Convergence of Anisotropically Decaying Solutions of a Supercritical Semilinear Heat Equation

We consider the Cauchy problem for a semilinear heat equation with a supercritical power nonlinearity. It is known that the asymptotic behavior of solutions in time is determined by the decay rate of their initial values in space. In particular, if an initial value decays like a radial steady state, then the corresponding solution converges to that steady state. In this paper we consider solutions whose initial values decay in an anisotropic way. We show that each such solution converges to a steady state which is explicitly determined by an average formula. For a proof, we first consider the linearized equation around a singular steady state, and find a self-similar solution with a specific asymptotic behavior. Then we construct suitable comparison functions by using the self-similar solution, and apply our previous results on global stability and quasi-convergence of solutions.     

Exploration of Nano-Saturns: A Spectacular Sphere–Ring Supramolecular System

Saturn-like systems consisting of nanoscale rings and spheres are fascinating motifs in supramolecular chemistry. Several ring molecules are known to include spherical molecules at the center of the cavity via noncovalent attractive interactions. In this Minireview, we generalize the molecular design, the structural features, and the supramolecular chemistry of such “nano-Saturns”, which consist of monocyclic rings and fullerene spheres (mainly C₆₀), on the basis of previous experimental and theoretical studies. Ring molecules are classified into three types (loop, belt, and disk) according to their shapes and possible interactions. Whereas typical belt-shaped rings tend to form tight complexes due to the wide contact area via π–π interactions, flat disk-shaped rings generally form weak complexes due to the narrow contact area mainly via CH–π interactions. In spite of the small association energies, disk-shaped rings are attractive because such rings can mimic the planet Saturn precisely as exemplified by an anthracene cyclic hexamer–C₆₀ complex.     

The Change of Grip Strength in a Patient with Congenital Myotonic Dystrophy Over a 4-year Period

Myotonic dystrophy (MyD) is a neuromuscular disease that is autosomal dominant and the most common form of muscular dystrophy affecting adults. The clinical features of MyD include a multisystemic disorder characterized by myotonia, progressive muscle weakness and wasting, cataracts, premature balding and mental retardation. The most severe type of MyD is classified as congenital MyD (CMyD). The muscle weakness in CMyD is very severe, but muscle development can be observed in the period of growth. However, no clinical case of this type has been reported yet. Therefore, we report on a girl with CMyD who had an increase in muscle strength over a four-year period. The girl with CMyD participated in this study from the age of 9 to the age of 12. The measurement of muscle strength was recorded as the maximum score of grip strength with the use of dynamometers. Grip strength was assessed once a year by the same two physical therapists. Grip strength of CMyD for each year was markedly weak when compared with the normal controls, but muscle strength changed within some specific growth areas. The muscle weakness in CMyD was remarkable, but the result showed that specific muscle strength of CMyD in childhood was actually increased.     

Synthesis of novel liquid crystals having the perfluoropyrrolidino group

Novel liquid crystals which have the perfluoropyrrolidino group, a heterocyclic perfluoroalkyl group, and which show smectic phases have been synthesized with perfluoro-(2-pyrrolidinopropionyl fluoride) as one of the starting materials. Analogues with a polymerizable functional group also have been prepared and polymerized to give side chain liquid crystal polymers.     

Preparation of Na+-selective electrodes by ion-implantation of lithium and silicon into single-crystal alumina wafer and its application to the production of ISFET

Summary Sodium ion-selective electrodes (Na⁺-ISE) were prepared by implanting Si⁺ and Li⁺ into alumina wafers and their characteristics were investigated. The alumina wafer had a thickness of 100 m and a diameter of 1.40 cm. The ionselective membrane was produced by ion-implanting of Li⁺ and Si⁺ on both sides of a single-crystal alumina wafer. The total doses of Li⁺ and Si⁺ were controlled to be the same, viz. 10¹³–10¹⁵ ions/cm². The ion-implanted alumina wafer with 10¹⁴ or 4×10¹⁴ ions/cm² of Li⁺ and Si⁺ showed better characteristics than the others.The response curves of the 10¹⁴ ions/cm² implanted alumina wafer had a slope of 42 mV/pNa in a concentration range from 1–10^–4mol/l. The full response achieved after about 1 min was reproducible. The proposed idea of producing Na⁺-ISE by ion-implantation technique was applied to functuate the gate surface of the field effect transitor to sodium ion. The sodium ion-sensitive FET (Na⁺-ISFET) prepared by implanting Li⁺ and Al⁺ at a dose of 5×10¹⁴ ions/cm² showed a slope of 30 mV/pNa in a concentration range from 1–10^–4mol/l.

