A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

A New Modal Lindström Theorem

We prove new Lindstr?m theorems for the basic modal propositional language, and for some related fragments of first-order logic. We find difficulties with such results for modal languages without a finite-depth property, high-lighting the difference between abstract model theory for fragments and for extensions of first-order logic. In addition we discuss new connections with interpolation properties, and the modal invariance theorem. Mathematics Subject Classification (2000): Primary 03B45; Secondary 03C95     

调制不稳定性对级联放大光纤传输系统信噪比的影响

在考虑光纤损耗和级联放大器的情况下，推导了调制不稳定性的产生条件和增益的普适解析表达式，分析了调制不稳定性对信噪比的影响，给出了一个新的计算信噪比的表达式。     

Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.     

Mössbauer study on LiFePO4 cathode material for lithium ion batteries

Crystalline LiFePO₄ has been synthesized using solid-state, spray pyrolysis, and wet chemical methods. The crystal parameters were obtained from Rietveld’s refinement methods of the X-ray diffraction patterns. A detailed investigation of the Fe valency carried out using Mössbauer spectroscopy at room temperature indicates that Fe is predominantly present in its bivalent state.     

双曲函数型辅助方程构造具5次强非线性项的波方程的新精确孤波解

在辅助方程法的基础上利用两种函数变换和一种双曲函数型辅助方程，通过符号计算系统Mathematica构造了在力学当中一个重要的模型，有5次强非线性项的波方程的新三角函数型和双曲函数型精确孤波解.这种方法寻找其他具5次强非线性项的非线性发展方程的新精确解方面具有普遍意义. 关键词： 双曲函数型辅助方程 函数变换 具5次强非线性项的波方程 精确孤波解     

Dimensional Properties of Fractional Brownian Motion

Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.     

Mechanosynthesis of YIG and GdIG: A Structural and Mössbauer Study

We have investigated the mechanosynthesis of gadolinium and yttrium iron garnets by high-energy ball-milling of α-Fe₂O₃ and Gd₂O₃ or α-Fe₂O₃ and Y₂O₃, respectively, followed by short thermal annealings conducted at moderate temperatures. The samples were characterized by X-ray diffraction and Mössbauer spectroscopy, in order to determine the influence of the milling time and annealing conditions on the final products. For as-milled samples of each rare-earth system, the results revealed the formation of perovskite phases, in relative amounts that depend on the milling time. The formation of garnet phases was observed in as-annealed samples treated at 1000°C for 2 h or 1100°C for 3 h, i.e., at very modest annealing requirements when compared with ordinary solid-state-reaction processes performed without previous high-energy milling. Also, the occurrence was verified of a milling time for which the relative amount of garnet phases formed by annealing was maximized. This time depends on the rare-earth composing the garnet phase and on the annealing temperature.     

Total absolute curvature and tightness of noncompact manifolds

In the first part we prove an extension of the Chern-Lashof inequality for noncompact immersed manifolds with finitely many ends. For this we give a lower bound of the total absolute curvature in terms of topological invariants of the manifold. In the second part we discuss tightness properties for such immersions. Finally, we give an upper bound for the substantial codimension.

     

Mössbauer study of nanodimensional nickel ferrite – mechanochemical synthesis and catalytic properties

Iron–nickel spinel oxide NiFe₂O₄ nanoparticles have been prepared by the combination of chemical precipitation and subsequent mechanical milling. For comparison, their analogue obtained by thermal synthesis is also studied. Phase composition and structural properties of iron–nickel oxides are investigated by X-ray diffraction and Mössbauer spectroscopy. Their catalytic behavior in methanol decomposition to CO and methane is tested. An influence of the preparation method on the reduction and catalytic properties of iron–nickel samples is established.