Theta lifting of nilpotent orbits for symmetric pairs

We consider a reductive dual pair (G, G') in the stable range with G' the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K'_C-orbits, where K' is a maximal compact subgroup of G' and we describe the precise K_C-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G, K). As an application, we prove sphericality and normality of the closure of certain nilpotent K_C-orbits obtained in this way. We also give integral formulas for their degrees.Comment: 26 page

On orbits in double flag varieties for symmetric pairs

Let $G$ be a connected, simply connected semisimple algebraic group over the complex number field, and let $K$ be the fixed point subgroup of an involutive automorphism of $G$ so that $(G, K)$ is a symmetric pair. We take parabolic subgroups $P$ of $G$ and $Q$ of $K$ respectively and consider the product of partial flag varieties $G/P$ and $K/Q$ with diagonal $K$-action, which we call a \emph{double flag variety for symmetric pair}. It is said to be \emph{of finite type} if there are only finitely many $K$-orbits on it. In this paper, we give a parametrization of $K$-orbits on $G/P \times K/Q$ in terms of quotient spaces of unipotent groups without assuming the finiteness of orbits. If one of $P \subset G$ or $Q \subset K$ is a Borel subgroup, the finiteness of orbits is closely related to spherical actions. In such cases, we give a complete classification of double flag varieties of finite type, namely, we obtain classifications of $K$-spherical flag varieties $G/P$ and $G$-spherical homogeneous spaces $G/Q$.Comment: 47 pages, 3 tables; add all the details of the classificatio

Estimating Productivity of Dairy Cows by Inductive Logic Programming

In this study, we attempt deriving rules to estimate the productivity of dairy cows using inductive logic programming (ILP) for dairy farming. The milk yield of dairy cows is economically important and, of course, should be large. Accordingly, we selected data using the total milk yield in a lifetime as a threshold, and our ILP algorithm learned about positive and negative cases. As a result, 42 rules in positive, and 11 rules in negative were derived. ILP is also applicable for dairy farming and can provide useful information for farmers

Optical–optical double-resonance dual-comb spectroscopy with pump-intensity modulation

We apply an intensity-modulation technique to dual-comb spectroscopy to improve its detection sensitivity. The scheme is demonstrated via Doppler-free optical–optical double-resonance spectroscopy of Rb by modulating the intensity of a pump laser with frequencies set at rates 3 times lower and 50,000 times higher than the difference in the repetition rates of the two frequency combs. The signal-to-noise ratios are enhanced by 3 and 6 times for slow and fast modulations, respectively, compared to those of conventional dual-comb spectroscopy without any intensity modulation. The technique is widely applicable to pump-probe spectroscopy with dual-comb spectroscopy and provides high detection sensitivity

多系統動物モデルを用いた尿路上皮癌の発癌進展における腫瘍微小環境の解明

科学研究費助成事業 研究成果報告書：基盤研究(B)2014-2017課題番号 : 2629334

Doppler-free dual-comb spectroscopy of Rb using optical-optical double resonance technique

We present a Doppler-free high-resolution dual-comb spectroscopy technique in which a dual-comb system is employed to perform optical-optical double-resonance (OODR) spectroscopy. In our experimental study, Doppler-free high-resolution and high-frequency-accuracy broadband measurements were realized using the proposed OODR dual-comb spectroscopic technique, which does not require high-power-per-mode frequency combs. We observed fully resolved hyperfine spectra of 5P3/2 - 4D5/2, 4D3/2 transitions of Rb at 1530 nm and precisely determined the absolute frequencies of the transitions, with an uncertainty of less than 1 MHz. The variations of the OODR spectral line shapes due to power broadening and alignment and the effects of polarization on the dual-comb OODR spectra were also analyzed. This study provides a widely applicable technique for Doppler-free dual-comb spectroscopy of various gaseous species