Ideal polytopes and face structures of some combinatorial optimization problems

Given a finite setX and a family of feasible subsetsF ofX, the 0–1 polytope P (F is defined as the convex hull of all the characteristic vectors of members ofF We show that under a certain assumption a special type of face ofP(F) is equivalent to the ideal polytope of some pseudo-ordered set. Examples of families satisfying the assumption are those related to the maximum stable set problem, set packing and set partitioning problems, and vertex coloring problem. Using this fact, we propose a new heuristic for such problems and give results of our preliminary computational experiments for the maximum stable set problem.Supported by a JSPS Fellowship for Young Scientists.Supported by Grant-in-Aids for Co-operative Research (06740147) of the Ministry of Education, Science and Culture.     

Synthesis of nitrogen-containing heterocycles. 7 Reaction of aliphatic diaminomethylenehydrazones with hindered ethoxymethylenecyanoacetate

Aliphatic diaminomethylenehydrazones 1 were reacted with ethyl 2-cyano-3-ethoxy-2-pentenoate 2 to give a number of heterocycles in low to moderate yields, according to the substitution pattern and the size of substituent. When 1 carried a single methyl group on the terminal nitrogen, it gave preferentially 6-oxo-1,6-dihydropyrimidines 4 incorporating N(4) into the ring. In contrast, the reaction between 1c or 1d and 2 led to 6-imino- and 6-oxo-1, 6-dihydropyrimidines 7 and 8 along with 3 . When the alkylidene moiety was bulky, 1e and 1f , the similar reaction gave 3 in high yields without any cyclized product. Upon exposure to acid, compound 3 yielded 6-oxo-1,6-dihydropyrimidines 6 , [1,2,4]triazolo[1,5-c]pyrimidine-8-carboxylate 5 and N-alkenyl-1,2,4-triazoles 9 in addition to 7 and 8 in proportions dictated by the nature of the substituents of 1 . The structural assignment and reaction mechanism are discussed.     

Distribution of 201Tl in the blood

Thallium-201 distribution in the blood was investigated both in vivo and in vitro. Thallium-201 was distributed into the erythrocytes and plasma with the ratio of 1.4 +/- 0.3 to 1.0, immediately after its administration. The uptake of 201Tl into the erythrocytes in vitro were affected by the incubation temperature and the presence of ouabain and KCl; indicating that the 201Tl was uptaken into cells partly through their membranes Na, K-ATPase. Erythrocytes could retain 201Tl in it, whereas 201Tl was present as free ion in the plasma. Thallium-201 was flew out of erythrocytes into the plasma, keeping the ratio of 201Tl in erythrocytes/plasma to be 1.9 +/- 0.2/1.0.     

Microdetermination of carbon and hydrogen in organic compounds using flushed-oxygen combustion tube

A rapid method of microanalysis for carbon and hydrogen in organic compounds using an empty combustion tube fused with two nozzles for flushing oxygen and employing reduced copper for the reduction of nitrogen oxide was investigated. A sample was decomposed rapidly in a sample heater for 2 min, and the gasified vapor was transported to the stationary combustion zone heated at 850 °C, where oxygen was flushing from two nozzles, the oxygen flow was then replaced with nitrogen for 3 min until all the combustion products were swept out towards the absorption train. The sample size was suggested to be around 1 mg for this rapid method, using a Mettler UM6, or an electrobalance having equal precision for the sampling.     

Dynamics of positive charge carriers on Si chains of polysilanes

The transient absorption of radical cations of a variety of substituted polysilanes is discussed quantitatively in terms of the molar extinction coefficient and oscillator strength by nanosecond pulse radiolysis. Oxygen-saturated polysilane solutions in benzene exhibit a strong transient absorption band ascribed to the polysilane radical cation. The transient species react with N,N,N',N'-tetramethyl-p-phenylene-diamine (TMPD) to produce TMPD radical cations. On the basis of the molar extinction coefficient of the TMPD radical cation, the molar extinction coefficients for the radical cations of polysilanes are found to increase in the range 3.3 x 10(4) to 2.0 x 10(5) M(-)(1) cm(-)(1) with increasing polymer segment length. The stepwise increase in the total oscillator strength with an increase in the number of phenyl rings directly bonded to the Si skeleton suggests the delocalization of the positive polaron state and/or the SOMO state over the phenyl rings, indicating the importance of phenyl rings in intermolecular hole transfer processes.     

