in this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. then we investigate for a ring $r$, when any fi...

In the classical growth model, with overlapping generations and continuous time starting at −∞, generically there exist a unique equilibrium in the policy-neighbourhood of any balanced growth equibrium as shown in [4]. Policies are endowment perturbations. In this paper we show that, for any such equilibrium selection, welfare is differentiable, and that the derivative at the balanced growth eq...

We discuss explicit solutions of the logistic model with variable parameters. Classical data on the sunflower seeds growth are revisited as a simple application of the logistic model with periodic coefficients. Some applications to related biological systems are briefly reviewed.

Parameter estimation problems of diffusion models are discussed. The problems of maximum likelihood estimation and model selections from continuous observations are illustrated through diffusion growth model which generalizes some classical ones.

HIGHLIGHTS This work introduces the Gudermannian function as a sigmoid growth model. Hyperbolic and trigonometric identities provide several parameterizations of this The model can be good alternative to classical models.

Abstract The spontaneous emission spectrum from a driven three-level atom placed inside a double-band photonic crystal has been investigated. We use the model which assumes the upper levels of the atomic transition are coupled via a classical driving field. The transition from one of the upper levels to lower level couples to the modes of the modified reservoir, and the transition from the oth...

Cancer cells co-cultured in vitro reveal unexpected differential growth rates that classical exponential growth models cannot account for. Two noninteracting cell lines were grown in the same culture, and counts of each species were recorded at periodic times. The relative growth of population ratios was found to depend on the initial proportion, in contradiction with the traditional exponentia...

We consider a moving-boundary problem associated with a limiting case of the fluid model for biofilm growth proposed by J. Dockery and I. Klapper, SIAM J. Appl. Math. 62(3), 2001. Concepts of classical, weak, and variational solutions for this problem are introduced. Classical solutions with radial symmetry are constructed, and estimates for their growth are given. Using a weighted Baiocchi tra...

Purpose: To analyze the capabilities of different classical mathematical models to describe growth multicellular spheroids simulated with an on-lattice agent-based Monte Carlo model that has already been validated. Methods: The exponential, Gompertz, logistic, potential, and Bertalanffy have fitted in situations volume data generated a simulates spheroid growth. Two samples pseudo-data, obtaine...

Econometric modelling is at the core of economic policy analysis. Such models have long been used to forecast the effects of various national economic policy measures or, at least, to inform policy analysts about likely trends such as inflation or employment rates in the absence of policy interventions. Econometric analysis has long been closely associated with equilibrium economic theory. The ...