In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/...In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.展开更多
Rapeseed(Brassica napus L.)is an important source of edible vegetable oil and feed protein;however,seed pigments affect the quality of rapeseed oil and the feed value of the residue from oil pressing.Here,we used a po...Rapeseed(Brassica napus L.)is an important source of edible vegetable oil and feed protein;however,seed pigments affect the quality of rapeseed oil and the feed value of the residue from oil pressing.Here,we used a population of rapeseed recombinant inbred lines(RILs)derived from the black-seeded male parent cultivar Zhongyou 821 and the yellow-seeded female parent line GH06 to map candidate genes controlling seed pigments in embryos and the seed coat.We detected 94 quantitative trait loci(QTLs)for seed pigments(44 for embryos and 50 for seed coat),distributed over 15 of the 19 rapeseed chromosomes.These included 28 QTLs for anthocyanidin content,explaining 2.41–44.66% of phenotypic variation;24 QTLs for flavonoid content,explaining 2.41–20.26% of phenotypic variation;16 QTLs for total phenol content,accounting for 2.74–23.68% of phenotypic variation;and 26 QTLs for melanin content,accounting for 2.37–24.82% of phenotypic variation,indicating that these traits are under multigenic control.Consensus regions on chromosomes A06,A09 and C08 were associated with multiple seed pigment traits,including 15,19 and 10 QTLs,respectively,most of which were major QTLs explaining>10% of the phenotypic variation.Based on the annotation of the B.napus"Darmor-bzh"reference genome,67 candidate genes were predicted from these consensus QTLs regions,and 12 candidate genes were identified as potentially involved in pigment accumulation by RNA-seq and qRT-PCR analysis.These preliminary results provide insight into the genetic architecture of pigment biosynthesis and lay a foundation for exploring the molecular mechanisms underlying seed coat color in B.napus.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236)Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)National Natural Science Foundation of China Youth Foud of China Youth Foud(Grant No.12101192).
文摘In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.
基金supported by the National Natural Science Foundation of China(31830067)the Major S&T Projects on the Cultivation of New Varieties of Genetically Modified Organisms,China(2018ZX08020001)+3 种基金the Fundamental Research Funds for the Central Universities,China(XDJK2020B030)the China Agriculture Research System of MOF and MARA(CARS-12)the Natural Science Foundation of Chongqing,China(cstc2017jcyjAX0321)the Higher Education Discipline Innovation Project,China(B12006)。
文摘Rapeseed(Brassica napus L.)is an important source of edible vegetable oil and feed protein;however,seed pigments affect the quality of rapeseed oil and the feed value of the residue from oil pressing.Here,we used a population of rapeseed recombinant inbred lines(RILs)derived from the black-seeded male parent cultivar Zhongyou 821 and the yellow-seeded female parent line GH06 to map candidate genes controlling seed pigments in embryos and the seed coat.We detected 94 quantitative trait loci(QTLs)for seed pigments(44 for embryos and 50 for seed coat),distributed over 15 of the 19 rapeseed chromosomes.These included 28 QTLs for anthocyanidin content,explaining 2.41–44.66% of phenotypic variation;24 QTLs for flavonoid content,explaining 2.41–20.26% of phenotypic variation;16 QTLs for total phenol content,accounting for 2.74–23.68% of phenotypic variation;and 26 QTLs for melanin content,accounting for 2.37–24.82% of phenotypic variation,indicating that these traits are under multigenic control.Consensus regions on chromosomes A06,A09 and C08 were associated with multiple seed pigment traits,including 15,19 and 10 QTLs,respectively,most of which were major QTLs explaining>10% of the phenotypic variation.Based on the annotation of the B.napus"Darmor-bzh"reference genome,67 candidate genes were predicted from these consensus QTLs regions,and 12 candidate genes were identified as potentially involved in pigment accumulation by RNA-seq and qRT-PCR analysis.These preliminary results provide insight into the genetic architecture of pigment biosynthesis and lay a foundation for exploring the molecular mechanisms underlying seed coat color in B.napus.
