一类泛函微分方程周期解的存在性与应用

本文给出了一类滞后型泛函微分方程有一个周期解的四个充分性定理，其结果明显地优于著名的Ｙｏｓｈｉｚａｗａ周期解定理，最后给出了应用实例。     

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.     

Irradiation-induced reduction and luminescence properties of Sm doped in BaBPO5

Usually, Sm²⁺ ions could be reduced by heating the materials in reducing atmospheres. Exposure to ionizing radiations is also known to cause Sm³⁺→Sm²⁺ conversion. In this work, BaBPO₅ doped with the samarium ion was prepared by high temperature solid-state reaction. Sm²⁺ ions were obtained by two different reduction methods, i.e., heating in H₂ reduced atmosphere and X-ray irradiation. The measurements of X-ray diffraction (XRD), and scanning electron microscope (SEM) were investigated. It is found that the conversion of Sm³⁺→Sm²⁺ is very efficient in BaBPO₅ hosts after X-ray irradiation. Sm²⁺ ions under these two reduction methods exhibit different characteristics that were studied by measurements of luminescence and decay. The results showed that the luminescence properties of Sm²⁺ ions in BaBPO₅ were highly dependent on the sample preparation conditions.     

Allophane: a natural gel in volcanic soils with interesting environmental properties

Volcanic (allophanic) soils are interesting in terms of the control of the greenhouse effect and the knowledge of the porous features is of importance to understand the mechanism of C and N sequestration. These soils contain a peculiar clay: allophane aggregates quite close to the synthetic mineral gels aggregates. These volcanic materials behave as gels during drying with a large irreversible shrinkage that can modify the soil physical properties. Consequently, as for silica gels, we use the CO₂ supercritical drying procedure (SD) to control the drying step and to preserve the structural and textural properties of the soils. The experimental results show that the N and C content in the soils is clearly dependent on the allophane content. We also show that the textural properties, such as specific surface area, are higher for the supercritically dried samples, compared to the classically dried samples, and SAXS results confirm the preserving effect of the SD. With these data, we propose possible effects of the specific surface area on the C and N content of the allophanic soils.     

Reply to Comments of Bassi,Ghirardi, and Tumulka on the Free Will Theorem

We respond to criticisms of our paper “The Free Will Theorem”, and produce a new form of the theorem based on weaker assumptions.