In this paper, spectral scheme based on Hermite interpolation for solving partial differential equations is presented. The idea of this Hermite spectral method comes from the spectral method on arbitrary grids of Carpenter and Gottlieb [J. Comput. Phys. 129(1996) 74-86] using the Lagrange interpolation.

We obtain some retarded integral inequalities of Bihari-type and apply these results to a retarded differential equation of Bernoulli-type.

In this paper, we obtain the generalized Hyers-Ulam stability of a functional equation and a system of functional equations on Jensen-quadratic mappings.

The effect of a solute concentration difference on the osmotic transport of water through the semi-permeable membrane of a simple cell model is investigated. So far, most studies on osmotic phenomena are described by simple diffusion-type equations ignoring all fluid motion or described by Stokes flow. In our work, as the governing equations, we consider the coupled full Navier-Stokes equations which describe the fluid motion and the full transport equation that takes into account of convection and diffusion effects. A two dimensional finite difference model has been developed to simulate the velocity field, concentration field, and semi-permeable membrane ment. It is shown that the cell swells to regions of lower solute concentration due to the uneven water flux through the semi-permeable membrane. The simulation is applied on a red blood cell geometry and the relevant results are presented.

Fingerprinting is a technique that permits automatic classification of strategies for playing a game. In this paper, the evolution of strategies for playing the iterated prisoner's dilemma (IPD) at three different noise levels is analyzed using fingerprinting and other techniques including a novel quantity, evolutionary velocity, derived from fingerprinting. The results are at odds with initial expectations and permit the detection of a critical difference in the evolution of agents with and without noise. Noise during fitness evaluation places a larger fraction of an agent's genome under selective pressure, resulting in substantially more efficient training. In this case, efficiency is the production of superior competitive ability at a lower evolutionary velocity. Prisoner's dilemma playing agents are evolved for 6400 generations, taking samples at eight exponentially spaced epochs. This permits assessment of the change in populations over long evolutionary time. Agents are evaluated for competitive ability between those evolved for different lengths of time and between those evolved using distinct noise levels. The presence of noise during agent training is found to convey a commanding competitive advantage. A novel analysis is done in which a tournament is run with no two agents from the same evolutionary line and one third of agents from each noise level studied. This analysis simulates contributed agent tournaments without any genetic relation between agents. It is found that in early epochs the agents evolved without noise have the best average tournament rank, but that in later epochs they have the worst.

Subterranean termites forage by digging a network of tunnels to come into contact with food sources. When 1000 termites (Coptotermes formosanus Shiraki) were placed in a laboratory arena, 6.7 primary tunnels were constructed. The aim of this study was to explain the empirical observation in which termites restrict the number of primary tunnels. To this end, we constructed a model to simulate termite tunnel patterns based on empirical data and to calculate food transportation efficiency, γ, for the tunnel patterns. The efficiency was defined as the ratio of the number of encountered food particles to the sum of the shortest length from the location of encountered food particles to the initial position of growth of the tunnel. The γ was maximized when the number of primary tunnels was 5 or 6, which was fairly consistent with the empirical number of primary tunnels. This result indicated that termites may restrict the number of their primary tunnels to improve the transportation efficiency, which is directly related to their survival.

The aim of this paper is to give relations between generalized Dedekind eta functions, theta functions, Dedekind sums, Hardy­Berndt sums and Hecke operators.