This paper deals with the expectation of monomials respect to stochastic area integral $A_{1,2}(t,t+h)=\int_{t}^{t+h}\int_{t}^{s}{\rm d} W_{1}(r){\rm W_{2}(s) -\int_{t}^{t+h}\int_{t}^{s}{\rm W_{2}(r){\rm W_{1}(s)$ and increments two Wiener processes, $\Delta{W}_{i}(t,t+h)=W_{i}(t+h)-W_{i}(t),\ i=1,2$. In a monomial, if exponent one or is an odd number, then monomial zero. However, any them even...

‎Small area estimates have received much attention from both private and public sectors due to the growing demand for effective planning of health services‎, ‎apportioning of government funds and policy and decision making‎. ‎Surveys are generally designed to give representative estimates at national or district level‎, ‎but estimates of variables of interest are oft...

Cardiac power (PWR) is the continuous product of flow and pressure in the proximal aorta. Our aim was to validate the PWR integral as a marker of left ventricular energy transfer to the aorta, by comparing it to stroke work (SW) under multiple different loading and contractility conditions in subjects without obstructions in the left ventricular outflow tract. Six pigs were under general anesth...

The continuity equation suggests that a ratio of velocities at two different cardiac valves is inversely proportional to the ratio of cross-sectional areas of the valves. To determine whether a ratio of mitral/aortic valve orifice velocities is useful in determining aortic valve area in patients with aortic stenosis, 10 control subjects and 22 patients with predominant aortic stenosis were exam...