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.     

Association Behavior of 4-Acylpyrazolone Derivative and Tertiary Amine of High Molecular Weight in Antagonistic Synergistic Extraction of Palladium

To find an effective extraction and removal method for palladium(II), which is one of the main fission products from an acidic nuclear spent fuel solution, the extraction behavior of palladium(II) from a nitric acid medium by an acidic chelating extractant, 1-phenyl-3-methyl-4-trifluoroacetylpyrazolone-5-one (HPMTP) and a tertiary amine of high molecular weight, tri-n-octylamine (TOA), has been studied by spectrophotometry. A noticeable antagonistic extraction effect was observed in the extraction system under the given conditions. To understand this phenomenon, a preliminary investigation was performed to explain the mechanism of this reaction. According to the theory of corresponding solutions (TCS), the association reaction between HPMTP and TOA is proposed in the organic phase. An associated species, HPMTP·TOA, formed through hydrogen bonding in a chloroform medium might be the main reason why an antagonistic extraction effect occurred. The association constant between HPMTP and TOA was calculated to be 2.86±0.05.     

Acoustic characteristics of Ni–Nb–Zr–H glassy alloys by ultrasonic shear waves

The propagation characteristics of shear horizontally polarized (SH) waves passing through (Ni₄₂Nb₂₈Zr₃₀)_100–x H_x (x = 0–15.2) glassy alloys were investigated as a function of hydrogen content. With an increase in hydrogen content, the propagation time and main frequency of the receiving waves show increase and decrease, respectively, indicating expan‐ sion in average atomic distance which comes from solution of hydrogen. In sharp contrast to crystalline alloys, the decrease in damping ratio and the delay in phase with increasing hydrogen suggest a strong settlement of hydrogen into four‐coordination sites surrounded tetrahedrally by four Zr atoms and the resulting increase in dynamic elasticity, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis and properties of furo[4,3,2-de][1]benzopyran

A new heterocycle, furo[4,3,2-de][1]benzopyran ( 2 ), was synthesized. A key step in the sequence was the allylic bromination of 3,4-dihydrofuro[4,3,2-de][1]benzopyran ( 8 ) to give 3-bromo-3,4-dihydrofuro[4,3,2-de][1]-benzopyran ( 10 ) using N-bromosuccinimide under irradiation and high dilution conditions. Bromide 10 was dealt with 1,8-diazabicyclo[5.4.0]undec-7-ene to afford compound 2 . Several reactions of 2 were examined. Protonation of 2 in trifluoroacetic acid occurred at the 2-position to form a pyrylium ion 12 . Catalytic hydrogenation of 2 with palladium on charcoal proceeded smoothly to give 8 . Reduction of 2 by sodium and ethanol afforded 3-ethyl-4-hydroxybenzofuran ( 14 ). Electrophilic substitutions of 2 such as formylation, acetylation, and bromination, occurred easily at the 2-position. The above results show that compound 2 has both properties of benzofuran and 4-methylenepyran.     

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.     

Structurally isomeric two pyridino macrocycles: complexation and structures

Pyridine-based, structurally isomeric two macrocyclic compounds displayed a remarkably different complexation nature. The cage-type compound has an ideal structure for spherical cations, especially for the NH₄⁺ ion, but the reaction with some transition metals and Ln³⁺ produced its protonated species. On the other hand, its isomer formed complexes with alkali metals and lanthanides (1:1) and also with transition metals. Some structures of the complexes were clarified by crystallographic analyses.     

Application of Automatic Chromatic Dispersion Compensation for Realization of All-Optical Network

We have studied the algorithm for the automatic chromatic dispersion compensation using bit error rate (BER) and Q-factor optimization for realization of dynamically reconfigurable all-optical network. We have made sure good performance using the compensation system by laboratory experiments.