symmetric division deg index is one of the 148 discrete adriatic indices that showed good predictive properties on the testing sets provided by international academy of mathematical chemistry.symmetric division deg index is defined by$$sdd(g) = sume left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right),$$where $d_i$ is the degree of vertex $i$ in graph $g$.in this pap...

in this paper, we investigate the existence of positive solutions for the ellipticequation $delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $omega$ of $r^{n}$, $ngeq2$, with navier boundary conditions. we show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

From past literature it is evident that the search for self-dual codes has been hampered by the computational difficulty of generating the Hadamard matrices required. The use of the cocyclic construction of Hadamard matrices has permitted substantial cut-downs in the search time, but the search space still grows exponentially. Here we look at an adaptation of image-processing techniques for the...

We show that there is a unique extremal even unimodular lattice of dimension 48 which has an automorphism of order 5 of type 5− (8, 16)− 8. Since the three known extremal lattices do not admit such an automorphism, this provides a new example of an extremal even unimodular lattice in dimension 48.

For lengths 64 and 66, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even selfdual codes were previously known to exist. We also construct new 40 inequivalent extremal doubly even self-dual [64, 32, 12] codes with covering radius 12 meeting the Delsarte bound.

We derive all the axi-symmetric, vacuum and electrovac extremal isolated horizons. It turns out that for every horizon in this class, the induced metric tensor, the rotation 1-form potential and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar, extremal Kerr– Newman solution on the event horizon. We also discuss the general case of a symmetric, ...

This paper investigates the power of Probabilistic Büchi Automata (PBA) when the threshold probability of acceptance is non-extremal, i.e., is a value strictly between 0 and 1. Many practical randomized algorithms are designed to work under non-extremal threshold probabilities and thus it is important to study power of PBAs for such cases. The paper presents a number of surprising expressivenes...

In this paper, we determine the dimensions of the residue codes of extremal Type II Z4-codes for lengths 32 and 40. We demonstrate that every binary doubly even self-dual code of length 32 can be realized as the residue code of some extremal Type II Z4-code. It is also shown that there is a unique extremal Type II Z4-code of length 32 whose residue code has the smallest dimension 6 up to equiva...

We investigate higher derivative corrections to the extremal Kerr black hole in context of heterotic string theory with $\alpha'$ and a cubic-curvature extension general relativity. By analyzing near-horizon geometry these holes, we are able compute Iyer-Wald entropy as well angular momentum via generalized Komar integrals. In case stringy corrections, obtain physically relevant relation $S(J)$...