Magneto-optical trapping of Stark-slowed metastable He atoms

We report on the first successful loading of a magneto-optical trap (MOT) with metastable He atoms from a Stark-slower. Thereby, deceleration of the atoms relies on laser-atom interaction in an inhomogeneous electric field. We show that the results obtained are comparable with early results from other groups achieved with a Zeeman slower. The Stark slower, which is able to fully control the final velocity of the atomic He beam, is the first step in achieving complete spin independent kinematic control based solely on electric fields. Received 2 October 2002 / Received in final form 20 January 2003 Published online 29 April 2003 RID="a" ID="a"e-mail: eichmann@mbi-berlin.de     

A unified view of some vertex operator constructions

We present a general vertex operator construction based on the Fock space for affine Lie algebras of typeA. This construction allows us to give a unified treatment for both the homogeneous and principle realizations of the affine Lie algebras as well as for some extended affine Lie algebras coordinatized by certain quantum tori.     

Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to N-waves

The goal of this article is to develop a new technique to obtain better asymptotic estimates for scalar conservation laws. General convex flux, f″(u)?0, is considered with an assumption . We show that, under suitable conditions on the initial value, its solution converges to an N-wave in L¹ norm with the optimal convergence order of O(1/t). The technique we use in this article is to enclose the solution with two rarefaction waves. We also show a uniform convergence order in the sense of graphs. A numerical example of this phenomenon is included.     

On the Combinatorics of Rooted Binary Phylogenetic Trees

We study subtree-prune-and-regraft (SPR) operations on leaf-labelled rooted binary trees, also known as rooted binary phylogenetic trees. This study is motivated by the problem of graphically representing evolutionary histories of biological sequences subject to recombination. We investigate some basic properties of the induced SPR-metric on the space of leaf-labelled rooted binary trees with n leaves. In contrast to the case of unrooted trees, the number |U(T)| of trees in which are one SPR operation away from a given tree depends on the topology of T. In this paper, we construct recursion relations which allow one to determine the unit-neighbourhood size |U(T)| efficiently for any tree topology. In fact, using the recursion relations we are able to derive a simple closed-form formula for the unit-neighbourhood size. As a corollary, we construct sharp upper and lower bounds on the size of unit-neighbourhoods and investigate the diameter of . Lastly, we consider an enumeration problem relevant to population genetics.AMS Subject Classification: 05C05, 92D15.     

一类非线性m-点边值问题正解的存在性

设α∈C[0,1],b∈C([0,1],(-∞,0)).设φ(t)为线性边值问题 u″+a(t)u′+b(t)u=0, u′(0)=0,u(1)=1的唯一正解.本文研究非线性二阶常微分方程m-点边值问题 u″+a(t)u′+b(t)u+h(t)f(u)=0, u′(0)=0,u(1)-sum from i=1 to(m-2)((a_i)u(ξ_i))=0正解的存在性.其中ξ_i∈(0,1),a_i∈(0,∞)为满足∑_(i=1)~(m-2)a_iφ_1(ξ_i)<1的常数,i∈{1,…,m-2}.通过运用锥上的不动点定理,在f超线性增长或次线性增长的前提下证明了正解的存在性结果.     

Liouville—Ttype Theorems for Conformal Gaussian Curvature Equations in R^2

In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions.     

Three-dimensional display by use of integral photography with dynamically variable image planes

A computer-generated integral photography system operating with a variable image plane is proposed. In this scheme, the gap between a lens array and a display panel is adjusted in real time. A synchronized elemental image array for real or virtual mode is integrated in front of or behind the lens array. This integration gives an observer an enhanced perception of depth. The proposed method can be applied to animated three-dimensional imaging.     

A Note on π-Engel Conditions

In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20     

A formula for -hyponormality of backstep extensions of subnormal weighted shifts

Let be a weight sequence of positive real numbers and let be a subnormal weighted shift with a weight sequence . Consider an extended weight sequence with and let 0: W_{\alpha (x)} \text{is} k \text{-hyponormal}\}$">for , where is the set of natural numbers. We obtain a formula to find the interval , which provides several examples to distinguish the classes of -hyponormal operators from one another.

     

Quantitation of localized (31)P magnetic resonance spectra based on the reciprocity principle

There is a need for absolute quantitation methods in (31)P magnetic resonance spectroscopy, because none of the phosphorous-containing metabolites is necessarily constant in pathology. Here, a method for absolute quantitation of in vivo (31)P MR spectra that provides reproducible metabolite contents in institutional or standard units is described. It relies on the reciprocity principle, i.e., the proportionality between the B(1) field map and the map of reception strength for a coil with identical relative current distributions in receive and transmit mode. Cerebral tissue contents of (31)P metabolites were determined in a predominantly white matter-containing location in healthy subjects. The results are in good agreement with the literature and the interexamination coefficient of variance is better than that in most previous studies. A gender difference found for some of the (31)P metabolites may be explained by different voxel composition.