Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha...Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.展开更多
We compute the Dirac indexes for the two spin structures κ_0 and κ_1 forEguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish ingeneral, and axial anomaly exists. When the metr...We compute the Dirac indexes for the two spin structures κ_0 and κ_1 forEguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish ingeneral, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes forthe spin structure κ_0 , and no axial anomaly exists in this case.展开更多
We show that a Ricci flow in four dimensions can develop singularities modeled on the Eguchi–Hanson space.In particular,we prove that starting from a class of asymptotically cylindrical U(2)-invariant initial metrics...We show that a Ricci flow in four dimensions can develop singularities modeled on the Eguchi–Hanson space.In particular,we prove that starting from a class of asymptotically cylindrical U(2)-invariant initial metrics on T S^(2),a Type II singularity modeled on the Eguchi–Hanson space develops in finite time.Furthermore,we show that for these Ricci flows the only possible blow-up limits are(i)the Eguchi–Hanson space,(ii)the flat R4/Z2 orbifold,(iii)the 4d Bryant soliton quotiented by Z2,and(iv)the shrinking cylinder R×RP^(3).As a byproduct of our work,we also prove the existence of a new family of Type II singularities caused by the collapse of a two-sphere of self-intersection|k|≥3.展开更多
Transparent photoresists with a high refractive index(RI)and high transmittance in visible wavelengths have promising functionalities in optical fields.This work reports a kind of tunable optical material composed of ...Transparent photoresists with a high refractive index(RI)and high transmittance in visible wavelengths have promising functionalities in optical fields.This work reports a kind of tunable optical material composed of titanium dioxide nanoparticles embedded in acrylic resin with a high RI for ultraviolet(UV)-imprint lithography.The hybrid film exhibits a tunable RI of up to 1.67(589 nm)after being cured by UV light,while maintaining both a high transparency of over 98%in the visible light range and a low haze of less than 0.05%.The precision machining of optical microstructures can be imprinted easily and efficiently using the hybrid resin,which acts as a light guide plate(LGP)to guide the light from the side to the top in order to conserve the energy of the display device.These preliminary studies based on both laboratory and commercial experiments pave the way for exploiting the unparalleled optical properties of nanocomposite resins and promoting their industrial application.展开更多
First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions ba...First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid （a,β, γ, ρ, h（.,.）, k（.,-）, w（-,., .）, w（.,., .）, 0）-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid （a, β, γ η, p, h（., .）, n（., .）, w（-,.,-）, ω（.,.,.）, 0）-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multi- objectve problems as well as multiobiective control problems.展开更多
1997年Isaac、Taylor、zac三兄弟组成的乐队Hansom出专辑《无处可逃》掀起清新流行摇滚风暴，在冠军曲“MmmBop“与抒情小品“I Will Come To You”的带领下专辑销售直上全美排行亚军．全球800万张+同时获得格策莱美奖年度唱片．新晋艺...1997年Isaac、Taylor、zac三兄弟组成的乐队Hansom出专辑《无处可逃》掀起清新流行摇滚风暴，在冠军曲“MmmBop“与抒情小品“I Will Come To You”的带领下专辑销售直上全美排行亚军．全球800万张+同时获得格策莱美奖年度唱片．新晋艺人与流行和唱三项大奖提名，史凡连《滚石》90年代最重要专辑之列。今年6月他们推出新专辑《Underneath》保留了乐团一贯的清新摇滚味道．并多了些成熟与力量．看着他们我想起张爱玲的名句：“出名要越早”。展开更多
文摘Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.
文摘We compute the Dirac indexes for the two spin structures κ_0 and κ_1 forEguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish ingeneral, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes forthe spin structure κ_0 , and no axial anomaly exists in this case.
文摘We show that a Ricci flow in four dimensions can develop singularities modeled on the Eguchi–Hanson space.In particular,we prove that starting from a class of asymptotically cylindrical U(2)-invariant initial metrics on T S^(2),a Type II singularity modeled on the Eguchi–Hanson space develops in finite time.Furthermore,we show that for these Ricci flows the only possible blow-up limits are(i)the Eguchi–Hanson space,(ii)the flat R4/Z2 orbifold,(iii)the 4d Bryant soliton quotiented by Z2,and(iv)the shrinking cylinder R×RP^(3).As a byproduct of our work,we also prove the existence of a new family of Type II singularities caused by the collapse of a two-sphere of self-intersection|k|≥3.
基金supported by the National Natural Science Foundation of China(22288102 and 22278027).
文摘Transparent photoresists with a high refractive index(RI)and high transmittance in visible wavelengths have promising functionalities in optical fields.This work reports a kind of tunable optical material composed of titanium dioxide nanoparticles embedded in acrylic resin with a high RI for ultraviolet(UV)-imprint lithography.The hybrid film exhibits a tunable RI of up to 1.67(589 nm)after being cured by UV light,while maintaining both a high transparency of over 98%in the visible light range and a low haze of less than 0.05%.The precision machining of optical microstructures can be imprinted easily and efficiently using the hybrid resin,which acts as a light guide plate(LGP)to guide the light from the side to the top in order to conserve the energy of the display device.These preliminary studies based on both laboratory and commercial experiments pave the way for exploiting the unparalleled optical properties of nanocomposite resins and promoting their industrial application.
文摘First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid （a,β, γ, ρ, h（.,.）, k（.,-）, w（-,., .）, w（.,., .）, 0）-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid （a, β, γ η, p, h（., .）, n（., .）, w（-,.,-）, ω（.,.,.）, 0）-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multi- objectve problems as well as multiobiective control problems.
文摘1997年Isaac、Taylor、zac三兄弟组成的乐队Hansom出专辑《无处可逃》掀起清新流行摇滚风暴，在冠军曲“MmmBop“与抒情小品“I Will Come To You”的带领下专辑销售直上全美排行亚军．全球800万张+同时获得格策莱美奖年度唱片．新晋艺人与流行和唱三项大奖提名，史凡连《滚石》90年代最重要专辑之列。今年6月他们推出新专辑《Underneath》保留了乐团一贯的清新摇滚味道．并多了些成熟与力量．看着他们我想起张爱玲的名句：“出名要越早”。
