Adaptive estimation of an ergodic diffusion process based on sampled data

We consider adaptive maximum likelihood type estimation of both drift and diffusion coefficient parameters for an ergodic diffusion process based on discrete observations. Two kinds of adaptive maximum likelihood type estimators are proposed and asymptotic properties of the adaptive estimators, including convergence of moments, are obtained.     

An augmented penalty function method with penalty parameter updates for nonconvex optimization

Given an augmented Lagrangian scheme for a general optimization problem, we use an epsilon subgradient step for improving the dual function. This can be seen as an update for an augmented penalty method, which is more stable because it does not force the penalty parameter to tend to infinity. We establish for this update primal-dual convergence for our augmented penalty method. As illustration, we apply our method to the test-bed kissing number problem.     

Convex regularization of local volatility models from option prices: Convergence analysis and rates

We study a convex regularization of the local volatility surface identification problem for the Black-Scholes partial differential equation from prices of European call options. This is a highly nonlinear ill-posed problem which in practice is subject to different noise levels associated to bid-ask spreads and sampling errors. We analyze, in appropriate function spaces, different properties of the parameter-to-solution map that assigns to a given volatility surface the corresponding option prices. Using such properties, we show stability and convergence of the regularized solutions in terms of the Bregman distance with respect to a class of convex regularization functionals when the noise level goes to zero.We improve convergence rates available in the literature for the volatility identification problem. Furthermore, in the present context, we relate convex regularization with the notion of exponential families in Statistics. Finally, we connect convex regularization functionals with convex risk measures through Fenchel conjugation. We do this by showing that if the source condition for the regularization functional is satisfied, then convex risk measures can be constructed.     

Existence results for some Kirchhoff-Carrier problems

Analyzing the viscoelastic problem for small vibrations of elastic strings, Kirchhoff and Carrier proposed two different models of nonlinear partial differential equations. By combining these two models, we deal here with some nonlocal hyperbolic problems that cover a large class of Kirchhoff and Carrier type problems. The existence of local solutions of degenerate problems as well as local and nonlocal solutions of nondegenerate problems is established. The proofs are based on the combination of the Schauder fixed point theorem with some asymptotic method.     

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities and integral systems on the Heisenberg group

In this paper, we study two types of weighted Hardy–Littlewood–Sobolev (HLS) inequalities, also known as Stein–Weiss inequalities, on the Heisenberg group. More precisely, we prove the |u|$\left|u\right|$ weighted HLS inequality in Theorem 1.1 and the |z|$\left|z\right|$ weighted HLS inequality in Theorem 1.5 (where we have denoted u=(z,t)$u=(z,t)$ as points on the Heisenberg group). Then we provide regularity estimates of positive solutions to integral systems which are Euler–Lagrange equations of the possible extremals to the Stein–Weiss inequalities. Asymptotic behavior is also established for integral systems associated to the |u|$\left|u\right|$ weighted HLS inequalities around the origin. By these a priori estimates, we describe asymptotically the possible optimizers for sharp versions of these inequalities.     

(L,M)-模糊拓扑空间中模糊紧性的测度

本文借助不等式,在(L,M)-拓扑空间中引入了模糊紧性度的概念,并讨论了它的性质.     

Modelling the formation of nanostructures on metal surface induced by femtosecond laser ablation

We employ the particle-in-cell method to simulate the mechanisms of femtosecond (fs) laser interactions with a metallic target. The theoretical approach considers the solid as a gas of free electrons in a lattice of immobile ions and the laser fluences close to the ablation threshold. At first moments of the interaction, our simulations mapped out different nanostructures. We carefully characterized the rippling phase and found that its morphology is dependent on the distribution of the electron density and the period of the ripples depends on the laser intensity. The simulation method provides new insights into the mechanisms that are responsible for surface grating formation.     

HL-2Mŷķ������Ȧ��ˮ������Ż�

利用ANSYS CFX有限元程序建立了HL-2M欧姆测试线圈和冷却水模型,应用热传导和对流换热方程建立了流固边界层,对线圈的温升和冷却进行了流固耦合计算。计算结果表明,线圈由焦耳热引起的最高温升与电流密度、等效放电运行时间有关,而冷却水流量对最高温升影响较小,冷却水流量主要决定线圈的冷却时间间隔的长度,欧姆测试线圈的最长冷却时间间隔为5min。