On a set of generating relations of the full transformation semigroups

A set of generating relations of the full transformation semigroup Σ_n consisting of all mappings of the set $\text{Ω = {1, …, n}}$ into itself with respect to a natural system of generators {γ_jⁱ, σ_jⁱ} (defined in Section 1) is given. The set of relations (1)～(15) given in Section 1 turns out to be a set of generating relations.     

Exponential two server queue withN-policy and general vacations

AnM/M/2 queueing system with vacations is studied in which two servers keep working until there are no customers, and then one of the two servers takes a vacation. The remaining server does not leave the system during the vacation, and keeps serving the arriving customers. The duration of vacation is general. We study both theN-policy multiple vacation model and the single vacation model. This paper is concerned with the determination of the stationary distribution of the number of customers in the systems, and their decomposition structures.     

Enantiospecific and diastereoselective synthesis of syn-β-amino-α-hydroxy acids

The reaction of chiral α-hydroxy β,γ-unsaturated esters with tosyl isocyanate followed by cyclization of the resulting allylic carbamates with iodine in the presence of sodium carbonate provided trans-4,5-disubstituted 2-oxazolidinone derivatives in a highly diastereoselective manner. The subsequent removal of the iodo group and the protective functionality afforded the syn-β-amino-α-hydroxy acids. Using the reaction sequence, (2R,3S)- and (2S,3R)-3-amino-2-hydroxy acids were synthesized with high enantioselectivity.     

Organocatalytic Asymmetric Nitroaldol Reaction: Cooperative Effects of Guanidine and Thiourea Functional Groups

Catalytic enantio‐ and diastereoselective nitroaldol reactions were explored by using designed guanidine–thiourea bifunctional organocatalysts under mild and operationally simple biphasic conditions. These catalytic asymmetric reactions have a broad substrate generality with respect to the variety of aldehydes and nitroalkanes. Based on this catalytic nitroaldol process, straightforward syntheses of cytoxazone and 4‐epi‐cytoxazone were achieved. These catalytic nitroaldol reactions require KI as an additive for highly asymmetric induction; it operates by inhibiting the retro mode of the reaction. On the basis of studies of structure and catalytic‐activity relationships, a plausible guanidine–thiourea cooperative mechanism and a transition state of the catalytic reactions are proposed. Drastic substituent effects on the catalytic properties of this catalyst may lead to the development of new chiral surfactants.     

Syntheses,X‐ray crystal structures,and emission properties of diprotonated tetrapyridylpyrazine and triprotonated terpyridine

A series of metal‐free compounds, that is, planar diprotonated tetraH₂(PF₆)₂ ( 1 ), planar monoprotonated bppzHPF₆ ( 2 ), nonplanar diprotonated bppzH₂(PF₆)₂ ( 3 ), and planar triprotonated terpyH₃Cl(PF₆)₂ ( 4 ), were prepared and characterized by electrospray ionization mass spectrometry, Ultraviolet–visible spectroscopy and cyclic voltammetry. Abbreviations used are tetra = tetra‐2‐pyridylpyrazine, bppz = 2,3‐bis(2‐pyridyl)pyrazine, and terpy = 2,2′:6′,2″‐terpyridine. The X‐ray crystal structures of the four compounds 1 , 2 , 3 , and 4 were determined. Both protonated pyridine rings are hydrogen bonded intramolecularly to the adjacent pyridine ring in compounds 1 and 3 . The π–π* absorption bands in the ultraviolet region for 1 , 2 , 3 , and 4 in acetonitrile were red‐shifted relative to those of the corresponding neutral unprotonated compounds. All the cyclic voltammetry for the protonated species, 1 , 2 , 3 , and 4 , showed the first reduction waves from ?0.37 to ?1.18 V, that were more positive than those of the neutral ones. Density functional theory was applied to interpret the planarity in 1 . The attachment of two protons to the two terminal tetra nitrogens in 1 leads to the remarkable emission (Φ = 0.031). The attachment of three protons to the three terpy nitrogens in 4 also gives the large quantum yield (Φ = 0.48). Copyright © 2015 John Wiley & Sons, Ltd.     

