We solve the inhomogeneous linear first order differential equations of the form y′(x) − λy(x) = Σm=0∞am(x − c)m, and prove an approximation property of exponential functions. More precisely, we prove the local Hyers-Ulam stability of
linear first order differential equations of the form y′(x) = λy(x) in a special class of analytic functions.
Monolayers of amphiphilic di-block copolymer, PEO40-b-PMA(Az)19 on water surface and solid surfaces, such as silicon wafer and quartz glass, were analyzed by surface pressure — molecular
area (π-A) isotherm, UV-Vis spectroscopy, atomic force microscopy (AFM) and total X-ray reflectivity (TXR). The monolayer
prepared at 22 mN m-1 consisted of H aggregated azobezene (Az) moieties, which orientated perpendicular to the solid surface.
The monolayer structure, including H aggregated Az and orientation of Az, was stable after annealing at 98�C, at which temperature
the hydrophilic PEO domain was the liquid phase and the hydrophobic PMA(Az) was in the smectic A phase.
We introduce a new characterization of linear isometries. More precisely, we prove that if a one-to-one mapping f:ℝn→ℝn(2≦n<∞) maps every regular pentagon of side length a> 0 onto a pentagon with side length b> 0, then there exists a linear isometry I :ℝn→ℝnup to translation such that f(x) = (b/a) I(x).
The phase transition and
nano-scale ordered structure of four types of blends prepared from four di-block
copolymers, consisting of hydrophilic poly(ethylenoxide) and hydrophobic poly(methacrylate)
having different PEO molecular length and same degree of polymerization of
PMA(Az) were investigated. All blend systems formed hexagonal packed PEO cylinder
structure, which was same with the nano-scale structure of these parent block
copolymers. The SAXS and AFM observation suggested that the size of hexagonal
structure of blend was larger than the average size of parent block copolymers.
The melting enthalpy of PEO in blends was larger than the average value of
parent block copolymers. DSC, SAXS and AFM observations indicated the miscible
Ionizing radiation, such as gamma-rays and electron-beams, has been applied to modify toxicity of refractory pollutants and
industrial wastewaters, however, very few studies reported the cause of toxicity changes by radiation treatment. In this work,
degradation of phenol and chlorophenols (5·10−4M) by gamma-ray treatment and consequent toxicity changes were evaluated. Toxicity of 2,4-dichlorophenol (2,4-DCP) and 2,4,6-trichlorophenol
(2,4,6-TCP) was gradually decreased with increasing absorbed dose of gamma-radiation. However, in the case of phenol and monochlorophenols
(2-, 3-, and 4-CPs), toxicity was dramatically increased particularly, for a dose of as low as 1 kGy. Hydroquinone, benzoquinone,
catechol, chlorohydroquinone, and 4-chlorocatechol were identified to be main by-products of gamma-ray treatment. From the
solid phase extraction (SPE) fractionation study, toxicity-causing by-products were found to be hydroquinone, benzoquinone,
chlorohydroquinone, and/or 4-chlorocatechol.
The concept of crystallization dynamics method evaluating the miscibility of binary blend system including crystalline component
was proposed. Three characteristic rates, nucleation, crystal growth rates (N*, G*) and growth rate of conformation (Gc*) were used to evaluate the miscibility of PVDF/at-PMMA and PVDF/iso-PMMA by the simultaneous DSC-FTIR. N*, G* and Gc* depended remarkably on both temperature and blend fraction (ϕPMMA) for PVDF/at-PMMA system, which indicated the miscible system. PVDF/iso-PMMA showed small ϕPMMA dependency of N*, G* and Gc*, was estimated the immiscible system. The ΔT/Tm0 values, corresponding to Gibbs energy required to attend the constant G* and Gc*, evaluated from G* and Gc* showed the good linear relationships with different slope. The experimental results suggested that the concentration fluctuation
existed in PVDF/iso-PMMA system.
Authors:S. Y. Jung, T. Yamada, H. Yoshida, and T. Iyoda
Summary The mixing state of amphiphilic di-block copolymers consisted of poly(ethylene oxide) and poly(methacrylate) having azobenzene moieties in the side chains p(EO)114pMA(Az)24 and poly(ethylene oxide) p(EO)114 was investigated from the viewpoints of isothermal crystallization and nano-scale ordered structure. The chemical potential, which required establishing the constant crystal growth rate, decreased with the p(EO) content up to 60%. The hexagonal packed cylinder structure was observed for the blends with the p(EO) content up to 60% and the lattice spacing of (100) and (110) planes increased with the p(EO) content up to 60%. The blends of amphiphilic p(EO)114pMA(Az)24 and p(EO)114 were miscible without in the p(EO) content below 60%.
Radiation treatment with gamma-rays was used to improve the biodegradability of EDTA that is known to be a non-biodegradable
substance. The effect of metal ions and catalysts on the treatment of EDTA was studied first. The removal of EDTA was definitely
decreased in the presence of metal ions such as Cr(III), Cd(II), Pb(II) and Cu(II) at doses greater than 3 kGy. The addition
of a TiO2
Authors:J. Jung, S. Hyun, J. Lee, Y. Cho, and P. Hahn
The prediction of the adsorption behavior of natural composite materials was studied by a single mineral approach. The adsorption
of U(VI) on single minerals such as goethite, hematite, kaolinite and quartz was fully modeled using the diffuse-layer model
in various experimental conditions. A quasi-thermodynamic database of surface complexation constants for single minerals was
established in a consistent manner. In a preliminary work, the adsorption of a synthetic mixture of goethite and kaolinite
was simulated using the model established for a single mineral system. The competitive adsorption of U(VI) between goethite
and kaolinite can be well explained by the model. The adsorption behavior of natural composite materials taken from the Koongarra
uranium deposit (Australia) was predicted in a similar manner. In comparison with the synthetic mixture, the prediction was
less successful in the acidic pH range. However, the model predicted well the adsorption behavior in the neutral to alkaline
pH range. Furthermore, the model reasonably explained the role of iron oxide minerals in the adsorption of U(VI) on natural