Real zeros of the zero-dimensional parametric piecewise algebraic variety

The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi-algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and sufficient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and sufficient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex. This work was supported by National Natural Science Foundation of China (Grant Nos. 10271022, 60373093, 60533060), the Natural Science Foundation of Zhejiang Province (Grant No. Y7080068) and the Foundation of Department of Education of Zhejiang Province (Grant Nos. 20070628 and Y200802999)     

A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion. It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion. For this type of partial information control, one sufficient (a verification theorem) and one necessary conditions of optimality are proved. The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable. This work was partially supported by Basic Research Program of China (Grant No. 2007CB814904), National Natural Science Foundation of China (Grant No. 10325101) and Natural Science Foundation of Zhejiang Province (Grant No. Y605478, Y606667)     

A new linear ordering of fuzzy numbers on subsets of {{\mathcal F}({\pmb{\mathbb{R}}}})

We introduce a novel linear order on every family of fuzzy numbers which satisfies the assumption that their modal values must be all different and must form a compact subset of . A distinct new feature is that our linear determined procedure employs the corresponding order of a class interval associated with a confidence measure which seems intuitively anticipated. It is worthy noting that although we start from an entirely different rationale, we introduce a fuzzy ordering which initially coincides with the one established earlier by Ramik and Rimanek. However, this fuzzy ordering does not apply when the supports of the fuzzy numbers overlap. In order to cover such cases we extent this initial fuzzy ordering to the “extended fuzzy order” (XFO). This new XFO method includes a possibility and a necessity measure which are compared with the widely accepted PD and NSD indices of D. Dubois and H. Prade. The comparison shows that our possibility and necessity measures comply better with our intuition.     

含有治愈部分的可加危险模型的估计

最近可加危险(AH)模型被广泛地应用于生存分析数据,模型的协变量可以假设为时间独立或时间相关的.基于混合治愈模型,有界累计危险治愈模型和"不正确"的比例危险模型.本文将上述的可乘危险模型延伸到可加的危险模型,这里的模型可以允许含治愈部分的生存数据的存在."不正确"的AH模型的识别和参数估计也将在本文给出讨论.     

Improving the robustness of a partial least squares (PLS) model based on pure component selectivity analysis and range optimization: case study for the analysis of an etching solution containing hydrogen peroxide

Pure component selectivity analysis (PCSA) was successfully utilized to enhance the robustness of a partial least squares (PLS) model by examining the selectivity of a given component to other components. The samples used in this study were composed of NH₄OH, H₂O₂ and H₂O, a popular etchant solution in the electronic industry. Corresponding near-infrared (NIR) spectra (9000-7500 cm⁻¹) were used to build PLS models. The selective determination of H₂O₂ without influences from NH₄OH and H₂O was a key issue since its molecular structure is similar to that of H₂O and NH₄OH also has a hydroxyl functional group. The best spectral ranges for the determination of NH₄OH and H₂O₂ were found with the use of moving window PLS (MW-PLS) and corresponding selectivity was examined by pure component selectivity analysis. The PLS calibration for NH₄OH was free from interferences from the other components due to the presence of its unique NH absorption bands. Since the spectral variation from H₂O₂ was broadly overlapping and much less distinct than that from NH₄OH, the selectivity and prediction performance for the H₂O₂ calibration were sensitively varied depending on the spectral ranges and number of factors used. PCSA, based on the comparison between regression vectors from PLS and the net analyte signal (NAS), was an effective method to prevent over-fitting of the H₂O₂ calibration. A robust H₂O₂ calibration model with minimal interferences from other components was developed. PCSA should be included as a standard method in PLS calibrations where prediction error only is the usual measure of performance.     

The actual structure of K6(VO)2(V2O3)2(PO4)4(P2O7): Ordered distribution of P2O7 groups and charge ordering of vanadium

The actual structure of the vanadium phosphate K₆(VO)₂(V₂O₃)₂(PO₄)₄(P₂O₇) has been determined, using a much larger single crystal than previously used for the isostructural Rb-phase. The actual supercell is four times larger than the corresponding orthorhombic subcell with , , , α=β=γ=90°. The structure resolution, performed in the triclinic space group C-1, shows that the P₂O₇ groups alone are responsible for the superstructure, all the other atoms keeping the atomic positions of the orthorhombic subcell. This structural study shows a perfect ordering of the P₂O₇ groups in the actual structure, in contrast to the results obtained from the subcell. Concomitantly, the V⁴⁺ and V⁵⁺ are found to be ordered in the form of [110] stripes.     

