A finiteness result for Heegaard splittings

In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of 3g−3 disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition.     

OADM环网的实验研究

研究了光分插复用器(OADM)的关键技术,重点分析了相关的实现技术,完成了利用OADM构建全光环网的实验研究,给出了重要的实验数据,包括眼图、光谱图、光信噪比、保护与恢复等,并对这些实验数据进行了分析,为光传送网的设计与构建提供了重要的参考依据.     

Rank one perturbations at infinite coupling in Pontryagin spaces

In this paper we relate the operators in the operator representations of a generalized Nevanlinna function N(z) and of the function −N(z)⁻¹ under the assumption that z=∞ is the only (generalized) pole of nonpositive type. The results are applied to the Q-function for S and H and the Q-function for S and H^∞, where H is a self-adjoint operator in a Pontryagin space with a cyclic element w, H^∞ is the self-adjoint relation obtained from H and w via a rank one perturbation at infinite coupling, and S is the symmetric operator given by S=H∩H^∞.     

Exponential decay of eigenfunctions in many-body type scattering with second-order perturbations

We show the exponential decay of eigenfunctions of second-order geometric many-body type Hamiltonians at non-threshold energies. Moreover, in the case of first-order and small second-order perturbations we show that there are no eigenfunctions with positive energy.     

Stability results for Mountain Pass and Linking type solutions of semilinear problems involving Dirichlet forms

Some stability results for Mountain Pass and Linking type solutions of semilinear problems involving a very general class of Dirichlet forms are stated. The non linear terms are supposed to have a suitable superlinear growth and the family of Dirichlet forms is required to be dominated from below and from above by a fixed diffusion type form. Some concrete examples are also given.     

Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds

This paper studies several aspects of asymptotically hyperbolic (AH) Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed conformal infinity. We then describe natural conditions which are sufficient to ensure finiteness.     

Minimal Bar Tableaux

Motivated by recent results of Stanley, we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of S_n vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur’s Q_λ symmetric functions in terms of the power sum symmetric functions. Received November 20, 2003     

70K温区混合工质分凝分离循环节流制冷机实验研究

混合工质节流制冷机正在许多方面获得越来越广泛的应用。文中设计了一种新型的混合工质分凝分离循环 ,建立了实验系统 ,并在 70 K温区进行了实验。实验结果表明 ,节流制冷机可以达到 6 5 .3K的低温 ,并在 72 K温度提供 1W的制冷量 ,输入功率为 5 0 0 W。     

新型菲涅尔线聚光太阳电池组件特性分析

以PMMA为材料,采用热压成型工艺加工线聚焦菲涅尔聚光棱镜,对在其聚光条件下不同入射角度情况下太阳电池的电流电压特性进行测试,结果表明:该菲涅尔线聚焦棱镜能有效提高太阳电池的单位输出功率,而且具有比较宽泛的集光角的特性,基本满足实际应用的要求.