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Abstract: In a filtered measure space, a characterization of weights for which the trace inequality of a positive operator holds is given by the use of discrete Wolffʼs potential. A refinement of the Carleson embedding theorem is also introduced. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doobʼs maximal operator holds is established by an application of our Carleson embedding theorem. Moreover, Hytönen–Pérez type one-weight norm estimate for Doobʼs maximal operator is obtained by the use of our two-weight characterization. [Copyright &y& Elsevier]

Abstract: Biotin protein ligase (BPL) mediates covalent attachment of biotin to a specific lysine residue of biotin carboxyl carrier protein (BCCP) of biotin-dependent enzymes. We recently found that the biotinylation reaction from thermophilic archaeon Sulfolobus tokodaii has a unique characteristic that the enzyme BPL forms a tight complex with the product, biotinylated BCCP (169 amino acid residues). In the current work, we attempted to apply this characteristic to a novel protein tagging system. Thus, the N terminus of S. tokodaii BCCP was truncated and the interaction of the resulting BCCP, BCCPΔ100 and BCCPΔ17 (with 69 and 152 residues, respectively), with BPL was investigated by surface plasmon resonance (SPR). It was found that the binding of BPL to the biotinylated BCCPΔ100 is extremely tight with a dissociation constant (K D) of 1.2 nM, whereas that to the unbiotinylated counterpart was moderate with a K D of 3.3μM. Furthermore, chimeric proteins of glutathione S-transferase (GST) and green fluorescence protein (GFP) with BCCPΔ100 fused to their C terminus were prepared. The resulting fusion proteins were successfully biotinylated and captured on the BPL-modified SPR sensor chip or BPL-modified magnetic beads. The function of GST and GFP was hardly impaired on fusion with BCCPΔ100 and biotinylation of the latter. [Copyright &y& Elsevier]

The Great East Japan tsunami, which occurred on 11 March 2011 (the 2011 tsunami), caused significant changes to the coastal and estuarine morphology along the Sendai coast, Miyagi prefecture, Japan. The recovery process, which took place subsequently after the tsunami, is investigated using aerial photographs, bathymetry data, and Empirical Orthogonal Function (EOF) method. Results from the aerial photograph analysis indicate that the shoreline was in the dynamic equilibrium condition in the period before the tsunami (Period 1). The recovery of the shoreline was very fast in the period of two years post event (Period 2). However, it was more stable for the period of the next 4.5 years (Period 3). The analysis on the bathymetry data indicates that, besides the sediment supply from adjacent coasts, eroded sediment of the offshore seabed was transported onshore and led to a mass recovery of the shoreline at the lagoon areas. The littoral system of the Sendai coast also changed significantly between the periods before and after the tsunami, as well as between Periods 2 and 3. The sediment deposited inland and in the lagoon areas is perceived as the main reason that caused the retreat inwardly of about 70 m–80 m of the shoreline after the tsunami. Regarding the EOF analysis, the reflected coastal processes of the first three dominant components from the EOF analysis for two shoreline data sets after the tsunami can be explained. In Period 2, the morphological recovery at severely damaged areas (lagoons) was the most dominant process, whilst the second one was the cross-shore variety of shoreline which was the most dominant process preceding tsunami. The contribution rate of the first and second components in Period 2 is about 4 times different. In the period of the next 4.5 years (Period 3), the cross-shore variety of shoreline which was induced by high waves came back to be the most dominant process, whilst the second component reflects the longshore sediment transport. These two dominant components are similar to the ones before the tsunami. The contribution rates of the first two components before and after the tsunami are relatively close as well. That confirms that the coastal processes have returned back to the conditions before the tsunami. This is an important finding which is deduced from this study because a strong tsunami such as the 2011 tsunami could have been a major disturbance, tipping the "normal" cross-, long-shore variability of shoreface water interface towards a different regime. [ABSTRACT FROM AUTHOR]

The Muckenhoupt–Wheeden conjecture is disproved for fractional integral operator. Both the strong ( p , p ) and the weak ( p , p ) type conjectures are proved to be false. The arguments rely upon a property of the characteristic function of an approximating sequence of the Cantor set. [ABSTRACT FROM AUTHOR]

There have been known two generalized Orlicz–Morrey spaces. One is defined earlier by Nakai and the other is by Sugano, the second and third authors. In this paper we investigate differences between these two spaces in some typical cases. The arguments rely upon property of the characteristic function of the Cantor set. [ABSTRACT FROM AUTHOR]