Non-existence of extremals for the Adimurthi–Druet inequality

The Adimurthi–Druet [1] inequality is an improvement of the standard Moser–Trudinger inequality by adding a $L^2$-type perturbation, quantified by $\alpha \in [0,{\lambda }_1)$, where ${\lambda }_1$ is the first Dirichlet eigenvalue of Δ on a smooth bounded domain. It is known [3], [10], [14], [19] that this inequality admits extremal functions, when the perturbation parameter α is small. By contrast, we prove here that the Adimurthi–Druet inequality does not admit any extremal, when the perturbation parameter α approaches ${\lambda }_1$. Our result is based on sharp expansions of the Dirichlet energy for blowing sequences of solutions of the corresponding Euler–Lagrange equation, which take into account the fact that the problem becomes singular as $\alpha \to {\lambda }_1$.     

Synthesis and Structural Study of Sr2CuO3+δ Superconductor under High Pressure

A single-phase Sr₂CuO_3+δ superconductor is synthesized under high temperature and high pressure, in which oxygen atoms only partially occupy the apical sites next to the CuO₂ planes and act as hole-dopants. Thesuperconducting transition temperature with T_c^max=75K is achieved in the material. Structure analysis from x-ray powder diffraction data show that this material crystallizes into a K₂NiF₄ structure with tetragonal unit cell of a=3.795(3)AAand c= 12.507(1)AA. Energy-dispersive synchrotron x-ray-diffraction studies at ambient are performed on powder samples of Sr₂CuO_3+δ in a diamond-anvil cell at pressure up to 35GPa. Anisotropic compressibility is found. Pressure-induced isostructural phase transition might exist as revealed by the discontinuous change of crystal cell volume V withpressure.     

Electronic structure of PCBM

We have studied the electronic structure of [6,6]-phenyl-C₆₁-butyric-acid-methyl-ester (PCBM) using synchrotron radiation photoelectron spectroscopy (PES) measurements and first-principles calculations. The PES spectrum of the entire occupied valence band is reported, which exhibits abundant spectral features from the Fermi level to ～24 eV binding energy. All the spectral features are broadened as compared with the cases of C₆₀. The reasons for the broadening are analysed by comparing the experimental data with the calculated energy levels and density of states. Special attention is paid to the analysis of the C₆₀ highest occupied molecular orbital (HOMO)-1 derived states, which can play a crucial role in the bonding at the interfaces of PCBM/polymer blenders or PCBM/electrodes. Besides the well-known energy level splitting of the C₆₀ backbone caused by the lowered symmetry, C 2p states from the side chain mix or hybridize with the molecular orbitals of parent C₆₀. The contribution of the O 2p states can substantially modify the PES spectrum.     

Optimal portfolios for DC pension plans under a CEV model

This paper studies the portfolio optimization problem for an investor who seeks to maximize the expected utility of the terminal wealth in a DC pension plan. We focus on a constant elasticity of variance (CEV) model to describe the stock price dynamics, which is an extension of geometric Brownian motion. By applying stochastic optimal control, power transform and variable change technique, we derive the explicit solutions for the CRRA and CARA utility functions, respectively. Each solution consists of a moving Merton strategy and a correction factor. The moving Merton strategy is similar to the result of Devolder et al. [Devolder, P., Bosch, P.M., Dominguez F.I., 2003. Stochastic optimal control of annunity contracts. Insurance: Math. Econom. 33, 227-238], whereas it has an updated instantaneous volatility at the current time. The correction factor denotes a supplement term to hedge the volatility risk. In order to have a better understanding of the impact of the correction factor on the optimal strategy, we analyze the property of the correction factor. Finally, we present a numerical simulation to illustrate the properties and sensitivities of the correction factor and the optimal strategy.     

First-Principles Study on the Electronic Structures for Y^3＋：PbWO4 Crystals

The possible defect models of Y^3＋：PbWO4 crystals are discussed by defect chemistry and the most possible substituting positions of the impurity Y^3＋ ions are studied by using the general utility lattice program （GULP）. The calculated results indicate that in the lightly doped Y^3＋ ：PWO crystal, the main compensating mechanism is [2Ypb^＋ ＋ VPb^2-], and in the heavily doped Y^3＋ ：PWO crystal, it will bring interstitial oxygen ions to compensate the positive electricity caused by YPb^＋, forming defect clusters of [2Ypb^＋ ＋Oi^2-] in the crystal. The electronic structures of Y3＋ ：PWO with different defect models are calculated using the DV-Xα method. It can be concluded from the electronic structures that, for lightly doped cases, the energy gap of the crystal would be broadened and the 420nm absorption band will be restricted; for heavily doped cases, because of the existence of interstitial oxygen ions, it can bring a new absorption band and reduce the radiation hardness of the crystal.     

The impact of illiquidity on the asset management of insurance companies

This paper investigates optimal asset management strategies for property and casualty insurance companies in illiquid markets. Using a cash-flow based liquidation model of an insurance company, we consider the effects of permanent and temporary price impact as well as commonality in price impact. Focusing on the interaction of a single large investor with the financial market makes the main results generally applicable for any institutional investor with stochastic future liabilities and restrictions on short-sales and financial leverage. Our analysis reveals a clear diversification benefit in illiquid markets apart from the one introduced by Markowitz [Markowitz, H., 1952. Portfolio selection. J. Financ. 7, 77-91]. In the presence of commonality, cash-flow matching is shown to be the optimal strategy for a large investor.     

Diophantine approximation in characteristiep

We study diophantine approximations to algebraic functions in characteristicp. We improve a theorem of Osgood, and give two classes of examples showing that this result is nearly sharp. One of these classes exhibits a new phenomenon.     

On Le’s and Bugeaud’s Papers about the Equation ax 2?+ b 2m?1 ?=?4 c p

 We correct an inaccuracy in the papers of Le, Mignotte, and Bugeaud on the generalized Ramanujan-Nagell equation. Received June 23, 2001