China
Africa
Explore chapters and articles related to this topic
Rate of Return
Published in S Kant Vajpayee, MD Sarder, Fundamentals of Economics for Applied EngineeringSecond Edition, 2019
The discussions presented in this chapter and the accompanying illustrations must have convinced you by now of the complexities of ROR-analysis. The repetitive nature of the calculations in the functional-notation method, arising from the trial and error approach, further accentuates the complexity. Programmable calculators and PCs ease the calculation efforts. Software are appropriate tools for solving problems under ROR-criterion. However, the objective of this chapter, indeed of the entire text, is the education focusing on the principles of engineering economics, rather than the training that can get emphasized in a software-centered learning environment. That is why I chose to take you through the “dirt road.”
A topic for integrated teaching of mathematics and biology: the parabola of chaos in tumour cell aneuploidy
Published in International Journal of Mathematical Education in Science and Technology, 2022
Dino G. Salinas, Mauricio O. Gallardo
A variant of this equation is given as which is known as the discrete version of the logistic equation (hereinafter simply the logistic equation), with indicating the time measured in integer values (such as seconds or years) and indicating the population (such as the number of insects in an ecosystem) at time . The variable is dimensionless (normalized, if necessary), ranging between 0 and 1. Outside this range, Equation (1) generates negative or zero values for , which are incompatible with the representation of the model. The temporal sequence of is obtained according to the following rule of recursive application: next year's population (left side of Equation (1)) is determined by a quadratic function of the current year's population (right side of Equation (1)). Indeed, if we perform the multiplication indicated in Equation (1), we see that the relationship between the populations of two consecutive years ( versus ) corresponds to a parabola. The only parameter of this parabola is , the growth parameter, which ranges between 0 and 4, assuring that the values of remain in the originally defined range. Starting with an initial value , the quadratic function is applied times, each time with an immediately preceding value as input; thus, a sequence of values is obtained. This sequence of values indicates the trajectory, or orbit, of the variable in the space of possible solutions. Currently, these orbits are studied computationally (Gould & Tobochnik, 1988), but many of their properties were discovered by Feigenbaum, in 1978, using a programmable calculator (Feigenbaum, 1978). Thus, it was verified that as time progresses, the orbit tends towards a characteristic final behaviour independent of the initial condition but dependent on the value assigned to the parameter .