本文利用具有重结点的自然样条函数,讨论了线性泛函Ff=sum from i=0 to n-1[integral from a to b a_i(x)D^i f(x)dx+sum from j=0 to L^1 b_(ij)D^i f(x_(ij))]的广义Sard逼近问题。文中给出了线性泛函Lf=sum from i=0 to k sum from j...本文利用具有重结点的自然样条函数,讨论了线性泛函Ff=sum from i=0 to n-1[integral from a to b a_i(x)D^i f(x)dx+sum from j=0 to L^1 b_(ij)D^i f(x_(ij))]的广义Sard逼近问题。文中给出了线性泛函Lf=sum from i=0 to k sum from j=0 to k_1-1 a_(ij)D^j f(x_i)逼近F为n-1阶准确的存在定理与唯一性定理;给出了L做为F的广义Sard逼近的充分必要条件。展开更多
将Rn的开子集上非线性映射的导算子,一致可微性等概念推广到定义在Rn的一般子集上的映射,然后建立相应的Sard定理,并将所得结果用于一类含参数的椭圆问题:∫Ωudx=α下解的通有有限性,-Δu+f(u)=(λ), u υ=0在约束条件:m(u):=1｜Ω...将Rn的开子集上非线性映射的导算子,一致可微性等概念推广到定义在Rn的一般子集上的映射,然后建立相应的Sard定理,并将所得结果用于一类含参数的椭圆问题:∫Ωudx=α下解的通有有限性,-Δu+f(u)=(λ), u υ=0在约束条件:m(u):=1｜Ω｜其中f严格单调递增,∈C1([0,1];L2(Ω)).我们证明存在零测集E R1使得对所有α∈R1\E,该问题只有有限个解(u,λ).展开更多
In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1&...In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1</sub>(b<sub>1</sub>f<sup>1</sup>（x<sub>1</sub>）)]) by a simpler linear functional Lf=sum from i=1 to m（a<sub>1</sub>f（x<sub>1</sub>）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.展开更多
Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ...Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.展开更多
Two signal molecules, salicylic acid (SA) and N-hydroxypipecolic acid (NHP), play critical roles in plant immunity. The biosynthetic genes of both compounds are positively regulated by master immune-regulating transcr...Two signal molecules, salicylic acid (SA) and N-hydroxypipecolic acid (NHP), play critical roles in plant immunity. The biosynthetic genes of both compounds are positively regulated by master immune-regulating transcription factors SARD1 and CBP60g. However, the relationship between the SA and NHP pathways is unclear. CALMODULIN-BINDING TRANSCRIPTION FACTOR 1 (CAMTA1), CAMTA2, and CAMTA3 are known redundant negative regulators of plant immunity, but the underlying mechanism also remains largely unknown. In this study, through chromatin immunoprecipitation and electrophoretic mobility shift assays, we uncovered that CBP60g is a direct target of CAMTA3, which also negatively regulates the expression of SARD1, presumably via an indirect effect. The autoimmunity of camta3-1 is suppressed by sard1 cbp60g double mutant as well as ald1 and fmo1, two single mutants defective in NHP biosynthesis. Interestingly, a suppressor screen conducted in the camta1/ 2/ 3 triple mutant background yielded various mutants blocking biosynthesis or signaling of either SA or NHP, leading to nearly complete suppression of the extreme autoimmunity of camta1/ 2/ 3, suggesting that the SA and NHP pathways can mutually amplify each other. Together, these results reveal that CAMTAs repress the biosynthesis of SA and NHP by modulating the expression of SARD1 and CBP60g, and that the SA and NHP pathways are coordinated to optimize plant immune response.展开更多
Summary Salicylic acid （SA） is an essential defence hormone in plants. Upon pathogen infection, induced biosynthesis of SA is mediated by Isochorismate synthase 1 （ICS1）, whose gene transcription is controlled mai...Summary Salicylic acid （SA） is an essential defence hormone in plants. Upon pathogen infection, induced biosynthesis of SA is mediated by Isochorismate synthase 1 （ICS1）, whose gene transcription is controlled mainly through two redundant transcription factors, SAR Deficient 1 （SARD0 and Calmodulin- binding protein 6o-like g （CBP60g）.展开更多
We have analyzed cardiac ische- mia-reperfusion in an animal model using epicardial electropotential mapping. We investigated the rela- tionship between ischemia and variability of multi- fractality in epicardial elec...We have analyzed cardiac ische- mia-reperfusion in an animal model using epicardial electropotential mapping. We investigated the rela- tionship between ischemia and variability of multi- fractality in epicardial electrograms. We present a new parameter called the singularity spectrum area reference dispersion (SARD) that clearly demon- strates the change in multifractility with the extent of myocardiaischemia. By contrasting the 3D ventricular epicardial SARD map with the activation map, we conclude that myocardial ischemia significantly in- fluences the variety of multifractality of ventricular epicardium electrograms and the SARD parameter is useful in correlating multifractality of epicardial elec- trograms with location of ischemia closely.展开更多
