A note on the Kutta condition in Glauert's solution of the thin aerofoil problem

Glauert's classical solution of the thin aerofoil problem (a coordinate transformation, and splitting the solution into a sum of a singular part and an assumed regular part written as a Fourier sine series) is usually presented in textbooks on aerodynamics without a great deal of attention being paid to the rôle of the Kutta condition. Sometimes the solution is merely stated, apparently satisfying the Kutta condition automatically. Quite often, however, it is misleadingly suggested that it is by the choice of a sine series that the Kutta condition is satisfied. It is shown here that if Glauert's approach is interpreted in the context of generalised functions, (1) the whole solution, i.e. both the singular part and any non-Kutta condition solution, can be written as a sine-series, and (2) it is really the coordinate transformation which compels the Kutta condition to be satisfied, as it enhances the edge singularities from integrable to non-integrable, and so sifts out solutions not normally representable by a Fourier series. Furthermore, the present method provides a very direct way to construct other, more singular solutions. A practical consequence is that (at least, in principle) in numerical solutions based on Glauert's method, more is needed for the Kutta condition than a sine series expansion

EphA2-receptor deficiency exacerbates myocardial infarction and reduces survival in hyperglycemic mice

Background We have previously shown that EphrinA1/EphA expression profile changes in response to myocardial infarction (MI), exogenous EphrinA1-Fc administration following MI positively influences wound healing, and that deletion of the EphA2 Receptor (EphA2-R) exacerbates injury and remodeling. To determine whether or not ephrinA1-Fc would be of therapeutic value in the hyperglycemic infarcted heart, it is critical to evaluate how ephrinA1/EphA signaling changes in the hyperglycemic myocardium in response to MI. Methods Streptozotocin (STZ)-induced hyperglycemia in wild type (WT) and EphA2-receptor mutant (EphA2-R-M) mice was initiated by an intraperitoneal injection of STZ (150 mg/kg) 10 days before surgery. MI was induced by permanent ligation of the left anterior descending coronary artery and analyses were performed at 4 days post-MI. ANOVAs with Student-Newman Keuls multiple comparison post-hoc analysis illustrated which groups were significantly different, with significance of at least p < 0.05. Results Both WT and EphA2-R-M mice responded adversely to STZ, but only hyperglycemic EphA2-R-M mice had lower ejection fraction (EF) and fractional shortening (FS). At 4 days post-MI, we observed greater post-MI mortality in EphA2-R-M mice compared with WT and this was greater still in the EphA2-R-M hyperglycemic mice. Although infarct size was greater in hyperglycemic WT mice vs normoglycemic mice, there was no difference between hyperglycemic EphA2-R-M mice and normoglycemic EphA2-R-M mice. The hypertrophic response that normally occurs in viable myocardium remote to the infarct was noticeably absent in epicardial cardiomyocytes and cardiac dysfunction worsened in hyperglycemic EphA2-R-M hearts post-MI. The characteristic interstitial fibrotic response in the compensating myocardium remote to the infarct also did not occur in hyperglycemic EphA2-R-M mouse hearts to the same extent as that observed in the hyperglycemic WT mouse hearts. Differences in neutrophil and pan-leukocyte infiltration and serum cytokines implicate EphA2-R in modulation of injury and the differences in ephrinA1 and EphA6-R expression in governing this are discussed. Conclusions We conclude that EphA2-mutant mice are more prone to hyperglycemia-induced increased injury, decreased survival, and worsened LV remodeling due to impaired wound healing

Effects of Complementary Creatine Monohydrate and Physical Training on Inflammatory and Endothelial Dysfunction Markers Among Heart Failure Patients

BACKGROUND: Previous studies have reported endothelial dysfunction and inflammatory cytokine in heart failure patients (HF). OBJECTIVES: The purpose of this study was to determine the effects of creatine monohydrate and exercise on inflammatory and endothelial dysfunction markers among HF patients. PATIENTS AND METHODS: One hundred patients were prospectively randomized into two groups: Intervention group which received 5 grams/day creatine monohydrate and exercised for 8 weeks; and control group which did not receive any interventions. Interleukine-6 (IL-6), high sensitivity C reactive protein (hs-CRP), P-selectin, intercellular adhesion molecule-1 (ICAM-1), and vascular cell adhesion molecule 1 (VCAM-1) were measured at the start and end of the study for both groups. RESULTS: In total, 100 patients including 50 controls and 50 intervention group (54 male, mean EF of 34.2 +/- 10.5 and 52 male, mean EF of 35.6 +/- 12.7, respectively) were analyzed. The serum levels of hs-CRP and IL-6 increased at the end of the study in the control group compared to the baseline, (7.5 +/- 1.5 mg/L vs. 6.9 +/- 1.3 mg/L, P 0.05). CONCLUSIONS: Combination of creatine monohydrate and exercise attenuated inflammation and endothelial dysfunction markers among heart failure patients