Synthesis of 5‐Radioiodoarabinosyl Uridine Analog for Probing the HSV‐1 Thymidine Kinase Gene

Tumor cells transduced with herpes simplex virus thymidine kinase gene have been intensively applied to the field of positron emission tomography via imaging of its substrate. As a pilot synthesis approach, a facile preparation of 5‐[¹²⁵I] iodoarabinosyl uridine starting from commercially available uridine is reported herein.     

Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.

     

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.     

Ab initio study on structure and phase transition of A- and B-type rare-earth sesquioxides Ln2O3 (Ln=La-Lu, Y, and Sc) based on density function theory

Ab initio energetic calculations based on the density functional theory (DFT) and projector augmented wave (PAW) pseudo-potentials method were performanced to determine the crystal structural parameters and phase transition data of the polymorphic rare-earth sesquioxides Ln₂O₃ (where Ln=La-Lu, Y, and Sc) with A-type (hexagonal) and B-type (monoclinic) configurations at ground state. The calculated results agree well with the limited experimental data and the critically assessed results. A set of systematic and self-consistent crystal structural parameters, energies and pressures of the phase transition were established for the whole series of the A- and B-type rare-earth sesquioxides Ln₂O₃. With the increase of the atomic number, the ionic radii of rare-earth elements Ln and the volumes of the sesquioxides Ln₂O₃ reflect the so-called “lanthanide contraction”. With the increase of the Ln³⁺-cation radius, the bulk modulus of Ln₂O₃ decreases and the polymorphic structures show a degenerative tendency.     

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.