque patterns without the contralateral leg,reduced pelvis stability,and increased knee and ankle stiffness during the upstroke.展开更多
Once I found a pink moth on our front porch. I was per-haps eight years old, and it happened as I stepped out throughmy front door into the glass-enclosed vestibule, nearly like agreenhouse, where we left our boots in...Once I found a pink moth on our front porch. I was per-haps eight years old, and it happened as I stepped out throughmy front door into the glass-enclosed vestibule, nearly like agreenhouse, where we left our boots in the winter. A mothwas desperately trying to find its way off the porch. Several times I had found a bee or a moth trapped on展开更多
Yuan Jianglei has an amazing story to tell. The 27 year old is one of a handful of people who can say they have cycled through Africa - solo.Yuan began his epic adventure in the West African country of Benin, ending 1...Yuan Jianglei has an amazing story to tell. The 27 year old is one of a handful of people who can say they have cycled through Africa - solo.Yuan began his epic adventure in the West African country of Benin, ending 10,544 km and 333 days later in his hometown of Ningbo, east China＇s Zhejiang Province.展开更多
I like to ride a bicycle in Beijing. But in the last 10 years automobile traffic has increased noticeably. When I go to Hohhot to stay with friends, I’ve noticed more cars on the streets. Bicycles are no longer the p...I like to ride a bicycle in Beijing. But in the last 10 years automobile traffic has increased noticeably. When I go to Hohhot to stay with friends, I’ve noticed more cars on the streets. Bicycles are no longer the prima-展开更多
The 'Bicycle Kingdom' seeks to be among medal nations in cycling events at the 2008 Olympic Games Although China has the largest number of people riding bicycles in the world, most Chinese ride to commute out ...The 'Bicycle Kingdom' seeks to be among medal nations in cycling events at the 2008 Olympic Games Although China has the largest number of people riding bicycles in the world, most Chinese ride to commute out of necessity and not really for sports, said Chen Jianmin, Head Coach of Hunan Cycling Club.展开更多
Yuan Jianglei,27,is one of a handful of people who can say they have cycled through Africa completely solo.Beginning his epic adventure in the West African country of Benin,Yuan finished 10,544 km and 333 days later i...Yuan Jianglei,27,is one of a handful of people who can say they have cycled through Africa completely solo.Beginning his epic adventure in the West African country of Benin,Yuan finished 10,544 km and 333 days later in his hometown of Ningbo, east China＇s Zhejiang Province. The journey, which came to a celebratory end in September 2017, took him through 16 countries.展开更多
Purpose: The purpose of this study was to establish the relationship between various expressions of relative exercise intensity percentage of maximal oxygen uptake(%VO_(2max)), percentage of maximal heart rate(%HR_(ma...Purpose: The purpose of this study was to establish the relationship between various expressions of relative exercise intensity percentage of maximal oxygen uptake(%VO_(2max)), percentage of maximal heart rate(%HR_(max)), %VO_2 reserve(%VO_2R), and %HR reserve(%HRR)) in order to obtain the more appropriate method for exercise intensity prescription when using an immersible ergocycle(IE) and to propose a prediction equation to estimate oxygen consumption(VO_2) based on IE pedaling rate(rpm) for an individualized exercise training prescription.Methods: Thirty-three healthy participants performed incremental exercise tests on IE and dryland ergocycle(DE) at equal external power output(Pext). Exercise on IE began at 40 rpm and was increased by 10 rpm until exhaustion. Exercise on DE began with an initial load of 25 W and increased by 25 W/min until exhaustion. VO_2 was measured with a portable gas analyzer(COSMED K4b^2) during both incremental tests. On IE and DE, %VO_2R, %HRmax, and %HRR at equal Pext did not differ(p > 0.05).Results: The %HRR vs. %VO_2R regression for both IE and DE did not differ from the identity line %VO_2R IE = 0.99 × HRR IE(%) + 0.01(r^2= 0.91, SEE = 11%); %VO_2R DE = 0.94 × HRR DE(%) + 0.01(r^2= 0.94, SEE = 8%). Similar mean values for %HRmax, %VO_2R, and %HRR at equal Pext were observed on IE and DE. Predicted VO_2 obtained according to rpm on IE is represented by: VO_2(L/min) = 0.000542 × rpm2-0.026 × rpm + 0.739(r = 0.91, SEE = 0.319 L/min).Conclusion: The %HRR–%VO_2R relationship appears to be the most accurate for exercise training prescription on IE. This study offers new tools to better prescribe, control, and individualize exercise intensity on IE.展开更多
This article is a technical review of the common techniques used in the treatment of lower-limb occlusive arterial disease associated with diabetes.The techniques described here reflect the author’s own practice and ...This article is a technical review of the common techniques used in the treatment of lower-limb occlusive arterial disease associated with diabetes.The techniques described here reflect the author’s own practice and are methods that the author finds helpful in avoiding complications and in making the technical aspects of the procedures easier.展开更多
