Greedy sums of distinct squares

When a positive integer is expressed as a sum of squares, with each successive summand as large as possible, the summands decrease rapidly in size until the very end, where one may find two 's, or several 's. We find that the set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way.

     

Novel stabilization mechanism on polar surfaces: ZnO(0001)-Zn

The (1x1) terminated (0001)-Zn surface of wurtzite ZnO was investigated with scanning tunneling microscopy. The surface is characterized by the presence of nanosized islands with a size-dependent shape and triangular holes with single-height, O-terminated step edges. It is proposed that the resulting overall decrease of the surface Zn concentration stabilizes this polar surface. Ab initio calculations of test geometries predict triangularly shaped reconstructions over a wide range of oxygen and hydrogen chemical potentials. The formation of these reconstructions appears to be electrostatically driven.     

Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons

We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics.     

Bonus or flat wage? An experiment into the principal-agent problem

We conduct a simple principal-agent experiment in order to find the effects of information asymmetry on compensation. Our aim is the analysis of the appropriate compensation and its impact on employee’s effort. Furthermore we want to compare the offered compensation and the supplied effort in the version without communication and we want to know whether the experimental observations are consistent with the theoretical considerations.The experimenters found out that compensations observed during the experiment were different from those suggested by the theory and although they were theoretically not enough to induce high effort, we could observe high performance supplied by the agents.     

Total harmonic distortion analysis for direct methanol fuel cell anode

In this study, total harmonic distortion (THD) analysis is put forward to illustrate nonlinear behavior of direct methanol fuel cell (DMFC) anode. THD simulations by means of different methanol oxidation kinetics as well as its experimental validation are both carried out. It is shown that the THD model adopting a three-step methanol oxidation mechanism with Kauranen–Frumkin/Temkin kinetics can be used to illustrate the THD variation for DMFC anode qualitatively. The experimental THD response at the frequency range from 0.063 Hz to 0.4 Hz is identified as the reflection of the nonlinearity variation of those kinetic steps involving intermediates in the methanol oxidation. In such a frequency domain, THD value decrease monotonously with decreasing methanol concentration, which notices its accessibility on methanol concentration detection.     

Analyzing the sustainability of harvesting behavior and the relationship to personality traits in a simulated Lotka–Volterra biotope

For the analysis presented in this paper we use experiments to study human behavior in a simulation environment based on a simple Lotka–Volterra predator–prey ecology. The aim is to study the influence of different harvesting strategies and of certain personality traits derived from the Hamburg Personality Inventory (HPI) [Andresen, B., 2002. HPI – Hamburger Persönlichkeitsinventar. Hogrefe, Göttingen] on the outcome in terms of sustainability and economic performance.     

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in (0, π). Two sequences of circle patterns are employed to approximate a given conformal map g and its first derivative. For the domain of g we use embedded circle patterns where all circles have the same radius decreasing to 0 and with uniformly bounded intersection angles. The image circle pattern has the same combinatorics and intersection angles and is determined from boundary conditions (radii or angles) according to the values of g′ (|g′| or arg g′). For quasicrystallic circle patterns the convergence result is strengthened to C ^∞-convergence on compact subsets.