We study the random conductance model on $\mathbb{Z}^d$ with ergodic, unbounded conductances. prove a Gaussian lower bound heat kernel given polynomial moment condition and some additional assumptions correlations of The proof is based well-established chaining technique. also obtain bounds Green's function.

Carbon nanoscrolls (CNSs) with tubular structure similar to the open multiwall carbonnanotube have been of hot debate during recent years. Due to its unique property, Graphene Nanoscroll (GNS) have attracted many research groups’ attention and have been used by them. They specially studied on energy storage devices such as batteries and super capacitors. These devices can be schematically...

it is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

Let L = − 1 w div ( A ∇ u ) + μ be the generalized degenerate Schrödinger operator in 2 R d with ≥ 3 suitable weight and measure μ. The main aim of this paper is threefold. Firstly, we obtain an upper bound for fundamental solution L. Secondly, prove some estimates heat kernel including bound, Hölder continuity a comparison estimate. Finally, apply results to study maximal function characteriza...

Abstract We study the -hard graph problem Collapsed k-Core where, given an undirected G and integers b , x k we are asked to remove vertices such that -core of remaining graph, is, (uniquely determined) largest induced subgraph with minimum degree has size at most . was introduced by Zhang et al. (2017) it is motivated engagement behavior users in a social network measuring resilience against u...

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time. These time-varying coefficient functions are well-suited to many practical applications and can be estimated conveniently by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional...

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time. These time-varying coefficient functions are well-suited to many practical applications and can be estimated conveniently by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional...

This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time. These time-varying coefficient functions are well-suited to many practical applications and can be estimated conveniently by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional...