In this paper we classify all extremal and -extremal binary self-dual codes of length 38. There are exactly 2744 extremal self-dual codes, two -extremal codes, and 1730 -extremal codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalization of this recursive algorithm for the shadow. T...

A compact hyperbolic surface of genus g is said to be extremal if it admits an extremal disc, a disc of the largest radius determined only by g. We discuss how many extremal discs are embedded in non-orientable extremal surfaces of genus 6. This is the final genus in our interest because it is already known for g = 3, 4, 5, or g > 6. We show that non-orientable extremal surfaces of genus 6 admi...

Abstract—In this paper we classify all extremal and s-extremal binary self-dual codes of length 38. There are exactly 2744 extremal [38, 19, 8] self-dual codes, two s-extremal [38, 19, 6] codes, and 1730 s-extremal [38, 19, 8] codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalizati...

We study, as hypersurfaces in toric varieties, elliptic Calabi–Yau fourfolds for F-theory compactifications dual to E8 × E8 heterotic strings compactified to four dimensions on elliptic Calabi–Yau threefolds with some choice of vector bundle. We describe how to read off the vector bundle data for the heterotic compactification from the toric data of the fourfold. This map allows us to construct...

‎For a simple graph $G$‎, ‎the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$‎, ‎where $q^{}_1‎, ‎q^{}_2‎, ‎dots‎, ‎q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$‎. ‎In this paper‎, ‎we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...

As in the grand canonical treatment of Reissner-Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes. Black hole thermodynam...

As in the grand canonical treatment of Reissner-Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes. Black hole thermodynam...

Let V (Λi) (resp., V (−Λj)) be a fundamental integrable highest (resp., lowest) weight module of Uq(ŝl2). The tensor product V (Λi)⊗ V (−Λj) is filtered by submodules Fn = Uq(ŝl2)(vi ⊗ vn−i), n ≥ 0, n ≡ i − j mod 2, where vi ∈ V (Λi) is the highest vector and vn−i ∈ V (−Λj) is an extremal vector. We show that Fn/Fn+2 is isomorphic to the level 0 extremal weight module V (n(Λ1 − Λ0)). Using this...

We study a variant, in the context of the Erdős–Ko–Rado Theorem for vector spaces [4], of an extremal problem of Erdős and Rothschild [3], who considered edge-colorings of graphs avoiding monochromatic triangles. For fixed positive integers r, k and ` with 1 ≤ ` < r, and a family F of linear r-dimensional subspaces in a linear n-dimensional vector space Vn over the fixed finite field GF (q), le...