Relative Compactness for Hyperspaces

The present paper contains results characterizing relatively compact subsets of the space of the closed subsets of a metrizable space, equipped with various hypertopologies. We investigate the hyperspace topologies that admit a representation as weak topologies generated by families of gap functionals defined on closed sets, as well as hit-and-miss topologies and proximal-hit and-miss topologies.

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.

Perturbations of Critical Values in Nonsmooth Critical Point Theory

* Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993). ** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).

Branching Processes with Immigration and Integer-valued Time Series

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary Ginar(d) and get consistency and asymptotic normality for the corresponding estimators. The technique covers autoregressive moving average time series as well.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

2000 Mathematics Subject Classification: 60J80.

CO adsorption over Pd nanoparticles:a general framework for IR simulations on nanoparticles

CO vibrational spectra over catalytic nanoparticles under high coverages/pressures are discussed from a DFT perspective. Hybrid B3LYP and PBE DFT calculations of CO chemisorbed over Pd4 and Pd13 nanoclusters, and a 1.1 nm Pd38 nanoparticle, have been performed in order to simulate the corresponding coverage dependent infrared (IR) absorption spectra, and hence provide a quantitative foundation for the interpretation of experimental IR spectra of CO over Pd nanocatalysts. B3LYP simulated IR intensities are used to quantify site occupation numbers through comparison with experimental DRIFTS spectra, allowing an atomistic model of CO surface coverage to be created. DFT adsorption energetics for low CO coverage (θ → 0) suggest the CO binding strength follows the order hollow > bridge > linear, even for dispersion-corrected functionals for sub-nanometre Pd nanoclusters. For a Pd38 nanoparticle, hollow and bridge-bound are energetically similar (hollow ≈ bridge > atop). It is well known that this ordering has not been found at the high coverages used experimentally, wherein atop CO has a much higher population than observed over Pd(111), confirmed by our DRIFTS spectra for Pd nanoparticles supported on a KIT-6 silica, and hence site populations were calculated through a comparison of DFT and spectroscopic data. At high CO coverage (θ = 1), all three adsorbed CO species co-exist on Pd38, and their interdiffusion is thermally feasible at STP. Under such high surface coverages, DFT predicts that bridge-bound CO chains are thermodynamically stable and isoenergetic to an entirely hollow bound Pd/CO system. The Pd38 nanoparticle undergoes a linear (3.5%), isotropic expansion with increasing CO coverage, accompanied by 63 and 30 cm− 1 blue-shifts of hollow and linear bound CO respectively.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

SG Pseudo-Differential Operators and Weak Hyperbolicity

2002 Mathematics Subject Classification: 35S05, 47G30, 58J42.

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.

Averaging operators and set-valued maps

MSC 2010: 54C35, 54C60.

Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

MSC 2010: 34A08, 34A37, 49N70

Statistical considerations in the kinetic analysis of PET-FDG brain tumour studies

Dynamic positron emission tomography (PET) imaging can be used to track the distribution of injected radio-labelled molecules over time in vivo. This is a powerful technique, which provides researchers and clinicians the opportunity to study the status of healthy and pathological tissue by examining how it processes substances of interest. Widely used tracers include 18F-uorodeoxyglucose, an analog of glucose, which is used as the radiotracer in over ninety percent of PET scans. This radiotracer provides a way of quantifying the distribution of glucose utilisation in vivo. The interpretation of PET time-course data is complicated because the measured signal is a combination of vascular delivery and tissue retention effects. If the arterial time-course is known, the tissue time-course can typically be expressed in terms of a linear convolution between the arterial time-course and the tissue residue function. As the residue represents the amount of tracer remaining in the tissue, this can be thought of as a survival function; these functions been examined in great detail by the statistics community. Kinetic analysis of PET data is concerned with estimation of the residue and associated functionals such as ow, ux and volume of distribution. This thesis presents a Markov chain formulation of blood tissue exchange and explores how this relates to established compartmental forms. A nonparametric approach to the estimation of the residue is examined and the improvement in this model relative to compartmental model is evaluated using simulations and cross-validation techniques. The reference distribution of the test statistics, generated in comparing the models, is also studied. We explore these models further with simulated studies and an FDG-PET dataset from subjects with gliomas, which has previously been analysed with compartmental modelling. We also consider the performance of a recently proposed mixture modelling technique in this study.

Characterization of High-Performance Organic Dyes for Dye-Sensitized Solar Cell: A DFT/TDDFT Study

Dye-sensitized solar cell (DSSC) is currently a promising technology that makes solar energy efficient and cost-effective to harness. In DSSC, metal free dyes, such indoline-containing D149 and D205, are proved to be potential alternatives for traditional metal organic dyes. In this work, a DFT/TDDFT characterization for D149 and D205 were carried out using different functionals, including B3LYP, MPW1K, CAM-B3LYP and PBE0. Three different conformers for D149 and four different conformers for D205 were identified and calculated in vacuum. The performance of different functionals on calculating the maximum absorbance of the dyes in vacuum and five common solvents (acetonitrile, chloroform, ethanol, methanol, and THF) were examined and compared to determine the suitable computational setting for predicting properties of these two dyes. Furthermore, deprotonated D149 and D205 in solvents were also considered, and the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) were calculated, which elucidates the substitution effect on the rhodanine ring of D149 and D205 dyes on their efficiency. Finally, D149 and D205 molecules were confirmed to be firmly anchored on ZnO surface by periodic DFT calculations. These results would shed light on the design of new highly efficiency metal-free dyes.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation

In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I a posteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented.