Projective Normality Of Algebraic Curves And Its Application To Surfaces

Let $L$ be a very ample line bundle on a smooth curve $C$ of genus $g$ with $\frac{3g+3}{2}<\deg L\le 2g-5$. Then $L$ is normally generated if $\deg L>\max\{2g+2-4h^1(C,L), 2g-\frac{g-1}{6}-2h^1(C,L)\}$. Let $C$ be a triple covering of genus $p$ curve $C'$ with $C\stackrel{\phi}\to C'$ and $D$ a divisor on $C'$ with $4p<\deg D< \frac{g-1}{6}-2p$. Then $K_C(-\phi^*D)$ becomes a very ample line bundle which is normally generated. As an application, we characterize some smooth projective surfaces.Comment: 7 pages, 1figur

Quartet consistency count method for reconstructing phylogenetic trees

Among the distance based algorithms in phylogenetic tree reconstruction, the neighbor-joining algorithm has been a widely used and effective method. We propose a new algorithm which counts the number of consistent quartets for cherry picking with tie breaking. We show that the success rate of the new algorithm is almost equal to that of neighbor-joining. This gives an explanation of the qualitative nature of neighbor-joining and that of dissimilarity maps from DNA sequence data. Moreover, the new algorithm always reconstructs correct trees from quartet consistent dissimilarity maps.Comment: 11 pages, 5 figure

Perfect Basis Theory for Quantum Borcherds-Bozec Algebras

In this paper, we develop the perfect basis theory for quantum Borcherds-Bozec algebras $U_{q}(\mathfrak g)$ and their irreducible highest weight modules $V(\lambda)$. We show that the perfect graph (resp. dual perfect graph) of every perfect basis (resp. dual perfect basis) of $U_{q}^{-}(\mathfrak g)$ (resp. $V(\lambda)$) is isomorphic to $B(\infty)$ (resp. $B(\lambda)$). For this purpose, we define a new class of Kashiwara operators which is different from the one given by Bozec and prove all the interlocking inductive statements in Kashiwara's grand loop argument, which shows the existence and the uniqueness of crystal bases for quantum Borcherds-Bozec algebras

Fast track fed-batch culture development for COVID-19 vaccine clinical study

Please click Additional Files below to see the full abstract