Abstract
We study a model of a Cournot duopoly where firms invest in R&D to reduce their production costs. Depending on the parameters, we may find regions with one, two or three Nash equilibria of the investment. Here, we study the effect of the parameters in these regions, in particular, we study the effect of the possible market saturation, the maximum relative cost reduction and the product differentiation, giving special attention to regions with multiple Nash equilibria. We observed that, in general, the competitive region, where both firms invest, is reduced as we increase the possible market saturation and the differentiation of the products and is enlarged when we increase the maximum relative cost reduction. © 2018, Springer International Publishing AG, part of Springer Nature.

Abstract

Abstract
We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 (IL-2) secretion. We model the suppression of the autoimmune line of T cells after a different line of T cells responded to a pathogen infection. In this paper, we show that if the population of the pathogen responding line of T cells becomes large enough, the competition for IL-2 and the increase in the death rates may lead to a depletion in the concentration of autoimmune T cells. Provided this lasts for a sufficiently long time, the concentration of autoimmune T cells can be brought down to values inside the basin of attraction of the controlled state, and autoimmunity can be suppressed.

Abstract

Abstract
Sensory tests are quality assurance tools commonly used to measure and/or detect the presence of abnormal characteristics perceived through the senses in lots of raw material and final products in many manufacturing and food industries. In this paper two acceptance sampling plans for sensory evaluation are designed, and an illustration of the performance of such plans applied to a real data set is presented.

Abstract