再谈Minc-Sathre不等式的上下界

用调和平均值、均值不等式之间的关系及对数平均不等式,对Minc-Sathre不等式的上下界进行改进,使结论更精确.     

非线性Black-Scholes模型下算术平均亚式期权定价问题

在非线性Black-Scholes模型下,研究了算术平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性.     

Diffeomorphisms with C 1-stably average shadowing

Let M be a closed smooth manifold M, and let f : M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f . We show that if f has the C1-stably average shadowing property on Λ, then Λ admits a dominated splitting.     

Crystal structure,physical properties and bond valence analysis of NaLuP2O7

Single crystals of a diphosphate NaLuP₂O₇ have been synthesized by the flux method and characterized by single-crystal X-Ray diffraction. NaLuP₂O₇ crystallizes in the monoclinic system with P2₁/n space group with cell parameters: a = 8.9985(8) Å, b = 5.3473(5) Å, c = 12.756(1) Å, β = 103.174° (1), V = 597.67 (9) Å³, Z = 4. Its structure consists of a three-dimensional framework of P₂O₇ units that are corner-shared by LuO₆ octahedra, forming tunnels running parallel to [010] which are occupied by Na atoms. NaLuP₂O₇ powder was characterized by XRD, SEM, FTIR and Raman spectroscopy. The activation energy of (1.49 eV) obtained by electrical measurements suggests the charge carriers to be the sodium cations. The activation energies obtained from impedance and loss spectra were analyzed in order to explain the mechanism of conduction. The correlation between ionic conductivity of NaLuP₂O₇ and its crystallographic structure was investigated and the most probable transport pathway model was determined.     

Synthesis,Crystal Structure,and Characterization of Na7Cu4(AsO4)5

Abstract

Sodium copper (II) arsenate Na₇Cu₄(AsO₄)₅ has been grown by conventional high-temperature, solid-state methods in molten-salt media. It was characterized by single crystal X-ray diffraction (XRD), thermal analysis (DTA–TGA), scanning electron microscopy (SEM), semiquantitative energy dispersive spectroscopy analysis (EDS), and vibrational spectroscopy. Na₇Cu₄(AsO₄)₅ exhibits a three-dimensional framework built up of CuO₅, CuO₄, and AsO₄ polyhedra, with intersecting channels in which the Na⁺ cations are located. The three-dimensional cohesion of the framework results from Cu–O–As bridges. CuO₅ and CuO₄ polyhedra are elongated due to the Jahn–Teller effect, whereas AsO₄ tetrahedra are almost regular. This new structural model is validated by the charge distribution (CD) analysis. The infrared and Raman spectra confirmed the presence of AsO₄ tetrahedra.

[Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfer, and Silicon and the Related Elements for the following free supplemental files: Additional tables and figures.]     

Erratum: The average degree of an edge-chromatic critical graph II

In the article “The average degree of an edge-chromatic critical graph II” by Douglas R. Woodall (J. Graph Theory 56 (2007), 194-218), it was claimed that the average degree of an edge-chromatic critical graph with maximum degree $\mathrm{\Delta }$ is at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+1\right)$ if $\mathrm{\Delta }⩾2$, at least $\text{◂+▸}\frac{2}{3}\mathrm{\Delta }+1$ if $\mathrm{\Delta }⩾8$, and at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+2\right)$ if $\mathrm{\Delta }⩾15$. Unfortunately there were mistakes in the proof of the last two of these results, which are now proved only if $\mathrm{\Delta }⩾18$ and $\mathrm{\Delta }⩾30$, respectively.     

Structural distortion,charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X‐ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high‐quality Fe₃O₄ single crystals and thin films grown on MgO by using resonant X‐ray scattering at the Fe K‐edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e^? with [0 0 1] and cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a–b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low‐temperature crystal structure refined in the non‐polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.     

Influence of Intermolecular Interactions on Valence Tautomeric Behaviors in Two Polymorphic Dinuclear Cobalt Complexes

Two polymorphic structures have been well determined in a valence tautomeric (VT) dinuclear cobalt complex. These polymorphs showed distinct thermal‐ and photomagnetic behavior, and are thus ideal for studying the “pure” intermolecular factors to VT transitions. In polymorph 1A , the VT cations are arranged head‐to‐waist with their neighbors and exhibit weak π???π interactions, resulting in a gradual and incomplete thermal VT transition. In contrast, the cations in polymorph 1B are arranged head‐to‐tail and exhibit relatively strong π???π interactions, leading to an abrupt and complete thermal VT transition with adjustable hysteresis loop at around room temperature. The VT process for both polymorphs can be induced by light, but the light‐excited state of 1B? 2H₂O has a higher thermal relaxation temperature than that of 1A? 3H₂O.