Whereas indirect euthanasia is a common clinical practice, active euthanasia remains forbidden in most countries. The reason for this differentiation is usually seen in the principle of double-effect (PDE). PDE states that there is a morally relevant difference between the intended consequences of an action and merely foreseen, unintended side-effects. This article discloses the fundamental ass...

For the simulation of tsunamis, the hydrostatic shallow water equations have established as a sound mathematical basis. However, due to the hydrostatic assumption, not all relevant physical effects—especially in coastal areas—can be modelled accurately. In this paper, we therefore show how to extend the PDE-framemwork sam(oa)2 towards modified non-hydrostatic shallow water equations. We use the...

In this set of notes we begin the theory of singular integral operators operators which are almost integral operators, except that their kernel K(x, y) just barely fails to be integrable near the diagonal x = y. (This is in contrast to, say, fractional integral operators such as Tf(y) := ∫ Rd 1 |x−y|d−s f(x) dx, whose kernels go to infinity at the diagonal but remain locally integrable.) These ...

We consider the focusing L2-critical half-wave equation in one space dimension i∂tu = Du− |u|u, where D denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold M∗ > 0 such that all H1/2 solutions with ‖u‖L2 < M∗ extend globally in time, while solutions with ‖u‖L2 > M∗ may develop singularities in finite time. In this paper, we first prove the ex...

Using the theory of the symmetry groups for PDEs of order two ([7], [17], [20]), one finds the symmetry group G associated to Ţiţeica surfaces PDE. One proves that Monge-Ampère-Ţiţeica PDE which is invariant with respect to G, where G is the maximal solvable subgroup of the symmetry group G, is just the PDE of Ţiţeica surfaces. One studies the inverse problem and one shows that the Ţiţeica surf...

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

The M-mode echocardiographic findings of ventricular septal defect (VSD) are nonspecific. A specific pulsed Doppler echocardiographic (PDE) diagnosis of VSD can be made by following the turbulent VSD jet through the septum. To assess the sensitivity, specificity and limitations of PDE diagnosis of VSD, 105 children undergoing cardiac catheterization were examined by PDE. These children had a va...

In this letter, we design a robust stabilizing controller for system composed of two sets linear heterodirectional hyperbolic PDEs, with actuation at one boundary the and couplings middle ODEs in PDE-ODE-PDE configuration. The is underactuated since only PDE systems actuated. approach employs backstepping transformation to move undesired proximal (where located). We can then express target as t...