Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities

In this paper we study the existence and concentration behaviors of positive solutions to the Kirchhoff type equations $$- \varepsilon^2 M \left(\varepsilon^{2-N}\!\!\int_{\mathbf{R}^N}|\nabla u|^2\,\mathrm{d} x \right) \Delta u \!+\! V(x) u \!=\! f(u) \quad{\rm in}\ \mathbf{R}^N, \quad u \!\in\! H^1(\mathbf{R}^N), \ N \!\geqq\!1,$$ where M and V are continuous functions. Under suitable conditions on M and general conditions on f, we construct a family of positive solutions \({(u_\varepsilon)_{\varepsilon \in (0,\tilde{\varepsilon}]}}\) which concentrates at a local minimum of V after extracting a subsequence (ε _k ).     

Nanoscale Effects in One-Dimensional Columnar Supramolecular Ferroelectrics

Organic ferroelectrics have been actively developed with the goal of fabricating environmentally friendly and low-cost memory devices. The remanent polarization of hydrogen-bonded organic ferroelectrics approaches that of the inorganic ones. Nanoscale fabrication of organic ferroelectrics is an essential aspect of high-density memory devices. A pyrene derivative with four tetradecylamide (−CONHC₁₄H₂₉) chains ( 1 ) formed an amide-type N−H⋅⋅⋅O hydrogen-bonded one-dimensional (1D) column, which demonstrated ferroelectricity in the discotic hexagonal columnar (Col_h) liquid crystalline phase through the inversion of the orientation of the hydrogen-bonded chains. On the contrary, similar chiral pyrene derivatives bearing 3,7-dimethyl-1-octhylamide chains (S- 2 and R- 2 ) did not indicate the Col_h phase and ferroelectricity. Homogeneous mixed liquid crystals ( 1 )_1−x(S- 2 )_x (i.e., between the ferroelectric 1 and the non-ferroelectric S- 2 ) enable the control of the nanoscale aggregation state of the organic ferroelectrics, resulting in a nanoscale effect of the 1D supramolecular ferroelectrics. Ferroelectric mixed liquid crystals ( 1 )_1−x(S- 2 )_x were observed at x≦0.03, where one S- 2 molecule was inserted after every thirty-three 1 molecule in the mixed liquid crystal ( 1 )₃₃(S- 2 ). An average ( 1 )₃₄ length of approximately 12 nm was required to maintain the 1D ferroelectricity, which was similar to the nanoscale limit of inorganic ferroelectrics, such as hafnium oxide thin film (≈15 nm).     

Application of FIRE for the calculation of photon matrix elements

The next-to-next-to-leading order (the order αα _s ²) corrections to the first moment of the polarized virtual photon structure function g ₁ ^γ (x,Q ², P ²) are studied in perturbative QCD for the kinematical region Λ² ≪ P ² ≪ Q ², where −Q ² (−P ²) is the mass square of the probe (target) photon and Λ is the QCD scale parameter. In order to evaluate the two-loop Feynman diagrams for the photon matrix element of the gluon operator, I apply the recently developed algorithm FIRE which reduces a complicated sum of scalar Feynman integrals to a linear combination of a few master integrals. The details of the calculation are presented.     

Elemental distribution analysis of type I collagen fibrils in tilapia fish scale with energy-filtered transmission electron microscope

Elemental distribution of calcium, phosphorus, oxygen, and carbon in a single collagen fibril obtained from tilapia fish scales was identified with an electron energy-loss spectroscopy and an energy-filtered transmission electron microscopy, for the first time. The carbon intensity profile of the single collagen fibril showed the specific D-periodic pattern at 67 nm of type I collagen fibrils. The calcium L_2,3-edge and oxygen K-edge peak positions were detected at 347/350 eV and 137 eV, respectively, and these positions were identical to those of hydroxyapatite. Calcium, phosphorus, and oxygen were present in the hole zones as the amorphous phase, while carbon was present in the overlap zone. Our results indicated that the hole zones preferentially attract calcium and phosphate ions and thus serve as possible nucleation sites for mineralization.     

Lithium ionic conduction in poly (methacrylic acid)-poly (ethylene oxide) complex containing lithium perchlorate

Polymeric solid electrolytes were prepared by dispersing homogeneously lithium perchlorate in a hydrogen-bonding type intermacromolecular complex of poly(methacrylic acid)-poly(ethylene oxide). They showed ionic conductivity of more than 10^-6 (S/cm) at room temperature. The conductivity depended on the molecular weight of the poly(ethylene oxide), the proportion of poly(ethylene oxide) and lithium perchlorate, and so on. Poly(ethylene oxide) with average molecular weights ranging from 400 to 2 × 10⁴ were used to clarify the effect of chain length on the conductivity. The conductivity increased and the flexibility of the films improved with increasing the content of poly(ethylene oxide) with average molecular weight of 400. The maximum conductivity of 1.3 × 10^-5 (S/cm) at 60°C was obtained for the flexible film when the composition of poly(methacrylic acid)/poly(ethylene oxide)/lithium perchlorate was in the ratio of 17.0/ 68.0/15.0 in unit mol%.     

Electron and hole traps in N-GaAs crystals

Deep traps were measured and their electronic and optical properties were determined by junction capacitance techniques in n-GaAs crystals grown by different methods. Four electron-traps and four hole-traps were detected. An electron trap was not observed in LPE wafers. A hole trap at 0.45 eV above the top of the valence band was detected in all wafers measured here.     

Ionic conductivity of LiX-oligo(ethylene oxide)-perfluoro polymer ternary hybrids

Polymeric solid electrolytes were prepared from inorganic lithium salts, endo-acetylated oligo(ethylene oxide) and polyanions with perfluoro(ethylene) main chain. High ionic conductivity was found when these ternary hybrids took micro-segregated structures with continuous cylindrical conduction columns of lithium salt-oligo(ethylene oxide) in the sea of perfluoro-poly(electrolytes). The ionic conductivity of more than 10^?5 S/cm was established at room temperature without affecting the processibility and flexibility of resulting hybrid films.     

Crystal Structures and Redox Responses Coupled with Ion Recognition of p‐Benzoquinone‐ and Hydroquinone‐Fused [18]crown‐6

The crystal structures and redox properties of p‐benzoquinone (BQ)‐fused [18]crown‐6 1 and bis‐BQ‐fused [18]crown‐6 2 were examined. The anion radicals of these BQ molecules were stabilized by addition of metal ions, through effective electrostatic interactions between the negatively charged BQ moiety and positively charged ion‐capturing [18]crown‐6 unit. The electrostatic interactions and solvation energy played important roles in determining the magnitudes of anodic redox shifts in the reduction potentials. Regular π‐stacking of BQ units and regular arrays of [18]crown‐6 units were observed in crystal 2 , in which one‐dimensional π‐electron columns were separated by ionic channels. The hydroquinone‐fused [18]crown‐6 molecule 3 and a new BQ‐ and phenol‐fused [18]crown‐6 derivative 4 were obtained as single crystals. The molecular conformations of [18]crown‐6 in crystal 3 and hydrated crystal 3 ?H₂O were different from each other.