Studies on the Synthesis and Properties of K_8[TiP_2W_17O_62]·12H_2O

The present paper covers a salt of 2:18 heteropoly complex of tungstotitanophosphate prepared with the method of improved sequence preparation. The title compound was characterized by elemental analysis, 31P NMR spectra, polarography, cyclic voltammetry, IR, UV, X-ray powder diffraction , X-ray photoelectron spectra and TG-DTA analysis. The results show that the complex with the formula K8[TiP2W17O62]·12H2O has Dawson structure. Its properties such as spectra, redox behavior and thermal stability are discussed.     

Christoffel functions and mean convergence for Lagrange interpolation for exponential weights

For exponential weights, a necessary condition of weighted mean convergence for Lagrange interpolation is given.     

Examples of non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property

In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces.     

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.     

Synthesis and magnetic properties of multilayer Ni/Cu and NiFe/Cu nanowires

Highly ordered composite nanowires with multilayer Ni/Cu and NiFe/Cu have been fabricated by pulsed electrodeposition into nanoporous alumina membrane. The diameter of wires can be easily varied by pore size of alumina, ranging from 30 to 100 nm. The applied potential and the duration of each potential square pulse determine the thickness of the metal layers. The nanowires have been characterized by transmission electron microscopy (TEM), magnetic force microscopy (MFM), and vibrating sample magnetometer (VSM) measurements. The MFM images indicate that every ferromagnetic layer separated by Cu layer was present as single isolated domain-like magnet. This technique has potential use in the measurement and application of magnetic nanodevices.     

Effects of SnO2 addition on the magnetic properties of manganese zinc ferrites

SnO₂ was added to high-permeability MnZn ferrites and MnZn ferrites for high-frequency power supplies. The effects of the SnO₂ addition were studied. Sn⁴⁺ ions can dissolve into the spinel lattice and form stable Fe²⁺–Sn⁴⁺ pairs and hence can compensate the magneto-crystalline anisotropy constant K₁ and improve the initial permeability effectively. The initial permeability of ferrites is also improved as abnormal grain growth caused by ion vacancy is controlled with SnO₂ doping. In addition, the SnO₂ doping also leads to a decrease in the relative loss factor and an increase in density. The power loss and minimum power loss temperature decrease with SnO₂ doping.     

Optimal production and rationing decisions in supply chains with information sharing

This paper considers a two-echelon capacitated supply chain with two non-identical retailers and information sharing. We characterize the optimal inventory policies. We also study the benefits of the optimal stock rationing policy over the first come first served (FCFS) and the modified echelon-stock rationing (MESR) policies.