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...

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...

Two useful measures of the robust stability of the discrete-time dynamical system xk+1 = Axk are the -pseudospectral radius and the numerical radius of A. The -pseudospectral radius of A is the largest of the moduli of the points in the -pseudospectrum of A, while the numerical radius is the largest of the moduli of the points in the field of values. We present globally convergent algorithms fo...

There are several parameters that have significant influence in metal forming process. One of the most important of them is friction coefficient. Friction can change the pattern of metal flow and the force needed for deformation. It is necessary to determine the friction coefficient to study the effect of friction on metal forming process. This study is concerned with numerical and experimental...

The two well-known numerical radius inequalities for the tensor product $$A \otimes B$$ acting on $${\mathbb {H}} {\mathbb {K}}$$ , where A and B are bounded linear operators defined complex Hilbert spaces $$ {K}},$$ respectively \frac{1}{2} \Vert A\Vert B\Vert \le w(A B) w(A)w(B) \min \{ w(A) w(B) \}. In this article, we develop new lower upper bounds $$w(A B)$$ of study equality conditions th...