The delivery man problem on a tree network

This note considers a variant of the traveling salesman problem in which we seek a route that minimizes the total of the vertex arrival times. This problem is called the deliverly man problem. The traveling salesman problem is NP-complete on a general network and trivial on a tree network. The delivery man problem is also NP-complete on a general network but far from trivial on a tree network. Various characteristics of the delivery man problem for tree networks are explored and a pseudo-polynomial time solution algorithm is proposed.This research was sponsored by NSF Grant #ECS-8104647.     

Benzocyclobutene in polymer synthesis. III. Heat-resistant thermosets based on Diels–Alder polymerization of a bisbenzocyclobutene and a bismaleimide

Several compatible mixtures of 2,2-bis[4-(N-4-benzocyclobutenyl) phthalimid-4-phenyl]hexafluoropropane (BCB) and 1,1′-(methylene di-4,1-phenylene)bismaleimide (BMI) were prepared according to the molar ratios (BCB : BMI): 1 : 1; 1 : 1.5; 1 : 3; 1.5 : 1. Complete compatibility of the mixtures was evidenced by a single initial T_g. All mixtures showed relatively low initial T_g's (61–70°C) and characteristic polymerization exotherms of benzocyclobutene-based systems (onset: 221–225°C; maximum: 257–259°C), providing an excellent processing window (ca. 155°C). The cured sample of the mixtures, pure BCB and BMI (250°C; N₂; 8 h) were subjected to comparative isothermal gravimetric analysis (ITGA). After 200 h at 650°F (343°C) in circulating air, the cured BMI sample retained only 3% of its original weight, whereas the mixtures of BCB and BMI exhibited thermo-oxidative stabilities similar to BCB (13–15% weight loss). A model compound was synthesized from the intimate mixture of N-phenylmaleimide and N-benzocyclobutenyl phthalimide in 63% yield. The ITGA results and isolation of the model Diels–Alder adduct render strong support to the conviction that Diels–Alder polymerization is indeed the predominant curing process in the BCB/BMI system.     

The asymptotic enumeration of rooted convex polyhedra

An asymptotic formula is obtained for the number of rooted c-nets with m vertices and n edges as m, n → ∞ with $\text{1}\text{2}\text{+ ε <}\text{n}\text{m}\text{< 2 ? ε}$ for some ε > 0.     

Fast Stimulation of Millimeter Wave Waveguide Filters by Boundary Marching Method

The boundary marching method is applied for the analysis of the waveguide bandpass filers. The vector finite element method with the perfectly matched layers (PML) as the matching load is given for parameter extraction of millimeter wave filters. The implementation of the fast boundary marching method is described in detail. The reflection and insertion losses of millimeter wave filters are obtained and compared with those obtained from literature.     

Self-Induced Electrostatic Fields

Electrostatic fields with localized sources induced by the electrostatic potential are introduced. The case in which such fields are determined by Schrödinger-like equations is considered. The problem of charge quantization is discussed.     

Fractal basin boundaries

Basin boundaries for dynamical systems can be either smooth or fractal. This paper investigates fractal basin boundaries. One practical consequence of such boundaries is that they can lead to great difficulty in predicting to which attractor a system eventually goes. The structure of fractal basin boundaries can be classified as being either locally connected or locally disconnected. Examples and discussion of both types of structures are given, and it appears that fractal basin boundaries should be common in typical dynamical systems. Lyapunov numbers and the dimension for the measure generated by inverse orbits are also discussed.