S-extremal strongly modular lattices maximize the minimum of the lattice and its shadow simultaneously. They are a direct generalization of the s-extremal unimodular lattices defined in [6]. If the minimum of the lattice is even, then the dimension of an s-extremal lattices can be bounded by the theory of modular forms. This shows that such lattices are also extremal and that there are only fin...

In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodular lattices in dimension 40 are studied. We give a classification of extremal singly even self-dual codes of length 40. We also give a classification of extremal odd unimodular lattices in dimension 40 with shadows having 80 vectors of norm 2 through their relationships with extremal doubly even sel...

S-extremal strongly modular lattices maximize the minimum of the lattice and its shadow simultaneously. They are a direct generalization of the s-extremal unimodular lattices defined in [6]. If the minimum of the lattice is even, then the dimension of an s-extremal lattices can be bounded by the theory of modular forms. This shows that such lattices are also extremal and that there are only fin...

The independence number α ( G ) $\alpha (G)$ and the dissociation diss $\text{diss}(G)$ of a graph $G$ are largest orders induced subgraphs maximum degree at most 0 1, respectively. We consider possible improvements obvious inequality 2 ≥ $2\alpha (G)\ge \text{diss}(G)$ . For connected cubic graphs distinct from K 4 ${K}_{4}$ , we show 5 3 $5\alpha 3\,\text{diss}(G)$ describe rich interesting s...

In the present thesis we consider extremal self-dual codes. We mainly concentrate on Type II codes (binary doubly-even codes), which may theoretically exist for lengths n = 8k ≤ 3928. It is noteworthy that extremal Type II codes have been actually constructed only for 13 lengths, 136 being the largest. Over the last decades the study of extremal codes became inseparable from the study of their ...

eccentric connectivity index has been found to have a low degeneracy and hence a significantpotential of predicting biological activity of certain classes of chemical compounds. wepresent here explicit formulas for eccentric connectivity index of various families of graphs.we also show that the eccentric connectivity index grows at most polynomially with thenumber of vertices and determine the ...

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric EinsteinMaxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of t...

0 < A0 = A1 = A3 < A2 = A4 < 0.0319, and extremal functions for A0 and A2 exist, but extremal functions for A1, A3 and A4 they do not exist. This is a simple normal families argument; it also shows that extremal functions for A0 have the boundary of the ring {z : A0 < |z| < 1} as the natural boundary, and extremal functions for A2 have the unit circle as the natural boundary. The problem is to ...

For the most part, this article is a survey of concrete results in extremal combinatorics obtained with the method of flag algebras. But our survey is also preceded, interleaved and concluded with a few general digressions about the method itself. Also, instead of giving a plain and unannotated list of results, we try to divide our account into several connected stories that often include histo...

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric EinsteinMaxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of t...