一类海冰-海水耦合热力学系统参数辨识问题的最优性

针对一维的海冰-海水耦合热力学系统,以该系统中的物理参数为辨识量,以温度偏差为目标函数,建立了一个参数辨识模型,并证明了该问题最优解的存在性,从而为这类海冰-海水耦合热力学系统参数辨识问题的数值计算提供数学理论依据.     

Explicit Stationary Distribution of the （L, 1）-reflecting Random Walk on the Half Line

In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.     

Similarity degrees for the crossed product of von Neumann algebras

In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.     

Consistent implementation of real fluid EOS in pseudopotential lattice Boltzmann models

Pseudopotential lattice Boltzmann models have emerged as successful methods to simulate liquid-vapor coexistence systems. However, the equation of state (EOS) of such systems, which is found to be thermodynamically consistent, is unique and lacks the potential to cover a broad range of physical fluids. In this study, we employ multiple pseudopotentials and extend the consistent EOS to enhance the capability of pseudopotential models in reproducing a wider range of thermodynamic states. The new system has the format which preserves the consistency between the lattice pressure tensor and the free energy density. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust linear optimization under matrix completion

Linear programming models have been widely used in input-output analysis for analyzing the interdependence of industries in economics and in environmental science.In these applications,some of the entries of the coefficient matrix cannot be measured physically or there exists sampling errors.However,the coefficient matrix can often be low-rank.We characterize the robust counterpart of these types of linear programming problems with uncertainty set described by the nuclear norm.Simulations for the input-output analysis show that the new paradigm can be helpful.     

Existence and stability of traveling waves for an integro-differential equation for slow erosion

We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order nonlinear conservation law where the flux function includes an integral term. We show that there exist unique traveling wave solutions that connect profiles with equilibrium slope at ±∞. Such traveling waves take very different forms from those in standard conservation laws. Furthermore, we prove that the traveling wave profiles are locally stable, i.e., solutions with monotone initial data approach the traveling waves asymptotically as t→+∞$t\to +\infty$.     

Affine embeddings and intersections of Cantor sets

Let E,F⊂R^d$E,F\subset {\mathbb{R}}^d$ be two self-similar sets. Under mild conditions, we show that F   can be C¹$C^1$-embedded into E if and only if it can be affinely embedded into E; furthermore if F cannot be affinely embedded into E  , then the Hausdorff dimension of the intersection E∩f(F)$E\cap f(F)$ is strictly less than that of F   for any C¹$C^1$-diffeomorphism f   on R^d${\mathbb{R}}^d$. Under certain circumstances, we prove the logarithmic commensurability between the contraction ratios of E and F if F can be affinely embedded into E  . As an application, we show that _dimH?E∩f(F)<min?{_dimH?E,_dimH?F}${\dim }_H?E\cap f(F)<\min ?\{{\dim }_H?E,{\dim }_H?F\}$ when E is any Cantor-p set and F any Cantor-q   set, where p,q?2$p,q?2$ are two integers with log?p/log?q∉Q$\log ?p/\log ?q\notin \mathbb{Q}$. This is related to a conjecture of Furstenberg about the intersections of Cantor sets.     

A semigroup approach to an integro-differential equation modeling slow erosion

The paper is concerned with a scalar conservation law with nonlocal flux, providing a model for granular flow with slow erosion and deposition. While the solution u=u(t,x)$u=u(t,x)$ can have jumps, the inverse function x=x(t,u)$x=x(t,u)$ is always Lipschitz continuous; its derivative has bounded variation and satisfies a balance law with measure-valued sources. Using a backward Euler approximation scheme combined with a nonlinear projection operator, we construct a continuous semigroup whose trajectories are the unique entropy weak solutions to this balance law. Going back to the original variables, this yields the global well-posedness of the Cauchy problem for the granular flow model.     

Morrey-Sobolev Spaces on Metric Measure Spaces

In this article, the authors introduce the Newton-Morrey-Sobolev space on a metric measure space (??, d, μ). The embedding of the Newton-Morrey-Sobolev space into the Hölder space is obtained if ?? supports a weak Poincaré inequality and the measure μ is doubling and satisfies a lower bounded condition. Moreover, in the Ahlfors Q-regular case, a Rellich-Kondrachov type embedding theorem is also obtained. Using the Haj?asz gradient, the authors also introduce the Haj?asz-Morrey-Sobolev spaces, and prove that the Newton-Morrey-Sobolev space coincides with the Haj?asz-Morrey-Sobolev space when μ is doubling and ?? supports a weak Poincaré inequality. In particular, on the Euclidean space \({\mathbb R}^n\) , the authors obtain the coincidence among the Newton-Morrey-Sobolev space, the Haj?asz-Morrey-Sobolev space and the classical Morrey-Sobolev space. Finally, when (??, d) is geometrically doubling and μ a non-negative Radon measure, the boundedness of some modified (fractional) maximal operators on modified Morrey spaces is presented; as an application, when μ is doubling and satisfies some measure decay property, the authors further obtain the boundedness of some (fractional) maximal operators on Morrey spaces, Newton-Morrey-Sobolev spaces and Haj?asz-Morrey-Sobolev spaces.     

改性松香键合二氧化硅高效液相色谱固定相的制备及其对三七总皂苷的分离

三七中发挥药效的主要成分为三七皂苷R1、人参皂苷Rg1、人参皂苷Re、人参皂苷Rb1和人参皂苷Rd,用于贫血、冠心病、高血压、脑卒中后遗症等疾病的治疗,但其化学成分多且难分离.将氢化松香丙烯酸羟乙酯(HRHA)通过巯基-烯点击化学反应键合到烷基化硅胶表面,制备出一种新型的改性松香键合二氧化硅高效液相色谱固定相(SiO2...