A general regularity theory for weak mean curvature flow

We give a new proof of Brakke’s partial regularity theorem up to $C^{1,\varsigma }$ for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic Lipschitz approximation and blow-up technique. The new proof extends to a general flow whose velocity is the sum of the mean curvature and any given background flow field in a dimensionally sharp integrability class. It is a natural parabolic generalization of Allard’s regularity theorem in the sense that the special time-independent case reduces to Allard’s theorem.     

Mathematical model for hysteresis phenomenon in moisture transport of concrete carbonation process

From civil engineering point of view it is very important to construct and analyze a mathematical model for a mechanism of concrete carbonation process. On this subject there are several mathematical results concerned with a one-dimensional model, in which hysteresis effects are neglected. Our aim is to give a model with hysteresis effects appearing in carbonation process. In this paper, as the first step of this research we focus only on moisture transport in the process and propose an initial boundary value problem for a system of partial differential equations as a mathematical model. Also, we give results on the existence of a solution to the problem, globally in time and the uniqueness in only one-dimensional case without proofs.     

Synthesis and characterization of Ti–Ni shape memory alloy thin films by pulsed laser deposition

Shape-memory alloys are crucial in various industrial fields. However, a high-quality film synthesis method has not been established yet. Here we examine optimum conditions for synthesis of thin films by pulsed laser deposition of Ti–Ni alloy target in vacuum. We investigated surface morphologies and chemical compositions of the films which were obtained under various conditions. We found that the suitable Ti/Ni ratio was obtained by adjusting the distance between the target and the substrate in vacuum. In parallel, we analyzed plasma plume by optical emission spectroscopy and time-of-flight mass spectrometry. We discuss the basic behavior of ablated particles in vacuum.     

General Information to Obtain Spherical Particles with Ordered Mesoporous Structures

Conditions for the synthesis of aluminum organophosphonate (AOP) and aluminophosphate (AlPO) spheres containing periodic mesopores were optimized and demonstrated to be general morphological controls for the surfactant‐assisted synthesis of mesoporous materials. High‐quality AOP and AlPO spheres with uniform mesopores were obtained at low and high temperatures, respectively. The aerosol‐assisted synthesis of materials with uniform mesopores was categorized by using the difference in relative density of soluble AOP and AlPO oligomers that interact with ethylene oxide (EO) units in EO_nPO_mEO_n triblock copolymer (PO=propylene oxide). Then, ordered mesoporous structures are constructed with the adequate amount of species in resultant frameworks, and the number of interactive points in soluble species determines the resultant density of the frameworks after self‐assembly. Consequently, temperature‐dependent synthesis, which allows controlled infiltration of soluble species to match the density of resultant frameworks, is required for the formation of ordered mesoporous structures under morphological control.     

Analytic smoothing effect for global solutions to nonlinear Schrödinger equations

We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrödinger equation in space dimension n?3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.     

Beam profile measurement with CR-39 track detector for low-energy ions

A CR-39 track detector was successfully used to measure the outline of thin low-energy ion beams. After the etching, the surface of the detector was examined with an observation system composed of a Normarski microscope, a CCD camera and a digital image processing computer. Beam images obtained with the system were in good agreement on the outline of the beam formed with a beam aperture. Also, the resolving power in the beam outline measurement was roughly explained from the consideration of the ion range and the etch-pit growth in the chemical etching for the CR-39 detector.     

Superconductivity in CoSr2(Y1−xCax)Cu2O7+δ

The roles of aliovalent Ca^II-for-Y^III substitution and high-pressure-oxygen annealing in the process of ‘superconducterizing’ the Co-based layered copper oxide, CoSr₂(Y_1−xCa_x)Cu₂O_7+δ (Co-1212), were investigated. The as-air-synthesized samples up to x=0.4 were found essentially oxygen stoichiometric (−0.03≤δ≤0.00). These samples, however, were not superconducting, suggesting that the holes created by the divalent-for-trivalent cation substitution are trapped on Co in the charge reservoir. Ultra-high-pressure heat treatment carried out at 5 GPa and 500 °C for 30 min in the presence of Ag₂O₂ as an excess oxygen source induced bulk superconductivity in these samples. The highest T_c was obtained for the high-oxygen-pressure treated x=0.3 sample at ∼40 K.     

Pyrene-appended alpha-cyclodextrin as a fluorescent pH probe responding to a wide range.

Pyrene-appended alpha-cyclodextrin (3) in which a trimethylenediamine linker connected the pyrene residue to the alpha-cyclodextrin moiety showed pH-dependent fluorescence intensity changes. The fluorescence intensity was almost linearly changed within the pH range of 5 - 10. The unique fluorescence response of 3 to the pH was due not only to the favorable pK(a) values (pK(a1) = 6.4 and pK(a2) = 8.8), but also to the almost equal contributions of the amino groups to the pyrene's fluorescence quenching.     

8-Hydroxyquinoline derivative as a fluorescent chemosensor for zinc ion.

8-Hydroxyquinoline derivative 1 as a fluorescent chemosensor for Zn2+ was synthesized. Because Cd2+ is often found with Zn2+ in the environment and can form fluorescent complexes with chelating fluorophores, a potentially important property of chemosensors for Zn2+ is their selectivity for Zn2+ over Cd2+. The Zn2+ or Cd2+ complexes of 1 gave an emission band from the 1:1 complex, but the fluorescence intensity for Cd2+ was a half of that for Zn2+. Ligand 1 is suited for use as a fluorescent chemosensor for Zn2+.