On Addition Formulae of KP, mKP and BKP Hierarchies

In this paper we study the addition formulae of the KP, the mKP and the BKP hierarchies. We prove that the total hierarchies are equivalent to the simplest equations of their addition formulae. In the case of the KP and the mKP hierarchies those results had previously been proved by Noumi, Takasaki and Takebe by way of wave functions. Here we give alternative and direct proofs for the case of the KP and mKP hierarchies. Our method can equally be applied to the BKP hierarchy

On the Expansion Coefficients of Tau-function of the BKP Hierarchy

We study the series expansion of the tau function of the BKP hierarchy applying the addition formulae of the BKP hierarchy. Any formal power series can be expanded in terms of Schur functions. It is known that, under the condition $\tau(x)\neq0$, a formal power series $\tau(x)$ is a solution of the KP hierarchy if and only if its coefficients of Schur function expansion are given by the so called Giambelli type formula. A similar result is known for the BKP hierarchy with respect to Schur's Q-function expansion under a similar condition. In this paper we generalize this result to the case of $\tau(0)=0$.Comment: 18page

On the Expansion Coefficients of KP Tau Function

We study the expansion coefficients of the tau function of the KP hierarchy. If the tau function does not vanish at the origin, it is known that the coefficients are given by Giambelli formula and that it characterizes solutions of the KP hierarchy. In this paper, we find a generalization of Giambelli formula to the case when the tau function vanishes at the origin. Again it characterizes solutions of the KP hierarchy.Comment: 21 page

Positive allosteric binding behavior of pyrene-appended triazole-modified thiacalix[4]arene-based fluorescent receptors

The novel heteroditopic receptors 5a∼c have been synthesized, which bear a thiacalix[4]arene in the 1,3-alternate conformation. Two urea moieties possessing various aryl groups with either electron-donating or -withdrawing groups at their p-positions function as anion-binding sites. At the opposite side of the cavity are two pyrene-appended triazole rings, which act as cation-binding sites. The binding property of receptor 5c was investigated by means of 1H NMR and UV–vis spectroscopy and by fluorescence titration experiments in the presence of various transition metal cations and anions in CH2Cl2–DMSO (10:1, v/v) solution. Interestingly, it was found that receptor 5c possessing two p-nitrophenyl ureido moieties, most efficiently complexes in the urea cavity or bistriazoles; the plausible allosteric effect of receptor 5c was also investigated

A novel Rac1-GSPT1 signaling pathway controls astrogliosis following central nervous system injury

Astrogliosis (i.e. glial scar), which is comprised primarily of proliferated astrocytes at the lesion site and migrated astrocytes from neighboring regions, is one of the key reactions in determining outcomes after CNS injury. In an effort to identify potential molecules/pathways that regulate astrogliosis, we sought to determine whether Rac/Rac-mediated signaling in astrocytes represents a novel candidate for therapeutic intervention following CNS injury. For these studies, we generated mice with Rac1 deletion under the control of the GFAP (glial fibrillary acidic protein) promoter (GFAP-Cre;Rac1(flox/flox)). GFAP-Cre;Rac1(flox/flox) (Rac1-KO) mice exhibited better recovery after spinal cord injury and exhibited reduced astrogliosis at the lesion site relative to control. Reduced astrogliosis was also observed in Rac1-KO mice following microbeam irradiation-induced injury. Moreover, knockdown (KD) or KO of Rac1 in astrocytes (LN229 cells, primary astrocytes, or primary astrocytes from Rac1-KO mice) led to delayed cell cycle progression and reduced cell migration. Rac1-KD or Rac1-KO astrocytes additionally had decreased levels of GSPT1 (G(1) to S phase transition 1) expression and reduced responses of IL-1β and GSPT1 to LPS treatment, indicating that IL-1β and GSPT1 are downstream molecules of Rac1 associated with inflammatory condition. Furthermore, GSPT1-KD astrocytes had cell cycle delay, with no effect on cell migration. The cell cycle delay induced by Rac1-KD was rescued by overexpression of GSPT1. Based on these results, we propose that Rac1-GSPT1 represents a novel signaling axis in astrocytes that accelerates proliferation in response to inflammation, which is one important factor in the development of astrogliosis/glial scar following CNS injury

Analysis of proton-induced fragment production cross sections by the Quantum Molecular Dynamics plus Statistical Decay Model

The production cross sections of various fragments from proton-induced reactions on $^{56}$Fe and $^{27}$Al have been analyzed by the Quantum Molecular Dynamics (QMD) plus Statistical Decay Model (SDM). It was found that the mass and charge distributions calculated with and without the statistical decay have very different shapes. These results also depend strongly on the impact parameter, showing an importance of the dynamical treatment as realized by the QMD approach. The calculated results were compared with experimental data in the energy region from 50 MeV to 5 GeV. The QMD+SDM calculation could reproduce the production cross sections of the light clusters and intermediate-mass to heavy fragments in a good accuracy. The production cross section of $^{7}$Be was, however, underpredicted by approximately 2 orders of magnitude, showing the necessity of another reaction mechanism not taken into account in the present model.Comment: 12 pages, Latex is used, 6 Postscript figures are available by request from [email protected]

On the expansion coefficients of Tau-functions of the KP hierarchy (Mathematical structures of integrable systems, its deepening and expansion)

Mathematical structures of integrable systems, its deepening and expansion. September 9-11, 2019. edited by Takao Suzuki. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.We study the coefficients of the tau function of the KP hierarchy. If the tau function does not vanish at the origin, it is known that the coefficients are given by Giambelli formula. We introduce a generalization of Giambelli formula to the case when the tau function vanishes at the origin. This paper is a summary of [6]

Genetic Analysis of 6-Phosphogluconate Dehydrogenase Isozymes in Cultivated and Wild Species of Section Cepa in Allium

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