On levi–typ conditions for hypoellipticity of certain diffrential operators

The hypoelliticity is discussed for operators of the form P=D² _x+a(x)D² _y+b(x)D_ywhere a (x) and b (x) are real–valued C^∞ functions satisfying a(0)=0 and a(x) >0 for x≠0.We seek the conditions for P to be hypoelliptic, especially in the case where both a (x) and b(x) vanish to infinite order on x=0.     

Electroreductive five- and six-membered cyclization of aromatic β- and γ-imino esters derived from (S)-aspartic acid and (S)-glutamic acid

The electroreduction of aromatic β-dimethylcarbamoyl-β-imino esters, prepared from (S)-aspartic acid, in the presence of chlorotrimethylsilane gave five-membered cyclized products, 1-benzoyl-4-hydroxy-5-aryl-N,N-dimethylpyrrolidine-2-carboxamides and 5-(dimethylcarbamoyl)-2-aryl-1H-pyrrol-3-yl benzoates, depending on the post-treatment after the electroreduction. The electroreduction of aromatic γ-dialkylcarbamoyl-γ-imino and γ-methoxylmethyl-γ-imino esters, prepared from (S)-glutamic acid, and following transformation gave six-membered cyclized products, 1-benzoyl-5-hydroxy-N,N-dialkyl-6-phenylpiperidine-2-carboxamides and 3-hydroxy-6-(methoxymethyl)-2-phenylpiperidin-1-yl)(phenyl)methanones, respectively.     

Finding market structure by sales count dynamics—Multivariate structural time series models with hierarchical structure for count data—

In this paper, we propose a multivariate time series model for sales count data. Based on the fact that setting an independent Poisson distribution to each brand’s sales produces the Poisson distribution for their total number, characterized as market sales, and then, conditional on market sales, the brand sales follow a multinomial distribution, we first extend this Poisson–multinomial modeling to a dynamic model in terms of a generalized linear model. We further extend the model to contain nesting hierarchical structures in order to apply it to find the market structure in the field of marketing. As an application using point of sales time series in a store, we compare several possible hypotheses on market structure and choose the most plausible structure by using several model selection criteria, including in-sample fit, out-of-sample forecasting errors, and information criterion.     

Rapid synthesis of tin-doped indium oxide microcrystals in supercritical water using hydrazine as reducing agent

Tin-doped indium oxide (ITO) microcrystals were successfully synthesized in supercritical water (SCW) using hydrazine (N₂H₄) as a reducing agent. Using a mixture of tin and indium hydroxides prepared at pH = 9.4 as a precursor, ITO microcrystals were synthesized at temperatures 400–450 °C under pressures 25–30 MPa. Synthesizing in SCW effectively shortened the time required to synthesize the ITO microcrystals to below 30 mins. The effect of reducing agents (ethanol, formic acid, and N₂H₄) and reaction conditions on the formation of ITO particles were investigated, and it was found that N₂H₄, which is superior to ethanol and formic acid, played a key role in the doping of the In₂O₃ structure with Sn⁴⁺ to form ITO particles with a blue color. Addition of N₂H₄ possibly depleted the oxygen in the In(Sn)OOH structure, accelerating the formation of cubic In₂O₃ and introduced Sn⁴⁺ into the structure along with the creation of oxygen vacancies. It was also found that the high temperatures and the properties of the SCW, such as ion product, strongly affected the morphology of the ITO particles and the Sn⁴⁺ doping. Based on these results, a mechanism has been proposed for the synthesis of ITO particles under SCW conditions. This study demonstrates that due to the unique properties of SCW, the synthesis of doped oxides in SCW is a plausible alternative method.     

Dependence of ortho-positronium pick-off annihilation lifetime on free volume in organic molecular liquids calculated by Kincaid Eyring method, and positronium bubble formation

Sizes of free volume were quantitatively calculated for 42 organic liquids by means of the Kincaid and Eyring method. The results were discussed in relation to the pick-off annihilation lifetime of ortho-positronium in molecular liquids. The presence of strong correlation was found between them, this fact made us conclude that the free volume size was the most essential physical parameter, which determines the pick-off annihilation rate of ortho-positronium. The problem that the calculated free volume was too small for the existence of ortho-positronium could be eliminated by the equilibristic formation of a bubble around ortho-positronium. Correlation was shown between the free volume radii and bubble radii. Our discussion will likely apply to a wider area for the analysis of empirical data on pick-off rate of ortho-positronium in organic liquids and to the experimental investigation of the pick-off process of ortho-positronium annihilation.     

A new furoxan derivative and its precursors formed by the reaction of sorbic acid with sodium nitrite

A new furoxan derivative ($\text{3}$) and its precursors ($\text{4a}$ and $\text{4b}$) were isolated from the reaction mixture of sorbic acid with sodium nitrite, and their structures were determined by spectroscopic and X-ray crystallographic analysis.     

Optimal management of waste loading into a river system with nonpoint source pollutants

An optimization model, fit for practical use, to allocate COD (Chemical Oxygen Demand)-based wasteload into a river system among outfalls is developed within the framework of robust optimization (RO). Nonpoint source COD loading, estimated based on the unit loading factor to be assumed known, is treated as uncontrollable one. The total amount of expected allowable COD load from point sources is then, under all possible scenarios of uncertain input information, maximized while satisfying the constraints on in-stream COD and DO (Dissolved Oxygen) transport, effluent standards and river water quality standards. Advantage of the ε-RO model using the ε-constraint method for optimization practice is brought to light from theoretical and practical aspects, in comparison with the conventional RO model resorting to the Lagrangian method. Solving a simple hypothetical example problem, it is demonstrated that the model developed is competent for successfully generating noninferior and robust solutions on optimal COD load allocation.     

Three-step synthesis of 4-(2′-hydroxyethyl) azetidin-2-one and its substituted derivatives from 4-acetoxy-2-pyridones

4-(2'-Hydroxyethyl)azetidin-2-one, an important synthetic intermediate for carbapenem, and its substituted derivatives have been synthesized from 4-acetoxy-2-pyridones by photolysis, catalytic hydrogenation, followed by basic hydrolysis in the presence of sodium borohydride.     

Electron spin resonance spectra and hyperfine coupling constants of the α-tocopheroxyl and 2,2,5,7,8-pentamethyl-chroman-6-oxyl radicals derived from vitamin E and its model and deuterated model compounds

Highly resolved electron spin resonance spectra of the α-tocopheroxyl or 2,2,5,7,8-pentamethylchroman-6-oxyl radicals were obtained from the oxidation of α-tocopherol (vitamin E) or its model compound, 2,2,5,7,8-pentamethylchroman-6-ol, with 2,2-diphenyl-1-picrylhydrazyl or superoxide ion. Complete assignments of the hyperfine coupling constants of these radicals were made on the basis of the spectra of the deuterated isotopomers of the 2,2,5,7,8-pentamethylchroman-6-oxyl radical. The large coupling constant due to the methyl group at C-5 in the α-tocopheroxyl radical may have implications for the high reactivity toward radicals of C-5 in α-tocopherol.