Eigenvalues of the Kählerian Dirac Operator

We get estimates on the eigenvalues of the Kählerian Dirac operator in terms of the eigenvalues of the scalar Laplace–Beltrami operator. In odd complex dimension, these estimates are sharp, in the sense that, for the first eigenvalue, they reduce to Kirchberg's inequality.     

A Minimal Triangulation of the Hopf Map and its Application

We give a minimal triangulation : S ₁₂ ³ S ₄ ² of the Hopf map h:S ³S ² and use it to obtain a new construction of the 9-vertex complex projective plane.     

Embeddings in generalized manifolds

We prove that a ()-connected map from a compact PL -manifold to a generalized -manifold with the disjoint disks property, , is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompact and proper maps that are properly ()-connected. The techniques developed lead to a general position result for arbitrary maps , , and a Whitney trick for separating submanifolds of that have intersection number 0, analogous to the well-known results when is a manifold.

     

The -theory of toric manifolds

Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.

     

Homology manifold bordism

The Bryant-Ferry-Mio-Weinberger surgery exact sequence for compact homology manifolds of dimension is used to obtain transversality, splitting and bordism results for homology manifolds, generalizing previous work of Johnston.

First, we establish homology manifold transversality for submanifolds of dimension : if is a map from an -dimensional homology manifold to a space , and is a subspace with a topological -block bundle neighborhood, and , then is homology manifold -cobordant to a map which is transverse to , with an -dimensional homology submanifold.

Second, we obtain a codimension splitting obstruction in the Wall -group for a simple homotopy equivalence from an -dimensional homology manifold to an -dimensional Poincaré space with a codimension Poincaré subspace with a topological normal bundle, such that if (and for only if) splits at up to homology manifold -cobordism.

Third, we obtain the multiplicative structure of the homology manifold bordism groups .

     

The national ignition facility: path to ignition in the laboratory

The National Ignition Facility (NIF) is a 192-beam laser facility presently under construction at LLNL. When completed, NIF will be a 1.8-MJ, 500-TW ultraviolet laser system. Its missions are to obtain fusion ignition and to perform high energy density experiments in support of the US nuclear weapons stockpile. Four of the NIF beams have been commissioned to demonstrate laser performance and to commission the target area including target and beam alignment and laser timing. During this time, NIF demonstrated on a single-beam basis that it will meet its performance goals and demonstrated its precision and flexibility for pulse shaping, pointing, timing and beam conditioning. It also performed four important experiments for Inertial Confinement Fusion and High Energy Density Science. Presently, the project is installing production hardware to complete the project in 2009 with the goal to begin ignition experiments in 2010. An integrated plan has been developed including the NIF operations, user equipment such as diagnostics and cryogenic target capability, and experiments and calculations to meet this goal. This talk will provide NIF status, the plan to complete NIF, and the path to ignition.     

Progress in direct-drive inertial confinement fusion research at the laboratory for laser energetics

Direct-drive inertial confinement fusion (ICF) is expected to demonstrate high gain on the National Ignition Facility (NIF) in the next decade and is a leading candidate for inertial fusion energy production. The demonstration of high areal densities in hydrodynamically scaled cryogenic DT or D₂ implosions with neutron yields that are a significant fraction of the “clean” 1-D predictions will validate the ignition-equivalent direct-drive target performance on the OMEGA laser at the Laboratory for Laser Energetics (LLE). This paper highlights the recent experimental and theoretical progress leading toward achieving this validation in the next few years. The NIF will initially be configured for X-ray drive and with no beams placed at the target equator to provide a symmetric irradiation of a direct-drive capsule. LLE is developing the “polar-direct-drive” (PDD) approach that repoints beams toward the target equator. Initial 2-D simulations have shown ignition. A unique “Saturn-like” plastic ring around the equator refracts the laser light incident near the equator toward the target, improving the drive uniformity. LLE is currently constructing the multibeam, 2.6-kJ/beam, petawatt laser system OMEGA EP. Integrated fast-ignition experiments, combining the OMEGA EP and OMEGA Laser Systems, will begin in FY08.     

7Li2分子23Πu激发态的解析势能函数、振动能级及其转动惯量

使用Gaussian03程序包中的“对称性匹配簇-组态相互作用”方法、在0.13—2.0nm的核间距范围内利用6-311 G(d,p)基组对7Li2(23Πu)分子的势能曲线进行了计算,同时使用最小二乘法将计算结果拟合成了解析势能函数.利用拟合出的解析势能函数并结合Rydberg-Klein-Rees方法,计算了该态的谐振频率,进而计算了该态的其他光谱常数,分别为Te=3.6701eV,De=1.0764eV,Re=0.3000nm,ωe=285.69cm-1,ωeχe=1.8351cm-1,αe=0.00942cm-1和Be=0.5340cm-1,其中光谱常数Te,De,Re和ωe的值与文献值相符很好.以得到的解析势能函数为基础,通过求解双原子分子核运动的径向Schr dinger方程,发现J=0时7Li2(23Πu)分子存在67个振动态,求出了相应于每一振动态的振动能级、振动经典转折点及转动惯量.     

3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem

We present a compared analysis of some properties of 3-Sasakian and 3-cosymplectic manifolds. We construct a canonical connection on an almost 3-contact metric manifold which generalises the Tanaka–Webster connection of a contact metric manifold and we use this connection to show that a 3-Sasakian manifold does not admit any Darboux-like coordinate system. Moreover, we prove that any 3-cosymplectic manifold is Ricci-flat and admits a Darboux coordinate system if and only if it is flat.