A continuous function space with a Faber basis

Let be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (P_n)_n=0^∞ with deg P_n=n such that every fC(S) has a unique representation f=∑_i=0^∞ α_iP_i and call such a basis Faber basis. In the special case of , 0<q<1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A(S_q)≠U(S_q)=C(S_q), where A(S_q) is the so-called Wiener algebra and U(S_q) is the set of all fC(S_q) which are uniquely represented by its Fourier series.     

复流形局部q-凸楔形上带权的同伦公式

本文得到复流形局部q-凸楔形上(r,s)型微分形式的带权的同伦公式和(r,s)型的方程的带权的连续解,并给出(r,s)型微分形式的不含边界积分的新的带权的同伦公式和(r,s)型的方程的新的带权的连续解.这些新的带权公式尤其适用于具有非光滑边界的局部q-凸楔形,这时不但可以避免边界积分的复杂估计,而且积分密度也不必在边界有定义,只要在区域上有定义就行.其次,引进权因子,带权的积分公式在应用上(比如在函数的插值方面)具有更大的灵活性.     

The course scheduling problem at Lufthansa Technical Training

Lufthansa Technical Training GmbH (LTT) performs training courses for Lufthansa Technik AG as well as for several other international airlines. Courses of about 670 different types are offered of which several hundred take place each year. The course scheduling problem faced by LTT is to construct a yearly schedule which maximizes the profit margin incurred while meeting a variety of complex precedence, temporal, and resource-related constraints. A “good” operational schedule should also meet a number of additional subordinate objectives. We formalize the problem and develop a heuristic scheme along with several priority rules, as well as a local search algorithm to determine well-suited weights for weighted composite rules. The operational planning situation of 1996 served as our major test instance; additional test instances were constructed by modifying this data. Several computational experiments were carried out to evaluate the performance of the algorithms. It turned out that the best so-found schedule is substantially better in terms of the profit margin incurred than the solution manually constructed by LTT.     

Polynomial expansion of basis sets: Alternatives to fully optimized exponents

Alternatives based on polynomial expansions of gaussian basis set exponents are introduced and evaluated. The formulas presented here outperform methods based upon the even-tempered formula or combinations of it. They closely match the performance of other methods based upon larger polynomial expansions of the logarithm of the exponents using the same or one less parameter per orbital angular symmetry.     

Fe/Zn双金属氰化物催化剂催化环氧丙烷聚合的活性结构研究

以氯化锌、铁氰化钾（含有整合剂）的水溶液为原料，合成了铁锌双金属氰化物（DMC）催化剂。为获得高活性的DMC催化剂，需将叔丁醇 、多元醇螯合剂螯合至其结构中，用XRD、XPS等分析手段，对铁锌DMC催化剂的结构与活性进行分析表征。实验发现，DMC催化剂的晶体结构与螯合剂密切相关，螯合剂能显著降低DMC催化剂的结晶程度，从而提高DMC催化剂的活性。同时，氯化锌过量也有利于DMC催化剂活性的提高。并表征了相关DMC催化剂的活性中心。     

Static atomic displacements of Sn in disordered NiAs/Ni2In type HT-Ni1+δSn

The crystal structures of the intermediate solid solution HT (high temperature) Ni_1+δSn with δ=0.28, 0.52 and 0.61 (refined Ni contents) have been analyzed in detail by X-ray diffraction on single crystals. The previously reported basic atomic arrangement, i.e., a NiAs/Ni₂In structure type (P6₃/mmc, Ni(1) on 2a, 0 0 0, Ni(2) with an occupancy δ on 2d, and Sn on 2c, ), is confirmed. However, strong anisotropic atomic displacements occur for Sn within the a-b plane of the hexagonal unit cell, which require a Gram-Charlier expansion of the probability density function of Sn in order to obtain a good fit to the diffraction data. Direction, magnitude and the concentration dependence of the displacements can be interpreted in terms of the geometrical requirements of the different local atomic configurations in the planes z=±1/4, so that the displacements can be identified as static ones.     

Hamiltonian nilpotent saddles of linear plus cubic homogeneous polynomial vector fields

We completely characterize the global phase portraits in the Poincaré disk for all planar Hamiltonian vector fields with linear plus cubic homogeneous terms having a nilpotent saddle at the origin.     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.     

An application of the generalized alternating polynomials to the numerical solution of Fredholm integral equations

Generalized alternating polynomials have been introduced by the author earlier. In the present paper their indirect analogue is constructed for numerical solution of the Fredholm linear integral equations. Although the proposed method is a particular case of the general projection scheme, its valuable feature is the presence of a sequence of parameters, which, for sufficiently smooth kernels and inhomogeneous terms, serves as an indicator of the quality of approximation.