The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost su...The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost surely not Fourier-Stieltjes series but determine pseudo-functions.This leads us to develop the theory of trigonometric multiplicative chaos,which produces a class of random measures.The kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly computed.The behavior of the partial sums of the above series is proved to be multifractal.Our theory holds on the torus Tdof dimension d≥1.展开更多
NADPH-dependent thioredoxin reductases （NTRs） are key regulatory enzymes determining the redox state of thioredoxins. There are two genes encoding NTRs （NTRA and NTRB） in the Arabidopsis genome, each encoding a cy...NADPH-dependent thioredoxin reductases （NTRs） are key regulatory enzymes determining the redox state of thioredoxins. There are two genes encoding NTRs （NTRA and NTRB） in the Arabidopsis genome, each encoding a cytosolic and a mitochondrial isoform. A double ntra ntrb mutant has recently been characterized and shows slower plant growth, slightly wrinkled seeds and a remarkable hypersensitivity to buthionine sulfoximine （BSO）, a specific inhibitor of gluta- thione biosynthesis. In this paper, we demonstrate that this mutant also accumulates higher level of flavonoids. Analysis of transcriptome data showed that several genes of the flavonoid pathway are overexpressed in the ntra ntrb mutant. Accumulation of flavonoids is generally considered a hallmark of plant stress. Nevertheless, no elevation of the expression of genes encoding ROS-detoxification enzymes was observed, suggesting that the ntra ntrb plants do not suffer from oxidative disease. Another hypothesis suggests that flavonoids are specifically synthesized in the ntra ntrb mutant in order to rescue the inactivation of NTR. To test this, the ntra ntrb mutant was crossed with transparent testa 4 （tt4） plants with a mutation in the gene encoding the first enzyme in flavonoid biosynthesis. As ntra ntrb plants are more resistant to UV-C treatment than wild-type plants, this higher resistance was abolished in the ntra ntrb tt4 mutant, suggesting that accumulation of flavonoids in the ntra ntrb mutant protects plants against UV-light.展开更多
Let Λ ? R^n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have ...Let Λ ? R^n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have f(x) = O(ω_Λ(x)) as |x| →∞ and ω_Λ(x) can be estimated(Theorem 4.1). This line of research was proposed by Jean-Pierre Kahane in 1957.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11971192)。
文摘The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost surely not Fourier-Stieltjes series but determine pseudo-functions.This leads us to develop the theory of trigonometric multiplicative chaos,which produces a class of random measures.The kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly computed.The behavior of the partial sums of the above series is proved to be multifractal.Our theory holds on the torus Tdof dimension d≥1.
文摘NADPH-dependent thioredoxin reductases （NTRs） are key regulatory enzymes determining the redox state of thioredoxins. There are two genes encoding NTRs （NTRA and NTRB） in the Arabidopsis genome, each encoding a cytosolic and a mitochondrial isoform. A double ntra ntrb mutant has recently been characterized and shows slower plant growth, slightly wrinkled seeds and a remarkable hypersensitivity to buthionine sulfoximine （BSO）, a specific inhibitor of gluta- thione biosynthesis. In this paper, we demonstrate that this mutant also accumulates higher level of flavonoids. Analysis of transcriptome data showed that several genes of the flavonoid pathway are overexpressed in the ntra ntrb mutant. Accumulation of flavonoids is generally considered a hallmark of plant stress. Nevertheless, no elevation of the expression of genes encoding ROS-detoxification enzymes was observed, suggesting that the ntra ntrb plants do not suffer from oxidative disease. Another hypothesis suggests that flavonoids are specifically synthesized in the ntra ntrb mutant in order to rescue the inactivation of NTR. To test this, the ntra ntrb mutant was crossed with transparent testa 4 （tt4） plants with a mutation in the gene encoding the first enzyme in flavonoid biosynthesis. As ntra ntrb plants are more resistant to UV-C treatment than wild-type plants, this higher resistance was abolished in the ntra ntrb tt4 mutant, suggesting that accumulation of flavonoids in the ntra ntrb mutant protects plants against UV-light.
基金supported by a grant from the Simons Foundation(Grant No.601950 YM)
文摘Let Λ ? R^n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have f(x) = O(ω_Λ(x)) as |x| →∞ and ω_Λ(x) can be estimated(Theorem 4.1). This line of research was proposed by Jean-Pierre Kahane in 1957.
