Nanocatalysis: Mature Science Revisited or Something Really New?

"Nanomania" has reached the area of heterogeneous catalysis. Nanosized catalyst constituents are important for functions that require structural control over several scales of dimension. Nanocatalysis may be understood as a redefinition of catalyst synthesis: multidimensional structural control is exerted by considering catalysts as inorganic polymers rather than as close-packed crystals. Primary, secondary, and tertiary structural hierarchies translate into molecular building blocks and linkers, the defect structure of crystals, and particle morphology. High-throughput techniques and in situ synthetic analysis are the tools required to arrive at better defined catalytic materials that can fulfil the high expectations created by the incorporation of catalysts into the "nano" research field.     

EXPLORATION AND PRACTICE OF HIGHER ORDER CONSTRUCTION FOR TEACHING OF THEORETICAL MECHANICS1)

课程是人才培养的核心要素,课程质量直接决定人才培养质量。为深入推进课堂教学改革,本文以理论力学课程的教学改革和实践为研究平台,结合学生的高阶思维能力培养和课程目标的高阶性设计思路,讨论了理论力学课程高阶性建设的思路和实践。通过构建"1+4+$N$"的课堂教学体系,梳理课程知识点,将教与学相统一。并以点的合成运动为例,分析了课程高阶性建设的实施路径和策略,从而为提高人才培养质量进行的课程教育教学改革提供一些思路和借鉴。     

One Class of Liouville-Type Systems

We prove that a class of systems with the Lagrangian of the form is of the Liouville type. We construct new integrable Hamiltonian systems related to the symmetries of the hyperbolic systems under consideration by substitutions of the Miura transformation type. For one of the systems obtained, we construct the second-order recursion operator.     

Higher Degrees of Distributivity in MV-Algebras

In this paper we deal with the (, )-distributivity of an MV-algebra , where and are nonzero cardinals. It is proved that if is singular and (, 2)-distributive, then it is (, )-distributive. We show that if is complete then it can be represented as a direct product of MV-algebras which are homogeneous with respect to higher degrees of distributivity.     

Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations

In this paper, the authors consider the boundary value problem

and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)-(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373-2379) are discussed.