Epsilon Dichotomy for Linear Models: The Archimedean Case

Let G = GL₂(ℝ) or G = GL(ℍ) and H = GL(ℂ) regarded as a subgroup of G. Here, ℍ is the quaternion division algebra over ℝ. For a character χ on Cˣ, we say that an irreducible smooth admissible moderate growth representation of G is χ[H]-distinguished if Hom[H](, χ ◦ det[H]) ≠ 0. We compute the root number of a χ[H]distinguished representation twisted by the representation induced from χ. This proves an Archimedean analogue of the conjecture by Prasad and Takloo-Bighash (J. Reine Angew. Math., 2011). The proof is based on the analysis of the contribution of H-orbits in a f lag manifold of G to the Schwartz homology of principal series representations. A large part of the argument is developed for general real reductive groups of inner type. In particular, we prove that the Schwartz homology H∗(H, ⊗ χ ) is finite-dimensional and hence it is Hausdorff for a reductive symmetric pair (G, H) and a finite-dimensional representation χ of H

Strichartz estimates for the (k,a)(k,a)-generalized Laguerre operators

In this paper, we prove Strichartz estimates for the $(k,a)$-generalized Laguerre operators $a^{-1}(-|x|^{2-a}\Delta_k+|x|^a)$ which were introduced by Ben Sa\"{\i}d-Kobayashi-{\0}rsted, and for the operators $|x|^{2-a}\Delta_k$. Here $k$ denotes a non-negative multiplicity function for the Dunkl Laplacian $\Delta_k$ and $a$ denotes a positive real number satisfying certain conditions. The cases $a=1,2$ were studied previously. We consider more general cases here. The proof depends on symbol-type estimates of special functions and a discrete analog of the stationary phase theorem inspired by the work of Ionescu-Jerison.Comment: 34 page

Shaking Table Test on Effects of Combination of Soil and Building Properties on Seismic Response of Building

To clarify seismic force to buildings and foundations, an effect of dynamic soil and structure interaction is very important. The seismic force to buildings and foundations is influenced by characteristics of both soil deposits and buildings. To investigate the effects of vibration of soil deposits and buildings, a scaled model of building, foundation, and soil deposit is set up on a shaking table. Through analyzing difference between response of foundation without buildings, and surface grounds under the steady state excitation, the horizontal response of foundation is less that of ground surface. This tendency is large with frequency. As one of parameters, there are three kinds of buildings that are 8, 11 and 15 stories models. Under combinations of soil deposits and building properties, seismic forces are compared. The building response is very large when a resonant frequency of building is near to that of soil deposit. The bending moment of piles are affected by not only a base shear of buildings but a displacement of surface ground

チョクセツ サヨウガタ コウウイルスヤク DAAs ニヨル Cガタ マンセイ カンシッカン シンリョウ

Hepatitis C virus（HCV）infection is a major worldwide health problem. Chronic infection induces continuous inflammation in the liver, progression of hepatic fibrosis, eventual cirrhosis, and possible hepatocellular carcinoma. Eradication of the virus is one of the most important treatment aims. A number of promising new direct-acting antivirals（DAAs）have been developed over the past １０ years. Due to their increased efficacy, safety, and tolerability, interferon-free oral therapies with DAAs have been approved for patients with HCV, including those with cirrhosis. This review introduces the characteristics and results of recent clinical trials of several DAAs : NS３/４ A protease inhibitors, NS５A inhibitors, and NS５B inhibitors. DAA treatment failure and prognosis after DAA therapy are also discussed

IN VITRO CYTOTOXICITY OF CPT-11 (SN-38) ALONE AND IN COMBINATION WITH CISPLATIN ON OVARIAN CANCER CELLS

We investigated the in vitro cytotoxic effects of CPT-11, a new derivative of camptothecin, and its metabolizable form in vivo, SN-38, on cisplatin-resistant (SHIN-3) and -sensitive (MN-1) ovarian cancer cell lines using the MTT assay. We also attempted to identify the optimal schedule of administration for cisplatin combined with low-dose continuous exposure to CPT-11 (3 μg/ml) or SN-38 (5 ng/ml). With either CPT-11 or SN-38 alone, a marked schedule-dependent inhibition of growth was obtained with exposure for over 40 hours to concentrations of those agents applicable to clinical use (CPT-11 : <7.58 μg/ml, SN-38 : <72 ng/ml), even in a cisplatin-resistant cell line. Increasing the assay AUC of these agents only by dose escalation did not enhance cytotoxity with both MN-1 (CPT-11 : 3-50 μg/ml, SN-38 : 2.16-72 ng/ml) and SHIN-3 (CPT-11 : 5-50 μg/ml, SN-38 : 21.6-720 ng/ml) cell lines up to 72 hours of exposure. Pretreatment of SHIN-3 cells with either CPT-11 (3 μg/ml) or SN-38 (5 ng/ml) for 48 hours before the administration of cisplatin (4-20 μg/ml) appeared to produce an inhibition which exceeded that produced by either a longer (96 hours) or shorter (0 hour) pretreatment with them. Flow cytometric analysis showed that treatment with CPT-11 and SN-38 in SHIN-3 cell line was associated with a peak in G₂/M phase at 24 hours and an increase in the G₀/G₁ phase fraction for up to 96 hours. It is thus suggested that the continuous administration of a low dose of CPT-11 or of SN-38 may be useful clinically. The in vitro cytotoxicity of cisplatin could be increased by pretreatment with either CPT-11 or SN-38