Diameter graphs of polygons and the proof of a conjecture of Graham

We show that for an n-gon with unit diameter to have maximum area, its diameter graph must contain a cycle, and we derive an isodiametric theorem for such n-gons in terms of the length of the cycle. We then apply this theorem to prove Graham's 1975 conjecture that the diameter graph of a maximal 2m-gon (m?3) must be a cycle of length 2m−1 with one additional edge attached to it.     

Fabrication of bamboo-shaped GaN nanorods

Bamboo-shaped GaN nanorods were formed through a simple sublimation method. They were characterized by means of X-ray powder diffraction (XRD), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) and selected-area electron diffraction (SAED). The TEM image showed that the nanorods were bamboo-like. XRD, HRTEM and SAED patterns indicated that the nanorods were single-crystal wurtzite GaN. Received: 8 January 2001 / Accepted: 28 April 2001 / Published online: 20 December 2001     

A mathematical analysis of a fish school model

A model proposed in the literature for fish schools of relatively large size is studied for mathematical and qualitative properties. Existence, uniqueness and positivity of solutions are established and bifurcation properties relative to diffusion and alignment parameters are studied.     

On universal central extensions of precrossed and crossed modules

We study the connection between universal central extensions in the categories of precrossed and crossed modules. They are compared with several kinds of universal central extensions in the categories of groups, epimorphisms of groups, groups with operators and modules over a group. We study the relationship between the homologies defined in these categories. Applications to relative algebraic K-theory are also obtained.     

Game theoretic analysis of the bargaining process over a long-term replenishment contract

This paper presents supplier–buyer models to describe the bargaining process between a supplier and a buyer over a long-term replenishment contract. Two different models are developed: one for the situation where the supplier has superior bargaining power over the buyer, and the other for the reverse situation. For each model, a method is derived that employs game theory-based analysis to determine the best strategy for each agent. A computational experiment is conducted to estimate the efficiency of the methods and to determine the economic implications of the results. The result indicates that each algorithm is very efficient compared to other strategies. We also verify that the solutions derived from each model are Nash equilibrium. Significantly improved outcomes are obtained for both agents by agreeing to the terms generated by the algorithms over the terms selected in the usual manner.     

Two classes of piecewise-linear difference equations with eventual periodicity three

In this paper, we will study two classes of difference equations which are piecewise-linear and of similar forms. We will show that all nontrivial solutions of one equation are eventually periodic with prime period three. We will show this result for one case of the second equation.     

Asymptotic and boundary integral formulae for the computational reconstruction of small conductivity imperfections

In this paper we investigate the electrostatic problem of determining conductivity profiles from the knowledge of boundary currents and voltages. We obtain an improved estimate for the voltage potential of a two-dimensional conductor having finitely many circular inclusions and piecewise constant conductivity profile. We derive an asymptotic expansion for the voltage potential in terms of the reference voltage potential and the location, size, and conductivity of the inhomogeneities. This representation is used to formulate the nonlinear least squares problem for estimating the location and size of the inhomogeneities. Required boundary data for the voltage potential are generated numerically by solving a system of integral equations. Computational experiments are presented to demonstrate the effectiveness of our identification procedure.     

Discovery of a new long-lived isomeric state in 125Ce

A new long-lived isomeric state in the near proton dripline nucleus ¹²⁵Ce has been identified with Schottky mass spectrometry at GSI. The excitation energy E ^* = 103(12)keV and the decay time of 193(1)s have been obtained from a single stored fully ionized ^125m Ce⁵⁸⁺ ion. The data implies an E3 transition and a 1/2⁺ assignment for the spin of the isomer.