The Coordination Chemistry of f-Block Elements in Molten Salts

The coordination chemistry of f-block elements (lanthanide and actinide) in molten salts has become a resounding topic in view of its great importance to the research and development (R&D) of molten salt reactors and pyroprocessing. In this Review article, a general overview of the coordination chemistry of f-block elements in molten salts is provided including past achievements and recent advances. Particular emphases are placed on the oxidation state, speciation, and solution structure of f-block metal ions in molten salts, as well as their relationships with the salt composition. Furthermore, this review briefly discusses the spectroscopic and theoretical methods that complement each other in revealing the coordination properties.     

On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

An investigation on the defect structures and spin Hamiltonian parameters for the two orthorhombic Ti3+ centers in ZnWO4

By employing the perturbation formulae of the spin Hamiltonian parameters (SHPs) (g factors g_xx, g_yy, g_zz, hyperfine structure constants A_xx, A_yy, A_zz and superhyperfine parameters A_xx׳, A_yy׳, A_zz׳) for a 3d¹ ion in orthorhombically elongated octahedra and tetrahedra, the defect structures and the experimental EPR spectra are theoretically and systematically investigated for the two orthorhombic Ti³⁺ centers C₁ and C₂ in ZnWO₄. Center C₁ is ascribed to the impurity Ti³⁺ at host W⁶⁺ site associated with two nearest neighbor oxygen vacancies due to charge compensation. The resultant tetrahedral [TiO₄]^5– cluster is determined to undergo the local orthorhombic elongation distortion, characterized by the axial distortion angle Δθ (=θ–θ₀≈–6.84°) of the local impurity-ligand bond angle θ related to θ₀ (≈54.74°) and the perpendicular distortion angle Δε (=ε–ε₀≈2.5°) related to ε₀ (≈45°) of an ideal tetrahedron because of the Jahn–Teller effect. Center C₂ is attributed to Ti³⁺ on Zn²⁺ site, and this octahedral [TiO₆]^9– cluster may experience the local axial elongation ΔZ (≈0.001 Ǻ) and the planar bond angle variation Δφ (≈9.1°) due to the Jahn–Teller effect, resulting in a more regular oxygen octahedron. All the calculated SHPs (i.e., g factors for both centers, the hyperfine structure constants for center C₂ and superhyperfine parameters of next nearest neighbor ligand W for center C₁) show good agreement with the observed values. However, the theoretical results based on the previous assignment of center C₁ as Ti³⁺ on W⁶⁺ site with only one nearest planar oxygen vacancy (i.e., five-fold coordinated octahedral [TiO₅]^7– cluster) show much worse agreement with the experimental data. The defect structures and the SHPs (especially the g anisotropies) are discussed for both centers. The present studies on the superhyperfine parameters of ligand W⁶⁺ for center C₁ would be helpful to further investigations on the superhyperfine interactions of cation ligands which were rather scarcely treated before.     

一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

随机发展方程适度解的存在唯一性(Ⅱ)

讨论如下Hilbert空间中的半线性随机发展方程的Cauchy问题 dy(t)=[Ay(t) f(t,y(t))]dt G(t,y(t))dw(t) y(O)=V_u的适度解的存在唯一性,在更一般的条件下,得到了该问题的适度解的存在唯一性。     

关于混合型多项式Hammerstein积分方程正解迭代求法

本文给出了混合型多项式Ｈａｍｍｅｒｓｔｅｉｎ积分方程正解的迭代求法，并将所得结果应用到二阶非线性常微分方程的边值问题     

Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg-Landau equation with variable coefficients

We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically.