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.     

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     

Influence of the Lanthanide Ion and Solution Conditions on Formation of Lanthanide Wells–Dawson Polyoxotungstates

Lanthanide complexes of polyoxometalates, including the α₂-P₂W₁₇O₆₁ ¹⁰⁻ ligand, have been pioneered by Michael T. Pope, to whom this paper is dedicated. Examination of the solid-state and solution behavior of lanthanide complexes of the α₂-P₂W₁₇O₆₁ ¹⁰⁻ ligand are reported here to identify trends that will facilitate rational synthesis of hybrid organic lanthanide polyoxometalate complexes. Therefore, combining our data with that obtained by Pope and others a number of trends come into view. It is clear that there are two structural types for the 1:1 or 2:2 [Ln(H₂O)_X(α₂-P₂W₁₇O₆₁)]₂ ¹⁴⁻ species. The early lanthanides show a “cap to cap” structure that allows the Ln ion to be 9 coordinate and accommodates the longer bond lengths. The mid-late lanthanides show a “cap to belt” structure that allows the lanthanides to be 8 coordinate; this structural type is appropriate for the shorter bond lengths of the later lanthanides. The 1:1⇌1:2 equilibrium, that was observed by Pope for the Ce(III) analog is prevalent for the early- mid lanthanides. This equilibrium is slightly dependent on pH; however, cations have a major influence on this equilibrium. Larger, poorly hydrated cations appear to favor the 1:2 species for the early to mid lanthanides. Cations do not appear to influence the equilibrium for the later lanthanides; for all counterions, the 1:1 species was stable with no trace of the 1:2 species. Stability constants, K1 and K2, for the early to mid lanthanides were measured in this study by a competitive method and compared well with other published stability constant determinations. We suggest that the stability constants are not only dependent on the strength of interaction of the Ln with the α₂-P₂W₁₇O₆₁ ¹⁰⁻ ligand, but are also significantly influenced by the medium. The medium may bias the equilibria of the early-mid lanthanides and later lanthanides. The log K₁/log K₂ ratios are very close, suggesting that it is difficult to separate the 1:1 and 1:2 Ln: α₂-P₂W₁₇O₆₁ ¹⁰⁻ species.Electronic Supplementary Material Supplementary material for this article is available at and is accessible for authorized users.This paper is dedicated to Professor Michael T. Pope in honor of his substantial and sustained contributions to polyoxometalate chemistry and his inspiration to scientists working in the field.     

Anwendung von 2D-NMR-Techniken zur Analyse komplexer Spektren. Maleopimarsäuremethylester

A combination of 2D-NMR-techniques including 2D-J-resolved spectroscopy, SECSY and¹H-¹³C-shift correlation is used to assign the¹H- and¹³C-spectrum of Maleopimaric acid methylester [17,19-Dinoratis-15-ene-4,13,14-tricarboxylic acid 4-methylester, 16-(1-methylethyl)cyclic-13,14-anhydrid (461/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">, 861/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">, 1261/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">)] (1).

     

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 $\alpha \to {\lambda }_1$.     

Femtosecond laser-induced ZnSe nanowires on the surface of a ZnSe wafer in water

We present a simple route for ZnSe nanowire growth in the ablation crater on a ZnSe crystal surface. The crystal wafer, which was horizontally dipped in pure water, was irradiated by femtosecond laser pulses. No furnace, vacuum chamber or any metal catalyst were used in this experiment. The size of the nanowires is about 1-3 μm long and 50-150 nm in diameter. The growth rate is 1-3 μm/s, which is much higher than that achieved with molecular-beam epitaxy and chemical vapor deposition methods. Our discovery reveals a rapid and simple way to grow nanowires on designed micro-patterns, which may have potential applications in microscopic optoelectronics.     

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.     

Asymptotically liberating sequences of random unitary matrices

A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asymptotic liberation” under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino, Caire, Shamai and Verdú.     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.