Search

The present paper analyzes an ODE model of a certain class of (open) enzymatic reactions. This type of model is used, for instance, to describe the interactions between messenger RNAs and microRNAs. It is shown that solutions defined by positive initial conditions are well defined and bounded on $$[0, \infty )$$ and that the positive octant of $${\mathbb {R}}^3$$ is a positively invariant set. We prove further that in this positive octant there exists a unique equilibrium point, which is asymptotically stable and a global attractor for any initial state with positive components; a controllability property is emphasized. We also investigate the qualitative behavior of the QSSA system in the phase plane $${\mathbb {R}}^2$$ . For this planar system we obtain similar results regarding global stability by using Lyapunov theory, invariant regions and controllability. [ABSTRACT FROM AUTHOR]

In the present paper we define the (pseudo) MV-algebras with n-ary operators, generalizing MV-modules and product MV-algebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MV-algebra and the operators defined on the corresponding ℓ-group. We also provide a categorical framework and we prove the analogue of Mundici's categorical equivalence between MV-algebras and abelian ℓ-groups with strong unit. Thus, the category of pseudo MV-algebras with operators is equivalent to some category of ℓ-groups with operators. [Copyright &y& Elsevier]

In the present paper, we define the MV-modules over PMV-algebras. These are structures that naturally correspond to ℓu-modules over ℓu-rings. Fixing an ℓu-ring (R,υ), we prove the equivalence between the category of ℓu-modules over (R,υ) and the category of MV-modules over Γ(R,υ). We also introduce the truncated modules, that are MV-algebras endowed with an external multiplication defined for any element in the positive cone of an ℓu-ring and we prove the natural equivalence between MV-modules and truncated modules. [Copyright &y& Elsevier]

Abstract: In order to evaluate the degree of endotoxin tolerance, expressed by the reduced cytokine/releasing capacity of the whole blood, data from a group of patients with trauma, severe acute pancreatitis (SAP), and diffuse peritonitis were analyzed. In SAP endotoxin levels and the tumor necrosing factor (TNF-α)–releasing capacity of the whole blood under lipopolysaccharide (LPS) stimulation were of an intermediate degree between systemic inflammatory response syndrome and severe sepsis. A mathematical model of ordinary differential equations of LPS signaling based on endotoxin kinetics and endotoxin tolerance was constructed. The mathematical model was used to reproduce the TNF-α production in trauma, SAP and peritonitis patients. The results of these numerical simulations are very similar to the determinations in real patients and argue that endotoxin tolerance may be a component of the immune dysregulation that complicates the clinical evolution of the patient with SAP. [Copyright &y& Elsevier]