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For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account. The depth-averaged equations of k-ɛ turbulence model are also obtained. Because it accounts for the three-dimensional effect, this model is named as the complete depthaveraged model. The boundaries of natural water bodies are usually curved. In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems.

The viscous dissipation and heat transfer in the Darcy-Forchheimer flow by a rotating disk are examined. The partial slip conditions are invoked. The optimal series solutions are computed via the optimal homotopic analysis method (OHAM). The thermophoresis and Brownian motions are studied. The Darcy-Forchheimer relation characterizes the porous space. The roles of influential variables on the physical quantities are graphically examined. A reduction in the local Nusselt number is observed through thermophoresis and thermal slip parameters. The local Sherwood number depicts an increasing trend for the higher Brownian motion and concentration slip parameters.

A boundary value problems for functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower solution, sufficient conditions for the existence of the problems' solution are established. A uniformly valid asymptotic expansions of the solution is also given.

In this paper, we study the solution of differential equation with Dirac function and Heaviside function, arising from discontinuous and impulsive excitation. Firstly, according to the theory of differential equation, we suggest, then we derive the equation of x 1 (t) and x 2 (t) by terms of property of distribution, and by solving x 1 (t) and x 2 (t) we obtain x(t); finally, we make a thorough investigation about periodic impulsive parametric excitation.

This paper presents a two-dimensional analytical solution for compound channel flows with vegetated floodplains. The depth-integrated N-S equation is used for analyzing the steady uniform flow. The effects of the vegetation are considered as the drag force item. The secondary currents are also taken into account in the governing equations, and the preliminary estimation of the secondary current intensity coefficient K is discussed. The predicted results for the straight channels and the apex cross-section of meandering channels agree well with experimental data, which shows that the analytical model presented here can be applied to predict the flow in compound channels with vegetated floodplains.

In this paper, we study iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities which include. as a special case, some known results in this field. Our results are the extension and improvements of the results of Siddiqi and Ansari, Ding, and Zeng.

The sufficient conditions are given for all solutions of certain non-autonomous differential equation to be uniformly bounded and convergence to zero as t→∞. The result given includes and improves that result obtained by Abou-El-Ela & Sadek.

Based upon the fundamental equations of three dimensional elasticity, the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate surface is expanded into Fourier-Bessel's series, therefore, an analytical solution for the problem is presented. Every fundamental equation of three dimensional elasticity can be exactly satisfied by the solution and all the independent elastic constants can be taken into account fully, furthermore, the continuity conditions between plies can also be satisfied.