2-Abolutely summable oeprators in certain Banach spaces by Komarchev I.A.

By Komarchev I.A.

Show description

Read or Download 2-Abolutely summable oeprators in certain Banach spaces PDF

Best mathematics books

Fuzzy Cognitive Maps: Advances in Theory, Methodologies, Tools and Applications

The idea of cognitive maps used to be built in 1976. Its major goal used to be the illustration of (causal) relationships between “concepts” sometimes called “factors” or “nodes”. suggestions may be assigned values. Causal relationships among innovations can be of 3 forms: optimistic, detrimental or impartial. bring up within the price of an idea could yield a corresponding optimistic or damaging bring up on the suggestions hooked up to it through relationships.

Additional info for 2-Abolutely summable oeprators in certain Banach spaces

Example text

23) We start with a population of resting CTL, denoted by m. Upon antigenic encounter, these cells become activated at a rate αym. These activated cells are denoted by m0 . Following activation, the CTL undergo n rounds of proliferation, and this is independent of antigenic stimulation. n − 1). The nth division gives rise to effector cells, denoted by z. They can kill infected cells (or alternatively have nonlytic activity). Effectors die at a rate δz and differentiate into memory cells at a rate γz.

After expansion, the population of CTL remains at an elevated memory level. 1. 3 Saturated CTL Expansion 31 The major advantage of this model is its analytic simplicity. However, it does have some unrealistic features. The CTL proliferation term is very strong. That is, the rate of CTL expansion is directly proportional to the number of CTL, and there is no saturation. In this case, the number of CTL is only regulated by the amount of antiviral activity exerted by the CTL. Assume that the CTL have lost their ability to kill and to perform any other antiviral activity.

Because our model is deterministic, the CTL response cannot reduce virus load y to exactly zero, although virus load may be reduced to very low levels. Hence we define an extinction threshold yext . If y < yext , the virus population has gone extinct. Note that this threshold is arbitrary. In reality it will depend on a complex balance between host and viral parameters as well as stochastic events. In general, the lower the virus load predicted by the model, the higher the chances of viral clearance.

Download PDF sample

Rated 4.26 of 5 – based on 9 votes