For any regular Lie algebroid A, the kernel K and the image F of its anchor map ρA, together with A itself fit into a short exact sequence, called the Atiyah sequence, of Lie algebroids. We prove that the Atiyah and ...For any regular Lie algebroid A, the kernel K and the image F of its anchor map ρA, together with A itself fit into a short exact sequence, called the Atiyah sequence, of Lie algebroids. We prove that the Atiyah and Todd classes of dg manifolds arising from a regular Lie algebroid respect the Atiyah sequence, i.e.,the Atiyah and Todd classes of A restrict to the Atiyah and Todd classes of the bundle K of Lie algebras on the one hand, and project onto the Atiyah and Todd classes of the integrable distribution F■T_M on the other hand.展开更多
Taking Tropical Cyclone (TC) No.9806 (Todd) as an example, the effects of Zhoushanarchipelago terrain on landfall TC are investigated by use of numerical simulation. Results show that, undertopographic influences of Z...Taking Tropical Cyclone (TC) No.9806 (Todd) as an example, the effects of Zhoushanarchipelago terrain on landfall TC are investigated by use of numerical simulation. Results show that, undertopographic influences of Zhoushan Islands, the westward-moving landfall TC deflects. And, small orographichighs and enhanced rainfall caused by climbing airflow on the windward slope of main mountains of theseislands are a result of effects of Zhoushan Islands. These results display some particular laws of effects ofsmall-sized islands on the landfall of TC.展开更多
We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection.Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a ...We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection.Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a generator of the 2nd integral cohomology group,we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c_(1)>,=,or<0.In particular,the values about the Todd genus,Â-genus,and A_(k)-genus can be derived from the elliptic genera of level N.展开更多
Refinements to inequalities on inner product spaces are presented. In this respect, inequali-ties dealt with in this paper are: Cauchy’s inequality, Bessel’s inequality, Fan-Todd’s inequality and Fan-Todd’s determ...Refinements to inequalities on inner product spaces are presented. In this respect, inequali-ties dealt with in this paper are: Cauchy’s inequality, Bessel’s inequality, Fan-Todd’s inequality and Fan-Todd’s determinantal inequality. In each case, a strictly increasing function is put for-ward, which lies between the smaller and the larger quantities of each inequality. As a result. an improved condition for equality of the Fan-Todd’s determinantal inequality is deduced.展开更多
The tyrosine \%O\%\|phosphorylation \%via\% Atherton\|Todd reaction, which was a classical reaction for phosphorylation amines, was first studied in this paper. Reaction of Boc\|Tyr\|OCH\-3, which was selected as mode...The tyrosine \%O\%\|phosphorylation \%via\% Atherton\|Todd reaction, which was a classical reaction for phosphorylation amines, was first studied in this paper. Reaction of Boc\|Tyr\|OCH\-3, which was selected as model substrate, with three dialkyl \%H\%\|phosphonate diester in the presence of CCl\-4 and triethylamine produced the corresponding tyrosine \%O\%\|phosphorylation products in a high yield(over 80%). The reaction was conducted in anhydrous THF solution and monitored by \{\}\+\{31\}P NMR and TLC. Then reaction of Boc\|Tyr\|OCH\-3 with a complicated H\|phosphonate diester, \%O\%\|3\|acetylthymidin\|5\|yl \%O\%\|isopropyl \%H\%\|phosphonate diester, also gave a good result and this would be an alternative approach for the synthesis of nucleotide \%O\%\|tyrosine (or tyrosine containing peptide) conjugate. Further, the successful \%O\%\|phosphoration of three tyrosine containing protected dipeptides, Boc\|Tyr\|Val\|OCH\-3, Boc\|Ala\|Tyr\|OCH\-3, Boc\|Tyr\|Tyr\|OCH\-3, with diisopropyl \%H\%\|phosphonate diester demonstrated the effectiveness of the method.展开更多
Six kinds of phosphorylated coumarins are successfully synthesized by an Atherton-Todd reaction. They are fully characterized by FTIR、1H NMR、31P NMR、ESI-MS and EA. For the 6,7-dihydroxy coumarin, there was selectiv...Six kinds of phosphorylated coumarins are successfully synthesized by an Atherton-Todd reaction. They are fully characterized by FTIR、1H NMR、31P NMR、ESI-MS and EA. For the 6,7-dihydroxy coumarin, there was selective phosphorylation in the 6-hydroxyl group in the reaction. XRD analysis of 2f is described. The crystal is nomoclinic, space group P2(1)/n. there is hydrogen-bonding interaction between O atom on P=O and H atom on O-H.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11901221)。
文摘For any regular Lie algebroid A, the kernel K and the image F of its anchor map ρA, together with A itself fit into a short exact sequence, called the Atiyah sequence, of Lie algebroids. We prove that the Atiyah and Todd classes of dg manifolds arising from a regular Lie algebroid respect the Atiyah sequence, i.e.,the Atiyah and Todd classes of A restrict to the Atiyah and Todd classes of the bundle K of Lie algebras on the one hand, and project onto the Atiyah and Todd classes of the integrable distribution F■T_M on the other hand.
