Boundary correlation numbers in one matrix model

We introduce one matrix model coupled to multi-flavor vectors. The two-flavor vector model is demonstrated to reproduce the two-point correlation numbers of boundary primary fields of two dimensional (2, 2p+1) minimal Liouville gravity on disk, generalizing the loop operator (resolvent) description. The model can properly describe non-trivial boundary conditions for the matter Cardy state as well as for the Liouville field. From this we propose that the n-flavor vector model will be suited for producing the boundary correlation numbers with n different boundary conditions on disk.Comment: 16 pages, 3 figures, add elaboration on matter Cardy state and reference

Stability of non-isolated asymptotic profiles for fast diffusion

The stability of asymptotic profiles of solutions to the Cauchy-Dirichlet problem for Fast Diffusion Equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy. It is noteworthy that this result can cover non-isolated profiles, e.g., those for thin annular domain cases. The method of proof is based on the Lojasiewicz-Simon inequality, which is usually used to prove the convergence of solutions to prescribed limits, as well as a uniform extinction estimate for solutions to FDE. Besides, local minimizers of an energy functional associated with this issue are characterized. Furthermore, the instability of positive radial asymptotic profiles in thin annular domains is also proved by applying the Lojasiewicz-Simon inequality in a different way

ブドウ‘マスカット・オブ・アレキサンドリア’に対する潅水制限が樹体の水分，葉温，果実温，果実の全フェノール含量，果皮色に及ぼす影響

　Effects of different deficit irrigation strategies on vine water status, canopy and cluster temperatures, fruit total phenolics, and the color of white table grapes (Vitis vinifera L., cv. Muscat of Alexandria) were compared to a well-irrigated control in 2004 from veraison to harvest at the Okayama University Experimental Vineyard, Japan. The treatments included: (1) well-irrigated control: re-irrigation when the soil moisture tension reached 15 kPa; (2) regulated deficit irrigation (RDI): re-irrigation 4 to 7 days after reaching a soil moisture tension of 15 kPa; (3) fixed partial root-zone wetting (FPRW): one part of the root system was re-irrigated when the soil moisture tension reached 15 kPa; and (4) alternate partial root-zone wetting (APRW): one part of the root system was re-irrigated when the soil moisture tension reached 15 kPa, and every week the irrigated part was switched. As the stress developed in RDI vines, leaf water potential and transpiration rate decreased and canopy and cluster temperatures increased as compared with the control. In contrast, both FPRW and APRW vines had similar leaf water potential and canopy and cluster temperatures, but less leaf transpiration rate as compared with the control. At harvest, fruits from all treatments had higher skin total phenolics and CIELAB a＊ values than the control. RDI fruit had higher total soluble solids (TSS), a similar acidity, and smaller size compared with the control. FPRW and APRW fruits had slightly higher TSS, lower acidity, and a similar size compared with the control.ベレゾーン期から収穫期までの潅水制限処理が‘マスカット・オブ・アレキサンドリア’ブドウ（Vitis vinifera L｡）の水分条件，葉温，果実温，果実の全フェノール，果皮色に及ぼす影響を，十分に潅水した樹と比較した．実験は2004年に岡山大学農学部内の実験圃場で行った．処理区は，１) 土壌水分張力が15kPa に達したときに潅水する対照区，２) 土壌水分張力が15kPa に達してから４～７日後に潅水する制限潅水区，３) 土壌水分張力が15kPa に達したときに根域の半分に潅水する片側潅水区，４) 片側潅水する根域部分を１週間ごとに変更する交互潅水区とした．制限潅水区では水分ストレスが強まるにつれて葉の水ポテンシャルと蒸散速度が対照区よりも低下し，果実温が高くなった．しかし，片側潅水区と交互潅水区では，葉の水ポテンシャルと葉温，果実温は対照区と同程度で，蒸散速度が低下した．収穫期の果皮の全フェノールと CIELAB a＊ 値は，潅水を制限した各区では標準区より高かった．制限潅水区の果実は，標準区より糖度が高く，酸度は低く，果粒は小さかった．片側潅水区，交互潅水区では糖度がやや高く，酸度は低く，果粒の大きさは同程度であった

K\"{a}hler structure in the commutative limit of matrix geometry

We consider the commutative limit of matrix geometry described by a large-$N$ sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a K\"{a}hler structure. We find an explicit relation between the K\"{a}hler structure and the matrix configurations which define the matrix geometry. We also find a relation between the matrix configurations and those obtained from the geometric quantization.Comment: 28 page

Emergent bubbling geometries in the plane wave matrix model

The gravity dual geometry of the plane wave matrix model is given by the bubbling geometry in the type IIA supergravity, which is described by an axially symmetric electrostatic system. We study a quarter BPS sector of the plane wave matrix model in terms of the localization method and show that this sector can be mapped to a one-dimensional interacting Fermi gas system. We find that the mean-field density of the Fermi gas can be identified with the charge density in the electrostatic system in the gravity side. We also find that the scaling limits in which the dual geometry reduces to the D2-brane or NS5-brane geometry are given as the free limit or the strongly coupled limit of the Fermi gas system, respectively. We reproduce the radii of $S^5$'s in these geometries by solving the Fermi gas model in the corresponding limits.Comment: 34 pages, 3 figures; typos correcte