In this article, we have described the Todd-Coxeter algorithm. Indeed, the Todd-Coxeter algorithm is a mathematical tool used in the field of group theory. It makes it possible to determine different possible presenta...In this article, we have described the Todd-Coxeter algorithm. Indeed, the Todd-Coxeter algorithm is a mathematical tool used in the field of group theory. It makes it possible to determine different possible presentations of a group, i.e. different ways of expressing its elements and operations. We have also applied this algorithm to a subgroup generated H by G;where we obtained a table of the subgroup, three tables of relators including: Table of the relator aaaa;Table of the relator abab;Table of the relator bbb and a multiplication table aa'bb'. Once the algorithm is complete, the unit of H in G is 6. We have explicitly obtained a homomorphism of G in the group of permutations of H/G which is isomorphic to G6;where we have noticed that it is injective: in fact, an element of the nucleus belongs to the intersection of the xHx−1for x∈G, in particular, it belongs to H;on the other hand, the image of H in G6 is of order 4, so the nucleus is reduced to the neutral element.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
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
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
文摘In this article, we have described the Todd-Coxeter algorithm. Indeed, the Todd-Coxeter algorithm is a mathematical tool used in the field of group theory. It makes it possible to determine different possible presentations of a group, i.e. different ways of expressing its elements and operations. We have also applied this algorithm to a subgroup generated H by G;where we obtained a table of the subgroup, three tables of relators including: Table of the relator aaaa;Table of the relator abab;Table of the relator bbb and a multiplication table aa'bb'. Once the algorithm is complete, the unit of H in G is 6. We have explicitly obtained a homomorphism of G in the group of permutations of H/G which is isomorphic to G6;where we have noticed that it is injective: in fact, an element of the nucleus belongs to the intersection of the xHx−1for x∈G, in particular, it belongs to H;on the other hand, the image of H in G6 is of order 4, so the nucleus is reduced to the neutral element.
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.
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.
