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In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature bounded below. Yau’s gradient estimates for harmonic functions is also obtained on Alexandrov spaces.
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local gradient estimate for positive solution to a simple nonlinear parabolic equation
We present a new, simple, and elegant algorithm for computing the optimal mapping for the Monge-Kantorovich problem with quadratic cost. The method arises from a reformulation of the dual problem into...
In this commentary we try to make clearer the state of the art concerning the relation between mechanical contact interactions and the di¤erent notions of stresses.
In this work, we present results of Almost Sure Convergence and in Quadratic Mean of the gradient stochastic process for the sequential estimation of a conditional expectation. This work is motived b...
We wish to find the potential function whose gradient best approximates an observed square integrable function. With an appropriate choice of topology we show that the gradient operator is a bounded l...
We consider a stochastic gradient process, which is used for the estimation of a conditional expectation : Xn+1 = Xn−an∇xφ(Vn,Xn)(φ(Vn,Xn)−Un). We give one theorem of almost sure con...
On the basis of the second gradient operator defined on curved surfaces,the second category of integral theorems for tensor fields, including the second divergence theorems, the second gradient theore...
This paper proposes a posteriori error estimators of gradient recovery type for the Ciarlet-Raviart formulation of the second biharmonic equations. By the appropriate modification of weighted Cle men′...
This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are ...
Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods. Under these line searches, global convergence results are established for several famous conjugate gr...

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