Nitrogen-doped zirconia: A comparison with cation stabilized zirconia

The conductivity behavior of nitrogen-doped zirconia is compared with that of zirconia doped with lower-valent cations and discussed in the framework of defect-defect interactions. While nominally introducing the same number of vacancies as yttrium, nitrogen dopants introduced in the anion sublattice of zirconia lead to substantially different defect kinetics and energetics. Compared to the equivalent yttrium doping nitrogen doping in the Y-Zr-O-N system substantially increases the activation energy and correspondingly decreases the conductivity at temperatures below in the vacancy range below 4 mol%. The comparison of N-doped zirconia and zirconia systems doped with size-matched cation stabilizers, such as Sc, Yb and Y, shows that elastically driven vacancy-vacancy ordering interactions can phenomenologically account for the temperature- and composition-dependence. It is striking that materials with superior high-temperature conductivities due to weak dopant-vacancy interactions undergo severe deterioration at low temperature due to the strong vacancy-ordering. The analysis also explains qualitatively similar effects of Y co-doping in Yb-, Sc-, and N-doped zirconia. Small amount of Y in N-doped zirconia as well as in Sc-doped zirconia appears to hinder the formation of the long-range ordered phase and thus enhance the conductivity substantially.     

Volumetric, Electric, and Magnetic Properties of Thioxanthen-9-one in Aprotic Solvents as Revealed by High-Precision Densitometry, High-Accuracy Refractometry and Magnetic Susceptibility Measurements and by DFT Calculations

High-precision densitometry measurements of solutions of thioxanten-9-one (TX) in 1,4-dioxane, DMSO, toluene, and benzene have been obtained at 293.15, 303.15, 313.15, 323.15, 333.15, and 343.15K. The partial molar volumes of TX ( ) and the corresponding values at infinite dilution ( ) were determined. The partial molar expansibility ( ) of TX at infinite dilution in each solvent is temperature independent. Dynamic electronic polarizabilities of TX in each aprotic solvent were determined by the Singer–Garito approach. These values are in excellent concordance with the theoretical value for TX of 2.611×10⁻²³cm³ estimated here using DFT/B3LYP/6-311++G(d,p). The partial molar volumes of TX at infinite dilution were calculated and interpreted in terms of the Scale Particle Theory (SPT). The solvent influence on the partial molar volume of TX was found to be due mainly to cavity formation and intermolecular dispersion forces.     

SULFATION OF PACHYMAN WITH CHLOROSULFONIC ACID USING THE IMPROVED WOLFROM METHOD

High purity polysaccharide of pachyman was isolated from the powder of Poria cocos sclerotium with an yield of 77.8%. The intrinsic viscosity of polysaccharide was found to be 78.95 mL/g in DMSO solution at 25℃. The isolated polysaccharide was reacted with chlorosulfonic acid to obtain pachyman sulfate using the improved Wolfrom method. The results of the orthogonality experiment on the sulfation reaction identified that the effectiveness of the reaction conditions on the degree of sulfation and the value of intrinsic viscosity is in the following order: molar ratio of chlorosulfonic acid to glucoside (3-5) ＞ reaction temperature (60-80℃) ＞ reaction time (1-2 h). The kinetic studies of the pachyman sulfationindicated that the hydrolysis is accompanied with the sulfation process. The decrease in intrinsic viscosity of the sulfated pachyman is proportional to the increase in the degree of sulfation under the mild reaction conditions of ＜ 80℃,chlorosulfonic acid/glucoside mole ratio ＜ 5, and reaction time ＜ 2 h. Beyond the above reaction conditions, excessive loss of -OH group occurs during hydrolysis. The NMR results indicated a complete sulfation on C-6 and a partial sulfation on the C-2 and C-4 of glucoside.     

Faceting and stability of smectic A droplets on a solid substrate

It is shown that a smectic A droplet deposited on a solid substrate treated for strong homeotropic anchoring is faceted at the top in spite of the fact that there are no steps at the free surface, but instead edge dislocations in the bulk. The radius of the facet and the full profile of the curved part of the droplet are determined as a function of the temperature in the vicinity of a nematic-smectic A phase transition. It is shown that the observed profiles do not correspond to the actual equilibrium shape, but to metastable configurations close to their point of marginal stability. In addition, we predict that the profiles must be different for a given temperature depending on whether the droplet has been heated or cooled down to reach this temperature. Finally, we discuss the problem of the formation of giant dislocations in big droplets (Grandjean terraces).