V-SHAPED TOEPLITZ OPERATOR

Generalised Slant Weighted Toeplitz Operator

A slant weighted Toeplitz operator Aφ is an operator on L(β) defined as Aφ = WMφ where Mφ is the weighted multiplication operator and W is an operator on L(β) given by We2n = βn β2n en, {en}n∈Z being the orthonormal basis. In this paper, we generalise Aφ to the k-th order slant weighted Toeplitz operator Uφ and study its properties. Keywords—Slant weighted Toeplitz operator, weighted multiplica...

On kth-Order Slant Weighted Toeplitz Operator

Let β = [formula: see text] be a sequence of positive numbers with β0 = 1, 0 < β(n)/β(n+1) ≤ 1 when n ≥ 0 and 0 < β(n)/β(n-1) ≤ 1 when n ≤ 0. A kth-order slant weighted Toeplitz operator on L(2)(β) is given by U(φ) = W(k)M(φ), where M(φ) is the multiplication on L(2)(β) and W(k) is an operator on L(2)(β) given by W(k)e(nk)(z) = (β(n)/β(nk))e(n)(z), [formula: see text] being the orthonormal basi...

Spatially Varied Flow Profiles in a V-Shaped Side-Channel

A Comprehensive Model for Stiffness Coefficients in V-Shaped Cantilevers

   During past decade the AFM based nanomanipulation has been focus of attention as the promising nano fabrication approach. The main challenge in this process is the real-time monitoring. Consequently, the dynamic models have been proposed as a solution to the existing challenge. In the modeling approach the magnitudes of the forces are proportional to the stiffness coefficients o...

Resistance to Flow in a V-Shaped Bottom Channel

Water flow in open channels is always subject to the resistance to flow and energy dissipation. For design purposes, one of the needed variables is the hydraulic resistance coefficient. For this mean, the influence of cross-sectional shape together with secondary flow cells and lateral distribution of true boundary shear stress have not yet been fully explored. This paper surveys the number of ...