Attouch's Theorem, which gives on a reflexive Banach space the equivalence between the Mosco epi-convergence of a sequence of convex functions and the graph convergence of the associated sequence of subgradients, has many important applications in convex optimization. In particular, generalized derivatives have been defined in terms of the epi-convergence or graph convergence of certain differe...

The present work illustrates the variable viscosity of dust nanofluid runs over a permeable stretched sheet with thermal radiation. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally analysis of entropy generation and Bejan number provides the fine points of the flow. The of model equations are transformed into non-linear or...

I present a bound on the rate of convergence of random walks in graphs that depends upon the conductance. This proof was developed by Lovàsz and Simonovits [LS90]. The name " holistic " is my fault. First, it's just cool. Second, it is very different from the spectral proof, and so is likely to extend to different situations. Third, it has algorithmic applications that the spectral proof does n...

We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This convergence, intended to play role already existing discrete graphs, means that restriction graph a randomly chosen ball has limiting distribution. prove any sequence graphs with uniformly bounded data convergent subsequence in this sense. then consider empirical spectral measure (with general boundary conditions ...

Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f:X → Y is a Frechet differentiable function and F:X ⇉ 2 is a set-valued mapping with closed graph. Uniform convergence of Chord method for solving generalized equation y ∈ f x + F x ...... . (∗), where y ∈ Y a parameter, is studied in the present paper. More clearly, we obtain the uniform convergence of the se...

We introduce a new graph operator, called the weak factor graph, which is close to the well-known clique-graph operator but which rather operates in terms of bicliques in a multipartite graph, and we address the problem of the convergence of the series of graphs obtained by the iterative application of this operator. As for the clique-graph operator, it is easy to find graphs for which the seri...

In recent work, Chow, Huang, Li and Zhou [6] introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When N ≥ 2 is the number of vertices of the graph, they show that the corresponding FokkerPlanck equation is a system of N nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices ...

Abstract We show that s‐convergence of graph sequences is equivalent to the convergence certain compact sets, called shapes, Borel probability measures. This result analogous characterization graphon (with respect cut distance) by envelopes, due Doležal, Grebík, Hladký, Rocha, and Rozhoň.