The present note is devoted to establish some extremal results for the zerothorder general Randić index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory for zeroth-order pseudodifferential operators tori, we consider viscosity limits in which operators, P, are replaced P + iν Δ, ν > 0. By adapting Helffer–Sjöstrand scattering resonances, show that, a complex neighbourhood continuous spectrum, eigenvalues Δ have as goes to In simplified setting this justifies claims ...

We propose and analyze a randomized zeroth-order optimization method based on approximating the exact gradient by finite differences computed in set of orthogonal random directions that changes with each iteration. A number previously proposed methods are recovered as special cases including spherical smoothing, coordinate descent, well discretized descent. Our main contribution is proving conv...

<abstract><p>The zeroth-order general Randić index of graph $ G = (V_G, E_G) $, denoted by ^0R_{\alpha}(G) is the sum items (d_{v})^{\alpha} over all vertices v\in V_G where \alpha a pertinently chosen real number. In this paper, we obtain sharp upper and lower bounds on ^0R_{\alpha} trees with given domination number \gamma for \alpha\in(-\infty, 0)\cup(1, \infty) \alpha\in(0, 1) r...

Most student modelling systems seek to develop a model of the internal operation of the cognitive system. In contrast, Input-Output Agent Modelling (IOAM) models an agent in terms of relationships between the inputs and outputs of the cognitive system. Previous IOAM systems have demonstrated high predictive accuracy in the domain of elementary subtraction. These systems use zeroth-order inducti...