A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, at...

We address the intractable multi-armed bandit problem with switching costs, for which Asawa and Teneketzis introduced in [M. Asawa and D. Teneketzis. 1996. Multi-armed bandits with switching penalties. IEEE Trans. Automat. Control, 41 328–348] an index that partially characterizes optimal policies, attaching to each project state a “continuation index” (its Gittins index) and a “switching index...

Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-ch...

Topological indices are of incredible significance in the field graph theory. Convex polytopes play a significant role both various branches mathematics and also applied areas, most notably linear programming. We have calculated some topological such as atom-bond connectivity index, geometric arithmetic K-Banhatti indices, K-hyper-Banhatti modified from families convex through M-polynomials. Th...

Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these ...

We introduce the Arithmetic Site: an algebraic geometric space deeply related to the non-commutative geometric approach to the Riemann Hypothesis. We prove that the non-commutative space quotient of the adèle class space of the field of rational numbers by the maximal compact subgroup of the idèle class group, which we had previously shown to yield the correct counting function to obtain the co...

In this paper a new aggregation operator for a class of LR Fuzzy Numbers i.e., Triangular Fuzzy Numbers (TFNs) in which the Land Rapex angles of the piecewise continuous linear membership function of the composite or resultant or aggregate TFN are the arithmetic means of the corresponding Land Rapex angles of the individual TFNs is proposed. The Land Rapex angles have been treated independently...