The magnetization behavior of nanocrystalline permanent magnets based on the Stoner–Wohlfarth Model

The magnetization behavior in nanocrystalline permanent magnets has been investigated using mean field Stoner–Wohlfarth model. The model is comparatively simple but allows the numerical treatment of extended nanostructures. The predominant intergrain exchange coupling is expressed by a mean field constant N_m in spite of no explicit relationship between N_m and the microstructure. By this model, the experimental phenomena, such as the remanence enhancement, the shape of demagnetization curve, the irreversible magnetization, the exchange bias field and their respective temperature dependence, can be well explained. The N_m dependence of magnetic properties has been extensively discussed in the present paper.     

Level of nodes in increasing trees revisited

Simply generated families of trees are described by the equation T(z) = ϕ(T(z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ { 1,…,n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are especially important: recursive trees, heap ordered trees, and binary increasing trees. They belong to the subclass of very simple families of increasing trees, which can be characterized in 3 different ways. This paper contains results about these families as well as about polynomial families (the function ϕ(u) is just a polynomial). The random variable of interest is the level of the node (labelled) j, in random trees of size n ≥ j. For very simple families, this is independent of n, and the limiting distribution is Gaussian. For polynomial families, we can prove this as well for j,n → ∞ such that n − j is fixed. Additional results are also given. These results follow from the study of certain trivariate generating functions and Hwang's quasi power theorem. They unify and extend earlier results by Devroye, Mahmoud, and others. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Certified reference materials for the quality control of analysis in the environment

Summary The Community Bureau of Reference (BCR) has undertaken the production of a wide range of certified reference materials (CRMs) for the improvement of accuracy and measurement harmony in various areas of concern at European Community level. This paper provides an overview of the sectors of the BCR-programme in the field of environment i.e. for water systems (water, sediment, biota), soil analysis (soil, fertiliser, waste), plant analysis (aquatic and terrestrial plants), analysis related to animals (e.g. muscle or liver) or man (e.g. industry and food).     

An analytic approach for the analysis of rotations in fringe-balanced binary search trees

This paper presents an analytic approach to the construction cost of fringe-balanced binary search trees. In [7], Mahmoud used a bottom-up approach and an urn model of Pólya. The present method is top-down and uses differential equations and Hwang's quasi-power theorem to derive the asymptotic normality of the number of rotations needed to construct such afringe balanced search tree. We also obtain the exact expectation and variance with this method. Although Pólya's urn model is no longer needed, we also present an elegant analysis of it based on an operator calculus as in [4].This research was supported by the Austrian Research Society (FWF) under the project number P12599-MAT.     

Colliding stacks: A large deviations analysis

We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely to shrink than grow, but with the probabilities of insertion and deletion allowed to depend arbitrarily on stack height as a fraction of m. New results are obtained on the m → ∞ asymptotics of the stack collision time, and of the final stack heights. The results of Wentzell and Freidlin on the large deviations of Markov chains are used, and the relation of their formalism to the Hamiltonian formulation of classical mechanics is emphasized. Certain results on higher-order asymptotics follow from WKB expansions.     

Monte Carlo Hamiltonian: Linear Potentials

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.     

Mesophase behaviour of 2,5-dibenzoyloxy-p-benzoquinone derivatives and tetrahydrobenzene tetraesters

The synthesis of 2,5-dibenzoyloxy-p-benzoquinone derivatives, their products after reduction and tetraesters from tetrahydroxybenzene prepared from those products is described. Their phase behaviour was investigated by differential scanning calorimetry and polarizing microscopy and is discussed in terms of their detailed structure.