硅团簇结构和碎片行为的紧束缚理论方法

利用紧束缚分子动力学模拟退火方法研究了硅团簇Sin(n=2—14)的结构性质和能量.通过与前人工作结果(Si2—Si10)的比较,发现本理论方法的结果相当准确地再现了从头计算的结论.对较大的硅团簇所作的计算给出了有意义的结构预测.从能量观点出发,计算结果表明原子数分别为4,6,7,10,12和14的硅团簇较为稳定.还进一步研究了硅团簇的碎片行为,理论计算的结果表明较大的硅团簇的稳定碎片产物通常包括一个或两个“幻数”团簇     

Cocycle deformations and Galois objects for semisimple Hopf algebras of dimension p3 and pq2

Let p and q be distinct prime numbers. We study the Galois objects and cocycle deformations of the noncommutative, noncocommutative, semisimple Hopf algebras of odd dimension $p^3$ and of dimension $p{q}^2$. We obtain that the $p+1$ non-isomorphic self-dual semisimple Hopf algebras of dimension $p^3$ classified by Masuoka have no non-trivial cocycle deformations, extending his previous results for the 8-dimensional Kac–Paljutkin Hopf algebra. This is done as a consequence of the classification of categorical Morita equivalence classes among semisimple Hopf algebras of odd dimension $p^3$, established by the third-named author in an appendix.     

An Upper Bound on the Number of Iterations for Transforming a Boolean Function of Degree Greater or Equal Than 4 to a Function of Degree 3

The difficulty involved in characterizing the weight distribution of all Boolean functions of degree 3 is well-known [2, p. 446]. In [1] the author introduces a transformation on Boolean functions which changes their weights in a way that is easy to follow, and which, when iterated, reduces the degree of the function to 2 or 3. He concludes that it is just as difficult to characterize the weight of any function of degree 3 as it is for any other degree. The application of this transformation on a Boolean function defined on , increases the number of its variables by two. On the other hand, in order to reduce the degree of a function to 2 or 3 it is necessary to apply the tranformation a number of times that grows exponentially with respect to m. In this paper, a factorization method on Boolean functions that allows the establishment of an upper bound for the number of applications of the transformation is presented. It shows that, in general, it is possible to significantly decrease the number of iterations in this process of degree reduction.     

Necessary Conditions for Optimal Terminal Time Control Problems Governed by a Volterra Integral Equation

We prove the maximum principle for optimal terminal time control problems with the state governed by a Volterra integral equation and constraints depending on the terminal time and the state. We use Pontryagin-type perturbations to reduce the problem to a well-known result of optimizati n theory.Communicated by D. A. Carlson     

On the Enumeration of ‐Optimal and Minimax‐Optimal k‐Circulant Supersaturated Designs

In recent years, several methods have been proposed for constructing ‐optimal and minimax‐optimal supersaturated designs (SSDs). However, until now the enumeration problem of such designs has not been yet considered. In this paper, ‐optimal and minimax‐optimal k‐circulant SSDs with 6, 10, 14, 18, 22, and 26 runs, factors and are enumerated in a computer search. We have also enumerated all ‐optimal and minimax‐optimal k‐circulant SSDs with (mod 4) and . The computer search utilizes the fact that theses designs are equivalent to certain 1‐rotational resolvable balanced incomplete block designs. Combinatorial properties of these resolvable designs are used to restrict the search space.     

Sommerfeld's solution as the limiting amplitude and asymptotics for narrow wedges

We analyze the Sommerfeld solution to the stationary diffraction by a half‐plane. We prove that this solution is the limiting amplitude for time‐dependent scattering of incident plane waves with a broad class of the profile functions. We also show that this solution is the asymptotics of the limiting amplitudes of solutions to time‐dependent scattering problem with narrow wedges when the angle of the wedge tends to zero.     

Topological超共形代数的Leibniz中心扩张

通过计算得到了Topological N=2超共形代数丁的Leibniz二上同调群,从而确定了此代数的Leibniz中心扩张.     

一种新型可光降解的PVC-OA-TiO_2纳米复合膜

采用包埋技术制备了一种新型可光降解的聚氯乙烯-草酸-TiO_2(PVC-OA-TiO_2)纳米复合膜,并研究了紫外光照射条件下该复合膜的光催化降解情况.结果表明,该纳米复合膜的光催化降解是一个氧化断链过程,经紫外光照射310 h后失重率达到55%,是PVC-TiO_2复合膜的2倍,是纯PVC膜的3.5倍,说明草酸的掺杂可以促进PVC-OA-TiO_2复合膜更快地被光降解.草酸作为一个良好的电子给体,能不可逆地与TiO_2表面产生的空穴或表面羟基反应,抑制电子和空穴的复合,从而显著提高PVC-OA-TiO_2的光催化降解速率.