In this paper we study the family of embeddings ?t a compact RCD?(K,N) space (X,d,m) into L2(X,m) via eigenmaps. Extending part classical results [10], [11] known for closed Riemannian manifolds, prove convergence as t?0 rescaled pull-back metrics ?t?gL2 in induced by ?t. Moreover discuss behavior with respect to measured Gromov-Hausdorff and t. Applications include quantitative Lp-convergence ...

In a Hilbert space setting H, we study the fast convergence properties as t → +∞ of the trajectories of the second-order differential equation ẍ(t) + α t ẋ(t) +∇Φ(x(t)) = g(t), where ∇Φ is the gradient of a convex continuously differentiable function Φ : H → R, α is a positive parameter, and g : [t0,+∞[→ H is a small perturbation term. In this inertial system, the viscous damping coefficient αt...

For each n let Y n t be a continuous time symmetric Markov chain with state space n −1 Z d. A condition in terms of the conductances is given for the convergence of the Y n t to a symmetric Markov process Yt on R d. We have weak convergence of {Y n t : t ≤ t0} for every t0 and every starting point. The limit process Y has a continuous part and may also have jumps.

Lattice-valued semiuniform convergence structures are important mathematical in the theory of lattice-valued topology. Choosing a complete residuated lattice $L$ as background, we introduce new type filters using tensor and implication operations on $L$, which is called $\top$-filters. By means $\top$-filters, propose concept $\top$-semiuniform counterpart structures. Different from usual discu...

In this paper, we prove the existence of fixed point for J-type multi-valuedmap T in CAT(0) spaces and also we prove the strong convergence theoremsfor Ishikawa iteration scheme without using the xed point of involving map.

For each n let Y (n) t be a continuous time symmetric Markov chain with state space n −1 Z d. Conditions in terms of the conductances are given for the convergence of the Y (n) t to a symmetric Markov process Yt on R d. We have weak convergence of {Y (n) t : t ≤ t0} for every t0 and every starting point. The limit process Y has a continuous part and may also have jumps.

Throughout this paper, we always assume thatH is a real Hilbert space, whose inner product and norm are denoted by 〈·, ·〉 and ‖ · ‖. → and ⇀ are denoted by strong convergence and weak convergence, respectively. Let C be a nonempty closed convex subset ofH and T : C → C a mapping. In this paper, we denote the fixed point set of T by F T . T is said to be a contraction if there exists a constant ...

Currently, simulation is usually used to estimate network degree distribution P(k) and to examine if a network model predicts a scale-free network when an analytical formula does not exist. An alternative Markovian chain-based numerical method was proposed by Shi [Phys. Rev. E 71, 036140 (2005)] to compute time-dependent degree distribution P(k,t) . Although the numerical results demonstrate a ...