Life span of solutions with large initial data for a semilinear parabolic system

We investigate the initial-boundary value problem

     

9-Azanoradamantane N-oxyl (Nor-AZADO): a highly active organocatalyst for alcohol oxidation

A highly active organocatalyst for alcohol oxidation has been developed. 9-Azanoradamantane N-oxyl (Nor-AZADO 4), constituting an unhindered, stable nitroxyl radical, exhibits superior catalytic activity to 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) and AZADOs in the oxidation of alcohols to their corresponding carbonyl compounds.     

The three-dimensional structure of aspergilloglutamic peptidase from Aspergillus niger

Aspergilloglutamic peptidase from Aspergillus niger is a novel pepstatin-insensitive acid endopeptidase distinct from the well-studied aspartic peptidases, and thus is an interesting target for protein structure/function studies. In the present study, we have determined the three-dimensional structure of the enzyme by X-ray crystallography to a 1.4-Å resolution. The results revealed that the enzyme has a unique structure, composed of two seven-stranded anti-parallel β-sheets which form a β-sandwich structure and appear to have a partial two-fold symmetry, suggesting its possible evolution by gene duplication and that the glutamic acid-110 and glutamine-24 in the heavy chain form a catalytic dyad, consistent with our results obtained by site-directed mutagenesis.     

Complex interpolation of various subspaces of Morrey spaces

In this article, we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works. The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al.(2015), it seems to be natural to consider the convolution property as well. Our result will extend the results by Hakim and Sawano(2017) and Hakim et al.(2017).     

A non-parametric Bayesian approach to decompounding from high frequency data

Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density \(f_0\) of its jump sizes, as well as of its intensity \(\lambda _0.\) We take a Bayesian approach to the problem and specify the prior on \(f_0\) as the Dirichlet location mixture of normal densities. An independent prior for \(\lambda _0\) is assumed to be compactly supported and to possess a positive density with respect to the Lebesgue measure. We show that under suitable assumptions the posterior contracts around the pair \((\lambda _0,\,f_0)\) at essentially (up to a logarithmic factor) the \(\sqrt{n\Delta }\)-rate, where n is the number of observations and \(\Delta \) is the mesh size at which the process is sampled. The emphasis is on high frequency data, \(\Delta \rightarrow 0,\) but the obtained results are also valid for fixed \(\Delta .\) In either case we assume that \(n\Delta \rightarrow \infty .\) Our main result implies existence of Bayesian point estimates converging (in the frequentist sense, in probability) to \((\lambda _0,\,f_0)\) at the same rate. We also discuss a practical implementation of our approach. The computational problem is dealt with by inclusion of auxiliary variables and we develop a Markov chain Monte Carlo algorithm that samples from the joint distribution of the unknown parameters in the mixture density and the introduced auxiliary variables. Numerical examples illustrate the feasibility of this approach.     

A predual of a predual of B_σ and its applications to commutators

A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation(BMO) and the singular integral operators.What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of B_σ-spaces and B_σ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to B_σ-spaces.     

Boundary integral equation methods in the theory of elasticity of hemitropic materials: A brief review

The theory of elasticity of hemitropic materials has recently been the object of rigorous mathematical analysis. In particular, the potential method and the theory of pseudodifferential equations have been used in studying the solvability in various function spaces of the main boundary value and transmission problems, in smooth and in Lipschitz domains. The main features and results of this boundary integral equations approach are briefly reviewed here.     

Fluorescence Properties and Exciplex Formation of Emissive Naphthyridine Derivatives: Application as Sensors for Amines

Water-soluble donor–acceptor-type fluorophore 15Nap-Cl having two trifluoromethyl groups and a Cl group on a 1,5-aminonaphthyridine framework was prepared. Fluorophore 15Nap-Cl showed strong solvatochromic fluorescence, and, as the solvent polarity increased, a bathochromic shift was observed accompanied by an increase in the fluorescence quantum yield. In addition, in the presence of amines such as ethylamine, diethylamine, and aniline, further considerable bathochromic shifts in the fluorescence were observed. Density functional calculations identified the source of the fluorescence behavior as exciplex formation between 15-Nap-Cl and the corresponding amine. The fluorescence behavior was exploited to fabricate a sensor that can identify various primary, secondary, and tertiary amines.