Femtosecond second-order solitons in optical fiber transmission

A propagation of the femtosecond second-order solitons in an optical fiber is studied. We show that a generalized nonlinear Schrödinger equation well describes the propagation of the second-order soliton even containing only a few optical cycles. The propagations of a 50 fs and a 10 fs second-order soliton in an optical fiber are numerically simulated. It is found that, for the case of 10 fs second-order soliton, the soliton decay is dominated by the third-order dispersion, in contrast to the case of 50 fs second-order solitons, where the soliton decay is dominated by the delayed Raman response. It is also found that the exact delayed Raman response form must be used for the propagation of the 50 fs or less than 50 fs second-order soliton.     

液相沉积法制备光催化活性TiO2薄膜和纳米粉体

采用液相沉积法，在35℃通过向六氟钛酸铵水溶液中添加硼酸和结晶诱导剂锐 铁矿型TiO2纳米晶，沉积出具有光催化活性的Ti02薄膜和纳米粉体．用XRD，AFM， 阶梯仪,UV-vis，BET法对Ti02薄膜和粉体的沉积条件、结构、厚度和性能进行了测 定和表征，并用亚甲兰的降解，评价了TiO2薄膜和纳米粉体的光催化活性．结果表 明，当反应物六氟钛酸铵与硼酸的摩尔比为1：2—1：4时，沉积的粉体和薄膜含有 锐钛矿相Ti02；经300℃热处理的Ti02薄膜和纳米粉体具有最高的光催化活性，它 的光催化活性是未经热处理前的5倍．本文还解释了经300℃热处理的薄膜和纳米粉 体具有最高光催化活性的原因．     

二氢卟吩e~6-6-酰胺衍生物的合成

首次报道了以蚕沙叶绿素初提物为基础原料,经酸降解得到含焦脱镁叶绿酸a和脱镁叶绿酸a的混合物,不经分离直接与胺类反应使脱镁叶绿酸a的戊酮环(V)裂开,合成得11种二氢卟吩e~6-6-酰胺衍生物。提供了一种合成二氢卟吩酰胺的新方法。     

低As压退火对GaAs(001)表面形貌与重构的影响

在低As压条件下退火处理原子级平坦的GaAs(001) βup 2(2×4)重构表面. 利用扫描隧道显微镜对表面进行研究, 发现随着低As压退火时间的延长, 表面形貌与表面重构的演变同步进行. 表面形貌经历了从有序平坦转变为无序平坦, 然后逐渐恢复到有序平坦状态的过程. 表面重构则由βup 2(2×4)重构逐渐转变为(2×6)重构, 然后再转变为锯齿状的(2×6)重构, 并且表面形貌与表面重构的演变存在一定的相互关系.     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.     

On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Pseudo-Anosov Flows and Incompressible Tori

We study incompressible tori in 3-manifolds supporting pseudo-Anosov flows and more generally ZZ subgroups of the fundamental group of such a manifold. If no element in this subgroup can be represented by a closed orbit of the pseudo-Anosov flow, we prove that the flow is topologically conjugate to a suspension of an Anosov diffeomorphism of the torus. In particular it is non singular and is an Anosov flow. It follows that either a pseudo-Anosov flow is topologically conjugate to a suspension Anosov flow, or any immersed incompressible torus can be realized as a free homotopy from a closed orbit of the flow to itself. The key tool is an analysis of group actions on non-Hausdorff trees, also known as R-order trees – we produce an invariant axis in the free action case. An application of these results is the following: suppose the manifold has an R-covered foliation transverse to a pseudo-Anosov flow. If the flow is not an R-covered Anosov flow, then it follows that the manifold is atoroidal.     

Function Spaces of Posets with Projections

This paper investigates function spaces of structures consisting of a partially ordered set together with some directed family of projections.More precisely, given a fixed directed index set (I,), we consider triples (D,,(p _i ) _iI ) with (D,) a poset and (p _i ) _iI a monotone net of projections of D. We call them (I,)-pop's (posets with projections). Our main purpose is to study structure preserving maps between (I,)-pop's. Such homomorphisms respect both order and projections.Any (I,)-pop is known to induce a uniformity and thus a topology. The set of all homomorphisms between two (I,)-pop's turns out to form an (I,)-pop itself. We show that its uniformity is the uniformity of uniform convergence. This enables us to prove that properties such as completeness and compactness transfer to function pop's.Concerning categorical properties of (I,)-pop's, we will see that we are in a lucky situation from a computer scientist's point of view: we obtain Cartesian closed categories. Moreover, by a D -construction we get (I,)-pop's that are isomorphic to their own exponent. This yields new models for the untyped -calculus.