We study the Hankel determinant generated by a singularly perturbed Jacobi weightIf t = 0, it is reduced to the classical symmetric Jacobi weight. For t > 0, the factor e − t x 2 induces an infinitely strong zero at the origin. This Hankel determinant is related to the Wigner time-delay distribution in chaotic cavities.In the finite n dimensional case, we obtain two auxiliary quantities R n (t) and r n (t) by using the ladder operator approach. We show that the Hankel determinant has an integral representation in terms of R n (t), where R n (t) is closely related to a particular Painlevé V transcendent. Furthermore, we derive a second-order nonlinear differential equation and also a second-order difference equation for the logarithmic derivative of the Hankel determinant.This quantity can be expressed in terms of the Jimbo-Miwa-Okamoto σ-function of a particular Painlevé V. Then we consider the asymptotics of the Hankel determinant under a suitable double scaling, i.e. n → ∞ and t → 0 such that s = 2n 2 t is fixed. Based on previous results by using the Coulomb fluid method, we obtain the large s and small s asymptotic behaviors of the scaled Hankel determinant, including the constant term in the asymptotic expansion.

A b s t r a c t M e c h a n i s m s o f P t e r i s v i t t a t a L . t o hyperaccumulate arsenic (As), especially the efficient translocation of As from rhizoids to fronds, are not clear yet. The present study aims to investigate the role of transpiration in the accumulation of As from the aspects of transpiration regulation and ecotypic difference. Results showed that As accumulation of P. vittata increased proportionally with an increase in the As exposure concentration. Lowering the transpiration rate by 28∼67 % decreased the shoot As concentration by 19∼56 %. Comparison of As distribution under normal treatment and shade treatment indicated that transpiration determines the distribution pattern of As in pinnae. In terms of the ecotypic difference, the P. vittata ecotype from moister and warmer habitat had 40 % higher transpiration and correspondingly 40 % higher shoot As concentration than the ecotype from drier and cooler habitat. Results disclosed that transpiration is the main driver for P. vittata to accumulate and redistribute As in pinnae.

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