陕西泾阳南塬黄土滑坡灾害与引水灌溉的关系

陕西泾阳南塬塬边黄土滑坡频繁发生，造成的经济损失和人员伤亡极为惨重。本文讨论了区内黄土滑坡灾害形成的地貌地形及地质环境特征，着重分析了人类不合理的引用地表水灌溉，改变了地下水文条件，从而降低了土体的抗剪强度，导致黄土滑坡形成的过程和机制。通过研究认为，合理进行灌溉，控制地下水位是改善塬边地质环境和防治滑坡灾害的关键措施。     

TTRISK: Tensor train decomposition algorithm for risk averse optimization

This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or partial differential equations [PDEs]) under uncertainty. As an example, we focus on the so-called Conditional Value at Risk (CVaR), but the approach is equally applicable to other coherent risk measures. Both the full and reduced space formulations are considered. The algorithm is based on low rank tensor approximations of random fields discretized using stochastic collocation. To avoid nonsmoothness of the objective function underpinning the CVaR, we propose an adaptive strategy to select the width parameter of the smoothed CVaR to balance the smoothing and tensor approximation errors. Moreover, unbiased Monte Carlo CVaR estimate can be computed by using the smoothed CVaR as a control variate. To accelerate the computations, we introduce an efficient preconditioner for the Karush–Kuhn–Tucker (KKT) system in the full space formulation.The numerical experiments demonstrate that the proposed method enables accurate CVaR optimization constrained by large-scale discretized systems. In particular, the first example consists of an elliptic PDE with random coefficients as constraints. The second example is motivated by a realistic application to devise a lockdown plan for United Kingdom under COVID-19. The results indicate that the risk-averse framework is feasible with the tensor approximations under tens of random variables.     

Intermittency generated by attracting and weakly repelling fixed points

Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay between a superexponentially attracting fixed point and an exponentially repelling fixed point. In this article we consider a closely related family of random systems with exponentially fast attraction to and polynomially fast repulsion from two fixed points, and show that such a phase transition still exists. The method of the proof however is different and relies on the construction of a suitable invariant set for the transfer operator.     

全身麻醉患者恢复期躁动的原因分析

目的分析全身麻醉患者恢复期发生躁动的原因,并探讨全麻患者恢复期躁动的预防措施。方法选取2014年12月至2016年7月期间在东莞市东城医院麻醉科接受全麻手术治疗的200例患者,统计恢复期躁动发生率、发生躁动的原因、各种原因导致躁动的发生率和严重程度,并总结预防措施。结果 200例全麻手术患者中共24例(12.00%)恢复期发生躁动,发生躁动的原因包括疼痛、气管导管刺激、导尿管刺激、药物残留、循环功能障碍,其中疼痛导致的躁动发生率为41.67%,与其他原因导致的躁动发生率比较存在的差异均具有统计学意义(P<0.05),由循环功能障碍导致的躁动程度最严重。结论导致全麻患者恢复期发生躁动的原因较多,躁动程度轻重不一,临床工作者应积极分析全麻患者恢复期发生躁动的原因,制定具有针对性的预防措施。     

Holomorphic Campanato spaces on the unit ball

As outlined below, this paper is devoted to a Carleson‐type‐measure‐based study of the holomorphic Campanato 2‐space on the open unit ball of , comprising all Hardy 2‐functions whose oscillations in non‐isotropic metric balls on the compact unit sphere are proportional to some power of the radius other than the dimension .     

Besov spaces via wavelets on metric spaces endowed with doubling measure,singular integral,and the T1 type theorem

The aim of this paper is twofold. We first establish the Besov spaces on metric spaces endowed with a doubling measure, via the remarkable orthonormal wavelet basis constructed recently by T. Hytönen and O. Tapiola, and characterize the dual spaces of these Besov spaces. Second, we prove the T1 type theorem for the boundedness of Calderón–Zygmund operators on these Besov spaces. Finally, we introduce a new class of Lipschitz spaces and characterize these spaces via the Littlewood–Paley theory. Copyright © 2016 John Wiley & Sons, Ltd.     

Convolution roots and embeddings of probability measures on Lie groups

We show that for a large class of connected Lie groups G, viz. from classC described below, given a probability measure μ on G and a natural number n, for any sequence {νi} of th convolution roots of μ there exists a sequence {zi} of elements of G, centralising the support of μ, and such that is relatively compact; thus the set of roots is relatively compact ‘modulo’ the conjugation action of the centraliser of suppμ. We also analyse the dependence of the sequence {zi} on n. The results yield a simpler and more transparent proof of the embedding theorem for infinitely divisible probability measures on the Lie groups as above, proved in [S.G. Dani, M. McCrudden, Embeddability of infinitely divisible distributions on linear Lie groups, Invent. Math. 110 (1992) 237-261].     

Non-sequential weak supercyclicity and hypercyclicity

A bounded linear operator T acting on a Banach space B is called weakly hypercyclic if there exists x∈B such that the orbit is weakly dense in B and T is called weakly supercyclic if there is x∈B for which the projective orbit is weakly dense in B. If weak density is replaced by weak sequential density, then T is said to be weakly sequentially hypercyclic or supercyclic, respectively. It is shown that on a separable Hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic. This is achieved by constructing a Borel probability measure μ on the unit circle for which the Fourier coefficients vanish at infinity and the multiplication operator Mf(z)=zf(z) acting on L₂(μ) is weakly supercyclic. It is not weakly sequentially supercyclic, since the projective orbit under M of each element in L₂(μ) is weakly sequentially closed. This answers a question posed by Bayart and Matheron. It is proved that the bilateral shift on ?p(Z), 1?p<∞, is weakly supercyclic if and only if 2<p<∞ and that any weakly supercyclic weighted bilateral shift on ?p(Z) for 1?p?2 is norm supercyclic. It is also shown that any weakly hypercyclic weighted bilateral shift on ?p(Z) for 1?p<2 is norm hypercyclic, which answers a question of Chan and Sanders.     

On a class of degenerate elliptic operators in <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript> spaces with respect to invariant measures

We consider a class of second order degenerate elliptic operators arising from second order stochastic differential equations in perturbed by noise. We study realizations of such operators in L ¹ spaces with respect to their (explicit) invariant measure, proving that they are m-dissipative.      

On homeomorphic Bernoulli measures on the Cantor space

Let be the Bernoulli measure on the Cantor space given as the infinite product of two-point measures with weights and . It is a long-standing open problem to characterize those and such that and are topologically equivalent (i.e., there is a homeomorphism from the Cantor space to itself sending to ). The (possibly) weaker property of and being continuously reducible to each other is equivalent to a property of and called binomial equivalence. In this paper we define an algebraic property called ``refinability' and show that, if and are refinable and binomially equivalent, then and are topologically equivalent. Next we show that refinability is equivalent to a fairly simple algebraic property. Finally, we give a class of examples of binomially equivalent and refinable numbers; in particular, the positive numbers and such that and are refinable, so the corresponding measures are topologically equivalent.