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 Journal of Science and Technology of Agriculture and Natural Resources , 2006, Abstract: Because of slight variation of the static head due to discharge fluctuations, the labyrinth weirs are considered to be economical structures for flood control and water level regulation in irrigation networks, as compared to other devices. Labyrinth weirs are composed of folded sections observed as trapezoidal and triangular in plan view. In this study, rectangular and U-shaped labyrinth weirs were investigated. Experiments were conducted on 15 labyrinth weir models. The models included eight rectangular labyrinth models and six U-shaped labyrinth models with different heights and lengths, and one linear model. All the experiments were performed in a horizontal rectangular flume, 7 m long, 0.32 m wide and 0.35 m high. The results indicated that for all the models, discharge coefficient increased sharply with an increase in Ht/P and attained a maximum value. This coefficient then decreased smoothly with a further increase in Ht/P. Increasing height of weirs increased the discharge coefficient for both rectangular and U-shaped weirs. The results also showed that increasing the length parallel to the flow direction decreased and increasing the length perpendicular to the flow direction increased the discharge coefficient. Generally, the discharge coefficient for rectangular weir was less than that of the U-shaped weir. The obtained results compared with those of Tullis et al. (1995) showed that discharge coefficient for U-shaped weir is more and for rectangular weir is less than that of the trapezoidal weir for angle of the side legs of 8 and 12 degrees.
 Mathematics , 2013, Abstract: We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the relation between crossed modules of groups and strict 2-groups. Then we explore topological applications. We show that by applying the rack-space functor, a crossed module of racks gives rise to a covering. Our main result shows how the fundamental racks associated to links upstairs and downstairs in a covering fit together to form a crossed module of racks.
 Guy Roger Biyogmam Mathematics , 2011, Abstract: In this paper, we introduce the category of Lie $n$-racks and generalize several results known on racks. In particular, we show that the tangent space of a Lie $n$-Rack at the neutral element has a Leibniz $n$-algebra structure. We also define a cohomology theory of $n$-racks..
 Mathematics , 2015, Abstract: We give a foundational account on topological racks and quandles. Specifically, we define the notions of ideals, kernels, units, and inner automorphism group in the context of topological racks. Further, we investigate topological rack modules and principal rack bundles. Central extensions of topological racks are then introduced providing a first step towards a general continuous cohomology theory for topological racks and quandles.
 Alexandr Malijevsky Physics , 2014, DOI: 10.1088/0953-8984/26/31/315002 Abstract: We consider fluid adsorption near a rectangular edge of a solid substrate that interacts with the fluid atoms via long range (dispersion) forces. The curved geometry of the liquid-vapour interface dictates that the local height of the interface above the edge $\ell_E$ must remain finite at any subcritical temperature, even when a macroscopically thick film is formed far from the edge. Using an interfacial Hamiltonian theory and a more microscopic fundamental measure density functional theory (DFT), we study the complete wetting near a single edge and show that $\ell_E(0)-\ell_E(\delta\mu)\sim\delta \mu^{\beta_E^{co}}$, as the chemical potential departure from the bulk coexistence $\delta\mu=\mu_s(T)-\mu$ tends to zero. The exponent $\beta_E^{co}$ depends on the range of the molecular forces and in particular $\beta_E^{co}=2/3$ for three-dimensional systems with van der Waals forces. We further show that for a substrate model that is characterised by a finite linear dimension $L$, the height of the interface deviates from the one at the infinite substrate as $\delta\ell_E(L)\sim L^{-1}$ in the limit of large $L$. Both predictions are supported by numerical solutions of the DFT.