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 novel pre-shearing technique for measurement of the electrorheological effect of a side-chain liquid crystalline polysiloxane

A side-chain liquid crystalline polysiloxane derivative possessing mesogens was synthesized. The mesogens included a large dielectrically-anisotropic moiety. Phase transition behaviour was investigated and the electrorheological (ER) effect of the polymer considered. No ER effect was observed in non-sheared polysiloxane derivative because of its high inherent viscosity. However, a large ER effect was observed after pre-shearing. Pre-shearing, i.e. shearing with a high shear rate before the measurements, arranges the terminal mesogens in the shearing direction. Furthermore, a dilution of the sample led to a larger ER effect exceeding 10 000 Pa. We thus were able to demonstrate a new approach for the appearance of the ER effect.     

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.     

Effects of poly(ethylene glycol) (PEG) concentration on the permeability of PEG-grafted liposomes

Poly(ethylene glycol)-grafted liposomes (PEG-liposomes) were prepared from dipalmitoylphosphatidylcholine (DPPC) with various amounts of distearoyl-N-monomethoxy poly(ethylene glycol)-succinyl-phosphatidylethanolamines (DSPE-PEG) with PEG molecular weights of 1000, 2000, 3000 and 5000. The effects of DSPE-PEG concentration on the permeability of PEG-liposomes were investigated using carboxyfluorescein (CF). In the gel state, the CF leakage from PEG-liposomes was decreased with increasing mole fractions of DSPE-PEG for all PEG molecular weights. In the liquid-crystalline state, the CF leakage from PEG-liposomes containing DSPE-PEG1000 gradually increased with increasing mole fractions of DSPE-PEG, while that of PEG-liposomes whose molecular weight in PEG units was above 2000 rapidly decreased by the addition of DSPE-PEG. Furthermore, no effect of PEG molecular weight on CF leakage was observed. The relationship between the fluorescence polarization of 1,6-diphenyl-1,3,5-hexatriene (DPH) (or 1-(4-trimethylammoniumphenyl)-6-phenyl-1,3,5-hexatriene (TMA-DPH)) and the mole fraction of DSPE-PEG for PEG-liposomes was also investigated. No significant changes in fluorescence polarization of DPH for liposomal bilayer membranes was observed in the gel and liquid-crystalline states due to the addition of DSPE-PEG, while that of TMA-DPH was decreased compared with that of liposomes without DSPE-PEG in both states.