X-ray absorption spectra of plasmas

In this paper we present a theoretical method to calculate the absorption spectra of hot dense plasmas. Based on our fully relativistic treatment incorporated with the quantum defect theory to handle the huge number of transition arrays from many configurations with high principal quantum number, we can calculate the absorption spectra for any element or multi-element plasmas with little computational efforts. We calculate the absorption spectra of C10H1605 plasmas, which are in good agreement with the experimental spectra. We can then provide diagnostic analysis for plasmas in relevant inertial confinement fusion (lCF) experiments; namely not only to determine plasmas' temperatures and densities, but also to provide the population densities of various ionic stages. Our theoretical method verified by "benchmark experiments" will be a basic tool to provide "precise" opacity data for the ICF research.``     

Regular simple geodesic loops on a tetrahedron

A regular simple geodesic loop on a tetrahedron is a simple geodesic loop which does not pass through any vertex of the tetrahedron. It is evident that such loops meet each face of the tetrahedron. Among these loops, the minimal loops are those which meet each face exactly once. Necessary and sufficient conditions for the existence of minimal loops are obtained. These conditions fall naturally into two categories, conditions in the first category being called coherence conditions and conditions in the second category being called separation conditions. It is shown that for the existence of three distinct minimal loops through any point on the face of a tetrahedron it is necessary and sufficient that the tetrahedron be isosceles, which, in turn, amounts to the tetrahedron satisfying three coherence conditions. All other regular simple geodesic loops on an isosceles tetrahedron are then classified. Finally, coherence conditions for the existence of similar loops on an arbitrary tetrahedron are found.     

Thermal Behavior of Urea-(D) Tartaric Acid and Urea-(DL) Tartaric Acid Crystals

The thermal behavior of two new non-linear optical (NLO) materials, urea-(D) tartaric acid (UDT) and urea-(DL) tartaric acid (UDLT) were studied by using DSC, TG and TMA. The results show that: 1) The two crystals have different melting points but similar decomposition temperatures due to the influences of intermolecular forces, which is attributed to the stereo effects of (D)-tartaric and (DL)-tartaric acid molecules; 2) There was only thermal expansion and no thermal contraction when the UDT and UDLT crystals were heated; 3) There was no phase transition within the measured temperature range; 4) The thermal expansion of the UDT and UDLT crystals shows a small anisotropy; 5) The specific heats of UDT and UDLT change linearly with temperature in the measured temperature range and the value for UDT is 1.321 J g-1 K-1 at 320 K while the specific heat of UDLT is 1.357 J g-1 K-1 at the same temperature. This revised version was published online in July 2006 with corrections to the Cover Date.     

铽－甲基吲哚乙酰丙酮三元配合物发光过程研究

测定和分析了ＲＥ．Ｌ１．Ｌ２（ＲＥ＝Ｔｂ（Ⅲ）、Ｇｄ（Ⅲ），Ｌ１＝３Ｍ（３甲基吲哚－１－乙酰基丙酮），Ｌ２＝ＴＰＰＯ、Ｐｈｅｎ、Ｄｉｐｙ）三元配合物的荧光光谱、磷光光谱、磷光寿命及变温荧光光谱等．讨论了Ｔｂ（Ⅲ）与配体之间的能级匹配和Ｌ１与Ｌ２的三重态之间传能的问题，说明了影响这些三元配合物荧光效率的主要因素及其发光过程．     

Optimal Domains for <Emphasis Type="Italic">L</Emphasis><Superscript>0</Superscript>-valued Operators Via Stochastic Measures

We study extension of operators T: E→ L⁰([0, 1]), where E is an F–function space and L⁰([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic measures and the corresponding spaces of integrable functions. Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain).     

Controllable synthesis of ZnS/PMMA nanocomposite hybrids generated from functionalized ZnS quantum dots nanocrystals

We reported controllable synthesis of ZnS nanocrystal-polymer transparent hybrids by using polymethylmethacrylate (PMMA) as a polymer matrix. In a typical run, the appropriate amounts of zinc chloride (ZnCl₂) and sodium sulfide (Na₂S) in the presence of 2-mercaptoethanol (ME) as the organic ligand were well dispersed in H₂O/dimethylformamide solution without any aggregation. In addition, the Mn-doped ZnS nanocrystals (NCs) were synthesized with similar method. Then, ZnS-PMMA hybrids were obtained via free radical polymerization in situ by using ZnS NCs functionalized with methacryloxypropyltrimethoxysilane (MPS). FT-IR characterization indicates the formation of robust bonding between ZnS NCs and the organic ligand. The TEM images show that ZnS NCs are well dispersed in PMMA matrix, and particle size of as-prepared ZnS NCs is about 2.6 nm, in agreement with the computing results of Brus’s model and Debye–Scherrer formula. The photoluminescence measurements present that ZnS NCs, Mn-doped ZnS NCs, and ZnS/PMMA hybrid show good optical properties.     

Existence for a degenerate diffusion problem with a nonlinear operator

We study a degenerate nonlinear variational inequality which can be reduced to a multivalued inclusion by an appropriate change of the unknown function. We establish existence, uniqueness and regularity results. An application arising in the theory of water diffusion in porous media is discussed as an example.      

A New Flow Instrument for Conductance Measurements at Elevated Temperatures and Pressures: Measurements on NaCl(aq) to 458 K and 1.4 MPa

A new flow electrical conductance instrument was constructed and tested on dilute NaCl solutions up to 458 K, and on more concentrated solutions (maximum 0.436 mol⋅kg⁻¹) at 373 K. The results of the new instrument agreed with those of previous authors within the estimated experimental errors. The model of Bernard et al. (J. Phys. Chem. 96, 3833–3840 (1992), MSA) was found to represent the high-temperature results without introducing an ion-pairing equilibrium constant. The Fuoss–Hsia conductance equation as given by Fernandez-Prini was found to represent the dilute concentrations with Λ° (NaCl) as the only adjustable parameter. It was found that Λ° (NaCl) could be expressed as a function of solvent viscosity and density by using three parameters found by regression of literature results between 278.15 and 523 K. This equation along with the FHFP theory permits the equivalent conductivity of dilute sodium chloride solutions to be calculated within the accuracy of the existing experimental measurements.     

An Interval-Parameter Fuzzy Approach for Multiobjective Linear Programming Under Uncertainty

An interval-parameter fuzzy linear programming method (IFMOLP) is proposed in this study for multiple objective decision-making under uncertainty. As a hybrid of interval-parameter and fuzzy methodologies, the IFMOLP incorporates interval-parameter linear programming and fuzzy multiobjective programming approaches to form an integrated optimization system. The method inherits advantages of interval-parameter programming, and allows uncertainties and decision-makers’ aspirations to be effectively communicated into its programming processes and resulting solutions. Membership functions for both objectives and constraints are formulated to reflect uncertainties in different system components and their interrelationships. An interactive solution procedure has been developed based on solution approaches of the interval-parameter and fuzzy programming techniques, plus necessary measures for handling the multiobjective feature. A didactic example is provided in the paper to illustrate the detailed solution process. Possibilities of further improvements by seeking Pareto optimum and incorporating flexible preference within constraints are also discussed.     

Frame Wavelets with Compact Supports for L^2（R^n）

The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in R^n. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.