Gradient-constrained discounted Steiner trees II: optimally locating a discounted Steiner point

A gradient-constrained discounted Steiner tree is a network interconnecting given set of nodes in Euclidean space where the gradients of the edges are all no more than an upper bound which defines the maximum gradient. In such a tree, the costs are associated with its edges and values are associated with nodes and are discounted over time. In this paper, we study the problem of optimally locating a single Steiner point in the presence of the gradient constraint in a tree so as to maximize the sum of all the discounted cash flows, known as the net present value (NPV). An edge in the tree is labelled as a b edge, or a m edge, or an f edge if the gradient between its endpoints is greater than, or equal to, or less than the maximum gradient respectively. The set of edge labels at a discounted Steiner point is called its labelling. The optimal location of the discounted Steiner point is obtained for the labellings that can occur in a gradient-constrained discounted Steiner tree. In this paper, we propose the gradient-constrained discounted Steiner point algorithm to optimally locate the discounted Steiner point in the presence of a gradient constraint in a network. This algorithm is applied to a case study. This problem occurs in underground mining, where we focus on the optimization of underground mine access to obtain maximum NPV in the presence of a gradient constraint. The gradient constraint defines the navigability conditions for trucks along the underground tunnels.     

Intermediate subfactors with no extra structure

If are type II factors with and we show that restrictions on the standard invariants of the elementary inclusions , , and imply drastic restrictions on the indices and angles between the subfactors. In particular we show that if these standard invariants are trivial and the conditional expectations onto and do not commute, then is or . In the former case is the fixed point algebra for an outer action of on and the angle is , and in the latter case the angle is and an example may be found in the GHJ subfactor family. The techniques of proof rely heavily on planar algebras.

     

Adsorption-induced surface stresses in alkanethiolate-au self-assembled monolayers

First-principles calculations were employed to elucidate the origin of adsorption-induced surface stresses in alkanethiolate self-assembled monolayers on an Au(111) surface. Our results suggest a mechanism that accounts for the huge relief of the tensile stress compared to the bare surface in terms of a local rearrangement of surface Au atoms accompanying charge removal from the surface towards the Au-S bond. A purely interadsorbate interaction model is shown to be inconsistent with the anisotropy and the magnitude of the calculated stress.     

Spectrophotometric determination of La, Ce, Pr and Nd in the presence of copper by use of arsenazo III

Summary Arsenazo III was applied to the determination of the total amount of La, Ce, Pr and Nd in the presence of Cu, using sodium thiosulphate for masking Cu up to 50 mg. The lanthanides can be analyzed within the range of 0–2.4 or in presence of Pb, Al, Ni, Fe 0–1.6 mg/l. Interferences of Zn, Mn, Ni, Al, Sn, Pb and Fe were examined. The procedure was applied to the determination of Ce in CuSnCe alloys and Al and Pb brasses without prior separation of the matrix.     

Experimental determination of propagation constant using end-etched fiber

We introduce the end-etched fiber technique to separate all guided modes into individual mode rings. A direct measurement of the propagation constant as a function of propagation angle and fiber parameters is demonstrated, for a single-mode fiber. We have favorable experimental results when compared to the theoretical values.