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3,4,8,9-Fluoranthenetetracarboxylic diimides (FDI) are first synthesized as stable yellow compounds by the Diels-Alder (DA) reaction of maleic anhydride and acecyclone derivative bearing an acenaphthylene imide unit and subsequent imidations. An X-ray crystallographic analysis of di(N-octyl)FDI derivative reveals the planar fluoranthene diimide π -system. The cyclic voltammograms of FDIs shows considerably high electron affinity. Moreover, its π -extended analogue involving an anthracene unit (DAAI) was also prepared by the DA reaction of acenaphthylene-3,4-dicarboxylic imide with o-xylylene derivative. The compound exhibits long wavelength absorption and intense fluorescence with moderate solvatofluorochromism (ΔλEM = 41 nm). Theoretical calculations based on density function theory (DFT) were performed to characterize the electronic feature of these diimides.

We revisit class number formulas, “ s = 0 ”-version of Kroneckerʼs limit formulas and Chowla–Selberg formulas for number fields, based on the theory at s = 0 of zeta functions. The main tool in our investigation is Heckeʼs formula (Corollary to Theorem 1), which represents the zeta function of an algebraic number field K by the integral of Epsteinʼs zeta series summed over Z r . The formulas are derived without residue computations of zeta functions. Theorem 2 for class numbers is quite useful. For Chowla–Selberg formulas, the second gamma function with a character is utilized.

The crystal quality and emission characteristics of InGaN-based laser diodes (LDs) with lattice-matched quaternary InAlGaN cladding layers on novel semi-polar {2 0 2 1} plane GaN substrates were investigated. Highly homogeneous InGaN quantum wells (QWs) with a suppressed piezoelectric field can be realized on the {2 0 2 1} plane even in the green spectral region. Optical polarization measurements revealed that [1 0 1 4] oriented stripes are advantageous for LDs on {2 0 2 1} planes. Gain-guided LDs on the novel (2 0 2 1) plane exhibited the longest lasing wavelength at 533.6 nm under pulsed operation. Continuous-wave (cw) operation at the lasing wavelength of 523.3 nm at 115 mA was also demonstrated. The I th , J th , V th , and the slope efficiency were 110 mA, 9.2 kA/cm 2 , 7.4 V, and 0.04 W/A, respectively. These results indicate that the green LDs on semi-polar {2 0 2 1} plane GaN substrates are promising candidates for laser display applications.

We obtain a “Kronecker limit formula” for the Epstein zeta function. This is done by introducing a generalized gamma function attached to the Epstein zeta function. The methods involve generalizing ideas of Shintani and Stark. We first show that a generalized gamma function appears as the value at s = 0 of the first derivative of the associated Epstein zeta function. Then this is used to yield Kronecker's limit formula and its “ s = 0 ”-version.

The first phosphor-free white LED based on II–IV compound materials is demonstrated. Our device utilizes a phenomenon unique to ZnSe homoepitaxy, where a portion of the main greenish-blue emission from the active layer of a pn junction diode is absorbed by the conductive substrate which in turn gives off an intense broad-band yellow emission centered around 585 nm by photoluminescence. These two emission bands combine to give a spectrum which appears white to the naked eye. A typical ZnSe-based white LED lamp exhibits a color temperature of approximately 3400 K with a CRI (color rendering index) of 68. The optical output power and operating voltage of such a device at a forward current of 20 mA is 2.0 mW and 2.7 V, respectively. The luminous efficiency estimated from these results is 10.4l m/W, which is comparable to the incandescent lamp as well as the commercial InGaN-based white LED. Device lifetimes (half-life) have exceeded 800 h at 20°C.