文摘本文利用具有重结点的自然样条函数,讨论了线性泛函Ff=sum from i=0 to n-1[integral from a to b a_i(x)D^i f(x)dx+sum from j=0 to L^1 b_(ij)D^i f(x_(ij))]的广义Sard逼近问题。文中给出了线性泛函Lf=sum from i=0 to k sum from j=0 to k_1-1 a_(ij)D^j f(x_i)逼近F为n-1阶准确的存在定理与唯一性定理;给出了L做为F的广义Sard逼近的充分必要条件。
文摘将Rn的开子集上非线性映射的导算子,一致可微性等概念推广到定义在Rn的一般子集上的映射,然后建立相应的Sard定理,并将所得结果用于一类含参数的椭圆问题:∫Ωudx=α下解的通有有限性,-Δu+f(u)=(λ), u υ=0在约束条件:m(u):=1｜Ω｜其中f严格单调递增,∈C1([0,1];L2(Ω)).我们证明存在零测集E R1使得对所有α∈R1\E,该问题只有有限个解(u,λ).
文摘In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1</sub>(b<sub>1</sub>f<sup>1</sup>（x<sub>1</sub>）)]) by a simpler linear functional Lf=sum from i=1 to m（a<sub>1</sub>f（x<sub>1</sub>）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.
基金Project supported by the National Natural Science Foundation ofChina (No. 10171090) and the Scientific Research Fund of ZhejiangProvincial Education Department (No. 20030341) China
文摘Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.
文摘Two signal molecules, salicylic acid (SA) and N-hydroxypipecolic acid (NHP), play critical roles in plant immunity. The biosynthetic genes of both compounds are positively regulated by master immune-regulating transcription factors SARD1 and CBP60g. However, the relationship between the SA and NHP pathways is unclear. CALMODULIN-BINDING TRANSCRIPTION FACTOR 1 (CAMTA1), CAMTA2, and CAMTA3 are known redundant negative regulators of plant immunity, but the underlying mechanism also remains largely unknown. In this study, through chromatin immunoprecipitation and electrophoretic mobility shift assays, we uncovered that CBP60g is a direct target of CAMTA3, which also negatively regulates the expression of SARD1, presumably via an indirect effect. The autoimmunity of camta3-1 is suppressed by sard1 cbp60g double mutant as well as ald1 and fmo1, two single mutants defective in NHP biosynthesis. Interestingly, a suppressor screen conducted in the camta1/ 2/ 3 triple mutant background yielded various mutants blocking biosynthesis or signaling of either SA or NHP, leading to nearly complete suppression of the extreme autoimmunity of camta1/ 2/ 3, suggesting that the SA and NHP pathways can mutually amplify each other. Together, these results reveal that CAMTAs repress the biosynthesis of SA and NHP by modulating the expression of SARD1 and CBP60g, and that the SA and NHP pathways are coordinated to optimize plant immune response.
基金supported by grants from the Natural Sciences and Engineering Research Council of Canada(NSERC)Discovery programthe Dewar Cooper Memorial Fund from the University of British Columbia(UBC)+1 种基金partially supported by a 4YF scholarship from UBCpartially supported by a Chinese Scholarship Council(CSC)fellowship
文摘Summary Salicylic acid （SA） is an essential defence hormone in plants. Upon pathogen infection, induced biosynthesis of SA is mediated by Isochorismate synthase 1 （ICS1）, whose gene transcription is controlled mainly through two redundant transcription factors, SAR Deficient 1 （SARD0 and Calmodulin- binding protein 6o-like g （CBP60g）.
基金supported by the Wellcome Trust and British Heart Foundationsupported by the National Natural Science Foundation of China(Grant No.60501003).
文摘We have analyzed cardiac ische- mia-reperfusion in an animal model using epicardial electropotential mapping. We investigated the rela- tionship between ischemia and variability of multi- fractality in epicardial electrograms. We present a new parameter called the singularity spectrum area reference dispersion (SARD) that clearly demon- strates the change in multifractility with the extent of myocardiaischemia. By contrasting the 3D ventricular epicardial SARD map with the activation map, we conclude that myocardial ischemia significantly in- fluences the variety of multifractality of ventricular epicardium electrograms and the SARD parameter is useful in correlating multifractality of epicardial elec- trograms with location of ischemia closely.
