Biased random walk on critical Galton–Watson trees conditioned to survive

We consider the biased random walk on a critical Galton–Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as certain one-dimensional trapping models with slowly-varying tails. Indeed, in each of these two settings, we establish closely-related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs.     

Facile synthesis of 2-azaazulenes from thiobenzoyl isocyanates using trimethylsilyldiazomethane

The reaction of trimethylsilyldiazomethane with thiobenzoyl isocyanates, in situ generated from thiazole-4,5-diones, yielded diazoketones, which were converted into 2-azaazulenes by the intramolecular Buchner reaction.     

A trace theorem for Dirichlet forms on fractals

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on Sierpinski gaskets and Sierpinski carpets to their boundaries, where the boundaries are represented by triangles and squares that confine the gaskets and the carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields. These processes behave as an appropriate fractal diffusion within each fractal component of the field.     

An effective synthesis of N,N-dimethylamides from carboxylic acids and a new route from N,N-dimethylamides to 1,2-diaryl-1,2-diketones

Carboxylic acids were heated at 150 °C in DMF in the presence of 1.25 equiv of thionyl chloride to give corresponding N,N-dimethylamides in good yields. Tandem chlorination and amidation reactions occurred in the one-pot procedure. Dicarboxylic acids needed prolonged reaction time to produce bisamides in good yields. Some benzamides were efficiently converted into corresponding 1,2-diaryl-1,2-diketones (benzils) under acyloin condensation conditions in the presence of 4,4′-di-tert-butylbiphenyl (DBB) in THF. Ultrasonic irradiation effectively accelerates the reaction, but it is not critical. However, the presence of DBB is fatal to the reaction. Although a few synthetic methods for benzils from benzoic acids have been reported so far, this method is one of the most convenient and highly reproducible procedures.     

Synthesis of β‐Methoxyacrylate Natural Products Based on Box‐PdII‐Catalyzed Intermolecular Methoxycarbonylation of Alkynoles

Bis(oxazoline)‐palladium(II) catalyzed carbonylation of homopropargyl alcohols afforded acyclic methoxyacrylate 2 and 6‐membered lactone 3a , 3b , 3d , 3e , 3f , 3g , 3h , 3i , 3j , 3k in good combined yield. In the case of propargyl alcohols, 5‐membered lactones 3p , 3q , 16 were obtained in moderate yields. The one‐pot synthesis of kawa lactones 3a , 3r , 3s and formal synthesis of dihydroxycystothiazole A and dihydroxycystothiazole C are presented. To elucidate the stereochemistry of (+)‐annularin G and (?)‐annularin H, the first asymmetric syntheses of these natural products were achieved.     

Analysis of Th, U, Pu, and Am in radioactive metal waste using extraction chromatography

In order to analyze actinide elements in radioactive metal waste, the dissolution and chemical separation conditions were optimized. The surfaces of a type 304 stainless steel plate and of pipe waste sampled from the prototype advanced thermal reactor (Fugen) were dissolved in mixed acid solution (HNO₃:HCl:H₂O = 1:1:4). The resulting solution was evaporated to dryness and dissolved with 2 mol/dm³ of HNO₃ to prepare sample solutions. In order to analyze trivalent actinide elements in the sample solution containing a large amount of Fe(III) (>0.1 g) using TRU resin, the effect of Fe(III) concentration on the recovery of Am(III) and reduction effect of Fe(III) to Fe(II) with ascorbic acid were studied. On the basis of results of this study, chemical separation scheme was constructed and Pu and Am in the sample solutions were separated. Thorium and U in the sample solutions were separated with UTEVA resin. High recoveries for all experimented elements were obtained from the analysis of spiked sample solutions, the effectiveness of the method was confirmed.     

Separation of zeros for source signature identification under reverberant path conditions

This paper presents an approach to distinguishing the zeros representing a sound source from those representing the transfer function on the basis of Lyon's residue-sign model. In machinery noise diagnostics, the source signature must be separated from observation records under reverberant path conditions. In numerical examples and an experimental piano-string vibration analysis, the modal responses could be synthesized by using clustered line-spectrum modeling. The modeling error represented the source signature subject to the source characteristics being given by a finite impulse response. The modeling error can be interpreted as a remainder function necessary for the zeros representing the source signature.