Functional inequalities on abstract Hilbert spaces and applications

We study the essential spectrum and the semigroup property for self-adjoint operators on abstract Hilbert spaces by using functional inequalities. Some known results obtained on the L ² -space w.r.t. a measure space are generalized. The functional inequality is also used to study non-symmetric semigroups. Mathematics Subject Classification (2000): 49R20, 58F19.Research supported in part by NNSFC (10121101, 10025105), TRAPOYT and the 973-Project.     

On order-preservation and positive correlations for multidimensional diffusion processes

Summary As a continuation of the study by Herbst and Pitt (1991), this note presents two criteria. The first one is on the order-preservation for two (may be different) multidimensional diffusion processes. The second one is on the preservation of positive correlations for a diffusion process.Research supported in part by the Ying-Tung Fok Educational Foundation and the National Natural Science Foundation of China     

Liouville theorem and coupling on negatively curved Riemannian manifolds

By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds with Ricci curvatures bounded below by a negative function. Indeed, for these manifolds we prove that all harmonic functions (maps) with certain growth are constant. In particular, the well-known Liouville theorem due to Cheng for sublinear harmonic functions (maps) is generalized. Moreover, our results imply the Brownian coupling property for a class of negatively curved Riemannian manifolds. This leads to a negative answer to a question of Kendall concerning the Brownian coupling property.     

Application of coupling methods to the Neumann eigenvalue problem

Summary By using coupling methods, some lower bounds are obtained for the first Neumann eigenvalue on Riemannian manifolds. This method is new and the results improve some known estimates. An example shows that our estimates can be sharp.Research supported in part by the Foundation of Beijing Normal University     

Estimates of logarithmic Sobolev constat for finite-volume continuous spin systems

LetM be a compact, connected Riemannian manifold (with or without boundary); we study the logarithmic Sobolev constant for stochastic Ising models on . Let {} be a sequence of cubes inZ ^d ; we show that the logarithmic Sobolev constant for the finite systems onM ^A shrinks at most exponentially fast in ||^(d-1)/d (d2), which is sharp in order for the classical Ising models withM=[–1, 1]. Moreover, a geometrical lemma proved by L. E. Thomas is also improved.     

胶黏剂中的化学*——2020年美国国家化学周活动介绍及启示

重点介绍2020年美国国家化学周——“胶黏剂中的化学”实验活动,对科学阅读和采访未来科学家活动作简要介绍。以此得出本次化学周活动对我国化学教学的几点启示:(1)大概念视角,加深结构化认识;(2)扎根实践,提高应用意识;(3)鼓励探析,深化本质意识;(4)跨界科学,渗透STSE理念;(5)精选主题,凸显微型项目;(6)勤研善思,塑造优秀品格。     

Bi2Fe4O9/g-C3N4/UiO-66三元复合材料的协同光催化作用

通过水热法合成具有协同机制的三元复合材料Bi₂Fe₄O₉/g-C₃N₄/UiO-66,研究表明三元复合光催化剂的催化活性要高于二元材料和纯材料。这主要是由于Bi₂Fe₄O₉更易于和g-C₃N₄结合形成稳定的Z-scheme异质结结构,使三元复合材料增强了可见光响应能力,提高了电子-空穴分离能力,增强了空穴和电子的氧化还原能力。     

Spectral gap for hyperbounded operators

Let be a probability space, and a symmetric linear contraction operator on with and . We prove that is the optimal sufficient condition for to have a spectral gap. Moreover, the optimal sufficient conditions are obtained, respectively, for the defective log-Sobolev and for the defective Poincaré inequality to imply the existence of a spectral gap. Finally, we construct a symmetric, hyperbounded, ergodic contraction -semigroup without a spectral gap.

     

Bi2Fe4O9/g-C3N4/UiO-66三元复合材料的协同光催化作用

通过水热法合成具有协同机制的三元复合材料Bi₂Fe₄O₉/g-C₃N₄/UiO-66,研究表明三元复合光催化剂的催化活性要高于二元材料和纯材料。这主要是由于Bi₂Fe₄O₉更易于和g-C₃N₄结合形成稳定的Z-scheme异质结结构,使三元复合材料增强了可见光响应能力,提高了电子-空穴分离能力,增强了空穴和电子的氧化还原能力。     

Log-Harnack inequality for stochastic Burgers equations and applications

By proving an L²-gradient estimate for the corresponding Galerkin approximations, the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density.