Recent developments have demonstrated that the brake pedal simulator(BPS)is becoming an indispensable apparatus for the break-by-wire systems in future electric vehicles.Its main function is to provide the driver with...Recent developments have demonstrated that the brake pedal simulator(BPS)is becoming an indispensable apparatus for the break-by-wire systems in future electric vehicles.Its main function is to provide the driver with a comfortable pedal feel to improve braking safety and comfort.This paper presents the development and control of an adjustable BPS,using a disk-type magnetorheological(MR)damper as the passive braking reaction generator to simulate the traditional pedal feel.A detailed description of the mechanical design of the MR damper-based BSP(MRDBBPS)is presented in this paper.Several basic performance experiments on the MRDBBPS prototype are conducted.A returnto-zero(RTZ)algorithm is proposed to avoid hysteresis and improve the repeatability of the pedal force.In addition,an RTZ algorithm-based real-time current-tracking controller(RTZRC)is designed in consideration of the response lag of the coil circuit.Finally,an experimental system is established by integrating the MRDBBPS prototype into a selfdeveloped automotive MR braking test bench(AMRBTB),and several control and braking experiments are performed.This research proposes a RTZRC control algorithm which can significantly increase the tracking accuracy of the brake pedal characteristic curve,particularly at a high pedal velocity.Additionally,the designed MRDBBPS prototype can achieve an effective and favorable control of the AMRBTB with a good repeatability.展开更多
IntroductionEarthquake location is one of the inverse problems in seismology. The accurate earthquake source location is the basis of studies of earthquake images, the relation analysis between seismicity and tectonic...IntroductionEarthquake location is one of the inverse problems in seismology. The accurate earthquake source location is the basis of studies of earthquake images, the relation analysis between seismicity and tectonics, and the important parameters of earthquakes. It is also the basic data used to study the space distribution of aftershocks after a strong earthquake. The earthquake location accuracy mainly depends on reliability of the velocity models for the earth￠s crust, the reasonable design of the seismograph network, the accuracy of arrival time, and the location method used (ZHAO, 1983; ZHU, ZHAO, 1997; LI, et al, 1999). The reliability of the velocity model directly influences loca-tion results. The reasonable seismograph network design can improve the location accuracy; otherwise it will in-troduce ill-conditioned equations and large location error. If arrival time is not accurate, for example, if the seismic phase is wrongly identified or the time service is inaccurate, large arrival time error will be produced, and the location results and real hypocenters will be discordant. Different location algorithms adopted will produce differ-ent location errors. The residual criterion chosen has influence on location results. Besides, whether the event is correctly associated also influences the location quality. In practice, it can often be seen that large location devia-tion introduced by wrong event association.展开更多
Reducing energy consumption has become a matter of increasing concern for electric vehicle owners. EcoDriver is a project funded by the European Commission, searching for new eco-driving solutions for reducing energy ...Reducing energy consumption has become a matter of increasing concern for electric vehicle owners. EcoDriver is a project funded by the European Commission, searching for new eco-driving solutions for reducing energy consumption in private and public transport. EcoDriver’s main purpose is to teach efficient driving strategies and facilitate drivers’ decision-making processes through several feedback modalities, in order to help increase driving efficiency and therefore reduce energy consumption. In the present study, the Full ecoDriver System combined with a haptic feedback gas pedal was tested in real driving conditions to give answers to some questions about its effectiveness, efficiency, workload and acceptability in an electric vehicle. The sample profile was composed by thirty young but experienced drivers. They had to drive around an open road track which allowed several possible scenarios such as curves, intersection or roundabout, speed limit changes and preceding vehicles. Average speed was registered on each lap, likewise other subjective measurements. The main results suggest that the efficiency benefits achieved while driving depend on the event type and the feedback modality provided. For instance haptic feedback seems to be especially indicated for roundabouts. In addition, the visual feedback provided by the FeDS nomadic device helps to save energy and learn eco-driving strategies. These outcomes indicate how several feedback modalities could facilitate the decision making process, changing driving behaviour, reducing energy consumption and increasing safety. These questions would help advance further research on eco-driving Intelligent Transport Systems and driving behaviour issues.展开更多
In this paper,we present inequalities for volumes of subsimplices of a simplex and its pedal simplex and generalize them to m ＋ 1 simplices and their pedal simplices.
