in this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. the conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. this study evaluates the advantages of using the integral form of the equations in the...

The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.

The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.

The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.

The last lecture has been more words than equations. Today we are going to do some paradigmatic calculations. We’ll start with -one at high Reynolds number and one at low Reynolds number –which represent critical ideas for the subject of fluid mechanics. The first calculation is arguably the most important applied-mathematical idea of the twentieth century (at least I would argue it), and it is...

Computing Science and Systems Theory can gain much from unified mathematical models and methodology, in particular formal reasoning (“letting the symbols do the work”). This is achieved by a wide-spectrum formalism. The language uses just four constructs, yet suffices to synthesize familiar notations (minus the defects) as well as new ones. It supports formal calculation rules convenient for ha...