含非局部源的反应扩散问题

本文对含非局部源反应扩散方程的定常问题讨论了正解的存在性，对依赖时间的解，给出了整体存在条件和有限时间爆破条件。     

溶胶-凝胶法制备NixCo1-xCoAlO4尖晶石型复合氧化物及其催化分解N2O性能

用溶胶凝胶法制备了一组Ni_xCo_1-xCoAlO₄尖晶石型复合氧化物,并采用表面润湿浸渍K₂CO₃溶液进行了K掺杂改性,用于有氧气氛下的N₂O催化分解反应.采用N₂物理吸附、X-射线衍射(XRD)、扫描电镜(SEM)、H₂-程序升温还原(H₂-TPR)等技术对催化剂进行了表征,考察了催化剂组成、母液pH值、K负载量等制备参数对其催化活性的影响.结果表明,母液pH值为3、K/(Ni+Co)物质的量比为0.1的K/Ni_0.15Co_0.85CoAlO₄催化剂具有较高的N₂O分解活性,450 ℃ N₂O可完全分解.助剂K的加入弱化了催化剂表面金属氧键,提高了催化剂的还原性、催化活性和抗水性.     

臭氧氧化结合湿法喷淋对玻璃窑炉烟气同时脱硫脱硝实验研究

采用臭氧氧化结合湿法喷淋对模拟玻璃窑炉烟气开展了同时脱硫脱硝实验研究.采用不同溶液(NaOH、Na₂S)进行了喷淋实验.结果表明,保证溶液pH值在10以上,NaOH浓度对NO_x脱除效率无影响,SO₂的存在促进了NO_x吸收.当O₃/NO物质的量比为1.6、溶液NaOH浓度为0.5%时,NO_x脱除效率可达70%,SO₂脱除效率在99%以上.往喷淋液中添加Na₂S,NO_x脱除效率随Na₂S浓度增加而提高,SO₂的存在对NO_x脱除效率无影响.当O₃/NO物质的量比为1.2、溶液中NaOH浓度为0.5%、添加剂Na₂S浓度为0.6%时,NO_x脱除效率可达70%,SO₂脱除效率在95%以上.60 min长时间运行实验证明,模拟烟气中的NO_x经碱液和添加剂吸收后主要以NO^-₂的形式存在于喷淋液中,且NO_x脱除效率不随溶液pH值的变化而变化.     

A Film-Flow Model to Describe Free Water Transport during Drying of a Hygroscopic Capillary Porous Medium

In this work, a two-phase film-flow model in a hygroscopic capillary tube is developed and extended to describe the two-phase capillary viscous transport in a network of parallel capillary tubes in terms of relative permeabilities. This film-flow approach is further considered to predict the longitudinal moisture transport in oak wood during drying. Numerical results obtained from this prediction are compared with data of convective drying experiments performed on samples of this wood. The comparison seems to confirm the physical relevance of a film-flow model to correctly represent the moisture transfer until the hygroscopic regime is reached.     

Regenerative cascade homotopies for solving polynomial systems

A key step in the numerical computation of the irreducible decomposition of a polynomial system is the computation of a witness superset of the solution set. In many problems involving a solution set of a polynomial system, the witness superset contains all the needed information. Sommese and Wampler gave the first numerical method to compute witness supersets, based on dimension-by-dimension slicing of the solution set by generic linear spaces, followed later by the cascade homotopy of Sommese and Verschelde. Recently, the authors of this article introduced a new method, regeneration, to compute solution sets of polynomial systems. Tests showed that combining regeneration with the dimension-by-dimension algorithm was significantly faster than naively combining it with the cascade homotopy. However, in this article, we combine an appropriate randomization of the polynomial system with the regeneration technique to construct a new cascade of homotopies for computing witness supersets. Computational tests give strong evidence that regenerative cascade is superior in practice to previous methods.     

一元多项式学习中易犯的几个错误

结合一元多项式中的一些重要概念,如多项式的最大公因式、多项式的重根及不可约多项式等,分析一元多项式学习中易犯的错误,并强调运用定理时要注意其适用的条件和前提．     

Bounds on the largest Kronecker and induced multiplicities of finite groups

We give new bounds and asymptotic estimates on the largest Kronecker and induced multiplicities of finite groups. The results apply to large simple groups of Lie type and other groups with few conjugacy classes.     

Factorizations of tropical and sign polynomials

In this text, we study factorizations of polynomials over the tropical hyperfield and the sign hyperfield, which we call tropical polynomials and sign polynomials, respectively. We classify all irreducible polynomials in either case. We show that tropical polynomials factor uniquely into irreducible factors, but that unique factorization fails for sign polynomials. We describe division algorithms for tropical and sign polynomials by linear terms that correspond to roots of the polynomials.     

Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type

We construct the Grothendieck rings of a class of 2n²dimensional semisimple Hopf Algebras H_2n²,which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H8.All irreducible H_2n²-modules are classified.Furthermore,we describe the Grothendieck rings r(H_2n²)by generators and relations explicitly.