Using theory of distance geometry and analytic method, the problem on relations about the volumes of some simplices is studied, and some new inequalities for the volumes of simplices are established. As special cases,...Using theory of distance geometry and analytic method, the problem on relations about the volumes of some simplices is studied, and some new inequalities for the volumes of simplices are established. As special cases, an inequality for the volume of the pedal simplex of a simplex and other inequalities for simplices are gotten.展开更多
Nephropathy is the significant complication of diabetes mellitus that affects about 40%of diabetics and a major cause of death and disability among diabetics.It is observed that even the patients having well-controlle...Nephropathy is the significant complication of diabetes mellitus that affects about 40%of diabetics and a major cause of death and disability among diabetics.It is observed that even the patients having well-controlled diabetes suffer from diabetic nephropathy.It needs intense management,such as dialysis and badly affects the quality of life.A male patient of 45 years visited the outpatient department complaining of bilateral pedal edema,frequent micturition,nausea especially during morning hours,reduced apetite,generalized weakness and itching all over body from past 4 years.He was known case of diabetes mellitus since 4 years.Routine investigations of kidney function tests and urine microscopic findings were also found disturbed.Patient was taking oral hypoglycemic drug(metformin 500 mg twice a day).He was diagnosed as a case of diabetic nephropathy on the basis of clinical signs&symptoms and with lab findings.According to ayurveda,the symptoms resembles with Prameha janya upadrava(post-diabetic complications).Patient was given ayurvedic medication for a period of 30 days and investigations were done after 30 days.There was marked relief in the symptoms along with considerable improvement in renal investigations like blood urea,serum creatinine&uric acid profile.This management may bring some new hope to the patients of diabetic nephropathy,which usually terminates to chronic renal failure and ultimately to death.展开更多
The tricks of many senior people who always keep themselves in good health is to massage their feet. There are many important acupuncture points on the soles of the feet, and the most important is located in the pit o...The tricks of many senior people who always keep themselves in good health is to massage their feet. There are many important acupuncture points on the soles of the feet, and the most important is located in the pit of the sole and is called Yong Quan Point, on the longevity point. Massaging this point frequently is good for improving the vitality of the body and replenishing展开更多
Intensive use of geometrical modelling started with the development of computer graphics and CAD/CAM technologies, comprising a wide area of mathematical disciplines. Geometrical modelling is a synthesis of the geomet...Intensive use of geometrical modelling started with the development of computer graphics and CAD/CAM technologies, comprising a wide area of mathematical disciplines. Geometrical modelling is a synthesis of the geometry and computer graphics, which enable us to develop complex mathematical models that would be rather difficult to display without using a computer. The author recognizes two basic methods of research of geometrical models, synthetic and analytic. The synthetic method makes use of geometrical constructions and in the analytic method geometrical objects are characterized by numerical data. The author uses these methods in this contribution. The aim of this research is to show central cyclides （Dupin＇s cyclides） as a special kind of the cyclical elliptical pedal surfaces. Firstly, applying the method of synthetic geometry, a new class of such surfaces in the 3-dimensional Euclidean space （model of the projective space） is defined. The geometrical construction of these surfaces is dependent on the given ellipse and the position of the pole P. It is the point at which the pencil of perpendicular planes passes to the plane of the ellipse, wherein the generating circles of the surface are lying. The parametric equations of the cyclical elliptical surface are derived applying the method of analytic geometry. The author classifies the surfaces according to the number of generating circles with a zero radius. The evolute of the ellipse divides the plane of the ellipse into two areas, Ω1 and Ω2. The shape of the surface depends on the position of the pole P in the areas of Ω1 and Ω2. The surface can have 4, 3 or 2 circles with a zero radius. The author then describes the relationship between these surfaces and the Dupin＇s cyclides, obtained in the case when the pole P is the point on the major axis of the ellipse. Finally, the transformation of these surfaces is shown by changing of the orthonormal base in the parameterization of the generating circles of the surface. The author visualizes the resulting surfaces obtained by the parametric approach in the MAPLE program environment.展开更多
基金supported by the University of Massachusetts Amherst(SP:Graduate School Fellowship,and School of Public Health and Health Sciences Dean’s PhD Summer FellowshipGEC:Faculty Research Grant).
