This paper takes a step toward defining a continuous time methodology to analyze a class of time inconsistent capital accumulation games when the discount rate is non-constant and commitment is not possible. The subgame perfect and history independent equilibrium consumption policies are characterized with an equation that must be satisfied by the value function. The equation is reminiscent of ...

Abstract: It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control pro...

We present a new method, the Coupled Escape Probability (CEP), for exact calculation of line emission from multi-level systems, solving only algebraic equations for the level populations. The CEP formulation of the classical two-level problem is a set of linear equations, and we uncover an exact analytic expression for the emission from two-level optically thick sources that holds as long as th...

Low-density lipoprotein cholesterol (LDL-C) is frequently estimated using the empirical Friedewald equation. We compared the accuracy of the novel equation named as the 180-cell method (180-c), which estimates LDL-C using a stratification approach, to those of 9 previously suggested formulas, including the Friedewald equation.We compared the accuracy of 10 equations by calculating intraclass co...

In this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in principle. The model can be naturally formulated as a first order partial integro-differential equation, and it has been studied extensively. In particular, it is w...

Dynamic population models are based on the Verhulst’s equation (logisitic equation), where the classic Malthusian growth rate is damped by intraspecific competition terms. Mainstream population models for mutualism are modifications of the logistic equation with additional terms to account for the benefits produced by the interspecies interactions. These models have shortcomings as the populati...

In this paper, Wright's equation formulated in 1931 is proven and applied to evolutionary computation. Wright's equation shows that evolution is doing gradient ascent in a landscape deÿned by the average ÿtness of the population. The average ÿtness W is deÿned in terms of marginal gene frequencies pi. Wright's equation is only approximately valid in population genetics, but it exactly describes...

One way of modeling the evolution in time of an age-structured population is to set up the evolution process as a partial diierential equation in which time and age are the independent variables. The resulting equation, known as the McKendrick equation, has received attention recently from mathematicians. Some advantages of the PDE are that it can easily be adapted to include more detail in the...