Brezis-Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem

We study Brezis-Nirenberg type theorems for the equation

     

Functional relations and special values of Mordell-Tornheim triple zeta and -functions

In this paper, we prove the existence of meromorphic continuation of certain triple zeta-functions of Lerch's type. Based on this result, we prove some functional relations for triple zeta and -functions of the Mordell-Tornheim type. Using these functional relations, we prove new explicit evaluation formulas for special values of these functions. These can be regarded as triple analogues of known results for double zeta and -functions.

     

Transformation of environment map by changing the captured position in a cuboidal room

Optical Review - In this paper, we consider the use of an environment map as a photographic support tool for understanding the condition of surrounding light. It is well known that an environment...     

Three-Step Spin State Transition and Hysteretic Proton Transfer in the Crystal of an Iron(II) Hydrazone Complex

A proton–electron coupling system, exhibiting unique bistability or multistability of the protonated state, is an attractive target for developing new switchable materials based on proton dynamics. Herein, we present an iron(II) hydrazone crystalline compound, which displays the stepwise transition and bistability of proton transfer at the crystal level. These phenomena are realized through the coupling with spin transition. Although the multi-step transition with hysteresis has been observed in various systems, the corresponding behavior of proton transfer has not been reported in crystalline systems; thus, the described iron(II) complex is the first example. Furthermore, because proton transfer occurs only in one of the two ligands and π electrons redistribute in it, the dipole moment of the iron(II) complexes changes with the proton transfer, wherein the total dipole moment in the crystal was canceled out owing to the antiferroelectric-like arrangement.     

Single-molecule magnet behavior enhanced by magnetic coupling between 4f and 3d spins

We synthesized and characterized a new compound [{Dy(hfac)₃}₂Pd(dpk)₂] ([Dy₂Pd]; Hdpk = di-2-pyridyl ketoxime), which is isostructural with the known [Dy₂Cu] and [Dy₂Ni]. The study of the [Dy₂Pd] compound containing diamagnetic Pd ion is indispensable to clarify a contribution of the exchange coupling for a 4f-3d single-molecule magnet behavior. From the ac susceptibility measurements on [Dy₂Pd], we obtained Δ/k_B = 28.6(11) K and T_B = 1.1 K. In accordance with the blocking behavior, the pulsed-field magnetization showed the hysteresis behavior below 1.1 K. These parameters on [Dy₂Pd] having S_Pd = 0 was compared with those of the derivatives having S_Cu = 1/2 (Δ/k_B = 47 K and T_B = 1.8 K) and S_Ni = 1 (Δ/k_B = 62(4) K and T_B = 2.5 K). The T_B and Δ steadily increase with the increasing 3d(4d) spin quantum number.     

Printed two-dimensional photonic crystals for single-step label-free biosensing of insulin under wet conditions

Two-dimensional photonic crystals (2D-PCs) fabricated on a cyclo-olefin polymer (COP) film using a printable photonics technology based on nano-imprint lithography (NIL) were used for label-free biosensing of insulin under wet conditions. In general, 2D-PC-based biosensing involves a complicated dry-up procedure after biosensing reactions on the 2D-PCs to obtain a high sensitivity through the large difference in refractive index. Therefore, it can be difficult to achieve simple operation involving single-step analysis. Performance of the biosensing under wet conditions would simplify the operational procedure. For label-free biosensing of insulin under wet conditions, the Fresnel reflection intensity change was used instead of the wavelength shift, which is the commonly used sensing signal. By detecting changes in refractive index caused by specific interactions between the antigen and antibody as the Fresnel reflection intensity changes, physiologically important concentrations of insulin could be detected, even under wet conditions. These results suggest that low-cost printed 2D-PCs offer great potential for single-step label-free biosensing through the introduction of a sample solution.     

Effect of Nonmagnetic Substitution on the Magnetic Properties and Charge-Transfer Phase Transition of an Iron Mixed-Valence Complex, (n-C(3)H(7))(4)N[Fe(II)Fe(III)(dto)(3)] (dto = C(2)O(2)S(2))

The iron mixed-valence complex (n-C(3)H(7))(4)N[Fe(II)Fe(III)(dto)(3)] exhibits a novel type of phase transition called charge-transfer phase transition (CTPT), where the thermally induced electron transfer between Fe(II) and Fe(III) occurs reversibly at ～120 K, in addition to the ferromagnetic phase transition at T(C) = 7 K. To investigate the mechanism of the CTPT, we have synthesized a series of magnetically diluted complexes (n-C(3)H(7))(4)N[Fe(II)(1-x)Zn(II)(x)Fe(III)(dto)(3)] (dto = C(2)O(2)S(2); x = 0-1), and carried out magnetic susceptibility and dielectric constant measurements and (57)Fe M?ssbauer spectroscopy. With increasing Zn(II) concentration (x), the CTPT is gradually suppressed and disappears at x ≈ 0.13. On the other hand, the ferromagnetic transition temperature (T(C)) is initially enhanced from 7 K to 12 K between x = 0.00 and 0.05, despite the nonmagnetic nature of Zn(II) ions, and then it decreases monotonically from 12 K to 3 K with increasing Zn(II) concentration. This anomalous dependence of T(C) on Zn(II) concentration is related to a change in the spin configuration of the ferromagnetic state caused by the partial suppression of the CTPT.     

Electrochemical properties of spinel-type manganese oxide/porous carbon nanocomposite powders in 1 M KOH aqueous solution

Spinel-type manganese oxide/porous carbon (Mn₃O₄/C) nanocomposite powders have been simply prepared by a thermal decomposition of manganese gluconate dihydrate under an Ar gas flow at above 600 °C. The structure and texture of the Mn₃O₄/C nanocomposite powders are investigated by X-ray diffraction (XRD), energy-dispersive X-ray spectroscopy (EDS) equipped scanning transmission electron microscopy (STEM), transmission electron microscopy (TEM), selected area-electron diffraction (SA-ED), thermogravimetric and differential thermal analysis (TG-DTA) and adsorption/desorption of N₂ gas at ?196 °C. The electrochemical properties of the nanocomposite powders in 1 M KOH aqueous solution are studied, focusing on the relationship between their structures and electrochemical capacitance.In the nanocomposite powders, Mn₃O₄ nano particles approximately 5 nm in size are dispersed in a porous carbon matrix. The nanocomposite powders prepared at 800 °C exhibit a high specific capacitance calculated from cyclic voltammogram of 350 and 600 F g^?1 at a sweep rate of 1 and 0.1 mV s^?1, respectively. The influence of the heating temperature on the structure and the electrochemical properties of nanocomposite powders is also discussed.