in almost all of the present mathematical models, the upstream subbasins, with overland flow as the dominant type of flow, are simulated as a rectangular plane. however, the converging plane is the closest shape to an actual upstream subbasin. the intricate nature of the governing equations of the overland flow on a converging plane is the cause of prolonged absence of an analytical or semi ana...

In convergent-extension (CE), a planar-polarized epithelial tissue elongates (extends) in-plane in one direction while shortening (converging) in the perpendicular in-plane direction, with the cells both elongating and intercalating along the converging axis. CE occurs during the development of most multicellular organisms. Current CE models assume cell or tissue asymmetry, but neglect the pref...

A straightforward procedure is described for accurately creating an incident focused light pulse in the 3-D finite-difference time-domain (FDTD) electromagnetic simulation of the image space of an aplanatic converging lens. In this procedure, the focused light pulse is approximated by a finite sum of plane waves, and each plane wave is introduced into the FDTD simulation grid using the total-fi...

The diverging and converging components of localized wave solutions are studied within the framework of both the Whittaker and Weyl plane wave expansions. The specific example of the splash pulse is considered because its evanescent components could be derived in an explicit closed form. It is shown that, in the Weyl picture, the evanescent fields associated with the diverging and converging co...

For a range of Hardy and Bergman spaces X and sets of uniqueness K we show that for any functional φ ∈ X∗ there exists a sequence of measures (μn) supported on K converging weak* to φ. In particular, we consider H2 of the right half plane and obtain a Carleman–type formula for the continuous wavelet transform.

We introduce a tiling problem between bounded open convex polyforms P ^⊂ℝ 2 with colored directed edges. If there exists of the polyform ^ by 1 , we construct monomorphism from sandpile group G Γ =ℤ /Δ(ℤ ) on =P ∩ℤ to one . provide several examples infinite series such tilings converging ℝ and thus define limit plane.