A functional graph is a digraph describing the action of a function on a set. The endomorphisms of such graphs are of interest in group theory: the centraliser of an element of the semigroup of all mappings of a set into itself coincides with the set of all endomorphisms of a digraph corresponding to this element.In this study, the functional graphs with a countable set of vertices are considered. We introduce the notion of lineals and calculate the cardinality of the set of endomorphisms of functional graphs which are not lineals.
In this paper, we consider a relation between adolescent obesity and dynamic changes in the complement system components and immune complexes of various fractions affected by antihypoxants, because obesity is one of the most common non-communicable diseases worldwide and rises an interest for many researchers. New studies emerge revealing an imbalanced immune system that aggravates upon obesity and affects multiple immune processes, as well as increasing interest in studying obstructive sleep apnea syndrome resulting in tissue hypoxia, thereby increasing a risk of cardiovascular diseases. Our study allowed to detect metabolic syndrome in 89% of obese patients (groups 1 and 2) and 25% of adolescents with normal body weight (control group 2). We analyzed the complement components and circulating immune complexes of various fractions and revealed positive dynamics of the examined parameters due to combination therapy with the anti-oxidant Mexidol and hyperbaric oxygenation, which may indicate that oxygen-dependent neuroimmune mechanisms might be involved in the pathogenesis of metabolic syndrome in obesity. Such systemic activation of regulatory mechanisms for maintaining homeostasis is necessary for formation of biologically active thymusderived serum factor ensuring lymphocyte differentiation, i.e. pathogenetic therapy corrects dysregulatory impact of traditional therapy for obesity and optimizes immune responses. During the study we observed that the combination treatment using Mexidol and HBO resulted in better recovery of clinical functions and immune responses, and that such therapy exerted a positive effect on dynamics of patient mental activity. We believe that such therapeutic effects were due to antioxidant and antihypoxic activity of the applied pharmacological drugs. We also found that obese children are featured with metabolic syndrome and predisposed to developing relevant complications. Hence, for early diagnostics of metabolic syndrome it is necessary to study children with normal body weight that will allow to diagnose metabolic changes at earlier stage, because changes in blood biochemical parameters such as triglycerides, very low-density lipoproteins, glycemia levels etc. occur long before initial changes in person appearance might emerge.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.