供应链视角下的增值税改革影响研究

构建了一个制造商和一个零售商所组成的两级供应链模型,研究增值税税率下调对供应链决策和社会福利的影响.结果表明,下调制造商、零售商增值税税率都会使产品零售价降低,提高零售商和制造商的利润.下调增值税税率给制造商带来的利润增量大于给零售商带来的利润增量.制造商税率下调导致批发价降低,零售商税率下调反而提高批发价.社会福利的变化趋势与潜在需求规模有关.当潜在需求规模较高时,社会福利总是随降税幅度的增大而增大,且税率降低后的社会福利大于税率降低前;当潜在需求规模中等时,社会福利随降税幅度的增大而减小,但税率降低后的社会福利仍大于税率降低前;当潜在需求规模较小时,社会福利随降税幅度的增大而减小,增值税税率下调损害了社会福利.     

Optimal control and numerical methods for hybrid stochastic SIS models

This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can influence the infectivity period, our aim is to minimize the expected discounted cost due to illness, medical treatment, and the adverse effect on the society. In addition, a model with the incorporation of vaccination is proposed. Numerical schemes are developed by approximating the continuous-time dynamics using Markov chain approximation methods. It is demonstrated that the approximation schemes converge to the optimal strategy as the mesh size goes to zero. Numerical examples are provided to illustrate our results.     

On the numerical solution of ill‐conditioned linear systems by regularization and iteration

We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning.     

Development of an improved divergence‐free‐condition compensated coupled framework to solve flow problems with time‐varying geometries

In this article a coupled version of the improved divergence‐free‐condition compensated method will be proposed to simulate time‐varying geometries by direct forcing immersed boundary method. The proposed method can be seen as a quasi‐multi‐moment framework due to the fact that the momentum equations are discretized by both cell‐centered and cell‐face velocity. For simulating time‐varying geometries, a semi‐implicit iterative method is proposed for calculating the direct forcing terms. Treatments for suppressing spurious force oscillations, calculating drag/lift forces, and evaluating velocity and pressure for freshly cells will also be addressed. In order to show the applicability and accuracy, analytical as well as benchmark problems will be investigated by the present framework and compared with other numerical and experimental results.     

1,3-丁二烯选择性加氢催化剂的设计策略以及构效关系

催化裂化是石油化工的核心单元之一.从催化裂化尾气中分离出来的碳四馏分富含许多的不饱和烯烃,如1-丁烯、顺、反式-2-丁烯以及少量的1,3-丁二烯,这些不饱和烯烃可以通过后续聚合反应,生成合成橡胶和工程塑料的重要原料,具有重要的应用价值.上述工艺过程对原料中1,3-丁二烯的含量(<100~200 ppm)有严苛的要求.采用选择性加氢技术对碳四馏分中的1,3-丁二烯进行选择性加氢,将其转化为更高附加值的单烯烃是一个理想的解决方案.然而,1,3-丁二烯加氢反应得到的单烯烃可能发生深度加氢得到副产物丁烷.因此,开发高效选择性加氢催化剂对碳四资源的利用具有重要的现实意义.另一方面,1,3-丁二烯加氢反应可以作为模型反应,用来考察选择性加氢催化剂的性能.基于此,该反应无论在工业界还是学术界均受到广泛关注.尽管如此,有关1,3-丁二烯加氢催化剂研究进展方面的综述极少.仅有关于1,3-丁二烯加氢作为模型反应的综述报道.本文对过去半个世纪以来1,3-丁二烯加氢反应中不同催化剂的发展历程进行系统综述,特别是包括Pd,Pt和Au等的单一贵金属催化剂.重点介绍以下内容:(1)固体催化剂构效关系,包括活性金属尺寸效应、晶面和形貌效应以及载体效应(晶相、孔道和酸碱性);(2)高性能催化剂的设计新策略,如单原子催化剂、核壳结构催化剂、金属-离子液复合催化体系以及载体的形貌调控;(3)催化剂的反应机理和失活机理.提出了1,3-丁二烯选择性加氢高性能催化剂开发面临的挑战,并对潜在的发展方向进行了展望.本文认为随着纳米技术和金属纳米材料合成方法的快速发展,对贵金属活性组分进行原子层面上的调控(包括形貌、尺寸以及单原子配位环境等)已成为可能.这将有助于研制出一类新型高性能选择性加氢催化材料,从而实现高转化率条件下高附加值单烯烃的定向转化.此外,载体的酸碱性和孔道结构的调控有助于进一步调节催化剂的抗积炭性能,也是未来发展的一个重要方向.     

新型功能碳材料的高压截获

高性能功能材料在诸多领域具有广泛的应用前景,是人们一直关注的研究热点。高压可以有效地改变物质的原子间距和成键方式,是获得新型功能材料的重要途径。在碳材料的高压研究中,许多有趣的功能碳材料,如光学透明碳、高强度弹性碳和超硬非晶碳等,已经通过不同的碳前驱体合成。本文简要介绍了作者近年来在低维碳基纳米复合材料高压研究中取得的进展,基于设计的不同低维碳前驱体,高压下截获了具有超硬特性、新型压致共价聚合及发光增强的碳材料。     

Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.     

On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.