Kyriaki Tsilika

Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics

In this paper we examine the property of asymptotic stability in several dynamic economic systems, modeled in ordinary differential equation formulations of time parameter t. Asymptotic stability ensures intertemporal equilibrium for the economic quantity the solution stands for, regardless of what the initial conditions happen to be. Existence of economic equilibrium in continuous time models is checked via a Symbolic language, the Xcas program editor. Using stability theorems of differential equations as background a brief overview of symbolic capabilities of free software Xcas is given. We present computational experience with a programming style for stability results of ordinary linear and nonlinear differential equations. Numerical experiments on traditional applications of economic dynamics exhibit the simplicity clarity and brevity of input and output of our computer codes.

Time series analysis of Earth's Northern Hemisphere temperature reconstructions using non-linear tools and statistical tests

This paper presents results concerning the non-linear analysis of the Earths Northern Hemisphere mean annual land temperature reconstructions for the time period of 713-2004. The non-linear analysis consists of the application of several filtering methods, the estimation of geometrical and dynamical characteristics in the reconstructed phase space, techniques of discrimination between non-linear low-dimensional and linear high-dimensional (stochastic) dynamics and tests for serial dependence and non-linear structure. The results of this study indicate the efficiency of the filtering methods in revealing non-linear structures and correlations in short noisy time series, such as Earths Northern Hemisphere temperature reconstructions. No low-dimensional chaotic behaviour evidence was found from the analysis.

A framework for stochastic simulation of distribution practices for hotel reservations

The focus of this study is primarily on the Greek hotel industry. The objective is to design and develop a framework for stochastic simulation of reservation requests, reservation arrivals, cancellations and hotel occupancy with a planning horizon of a tourist season. In Greek hospitality industry there have been two competing policies for reservation planning process up to 2003: reservations coming directly from customers and a reservations management relying on tour operator(s). Recently the Internet along with other emerging technologies has offered the potential to disrupt enduring distribution arrangements. The focus of the study is on the choice of distribution intermediaries. We present an empirical model for the hotel reservation planning process that makes use of a symbolic simulation, Monte Carlo method, as, requests for reservations, cancellations, and arrival rates are all sources of uncertainty. We consider as a case study the problem of determining the optimal booking strategy for a medium size hotel in Skiathos Island, Greece. Probability distributions and parameters estimation result from the historical data available and by following suggestions made in the relevant literature. The results of this study may assist hotel managers define distribution strategies for hotel rooms and evaluate the performance of the reservations management system.