We investigate the reversible diffusion-influenced reaction of an isolated pair in two space dimensions in the context of the area reactivity model. We compute the exact Green’s function in the Laplace domain for the initially unbound molecule. Furthermore, we calculate the exact expression for the Green’s function in the time domain by inverting the Laplace transform via the Bromwich contour i...

We introduce the notion of free polygons as combinatorial building blocks for convex integral polygons; that is, polygons with vertices having integer coordinates. In this context, an Euler-type formula is derived for the number of integer points in the interior of an integral polygon. This leads in turn to a formula for the area of an integral polygon P via the enumeration of free integral tri...

For 0 < p < ∞ and −2 ≤ α ≤ 0 we show that the L integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1−|z|) dA(z) is a logarithmically convex function of r on (0, 1).

quantification of the habitat available for fish species named rainbow trout (oncorhynchusmykiss) were evaluated in lees ferry, colorado river using water depth, water temperature, sediment transport,flow velocity in 2004 as environmental index. for the flow velocity and temperature distribution calculationsin the river, the navier-stokes equation and energy conservation equations with finite v...

because of a lack of means to match the traditional operating rules and regulations with time dependent variant of water needs in the present irrigation networks, a considerable portion of available water is wasted in these systems. this makes research on methods of operation and determination of types of controls as well as optimization approaches, attainable through using hydrodynamic models ...

This paper is the second of a two-part series assessing the feasibility of using the J-integral with full-field deformation data from Digital Image Correlation (DIC) to characterize toughness in continuous fiber, SiCf/SiCc ceramic matrix composites (CMCs). In Part I, line and area integral adaptations of the J-integral were validated with analytical and experimental deformation fields. It was f...