We investigate the timing of adoption of product and process innovation by using a differential game in which firms may invest in both activities. We consider horizontal product innovation that reduces product substitutability, and process innovation that reduces marginal cost. First, we demonstrate that the incentive for cost-reducing investment is relatively higher than the incentive to incre...

This paper is devoted to the study of some qualitative and quantitative aspects of nonlinear propagation phenomena in diffusive media. More precisely, we consider the case a reaction-diffusion equation in a periodic medium with ignition-type nonlinearity, the heterogeneity being on the nonlinearity, the operator and the domain. Contrary to previous works, we study the asymptotic spreading prope...

“Investigations” is a great book. It is a huge step in bringing closer biology and physics, the so called “soft” and “hard” sciences. Not because it is able to reduce biology to physics. Quite the opposite. It argues for the need of new laws for understanding biospheres, but nevertheless related to the physical laws. It is just that living organisms have properties that systems which can be stu...

We present a backstepping procedure for the design of globally stabilizing state feedback control laws such that the magnitudes of the control signals and their derivatives are bounded by constants which do not depend on the initial conditions. We accomplish this by propagating such boundedness properties through each step of the recursive design.

Fly ball trajectories games played during the 2015-2017 seasons at Tropicana Field are investigated. A randomly selected half of the 2016 data are used to establish a model for the drag and lift coefficients. That model is then used to calculate the trajectories for the remaining data, with fixed initial conditions determined by Statcast. The calculated distances are then compared to the actual...

This article examines the evolution of trust, control, and learning in a joint venture relationship. Using a coevolutionary approach, we develop a framework that shows how initial joint venture conditions give way to evolved conditions as joint venture partners develop an understanding of each other and adjust the collaborative process. We explore the relationship between trust and control in j...

A fractional generalized pure birth process is studied based on the master equation approach. The exact analytic solution of the generating function of the probability density for the process is given in terms of the Gauss hypergeometric function. The expressions of moments are also obtained in an explicit form. The effects of fixed and distributed initial conditions are also elucidated. The ef...

In this paper we find a general approach to find closed forms of sums of products of arbitrary sequences satisfying the same recurrence with different initial conditions. We apply successfully our technique to sums of products of such sequences with indices in (arbitrary) arithmetic progressions. It generalizes many results from literature. We propose also an extension where the sequences satis...

This paper focuses on the dynamic aspects of individual behavior affected by its social embedding, either at large (society-wide norms or averages) or at a local neighborhood. The emphasis is on how initial conditions can affect the long run outcome and to derive, discuss and apply the conditions for such thresholds. For this purpose, intertemporal social pressure (from peers, from norms, or fr...

We prove existence of a unique bounded classical solution for a onephase free-boundary problem with kinetics for continuous initial conditions. The main result of this paper establishes existence of a compact attractor for classical solutions of the problem.