Morphology-dependent photoluminescence property of red-emitting LnOCl:Eu (Ln=La and Gd)

Three different synthetic methods, the liquid phase process in HCl solution, the solvothermal reaction, and the surfactant-assisted solvothermal reaction, were explored to selectively control the particle shape and to enhance the luminescence intensity of the PbFCl-type red-emitting oxychloride phosphors LnOCl:Eu (Ln=La and Gd). The solvothermal pressure facilitated the low-temperature crystallization of the rod-shape particles for both Ln=La and Gd. It is noted that LaOCl:Eu nanorods show highly porous particle surface and quite low photoemission intensity. In contrast, the solvothermal synthesis could highly enhance the red-emission of GdOCl:Eu with no porous surface so as to be comparable to that of commercial Y₂O₃:Eu phosphor. An addition of surfactant material during solvothermal reaction yielded a rhomboidal-shape phosphor particles with no porous surface for both Ln=La and Gd. Interestingly, the elimination of surface porosity by using a surfactant significantly increased the emission intensity of LaOCl:Eu. It is proposed that the application of solvothermal technique for the synthesis of the PbFCl-type oxychloride phosphors is very effective to selectively control the particle shape and consequently to enhance the photoemission intensity if we use an appropriate surfactant material.     

In situ disorder-order transformation in synthetic gallosilicate zeolites with the NAT topology

Here, we report that synthetic gallosilicate molecular sieves with the NAT topology and Si/Ga ratios close to but slightly higher than 1.50 undergo an in situ transformation under their crystallization conditions. The materials have been studied ex situ by using powder X-ray diffraction, elemental and thermal analyses, and multinuclear MAS NMR. The transformation is characterized by a change in the distribution of Si and Ga of the NAT framework, from a quite (but not completely) disordered phase to a very highly (but not completely) ordered one, accompanied by a change from tetragonal to orthorhombic symmetry. During most of the solution-mediated transformation, no noticeable signs of fresh precipitation, phase segregation, or changes in the chemical composition are detected. Intermediate materials show variations in the degree of Si-Ga ordering and orthorhombic distortion and are not physical mixtures of the disordered and ordered phases. Ab initio calculations strongly suggest a preferential siting of Si in the tetrahedral sites involved in a smaller number of 4-rings in the NAT topology (i.e., the low multiplicity site). The cost of violations of Loewenstein's rule has also been calculated. For this topology and chemical composition the preferential siting and Loewenstein's rule drive together the system to the ordered configuration. A Monte Carlo sampling procedure affords a reasonable model for the initial, mainly disordered state, which fits well within the experimental disorder-order series.     

Forming the graded-refractive-index antireflection layers on light-emitting diodes to enhance the light extraction

Distributed antireflection (AR) layers with different composition ratios of ITO and SiO(2) formed on an ITO electrode of GaN-based LEDs provide substantial enhancement in light-extraction efficiency. By using the coradio frequency magnetron sputtering deposition, four 50 nm thick AR layers with graduated refractive indices were fabricated. The effect of the AR layers on enhancing the efficiency of the LED device was analyzed by electroluminescence (EL) and I-V measurements. As a result, the EL intensity of the LED device grown on the patterned sapphire substrate with AR layers was increased by up to 13% compared to the conventional patterned sapphire substrate-applied LED device without AR layers at a drive current of 20 mA. The AR layers on top of the LED device gradually changed the refractive indices between ITO (n=2.1) and air (n=1.0), which minimized the total internal reflection of generated light. And no degradation in the electrical characteristic of the LEDs was observed according to the I-V measurements.     

Imaginary quadratic fields with noncyclic ideal class groups

Let g be an odd positive integer and X be a positive real number. We shall show that for any ∊ > 0, the number of imaginary quadratic fields with discriminant ≥ − X and ideal class group having a subgroup isomorphic to ℤ/g ℤ× ℤ/g ℤ is ≫ X^1/g−∊. 2000 Mathematics Subject Classification Primary—11R11, 11R29 This work was supported by KRF-R08-2003-000-10243-0 and partially by KRF-2002-003-C00001.     

Real Quadratic Fields with Class Number Divisible by 5 or 7

We shall show that the number of real quadratic fields whose absolute discriminant is ≤ x and whose class number is divisible by 5 or 7 is improving the existing best known bound for g = 5 and for g = 7 of Yu (J Number Theory 97:35–44, 2002).This work was supported by KRF-R08-2003-000-10243-0 and partially by KRF-2005-070-C00004.     

On the Hénon equation with a Neumann boundary condition: Asymptotic profile of ground states

Consider the Hénon equation with the homogeneous Neumann boundary condition

$?\mathrm{\Delta }u+u=|x{|}^{\alpha }{u}^p,u>0\text{in}\mathrm{\Omega },\frac{?u}{?\nu }=0\text{ on }?\mathrm{\Omega },$

where $\mathrm{\Omega }?B(0,1)?{\mathbb{R}}^N,N\ge 2$ and $?\mathrm{\Omega }\cap ?B(0,1)\ne ?$. We are concerned on the asymptotic behavior of ground state solutions as the parameter $\alpha \to \infty$. As $\alpha \to \infty$, the non-autonomous term $|x{|}^{\alpha }$ is getting singular near $|x|=1$. The singular behavior of $|x{|}^{\alpha }$ for large $\alpha >0$ forces the solution to blow up. Depending subtly on the $(N?1)?$dimensional measure $|?\mathrm{\Omega }\cap ?B(0,1){|}_{N?1}$ and the nonlinear growth rate p, there are many different types of limiting profiles. To catch the asymptotic profiles, we take different types of renormalization depending on p and $|?\mathrm{\Omega }\cap ?B(0,1){|}_{N?1}$. In particular, the critical exponent $2_{?}=\frac{2(N?1)}{N?2}$ for the Sobolev trace embedding plays a crucial role in the renormalization process. This is quite contrasted with the case of Dirichlet problems, where there is only one type of limiting profile for any $p\in (1,2^{?}?1)$ and a smooth domain Ω.     

Elliptic curves of rank 1 satisfying the 3-part of the Birch and Swinnerton–Dyer conjecture

Let E be an elliptic curve over Q of conductor N and K be an imaginary quadratic field, where all prime divisors of N split. If the analytic rank of E over K is equal to 1, then the Gross and Zagier formula for the value of the derivative of the L-function of E over K, when combined with the Birch and Swinnerton–Dyer conjecture, gives a conjectural formula for the order of the Shafarevich–Tate group of E over K. In this paper, we show that there are infinitely many elliptic curves E such that for a positive proportion of imaginary quadratic fields K, the 3-part of the conjectural formula is true.     

Atomic-level investigations on the amyloid-β dimerization process and its driving forces in water

We report the spontaneous dimerization process of the full-length Aβ42 proteins in water by using unguided, fully atomistic, explicit-water molecular dynamics simulations. Based on the thermodynamic analysis, we demonstrate that Aβ42 dimerization in water occurs via a two-step nucleation-accommodation mechanism driven by water-induced force and by protein internal force, respectively.