In the Manning equation the hydraulic radius can be defined as the cross-section dimension of the shape. In pipe flow the bed shear stress is assumed to be uniformly distributed along the wetted perimeter which cannot be true in open channel flow. Hence, three approximation of the true boundary shear-stress distribution are examined and more practical conveyance depth or resistance radius formu...

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/mfms/notes 2015-16/06d functional equation.pdf] 1. L(s, χ) for even χ 2. L(s, χ) for odd χ We prove the analytic continuation and function equation of Dirichlet L-functions L(s, χ) imitating the argument Riemann used for proving the analytic continuation of ζ(s) and its funct...

In this research, a theoretical study has been undertaken on the density and also on the relationship between refractive index and density for aqueous solutions. A simple linear equation is suggested to show this relationship. Also, a semi-empirical equation has been developed for estimating the constant of this linear equation. By using our suggested equations, the refractive indices of aq...

In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A in R^{ntimes n}$ , $C in R^{ntimes n}$ , $B in R^{stimes s}$ and  $D in R^{stimes s}$ are given matrices and $X in R^{stimes s}$  is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm for solving linear system of equations with multiple right-han...

cash flow forecasting is an indispensable tool for construction companies, and is essential for the survivalof any contractor at all stages of the work. the time available for a detailed pre-tender cash flow forecast is oftenlimited. therefore, contractors require simpler and quicker techniques which would enable them to forecast cash flowwith reasonable accuracy. forecasting s-curves in constr...

When the reservoir parameters are stochastic, then the flow in a reservoir is described by stochastic partial differential equations. Spatial stochastic relative permeability in one spatial dimension is modeled by the stochastic Buckley–Leverett equation s(x, t)t + f(s(x, t), x)x = 0 for x > 0 and t > 0. f is the stochastic flux function and s is the saturation. This equation is analyzed, and i...

In this paper, we introduce the following additive type functional equation f(rx+ sy) = r + s 2 f(x+ y) + r − s 2 f(x− y), where r, s ∈ R with r + s, r − s 6= 0. Also we investigate the Hyers–Ulam–Rassias stability of this functional equation in Banach modules over a unital C∗-algebra. These results are applied to investigate homomorphisms between C∗-algebras. 2000 Mathematics Subject Classific...

In this paper we consider nite element methods for a degenerate elliptic-parabolic partial diierential system which describes the ow of two incompressible, immiscible uids in porous media. Local mesh reenement techniques for solving this degenerate system are discussed. 1. TWO-PHASE FLOW EQUATIONS In this paper we consider nite element methods for the ow of two incompressible, immiscible uids i...

We study Sobolev-type metrics of fractional order on the group of compactly supported diffeomorphisms Diffc(M), where M is a Riemannian manifold of bounded geometry. We prove that the geodesic distance, induced by the Riemannian metric, vanishes if the order s satisfies 0 ≤ s < 1 2 . For M 6= R we show the vanishing of the geodesic distance also for s = 1 2 , and for dim(M) = 1 we show that the...

Abstract: A new adaptive fuzzy fault-tolerant control scheme for complex non-linear systems is proposed in this paper. The approach presented here combines fuzzy T-S dynamic model with Riccati equation. In each local linear model of the fuzzy dynamic model, Riccati equation is used in the design of fault-tolerant control. These local models are linked together by fuzzy membership functions to f...