Isotone solutions of parametric linear complementarity problems

The parametric linear complementarity problem is given by the conditions:q + p + Mz 0, 0,z 0,z ^T (q + p + Mz) = 0. Under the assumption thatM is a P-matrix, Cottle proved that the solution mapz() of the above problem is montonically nondecreasing in the parameter for every nonnegativeq and everyp if and only ifM is a Minkowski matrix. This paper examines whether a similar result holds in various other settings including a nonlinear case.     

Grinding-induced equimolar complex formation between thiourea and ethenzamide

We prepared and characterized a grinding-induced equimolar complex of thiourea with ethenzamide. When thiourea and ethenzamide were co-ground at a molar ratio of 3 : 1, new powder X-ray diffraction (PXRD) peaks were observed in addition to PXRD peaks of thiourea crystals. The optimum stoichiometry of the new structure was confirmed as 1 : 1 mol/mol. Effect of grinding time on the thiourea-ethenzamide equimolar complex formation was investigated by using PXRD, differential scanning calorimetry and Fourier transform infrared spectroscopy. The equimolar crystal structure was confirmed by X-ray diffraction measurements of the single crystal which was recrystallized from ethanol. It was found that the intermolecular hydrogen bond formations between thiourea and ethenzamide molecules contributed to the equimolar complex formation. The complex formation was not observed in the cases where benzamide, salicylamide or 3-ethoxybenzamide was co-ground with thiourea. 2-Alcoxyl benzamide structures should be required for the grinding-induced equimolar complex formation with thiourea.     

Relaxations of selenium in crystalline and amorphous states

Complex shear modulus at 33 kc./sec. is measured at temperatures of ?150–150°C. for amorphous selenium and crystalline selenium with different crystallinities. The dielectric relaxation at 10 kc./sec. to 3 kc./sec. to 3 Mc./sec. is observed at temperatures of ?32–25°C. for iodine-doped crystalline selenium. It is concluded from the results of this study and of others' that selenium exhibits four relaxations, α, β γ, and δ, in order of descending temperature. The β relaxation is observed only in the amorphous sample above the glass temperature and is assigned to the primary relaxation. The α, γ, and δ relaxations are found in the crystalline selenium. The α relaxation, which is prominent in a highly crystalline sample, is assigned to the crystalline relaxation. The γ and δ relaxations increase in peak height with decreasing crystallinity and are attributed to the disordered region in the crystalline selenium. The dispersion map (logarithm of frequency versus reciprocal absolute temperature of loss maximum) of selenium is presented.     

STUDIES ON AMINODIOXETANES AS A MODEL OF BIOLUMINESCENCE INTERMEDIATES. 1-(1-METHYL-3-INDOLYL)-6-PHENYL-2,5,7,8-TETRAOXABICYCLO[4,2,0]OCTANE,AN AMINODIOXETANE RESULTING IN EFFICIENT ULTRAVIOLET AND EXCIPLEX CHEMILUMINESCENCE*

Abstract— The title aminodioxetane prepared by photooxygenation of 2–(l-methyl-3-indolyl-3-phenyl-1,4-dioxene is fairly stable at ?46°C and gives on warming to room temperature an ultraviolet light at Λ_max 320 nm, which corresponds to 377kJ/mol; the highest energy ever observed among the efficient chemiluminescent compounds. The efficiency of chemiluminescence and excited singlet molecule formation in n-hexane were 3.6% and at least 50%, respectively. Substitution and solvent effects suggest polar nature of the transition state as expected from the ‘CIEEL’ mechanism. In polar solvents, the dioxetane gives visible light (Λ_max 400 nm in dichloromethane) as well as the UV light; the former being quenched by methanol. This is interpreted in terms of an intramolecular exciplex formation between the indole and phenyl groups. This is the first example of an intramolecular exciplex produced by the dioxetane decomposition.     

Development of a new file search system for nuclear magnetic resonance spectra: Production of an Enlarged Data Base and Search Test

A practical search system for proton n.m.r. spectra is reported. The coding rules and search algorithms are described in detail. Data for 8000 spectra have been converted into a computer-readable file from printed charts. Several search tests are used to evaluate the usefulness of the search system, and various effects of experimental conditions such as different instruments, frequencies and solvents on recall efficiency are described. The results presented indicate that the system should be applicable to routine analytical work.     

A mixed version of Menger's theorem

An(a, b)-n-fan means a union ofn internally disjoint paths. Menger's theorem states that a graphG has an(a, b)-n-fan if and only ifG isn-connected betweena andb. We show thatG contains edge-disjoint(a, b)-n-fans if and only if for anyk withk0min{n–1, |V(G)|–2} and for any subsetX ofV(G)-{a, b} with cardinalityk, G-X is (n-k)-edge-connected betweena andb.     

Evolution of host-parasitoid network through homeochaotic dynamics

Host-parasitoid systems with evolving mutation rates are studied. By increasing the growth rate of hosts, the diversity of both species is maintained dynamically. For the lower growth rate, diversity is brought about by mere parasitism. The average mutation rate for parasites is elevated to a high value, while that for hosts is suppressed at a low level. For the higher growth rate, the mutation rates for both hosts and parasites are elevated to form a symbiotic cluster connected by on-going mutation. This symbiotic state is sustained through a chaotic oscillation keeping some coherency among species. For a flat landscape for hosts, dynamical clustering of oscillation is observed. Lyapunov spectra of such oscillations show that high dimensional chaos with small positive exponents underlies in the symbiotic state. This weak high dimensional chaos, termed "homeochaos," is essential to the maintenance of symbiosis in ecosystems.     

Heavenly blue anthocyanin II trans-4-0-(6-0-(trans-3-0-(β -d-glucopyranosyl)caffeyl)-β-d-glucopyranosyl)- caffeic acid,a novel component in heavenly blue anthocyanin

Structure of an alkaline hydrolysis product of heavenly blue anthocyanin was determined to be $\text{trans}$-4-0-(6-0-($\text{trans}$-3-0-(β-D-glucopyranosyl)caffeyl)-β-D- glucopyranosyl)caffeic acid ($\text{1}$).     

Oxidative cyclization of morusin

Oxidative cyclization of morusin (I) by using one-electron transfer oxidizing agents (manganese dioxide, silver oxide) afforded morusin hydroperoxide (II). A similar reaction was carried out in the presence of 2,4,6-tri-t-butylphenol, a radical quencher, to give compounds (IV, V, VI and VII) coupled with the 2,4,6-tri-t-butylphenoxy radical. On the basis of above results, the possible mechanism of this oxidative cyclization was discussed. In addition, morusin hydroperoxide (II) was also obtained by photo-sensitized oxidation of morusin (I) in the presence of sensitizers (Rose Bengal, hematoporphyrin). To elucidate the reaction mechanism similar reactions were carried out in the presence of radical quencher (2,4,6-tri-t-butylphenol) or singlet oxygen quencher (triethylenediamine). From these results, the possible mechanism of the formation of morusin hydroperoxide (II) from morusin (I) was discussed.