Fitting concentric circles to measurements

Measurements for fitting a given number of concentric circles are recorded. For each concentric circle several measurements are taken. The problem is to fit the given number of circles to the data such that all circles have a common center. This is a generalization of the problem of fitting a set of points to one circle. Three objectives, to be minimized, are considered: the least squares of distances from the circles, the maximum distance from the circles, and the sum of the distances from the circles. Very efficient optimal solution procedures are constructed. Problems based on a total of 10,000 measurements are solved in about 10 s with the least squares objective, $<$ 2 s with the maximum distance objective, and a little more than 1 min for the minisum objective.     

Solving the ordered one-median problem in the plane

In this paper, we propose a general approach solution method for the single facility ordered median problem in the plane. All types of weights (non-negative, non-positive, and mixed) are considered. The big triangle small triangle approach is used for the solution. Rigorous and heuristic algorithms are proposed and extensively tested on eight different problems with excellent results.     

Strategic competitive location: improving existing and establishing new facilities

Competitive facility location models consider two main strategies for increasing the market share captured by a chain subject to a budget constraint. One strategy is the improvement of existing facilities. The second strategy is the construction of new facilities. In this paper we analyse these two strategies as well as the joint strategy which is a combination of the two. All three strategies are formulated as a unified model. The best solution to an individual strategy is a feasible solution to the joint one. Therefore, the joint strategy must yield solutions that are at least as good as the solutions to each of the individual strategies. Based on the results of extensive experiments, we conclude that the increase in market share captured by a chain when the joint strategy is employed can be significantly higher than increases obtained by individual strategies. A branch and bound procedure and a tabu search heuristic are constructed for the solution of the unified model. Both algorithms performed very well on a set of test problems with up to 900 demand points. A total of 62% of the test problems were optimally solved by the branch and bound procedure.     

The first example of isomeric solid amide and its enol

[Structure: see text] The first example of a crystalline amide and its tautomeric enol was obtained for the amide MeNHCSCH(CN)CONHMe (8) and its enol MeNHCSC(CN)=C(OH)NHMe (9). Their X-ray structures were determined, and their structural features resemble those of other related amides and enols. No other example of a similar pair was obtained. In solution, both 8 and 9 and a small percentage of the isomeric enol of thioamide MeNHCOC(CN)=C(SH)NHMe (10) were obtained in solvent-dependent compositions, which are rapidly established.     

Isomeric solid enols on ring- and amide-carbonyls of substituted 2-carbanilido-1,3-indandiones

Both isomeric enols on ring carbonyl (5b) and on amide carbonyl (6b) derived from N-p-methoxyphenyl-2-carbamido-1,3-indandione (4b) were isolated, and their X-ray structures were determined. X-ray diffraction of the N-o,p-dimethoxy analogue indicated a disorder ascribed to the presence of a 6:4 mixture of 5c and 6c. Calculation (B3LYP/6-31+G*) gave good agreement with observed geometries. The calculated energies indicated that enols 6 are more stable by <1 kcal/mol than enols 5 and much more stable than amides 4.     

The expropriation location problem

In this paper, we consider the location of a new obnoxious facility that serves only a certain proportion of the demand. Each demand point can be bought by the developer at a given price. An expropriation budget is given. Demand points closest to the facility are expropriated within the given budget. The objective is to maximize the distance to the closest point not expropriated. The problem is formulated and polynomial algorithms are proposed for its solution both on the plane and on a network.     

A distribution map for the one-median location problem on a network

In this paper we consider the Weber (one-median) location problem on a network. The weights at the nodes are drawn from a multivariate normal distribution. We find the probability that the optimal location is at each of the nodes. This set of probabilities is the distribution map. The methodology is illustrated on two networks of 20 nodes each.     

Development of an oligoamide coating as a surface mimetic for aromatic polyamide films used in reverse osmosis membranes

We developed a method for the in situ synthesis of an oligoamide coating on gold. The resultant surface chemical composition, wettability, and chemical nature were comparable to aromatic polyamide films used as reverse osmosis membranes. Hence, the oligoamide wafer may be used in adsorption/fouling studies as a surface mimetic of reverse osmosis membranes.     

Strategic design of competing supply chain networks for inelastic demand

A model for designing the network of a new entrant supply chain under inelastic demand and in the presence of pre-existing competing chains is proposed. These supply chains provide an identical product for a market area. The model considers the location of distribution centres and retail outlets on a discrete set of potential locations. The assumptions of the model are: (1) static competition between the new and pre-existing chains and (2) a probabilistic customer behaviour based on an attraction function depending on both the location and the quality of the retailers. This model also incorporates the impact of the facilities’ location decisions on the operational inventory and shipment decisions. The resulting model is formulated as a mixed integer non-linear programme (MINLP). To solve the MINLP it is transformed to a linear one. We illustrate the model, discuss the results of a real-world case, and investigate the effectiveness of the proposed algorithm using randomly generated examples.     

Connectivity guarantees for wireless networks with directional antennas

We study a combinatorial geometric problem related to the design of wireless networks with directional antennas. Specifically, we are interested in necessary and sufficient conditions on such antennas that enable one to build a connected communication network, and in efficient algorithms for building such networks when possible.We formulate the problem by a set P of n points in the plane, indicating the positions of n transceivers. Each point is equipped with an α-degree directional antenna, and one needs to adjust the antennas (represented as wedges), by specifying their directions, so that the resulting (undirected) communication graph G is connected. (Two points p,q∈P are connected by an edge in G, if and only if q lies in p?s wedge and p lies in q?s wedge.) We prove that if α=60°, then it is always possible to adjust the wedges so that G is connected, and that α?60° is sometimes necessary to achieve this. Our proof is constructive and yields an time algorithm for adjusting the wedges, where k is the size of the convex hull of P.Sometimes it is desirable that the communication graph G contain a Hamiltonian path. By a result of Fekete and Woeginger (1997) [8], if α=90°, then it is always possible to adjust the wedges so that G contains a Hamiltonian path. We give an alternative proof to this, which is interesting, since it produces paths of a different nature than those produced by the construction of Fekete and Woeginger. We also show that for any n and ε>0, there exist sets of points such that G cannot contain a Hamiltonian path if α=90°−ε.