Teeth and bones are highly mineralized tissues containing inorganic minerals such as calcium phosphate, and a growing number of evidences show that their mineral content is associated with many diseases. Although the quantification of mineral contents by micro-computed tomography(micro- CT) has been used in diagnosis and evaluation for treating bone diseases, its application for teeth diseases has not been well established. In this study, we attempted to estimate a usefulness of a high-resolution micro-CT in analysis of human teeth. The teeth were scanned by using the Skyscan 1172 micro-CT. In order to measure tooth mineral content, beam hardening effect of the machine was corrected with a radiopaque iodinecontaining substance, iodoacetamide. Under the maximum resolution of 6.6 μm, X-ray densities in teeth and hydroxyapatite standards were obtained with Hounsfield unit (HU), and they were then converted to an absolute mineral concentration by a CT Analyzer software. In enamel layer of cusp area, the mean mineral concentration was about 2.14 mg/mm3 and there was a constant mineral concentration gradient from the enamel surface to the dentinoenamel junction. In the dentin of middle 1/3 of tooth, the mean mineral concentration was approximately 1.27 mg/mm3 and there was a constant mineral concentration gradient from the outer of root to the pulp side, ranging from 1.3 to 1.06 mg/mm3. In decay region of dentin, the mineral content was gradually decreased from the intact inner side to the decayed surface. These results suggest that high-resolution micro-CT can be as a useful tool for non-invasive measurement of mineral concentration in teeth.

In this paper, we propose a new ship scheduling set packing model considering limited risk or variance. The set packing model is used in many applications, such as vehicle routing, crew scheduling, ship scheduling, cutting stock and so on. As long as the ship scheduling is concerned, there exits many unknown external factors such as machine breakdown, climate change and transportation cost fluctuation. However, existing ship scheduling models have not considered those factors apparently. We use a quadratic set packing model to limit the variance of expected cost of ship scheduling problems under stochastic spot rates. Set problems are NP-complete, and additional quadratic constraint makes the problems much harder. We implement Kelley's cutting plane method to replace the hard quadratic constraint by many linear constrains and use branch-and-bound algorithm to get the optimal integral solution. Some meaningful computational results and comments are provided.

Column subtraction, originally proposed by Harche and Thompson(1994), is an exact method for solving large set covering, packing and partitioning problems. Since the constraint set of ship scheduling problem(SSP) have a special structure, most instances of SSP can be solved by LP relaxation This paper aim, at applying the column subtraction method to solve SSP which am not be solved by LP relaxation For remained instances of unsolvable ones, we subtract columns from the finale simplex table to get another integer solution in an iterative manner. Computational results having up to 10,000 0-1 variables show better performance of the column subtraction method solving the remained instances of SSP than complex branch and-bound algorithm by LINDO.