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Lecture notes at a conference on Arithmetic Geometry, Goettingen, July/August 2006: Density of ordinary Hecke orbits and a conjecture by Grothendieck on deformations of p-divisible groups.

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For a local field K with positive residue characteristic p, we introduce, in the first part of this paper, a refinement bAr_K of the classical Artin distribution Ar_K. It takes values in cyclotomic extensions of Q which are unramified at p, and it bisects Ar_K in the sense that Ar_K is equal to the sum of bAr_K and its conjugate distribution. Compared with 1/2 Ar_K, the bisection bAr_K provides a higher resolution on the level of tame ramification. In the second part of this article, we prove that the base change conductor c(T) of an analytic K-torus T is equal to the value of bAr_{K} on the Q_p-rational Galois representation X^*(T)_{Q_p} that is given by the character module X^*(T) of T. We hereby generalize a formula for the base change conductor of an algebraic K-torus, and we obtain a formula for the base change conductor of a semiabelian K-variety with potentially ordinary reduction.

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Tumor suppressor WOX1 (also named WWOX or FOR) is known to participate in neuronal apoptosis in vivo. Here, we investigated the functional role of WOX1 and transcription factors in the delayed loss of axotomized neurons in dorsal root ganglia (DRG) in rats.

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A "pre-modular form" $Z_n(\sigma; \tau)$ of weight $\tfrac{1}{2} n(n + 1)$ is introduced for each $n \in \Bbb N$, where $(\sigma, \tau) \in \Bbb C \times \Bbb H$. Let $E_\tau = \Bbb C/(\Bbb Z + \Bbb Z \tau)$. Then the pre-modular form has the property that every non-trivial zero of $Z_n(\sigma; \tau)$, namely $\sigma \not\in E_\tau[2]$, corresponds exactly to the solution to the non-linear mean field equation (MFE) $$ \triangle u + e^u = 8\pi n\, \delta_0 $$ on the flat torus $E_\tau$. This paper is a sequel to Part I (Cambridge J. Math 3 (2015), 127-274), where the hyperelliptic curve $\bar X_n(\tau) \subset {\rm Sym}^n E_\tau$ associated to the MFE is constructed. Our construction of $Z_n(\sigma; \tau)$ relies on a detailed study of the correspondence $\Bbb P^1 \leftarrow \bar X_n(\tau) \to E_\tau$ where the former map is the hyperelliptic projection and the latter map is induced from the addition law.

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We develop a theory connecting the following three areas: (a) the mean field equation (MFE) $\triangle u + e^u = \rho\, \delta_0$, $\rho \in \mathbb R_{>0}$ on flat tori $E_\tau = \mathbb C/(\mathbb Z + \mathbb Z\tau)$, (b) the classical Lam\'e equations and (c) modular forms. A major theme in part I is a classification of developing maps $f$ attached to solutions $u$ of the mean field equation according to the type of transformation laws (or monodromy) with respect to $\Lambda$ satisfied by $f$. We are especially interested in the case when the parameter $\rho$ in the mean field equation is an integer multiple of $4\pi$. In the case when $\rho = 4\pi(2n + 1)$ for a non-negative integer $n$, we prove that the number of solutions is $n + 1$ except for a finite number of conformal isomorphism classes of flat tori, and we give a family of polynomials which characterizes the developing maps for solutions of mean field equations through the configuration of their zeros and poles. Modular forms appear naturally already in the simplest situation when $\,\rho=4\pi$. In the case when $\rho = 8\pi n$ for a positive integer $n$, the solvability of the MFE depends on the \emph{moduli} of the flat tori $E_\tau$ and leads naturally to a hyperelliptic curve $\bar X_n=\bar X_{n}(\tau)$ arising from the Hermite-Halphen ansatz solutions of Lam\'e's differential equation $\frac{d^2 w}{dz^2}-(n(n+1)\wp(z;\Lambda_{\tau}) + B) w=0$. We analyse the curve $\bar X_n$ from both the analytic and the algebraic perspective, including its local coordinate near the point at infinity, which turns out to be a smooth point of $\bar{X}_n$. We also specify the role of the branch points of the hyperelliptic projection $\bar X_n \to \mathbb P^1$ when the parameter $\rho$ varies in a neighborhood of $\rho = 8\pi n$.

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To develop an effective ocular drug delivery carrier, we prepared two different charged gelatin nanoparticles (GPs) and evaluated particle size, surface charge, and morphology. The in vitro biocompatibility of GPs was assessed using human corneal epithelium (HCE) cells and in vivo safety by administering them as eye drops to New Zealand rabbits. The GPs prepared using type A gelatin were positively charged (GP(+), +33？mV; size, ？nm). Water-soluble tetrazolium salt (WST)-1 assay showed that both GPs were nontoxic to HCE cells. The fluorescence intensity of HCE cells cultured with cationic GPs conjugated with a fluorescent dye was higher than that of the anionic GP-treated HCE cells. In vivo examination showed no serious irritation to the rabbit eyes. Furthermore, corneal thickness and ocular pressure in the eyes of the treated rabbits were similar to those in the eyes of normal rabbits. Microscopic examination of corneal cryosections showed widely distributed fluorescent nanocarriers, from the anterior to the posterior part of the cornea of the GP(+) group, and higher fluorescence intensity in the GP(+) group was also observed. In conclusion, GPs as cationic colloidal carriers were efficiently adsorbed on the negatively charged cornea without irritating the eyes of the rabbits and can be retained in the cornea for a longer time. Thus, GPs(+) have a great potential as vehicles for ocular drug delivery. 1. Introduction The eye poses unique challenges for drug delivery. The main objective of ocular therapeutics is to provide and maintain adequate concentration of the drug at the target site. Most ocular diseases are treated with topical application of solutions administered as eye drops. The major disadvantages of this dosage form include (i) poor ocular drug bioavailability because of the anatomical and physiological constraints of the eye that limit drug retention, (ii) pulse-drug entry with high variation in dose, (iii) nasolacrimal duct drainage, which causes systemic exposure, and (iv) poor entrance to the posterior segments of the eye because of the lens-iris diaphragm [1, 2]. The above disadvantages result in clearance of 90% of the eye drops within 2？min, and only 5% of the administered dose permeates to the eye [3]. Most efforts in ocular delivery have been focused on increasing the corneal retention of drugs with the final goal of improving the efficacy of treatments for different ocular diseases. These attempts include the use of colloidal drug delivery systems such as liposomes [4], nanoparticles [5–8], and nanospheres [9]. The results of

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The high frequency transient recovery voltage caused by usually switching operation of the circuit breakers, used on shunt reactor switching, have become a noticeable problem recently. For extension the service life time and normal operation of the circuit breakers, a well modified maintenance strategy is proposed. The field testing and experimental measurement showed the maintenance strategy proposed had been proved effectively and adopted in Taiwan Power Company.

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Based on a telephone interview with all of the technological Institute and Junior College Libraries in Taiwan, we analyzed the current status of library automation and the level of service satisfaction. Through the survey results, we determined the current condition of our country’s library automation system and the difficulties encountered in its use. We also point out the factors to consider when choosing a system. In addition, in this digital age, we expect further developments in library automation systems. We hope these developments will improve the serviceability of library automation systems and help in the planning of new library automation systems.[Article content in Chinese]