In the present paper we prove that the polynomial quadratic triangular Bézier surfaces are LN-surfaces. We demonstrate how to reparameterize the surfaces such that the normals obtain linear coordinate functions. The close relation to quadratic Cremona transformations is elucidated. These reparameterizations can be effectively used for the computation of convolution surfaces.

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...

The surfaces of molybdenum carbide were varied by changing the carburization temperature between 823 and 1123 K. The surfaces of the catalytic material were investigated using in-situ temperature program carburization followed by temperature program reduction and oxidation. In-situ temperature program oxidation (TPO) showed the surfaces of the catalysts contain a similar amoun...

Let M be a Kähler surface and Σ be a closed symplectic surface which is smoothly immersed in M . Let α be the Kähler angle of Σ in M . We first deduce the Euler-Lagrange equation of the functional L = ∫ Σ 1 cosα dμ in the class of symplectic surfaces. It is cos αH = (J(J∇ cosα)), where H is the mean curvature vector of Σ in M , J is the complex structure compatible with the Kähler form ω in M ,...

The first major step in proving that every complex surface diffeomorphic to a rational surface is rational was Yau’s theorem [40] that every complex surface of the same homotopy type as P is biholomorphic to P. After this case, however, the problem takes on a different character: there do exist nonrational complex surfaces with the same oriented homotopy type as rational surfaces, and the issue...

In 1899, Hutchinson [Hut99] presented a way to obtain a threeparameter family of Hessians of cubic surfaces as blowups of Kummer surfaces. We show that this family consists of those Hessians containing an extra class of conic curves. Based on this, we find the invariant of a cubic surface C in pentahedral form that vanishes if its Hessian is in Hutchinson’s family, and we give an explicit map b...

we have used lithium aluminum hydroxide reducing method of silver nitrate to prepare heterogeneous silver-silica nanocomposite particles with thiol and amino groups serving to bind the ag nanoparticles to the surfaces of the sio2 nanoparticles. we examined products of these reductions using ftir, sem, xrd and uv-vis. spectroscopy. the sio2 nanoparticles had diameters ranging from 70 to 90 nm; t...

Iran has great potential in utilizing solar energy. In order to maximize the amount of absorbed solar radiation to absorber surfaces, the surfaces should be installed at a suitable angle slope to the horizon that is discussed in this article. The calculations performed in this study was done using MATLAB software. In this study, radiation received on the ground in 31 provincial capitals of the ...