Singular cauchy problems for a class of weakly hyperbolic differential operators

In this paper singular Cauchy problems of Hamada's type are studied in the category of holomorphic functions and hyperfunctions for a class of hyperbolic differential operators with non-involutive multiple characteristics. Integral representations of their solutions are obtained.     

Quasi-classical limit of BKP hierarchy andW-infinity symmetries

Previous results on quasi-classical limit of the KP and Toda hierarchies are now extended to the BKP hierarchy. Basic tools such as the Lax representation, the Baker-Akhiezer function and the tau function are reformulated so as to fit into the analysis of quasi-classical limit. Two subalgebrasW ₁ ^B ₊ andw ₁ ^B ₊ of theW-infinity algebrasW _{1 +} andw _{1 +} are introduced as fundamental Lie algebras of the BKP hierarchy and its quasi-classical limit, the dispersionless BKP hierarchy. The quantumW-infinity algebraW ₁ ^B ₊ emerges in symmetries of the BKP hierarchy. In quasi-classical limit, theseW ₁ ^B ₊ symmetries are shown to be contracted intow ₁ ^B ₊ symmetries of the dispersionless BKP hierarchy.     

Accurate nano-injection system for capillary gas chromatography

The first version of nano-injection device for capillary gas chromatography (cGC) based on inkjet microchip was developed. The nano-injector could accurately control the injection volume in nano-liter, even pico-liter range. Its configuration and mechanism were discussed in detail. Adopting photolithography and plasma etching technology, we firstly fabricated the inkjet microchip and stuck to a piezoelectric device to eject droplets. Then, a special feedback tube was added to make it function as a nano-injector for cGC, which was an important design to compensate pressure difference between the evaporation chamber of cGC and the sample extrusion chamber of inkjet microchip. The injected volume can be precisely controlled by the number of injected droplets. Excellent precision (RSDs were below 10.0%, n = 5) was observed for the injection of ethanol at elevated pressure. Minimum injection volume was about 1.25 nL at present. Additionally, good repeatability of the calibration curves for the hydrocarbons ethanolic solution (the RSDs of all components were below 5.30%, n = 5) confirmed its feasibility in quantitative analysis regardless of concentration. These results suggested that it can be an accurate nano-injector for cGC.     

Enhanced lasing properties of dissymmetric Eu(III) complex with bidentate phosphine ligands

The luminescent and lasing properties of Eu(III) complexes were enhanced by using an dissymmetric Eu(III) complex. The photophysical properties (the emission spectral shapes, the emission lifetimes, the emission quantum yields, and the stimulated emission cross section (SEC)) were found to be dependent on the geometrical structures of Eu(III) complexes. The geometrical structures of Eu(III) complexes were determined by X-ray single crystal analyses. The symmetrical group of Eu(hfa)3(BIPHEPO) (tris(hexafluoroacetylacetonato)europium(III) 1,1'-biphenyl-2,2'-diylbis(diphenylphosphine oxide)) was found to be C1, which was more dissymmetric than Eu(hfa)3(TPPO)2 (tris(hexafluoroacetylacetonato)europium(III) 1,2-phenylenebis(diphenylphosphine oxide): C2 symmetry) and Eu(hfa)3(OPPO)2 (tris(hexafluoroacetylacetonato)europium(III) 1,2-phenylenebis(diphenylphosphine oxide): C2 symmetry). The analytical data were supported by Judd-Ofelt analysis. The most dissymmetrical Eu(III) complex, Eu(hfa)3(BIPHEPO), showed large electron transition probability and large SEC (4.64 x 10(-20) cm2). The SEC of Eu(hfa)3(BIPHEPO) was superior to even the values of Nd-glass laser for practical use (1.6-4.5 x 10(-20) cm2). The lasing properties of Eu(III) complexes in polymer thin film were measured by photopumping of a Nd:YAG laser (355 nm). The threshold energy of lasing oscillation was found to be 0.05 mJ. The increasing rate of the lasing intensity of Eu(hfa)3(BIPHEPO) as a function of the excitation energy was much larger than that of Eu(hfa)3(TPPO)2 and Eu(hfa)3(OPPO)2. The dissymmetrical structure of Eu(hfa)3(BIPHEPO) promoted the enhancement of the lasing property.