文摘Background:One-legged pedaling is of interest to elite cyclists and clinicians.However,muscular usage in 1-legged vs.2-legged pedaling is not fully understood.Thus,the study was aimed to examine changes in leg muscle activation patterns between 2-legged and 1-legged pedaling.Methods:Fifteen healthy young recreational cyclists performed both 1-legged and 2-legged pedaling trials at about 30 Watt per leg.Surface electromyography electrodes were placed on 10 major muscles of the left leg.Linear envelope electromyography data were integrated to quantify muscle activities for each crank cycle quadrant to evaluate muscle activation changes.Results:Overall,the prescribed constant power requirements led to reduced downstroke crank torque and extension-related muscle activities(vastus lateralis,vastus medialis,and soleus)in 1-legged pedaling.Flexion-related muscle activities(biceps femoris long head,semitendinosus,lateral gastrocnemius,medial gastrocnemius,tensor fasciae latae,and tibialis anterior)in the upstroke phase increased to compensate for the absence of contralateral leg crank torque.During the upstroke,simultaneous increases were seen in the hamstrings and uni-articular knee extensors,and in the ankle plantarflexors and dorsiflexors.At the top of the crank cycle,greater hip flexor activity stabilized the pelvis.Conclusion:The observed changes in muscle activities are due to a variety of changes in mechanical aspects of the pedaling motion when pedaling with only 1 leg,including altered crank torque patterns without the contralateral leg,reduced pelvis stability,and increased knee and ankle stiffness during the upstroke.
文摘Once I found a pink moth on our front porch. I was per-haps eight years old, and it happened as I stepped out throughmy front door into the glass-enclosed vestibule, nearly like agreenhouse, where we left our boots in the winter. A mothwas desperately trying to find its way off the porch. Several times I had found a bee or a moth trapped on
文摘Yuan Jianglei has an amazing story to tell. The 27 year old is one of a handful of people who can say they have cycled through Africa - solo.Yuan began his epic adventure in the West African country of Benin, ending 10,544 km and 333 days later in his hometown of Ningbo, east China＇s Zhejiang Province.
文摘I like to ride a bicycle in Beijing. But in the last 10 years automobile traffic has increased noticeably. When I go to Hohhot to stay with friends, I’ve noticed more cars on the streets. Bicycles are no longer the prima-
文摘The 'Bicycle Kingdom' seeks to be among medal nations in cycling events at the 2008 Olympic Games Although China has the largest number of people riding bicycles in the world, most Chinese ride to commute out of necessity and not really for sports, said Chen Jianmin, Head Coach of Hunan Cycling Club.
文摘Yuan Jianglei,27,is one of a handful of people who can say they have cycled through Africa completely solo.Beginning his epic adventure in the West African country of Benin,Yuan finished 10,544 km and 333 days later in his hometown of Ningbo, east China＇s Zhejiang Province. The journey, which came to a celebratory end in September 2017, took him through 16 countries.
基金provided by the éPIC Foundation and the Montreal Heart Institute Foundation
文摘Purpose: The purpose of this study was to establish the relationship between various expressions of relative exercise intensity percentage of maximal oxygen uptake(%VO_(2max)), percentage of maximal heart rate(%HR_(max)), %VO_2 reserve(%VO_2R), and %HR reserve(%HRR)) in order to obtain the more appropriate method for exercise intensity prescription when using an immersible ergocycle(IE) and to propose a prediction equation to estimate oxygen consumption(VO_2) based on IE pedaling rate(rpm) for an individualized exercise training prescription.Methods: Thirty-three healthy participants performed incremental exercise tests on IE and dryland ergocycle(DE) at equal external power output(Pext). Exercise on IE began at 40 rpm and was increased by 10 rpm until exhaustion. Exercise on DE began with an initial load of 25 W and increased by 25 W/min until exhaustion. VO_2 was measured with a portable gas analyzer(COSMED K4b^2) during both incremental tests. On IE and DE, %VO_2R, %HRmax, and %HRR at equal Pext did not differ(p > 0.05).Results: The %HRR vs. %VO_2R regression for both IE and DE did not differ from the identity line %VO_2R IE = 0.99 × HRR IE(%) + 0.01(r^2= 0.91, SEE = 11%); %VO_2R DE = 0.94 × HRR DE(%) + 0.01(r^2= 0.94, SEE = 8%). Similar mean values for %HRmax, %VO_2R, and %HRR at equal Pext were observed on IE and DE. Predicted VO_2 obtained according to rpm on IE is represented by: VO_2(L/min) = 0.000542 × rpm2-0.026 × rpm + 0.739(r = 0.91, SEE = 0.319 L/min).Conclusion: The %HRR–%VO_2R relationship appears to be the most accurate for exercise training prescription on IE. This study offers new tools to better prescribe, control, and individualize exercise intensity on IE.
