The complexity of cutting complexes

This paper investigates the combinatorial and computational aspects of certain extremal geometric problems in two and three dimensions. Specifically, we examine the problem of intersecting a convex subdivision with a line in order to maximize the number of intersections. A similar problem is to maximize the number of intersected facets in a cross-section of a three-dimensional convex polytope. Related problems concern maximum chains in certain families of posets defined over the regions of a convex subdivision. In most cases we are able to prove sharp bounds on the asymptotic behavior of the corresponding extremal functions. We also describe polynomial algorithms for all the problems discussed.Bernard Chazelle wishes to acknowledge the National Science Foundation for supporting this research in part under Grant No. MCS83-03925. Herbert Edelsbrunner is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862.     

Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit

We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.     

Neighborhood Complexes and Generating Functions for Affine Semigroups

Given a₁,a₂,...,a_n ∈ ℤ^d$, we examine the set, G, of all non-negative integer combinations of these a_i. In particular, we examine the generating function f(z) = ∑_{b ∈ G}z_b. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in ℤ_n. In the generic case, this follows from algebraic results of Bayer and Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice.     

Phase rotation scheme of laser-produced ions for reduction of the energy spread

In order to widely spread out particle beams utilized in cancer therapy, laser-produced ions are developed as the injection beam for an ion synchrotron dedicated for cancer therapy. Such a laser ion source is expected to contribute largely to the realization of compactness of the size and low cost of the cancer therapy accelerator. The energy spectrum of the laser-produced ions, however, has no peak, but their intensities decrease exponentially according to the increase of the energy. For the purpose of modifying such a situation, we have proposed a scheme to rotate the beam in the longitudinal phase space with the use of the RF electric field, which is phase-adjusted with the pulse laser. We aim for a reduction of the energy spread of ± 5% selected by an energy analyzer and slits to ±1% by such phase rotation. For this purpose, a quarter wavelength resonator with two gaps with the same resonant frequency as the source laser has already been fabricated, together with its RF power source. The above phase rotation system and its recent experimental realization are presented.     

双奇核188Au的准粒子带结构研究

利用在束γ谱学实验技术, 通过¹⁷³Yb(¹⁹F,4nγ)反应 布居了¹⁸⁸Au的高自旋态, 并对其准粒子带结构进行了研究. 基于实验测量结果, 对原有的双奇核¹⁸⁸Au能级纲图做了较大的修改. 通过系统性比较, 对15⁺以上的能级结构进行了讨论.