A new reforming process based on CH4 decomposition using a hydrogen-permeating membrane reactor

A new reforming process was studied using Ni/SiO₂ with a hydrogen-permeating membrane reactor. Nickel catalyst supported on SiO₂ is highly active for CH₄-H₂O-O₂ reaction in membrane reactor and the reaction close to CH₄ + 0.35O₂ + 1.3H₂O → CO₂ + 3.3H₂ proceeds at 873 K. Since the selectivity to carbon and CO₂ increased and decreased with decreasing contact time respectively, it is considered that the reaction was started by decomposition of CH₄ followed by oxidation of C and water shift reaction. Therefore, the reaction mechanism was different from so-called autothermal reforming (ATR) reaction.     

A systematic preparation of new contracted Gaussian-type orbital sets. VI. Ab initio calculation on molecules containing Na through Cl

Compact contracted Gaussian basis sets introduced in the preceding article are tested for ab initio molecular calculations on molecules containing third-row atoms (Na through Cl). It is found that the effect of splitting valence orbitals is essential for these molecules and addition of polarization functions to split basis sets can yield computed geometries, spectroscopic constants, and atomization energies in close agreement with the result of near Hartree–Fock calculations.     

Transfer hydrogenation and transfer hydrogenolysis—21 : Dehydrogenation of alcohols by quinones

Dehydrogenation of benzyl-type alcohols and hydroaromatic compounds by 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) and tetrachloro-p-benzoquinone were examined, and the hydrogen transfer from 1-phenyl-1-propanol to DDQ was investigated in detail. The yield of the propiophenone increased when solvents which would be expected to increase the concentration of the charge transfer complex between the alcohol and DDQ were used. Initial rates of the reaction in dioxane were proportional to the concentration of the hydrogen donor and that of the hydrogen acceptor. In the dehydrogenation of several para- or meta-substituted 1-phenyl-1-propanols at 60°, ?3.30 was obtained as a value of reaction constant. Relative rates of the reaction of PhCH(OH)Et, PhCH(OD)Et, PhCD(OH)Et, and PhCD(OD)Et were 8.9,9.1,1.0 and 1, respectively. This result suggests that the transfer of the H atom attached to the α-carbon of the alcohol is the rate-determining step. This and some other results support a two-step ionic mechanism for the dehydrogenation of alcohols.     

Small ring compounds—XXX : Homolytical aromatic substitution and hydrogen abstraction reaction with cyclopropyl radical

Homolytic aromatic substitution and hydrogen abstraction reactions with cyclopropyl radical were carried out to determine the reactivity and ionic character of cyclopropyl radical by examination of the orientation effect, partial rate factor and influence of substituents. By thermal decomposition of biscyclopropaneformyl peroxide in a series of substituted benzenes, the corresponding cyclopropylated benzene derivatives (the mixture of ortho, meta and para isomers) were obtained in moderate yield. In view of the orientation effect and the partial rate factor, the cyclopropyl radical seems to be fairly free from polar effect, and to resemble the phenyl radical more than the common alkyl radical although the cyclopropyl radical has a slightly higher reactivity than the phenyl radical. The relative reactivity of the 2-phenylcyclopropyl radical in the hydrogen abstraction reaction toward the benzylic position of ring-substituted toluenes gave good Hammett's correlation with the slope of + 0·20 suggesting little ionic character in the transition state. This result was in good agreement with the conclusion obtained from homolytic aromatic substitution reaction and with the chemical reactivity to be expected from the non-planar nearly sp²-hybridized conformation of the cyclopropyl radical.     

A rapid method for the microdetermination of nitrogen in organic compounds using a flushed-oxygen combustion tube

A micromethod to determine nitrogen in organic compounds of 1–1.5 mg has been studied by the combustion method where oxygen is flushed into an empty combustion tube heated at 850 °C. The flushing nozzle is consisted of two silica filters in a L-tube and oxygen flowing out of the nozzle rapidly oxidizes the organic vapor gasified in a sample heater. Excess oxygen and nitrogen oxides are absorbed and reduced with reduced copper heated at 500–600 °C.