文摘This article is a technical review of the common techniques used in the treatment of lower-limb occlusive arterial disease associated with diabetes.The techniques described here reflect the author’s own practice and are methods that the author finds helpful in avoiding complications and in making the technical aspects of the procedures easier.
基金National Natural Science Foundation of China(Grant Nos.52175047 and 51505114)Anhui Provincial Natural Science Foundation of China(Grant No.2008085ME140).
文摘Recent developments have demonstrated that the brake pedal simulator(BPS)is becoming an indispensable apparatus for the break-by-wire systems in future electric vehicles.Its main function is to provide the driver with a comfortable pedal feel to improve braking safety and comfort.This paper presents the development and control of an adjustable BPS,using a disk-type magnetorheological(MR)damper as the passive braking reaction generator to simulate the traditional pedal feel.A detailed description of the mechanical design of the MR damper-based BSP(MRDBBPS)is presented in this paper.Several basic performance experiments on the MRDBBPS prototype are conducted.A returnto-zero(RTZ)algorithm is proposed to avoid hysteresis and improve the repeatability of the pedal force.In addition,an RTZ algorithm-based real-time current-tracking controller(RTZRC)is designed in consideration of the response lag of the coil circuit.Finally,an experimental system is established by integrating the MRDBBPS prototype into a selfdeveloped automotive MR braking test bench(AMRBTB),and several control and braking experiments are performed.This research proposes a RTZRC control algorithm which can significantly increase the tracking accuracy of the brake pedal characteristic curve,particularly at a high pedal velocity.Additionally,the designed MRDBBPS prototype can achieve an effective and favorable control of the AMRBTB with a good repeatability.
文摘IntroductionEarthquake location is one of the inverse problems in seismology. The accurate earthquake source location is the basis of studies of earthquake images, the relation analysis between seismicity and tectonics, and the important parameters of earthquakes. It is also the basic data used to study the space distribution of aftershocks after a strong earthquake. The earthquake location accuracy mainly depends on reliability of the velocity models for the earth￠s crust, the reasonable design of the seismograph network, the accuracy of arrival time, and the location method used (ZHAO, 1983; ZHU, ZHAO, 1997; LI, et al, 1999). The reliability of the velocity model directly influences loca-tion results. The reasonable seismograph network design can improve the location accuracy; otherwise it will in-troduce ill-conditioned equations and large location error. If arrival time is not accurate, for example, if the seismic phase is wrongly identified or the time service is inaccurate, large arrival time error will be produced, and the location results and real hypocenters will be discordant. Different location algorithms adopted will produce differ-ent location errors. The residual criterion chosen has influence on location results. Besides, whether the event is correctly associated also influences the location quality. In practice, it can often be seen that large location devia-tion introduced by wrong event association.
文摘Reducing energy consumption has become a matter of increasing concern for electric vehicle owners. EcoDriver is a project funded by the European Commission, searching for new eco-driving solutions for reducing energy consumption in private and public transport. EcoDriver’s main purpose is to teach efficient driving strategies and facilitate drivers’ decision-making processes through several feedback modalities, in order to help increase driving efficiency and therefore reduce energy consumption. In the present study, the Full ecoDriver System combined with a haptic feedback gas pedal was tested in real driving conditions to give answers to some questions about its effectiveness, efficiency, workload and acceptability in an electric vehicle. The sample profile was composed by thirty young but experienced drivers. They had to drive around an open road track which allowed several possible scenarios such as curves, intersection or roundabout, speed limit changes and preceding vehicles. Average speed was registered on each lap, likewise other subjective measurements. The main results suggest that the efficiency benefits achieved while driving depend on the event type and the feedback modality provided. For instance haptic feedback seems to be especially indicated for roundabouts. In addition, the visual feedback provided by the FeDS nomadic device helps to save energy and learn eco-driving strategies. These outcomes indicate how several feedback modalities could facilitate the decision making process, changing driving behaviour, reducing energy consumption and increasing safety. These questions would help advance further research on eco-driving Intelligent Transport Systems and driving behaviour issues.
