LetΓbe a Jordan curve in the complex plane and let Γ_(λ) be the constant distance boundary ofΓ.Vellis and Wu[10]introduced the notion of a(ζ,r_(0))-chordal property which guarantees that,whenλis not too large, ...LetΓbe a Jordan curve in the complex plane and let Γ_(λ) be the constant distance boundary ofΓ.Vellis and Wu[10]introduced the notion of a(ζ,r_(0))-chordal property which guarantees that,whenλis not too large, Γ_(λ) is a Jordan curve whenζ=1/2 and Γ_(λ) is a quasicircle when 0<ζ<1/2.We introduce the(ζ,r_(0),t)-chordal property,which generalizes the(ζ,r_(0))-chordal property,and we show that under the condition thatΓis(ζ,r_(0),√t)-chordal with 0<ζ<r_(0)^(1−√t)/2,there existsε>0 such that Γ_(λ) is a t-quasicircle once Γ_(λ) is a Jordan curve when 0<λ<ε.In the last part of this paper,we provide an example:Γis a kind of Koch snowflake curve which does not have the(ζ,r_(0))-chordal property for any 0<ζ<1/2,however Γ_(λ) is a Jordan curve whenλis small enough.Meanwhile,Γhas the(ζ,r_(0),√t)-chordal property with 0<ζ<r_(0)^(1−√t)/2 for any t∈(0,1/4).As a corollary of our main theorem, Γ_(λ) is a t-quasicircle for all 0<t<1/4 whenλis small enough.This means that our(ζ,r_(0),t)-chordal property is more general and applicable to more complicated curves.展开更多
The effect of vernalization and two growth regulators Fascination^TM and Pro-Gibb^R on the growth, inflorescence development and flowering of Omithogalurrt Chesapeake Snowflake＇ was studied. Regardless of growth regu...The effect of vernalization and two growth regulators Fascination^TM and Pro-Gibb^R on the growth, inflorescence development and flowering of Omithogalurrt Chesapeake Snowflake＇ was studied. Regardless of growth regulator treatment, chilling bulbs for 3 weeks at 10℃ before planting accelerated flowering of the first inflorescence by 5 to 6 days, elongated floral stem length by 1.5 to 2 cm and shortened leaf length by 4 to 5 cm as compared with non-chilled bulbs. When bulbs were chilled 3 weeks at 10℃ before planting, Fascination 2% and Pro-Gibb accelerated flowering of the first inflorescence by 2 to 6 days respectively as compared with the control. When bulbs were not chilled before planting, Fascination 2% and Pro-Gibb accelerated flowering of the first inflorescence by 6 to12 days respectively as compared with the control. The lengths of the leaves and the inflorescences were not affected by PGR treatment. Higher rates of Pro-Gibb （100 mg.L^-1 and 200 mg.L^-1） and more amount of Fascination 2%（100 μL and 200 μL） can cause abortion of inflorescence.展开更多
Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the propo...Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.展开更多
The Chinese Fusion Engineering Test Reactor(CFETR)represents the next generation of full superconducting fusion reactors in China.Recently,CFETR was redesigned with a larger size and will be operated in two phases.To ...The Chinese Fusion Engineering Test Reactor(CFETR)represents the next generation of full superconducting fusion reactors in China.Recently,CFETR was redesigned with a larger size and will be operated in two phases.To reduce the heat flux on the target plate,a snowflake(SF)divertor configuration is proposed.In this paper we show that by adding two dedicated poloidal field(PF)coils,the SF configuration can be achieved in both phases.The equilibria were calculated by TEQ code for a range of self-inductances l_i3.The coil currents were calculated at some fiducial points in the flattop phase.The results indicate that the PF coil system has the ability to maintain a long flattop phase in 7.5 and 10 MA inductive scenarios for the single null divertor(SND)and SF divertor configurations.The properties of the SF configuration were also analyzed.The connection length and flux expansion of the SF divertor were both increased significantly over the SND.展开更多
文摘LetΓbe a Jordan curve in the complex plane and let Γ_(λ) be the constant distance boundary ofΓ.Vellis and Wu[10]introduced the notion of a(ζ,r_(0))-chordal property which guarantees that,whenλis not too large, Γ_(λ) is a Jordan curve whenζ=1/2 and Γ_(λ) is a quasicircle when 0<ζ<1/2.We introduce the(ζ,r_(0),t)-chordal property,which generalizes the(ζ,r_(0))-chordal property,and we show that under the condition thatΓis(ζ,r_(0),√t)-chordal with 0<ζ<r_(0)^(1−√t)/2,there existsε>0 such that Γ_(λ) is a t-quasicircle once Γ_(λ) is a Jordan curve when 0<λ<ε.In the last part of this paper,we provide an example:Γis a kind of Koch snowflake curve which does not have the(ζ,r_(0))-chordal property for any 0<ζ<1/2,however Γ_(λ) is a Jordan curve whenλis small enough.Meanwhile,Γhas the(ζ,r_(0),√t)-chordal property with 0<ζ<r_(0)^(1−√t)/2 for any t∈(0,1/4).As a corollary of our main theorem, Γ_(λ) is a t-quasicircle for all 0<t<1/4 whenλis small enough.This means that our(ζ,r_(0),t)-chordal property is more general and applicable to more complicated curves.
文摘The effect of vernalization and two growth regulators Fascination^TM and Pro-Gibb^R on the growth, inflorescence development and flowering of Omithogalurrt Chesapeake Snowflake＇ was studied. Regardless of growth regulator treatment, chilling bulbs for 3 weeks at 10℃ before planting accelerated flowering of the first inflorescence by 5 to 6 days, elongated floral stem length by 1.5 to 2 cm and shortened leaf length by 4 to 5 cm as compared with non-chilled bulbs. When bulbs were chilled 3 weeks at 10℃ before planting, Fascination 2% and Pro-Gibb accelerated flowering of the first inflorescence by 2 to 6 days respectively as compared with the control. When bulbs were not chilled before planting, Fascination 2% and Pro-Gibb accelerated flowering of the first inflorescence by 6 to12 days respectively as compared with the control. The lengths of the leaves and the inflorescences were not affected by PGR treatment. Higher rates of Pro-Gibb （100 mg.L^-1 and 200 mg.L^-1） and more amount of Fascination 2%（100 μL and 200 μL） can cause abortion of inflorescence.
基金Project supported by the National Natural Science Foundation of China(Nos.10872114,11072125,and 11272175)the National Natural Science Foundation of Jiangsu Province(No.SBK201140044)the Fundation of Tutor for Doctor Degree of Higher Education of China(No.20130002110044)
文摘Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.
基金supported by the National Magnetic Confinement Fusion Program under grant nos 2014GB106001,2014GB110003 and 2013GB111000National Natural Science Foundation of China under grant no.11675221
文摘The Chinese Fusion Engineering Test Reactor(CFETR)represents the next generation of full superconducting fusion reactors in China.Recently,CFETR was redesigned with a larger size and will be operated in two phases.To reduce the heat flux on the target plate,a snowflake(SF)divertor configuration is proposed.In this paper we show that by adding two dedicated poloidal field(PF)coils,the SF configuration can be achieved in both phases.The equilibria were calculated by TEQ code for a range of self-inductances l_i3.The coil currents were calculated at some fiducial points in the flattop phase.The results indicate that the PF coil system has the ability to maintain a long flattop phase in 7.5 and 10 MA inductive scenarios for the single null divertor(SND)and SF divertor configurations.The properties of the SF configuration were also analyzed.The connection length and flux expansion of the SF divertor were both increased significantly over the SND.
