On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Antioxidant and inflammatory aspects of lipoprotein-associated phospholipase A2 (Lp-PLA2 ): a review

The association of cardiovascular events with Lp-PLA2 has been studied continuously today. The enzyme has been strongly associated with several cardiovascular risk markers and events. Its discovery was directly related to the hydrolysis of the platelet-activating factor and oxidized phospholipids, which are considered protective functions. However, the hydrolysis of bioactive lipids generates lysophospholipids, compounds that have a pro-inflammatory function. Therefore, the evaluation of the distribution of Lp-PLA2 in the lipid fractions emphasized the dual role of the enzyme in the inflammatory process, since the HDL-Lp-PLA2 enzyme contributes to the reduction of atherosclerosis, while LDL-Lp-PLA2 stimulates this process. Recently, it has been verified that diet components and drugs can influence the enzyme activity and concentration. Thus, the effects of these treatments on Lp-PLA2 may represent a new kind of prevention of cardiovascular disease. Therefore, the association of the enzyme with the traditional assessment of cardiovascular risk may help to predict more accurately these diseases.

Influence of obesity and cardiometabolic makers on lipoprotein-associated phospholipase A2 (Lp-PLA2) activity in adolescents: the healthy young cross-sectional study

Abstract Background Lipoprotein-associated phospholipase A2 activity (Lp-PLA2) is a good marker of cardiovascular risk in adults. It is strongly associated with stroke and many others cardiovascular events. Despite this, the impact of obesity on this enzyme activity and its relation to biomarkers of cardiovascular disease in adolescents is not very well investigated. The purpose of this article is to evaluate the influence of obesity and cardiometabolic markers on Lp-PLA2 activity in adolescents. Results This cross-sectional study included 242 adolescents (10–19 years) of both gender. These subjects were classified in Healthy Weight (n = 77), Overweight (n = 82) and Obese (n = 83) groups. Lipid profile, glucose, insulin, HDL size, LDL(−) and anti-LDL(−) antibodies were analyzed. The Lp-PLA2 activity was determined by a colorimetric commercial kit. Body mass index (BMI), waist circumference and body composition were monitored. Food intake was evaluated using three 24-hour diet recalls. The Lp-PLA2 activity changed in function to high BMI, waist circumference and fat mass percentage. It was also positively associated with HOMA-IR, glucose, insulin and almost all variables of lipid profile. Furthermore, it was negatively related to Apo AI (β = −0.137; P = 0.038) and strongly positively associated with Apo B (β = 0.293; P < 0.001) and with Apo B/Apo AI ratio (β = 0.343; P < 0.001). The better predictor model for enzyme activity, on multivariate analysis, included Apo B/Apo AI (β = 0.327; P < 0.001), HDL size (β = −0.326; P < 0.001), WC (β = 0.171; P = 0.006) and glucose (β = 0.119; P = 0.038). Logistic regression analysis demonstrated that changes in Apo B/Apo AI ratio were associated with a 73.5 times higher risk to elevated Lp-PLA2 activity. Conclusions Lp-PLA2 changes in function of obesity, and that it shows important associations with markers of cardiovascular risk, in particular with waist circumference, glucose, HDL size and Apo B/Apo AI ratio. These results suggest that Lp-PLA2 activity can be a cardiovascular biomarker in adolescence.