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...

The purpose of this paper is to study how the geometry and the spatial distribution of energy fluctuations of different length scales in a spiral vortex layer are related to each other in a time-dependent way. The numerical solution of Krasny [J. Comput. Phys. 65, 292 (1986)], corresponding to the development of the Kelvin-Helmholtz instability, is analyzed in order to determine some geometrica...

1. Abstract Motivated by field measurements of aquifer hydraulic conductivity (K), recent tech5 niques were developed to construct anisotropic fractal random fields, in which the scaling, 6 or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble 7 numerical results are analyzed for solute transport through these 2-D “operator-scaling” 8 fractional Brownian motio...

We show that if T is a bounded linear operator on a complex Hilbert space, then 1 2 ‖T‖ ≤ √ w2(T ) 2 + w(T ) 2 √ w2(T )− c2(T ) ≤ w(T ), where w(·) and c(·) are the numerical radius and the Crawford number, respectively. We then apply it to prove that for each t ∈ [0, 12 ) and natural number k, (1 + 2t) 1 2k 2 1 k m(T ) ≤ w(T ), where m(T ) denotes the minimum modulus of T . Some other related ...

In previous work a model was developed to predict the annual average cumulative distribution of the effective earth radius factor, the k-factor, for telecommunications applications in South Africa. Long term meteorological radiosonde data from eight stations were used for this purpose. In this paper, the model is used to predict the cumulative effective earth radius, or k-factor, distribution f...

Viscous flow through fibrous media is characterized macroscopically by the Darcy permeability ( K D). The relationship between K D and the microscopic structure of the medium has been the subject of experimental and theoretical investigations. Calculations of K D based on the solution of the hydrodynamic flow at fiber scale exist in literature only for two-dimensional arrays of parallel fibers....

We study the spectral radius of graphs with n vertices and k cut edges. In this paper, we show that of all the connected graphs with n vertices and k cut edges, the maximal spectral radius is obtained uniquely at Kk n , where K k n is a graph obtained by joining k independent vertices to one vertex of Kn−k . We also discuss the limit point of the maximal spectral radius. © 2004 Elsevier Inc. Al...

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...