Irradiation-induced reduction and luminescence properties of Sm doped in BaBPO5

Usually, Sm²⁺ ions could be reduced by heating the materials in reducing atmospheres. Exposure to ionizing radiations is also known to cause Sm³⁺→Sm²⁺ conversion. In this work, BaBPO₅ doped with the samarium ion was prepared by high temperature solid-state reaction. Sm²⁺ ions were obtained by two different reduction methods, i.e., heating in H₂ reduced atmosphere and X-ray irradiation. The measurements of X-ray diffraction (XRD), and scanning electron microscope (SEM) were investigated. It is found that the conversion of Sm³⁺→Sm²⁺ is very efficient in BaBPO₅ hosts after X-ray irradiation. Sm²⁺ ions under these two reduction methods exhibit different characteristics that were studied by measurements of luminescence and decay. The results showed that the luminescence properties of Sm²⁺ ions in BaBPO₅ were highly dependent on the sample preparation conditions.     

Preparation and characterization of rigid poly(vinyl chloride)/MMT nanocomposites. II. XRD,morphological and mechanical characteristics

A Haake torque rheometer equipped with an internal mixer is used to study the influence of the amount of sodium montmorillonite (Na⁺‐MMT) and organically modified MMT (O‐MMT) on X‐ray diffraction (XRD), morphology, and mechanical characteristics of rigid poly (vinyl chloride) (PVC)/Na⁺‐MMT and PVC/O‐MMT nanocomposites, respectively. Results of XRD and transmission electron microscopy (TEM) indicate that MMT is partially encapsulated and intercalated in the rigid PVC/Na⁺‐MMT nanocomposites. However, results of XRD and TEM show MMT is partially intercalated and exfoliated in the rigid PVC/O‐MMT nanocomposites. Tensile strength, yield strength, and elongation at break of the rigid PVC/MMT nanocomposites were improved simultaneously with adding 1–3 wt % Na⁺‐MMT or O‐MMT with respect to that of pristine PVC. However, the addition of Na⁺‐MMT or O‐MMT should be kept as not more than 3 wt % to optimize the mechanical properties and the processing stability of the rigid PVC/MMT nanocomposites. SEM micrographs of the fractured surfaces of the rigid PVC/Na⁺‐MMT and PVC/O‐MMT nanocomposites both before and after tensile tests were also illustrated and compared. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2145–2154, 2006     

Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

Multiple ergodic theorems

Given measure preserving transformationsT ₁,T ₂,...,T _s of a probability space (X,B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {T_1^n f_1 \cdot T_2^n f_2 } \cdot \cdots \cdot T_s^n f_s $$ wheref ₁,f ₂,...,f _s ?L ^∞(X,B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) inL ²-norm is ∫ _x f ₁ dμ·∫ _x f ₂ dμ...∫ _x f _s dμ for anyf ₁,f ₂...,f _s ?L ^∞(X,B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.     

Correlation length bounds for disordered Ising ferromagnets

Thed-dimensional, nearest-neighbor disordered Ising ferromagnet: $$H = - \sum {J_{ij} \sigma _i \sigma _j }$$ is studied as a function of both temperature,T, and a disorder parameter,λ, which measures the size of fluctuations of couplingsJ _ij ≧0. A finite-size scaling correlation length,ζ _f (T, λ), is defined in terms of the magnetic response of finite samples. This correlation length is shown to be equivalent, in the scaling sense, to the quenched average correlation lengthζ(T, λ), defined as the asymptotic decay rate of the quenched average two-point function. Furthermore, the magnetic response criterion which definesζ _f is shown to have a scale-invariant property at the critical point. The above results enable us to prove that the quenched correlation length satisfies: $$C\left| {\log \xi (T)} \right|\xi (T) \geqq \left| {T - T_c } \right|^{ - {2 \mathord{\left/ {\vphantom {2 d}} \right. \kern-\nulldelimiterspace} d}}$$ which implies the boundv≧2/d for the quenched correlation length exponent.