Minimal Ellipsoid Circumscribing a Polytope Defined by a System of Linear Inequalities

In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system of linear inequalities. If we know all vertices of the polytope and its cardinality is not very large, we can solve the problem in an efficient manner by a number of existent algorithms. However, when the polytope is defined by linear inequalities, these algorithms may not work since the cardinality of vertices may be huge. Based on a fact that vertices determining an ellipsoid are only a fraction of these vertices, we propose algorithms which iteratively calculate an ellipsoid which covers a subset of vertices. Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven.     

A two step algorithm for solving a large scale semi-definite logit model

This paper proposes a two step algorithm for solving a large scale semi-definite logit model, which is appreciated as a powerful model in failure discriminant analysis. This problem has been successfully solved by a cutting plane (outer approximation) algorithm. However, it requires much more computation time than the corresponding linear logit model. A two step algorithm to be proposed in this paper is intended to reduce the amount of computation time by eliminating a certain portion of the data based on the information obtained by solving an associated linear logit model. It will be shown that this algorithm can generate a solution with almost the same quality as the solution obtained by solving the original large scale semi-definite model within a fraction of computation time.     

Minimum concave cost production system: A further generalization of multi-echelon model

We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n ⁴ m) algorithm for this class of problems.     

Liquid crystalline gel with refractive index gradient of curdlan

Curdlan dissolved in aqueous sodium hydroxide was dialyzed to aqueous calcium chloride to form a gel. Transparent and turbid concentric layers observed in the gel cross section perpendicular to the long axis of the dialysis tube were identified as liquid crystalline gels with refractive index gradient and amorphous gels, respectively. The thickness of each layer was proportional to the diameter of the dialysis tube, and the gelation proceeded in proportion to the root of time. The unique pattern formation was attributed to the change of curdlan conformation and calcium-induced cross-linking resulting from a diffusion of calcium cations and hydroxide anions through the dialysis tube. It is suggested that the orderedness of the curdlan molecules decreases by the increase of the curvature of the concentric liquid crystal layers as the layer comes toward the center of the dialysis tube.     

Highly regio- and stereoselective hydrometallation reactions of fluorine-containing internal alkynes: Novel approaches to fluoroalkylated alkenes

Hydroalumination, hydrocupration, and hydroboration reactions of various fluorine-containing alkynes were investigated. The alkyne reacted smoothly with 2.0 equiv. of Red-Al at −78 °C to give the hydroaluminated adduct in a highly regio- and stereoselective manner, which was treated with iodine, the corresponding vinyliodide being produced in moderate yield. Hydrocupration of the alkynes also took place, but the resulting vinylmetal reacted with various electrophiles sluggishly. In sharp contrast, the reaction with dicyclohexylborane proceeded smoothly to afford the cis-addition products preferentially, which were subjected to Suzuki-Miyaura cross-coupling reaction, leading to trisubstituted alkenes in high yields.     

Total synthesis of cis-solamin and its inhibitory action with bovine heart mitochondrial complex I

A convergent total synthesis of cis-solamin (1a) and its diastereomer (1b) was accomplished. A key reaction of this approach was the use of VO(acac)₂-catalyzed diastereoselective epoxidation of (Z)-bis-homoallylic alcohol 3 followed by spontaneous cyclization for the cis-THF ring formation. By comparison of the optical rotation of the two possible diastereomers, it is suggested that the absolute configuration of natural cis-solamin is 1a. Inhibitory action of synthetic 1a and 1b with bovine heart mitochondrial complex I are reported.