Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems

We investigate the existence and multiplicity of positive solutions of multi-point boundary value problems for systems of nonlinear higher-order ordinary differential equations.     

Free energy and states of fractional-order hereditariness

Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.     

Computing high precision Matrix Padé approximants

We describe a new method of computing matrix Padé approximants of series with integer data in an efficient and fraction-free way, by controlling the growth of the size of intermediate coefficients. This algorithm is applied to compute high precision Padé approximants of matrix-valued generating functions of time series. As an illustration we show that we can successfully recover from noisy equidistant sampling data a joint damped signal of four antenna, even in the presence of background signals.     

Finite-volume complex surfaces without cuspidal Einstein metrics

We derive an obstruction to the existence of cuspidal Einstein metrics on finite-volume complex surfaces. This generalizes a theorem of LeBrun for compact complex surfaces. As in the compact case, such a result relies on a scalar curvature estimate. Finally, the obstruction is made explicit on some examples.     

Coronary fluid mechanics in an ageing cardiovascular system

Coronary artery diseases are a leading cause of mortality and are increasingly prevalent with age. However, the large number of age-increasing co-morbidities make difficult to understand the impact of cardiovascular ageing alone on the coronary flow pattern. The present study aims to shed light on the effect of arterial and ventricular ageing on the coronary circulation, which is here studied by means of a validated mathematical model. Forward and backward pressure and flow waves are analysed, as well as their intensity. Results highlight a complex spatiotemporal coronary wave pattern, where intense waves originate from the aorta (particularly in systole) and from the deep myocardium, during both the isovolumic compression and the diastolic phase. The subendocardial viability ratio decreases with age, the total coronary flow is slightly reduced, and the left-ventricular work increases. Consequently, the left-ventricular work per unit of blood flow increases, thus limiting the cell oxygen availability abundance, and therefore increasing the risk of myocardial infarction. Our results highlight a physiological age-induced supply/demand unbalance, which can augment the risk of myocardial ischemia and can contribute to pave the way to other typical coronary pathological processes.