基金Natural Science Foundation of China (40275016) Innovative Planning Project for Post-graduates in Jiangsu Province
文摘Taking Tropical Cyclone (TC) No.9806 (Todd) as an example, the effects of Zhoushanarchipelago terrain on landfall TC are investigated by use of numerical simulation. Results show that, undertopographic influences of Zhoushan Islands, the westward-moving landfall TC deflects. And, small orographichighs and enhanced rainfall caused by climbing airflow on the windward slope of main mountains of theseislands are a result of effects of Zhoushan Islands. These results display some particular laws of effects ofsmall-sized islands on the landfall of TC.
基金the Natural Science Foundation of Tianjin City of China(Grant No.19JCY-BJC30300)the National Natural Science Foundation of China(Grant No.12071337).
文摘We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection.Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a generator of the 2nd integral cohomology group,we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c_(1)>,=,or<0.In particular,the values about the Todd genus,Â-genus,and A_(k)-genus can be derived from the elliptic genera of level N.
文摘Refinements to inequalities on inner product spaces are presented. In this respect, inequali-ties dealt with in this paper are: Cauchy’s inequality, Bessel’s inequality, Fan-Todd’s inequality and Fan-Todd’s determinantal inequality. In each case, a strictly increasing function is put for-ward, which lies between the smaller and the larger quantities of each inequality. As a result. an improved condition for equality of the Fan-Todd’s determinantal inequality is deduced.
文摘The tyrosine \%O\%\|phosphorylation \%via\% Atherton\|Todd reaction, which was a classical reaction for phosphorylation amines, was first studied in this paper. Reaction of Boc\|Tyr\|OCH\-3, which was selected as model substrate, with three dialkyl \%H\%\|phosphonate diester in the presence of CCl\-4 and triethylamine produced the corresponding tyrosine \%O\%\|phosphorylation products in a high yield(over 80%). The reaction was conducted in anhydrous THF solution and monitored by \{\}\+\{31\}P NMR and TLC. Then reaction of Boc\|Tyr\|OCH\-3 with a complicated H\|phosphonate diester, \%O\%\|3\|acetylthymidin\|5\|yl \%O\%\|isopropyl \%H\%\|phosphonate diester, also gave a good result and this would be an alternative approach for the synthesis of nucleotide \%O\%\|tyrosine (or tyrosine containing peptide) conjugate. Further, the successful \%O\%\|phosphoration of three tyrosine containing protected dipeptides, Boc\|Tyr\|Val\|OCH\-3, Boc\|Ala\|Tyr\|OCH\-3, Boc\|Tyr\|Tyr\|OCH\-3, with diisopropyl \%H\%\|phosphonate diester demonstrated the effectiveness of the method.
文摘Six kinds of phosphorylated coumarins are successfully synthesized by an Atherton-Todd reaction. They are fully characterized by FTIR、1H NMR、31P NMR、ESI-MS and EA. For the 6,7-dihydroxy coumarin, there was selective phosphorylation in the 6-hydroxyl group in the reaction. XRD analysis of 2f is described. The crystal is nomoclinic, space group P2(1)/n. there is hydrogen-bonding interaction between O atom on P=O and H atom on O-H.
