Recently, Lehmann, Sengupta, and Tanimoto proposed a conjectural construction of the exceptional set in Manin’s Conjecture, which we call geometric set. We construct del Pezzo surface degree 1 whose is Zariski dense. In particular, this provides first counterexample to original version Conjecture dimension 2 characteristic 0. Assuming finiteness Tate-Shafarevich groups elliptic curves over $${\...

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

In this paper we introduce the characteristic dimension of a four dimensional $\mathcal{N}=2$ superconformal field theory, which is an extraordinary simple invariant determined by scaling dimensions its Coulomb branch operators. We prove that only nine values are allowed, $-\infty$, 1 ,6/5, 4/3, 3/2, 2, 3, 4, and 6, thus giving new organizing principle to vast landscape 4d $\mathcal N=2$ SCFTs....

Now-a-days, to access any information is not the problem. Internet facilitated the users to have any graphics or textual data at any time any where. Multimedia data is the key player in information transmission and retrieval domain. Multimedia processing is involved in the key areas like business, entertainment, technology, games, and advertisement etc. To improve the visualization of any graph...