A multiple character sum and a multipleL-function

In this paper we introduce a certain sum by using Dirichlet characters. We investigate the Riesz mean of the sum using the analytic properties of the MultipleL-function systematically. Eine überarbeitete Fassung ging am 6. 8. 2001 ein     

Fuzzy logic in measurements

Our main interest in this paper is to translate from “natural language” into “system theoretical language”. This is of course important since a statement in system theory can be analyzed mathematically or computationally. We assume that, in order to obtain a good translation, “system theoretical language” should have great power of expression. Thus we first propose a new frame of system theory, which includes the concepts of “measurement” as well as “state equation”. And we show that a certain statement in usual conversation, i.e., fuzzy modus ponens with the word “very”, can be translated into a statement in the new frame of system theory. Though our result is merely one example of the translation from “natural language” into “system theoretical language”, we believe that our method is fairly general.     

On the index of a holomorphic vector field tangent to a singular variety

In this article we define and compute an index for a holomorphic vector field on a (possibly singular) subvariety of a complex manifold, provided the subvariety is a local complete intersection. This index reduces to the usual Poincaré-Hopf index in case the subvariety is smooth, and is equal more generally to the index defined in [GSV] and [SS].     

Observation of a new DsJ meson in B+-->D0D0K+ decays

We report the observation of a new DsJ meson produced in B+-->D0DsJ-->D0D0K+. This state has a mass of M=2708+/-9(-10)(+11) MeV/c2, a width Gamma=108+/-23(-31)(+36) MeV/c2 and a 1- spin-parity. The statistical significance of this observation is 8.4 sigma. The results are based on an analysis of 449 x 10(6) BB events collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.     

A Flat Spectral Response AWG Demultiplexer Composed of Slabs with Islands and Peninsulas

Phase adjustment elements called islands and peninsulas are introduced to obtain an AWG demultiplexer with a flat spectral response. Use of the peninsulas enables us to achieve a 1dB bandwidth of 0.5 nm.     

Mid-infrared emissions from Ho3+ in Ga2S3-GeS2-Sb2S3 glass

Emission properties were investigated in the infrared region for Ga₂S₃-GeS₂-Sb₂S₃ glasses doped with Ho³⁺. We performed Judd–Ofelt analysis and lifetime measurements of the ⁵I₄, ⁵I₅, and ⁵I₆ levels, which are the initial levels of the mid-infrared emissions between 3 to 5 μm of Ho³⁺. The quantum efficiencies reached approximately 18%, 64%, and ～100% for the ⁵I₄, ⁵I₅, and ⁵I₆, respectively. Population analyses were carried out from the relative intensities of the emissions in the near-infrared region. We investigated the dependences on the Ho³⁺ ion concentration of the population ratio of the initial levels to the final levels, [initial]/[final], of the mid-infrared emissions. The population ratio of [⁵I₅]/[⁵I₆] decreased with increase of the Ho³⁺ concentration while those of [⁵I₄]/[⁵I₅] and [⁵I₆]/[⁵I₇] increased. Particularly, the former, [⁵I₄]/[⁵I₅], rapidly increased because of the strong concentration quenching of the ⁵I₅ level through cross relaxation. It was found that the population inversion for the 4.8 μm emission due to the transition, ⁵I₄→⁵I₅, was achieved at high Ho³⁺ concentration in the present experiments.     

Gamow-teller strengths of the inverse beta transition 176Yb-->176Lu for spectroscopy of proton-proton and other sub-MeV solar neutrinos

Discrete Gamow-Teller (GT) transitions 176Yb-->176Lu at low excitation energies have been measured via the ( 3He,t) reaction at 450 MeV and at 0 degrees. For 176Yb, two low-lying states are observed, setting low thresholds Q(nu) = 301 and 445 keV for neutrino ( nu) capture. Capture rates estimated from the measured GT strengths, the simple two-state excitation structure, and the low Q(nu) in Yb-Lu indicate that Yb-based nu detectors are well suited for a direct measurement of the sub-MeV solar electron-neutrino ( nu(e)) spectrum including pp neutrinos.