This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical di...This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines,previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for P2.A ma jor insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror side.We obtain proper superpotentials which agree on an open part with those classically known for toric varieties.Examples include mirror LG models for non-singular and singular del Pezzo surfaces,Hirzebruch surfaces and some Fano threefolds.展开更多
The phase diagrams of the CH3CH2OH-Cs2CO3-H2O system were determined at 10, 30 and 50 ℃, respectively. It was found that the effect of the temperature on the phase equilibrium was insignificant within the investigate...The phase diagrams of the CH3CH2OH-Cs2CO3-H2O system were determined at 10, 30 and 50 ℃, respectively. It was found that the effect of the temperature on the phase equilibrium was insignificant within the investigated range. The binodal curves were given using a five-parameter equation and the tie lines were fitted using the Oth-mer-Tobias and Bancroft correlations. Correlation coefficients (R) for all equations exceeded 0.99. Samples of the solid phase at 30 ℃ were analyzed by TGA showing that it consisted of Cs2CO3·3.5H2O. The refractive index of the systems was also determined.展开更多
如果一个图的边集能划分成偶数长度圈的集合,则称该图有一个偶圈分解.如果一个图的任何一个具有偶数条边的细分,都有一个偶圈分解,则称该图是强偶圈分解的.在文献[European Journal of Combinatorics,94(2021),103315]中已证明:对于2-...如果一个图的边集能划分成偶数长度圈的集合,则称该图有一个偶圈分解.如果一个图的任何一个具有偶数条边的细分,都有一个偶圈分解,则称该图是强偶圈分解的.在文献[European Journal of Combinatorics,94(2021),103315]中已证明:对于2-连通立方图G,如果它存在一个圈C使得G-V(C)是一个线性森林(即这个森林仅仅由路组成),则L(G)是强偶圈分解的.本文推广上述结论,证明了如下定理:对于2-连通立方图G,如果它存在一个圈C使得G-V(C)是一个森林,则L(G)是强偶圈分解的.展开更多
基金supported by the Studienstiftung des deutschen Volkessupported by NSF grant DMS-1903437。
文摘This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines,previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for P2.A ma jor insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror side.We obtain proper superpotentials which agree on an open part with those classically known for toric varieties.Examples include mirror LG models for non-singular and singular del Pezzo surfaces,Hirzebruch surfaces and some Fano threefolds.
基金the National Natural Science Foundation of China (No. 20171032).
文摘The phase diagrams of the CH3CH2OH-Cs2CO3-H2O system were determined at 10, 30 and 50 ℃, respectively. It was found that the effect of the temperature on the phase equilibrium was insignificant within the investigated range. The binodal curves were given using a five-parameter equation and the tie lines were fitted using the Oth-mer-Tobias and Bancroft correlations. Correlation coefficients (R) for all equations exceeded 0.99. Samples of the solid phase at 30 ℃ were analyzed by TGA showing that it consisted of Cs2CO3·3.5H2O. The refractive index of the systems was also determined.
文摘如果一个图的边集能划分成偶数长度圈的集合,则称该图有一个偶圈分解.如果一个图的任何一个具有偶数条边的细分,都有一个偶圈分解,则称该图是强偶圈分解的.在文献[European Journal of Combinatorics,94(2021),103315]中已证明:对于2-连通立方图G,如果它存在一个圈C使得G-V(C)是一个线性森林(即这个森林仅仅由路组成),则L(G)是强偶圈分解的.本文推广上述结论,证明了如下定理:对于2-连通立方图G,如果它存在一个圈C使得G-V(C)是一个森林,则L(G)是强偶圈分解的.
