Multi-adjoint algebras versus non-commutative residuated structures

Adjoint triples and pairs are basic operators used in several domains, since they increase the flexibility in the framework in which they are considered. This paper introduces multi-adjoint algebras and several properties; also, we will show that an adjoint triple and its “dual” cannot be considered in the same framework.Moreover, a comparison among general algebraic structures used in different frameworks, which reduce the considered mathematical requirements, such as the implicative extended-order algebras, implicative structures, the residuated algebras given by sup-preserving aggregations and the conjunctive algebras given by semi-uninorms and u-norms, is presented. This comparison shows that multi-adjoint algebras generalize these structures in domains which require residuated implications, such as in formal concept analysis, fuzzy rough sets, fuzzy relation equations and fuzzy logic.     

Modeling of pair distribution functions for XAFS in disordered systems

A commonly used expression for modeling the XAFS of highly disordered systems is shown to generate substantial systematic errors in the coordination number in many cases of practical interest. This expression is corrected and generalized. Further, a simpler and more flexible model distribution is proposed, and the corresponding XAFS expression is derived. Comparison with experimental and simulated data show that the new expressions are useful in cases of high disorder for which the cumulant expansion loses its utility, and they explicitly account for the k-dependence of the mean free path.     

A note on limiting infisup theorems

We show that the limiting infisup theorem of Blair, Duffin and Jeroslow (1982) is a consequence of the classical bifunctional duality. By doing so we generalize their results and prove another limiting infisup theorem for convex quasi-concave functions.     

Weak Density of Smooth Maps in W 1, 1(M,N) for Non-Abelian π1(N)

We prove that smooth maps are dense in the sense of biting convergence in W ^{1, 1}(M, N) when M and Nare compact Riemannian manifolds and N is closed.     

Children’s use of realistic considerations in problem solving: some English evidence

This is the second of two papers exploring children’s responses to an extended version of a division-with-remainder problem intended to elicit general rather than particular realistic considerations during mathematical problem solving. Responses to two problems are analyzed. The first is a ‘realistically’ contextualised item drawn from national tests in England whose ambiguities have been previously discussed (Cooper, 1992); the second is a version of this problem revised to encourage a wider range of realistic responses. In Cooper and Harries (2002), the responses of children at the end of their first year of secondary schooling were analyzed. Here the responses of children at the end of their primary schooling are analyzed and compared with the previous results. It is shown that many children, given suitable encouragement, are willing and able to enter into an extended form of realistic thinking during problem solving, although the original test item renders this invisible.     

Computing lower and upper bounds for a large-scale industrial job shop scheduling problem

In this paper we present a case study from the lighting industry concerned with the scheduling of a set of job families each representing the production of a particular end-item in a given quantity. It is a job shop type problem, where each job family has a number of routing alternatives, and the solution has to respect batching and machine availability constraints. All jobs of the same job family have a common release date and a common due date, and they differ only in size. The objective is to minimize the total tardiness of the job families, rather than that of individual jobs. We propose a two-phase method based on solving a mixed-integer linear program and then improving the initial solution by tabu search. We evaluate our method on real-world as well as generated instances.     

循环流动固定床光催化反应器动力学数学模拟

以甲基橙为模型反应物,研究了连续循环固定床光催化反应器的动力学过程.根据光催化氧化过程特点,分析并建立了准一级反应动力学方程,对该反应系统的动力学过程进行动态数学模拟,用四阶Runge-Kutta法进行数值计算,结果表明数学模拟与实验数据相吻合.在该光催化反应体系中,处理量增加时实际反应速率常数k基本不变,而表观反应速率常数kapp变小,二者之间关系与反应器体积对处理量体积比（γ）密切相关;反应速率常数受起始浓度影响很大,在15～150 μmol•L－1浓度范围内,lnk=－0.48ln[c0]＋1.42;反应速率常数与光强的关系为k∝I0.5;反应速率常数受溶液pH值的影响也很大.     

Position of starting spot in TLC: Influence on average plate height

Summary The influence of the distance between the solvent entry and the starting zone positions, Z₀, on the average plate height was studied. This factor was found to be of major importance and could be optimized. The Guiochon and Siouffi model greatly underestimates the plate height for low values of Z₀.