基金Project supported by the National Natural Science Foundation of China (Grant No.10671117)the Foundation of the Education Department of Gansu Province (Grant No.0709-03)
文摘In this paper,we present inequalities for volumes of subsimplices of a simplex and its pedal simplex and generalize them to m ＋ 1 simplices and their pedal simplices.
文摘Using theory of distance geometry and analytic method, the problem on relations about the volumes of some simplices is studied, and some new inequalities for the volumes of simplices are established. As special cases, an inequality for the volume of the pedal simplex of a simplex and other inequalities for simplices are gotten.
文摘Nephropathy is the significant complication of diabetes mellitus that affects about 40%of diabetics and a major cause of death and disability among diabetics.It is observed that even the patients having well-controlled diabetes suffer from diabetic nephropathy.It needs intense management,such as dialysis and badly affects the quality of life.A male patient of 45 years visited the outpatient department complaining of bilateral pedal edema,frequent micturition,nausea especially during morning hours,reduced apetite,generalized weakness and itching all over body from past 4 years.He was known case of diabetes mellitus since 4 years.Routine investigations of kidney function tests and urine microscopic findings were also found disturbed.Patient was taking oral hypoglycemic drug(metformin 500 mg twice a day).He was diagnosed as a case of diabetic nephropathy on the basis of clinical signs&symptoms and with lab findings.According to ayurveda,the symptoms resembles with Prameha janya upadrava(post-diabetic complications).Patient was given ayurvedic medication for a period of 30 days and investigations were done after 30 days.There was marked relief in the symptoms along with considerable improvement in renal investigations like blood urea,serum creatinine&uric acid profile.This management may bring some new hope to the patients of diabetic nephropathy,which usually terminates to chronic renal failure and ultimately to death.
文摘The tricks of many senior people who always keep themselves in good health is to massage their feet. There are many important acupuncture points on the soles of the feet, and the most important is located in the pit of the sole and is called Yong Quan Point, on the longevity point. Massaging this point frequently is good for improving the vitality of the body and replenishing
文摘Intensive use of geometrical modelling started with the development of computer graphics and CAD/CAM technologies, comprising a wide area of mathematical disciplines. Geometrical modelling is a synthesis of the geometry and computer graphics, which enable us to develop complex mathematical models that would be rather difficult to display without using a computer. The author recognizes two basic methods of research of geometrical models, synthetic and analytic. The synthetic method makes use of geometrical constructions and in the analytic method geometrical objects are characterized by numerical data. The author uses these methods in this contribution. The aim of this research is to show central cyclides （Dupin＇s cyclides） as a special kind of the cyclical elliptical pedal surfaces. Firstly, applying the method of synthetic geometry, a new class of such surfaces in the 3-dimensional Euclidean space （model of the projective space） is defined. The geometrical construction of these surfaces is dependent on the given ellipse and the position of the pole P. It is the point at which the pencil of perpendicular planes passes to the plane of the ellipse, wherein the generating circles of the surface are lying. The parametric equations of the cyclical elliptical surface are derived applying the method of analytic geometry. The author classifies the surfaces according to the number of generating circles with a zero radius. The evolute of the ellipse divides the plane of the ellipse into two areas, Ω1 and Ω2. The shape of the surface depends on the position of the pole P in the areas of Ω1 and Ω2. The surface can have 4, 3 or 2 circles with a zero radius. The author then describes the relationship between these surfaces and the Dupin＇s cyclides, obtained in the case when the pole P is the point on the major axis of the ellipse. Finally, the transformation of these surfaces is shown by changing of the orthonormal base in the parameterization of the generating circles of the surface. The author visualizes the resulting surfaces obtained by the parametric approach in the MAPLE program environment.
