Adaptive decomposition finite difference methods for solving singular problems—A review

Decomposition, or splitting, finite difference methods have been playing an important role in the numerical solution of nonsingular differential equation problems due to their remarkable efficiency, simplicity, and flexibility in computations as compared with their peers. Although the numerical strategy is still in its infancy for solving singular differential equation problems arising from many applications, explorations of the next generation decomposition schemes associated with various kinds of adaptations can be found in many recent publications. The novel approaches have been proven to be highly effective and reliable in operations. In this article, we will focus on some of the latest developments in the area. Key comments and discussion will be devoted to two particularly interesting issues in the research, that is, direct solutions of degenerate singular reaction-diffusion equations and nonlinear sine-Gordon wave equations. Numerical experiments with simulated demonstrations will be given.     

Flexible nanocrystalline‐titania/polyimide hybrids with high refractive index and excellent thermal dimensional stability

In this study, a novel synthetic route was developed to prepare polyimide–nanocrystalline–titania hybrid optical films with a relatively high titania content (up to 50 wt %) and thickness (20–30 μm) from soluble polyimides containing hydroxyl groups. Two series of newly soluble polyimides were synthesized from the hydroxy‐substituted diamines with various commercial tetracarboxylic dianhydrides. The hydroxyl groups on the backbone of the polyimides could provide the organic–inorganic bonding and resulted in homogeneous hybrid solutions by controlling the mole ratio of titanium butoxide/hydroxyl group. AFM, SEM, TEM, and XRD results indicated the formation of well‐dispersed nanocrystalline‐titania. The flexible hybrid films could be successfully obtained and revealed relatively good surface planarity, thermal dimensional stability, tunable refractive index, and high optical transparency. A three‐layer antireflection coating based on the hybrid films was prepared and showed a reflectance of less than 0.5% in the visible range indicated its potential optical applications. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1433–1440, 2010     

有理插值问题不适定的根本原因

1　在 Rm,n中的有理插值问题本文记 Pn为次数不超过 n的一元多项式函数类 ,约定零多项式的次数为 -∞ ,即deg(0 ) =-∞ ;记 Rm,n为分子属于 Pm,分母属于 Pn\{ 0 }的一元有理函数类 .对既约分式Am/Bn∈Rm,n,如果 Bn满足尾项规范条件 (即 Wuytack条件 ) [2 ] ,则称其为标准既约分式 .引进一个新的有理函数类 ,记Rl =Rl- 1 ,0 ∪ Rl- 2 ,1 ∪…∪ R0 ,l- 1 .称 Rl 是自由度为 l的一元有理函数类 .并称其中有理函数类 Rl- 1 - i,i为有理函数类 Rl 的基本子类 ,(i=0 ,1 ,… ,l-1 ) .我们约定 :本文中“有理插值问题”如不特殊声明 ,系指文…     

气相色谱/质谱/质谱法分析石油基引燃物

应用Ｖａｒｉａｎ ３８００ ＧＣ／Ｓａｔｕｒｎ ２０００ ＭＳ 气相色谱／质谱联用分析仪（简称ＧＣ／ＭＳ／ＭＳ）对以汽油、煤渍和紫油为引燃物，燃烧聚丙稀化纤地毯和土壤时的模拟现场物品进行了引燃物的检出。发现采用ＧＣ／ＭＳ／ＭＳ方法比用ＧＣ／ＭＳ方法可以较彻底地排队由于柱注失、地毯燃物分解产物、土壤背景产物和地毯增塑剂等引起的干扰，而且可以提高检测灵敏度。详细考察了以不同质荷比的离子作母离子时对ＧＣ     

Magnetic properties and magnetocaloric effects in amorphous and crystalline Gd55Co35Ni10 ribbons

The magnetic properties and magnetocaloric effects of amorphous and crystalline Gd55Co35Ni10 ribbons are investigated.A main phase with a Ho 12 Co 7-type monoclinic structure(space group P21/c) and a minor phase with a Ho4Co3-type hexagonal structure(space group P63/m) are obtained for crystalline ribbon after annealing.The amorphous ribbons order ferromagnetically and undergo a second-order transition at 192 K.For crystalline Gd55Co35Ni10 ribbons,two magnetic phase transitions occur at 158 and 214 K,respectively.The peak value of-△SM under a field change of 0-5 T is 6.5 J/kg K at 192 K for amorphous Gd55Co35Ni10 ribbons.A relatively large magnetic entropy change(～5.0 J/kg K) under a field change of 0-5 T for the crystalline Gd55Co35Ni10 ribbons is obtained in the temperature interval range of 154-214 K.The large platform of magnetic entropy change and the negligible thermal/magnetic hysteresis loss mean the crystalline Gd55Co35Ni10 compound can satisfy the requirement of the Ericsson-type refrigerator working in the temperature range from 154K to 214K.     

Bis‐benzimidazolium‐palladium system catalyzed Suzuki‐Miyaura coupling reaction of aryl bromides under mild conditions

Bis‐benzimidazolium salts were prepared successfully from commercially available and inexpensive o‐phenylenediamine through a series of simple reactions. The bis‐NHC‐Pd complexes prepared in situ can catalyze Suzuki‐Miyaura cross‐coupling reaction under very mild conditions in aqueous media with excellent yields. The efficiency of this reaction is demonstrated by its compatibility with a range of functional groups. Di‐ortho‐substituted biaryls could be accomplished in 89–99% yields. Moreover, the rigorous exclusion of air or moisture is not required in these transformations.