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Herstellung Na⁺-ionenselektiver Elektroden durch Einbau von Lithium und Silicium in Einkristall-Alumniumoxidblättchen und Anwendung zur Erzeugung von ISFET

Zusammenfassung Na⁺-selektive Elektroden wurden durch Einbau von Si⁺ und Li⁺ in Aluminiumoxidblättchen hergestellt und ihre Charakteristiken untersucht. Die Blättchen hatten eine Dicke von 100 m und einen Durchmesser von 1,40 cm. Ebenso wurde die Membran für einen ISFET hergestellt. Die Gesamtmenge von Li⁺ und Si⁺ wurde auf 10¹³–10¹⁵ Ionen/cm² eingestellt, wobei sich bei 10¹⁴ oder 4×10¹⁴ Ionen/cm² die beste Charakteristik ergab.Die Responsekurven der mit 10¹⁴ Ionen/cm² versehenen Aluminiumoxidplättchen hatten eine Neigung von 42 mV/pNa in einem Konzentrationsbereich von 1–10^–4mol/l. Der nach 1 min erhaltene volle Response war reproduzierbar. Die vorgeschlagene Technik wurde zur Einstellung der Gate-Oberfläche des Feldeffekt-Transistors auf Natriumion benutzt. Der Na⁺-sensitive FET (Na⁺-ISFET), der durch Einbau von Li⁺ und Al⁺ mit 5×10¹⁴ Ionen/cm² hergestellt wurde, zeigte eine Neigung der Signalkurve von 30 mV/pNa in einem Bereich von 1–10^–4mol/l.

     

Production of doubly charged helium ions by two-photon absorption of an intense sub-10-fs soft x-ray pulse at 42 eV photon energy

We report on the observation of doubly charged helium ions produced by a nonlinear interaction between a helium atom and photons with a photon energy of 42 eV which are generated with the 27th harmonic of a femtosecond pulse from a Ti:sapphire laser. The number of ions is proportional to the square of the intensity of the 27th harmonic pulse, and thus two-photon double ionization should be dominantly induced as compared with other nonlinear processes accompanying sequential ionization via a singly charged ion. This phenomenon is utilized to measure the pulse duration of the 27th harmonic pulse by using an autocorrelation technique, for the first time to our knowledge, and as a result a duration of 8 fs is found.     

Ruthenium-catalyzed hydrogenation of alkynylstannanes with migration of the stannyl group

Molecular hydrogen adds to aliphatic and aromatic alkynylstannanes in the presence of a ruthenium catalyst, pushing the stannyl group to the adjacent carbon atom to give alpha-substituted vinylstannanes. This is the first achievement of hydrogenation of alkynylstannanes, which is applicable also to the deuteration affording precursors for an important class of deuterium-labeled compounds.     

X-ray emission spectra of vanadium atoms in a new series of (Cu,V)-based high-Tc superconductors

Non-resonant V L_2,3 and OKα X-ray emission spectra of a new series of (Cu,V)Sr₂Ca_n−1Cu_nO_y (n=3-7) superconductors are presented. We have found that oxygen atoms surround V-atoms in the given compounds, form a (VO₄)³⁻ tetrahedrons and have a pentavalent state. This induces holes due to the substitution of divalent copper by pentavalent vanadium ions providing a hole-doping mechanism of superconductivity in this series of compounds. A spectral estimation of the oxygen concentration shows that the oxygen content under high-pressure/high-temperature synthesis conditions is not changed considerably from the start to the final product.