Turbulent boundary layer around a group of obstacles in the direction of flow

Results of an investigation of a boundary layer in a turbulent flow on the surface of a wall having a group of obstacles on the path of flow are presented with regard to the mean velocity field, velocity distribution of the two dimensional flow, wall surface shear stresses and Reynolds stresses measured in a downstream cross section where an interference of boundary layers takes place in a flow around adjacent obstacles arranged on the path of flow

Computation of weighted Bergman inner products on bounded symmetric domains and Parseval-Plancherel-type formulas for (SpSp(rr, mathbbRmathbb{R}), SpSp(r′r', mathbbRmathbb{R})timestimesSpSp(r′′r'', mathbbRmathbb{R})) (Various Issues on Representation Theory and Related Topics)

Let (G, G') = (G, (G[δ]⁻)₀ ) be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces D' = G'/K' ⊂ D = G/K, realized as bounded symmetric domains in complex vector spaces P₁⁺ := (p⁺)[δ] ⊂ p⁺ respectively. Then the universal covering group G~ of G acts unitarily on the weighted Bergman space H[λ](D) ⊂ O(D) = O[λ](D) on D for sufficiently large λ. Its restriction to the subgroup G~' decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua-Kostant-SchmidKobayashi's formula in terms of the K~'-decomposition of the space P(p₂⁺) of polynomials onp₂⁺ := (p⁺)⁻[δ] ⊂ p⁺. Our goal is to understand the decomposition of the restriction H[λ](D)|[G~'] by studying the weighted Bergman inner product on each K~'-type in P(p₂⁺) ⊂ H[λ](D). In this article we mainly deal with the symmetric pair (G, G') = (Sp(r, ℝ), Sp(r', ℝ) x Sp(r'', ℝ))

Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval-Plancherel-Type Formulas under Subgroups

Let $(G,G_1)=(G,(G^\sigma)_0)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded symmetric domains in complex vector spaces ${\mathfrak p}^+_1:=({\mathfrak p}^+)^\sigma\subset{\mathfrak p}^+$ respectively. Then the universal covering group $\widetilde{G}$ of $G$ acts unitarily on the weighted Bergman space ${\mathcal H}_\lambda(D)\subset{\mathcal O}(D)={\mathcal O}_\lambda(D)$ on $D$ for sufficiently large $\lambda$. Its restriction to the subgroup $\widetilde{G}_1$ decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua-Kostant-Schmid-Kobayashi's formula in terms of the $\widetilde{K}_1$-decomposition of the space ${\mathcal P}({\mathfrak p}^+_2)$ of polynomials on ${\mathfrak p}^+_2:=({\mathfrak p}^+)^{-\sigma}\subset{\mathfrak p}^+$. The object of this article is to understand the decomposition of the restriction ${\mathcal H}_\lambda(D)|_{\widetilde{G}_1}$ by studying the weighted Bergman inner product on each $\widetilde{K}_1$-type in ${\mathcal P}({\mathfrak p}^+_2)\subset{\mathcal H}_\lambda(D)$. For example, by computing explicitly the norm $\Vert f\Vert_\lambda$ for $f=f(x_2)\in{\mathcal P}({\mathfrak p}^+_2)$, we can determine the Parseval-Plancherel-type formula for the decomposition of ${\mathcal H}_\lambda(D)|_{\widetilde{G}_1}$. Also, by computing the poles of $\langle f(x_2),{\rm e}^{(x|\overline{z})_{{\mathfrak p}^+}}\rangle_{\lambda,x}$ for $f(x_2)\in{\mathcal P}({\mathfrak p}^+_2)$, $x=(x_1,x_2)$, $z\in{\mathfrak p}^+={\mathfrak p}^+_1\oplus{\mathfrak p}^+_2$, we can get some information on branching of ${\mathcal O}_\lambda(D)|_{\widetilde{G}_1}$ also for $\lambda$ in non-unitary range. In this article we consider these problems for all $\widetilde{K}_1$-types in ${\mathcal P}({\mathfrak p}^+_2)$

Enrichments of gene replacement events by Agrobacterium-mediated recombinase-mediated cassette exchange

We report recombinase-mediated cassette exchange (RMCE), which can permit integration of transgenes into pre-defined chromosomal loci with no co-expressed marker gene by using Agrobacterium-mediated transformation. Transgenic tobacco plants which have a single copy of negative marker genes (codA) at target loci in heterozygous and homozygous conditions were used for gene exchange by the RMCE method. By negative selection, we were able to obtain five heterozygous and four homozygous transgenic plants in which the genes were exchanged from 64 leaf segments of heterozygous and homozygous target plants, respectively. Except for one transgenic plant with an extra copy, the other eight plants had only a single copy of marker-free transgenes, and no footprint of random integrated copies was detected in half of the eight plants. The RMCE re-transformation frequencies were calculated as 6.25 % per explant and were approximately the same as the average percentage of intact single-copy transformation events for standard tobacco Agrobacterium-mediated transformation

Measuring beta_s with Bs -> K0(*) K0bar(*) -- a Reappraisal

The Bs-Bsbar mixing phase, beta_s, can be extracted from Bs -> K0(*) K0bar(*), but there is a theoretical error if the second amplitude, Vub* Vus P'uc, is non-negligible. Ciuchini, Pierini and Silvestrini (CPS) have suggested measuring Puc in Bd -> K0(*) K0bar(*), and relating it to P'uc using SU(3). For their choice of the direct and indirect CP asymmetries in Bd -> K0(*) K0bar(*), they find that the error on beta_s is very small, even allowing for 100% SU(3) breaking. In this paper, we re-examine the CPS method, allowing for a large range of the Bd -> K0(*) K0bar(*) observables. We find that the theoretical error in the extraction of beta_s can be quite large, up to 18 degrees. This problem can be ameliorated if the value of SU(3) breaking were known, and we discuss different ways, both experimental and theoretical, of determining this quantity.Comment: 16 pages, 5 figures, LaTeX. References added, text slightly modified, analysis and conclusions unchange

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