Mesoscopic structure and properties of liquid crystalline mesophase pitch and its transformation into carbon fiber

The history and present state of the art in the chemistry of mesophase pitch, which is an important precursor for carbon fiber and other high-performance industrial carbons, are reviewed relative to their structural properties. The structural concepts in both microscopic and macroscopic views are summarized in terms of the sp(2) carbon hexagonal plane as a basic unit common to graphitic materials, its planar stacking in clusters, and cluster assembly into microdomains and domains, the latter of which reflect the isochromatic unit of optical anisotropy. Such a series of structural units is described in a semiquantitative manner corresponding to the same units of graphitic materials, although the size and stacking height of the hexagonal planes (graphitic sheets) are very different. Mesophase pitch is a liquid crystal material whose basic structural concepts are maintained in the temperature range of 250 to 350 degrees C. The melt flow and thermal properties are related to its micro- and mesoscopic structure. The structure of mesophase-pitch-based carbon fiber of high tensile strength, modulus, and thermal conductivity has been formed through spinning, and has inherited the same structural concepts of mesophase pitch. Stabilization settles the structure in successive heat treatments up to 3000 degrees C. Carbonization and graphitization enable growth of the hexagonal planes and their stacking into units of graphite. Such growth is governed and controlled by the alignment of micro- and mesoscopic structures in the mesophase pitch, which define the derived carbon materials as nanostructural materials. Their properties are controlled by the nanoscopic units that are expected to behave as nanomaterials when appropriately isolated or handled.     

6-氨基青霉烷酸在弱碱性阴离子树脂IRA67上的吸附研究

用静态法研究了6-氨基青霉烷酸在弱碱性阴离子交换树脂IRA67上的吸附行为．在溶液pH为8．0，6-APA起始浓度介子3.00mg／m1-20．00mg／ml条件下，测定了25℃时IRA67树脂的静态交换动力学曲线、吸附等温线，并求得了IRA67树脂的平衡速率常数及吸附等温线方程．分别用Langmuir型和Frendlich型方程对IRA67树脂吸附等温线进行线性回归拟合，结果表明，6-APA在IRA67树脂上的吸附更符合Langmuir型吸附．     

Covering projective planar graphs with three forests

It is known that all planar graphs and all projective planar graphs have an edge partition into three forests. Gonçalves proved that every planar graph has an edge partition into three forests, one having maximum degree at most four [5]. In this paper, we prove that every projective planar graph has an edge partition into three forests, one having maximum degree at most four.     

The critical probability for Voronoi percolation in the hyperbolic plane tends to 1/2

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster tends to 1/2 as the intensity of the Poisson process tends to infinity. This confirms a conjecture of Benjamini and Schramm [5].     

Metastable decay rates,asymptotic expansions,and analytic continuation of thermodynamic functions

The grand potentialP(z)/kT of the cluster model at fugacityz, neglecting interactions between clusters, is defined by a power series _n Q _n z ⁿ , whereQ _n , which depends on the temperatureT, is the partition function of a cluster of sizen. At low temperatures this series has a finite radius of convergencez _s . Some theorems are proved showing that ifQ _n , considered as a function ofn, is the Laplace transform of a function with suitable properties, thenP(z) can be analytically continued into the complexz plane cut along the real axis fromz _s to + and that (a) the imaginary part ofP(z) on the cut is (apart from a relatively unimportant prefactor) equal to the rate of nucleation of the corresponding metastable state, as given by Becker-Döring theory, and (b) the real part ofP(z) on the cut is approximately equal to the metastable grand potential as calculated by truncating the divergent power series at its smallest term.     

Characterization of the organization in shear layers via the Proper Orthogonal Decomposition

Experiments are performed in an incompressible plane turbulent mixing layer, using various hot wire rake configurations. From these experiments, the Proper Orthogonal Decomposition is applied for kernels where the space-time correlation tensor is evaluated over different spatial meshes and velocity components configurations. The resulting decompositions are then discussed in terms of characterization of the organization of the flow for various scalar or vectorial approaches of the POD. An incrtial range law is evidenced. The instantaneous contribution of the first modes of the POD to the organization of the flow is analyzed. A dynamical behavior for the organization of the flow is observed from the correlation between the first two modes contribution.     

The law of the solution to a nonlinear hyperbolicSPDE

Let { _s,t ,(s,t ₊ ² } be a white noise on ₊ ² . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.This work has been partially supported by the grant of the DGICYT No. PB 930052 and the EU Science project CT 910459.     

Weak separation properties for self-similar sets

We develop a theory for self-similar sets in that fulfil the weak separation property of Lau and Ngai, which is weaker than the open set condition of Hutchinson.

     

On two--block--factor sequences and one--dependence

The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.

     

Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.