Mean dimension and an embedding problem: An example

For any positive integer D, we construct a minimal dynamical system with mean dimension equal to D/2 that cannot be embedded into (([0, 1] ^D )^?, shift).     

Selective photocatalytic oxidation of alcohols to aldehydes in water by TiO2 partially coated with WO3

Semiconductor TiO₂ particles loaded with WO₃ (WO₃/TiO₂), synthesized by impregnation of tungstic acid followed by calcination, were used for photocatalytic oxidation of alcohols in water with molecular oxygen under irradiation at λ>350 nm. The WO₃/TiO₂ catalysts promote selective oxidation of alcohols to aldehydes and show higher catalytic activity than pure TiO₂. In particular, a catalyst loading 7.6 wt % WO₃ led to higher aldehyde selectivity than previously reported photocatalytic systems. The high aldehyde selectivity arises because subsequent photocatalytic decomposition of the formed aldehyde is suppressed on the catalyst. The TiO₂ surface of the catalyst, which is active for oxidation, is partially coated by the WO₃ layer, which leads to a decrease in the amount of formed aldehyde adsorbed on the TiO₂ surface. This suppresses subsequent decomposition of the aldehyde on the TiO₂ surface and results in high aldehyde selectivity. The WO₃/TiO₂ catalyst can selectively oxidize various aromatic alcohols and is reusable without loss of catalytic activity or selectivity.     

Effect of topology on the multiplicity of solutions for some semilinear elliptic systems with critical Sobolev exponent

In this paper, we are concerned with the effect of the domain topology on the multiplicity of solutions for some semilinear elliptic systems involving critical Sobolev exponent. We show that if the interaction term is sufficiently small, then the number of solutions of the system is estimated from below by 2 catΩ. The proof of this fact requires analysis of the structure of the Nehari manifold associated with the system. This research was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.     

Dissociation processes of Kr2(+) and Kr3(+) studied by threshold photoelectron-photoion coincidence measurements

A time-of-flight (TOF) ion mass spectrum in coincidence with threshold photoelectrons was measured in the photon energy region between the first and second dissociation limits of Kr2(+) to examine the decay processes of the Kr2(+) II(1/2u) state. The measured TOF spectrum reveals that Kr+ fragment ions are produced through dissociation of the repulsive I(1/2g) state, which can be formed by the decay process of the II(1/2u) state accompanied with emission of photons. The potential-energy curve of the I(1/2g) state is deduced with detailed analysis of the observed TOF spectrum, in which the radiative lifetime of the II(1/2u) state was also derived to be 2.5 micros. Additionally, evidence of the dissociation process of Kr3(+) ions was obtained in the same photon energy region, where the dominant channel is Kr3(+) --> Kr2(+) + Kr.     

A solid-supported acidic oxazolium perchlorate as an easy-handling catalyst for the synthesis of modified pyrimidine nucleosides via Vorbrüggen-type N-glycosylation

A solid-supported acidic oxazolium perchlorate was investigated as a heterogeneous catalyst in N-glycosylation reactions using silylated modified pyrimidines and an acylated ribose or glucose to afford the corresponding pyrimidine nucleosides. This salt is a nonhygroscopic and stable powder whose activity is comparable to that of 2-methyl-5-phenylbenzoxazolium perchlorate. A reaction with this polymer catalyst can be conducted on a gram scale. Reusability of the solid-supported catalyst was also investigated.     

A novel synthesis of 3-aminoazetidines by ring transformation of 2-(bromomethyl)aziridines

A one-step approach to the biologically interesting 3-aminoazetidines is described. The reaction concerns a ring transformation of 1-arylsulfonyl-2-(halomethyl)aziridines with aliphatic amines under various reaction conditions.