Relationship Between Hyperglycemia and Infection in Critically Ill Patients

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90178/1/phco.2005.25.7.963.pd

Remarks on the Cauchy functional equation and variations of it

This paper examines various aspects related to the Cauchy functional equation $f(x+y)=f(x)+f(y)$, a fundamental equation in the theory of functional equations. In particular, it considers its solvability and its stability relative to subsets of multi-dimensional Euclidean spaces and tori. Several new types of regularity conditions are introduced, such as a one in which a complex exponent of the unknown function is locally measurable. An initial value approach to analyzing this equation is considered too and it yields a few by-products, such as the existence of a non-constant real function having an uncountable set of periods which are linearly independent over the rationals. The analysis is extended to related equations such as the Jensen equation, the multiplicative Cauchy equation, and the Pexider equation. The paper also includes a rather comprehensive survey of the history of the Cauchy equation.Comment: To appear in Aequationes Mathematicae (important remark: the acknowledgments section in the official paper exists, but it appears before the appendix and not before the references as in the arXiv version); correction of a minor inaccuracy in Lemma 3.2 and the initial value proof of Theorem 2.1; a few small improvements in various sections; added thank

The impact of diabetes on the pathogenesis of sepsis

Diabetes is associated with an increased susceptibility to infection and sepsis. Conflicting data exist on whether the mortality of patients with sepsis is influenced by the presence of diabetes, fuelling the ongoing debate on the benefit of tight glucose regulation in patients with sepsis. The main reason for which diabetes predisposes to infection appears to be abnormalities of the host response, particularly in neutrophil chemotaxis, adhesion and intracellular killing, defects that have been attributed to the effect of hyperglycaemia. There is also evidence for defects in humoral immunity, and this may play a larger role than previously recognised. We review the literature on the immune response in diabetes and its potential contribution to the pathogenesis of sepsis. In addition, the effect of diabetes treatment on the immune response is discussed, with specific reference to insulin, metformin, sulphonylureas and thiazolidinediones