Asymptotic behavior toward nonlinear waves for radially symmetric solutions of the multi-dimensional Burgers equation

The present paper is concerned with the asymptotic behaviors of radially symmetric solutions for the multi-dimensional Burgers equation on the exterior domain in ${\mathbb{R}}^n,n\ge 3$, where the boundary and far field conditions are prescribed. We show that in some case where the corresponding 1-D Riemann problem for the non-viscous part admits a shock wave, the solution tends toward a linear superposition of stationary and rarefaction waves as time goes to infinity, and also show the decay rate estimates. Furthermore, we improve the results on the asymptotic stability of the stationary waves which are treated in the previous papers [2], [3]. Finally, for the case of $n=3$, we give the complete classification of the asymptotic behaviors, which includes even a linear superposition of stationary and viscous shock waves.     

2′,4′-BNA/LNA with 9-(2-Aminoethoxy)-1,3-diaza-2-oxophenoxazine Efficiently Forms Duplexes and Has Enhanced Enzymatic Resistance**

Artificial nucleic acids are widely used in various technologies, such as nucleic acid therapeutics and DNA nanotechnologies requiring excellent duplex-forming abilities and enhanced nuclease resistance. 2′-O,4′-C-Methylene-bridged nucleic acid/locked nucleic acid (2′,4′-BNA/LNA) with 1,3-diaza-2-oxophenoxazine (BNAP ( B^H )) was previously reported. Herein, a novel B^H analogue, 2′,4′-BNA/LNA with 9-(2-aminoethoxy)-1,3-diaza-2-oxophenoxazine (G-clamp), named BNAP-AEO ( B^AEO ), was designed. The B^AEO nucleoside was successfully synthesized and incorporated into oligodeoxynucleotides (ODNs). ODNs containing B^AEO possessed up to 10⁴-, 152-, and 11-fold higher binding affinities for complementary (c) RNA than those of ODNs containing 2′-deoxycytidine ( C ), 2′,4′-BNA/LNA with 5-methylcytosine ( L ), or 2′-deoxyribonucleoside with G-clamp ( P^AEO ), respectively. Moreover, duplexes formed by ODN bearing B^AEO with cDNA and cRNA were thermally stable, even under molecular crowding conditions induced by the addition of polyethylene glycol. Furthermore, ODN bearing B^AEO was more resistant to 3′-exonuclease than ODNs with phosphorothioate linkages.     

Synthesis and toxicity assay of ceramic nanophosphors for bioimaging with near-infrared excitation

Yttrium hydroxyl carbonate (Y(OH)CO₃) precursors were synthesized by the homogeneous co-precipitation method in the presence of polyacrylic acid (PAAc). Resultant precursor particle size is about 15–20 nm with narrow size distribution whereas the particle size is smaller than those acquired by the conventional homogeneous precipitation method. Effective decrease of Y(OH)CO₃ particle size was found to be higher for the presence of weak polyanionic ionomer such as PAAc than the presence of strong polyanionic ionomer such as sodium polystyrene sulfonate (PSS). It was observed that the morphology and size of the precursors are almost unchanged after the calcination process. Er³⁺ doped Y₂O₃ nanoparticles were synthesized by PAAc assisted homogeneous co-precipitation method showed bright green (550 nm) and red (660 nm) upconversion (UC) as well as near-infrared (NIR) fluorescence (1550 nm) under 980-nm excitation. UC and NIR fluorescence bioimaging and in-vitro cytotoxicity assay of Er³⁺ doped Y₂O₃ nanoparticles were successfully attempted with commercially available macrophages and B-cell hybridomas. Cellular uptake of nanoparticles is evidenced from bright field, UC and NIR fluorescence images of macrophages.     

Enhancement in the rate of conversion of peptide Cys-Pro esters to peptide thioesters by structural modification

We previously reported that the peptide containing a Cys-Pro ester (CPE) moiety is spontaneously transformed into a peptide thioester via an N to S acyl shift followed by diketopiperazine formation. In an attempt to identify more reactive structures for the formation of a peptide thioester, we modified the CPE structure, in which the Pro residue in the CPE moiety was replaced with N-substituted glycine derivatives. These peptides were transformed into a peptide thioester more rapidly. Alternatively, the addition of an amino acid residue at the C-terminus of the CPE moiety also accelerated thioester formation.     

Interaction of Short Laser Pulses in Wavelength Range from Infrared to X‐ray with Metals,Semiconductors, and Dielectrics

Laser‐matter interaction is defined by an electronic band structure of condensed matter and frequency ω_L of electromagnetic radiation. In the range of moderate fluences, the energy absorbed by electrons from radiation finally thermalizes in the ion thermal energy. The thermalization processes are different for optical as compared with X‐ray quanta and for metals relative to semiconductors and dielectrics, since the light absorption and electron‐electron, electron‐ion dynamics are sensitive to the electron population in a conduction band and the width of a forbidden gap. Although the thermalization processes are different, the final state is simply a heated matter. Laser heating creates powerful stresses in a target if duration of a laser pulse τ_L is short in acoustic time scale. Nucleation and material removal take place under such stresses. Such way of removal is called here the spallative ablation. Thus the spallative ablation is an ablation mechanism universally important for qualitatively different materials and quanta (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Commutativity in special unitary groups at odd primes

It is a classical result by Bott that SU(s) and SU(t) homotopy commute in SU(n) if and only if s+t?n. We consider the p-localization analog of this problem and give an answer at odd primes.     

In-flight (K~-,N) Reactions for Study of Kaon-nucleus Interaction

We would like to emphasize that the in-flight (K~-,N) reactions are particularly useful for the study of the K-nucleus interaction.Since the reaction mechanism is well known,there is little ambiguity to derive the K-nucleus interaction from the measured missing mass spectra.Here we discuss the missing mass spectra of the (K~-,N) reactions on the ~(12)C and ~(16)O targets.The spectra show an appreciable amount of strength below the K-nucleus threshold which indicates that the K-nuclear potential is strongly attractive.Comparison of the missing mass spectra with theoretical calculations leads to a potential depth of around-190 MeV for the ~(12)C(K~-,n) reaction.A less deep potential of around-160 MeV reproduces well that of the ~(12)C(K~-,p) reaction.The difference can be due to isospin dependence of the interaction.Our data show that the K-nucleus potential is very deep to realize kaon condensation in the core of neutron stars.