The harmonic index of a graph $G$, denoted by $H(G)$, is defined asthe sum of weights $2/[d(u)+d(v)]$ over all edges $uv$ of $G$, where$d(u)$ denotes the degree of a vertex $u$. Hu and Zhou [Y. Hu and X. Zhou, WSEAS Trans. Math. {bf 12} (2013) 716--726] proved that for any bicyclic graph $G$ of order $ngeq 4$, $H(G)le frac{n}{2}-frac{1}{15}$ and characterize all extremal bicyclic graphs.In this...

Abstract We present an error bound for a least squares version of the kernel based meshless finite difference method elliptic differential equations on smooth compact manifolds arbitrary dimension without boundary. In particular, we obtain sufficient conditions convergence this method. Numerical examples are provided equation $$-\Delta _{\mathcal {M}} u + = f$$ <mml:math xmlns:mml="http://www.w...

The exponentially decaying behavior of the momentum-momentum and momentumforce time correlation functions of Brownian motion at large times has been extensively used for the numerical evaluation of the friction coefficient γ from molecular dynamics simulations. We perform numerical analysis on these methods and address issues related to the appropriate choice of large time and the rate of conve...

This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of functions in an extended multifunction space (Sengupta and Ray, 2000), and the topological theory of convergence. Order, chaos, and complexity are described as dis...

This paper develops a novel passive stochastic gradient algorithm. In approximation, the algorithm does not have control over location where noisy gradients of cost function are evaluated. Classical algorithms use kernel that approximates Dirac delta to weigh based on how far they evaluated from desired point. this we construct multi-kernel The performs substantially better in high dimensional ...

In this note we give simplified proofs of rectifiability RCD(K,N) spaces as metric measure and lower semicontinuity the essential dimension, via \(\delta\)-splitting maps. The arguments are inspired by Cheeger-Colding theory for Ricci limits rely on second order differential calculus developed Gigli convergence stability results Ambrosio-Honda.

The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2012) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random variables. In the first part of the talk, we extend his main result to the case of serial dependent random variables by means of the powerful and elegant fun...