Asymptotic behavior of a discrete-time density-dependent SI epidemic model with constant recruitment.

We use the epidemic threshold parameter, , and invariant rectangles to investigate the global asymptotic behavior of solutions of the density-dependent discrete-time SI epidemic model where the variables and represent the populations of susceptibles and infectives at time , respectively. The model features constant survival "probabilities" of susceptible and infective individuals and the constant recruitment per the unit time interval into the susceptible class. We compute the basic reproductive number, , and use it to prove that independent of positive initial population sizes, implies the unique disease-free equilibrium is globally stable and the infective population goes extinct.

Birkhoff normal forms and KAM theory for Gumowski-Mira equation.

By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1=(2ax n)/(1+x n2)-xn-1, n=0,1,…, where x-1, x0∈(-∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.

Global dynamics of certain homogeneous second-order quadratic fractional difference equation.

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x(n+1) = x²(n-1)/(ax²(n) + bx(n)x(n-1) + cx²(n-1)), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x₋₁ and x₀ are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable.

Balint groups as a driving force of ego development.

This paper gives an overview of one of the main components in the process of Balint groups. The paper is based on the authors' research on the work of Balint groups and the study of literature which deals with the development of ego and the role of Balint groups in the development of participants' ego. This field is of great interest to the Balint movement and education in medicine.

Health status as geneologic burden in aging process.

Unlabelled: Knowledge of modern molecular biology is leading to the idea that aging and diseases of the aged are two different entities. Healthy life is relatively limited by the specific number of chronic conditions which are present more in old age. Up to now the idea of aging as a process in relation to the individual, organ, tissue, cell or a molecule.